Answer with Step-by-step explanation:
We have to prove that
[tex]sin 2\theta=2sin\theta cos\theta[/tex] by using Euler's formula
Euler's formula :[tex]e^{i\theta}=cos\theta+isin\theta[/tex]
[tex]e^{i(2\theta)}=(e^{i\theta})^2[/tex]
By using Euler's identity, we get
[tex]cos2\theta+isin2\theta=(cos\theta+isin\theta)^2[/tex]
[tex]cos2\theta+isin2\theta=(cos^2\theta-sin^2\theta+2isin\theta cos\theta)[/tex]
[tex](a+b)^2=a^2+b^2+2ab, i^2=-1[/tex]
[tex]cos2\theta+isin2\theta=cos2\theta+i(2sin\theta cos\theta)[/tex]
[tex]cos2\theta=cos^2\theta-sin^2\theta[/tex]
Comparing imaginary part on both sides
Then, we get
[tex]sin2\theta=2sin\theta cos\theta[/tex]
Hence, proved.
the number of newly reported cases of HIV in the united states from 2000 to 2010can be modeled by the following formule f(t)=41(0.9842)t where t is the number of years after 2000 calculate the estimated number of new HIV cases reported in 2004
Answer:
38
Step-by-step explanation:
The year 2004 is 4 years after the year 2000, so the corresponding value of t is 4. Using that value in the formula, we get ...
f(4) = 41(0.9842^4) ≈ 38.47 ≈ 38
The estimated number of new HIV cases reported in 2004 is 38.
A rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters. A dart is randomly thrown at the board. A triangle is inside of a rectangle. The height of the triangle is the same as the height of the rectangle. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle?
Answer:
25%.
Step-by-step explanation:
Let E be the event that the dart lands inside the triangle.
We have been given that a rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters.
We know that probability of an event represents the chance that an event will happen.
[tex]\text{Probability}=\frac{\text{Favorable no. of events}}{\text{Total number of possible outcomes}}[/tex]
[tex]\text{Probability that dart lands inside the triangle}=\frac{\text{Area of triangle}}{\text{Area of rectangle}}[/tex]
[tex]\text{Probability that dart lands inside the triangle}=\frac{162}{648}[/tex]
[tex]\text{Probability that dart lands inside the triangle}=0.25[/tex]
Convert into percentage:
[tex]0.25\times 100\%=25\%[/tex]
Therefore, the probability that dart lands inside the triangle is 25%.
Answer:
25%
Step-by-step explanation:
A road that is 11 miles long is represented on a map that shows a scale of 1 centimeter being equivalent to 10 kilometers. How many centimeters long does the road appear on the map? Round your result to the nearest tenth of a centimeter.
The 11 kilometer road will be 1.1 cm long on the map
Step-by-step explanation:
Scale is used on maps to show large locations or roads as small representatives of the larger objects.
The scale factor is usually in proportion to the original length or dimensions.
Given that
1 cm = 10 km
Then, we will divide the number of kilometers by 10 to find the length of road on map
11 km on map = [tex]\frac{11}{10}[/tex]
Hence,
The 11 kilometer road will be 1.1 cm long on the map
Keywords: Maps, Scales
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Suppose you begin a job with an annual salary of $32,900. Each year you are assured of a 5.5% raise. What its the total amount that you can earn in 15 years? A) $34,815 B) $51,751 C) $737,245 D) $1,682,920
Answer: the total amount that you can earn in 15 years is $737245. Option C
Step-by-step explanation:
You receive an annual salary of $32,900 and each year, you are assured of a 5.5% raise. Assuming there was no raise, you get 100% of your previous salary each year. With a raise of 5.5%, you will get 100 + 5.5 = 105.5% of your previous salary for each year. This is a geometric progression and we want to determine the sum of 15 terms(15 years).
The formula for the sum of terms in a geometric progression is
Sn = [a(r^n - 1)]/ r - 1
Sn = sum of n terms
a = the first term
n = number of terms
r = common ratio
From the information given,
a = 32900
n = 15
r = 105.5/100 = 1.055
S15 = [32900(1.055^15 - 1)] / 1.055 - 1
S15 = [32900(2.23247649 - 1)] / 0.055
S15 = 32900 × 1.23247649) / 0.055
S15 = 737245.0277
S15 = $737245
Suppose Adam wants to have $750,000 in his IRA at the end of 30 years. He decides to invest in an annuity paying 6% interest, compounded annually. What does he have to contribute each year to reach this goal?
Answer:
$9486.68
Step-by-step explanation:
The future value of a annuity formula can be used:
FV = P((1+r)^n -1)/r
750000 = P(1.06^30 -1)/0.06
P = 750000(.06)/(1.06^30 -1) = 9486.68
Adam has to contribute $9,486.68 each year to reach his goal.
Adam can calculate how much he needs to contribute to his IRA each year using the future value of an annuity formula. By substituting the known values into the rearranged formula, he can find the required annual payment.
Explanation:To find out how much Adam needs to contribute each year, we can use the formula for the future value of an annuity. The future value (FV) of an annuity formula is:
FV=P*[((1+r)^n -1)/r]
Where:
P is the annual payment, r is the annual interest rate (expressed as a decimal), n is the number of periods, which in this case will be years.
In this question, we want to find P, so we rearrange the formula as follows:
P = FV / [((1+r)^n -1)/r]
Substituting the given values:
P= $750,000 / [((1+0.06)^30 -1)/0.06]
By calculating the above expression, we will get the amount Adam needs to contribute annually to reach his goal.
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A study found out that 1% of social security recipients are too young to vote. If 800 social security recipients are randomly selected, find the mean, variance and standard deviation of the number of recipients who are too young to vote
Answer:
Mean : [tex]\mu=8[/tex]
Variance : [tex]\sigma^2=7.92[/tex]
Standard deviation = [tex]\sigma=2.81[/tex]
Step-by-step explanation:
We know that , in Binary Distribution having parameters p (probability of getting success in each trial) and n (Total number trials) , the mean and variance is given by:-
Mean : [tex]\mu=np[/tex]
Variance : [tex]\sigma^2=np(1-p)[/tex]
We are given that ,
Total social security recipients : n=800
The probability of social security recipients are too young to vote : p=1%= 0.01
Here success is getting social security recipients are too young to vote .
Then, the mean, variance and standard deviation of the number of recipients who are too young to vote will be :-
Mean : [tex]\mu=800\times0.01=8[/tex]
Variance : [tex]\sigma^2=800\times 0.01(1-0.01)=8\times0.99=7.92[/tex]
Standard deviation = [tex]\sigma=\sqrt{\sigma^2}=\sqrt{7.92}=2.81424945589\approx2.81[/tex]
Hence, the mean, variance and standard deviation of the number of recipients who are too young to vote :
Mean : [tex]\mu=8[/tex]
Variance : [tex]\sigma^2=7.92[/tex]
Standard deviation = [tex]\sigma=2.81[/tex]
In a sample of 800 social security recipients, with 1% being too young to vote, the mean is 8, the variance is 7.92, and the standard deviation is approximately 2.81.
The study indicates that 1% of social security recipients are too young to vote. When sampling 800 social security recipients, we treat the number of recipients too young to vote as a binomial random variable (since each recipient is either too young or not, with a fixed probability of being too young).
To find the mean of the binomial distribution, we use the formula:
Mean = n * p
Where n is the sample size (800) and p is the probability of success (0.01).
Mean = 800 * 0.01 = 8
The variance of the binomial distribution is given by the formula:
Variance = n * p * (1 - p)
Variance = 800 * 0.01 * (1 - 0.01) = 7.92
To calculate the standard deviation, we take the square root of the variance.
Standard Deviation = √(Variance) = √(7.92) = 2.81
Add or subtract
x/x^2-4 -2/x^2-4
A phone store employee earns a salary of $450 per week plus 10% comission on her weekly sales. A) What function rule models the employee's weekly earnings? B)If the employee earned $570 in a week, what was the amount of her sales for that week?
Answer:
A) [tex]E(w)=450+0.10w[/tex]
B) $1200
Step-by-step explanation:
Let w represent employee's weekly sales and [tex]E(w)[/tex] be total weekly earnings.
We have been given that a phone store employee earns a salary of $450 per week plus 10% commission on her weekly sales.
A) The total weekly earnings of employee would be weekly salary plus 10% of weekly sales.
10% of weekly sales, w, would be [tex]\frac{10}{100}*w=0.10w[/tex]
[tex]E(w)=450+0.10w[/tex]
Therefore, the function [tex]E(w)=450+0.10w[/tex] models the employee's weekly earnings.
B) To find the weekly sales in the week, when employee earned $570, we will substitute [tex]E(w)=570[/tex] in our formula and solve for w as:
[tex]570=450+0.10w[/tex]
[tex]570-450=450-450+0.10w[/tex]
[tex]120=0.10w[/tex]
[tex]0.10w=120[/tex]
[tex]\frac{0.10w}{0.10}=\frac{120}{0.10}[/tex]
[tex]x=1200[/tex]
Therefore, the amount of employee's weekly sales was $1200.
A rectangular poster is to contain 81 square inches of print. The margins at the top and bottom and on each side are to be 5 inches. Find the dimensions of the page which will minimize the amount of paper used.
To minimize the paper used for a poster with a specific print area and margin size, we derive a formula for total paper area, take its derivative with respect to the print width, solve for the width, and then find the matching height.
To find the dimensions of the page that will minimize the amount of paper used for a rectangular poster that contains 81 square inches of print with 5-inch margins on all sides, we need to set up a function to minimize. Let the width of the print area be x inches, and the height be y inches. Therefore, the total dimensions of the poster will be (x + 10) inches wide and (y + 10) inches high due to the margins on each side.
The area of print is given, so x*y = 81. We will minimize the total area of the page, A = (x+10)(y+10). Substituting the value of y from the print area equation, y =[tex]\frac{81}{x}[/tex], we get A(x) = (x+10)([tex]\frac{81}{x}[/tex]+10).
Now, to find the dimensions that minimize the paper used, we will take the derivative of A(x) with respect to x, set it to zero, and solve for x. From there, we can find the corresponding value of y to get the dimensions that will use the least amount of paper while still fitting the print area and margins.
blake buys paperback from the used bookstore for $ 5 . 5 . Natalie purchased an annual membership to the same bookstore for $ 35 35 so she can buy paperbacks at a discounted price $ 2.50 2.50 each. How many books would Natalie and Blake have to buy this year for their spending at the bookstore to be the same? What would their total cost be? Evaluate
Answer:
Step-by-step explanation:
1:22
Answer:
Step-by-step explanation:
so
b buys a paperback for 5.5, while after natalie purchases 35.35 for membership- her books are 2.50
blake paid 5.5
nat paid 37.85
lets see how many books blake has to pay to reach 37.85 shall we?
5.5*22=121
2.5*35=87.5
35.35+87.5=122.85
i dont think its possible
Question 1(Multiple Choice Worth 1 points) (01.04 LC) Solve for x: −3x + 3 < 6 x > −1 x < −1 x < −3 x > −3
To solve -3x + 3 < 6 and find the value of x, subtract 3 from both sides and divide by -3. The solution is x > -1.
Explanation:To solve the inequality -3x + 3 < 6, we want to isolate the variable x. First, subtract 3 from both sides to get -3x < 3. Then, divide both sides by -3 (remember to flip the inequality sign when dividing by a negative) to obtain x > -1. Therefore, the solution is x > -1.
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Before school, Janine spends 1/10 hour making her bed, 1/5 hour getting dress, and 1/2 hour eating breakfast. What fraction of an hour does she spend doing these activities?
Answer:
4/5
Step-by-step explanation:
This is a long-winded way to ask you the sum of the three fractions:
1/10 + 1/5 + 1/2
= 1/10 + 2/10 + 5/10 = (1 +2 +5)/10 = 8/10
= 4/5
Janine spends 4/5 hour doing morning activities.
An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of the three factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman has all three risk factors, given that she has A and B, is 1/3. Calculate the probability that a woman has none of the three risk factors, given that she does not have risk factor A?
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The probability that a woman has none of the three risk factors, given that she does not have risk factor A, is calculated to be 0.54.
Explanation:To find the probability that a woman has none of the three risk factors, given that she does not have risk factor A, we will use the given probabilities and apply the principles of probability. Let's denote the probabilities of having only the risk factors as P(A), P(B), and P(C), the probabilities of having exactly two risk factors as P(A and B), P(A and C), and P(B and C), and the probability of having all three risk factors as P(A and B and C).
Given:
P(A) = P(B) = P(C) = 0.1
P(A and B) = P(A and C) = P(B and C) = 0.12
P(A and B and C | A and B) = 1/3
We can calculate P(A and B and C) using the conditional probability:
P(A and B and C) = P(A and B) × P(A and B and C | A and B) = 0.12 × 1/3 = 0.04
To find the probability of not having A, denoted as P(A'), we can use the complement rule:
P(A') = 1 - P(A) - P(A and B) - P(A and C) - P(A and B and C) = 1 - 0.1 - 0.12 - 0.12 - 0.04 = 0.62
Since P(A') includes probabilities of women with neither of the risk factors or only with B or C, we need to subtract the probabilities of having only risk factors B and C:
P(None | A') = P(A') - P(B) - P(C) + P(B and C) = 0.62 - 0.1 - 0.1 + 0.12 = 0.54
The probability that a woman has none of the three risk factors, given that she does not have risk factor A, is thus 0.54.
Please help answer this two question correctly and please show work please don't answer if you don't don't know the answer .
Answer:
Question 1 = $59.85.
Question 2 = 0.45
Step-by-step explanation:
Doug did cleaning for 1 ¾ hours.
Doug did paperwork for 2 1/3 hours.
Doug did serving for 1 5/8 hours.
Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.
=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.
In one hour Doug earns $10.50.
Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.
Hence, the total which Doug earned is $59.85.
Second question answer
5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5
Answer:
Answer:
Question 1 = $59.85.
Question 2 = 0.45
Step-by-step explanation:
Doug did cleaning for 1 ¾ hours.
Doug did paperwork for 2 1/3 hours.
Doug did serving for 1 5/8 hours.
Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.
=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.
In one hour Doug earns $10.50.
Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.
Hence, the total which Doug earned is $59.85.
Second question answer
5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5
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Question 1 = $59.85.
Question 2 = 0.45
Step-by-step explanation:
Doug did cleaning for 1 ¾ hours.
Doug did paperwork for 2 1/3 hours.
Doug did serving for 1 5/8 hours.
Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.
=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.
In one hour Doug earns $10.50.
Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.
Hence, the total which Doug earned is $59.85.
Second question answer
5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5
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Step-by-step explanation:
Joe has $200 in his savings account and is depositing $50 per month. Kathy has $50 in her account and is depositing $75 per month. In how many months will they have the same amount of money? Please show work
In 6 months, they will have same amount of money.
Step-by-step explanation:
Let,
x be the number of months
Given,
Joe's savings = $200
Per month deposit = $50
J(x)=200+50x Eqn 1
Kathy savings = $50
Per month deposit = $75
K(x)=50+75x Eqn 2
For same amount;
J(x)=K(x)
[tex]200+50x=50+75x\\50x-75x=50-200\\-25x=-150[/tex]
Dividing both sides by -25;
[tex]\frac{-25x}{-25}=\frac{-150}{-25}\\x=6[/tex]
In 6 months, they will have same amount of money.
Keywords: functions, division
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Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
Answer:
t=4 seconds to reach the cannon floor
Step-by-step explanation:
ax^2+bx+c=0
0=-16t^2+255
-255=-16t^2
t^2=15.9375
t= 3.99
round it up...
t=4 seconds to reach the cannon floor
hope this helps!!! :)
]An electrician charges $40 for each hour he works plus a $125 service charge. The total charge for a recent job was $1,205. Which equation could be used to determine the number of hours, h, that the electrician worked on the job
Answer:
40h+125=1205
Step-by-step explanation:
He is paid $40 for an unknown amount of hours which in this case would be considered as (h) plus a 125 service charge. Overall, he was paid $1205
What is the sum of a common geometric series if the first term is 8 and the common ratio is 1/2?
Answer: A
Step-by-step explanation:
The sum to infinity of a geometric series is
S (∞ ) = \frac{a}{1-r} ( - 1 < r < 1 )
where a is the first term 8 and r is the common ratio, hence
S(∞ ) = {8}{1-\{1}{2} } = {8}{1}{2} } = 16
Answer:
Step-by-step explanation:
32 i think
A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct. 0.1492 0.3508 0.0901 0.8508 Normal approximation is not suitable.
Answer:
Option 4 - 0.8508
Step-by-step explanation:
Given : A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses.
To find : Estimate the probability of getting at least 20% correct ?
Solution :
20% correct out of 60,
i.e. [tex]20\%\times 60=\frac{20}{100}\times 60=12[/tex]
Minimum of 12 correct out of 60 i.e. x=12
Each question has 4 possible answers of which one is correct.
i.e. probability of answering question correctly is [tex]p=\frac{1}{4}=0.25[/tex]
Total question n=60.
Using a binomial distribution,
[tex]P(X\geq 12)=1-P(X\leq 11)[/tex]
[tex]P(X\geq 12)=1-[P(X=0)+P(X=1)+P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)][/tex]
[tex]P(X\geq 12)=1- [^{60}C_0(0.25)^0(1-0.25)+^{60-0}+^{60}C_1(0.25)^1(1-0.25)^{60-1}+^{60-1}+^{60}C_2(0.25)^2(1-0.25)^{60-2}+^{60}C_3(0.25)^3(1-0.25)^{60-3}+^{60}C_4(0.25)^4(1-0.25)^{60-4}+^{60}C_5(0.25)^5(1-0.25)^{60-5}+^{60}C_6(0.25)^6(1-0.25)^{60-6}+^{60}C_7(0.25)^7(1-0.25)^{60-7}+^{60}C_8(0.25)^8(1-0.25)^{60-8}+^{60}C_9(0.25)^9(1-0.25)^{60-9}+^{60}C_{10}(0.25)^{10}(1-0.25)^{60-10}+^{60}C_{11}(0.25)^{11}(1-0.25)^{60-11}][/tex]
[tex]P(X\geq 12)\approx 0.8508 [/tex]
Therefore, option 4 is correct.
Bowling cost $2 to rent shoes,plus $5 per game. Mini golf cost $5 to rent a club, plus $4 per game. How many games would be the same total cost for bowling and mini golf? And what is that cost
Answer:
Step-by-step explanation:
Assuming the same number of bowling and mini golf games are played, let x represent the total number of games played, either bowling or mini golf. let y represent the total cost of bowling. Let z represent the total cost of golfing
Bowling cost $2 to rent a club plus $5 per game. It means that the cost, y for x bowling games will be
y = 2 + 5x
Mini golf cost $5 to rent a club, plus $4 per game. It means that the cost, y for x mini golf games will be
z = 5 + 4x
For the total cost to be the same, we will equate both equations(y = zl
2 + 5x = 5 + 4x
5x - 4x = 5 - 2
x = 3
There would be 3 games before total cost would be the same
Two cars leave towns 400 kilometers apart at the same time and travel toward each other. One car's rate is 14 kilometers per hour less than the other's. If they
meet in 2 hours, what is the rate of the slower car?
Do not do any rounding.
Answer:
Step-by-step explanation:
v*2+(v-14)*2=400
2v+2v-28=400
4v=400+28
4v=428
v=107 km/h
speed of slowest car=107-14=93 km/h
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1. Write an inequality for the range of the third side of a triangle if two sides measure 4 and 13.
2. If LM = 12 and NL = 7 of ∆LMN, write an inequalty to describe the lenght of MN.
3. Use the Hinge Theorem to compare the measures of AD and BD.
Answer:
1. 9 < s < 17
2. 5 < MN < 19
3. AD > BD
Step-by-step explanation:
1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:
the sum of the shortest two sides is greater than the length of the longest sidethe length of any side lies between the sum and the difference of the other two sidesHere, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...
9 < s < 17
(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)
__
2. Same as (1) using different numbers.
12 -7 < MN < 12 +7
5 < MN < 19
__
3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:
AD > BD
A food manufacturer uses an extruder (a machine that makes bite size cookies)that yields revenue for the firm at a rate of $200 per hour when in operation. However, the extruder breaks down an average of two times every day it operates. If Y denotes the number of breakdowns per day, the daily revenue generated by the machine is
R=1600−50Y².
Find the expected daily revenue for the extruder.
Answer:
$1300
Step-by-step explanation:
The extruder yields a revenue of $200per hour
Y denotes the number of breakdown per day.
The daily revenue generated is given as
R = 1600 - 50Y^2
We have an average of 2 breakdown per day
Lamda = 2
Represent lamda as β
E(Y) = β
E(Y(Y-1)) = β^2
E(Y^2) = E[Y(Y-1)] + E(Y)
= β^2 + β
E(R) = E(1600 - 50Y^2)
= 1600 - 50E(Y^2)
= 1600 - 50(β^2 +β)
Recall that β = lamda = 2
= 1600 - 50(2^2 + 2)
= 1600 - 50(4+2)
= 1600 - 50(6)
= 1600 - 300
= 1300
$1300
The expected daily revenue of the extruder is $1300
DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data is displayed.
Poisoned rats 12.207 16.869 25.050 22.429 8.456 20.589
Unpoisoned rats 11.074 9.686 12.064 9.351 8.182 6.642
Let μ 1 be the mean nerve sensitivity for rats poisoned with DDT.
Let μ 2 be the mean nerve sensitivity for rats not poisoned with DDT. The P ‑value for this test was between 0.01 and 0.05. Which statement is a reasonable conclusion?
Answer:
The p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to don't reject the claim that the group with DDT have a mean greater than the group for rats not poisoned.
Step-by-step explanation:
1) Data given and notation
P:[12.207 ,16.869, 25.050, 22.429, 8.456, 20.589]
UP:[11.074, 9.686 ,12.064, 9.351, 8.182, 6.642]
[tex]\bar X_{P}=17.6[/tex] represent the mean for the sample poisoned
[tex]\bar X_{UP}=9.50[/tex] represent the mean for the sample unpoisoned
[tex]s_{P}=6.34[/tex] represent the sample standard deviation for the sample poisoned
[tex]s_{UP}=1.95[/tex] represent the sample standard deviation for the sample unpoisoned
[tex]n_{P}=6[/tex] sample size for the group poisoned
[tex]n_{UP}=6[/tex] sample size for the group unpoisoned
t would represent the statistic (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the mean for rats exposed to DDT is greater than that for rats not poisoned , the system of hypothesis would be:
Null hypothesis:[tex]\mu_{P} \leq \mu_{UP}[/tex]
Alternative hypothesis:[tex]\mu_{P} > \mu_{UP}[/tex]
If we analyze the size for the samples both are less than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{P}-\bar X_{UP}}{\sqrt{\frac{s^2_{P}}{n_{P}}+\frac{s^2_{UP}}{n_{UP}}}}[/tex] (1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
3) Calculate the statistic
We can replace in formula (1) the results obtained like this:
[tex]t=\frac{17.6-9.5}{\sqrt{\frac{(6.34)^2}{6}+\frac{(1.95)^2}{6}}}}=2.99[/tex]
4) Statistical decision
For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{P}+n_{UP}-2=6+6-2=10[/tex]
Since is a unilateral test the p value would be:
[tex]p_v =P(t_{(10)}>2.99)=0.0067[/tex]
So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to don't reject the claim that the group with DDT have a mean greater than the group for rats not poisoned.
At the center of espionage in Kznatropsk one is thinking of a new method for sending Morse telegrams. Instead of using the traditional method, that is, to send letters in groups of 5 according to a Poisson process with intensity 1, one might send them one by one according to a Poisson process with intensity 5. Before deciding which method to use one would like to know the following: What is the probability that it takes less time to send one group of 5 letters the traditional way than to send 5 letters the new way (the actual transmission time can be neglected).
Answer:
It takes less time sending 5 letters the traditional way with a probability of 36.7%.
Step-by-step explanation:
First we must take into account that:
- The traditional method is distributed X ~ Poisson(L = 1)
- The new method is distributed X ~ Poisson(L = 5)
[tex]P(X=x)=\frac{L^{x}e^{-L}}{x!}[/tex]
Where L is the intensity in which the events happen in a time unit and x is the number of events.
To solve the problem we must calculate the probability of events (to send 5 letters) in a unit of time for both methods, so:
- For the traditional method:
[tex]P(X=5)=\frac{1^{5}e^{-1}}{1!}\\\\P(X=5) = 0.367[/tex]
- For the new method:
[tex]P(X=5)=\frac{5^{5}e^{-5}}{5!}\\\\P(X=5) = 0.175[/tex]
According to this calculations we have a higher probability of sending 5 letters with the traditional method in a unit of time, that is 36.7%. Whereas sending 5 letters with the new method is less probable in a unit of time. In other words, we have more events per unit of time with the traditional method.
At the end of the year a library reported 32books lost or stolen and 24 books were sent out for repair if the Library originally had 1219 books how many were left on the shelves or in circulation
Answer:
The number of books left on shelves or in circulation is 1,163 .
Step-by-step explanation:
Given as :
The total number of Books in the Library = 1219
The number of lost or stolen books = 32
The number of books sent fro repair = 24
Now, Let The number of books left on shelves or in circulation = x
So,
The total number of Books in the Library = The number of lost or stolen books + The number of books sent fro repair + The number of books left on shelves or in circulation
I.e 1219 = 32 + 24 + x
Or, 1219 = 56 + x
Or, x = 1219 - 56
∴ x = 1,163
Hence The number of books left on shelves or in circulation is 1,163 Answer
Answer: Number of books in circulation or left on the shelf is 1163
Step-by-step explanation:
At the end of the year, 32 books were reported to be lost or stolen and 24 books were sent out for repair. This means that the number of books not in circulation is the sum of the number books that was lost or reportedly stolen and the number of books that were sent out for repair.
Therefore,
Number of books not in circulation = 32+24 = 56
The Library originally had 1219 books.
The number of books left on the shelves or in circulation will be total number of books initially - number of books not in circulation. This becomes
1219 - 56 = 1163 books
Which expression is equal to 2x/x−2−x+5/x+3 ?
A. x^2+11x−6/(x−2)(x+3)
B. x^2+9x+6/(x−2)(x+3)
C. 3x^2+11x+6/(x−2)(x+3)
D. x^2+3x+10/(x−2)(x+3) I think is the correct answer.
Please help, thanks!
Answer:
D is correct
Step-by-step explanation:
2x/(x-2) - (x+5)/(x+3)
2x(x+3)/(x-2)(x+3) - (x+5)(x-2)/(x+3)(x-2)
2x^2+6x/(x-2)(x+3)-(x^2+3x-10)(x+3)(x-2)
(x^2+3x+10)/(x+3)(x-2)
Answer:
x^2+3x+10/(x-2)(x+3)
Step-by-step explanation:
Just took the test
Samantha had $620 in her savings. She wanted to have at least $200 in her account after her five days in San Diego. Write an inequality to show how much she can spend each day. PLZ HELP
Answer:
Step-by-step explanation:
Samantha had $620 in her savings. She wanted to have at least $200 in her account after her five days in San Diego. This means that the amount that she can spend in 5 days would be her savings minus the least amount that she wants to have left. It becomes 620 - 200 = $420
If she decides to spend her spendable amount of $420 equally per day, it means that each day, she will spend 420/5 = $84
The inequality representing the amount that she can spend for each day will be
Let y = the amount that she can pend each day. Then, it will be
y lesser than or equal to 84
The Olsens rented a car for a $35.99 a day plus an additional fee per mile.The rental company charged them $90.99. If they traveled 550 miles total,what was the additional fee per mile that they were charged?
Answer:
$0.1 is the additional fee per mile.
Step-by-step explanation:
Given:
Fixed charge = $35.99
Total Bill charged = $90.99
Number of miles traveled = 550 miles
Let additional fee per mile be x.
Now total bill Charge = Fixed charge + additional fee per mile × Number of miles traveled
The expression can be represented as;
[tex]\$35.99 + 550x = \$90.99\\550x = \$90.99-\$35.99\\550x= 55\\x= \frac{55}{550}=\$0.1[/tex]
Hence, the additional fee per mile is $0.1.
The area of a square is decreasing at a rate of 43 square inches per second. At the time when the side length of the square is 7, what is the rate of change of the perimeter of the square? Round your answer to three decimal places (if necessary).
Answer: -12.286 in/sec
Step-by-step explanation:
Differentiate A=s^2 to get d(A)/d(t) = 2s * d(s)/d(t).
Plug in -43 for d(A)/d(t) since it is the rate of change for area. Plug in 7 for s since it is the value of the side length. -43 = 2(7) * d(s)/d(T).
d(s)/d(T) equals -3.0714286
Differentiate P=4s to get d(P)/d(t) = 4 * d(s)/d(t)
Plug in -3.0714286 to d(P)/d(t) = 4 * d(s)/d(t).
d(P)/d(s)= -12.286 in/sec
Final answer:
To find the rate of change of the perimeter when the square's side length is 7 inches and its area decreases at a rate of 43 square inches/sec, we calculate ds/dt and then use it to find dP/dt. The perimeter is decreasing at a rate of approximately -12.284 inches/sec.
Explanation:
The question involves finding the rate at which the perimeter of a square changes given that the area of the square is decreasing at a rate of 43 square inches per second. To solve this problem, let's denote the side length of the square as s and the area as A, so A = s². The perimeter of the square, P, is given by P = 4s.
Given that the area is decreasing at a rate of -43 square inches per second, we represent this rate of change as dA/dt = -43 inches^2/sec. We also know that at the instant when s = 7 inches, we want to find dP/dt, the rate at which the perimeter is changing.
First, we find the rate of change of the side length, ds/dt, given by differentiating A = s² with respect to time (t), giving 2s(ds/dt) = dA/dt. Substituting the given values, we get 2*7(ds/dt) = -43, solving for ds/dt gives us -43/14 = -3.071 inches/sec.
Finally, since the perimeter's rate of change, dP/dt, is 4(ds/dt), we substitute the value we found for ds/dt, resulting in dP/dt = 4*(-3.071), which equals -12.284 inches/sec. Hence, the perimeter of the square is decreasing at a rate of approximately -12.284 inches per second.