Answer:
The probability that the student is going to pass the test is 0.0545
Step-by-step explanation:
The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:
[tex]P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}[/tex]
Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2
Then, if the student pass the test with at least 8 questions correct, the probability P of that is:
P = P(8) + P(9) + P(10)
[tex]P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})[/tex]
P = 0.0439 + 0.0097 + 0.0009
P = 0.0545
A positive integer from one to six is to be chosen by casting a die. Thus the elements c of the sample space C are 1, 2, 3, 4, 5, 6. Suppose C1 = {1, 2, 3, 4} and C2 = {3, 4, 5, 6}. If the probability set function P assigns a probability of 1 6 to each of the elements of C, compute P(C1), P(C2), P(C1 ∩ C2), and P(C1 ∪ C2).
Answer with Step-by-step explanation:
We are given that six integers 1,2,3,4,5 and 6.
We are given that sample space
C={1,2,3,4,5,6}
Probability of each element=[tex]\frac{1}{6}[/tex]
We have to find that [tex]P(C_1),P(C_2),P(C_1\cap C_2) \;and\; P(C_1\cup C_2)[/tex]
Total number of elements=6
[tex]C_1[/tex]={1,2,3,4}
Number of elements in [tex]C_1[/tex]=4
[tex]P(E)=\frac{number\;of\;favorable \;cases}{Total;number \;of\;cases}[/tex]
Using the formula
[tex]P(C_1)=\frac{4}{6}=\frac{2}{3}[/tex]
[tex]C_2[/tex]={3,4,5,6}
Number of elements in [tex]C_2[/tex]=4
[tex]P(C_2)=\frac{4}{6}=\frac{2}{3}[/tex]
[tex]C_1\cap C_2[/tex]={3,4}
Number of elements in [tex](C_1\cap C_2)=2[/tex]
[tex]P(C_1\cap C_2)=\frac{2}{6}=\frac{1}{3}[/tex]
[tex]C_1\cup C_2=[/tex]{1,2,3,4,5,6}
[tex]P(C_1\cup C_2)=\frac{6}{6}=1[/tex]
A cash register contains only five dollar and ten dollar bills. It contains twice as many five's as ten's and the total amount of money in the cash register is 620 dollars. How many ten's are in the cash register?
Answer:
31
Step-by-step explanation:
Let number of ten dollar bills be x .
So, number of five dollar bills = 2 x
Total amount of money in the cash register = 620 dollars
Amount of money in total cash as a result of five dollar bills = 2 x × 5 = 10 x dollars
Amount of money in total cash as a result of ten dollar bills = x × 10 = 10 x dollars
According to question ,
Total amount of money in the cash register = Amount of money in total cash as a result of five dollar bills + Amount of money in total cash as a result of ten dollar bills
⇒ 620 = 10 x + 10 x
⇒ 620 = 20 x
⇒ x = [tex]\frac{620}{20}[/tex] = 31
So, number of ten dollar bills = 31
Final answer:
By setting up an algebraic equation based on the information provided, we can determine there are 31 ten dollar bills in the cash register.
Explanation:
To solve the question: A cash register contains only five dollar and ten dollar bills. It contains twice as many five's as ten's and the total amount of money in the cash register is 620 dollars. How many ten's are in the cash register? we need to use algebra.
Let's let x represent the number of ten dollar bills. Since the register contains twice as many five dollar bills as ten dollar bills, we can represent the number of five dollar bills as 2x.
The value of the ten dollar bills is 10x dollars, and the value of the five dollar bills is 5(2x) = 10x dollars. The total amount of money in the cash register is the sum of these values, which equals 620 dollars. So, we have the equation:
10x + 10x = 620
Simplifying, this becomes 20x = 620. Dividing both sides by 20 gives us x = 31.
Therefore, there are 31 ten dollar bills in the cash register.
Please help!!!step by step
Step-by-step explanation:
3y-x-5=0
3y=x+5
y=(x+5)/3
y= (1/3)*x + (5/3)
The general equation of y is:
y=mx+b
where:
slope=m
b= y intercept
so, slope is (1/3) and y intercept is (5/3)
and x intercept=0, when you star to graphic you can see that the only option for have y=(5/3) is necessary that the value of x=0. Or:
y intercept= (1/3)*x +(5/3) =(5/3)
(5/3)-(5/3)=(1/3)x
0=(1/3)*x
0/(1/3)=x
x=0.
Alexis has two ribbons one of the Rubens is 40 cm long and the other is 70 m long she wants to cut a trip into equal pieces of the same like with no ribbon left over what is the longest length she can cut the ribbons in centimeters
Answer: 17.5cm
Steps: 70m = 700cm
40cm = 40cm
700cm/40cm
=17.5cm
vous êtes les bienvenus, baisers cher!
Answer:
40 cm
Step-by-step explanation:
She has one ribbon of 40 cm and another ribbon of 70 m
First, we have to change 70 m to cm, to do this we know that 1m = 100 cm
so we multiply 70*100 = 7,000 cm.
Now we have to find the longest length she can cut the ribbons in centimeters.
To do this we have to find the Greatest Common Factor of 40 and 7000 to know what is the longest length she can cut the ribbons.
To find the Greatest Common Factor we have to find the factors for each number:
Factors of 40:
1, 2, 4, 8, 10, 20, 40
Factors of 7000
1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40
The Greatest Common Factor is 40, so she can have pieces of 40 cm long.
13. The length of a rectangle is 2 meters more than its width. The area of the rectangle is 80 square meters. What is the length and with
of the rectangle?
A length
B. length
C. length
D. length
14 meters, width 12 meters
10 meters width 8 meters
20 meters, width 4 meters
3 meters, width 6 meters
Answer:
Remember that if you want the area on a rectangle you have to think, lengh x width. In this case, the correct answer is C.
Step-by-step explanation:
There is something wrong in this, because 20 is not 2 meters than its width.
Anna has the following averages in his math class:
Homework Avg: 95
Quiz Avg: 90
Test Avg: 87
Final Exam: ??
If the teacher weights homework at 20%, Quizzes at 20%, Test at 40%, and the final exam at 20%, what is the minimum grade Anna can make on the final so that she scores a 90 in the class?
a. 86 c. 94
b. 91 d. 98
Answer: Option 'b' is correct.
Step-by-step explanation:
Since we have given that
Average marks in Homework = 95
Average marks in Quiz = 90
Average marks in Test = 87
According to question, we have that the teacher weights homework at 20%, Quizzes at 20%, Test at 40%, and the final exam at 20%
Total score in the class = 90
So, Score of homework is given by
[tex]0.2\times 95\\\\=19[/tex]
Score of Quiz is given by
[tex]0.2\times 90\\\\=18[/tex]
Score of test is given by
[tex]0.4\times 87\\\\=34.8[/tex]
So, it becomes,
[tex]19+18+34.8+x=90\\\\71.8+x=90\\\\x=90-71.8\\\\x=18.2[/tex]
So, minimum grade Anna can make on the final is given by
[tex]\dfrac{20}{100}\times y=18.2\\\\y=\dfrac{18.2}{0.2}\\\\y=91[/tex]
Hence, Option 'b' is correct.
Solve for x.
-43 = x/8
Simplify your answer as much as possible.
Answer:
x = -8(-43)
x = 344 is the solution
Please help me out with this!!!!!!!!
Answer:
f(- 3) = 5
Step-by-step explanation:
The absolute value always returns a positive value, that is
| - a | = | a | = a
Given
f(x) = | x - 2 |
To evaluate f(- 3) substitute x = - 3 into f(x)
f(- 3) = | - 3 - 2 | = | - 5 | = 5
Ken drew a pair of intersecting rays and marked a angle between them.
Which of these statements best compares the pair of intersecting rays with the angle?
1) The rays and the angle have two endpoints each.
2) The rays have the number lying on them, and the angle has only one point lying on it.
3) The rays extend infinity, and the angle is made by the rays,which have a common endpoint.
4) The rays and the angles have their lines extending in opposite directions.
Answer:
Option 3 is the best option that compares the pair of intersecting rays with the angle
Step-by-step explanation:
The definition of angle says that an angle is a shape that is produced by the intersection of two rays that have a common end point.
A ray is a line segment that has only one end point and is extended infinitely in a unique direction
So Yeah. :) Hope I've helped
Sock hop (ExH). You have 10 pairs of socks, fi ve black and fi ve blue, but they are not paired up. Instead, they are all mixed up in a drawer. It ’ s early in the morning, and you don ’ t want to turn on the lights in your dark room. How many socks must you pull out to guarantee that you have a pair of one color? How many must you pull out to have two good pairs (each pair is the same color)? How many must you pull out to be certain you have a pair of black socks?
Final answer:
You need to pull out 6 socks to guarantee a pair of one color, 11 socks to guarantee two pairs, and 7 socks to be certain you have a pair of black socks.
Explanation:
To guarantee that you have a pair of one color when selecting from a mix of 10 pairs of socks (5 black and 5 blue), you must consider the worst-case scenario. This occurs when you alternatively pick one of each color. Therefore, after picking 5 black and 4 blue socks, the next sock you pick will guarantee a pair. So, you need to pull out 6 socks to ensure a pair of one color (5 of one color and 1 of the other).
To have two good pairs, you would continue this pattern. After the first pair is secured with 6 pulls, you would possibly pick the alternating color for the next 4 pulls, and then any subsequent sock would complete a second pair of one color. In total, this would require pulling out 11 socks to ensure two pairs.
To be certain you have a pair of black socks, prepare for the possibility of pulling out all 5 blue socks first. After these 5, the next 2 socks you pull out will be black, giving you at least one pair of black socks. Therefore, you would need to pull out 7 socks to be certain.
In 2017, Moreno Cheeses had a net income of $42,390, paid preferred dividends of $6,000 and 18,000 shares of common stock outstanding. What was their earnings per share for 2017?a) $1.69 b) $2.69 c) $2.02 d) $2.36
Answer:
Option c.
Step-by-step explanation:
In 2017, Moreno Cheeses had a net income of $42,390, paid preferred dividends of $6,000.
value of the shares = Net income - preferred dividends
= 42,390 - 6,000
= $36,390
To find their earnings per share = [tex]\frac{\text{Value of the shares}}{\text{total number of shares}}[/tex]
= [tex]\frac{36,390}{1,8000}[/tex]
= $2.02 per share
Option c) $2.02 per share
The qualifying time for the race is set at 37.895 seconds. If the track is 2.5 miles,how many feet per seconds was the driver going?. And how many miles per hour?
(5280 feet in 1 mile).
Answer:
348.331 ft/s237.498 mi/hStep-by-step explanation:
There are two parts to this problem:
compute the speed from distance and timeexpress it in appropriate units.As you can learn from any speed limit sign, speed is in units of distance per time--miles per hour in the US. To compute speed, you divide distance by time.
If we were to use the given numbers directly, dividing distance in miles by time in seconds, our speed would have units of miles per second. In order to change the units to the ones asked for by the problem statement, we need to make one of two conversions.
For the first part, we need to convert miles to feet, so our speed is in feet per second instead of miles per second. For the second part, we need to convert seconds to hours, so the speed is in miles per hour.
__
Any units conversion can be done using a conversion factor that is a fraction that has a value of 1. That is, its numerator is equal to its denominator.
For the conversion from miles to feet, we want to cancel units of miles and leave units of feet. The operation on units looks like ...
[tex]\dfrac{miles}{second}\times\dfrac{feet}{mile}=\dfrac{feet}{second}[/tex]
The units of miles in the numerator cancel the units of miles in the denominator, so we're left with feet per second, as we want. In order to make the conversion factor have a value of 1, it must be ...
(5280 ft)/(1 mi) . . . . . . numerator equal to denominator
(a) Express the speed in ft/s:
(2.5 mi)/(37.895 s) × (5280 ft)/(1 mi) = 2.5·5280/37.895 ft/s ≈ 348.331 ft/s
__
(b) For the conversion to miles per hour from miles per second, we need to cancel the units of seconds in the denominator and replace them with hours. The conversion factor for that is ...
(3600 s)/(1 h) . . . . . . numerator equal to denominator
(2.5 mi)/(37.895 s) × (3600 s)/(1 h) = 2.5·3600/37.895 mi/h ≈ 237.498 mi/h
At a picnic there were 3 times as many adults as children and twice as many women as men. If there was a total of x men, women, and children at the picnic, how many men were there, in terms of x ?
A. x/2B. x/3C. x/4D. x/5E. x/6
Answer:
[tex]\dfrac{x}{4}[/tex]
C is correct.
Step-by-step explanation:
At a picnic,
Number of adults is 3 times as number of children.
Number of women is twice as number of men.
Total number of men, women and children at the picnic be x
Let number of children be c
Let number of men be m
Let number of women be w
# Number of women is twice as number of men, w = 2m
# Number of adults is 3 times as number of children, w + m = 3c
2m + m = 3c (∴ w=2m )
c = m
Total number of men, women and children at the picnic be x
∵ c + m + w = x
m + m + 2m = x
4m = x
Number of men, [tex]m=\dfrac{x}{4}[/tex]
Hence, The total number of men will be [tex]\dfrac{x}{4}[/tex]
I need help with 25.
so the area A is no more than 10, namely A ⩽ 10 , it could be 10 or less, but no more than that.
let's recall the area of a triangle is A = (1/2)bh
[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=4\\ h=2x-3 \end{cases}\implies A=\cfrac{1}{2}(4)(2x-3) \\\\[-0.35em] ~\dotfill\\\\ A\leqslant 10\implies \cfrac{1}{2}(4)(2x-3)\leqslant 10\implies 2(2x-3)\leqslant 10\implies 4x-6\leqslant 10 \\\\\\ 4x\leqslant 16\implies x\leqslant \cfrac{16}{4}\implies x\leqslant 4 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{maximum height of the triangle}}{2(4)-3}\implies 8-3\implies 5[/tex]
when x = 4 is the maximum height, since x ⩽ 4, so it could be 4 at most, could be less than 4 or equals but never higher.
A population of bacteria is growing exponentially. At 7:00 a.m. the mass of the population is 12 mg. Five hours later it is 14 mg. (a) What will be the mass of the bacteria after another 5 hours? (b) At 7:00 p.m. what do we expect the mass to be? (c) What was the mass of the population at 8:00 a.m.? Given your answer, by what percent is the mass of the population increasing each hour? By what percent is it increasing each day?
Answer with Step-by-step explanation:
The exponential growth function is given by
[tex]N(t)=N_oe^{mt}[/tex]
where
[tex]N(t)[/tex] is the population of the bacteria at any time 't'
[tex]N_o[/tex] is the population of the bacteria at any time 't = 0'
'm' is a constant and 't' is time after 7.00 a.m in hours
Assuming we start our measurement at 7.00 a.m as reference time t = 0
Thus we get[tex]N(0)=N_oe^{m\times 0}\\\\12=N_o[/tex]
Now since it is given after 5 hours the population becomes 14 mg thus from the above relation we get
[tex]12\times e^{m\times 5}=14\\\\e^{5m}=\frac{14}{12}\\\\m=\frac{1}{5}\cdot ln(\frac{14}{12})\\\\m=0.031[/tex]
Thus the population of bacteria at any time 't' is given by
[tex]N(t)=12e^{0.031t}[/tex]
Part a)
Population of bacteria after another 5 hours equals the population after 10 hours from start
[tex]N(10)=12e^{0.031\times 10}=16.361mg[/tex]
Part b)
Population of bacteria at 7:00 p.m is mass after 12 hours
[tex]N(1)=12e^{0.031\times 12}=17.41mg[/tex]
Part c)
Population of bacteria at 8:00 p.m is mass after 1 hour
[tex]N(1)=12e^{0.031\times 1}=12.3378mg[/tex]
Part d)
Differentiating the relation of population with respect to time we get
[tex]N'(t)=\frac{d(12\cdot e^{0.031t})}{dt}\\\\N'(t)=12\times 0.031=0.372e^{0.031t}[/tex]
Thus we can see that the percentage increase varies with time initially the percentage increase is 37.2% but this percentage increase increases with increase in time
Part 4)
Since there are 24 hours in 1 day thus the percentage increase in the population is
[tex]\frac{N(24)-N_o}{N_o}\times 100\\\\=\frac{25.25-12}{12}\times 100=110.42[/tex]
Thus there is an increase of 110.42% in the population each day.
Mrs. Shoelady gave her children $2.40 in quarters, dimes, and nickles. The number of nickles was twice the number of quarters. The number of quarters was twice the number of dimes. How many of each coin did she give out?
Answer:
6 quarters, 3 dimes, and 12 nickles
Step-by-step explanation:
Let's say Q is the number of quarters, D is the number of dimes, and N is the number of nickles.
From the information in the problem, we can write three equations:
25Q + 10D + 5N = 240
N = 2Q
Q = 2D
Solve the system of equations using substitution.
25(2D) + 10D + 5(2Q) = 240
50D + 10D + 10Q = 240
60D + 10(2D) = 240
60D + 20D = 240
80D = 240
D = 3
Q = 6
N = 12
There are 6 quarters, 3 dimes, and 12 nickles.
Please help me with this problem..........
Answer:
y= 2/3x + 3
Step-by-step explanation: I suggest to look up slope intercept calculator it really helps.
Answer:
y = [tex]\frac{2}{3}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange - 2x + 3y = 9 into this form
Add 2x to both sides
3y = 2x + 9 ( divide all 3 terms by 3 )
y = [tex]\frac{2}{3}[/tex] x + 3 ← in slope- intercept form
Tickets to a Broadway show cost $35 for adults and $27 for children. The total receipts for 1229 tickets at one performance were $40335. How many adult and child tickets were sold?
Answer:
The number of adults tickets sold was 894 and the number of children tickets sold was 335
Step-by-step explanation:
Let
x ----> the number of adults tickets sold
y ----> the number of children tickets sold
we know that
x+y=1,229 -----> equation A
35x+27y=40,335 ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (894,335)
see the attached figure
therefore
The number of adults tickets sold was 894 and the number of children tickets sold was 335
To solve for the number of adult and child Broadway show tickets sold, we set up and solve a system of equations. After calculation, we find that 894 adult tickets and 335 child tickets were sold.
The question asks to determine the number of adult and child tickets sold when tickets to a Broadway show cost $35 for adults and $27 for children, with a total of 1229 tickets sold for a total amount of $40335. This is a typical example of a system of equations problem.
Step-by-Step Solution:
Let x be the number of adult tickets sold and y be the number of child tickets sold.
We have two equations:
To solve the system, multiply the first equation by -27 to eliminate y:
Add this result to the second equation:
Divide by 8 to find x:
Substitute x = 894 into the first equation to find y:
Therefore, 894 adult tickets and 335 child tickets were sold.
please help me out........!!!!!!!
Answer:
h(- 8) = - 8
Step-by-step explanation:
To evaluate h(- 8) substitute x = - 8 into h(x), that is
h(- 8) = [tex]\frac{(-8)^2+3(-8)}{4(-8)+27}[/tex]
= [tex]\frac{64-24}{-32+27}[/tex]
= [tex]\frac{40}{-5}[/tex] = - 8
A submarine traveling 200 meters below the surface of the ocean increases its depth by 45 meters. Adam says that the new location of the submarine is -155 meters. Describe an error Adam could have made that would result in the answer he gave
Answer:
The error that Adam could have made is added 45 to the depth of
submarine instead of adding -45
Step-by-step explanation:
* Lets explain how to solve the problem
- A submarine traveling 200 meters below the surface of the ocean
- Increases its depth by 45 meters
- Adam says that the new location of the submarine is -155 meters
- We need to know the error of Adam
∵ We consider the surface of the ocean is the zero level
∵ The submarine is 200 meters below the surface of the ocean
∵ Below means negative
∴ The depth of submarine is -200 meters
∵ It increases the depth by 45 meters
- That means it travels down another 45 meters
∵ Down means negative
∴ The depth of submarine = -200 + (-45) = -245 meters
∴ The depth of submarine is 245 below the surface of the ocean
- Adam could thought that the submarine traveled up for 45 meters
then he add 45 to -200
∵ -200 + 45 = -155 meters
∴ The error that Adam could have made is added 45 to the
depth of submarine instead of adding -45
Final answer:
Adam incorrectly subtracted the increased depth from the initial depth, but the correct method is to add the increased depth to the initial negative depth, resulting in a depth of -245 meters.
Explanation:
The error Adam made in his calculation is that he subtracted the increased depth from the initial depth, instead of adding it. When a submarine dives deeper from any initial depth below sea level, we must add the increase to the existing negative depth.
The submarine was originally at -200 meters (below the surface), and then it went 45 meters deeper. Thus, the correct new depth is -200 meters - 45 meters = -245 meters.
Shiela is 1.7m tall. Her son is 109cm tall. How many meters taller is Shiela than her son?
__m
Answer:
Sheila is 0.61 meters taller than her son.
Step-by-step explanation:
First, you would convert 109 cm into meters. Once converted, Sheila's son would be 1.09. Then you would subtract 1.09 from 1.7 to find your answer!
Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data.
A company's international marketing group asked the following question to residents of 50 countries: "What has been your experience with American products?"
1) Below Average 2) Average 3) Above Average 4) Good to Excellent
A supervisor must give a summary evaluation rating from among the choices given below:
1) Poor 2) Fair 3) Good 4) Very good 5) Excellent
Are these data qualitativeor quantitative?
Are these data discrete or continuous?
What is the highest level of measurement the data possesses?
1) Nominal
2) Ordinal
3) Interval
4) Ratio
The data obtained from both questions is qualitative and discrete. The highest level of measurement for the data is ordinal.
Explanation:The data obtained from the first question, "What has been your experience with American products?", is qualitative as it involves responses categorized into below average, average, above average, and good to excellent. The data from the second question, where a supervisor gives a summary evaluation rating, is also qualitative, with choices ranging from poor to excellent.
Both sets of data are discrete since they are categorized into distinct choices. The highest level of measurement for these data is ordinal since the choices have a specific order but do not have equal intervals between them.
(30 Points)
Solve the compound inequality 6b < 36 or 2b + 12 > 6.
A) b < 6 or b > 6
B) b < 6 or b > 3
C) b > 6 or b < −3
D) b < 6 or b > −3
Answer:
C is your answer
Step-by-step explanation:
1.7/14 reduced=
2.6/9 reduced=
3.3/8 reduced=
4.16/20 reduced=
Help plsssssss
1. 14 can be divided by 7 ( 14/7 = 2) so 7/14 reduces to 1/2
2. Both 6 and 9 can be divided by 3: 6/9 reduces to 2/3
3. 3/8 cannot be reduced, they do not have a common multiple, so this stays 3/8
4. Both 16 and 20 can be divided by 4, so this reduces to 4/5
Margo lists the sizes, inches, of set of screws: 9/64, 5/32, 1/16, 1/8. She reasons that because the denominators are in order from greatest to least, the list is in order from least to greatest. Is Margo correct? Why or why not ?
Answer:
I think she is incorrect she need to change all the fractions to the same denominators
Step-by-step explanation:
We are going to change all the fractions to 64
9/64 stays the same
5/32 multiply 2 then 10/64
1/16 multiply by 4 then 4/64
1/8 multiply by 8 then 8/64
Now we can order then
5/32 > 9/64 > 1/8 > 1/16 This is the right order
She was wrong.
The order of the list from least to greatest is 1/16 < 1/8 < 9/64 < 5/31.
What is ascending order?Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.
Now the given sizes of sets of screws are,
9/64, 5/32, 1/16, 1/8
Now We shall convert the values into decimals for simplicity.
So,
9/64 = 0.1406
5/32 = 0.1562
1/16 = 0.0625
1/8 = 0.125
So, arranging them from least to greatest :
0.0625 < 0.125 < 0.1406 < 0.1562
So, the required order of sizes of sets of screws are,
1/16 < 1/8 < 9/64 < 5/31
Thus, The order of the list from least to greatest is 1/16 < 1/8 < 9/64 < 5/31.
To learn more about least to greatest:
https://brainly.com/question/17319861
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Jayden has a collection of 800 baseball cards and his brother Dylan has a collection of baseball cards that is 1/10 as large. How many cards does Dylan h.
To determine the size of Dylan's collection, we multiply Jayden's collection (800 cards) by 1/10. The result is that Dylan has 80 baseball cards in his collection.
Explanation:In this problem, Jayden has a collection of 800 baseball cards. His brother Dylan has a collection that is 1/10 as large. To find out how many cards Dylan has, we perform a simple multiplication problem: we multiply Jayden's collection (800 cards) by the fraction representing Dylan's collection size (1/10).
Therefore, Dylan has 800 * 1/10 = 80 baseball cards.
Learn more about Multiplication here:https://brainly.com/question/35502092
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A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. It is known that the standard deviation in the cutting length that this machine produces is 0.20 feet. A sample of 75 cut sheets yields a mean length of 12.25 feet. This sample will be used to obtain a confidence interval for the mean length cut by machine. Referring to Scenario 1, the Z value to use in obtaining the 95% confidence interval is approximately .
A. 2.58.
B.1.96.
C. 1.75.
D. 1.645.
Answer: B.1.96.
Step-by-step explanation:
The critical z-value used for [tex](1-\alpha)[/tex] confidence interval istwo tailed value with the significance level of [tex](\alpha)[/tex] i.e.[tex]z_{\alpha/2}[/tex] from the standard normal distribution table for z.
Given : Level of confidence : [tex]1-\alpha=0.95[/tex]
Significance level : [tex]\alpha:1-0.95=0.05[/tex]
By using the standard normal distribution table for z,
The z-value = [tex]z_{0.05/2}=z_{0.025}=1.96[/tex]
The correct Z value to use in obtaining a 95% confidence interval for the mean length of cut sheet insulation using a known standard deviation is 1.96.
Explanation:The Z value to use in obtaining the 95% confidence interval for the mean length cut by a machine (which is distributed normally) is 1.96. This is because a 95% confidence interval excludes 5% of the probability, with 2.5% in each tail of the normal distribution. The critical Z value for 0.025 in one tail is roughly 1.96, which is the standard score that corresponds to the 97.5th percentile of the standard normal distribution.
The quality control engineer, who is working on automatically cut sheet insulation, found a mean of 12.25 feet from a sample of 75 cuts. Given the known standard deviation of 0.20 feet, using the Z value of 1.96 will allow for the construction of the desired confidence interval around the sample mean. This critical value enables us to estimate the range in which the true population mean is likely to fall with 95% certainty.
Lana has 18 pencils, 24 erasers and 36 crayons that she wants to put evenly into her pencil boxes. If she put the same number of each type of item in her pencil boxes, what is the most number of pencil boxes will she fit
Answer:
6
Step-by-step explanation:
The largest factor that is common to all these numbers is 6. That is the number of pencil boxes Lana can fill.
18 = 6×3
24 = 6×4
36 = 6×6
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Each of her six (6) pencil boxes will have 3 pencils, 4 erasers, and 6 crayons.
please solve
-(6x+7)+8=19
On solving the equation -(6x+7)+8=19, we get value of x = -3.
To solve the equation -(6x+7)+8=19, we will first simplify each side of the equation and then solve for x. Here's how to do it step-by-step:
Distribute the negative sign across the parenthesis: -6x - 7 + 8 = 19.
Combine like terms on the left side: -6x + 1 = 19.
Subtract 1 from both sides: -6x = 18.
Divide both sides by -6 to find the value of x: x = -3.
Please please help me out with this problem
Answer:
y = 3x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line
m = [tex]\frac{2+4}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3
Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4
y = 3x - 4 ← equation of line