Answer: A. 10% of the time, the population parameter will lie outside of the interval.
Step-by-step explanation:
If we have [tex]b\%[/tex] confidence interval is that we are [tex]b\%[/tex] certain that it contains the true population parameter in it.
Similarly , if we have a 90% confidence interval for a population parameter, then we are 90% certain that it contains the true population parameter in it.
i.e. 10% not certain that it contains the true population parameter in it.
i.e. 10% of the time, the population parameter will lie outside of the interval.
a) What is the numerical value of the golden ratio? b) What is the decimal approximation of e to six decimal places
Answer:
a) 1.6180339875
b) 2.7182818
Step-by-step explanation:
a) Golden ratio is the ratio that divides a quantity in such a manner that when the larger quantity is divided by the smaller quantity, it is equal to the value when the whole quantity is divided by the larger quantity. It is also known by the name golden mean or divine ratio.
It is generally denoted by [tex]\phi[/tex]
Its numeric value is: 1.6180339875
b) Approximate value of e can be calculated with the help of taylors expansion of [tex]e^x[/tex] at x = 1.
Approximate value of e upto 6 decimal places: 2.7182818
A heavy rainstorm dumps 1.0 cm of rain on a city 4 km wide and 8 km long in a 2-h period. Part A How many metric tons (1 metricton = 103 kg) of water fell on the city? (1 cm3 of water has a mass of 1 gram = 10-3 kg.) Express your answer using o
To find the mass of water that fell on the city, multiply the volume of the rainstorm by the density of water.
Explanation:To calculate the amount of water that fell on the city, we first calculate the volume of water by multiplying the width, length, and height of the rainstorm. Using the given values of 1.0 cm of rain, 4 km wide, and 8 km long, we find that the volume is 1.5 × 1018 m³. Since water has a density of 1 ton per cubic meter, we can calculate the mass by multiplying the volume by the density, which gives us 1.5 × 1018 metric tons.
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Formulate but do not solve the problem. Michael Perez deposited a total of $2000 with two savings institutions. One pays interest at a rate of 5%/year, whereas the Other pays interest at a rate of 8%/year. If Michael earned a total of $130 in interest during a single year, how much did he deposit in each institution? (Let x and y denote the amount of money, in dollars, invested at 5% and 8%, respectively.) 0.06x 0.08yx130 X2000
Answer:
Step-by-step explanation:
Michael Perez deposited a total of $2,000 with two savings institutions.
One pays interest at a rate of 5% per year whereas the other pays interest at a rate of 8% per year.
Let x denote the amount of money invested at 5%
y = 2000 - x ---(1)
Let y denote the amount of money invested at 8%
so 5x/100 + 8(2000-x)/100 = $130 ----(2)
Michael earned $130 in interest during a single year.
A person has 14000 invested in stock A and stock B. A currently sells for $40 a share and stock B sells for 60 a share. If stock B doubles in value and stock A goes up 50%, his stock will be worth 24,000. How many shares of each stock does he own?
Answer:
He own 200 shares of stock A and 100 shares of stock B.
Step-by-step explanation:
Let x be the number of shares of stock A and y be the number of shares of stock B.
Current value of a share of stock A = $40
Current value of a share of stock B = $60
A person has 14000 invested in stock A and stock B.
[tex]40x+60y=14000[/tex]
Divide both sides by 20.
[tex]2x+3y=700[/tex] .... (1)
Stock B doubles in value and stock A goes up 50%, his stock will be worth 24,000.
New value of a share of stock A = $40 + (50% of 40)= $40 + $20 = $60
New value of a share of stock B = $60 × 2 = $120
[tex]60x+120y=24000[/tex]
Divide both sides by 60.
[tex]x+2y=400[/tex] .... (2)
Solve equation (1) and (2) by elimination method.
Multiply 2 on both sides in equation (2).
[tex]2x+4y=800[/tex] .... (3)
Subtract equation (3) from equation (1).
[tex]2x+3y-2x-4y=700-800[/tex]
[tex]-y=-100[/tex]
[tex]y=100[/tex]
The value of y is 100.
Substitute y=100 in equation (1).
[tex]2x+3(100)=700[/tex]
[tex]2x+300=700[/tex]
Subtract 300 from both sides.
[tex]2x=700-300[/tex]
[tex]2x=400[/tex]
Divide both sides by 2.
[tex]x=200[/tex]
The value of x is 200.
Therefore he own 200 shares of stock A and 100 shares of stock B.
Consider the quadratic function f(x)=−x^2+x+30
Determine the following:
The smallest xx-intercept is x=
The largest xx-intercept is x=
The yy-intercept is y=
Answer and Explanation:
Given : The quadratic function [tex]f(x)=-x^2+x+30[/tex]
To find : Determine the following ?
Solution :
The x -intercept are where f(x)=0,
So, [tex]-x^2+x+30=0[/tex]
Applying middle term split,
[tex]-x^2+6x-5x+30=0[/tex]
[tex]-x(x-6)-5(x-6)=0[/tex]
[tex](x-6)(-x-5)=0[/tex]
[tex]x=6,-5[/tex]
The x-intercepts are (6,0) and (-5,0).
The smallest x-intercept is x=-5
The largest x-intercept is x=6
The y -intercept are where x=0,
So, [tex]f(0)=-(0)^2+0+30[/tex]
[tex]f(0)=30[/tex]
The y-intercept is y=30.
In 1970 the male incarceration rate in the U.S. was approximately 190 inmates per 100,000 population. In 2008 the rate was 960 inmates per 100,000 population. What is the percent increase in the male incarceration rate during this period?
Answer:
40.53%
Step-by-step explanation:
[tex]Percentage Increase = \frac{New Value - Old Value}{Old Value}\times100[/tex]
Here, New Value = 960÷100,000
Old Value = 190÷ 100,000
∴ [tex]Percentage Increase = \dfrac{\frac{960}{100,000} - \frac{190}{100 ,000} }{\frac{190}{100,000}}\times100[/tex]
⇒ Percentage Increase = 40.53%
Thus, percent increase in the male incarceration rate during given period is 40.53%.
Okay, let's say back in my fleet-footed days (my twenties--when I was also forty pounds lighter! EEK!) I could run 3 miles in 18 minutes. Actually, my fastest time was 17:25--stud! Calculate my miles per hour for running 3 miles in 18 minutes. (Now I'm doing great to run 3 kilometers in 18 minutes!)
Answer:
Your velocity is 10 miles per hour.
Step-by-step explanation:
This can be solved as a simple rule of three problem.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Here, our measures are:
- The distance you ran, in miles
- The time you spent running.
As the time increases, so does the distance, it means there is a direct relationship between the measures.
Each hour has 60 minutes. You ran 3 miles in 18 minutes. So how many miles you ran in 60 minutes?
3 miles - 18 minutes
x miles - 60 minutes
18x = 180
[tex]x = \frac{180}{18}[/tex]
x = 10 miles.
Your velocity is 10 miles per hour.
a 55 ft long drainage pipe must be cut into two pieces before installation. one piece is two-thirds as long as the other. find the length of each piece
Answer:
33 feet
22 feet
Step-by-step explanation:
Let the longer piece be x
Therefore the shorter piece is (2/3)x
x + (2/3)x = 55 Combine the left 2 terms.
(3/3)x + (2/3)x = 55 Add
(5/3)x = 55 Multiply both sides by (3/5)
(3/5) * (5/3)x = (3/5)*55
x = 33
The larger piece is 33 feet
The smaller piece is (2/3) * 33 = 22 feet
11. A graduating senior seeking a job has interviews with two companies. After the interviews, he estimates that his chance of getting an offer from the first company is 0.6. He thinks he has a 0.5 chance with the second company, and that the probability that at least one will reject him is 0.8. What is the probability that he gets at least one offer?
Answer: 0.2
Step-by-step explanation:
Let F denotes the event that graduate senior will get offer from the first company and S denotes the event that graduate senior will get offer from the second company .
Then, we have : [tex]P(F)=0.6[/tex] [tex]P(S)=0.5[/tex]
The probability that at least one will reject him ( neither first nor second ) = [tex]P(F'\cap S')=0.8[/tex]
Now, [tex]P(F\cup S)=1-P(F'\cap S')=1-0.8=0.2[/tex]
Hence, the probability that he gets at least one offer ( either first or second)= 0.2
Solve the following system of equations. Write each of your answers as a fraction reduced to lowest terms. In other words, write the numbers in the exact form that the row operation tool gives them to you when you use the tool in fraction mode. No decimal answers are permitted.
15x + 15y + 10z = 106
5x + 15y + 25z = 135
15x + 10y - 5z = 42
x = _____
y = _____
z = _____
Answer:
[tex]x\ =\ \dfrac{209}{30}[/tex]
[tex]y\ =\ \dfrac{29}{18}[/tex]
[tex]z\ =\ \dfrac{64}{15}[/tex]
Step-by-step explanation:
Given equations are
15x + 15y + 10z = 106
5x + 15y + 25z = 135
15x + 10y - 5z = 42
The augmented matrix by using above equations can be written as
[tex]\left[\begin{array}{ccc}15&15&10\ \ |106\\5&15&25\ \ |135\\15&10&-5|42\end{array}\right][/tex]
[tex]R_1\ \rightarrow\ \dfrac{R_1}{15}[/tex]
[tex]=\ \left[\begin{array}{ccc}1&1&\dfrac{10}{15}|\dfrac{106}{15}\\5&15&25|135\\15&15&-5|42\end{array}\right][/tex]
[tex]R_1\rightarrowR_2-5R1\ and\ R_3\rightarrow\ R_3-15R_1[/tex]
[tex]=\ \left[\begin{array}{ccc}1&1&\dfrac{10}{15}|\dfrac{106}{15}\\\\0&10&\dfrac{65}{3}|\dfrac{299}{3}\\\\0&0&-15|-64\end{array}\right][/tex]
[tex]R_2\rightarrow\ \dfrac{R_2}{10}[/tex]
[tex]=\ \left[\begin{array}{ccc}1&1&\dfrac{10}{15}|\dfrac{106}{15}\\\\0&1&\dfrac{65}{30}|\dfrac{299}{30}\\\\0&0&-15|-64\end{array}\right][/tex]
[tex]R_3\rightarrow\ \dfrac{R_3}{-15}[/tex]
[tex]=\ \left[\begin{array}{ccc}1&1&\dfrac{10}{15}|\dfrac{106}{15}\\\\0&1&\dfrac{65}{30}|\dfrac{299}{30}\\\\0&0&1|\dfrac{64}{15}\end{array}\right][/tex]
[tex]R_1\rightarrow\ R_1-R_2[/tex]
[tex]=\ \left[\begin{array}{ccc}1&0&\dfrac{-3}{2}|\dfrac{17}{30}\\\\0&1&\dfrac{65}{30}|\dfrac{299}{30}\\\\0&0&1|\dfrac{64}{15}\end{array}\right][/tex]
[tex]R_1\rightarrow\ R_1+\dfrac{3}{2}R_3[/tex]
[tex]=\ \left[\begin{array}{ccc}1&0&0|\dfrac{209}{30}\\\\0&1&\dfrac{65}{30}|\dfrac{299}{30}\\\\0&0&1|\dfrac{64}{15}\end{array}\right][/tex]
[tex]R_2\rightarrow\ R_2-\dfrac{65}{30}R_3[/tex]
[tex]=\ \left[\begin{array}{ccc}1&0&\0|\dfrac{209}{30}\\\\0&1&0|\dfrac{29}{18}\\\\0&0&1|\dfrac{64}{15}\end{array}\right][/tex]
Hence, we can write from augmented matrix,
[tex]x\ =\ \dfrac{209}{30}[/tex]
[tex]y\ =\ \dfrac{29}{18}[/tex]
[tex]z\ =\ \dfrac{64}{15}[/tex]
Suppose a professor counts the final exam as being equal to each of the other tests in her course, and she will also change the lowest test score to match the final exam score if the final exam score is higher. If a student's four test scores are 83, 67, 52, and 90, what is the lowest score the student can earn on the final exam and still obtain at least an 80 average for the course?
Answer:
80
Step-by-step explanation:
The three highest exam scores have an average of 80. To maintain an average of 80, the final exam score must be at least 80.
(83 +67 +90)/3 = 240/3 = 80
_____
Essentially, the final exam score counts as two tests, and the lowest test score is thrown out.
The lowest score the student can obtain is 80
The student would take 5 tests. The total marks obtainable is 500( 100 x 5). The student wants to score at least 80 in the course. So she needs to have at least a total score of 400(80 x 5).
In this calculation 52, which is the lowest score would be excluded. This is because the professor would replace this score with her exam score. The student has the scores for 3 tests already.
Total scores of the student for the 3 tests = 83 + 67 + 90 = 240
Sum of scores on the remaining two tests = 400 - 240 = 160
Average score on the remaining two tests = 160/ 2 = 80
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If a projectile (such as cannonball) is fired into the air with an initial velocity at an angle of elevation , then the height of the projectile at time t is given by . If the cannonball is shot with an initial velocity of 600 feet per second with an angle of elevation at , determine the equation of , in exact form. What is the height of the canon after 2 seconds?
Answer: Hi, first, the cannon only gives the cannonball the initial velocity, and when the cannonball is in the air, the only force acting on the ball is the gravitational force.
First, let's compute the initial velocity, if the ball is fired with angle A (measured from the ground, or +x in this case) and velocity V0. then the vector of the velocity is (cos(A)*V0, Sin(A)*V0)
now start describing all the equations.
Acceleration, we know that an object in the air will fall with acceleration g = 9.8 m/s.
then a(t) = (0, -g)
Velocity: integrating the acceleration over the time, we obtain v(t) = (0,-g*t) +C
where C is a integration constant, equal to the initial velocity. Then v(t) = (cos(A)*V0, Sin(A)*V0 - g*t)
Position; For the position we need to integrate again over time, then:
p(t)= (cos(A)*V0*t, Sin(A)*V0*t - [tex]g*\frac{t^{2} }{2}[/tex]) + K.
where again K is an integration constant, in this case the initial position, that write it as (X0,Y0).
The height of the cannonball after 2 seconds is the y component valued in t=2
height = Y0 + Sin(A)*V0*2 - [tex]g*\frac{2^{2} }{2}[/tex].
where you can put the angle A and the initial velocity V0 to obtain the height.
If a well was 70-feet deep, the frog climbs 7 feet per hour, and it slips back 2 feet while resting? How long (in hours) will it take for the frog to get out of the well?
Answer:
It took 14 hours to get out of the well.
Step-by-step explanation:
Consider the provided information.
The well was 70-feet deep, the frog climbs 7 feet per hour, and it slips back 2 feet while resting.
In first hr frog climbs 7 feet and slips back 2 feet, that means it climbs 5 feet in an hour.
In 2 hour it climbs 2 × 5 = 10 feet, in 3 hours it climbs 3 × 5 = 15 feet and so on.
Now we need to find the time taken by the frog to get out of the well.
By observing the above pattern we can say that after 13 hours it can climb 65 feet.
13 × 5 = 65 feet
In next hour frog will climb 65 feet + 7 feet = 72 feet.
That means after 14 hours frog can get out of the well.
Hence it took 14 hours to get out of the well.
how to solve this problem step by step (3×4)÷(7+9-10)
Answer:
2
Step-by-step explanation:
1. solve for the multiplication (3x4)= 12
2. solve for (7+9-10) take 7+9 which =16 and then subtract by 10. (16-10=6)
3. take the 12 and divide by 6
To solve the expression (3×4)÷(7+9-10), perform the operations inside the brackets first, then multiply and divide according to BODMAS/BIDMAS rules. The correct answer after simplifying is 2.
Explanation:To solve the problem (3×4)÷(7+9-10), you should follow the steps of BEDMAS/BIDMAS (Brackets, Exponents/Indices, Division and Multiplication, Addition and Subtraction), also known as the order of operations.
Firstly, address the operations within the parentheses. Calculate the sum and difference within the second set of brackets (7+9-10), which simplifies to 6.Next, perform the multiplication within the first set of brackets (3×4), which equals 12.Now you have simplified the original expression to 12÷6.Finally, divide 12 by 6 to get the answer, which is 2.Always remember to check the answer to see if it is reasonable by reviewing your calculation steps.
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PLEASE HELP ASAP
The graph below shows four straight lines, A, B, C, and D:
Graph of line A going through ordered pairs negative 2, negative 3 and 2, 5. Graph of line B going through ordered pairs negative 2, negative 4 and 2, 4. Graph of line C going through ordered pairs negative 2, negative 5 and 3, 5. Graph of line D going through ordered pairs 0, negative 4 and 4, 4
Which line is represented by the function f(x) = 2x + 1?
Answer:
Line A is represented by the function f(x) = 2x + 1.
Step-by-step explanation:
This can be solved by trial and error. What it means? It means that we are going to replace the ordered pairs in the function, and the equality must be satisfied.
Line A
(-2,-3)
When x = -2, f(x) = -3. Does it happen in the function?
[tex]f(x) = 2x + 1[/tex]
[tex]-3 = 2(-2) + 1[/tex]
[tex]-3 = -3[/tex]
The first equality is OK. Let's see the second
(2,5)
When x = 2, y = 5.
[tex]f(x) = 2x + 1[/tex]
[tex]5 = 2(2) + 1[/tex]
[tex]5 = 5[/tex]
Also OK.
So line A is represented by the function f(x) = 2x + 1.
Now let's see why the other lines are not represented by this function.
Line B
(-2,-4)
[tex]f(x) = 2x + 1[/tex]
[tex]-4 = 2(-2) + 1[/tex]
[tex]-4 = -3[/tex]
False
Line C
(-2,-5)
[tex]f(x) = 2x + 1[/tex]
[tex]-5 = 2(-2) + 1[/tex]
[tex]-5 = -3[/tex]
False
Line D
(0,-4)
[tex]f(x) = 2x + 1[/tex]
[tex]-4 = 2(0) + 1[/tex]
[tex]-4 = 1[/tex]
False
Answer:
line a
Step-by-step explanation:
Drug B has is to be given 10 mg/kg/day in 2 divided doses. The patient weighs 220 pounds. The pharmacy has 250 mg capsules on hand. (Round to the nearest tenth if applicable) a. How many milligrams should the patient receive per day? ________ b. How many milligrams should the patient receive per dose? ________ c. How many capsules should the patient receive per day? ________ d. How many capsules should the patient receive per dose? ________
Answer:
a) 996.6 mg
b) 498.96 mg
c) 4
d) 2
Step-by-step explanation:
Given:
Dose to be given = 10 mg/kg/day
Number of dose to be divided = 2
weight of the patient = 220 pounds
now,
1 pound = 0.453 kg
thus,
weight of the patient = 220 × 0.4536 = 99.792 kg
a) Amount of Drug patient should receive per day = dose × weight of patient
or
Amount of Drug patient should receive per day = 10 × 99.792
or
Amount of Drug patient should receive per day = 997.92 mg
b) Now, the dose is divided in to 2 per day
thus,
The amount of drug received per dose = [tex]\frac{\textup{Drug received per day}}{\textup{Number of dose per day}}[/tex]
or
The amount of drug received per dose = [tex]\frac{\textup{997.92 mg}}{\textup{2}}[/tex]
or
The amount of drug received per dose = 498.96 mg
c) weight of capsule = 250 mg
Thus,
capsules received by patient per day = [tex]\frac{\textup{Dose per day in mg}}{\textup{weight of capsule in mg}}[/tex]
or
capsules received by patient per day = [tex]\frac{\textup{997.92}}{\textup{250}}[/tex]
or
capsules received by patient per day = 3.99168 ≈ 4
d) Capsules to be received per dose = [tex]\frac{\textup{Amount of drug per dose in mg}}{\textup{weight of capsule in mg}}[/tex]
or
capsules received by patient per dose = [tex]\frac{\textup{498.86}}{\textup{250}}[/tex]
or
capsules received by patient per dose = 1.99544 ≈ 2
This problem has been solved!
See the answer
Accuracy and Precision
For the following, determine whether the information is accurate, precise, both or neither.
1. During gym class, four students decided to see if they could beat the norm of 45 sit-ups in a minute. The first student did 64 sit-ups, the second did 69, the third did 65, and the fourth did 67.
2. The average score for the 5th grade math test is 89.5. The top 5th graders took the test and scored 89,
93, 91 and 87.
3. Yesterday the temperature was 89 �F, tomorrow it�s supposed to be 88 �F and the next day it�s supposed to be 90 �F, even though the average for September is only 75 �F degrees!
4. Four friends decided to go out and play horseshoes. They took a picture of their results shown to the right:
5. A local grocery store was holding a contest to see who could most closely guess the number of pennies that they had inside a large jar. The first six people guessed the numbers 735, 209, 390, 300, 1005 and
689. The grocery clerk said the jar actually contains 568 pennies.
Accuracy and Precision
For the following, determine whether the information is accurate, precise, both or neither.
1. During gym class, four students decided to see if they could beat the norm of 45 sit-ups in a minute. The first student did 64 sit-ups, the second did 69, the third did 65, and the fourth did 67.
2. The average score for the 5th grade math test is 89.5. The top 5th graders took the test and scored 89,
93, 91 and 87.
3. Yesterday the temperature was 89 �F, tomorrow it�s supposed to be 88 �F and the next day it�s supposed to be 90 �F, even though the average for September is only 75 �F degrees!
4. Four friends decided to go out and play horseshoes. They took a picture of their results shown to the right:
5. A local grocery store was holding a contest to see who could most closely guess the number of pennies that they had inside a large jar. The first six people guessed the numbers 735, 209, 390, 300, 1005 and
689. The grocery clerk said the jar actually contains 568 pennies.
Answer:
1. Precise
2.Both
3.Precise
5.Neither
Step-by-step explanation:
Accuracy is the closeness of a measured value to a standard value.
Precision is the closeness of two or more measurements to each other.
1.The norm is 45 sit-ups in a minute.The students did, 64, 69,65 and 67. Values are not accurate compared to standard value 45.
Values are precise
Answer--Precise
2. Average score is 89.5
Scores are 89,93,91,87
Values are precise i.e a difference of 2 from each score
Values are accurate because the average score is 90 thus compared to the known average score of 89.5 they are accurate.
Answer-Both
3. Yesterday temperature=89
Tomorrow=88
Next day=90
Average =75
Values are precise i.e. difference of ± 1°
Values are not accurate compared to the average temperatures of 75 F
Answer---Precise
5. The jar contained 568 pennies
The 6 people guessed the numbers as
735,209,390,300,1005, 689
The values are not precise
The values are not accurate
Answer---Neither
Accuracy refers to the closeness of a measurement to the true value, while precision is about the repeatability of measurements. The student examples show diverse cases where results can be accurate, precise, both, or neither. Without the actual value or other measurements, assessment of accuracy and precision is often not possible.
Explanation:The terms accuracy and precision have distinct meanings in science. Accuracy refers to how close a measurement is to the correct or accepted value. In contrast, precision indicates how close a set of measurements are to each other, demonstrating the consistency of the measurements.
The gym class students' results are precise because their sit-up counts are close to each other but we don't have a 'true value' with which to assess accuracy.The 5th graders' math test scores are both precise and accurate as they are close to each other and to the average score of 89.5.The temperatures are neither precise nor accurate, as they are not close to each other (relative to the usual fluctuation of daily temperatures) nor close to the average September temperature of 75 °F.Without the results shown to the right, we cannot assess the accuracy or precision of the horseshoe game.The guesses for the number of pennies are neither accurate nor precise; the values are not close to one another and do not closely approximate the actual number of pennies (568).
Suppose that 25 days are chosen at random from a calendar. Explain why at least 3 of the 25 days must lie in the same month. Do some research to find the name of the principle you've used, and clearly describe it in your own words.
Answer:
Step-by-step explanation:
If you have to choose 25 days, you have to think how many months there are.
The year has 12 months, so, if you divide 25 days /12 months =2,08333. (more than 2--> 3)
So if you happen to choose 2 of every month you have 24 days chosen, you have to pick one extra day and will add 3 to the month it belongs.
In any way you choose, you an be sure there is at least one month with 3 or more days chosen.
Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.
Answer:
6.75g
Step-by-step explanation:
The first step is converting everything to grams, by rules of three. Then we add.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Unit conversion problems, like this one, is an example of a direct relationship between measures.
First step: 0.0025kg to g
Each kg has 1000g, so:
1kg - 1000g
0.0025kg - xg
x = 1000*0.0025 = 2.5g
0.0025kg = 2.5g
Second step: 1750 mg
Each g has 1000mg, so:
1g - 1000mg
xg - 1750mg
1000x = 1750
[tex]x = \frac{1750}{1000}[/tex]
x = 1.75g
1750 mg = 1.75g
2.25g - OK
Third step: 825,000 μg to g
Each g has 1,000,000 ug, so:
1g - 1,000,000 ug
xg - 825,000 ug
1,000,000x = 825,000
[tex]x = \frac{825,000}{1,000,000}[/tex]
x = 0.25g
825,000 μg = 0.25g
Final step: adding everyting
0.25g + 2.25g + 1.75g + 2.50g = 6.75g
Taking into account the change of units, the sum results in 7.325 g.
Rule of threeThe rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
The direct rule of three is the rule applied in this case where there is a change of units.
To perform in this case the conversion of units, you must first know that 1 kg= 1000 g, 1 mg= 0.001 g and 1 μg=1×10⁻⁶ g. So:
If 1 kg is 1000 g, 0.0025 kg equals how many g?1 kg ⇒ 1000 g
0.0025 kg ⇒ x
So: [tex]x=\frac{0.0025 kgx1000 g}{1 kg}[/tex]
Solving:
x= 2.5 g
So, 0.0025 kg is equal to 2.5 g.
If 1 mg is 0.001 g, 1750 mg equals how many g?1 mg ⇒ 0.001 g
1750 mg ⇒ x
So: [tex]x=\frac{1750 mgx0.001 g}{1 mg}[/tex]
Solving:
x= 1.75 g
So, 1750 mg is equal to 1.75 g.
If 1 μg is 1×10⁻⁶ g, 825000 μg equals how many g?1 μg ⇒ 1×10⁻⁶ g
825000 μg ⇒ x
So: [tex]x=\frac{825000 ugx1x10^{-6} g}{1 ug}[/tex]
Solving:
x= 0.825 g
So, 825000 μg is equal to 0.825 g.
Now you add all the values in the same unit of measure:
2.5 g + 1.75 g + 2.25 g + 0.825 g= 7.325 g
Finally, the sum results in 7.325 g.
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Show that 2 - sqrt(2) is irrational
Answer:
This proof can be done by contradiction.
Let us assume that 2 - √2 is rational number.
So, by the definition of rational number, we can write it as
[tex]2 -\sqrt{2} = \dfrac{a}{b}[/tex]
where a & b are any integer.
⇒ [tex]\sqrt{2} = 2 - \dfrac{a}{b}[/tex]
Since, a and b are integers [tex]2 - \dfrac{a}{b}[/tex] is also rational.
and therefore √2 is rational number.
This contradicts the fact that √2 is irrational number.
Hence our assumption that 2 - √2 is rational number is false.
Therefore, 2 - √2 is irrational number.
By assuming 2 - √2 is rational and showing this leads to a contradiction as both a and b would have to be even, which violates the initial condition that they have no common factors other than 1, it has been proven that 2 - √2 is irrational.
To show that 2 - √2 is irrational, we shall assume the opposite, that 2 - √2 is rational, and look for a contradiction. By definition, if 2 - √2 is rational, it can be expressed as a fraction of two integers, say √2 = a/b, where a and b are integers with no common factors other than 1, and b is not zero.
We can rearrange the equation to obtain √2 = 2 - a/b. Multiplying both sides by b gives us b√2 = 2b - a. Squaring both sides of this equation gives us 2b² = (2b - a)² = 4b² - 4ab + a².
Rearranging to solve for a² gives us a² = 2b², implying that a² is an even number, and hence a must be even. Let's say a = 2k for some integer k. Substituting this back into the equation gives us (2k)² = 2b², which simplifies to 4k² = 2b², and further to 2k² = b². This implies that b² is also even, which means b is even as well.
However, this is a contradiction because we assumed that a and b have no common factors other than 1; yet, we've just shown that both must be even, so they have at least a factor of 2 in common. This contradiction shows that the assumption that 2 - √2 is rational is false, and therefore 2 - √2 must be irrational.
Triangles are formed by the intersection of the lines y=x, y 2x, y=-2x, and y=-4. Solve for angles ABC and ABD A D B
Answer and Step-by-step explanation:
To find the angles between the lines, we can use the formula:
tanα = |ms - mr| / | 1 + ms.mr|
where ms and mr are the linear coefficients of the lines you want to find. It always finds the smaller angle formed.
Let's find all the angles from the triangles formed.
y=x ms = 1
y=2x mr = 2
tanα = |1 - 2| / | 1 + 1.2|
tanα = |-1| / | 1 + 2|
tanα = |-1/3|
tanα = 1/3
α = tan⁻¹1/3
α = 18.4°
y=x ms = 1
y=-4 mr = 0
tanα = |1 - 0| / | 1 + 1.0|
tanα = |1| / | 1 + 0|
tanα = |1/1|
tanα = 1
α = tan⁻¹1
α = 45°
y=2x ms = 2
y=-4 mr = 0
tanα = |2 - 0| / | 1 + 2.0|
tanα = |2| / | 1 + 0|
tanα = |2/1|
tanα = 2
α = tan⁻¹2
α = 63.4°
As these 2 lines are in both triangles, the suplement of this angle is also asked, so, 180° - 63.4° = 116.6°
For y=2x and y=-4, it's the same: α = 63.4°
y=2x ms = 2
y=-2x mr = -2
tanα = |2 - (-2)| / | 1 + 2.(-2)|
tanα = |4| / | 1 - 4|
tanα = |4/3|
tanα = 4/3
α = tan⁻¹ 4/3
α = 53.1°
Final answer:
To find angles ABC and ABD in the intersecting lines problem, analyze the slopes of the lines and their intersections.
Explanation:
Triangles can be formed by the intersection of lines with given equations. In this case, the lines are y=x, y= 2x, y=-2x, and y=-4. To find angles ABC and ABD, one must analyze the slopes of these lines and their intersections.
Angle ABC= arctan(∣ m2 −m 1 ∣)
Angle ABC = arctan(∣2−1∣)
Angle ABC = 45 degree
Angle ABD:
This angle is formed by the lines
Angle ABD= arctan (∣m 2 −m 1 ∣)
Angle ABD = arctan(∣−2−1∣)
Angle ABD ≈ 71.57 degree
What is the total resistance of a parallel circuit that has three loads? Load one has a resistance of 6 ohms. Load two has a resistance of 3 ohms. Load three has a resistance of 12 ohms. (YOU MUST SHOW YOUR WORK)!!! 3R 2
Answer:
The total resistance of these three resistors connected in parallel is [tex]1.7143\Omega[/tex]
Step-by-step explanation:
The attached image has the circuit for finding the total resistance. The circuit is composed by a voltage source and three resistors connected in parallel: [tex]R_1=6\Omega [/tex], [tex]R_2=3\Omega [/tex] and [tex]R_3=12\Omega [/tex].
First step: to find the source current
The current that the source provides is the sum of the current that each resistor consumes. Keep in mind that the voltage is the same for the three resistors ([tex]R_1[/tex], [tex]R_2[/tex] and [tex]R_3[/tex]).
[tex]I_{R_1}=\frac{V_S}{R_1}[/tex]
[tex]I_{R_2}=\frac{V_S}{R_2}[/tex]
[tex]I_{R_3}=\frac{V_S}{R_3}[/tex]
The total current is:
[tex]I_S=I_{R_1}+I_{R_2}+I_{R_3}=\frac{V_S}{R_1}+\frac{V_S}{R_2}+\frac{V_S}{R_3}=\frac{R_2\cdot R_3 \cdot V_S+R_1\cdot R_3 \cdot V_S+R_1\cdot R_2 \cdot V_S}{R_1\cdot R_2\cdot R_3}[/tex]
[tex]I_S=V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}[/tex]
The total resistance ([tex]R_T[/tex]) is the source voltage divided by the source current:
[tex]R_T=\frac{V_S}{I_S}[/tex]
Now, replace [tex]I_S[/tex] by the previous expression and the total resistance would be:
[tex]R_T=\frac{V_S}{V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}}[/tex]
Simplify the expression and you must get:
[tex]R_T=\frac{R_1\cdot R_2\cdot R_3}{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}[/tex]
The last step is to replace the values of the resistors:
[tex]R_T=\frac{(6\Omega )\cdot (3\Omega)\cdot (12\Omega)}{(3\Omega)\cdot (12\Omega)+(6\Omega)\cdot (12\Omega)+(6\Omega)\cdot (3\Omega)}=\frac{12}{7}\Omega=1.7143\Omega [/tex]
Thus, the total resistance of these three resistors connected in parallel is [tex]1.7143\Omega[/tex]
The total resistance of a parallel circuit with resistors of 6 ohms, 3 ohms, and 12 ohms is calculated using the parallel resistance formula, resulting in approximately 1.71 ohms.
The subject of your question falls under Physics, where we need to calculate the total resistance of a parallel circuit with three different resistors.
To find the total resistance in a parallel circuit, we use the formula:
1/Rtotal = 1/R1 + 1/R2 + 1/R3
For the given values, R1 = 6 ohms, R2 = 3 ohms, and R3 = 12 ohms. Plugging in these values:
1/Rtotal = 1/6 + 1/3 + 1/12
1/Rtotal = 2/12 + 4/12 + 1/12
1/Rtotal = 7/12
Rtotal = 12/7 ohms
Rtotal ≈ 1.71 ohms
Thus, the total resistance of the parallel circuit is approximately 1.71 ohms.
Let A = {l,m,n,o,p}, B = {o,p,q,r}, and C = {r,s,t,u}. Find the following
(A ∪ B) ∩ C
A ∩ (C ∪ B)
(A ∩ B) ∪ C
At a newsstand, out of 46 customers, 27 bought the Daily News, 18 bought the Tribune, and 6 bought both papers. Use a Venn diagram to answer the following questions:
How many customers bought only one paper?
How many customers bought something other than either of the two papers?
State whether each pair of sets is equal, equivalent, or neither.
{d,o,g}: {c,a,t}
{run} : {{r,u,n}
{t,o,p} :{p,o,t}
Answer and Step-by-step explanation:
A = {l,m,n,o,p}
B = {o,p,q,r}
C = {r,s,t,u}
(A ∪ B) ∩ C
(A ∪ B) = {l,m,n,o,p,q,r}
C = {r,s,t,u}
(A ∪ B) ∩ C = {r}
A ∩ (C ∪ B)
(C ∪ B) = {o,p,q,r,s,t,u}
A = {l,m,n,o,p}
A ∩ (C ∪ B) = {o,p}
(A ∩ B) ∪ C
(A ∩ B) = {o,p}
C = {r,s,t,u}
(A ∩ B) ∪ C = {o,p,r,s,t,u}
At a newsstand, out of 46 customers, 27 bought the Daily News, 18 bought the Tribune, and 6 bought both papers. Use a Venn diagram to answer the following questions:
only daily news: 21 (27-6)
only tribune: 12 (18-6)
Total newspaper: 39 (21+12+6)
Other than newspapers: 7 (46 - 39)
How many customers bought only one paper? 21+12 = 33
How many customers bought something other than either of the two papers? 7
equal, equivalent, or neither.
{d,o,g}: {c,a,t} equivalent
{run} : {{r,u,n} equal
{t,o,p} :{p,o,t} equal
Shirtbarn is having a sale where everything in the store is 40% off. How much will be saved by purchasing $224 of cloths be at the register? Of
course you should really be worrying about how much it will cost you!
Answer:
$89.60 will be saved by purchasing $224 of cloths be at the register
Step-by-step explanation:
This problem can be solved by a rule of three.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
In this problem, we have the following measures:
-The total money
-The percentage of money
As the percentage of money increases, so does the total money. It means that the relationship between the measures is direct.
The problem states that Shirtbarn is having a sale where everything in the store is 40% off. It means that in every purchase, you save 40% of the money.
How much will be saved by purchasing $224 of cloths be at the register?
40% of 224 will be saved. So
$224 - 1
$x - 0.4
x = 224*0.4
x = $89.60
$89.60 will be saved by purchasing $224 of cloths be at the register
Construct the truth tables for the following expressions"
a) (p ∧ q) ∨ r
b) (p ∨ q) ⇒ (p ∧ r)
c) (p ⇒ q) ∨ (¬p ⇒ q)
d) (p ⇒ q) ∧ (¬p ⇒ q)
Answer:
In the files are the truth tables.
c) and d) are the same.
The student's question is about constructing truth tables for four different logical expressions, which involves the step-by-step process of calculating the truth values based on the logical operators for conjunction, disjunction, conditional, and negation.
Constructing Truth Tables
To construct truth tables for the given logical expressions, we enumerate all the possible truth values for the propositions p, q, and r, and calculate the truth values of the complex expressions based on logical operators like conjunction (∧), disjunction (∨), conditional (⇒), and negation (¬).
a) (p ∧ q) ∨ r
This expression involves the conjunction of p and q, followed by the disjunction with r. To construct the truth table, we first list all possible binaries (true/false) for p, q, and r, then determine the result of p ∧ q, and finally the disjunction with r.
b) (p ∨ q) ⇒ (p ∧ r)
The expression starts with the disjunction of p and q, which implies (p ∧ r). Calculate the truth values step by step.
c) (p ⇒ q) ∨ (¬p ⇒ q)
Here, we have two conditional expressions connected by disjunction. The truth value of each conditional is ascertained separately, and then combined using the disjunction ∨.
d) (p ⇒ q) ∧ (¬p ⇒ q)
Similarly, for the conjunction, the truth of both conditionals must hold. Construct each column gradually, concluding with the combined result.
By following logical operators' rules and systematically filling in every row, we can complete these truth tables to see which combinations of propositions render the expressions true or false.
Round the following number to the indicated place. 0.0600609 to hundred-thousandths
Answer:
The rounded number is 0.06006 to the hundred-thousandths place.
Step-by-step explanation:
Consider the provided number.
0.0600609
Here we need to round the number to the nearest hundred-thousandths.
Rounding to the hundred-thousandths means that there should be maximum 5 digits after the decimal point.
Here, the provided number 0.0600609 contains 7 digit after the decimal point and we want only 5 digits after decimal. So we will remove the last 3 digit.
For this we need to round the number to the nearest hundred thousands place.
The rule of rounding a number is:
If 0, 1, 2, 3, or 4 follow the number, then no need to change the rounding digit.
If 5, 6, 7, 8, or 9 follow the number, then rounding digit rounds up by one number.
The 6th digit after the decimal is 0, so there is no need to change the rounding digit.
So, the rounded number is 0.06006 to the hundred-thousandths place.
jacob the dog eats dry food that contains 324kcal/cup. Jacob eats 3.5 cups a day. The food contains 3.6 g of fat in 100 kcals of energy. what is his daily fat intake?
the food contains 25.6 IU of Vitamin D3 in 100 kcals of energy. what is his daily Vitamin D inake?
Answer:
His daily fat intake is 40.824g.
His daily Vitamin D intake is 290.304 IU.
Step-by-step explanation:
The first step to solve this problem is finding the daily kcal intake of the dogs.
Each cup has 324 kcal, and he eats 3.5cups a day. So:
1 cup - 324 kcals
3.5 cups - x kcals
[tex]x = 324*3.5[/tex]
[tex]x = 1134[/tex] kcals.
His daily intake is of 1134 kcals.
The food contains 3.6 g of fat in 100 kcals of energy. what is his daily fat intake?
There are 3.6g of fat in 100 kcals of energy. How many g of fat are there in 1134 kcals?
3.6g - 100 kcals
xg - 1134 kcal
[tex]100x = 1134*3.6[/tex]
[tex]x = \frac{1134*3.6}{100}[/tex]
[tex]x = 11.34*3.6[/tex]
[tex]x = 40.824[/tex]g
His daily fat intake is 40.824g.
The food contains 25.6 IU of Vitamin D3 in 100 kcals of energy. what is his daily Vitamin D inake?
Similar logic as above.
25.6IU - 100 kcals
x IU - 1134 kcal
[tex]100x = 1134*25.6[/tex]
[tex]x = \frac{1134*25.6}{100}[/tex]
[tex]x = 11.34*25.6[/tex]
[tex]x = 290.304[/tex]IU
His daily Vitamin D intake is 290.304 IU.
The owner of a local health food store recently started a new ad campaign to attract more business and wants to test whether average daily sales have increased. Historically average daily sales were approximately $2,700. After the ad campaign, the owner took another random sample of forty-five days and found that average daily sales were $2,984 with a standard deviation of approximately $585. Calculate the upper bound of the 95% range of likely sample means for this one-sided hypothesis test using the CONFIDENCE.NORM function.
Answer:
The upper limit of the confidence interval is 3127 $/day.
Step-by-step explanation:
With the new sample we can estimate the one-sided 95% confidence interval.
For this interval (one sided, 95% of confidence), z=1.64.
The number of observations (n) is 45 days.
The mean is 2984 and the standard deviation is 585.
We can estimate the upper limit of the confidence interval as
[tex]UL=X+z*s/\sqrt{n} \\UL = 2984 + 1.64*585/\sqrt{45}=2984+ 959.4/6.708=2984+143=3127[/tex]
In a recent issue of the IEEE Spectrum, 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference.
(a) Organize the data in a chart. (Round your answers to four decimal places.)
(b) Find the first quartile.
(c) Find the third quartile.
(d) Find the 65th percentile.
(e) Find the 40th percentile.
(f) The middle 50% of the conferences last from.......days to........ days.
Answer:
b) 3
c) 5
d) 4
e) 3
f) 3 days to 5 days
Step-by-step explanation:
Total number of conferences = 84
Part a) We can make a pie chart to represent the distribution of number of days. The area of each sector represents the percentage of duration compared to all events. For example, the conferences that lasted 2 days occurred for 4.7619% or approximately 5% of the time.
Part b) The first quartile
The number of days for which the conferences last as per the given data in ascending order are listed below in the second image. In order to find First Quartile, we first need to find the Median. Since, total number of quantities is 84, the median will be the average of middle two values (42nd and 43rd). These values are made bold in the second image below. So median of the data is 4. Median divides the data into halves, both of which are colored separately in the image. First Quartile is the middle value of the first half. Since, values in first are 42, the middle value will be the average of central two values (21st and 22nd). These are made bold and colored red. Thus, First Quartile of the data is 3.
Part c) The third quartile
Similar to last step, the 3rd Quartile is the middle value of second half of the data. The second half of the data is colored purple. Number of values in this half are again 42, so middle value will be the average of digits at 21st and 22nd place, which comes out to be 5. Therefore, 3rd quartile is 5.
Part d) The 65th percentile.
65th percentile means, 65% of the data values are below this point. 65% of the 84 is 54.6. This means 54.6 values should be below the 65th percentile. Thus, 65th percentile occurs at 55th position. Counting from the start, the digit at 55th position comes out to be 4. So, the 65th percentile is 4.
Part e) The 40th percentile
40th percentile means, 40% of the data values are below this point. 40% of the 84 is 33.6. This means 33.6 values should be below the 40th percentile. Thus, 40th percentile occurs at 34th position. Counting from the start, the digit at 34th position comes out to be 3. So, the 40th percentile is 3.
Part f) Middle 50% of the conferences
Since, First Quartile is 25th percentile and Third Quartile is 75th percentile, in between these two Quartiles 50% of the data is present. The difference of first quartile and third quartile is known as IQR, Inter Quartile range and is a common measure of spread in stats.
Therefore, for the given data:
The middle 50% of the conferences last from 3 days to 5 days
a. The organized chart is attached below.
b. The First Quartile of the data is 3.
c. The 3rd quartile is 5.
d. The 65th percentile is 4.
e. The 40th percentile is 3
f. The middle 50% of the conferences last from 3 days to 5 days
a. We can create a pie chart to show how many days each event lasted. Each slice of the pie represents the percentage of time that event took compared to all the events.
For example, if conferences that lasted 2 days happened for about 5% of the time, their slice in the pie chart would be around that size.
b. According to the information provided, the conferences last for a certain number of days. To find the first quartile, we first need to find the median. Since there are a total of 84 quantities, the median would be the average of the middle two values (the 42nd and 43rd values). These values are highlighted in bold in the image. So, the median of the data is 4. The median divides the data into two halves, which are shown in different colours in the image.
The First Quartile is the middle value of the first half. Since the values in the first are 42, the middle value will be the average of the central two values (21st and 22nd). These are made bold and coloured red.
Thus, the First Quartile of the data is 3.
c. Similar to the last step, the 3rd Quartile is the middle value of the second half of the data. The second half of the data is coloured purple. The number of values in this half is again 42, so the middle value will be the average of digits at 21st and 22nd place, which comes out to be 5.
Therefore, the 3rd quartile is 5.
d. 65th percentile means, 65% of the data values are below this point. 65% of the 84 is 54.6.
This means 54.6 values should be below the 65th percentile. Thus, the 65th percentile occurs at the 55th position.
Counting from the start, the digit at the 55th position comes out to be 4. So, the 65th percentile is 4.
e. 40th percentile means, 40% of the data values are below this point. 40% of the 84 is 33.6. This means 33.6 values should be below the 40th percentile.
Thus, the 40th percentile occurs at the 34th position.
Counting from the start, the digit at the 34th position comes out to be 3.
So, the 40th percentile is 3.
f. Based on the given data, we can say that the middle 50% of the conferences last between 3 days and 5 days.
As the first Quartile is the 25th percentile and the Third Quartile is the 75th percentile, in between these two Quartiles 50% of the data is present. The difference of the first quartile and the third quartile is known as IQR, Inter Quartile range and is a common measure of spread in stats.
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An oral liquid concentrate of sertraline hydrochloride (Zoloft) contains 20 mg/mL of the drug. How many grams of sertraline hydrochloride are in each 60-mL container of the concentrate?
Answer:
1.2 grams.
Step-by-step explanation:
We have been given that an oral concentrate of sertraline hydro-chloride (Zoloft) contains 20 mg/mL of the drug.
First of all, we will find number of mg in 60 mL container of the concentrate as:
[tex]\frac{\text{20 mg}}{\text{ml}}\times \text{60 ml}[/tex]
[tex]\text{20 mg}\times 60[/tex]
[tex]\text{1200 mg}[/tex]
We know 1 gram equals 1000 mg.
[tex]\text{1200 mg}\times \frac{\text{1 gram}}{\text{1000 mg}}[/tex]
[tex]1.2\times\text{1 gram}[/tex]
[tex]1.2\text{ grams}[/tex]
Therefore, 1.2 grams of sertraline hydrochloride are in each 60-mL container of the concentrate.