Answer:
The null hypothesis is [tex]H_0: p \geq 0.2[/tex]
The alternative hypothesis is [tex]H_1: p < 0.2[/tex]
The p-value of the test is of 0.0154 > 0.01, which means that at the 0.01 significance level, there is not significant evidence that the return rate is less than 20%.
Step-by-step explanation:
Test the claim that the return rate is less than 20%.
At the null hypothesis, we test if the return rate is of at least 20%, that is:
[tex]H_0: p \geq 0.2[/tex]
At the alternative hypothesis, we test if the return rate is less than 20%, that is:
[tex]H_1: p < 0.2[/tex]
Normal distribution as an approximation to the binomial distribution to find the Z-score.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
0.2 is tested at the null hypothesis. Sample of 6957.
This means that [tex]p = 0.2, n = 6957[/tex]. So
[tex]\mu = E(X) = np = 6957*0.2 = 1391.4[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6957*0.2*0.8} = 33.36[/tex]
1319 surveys returned
This means that, due to continuity correction, [tex]X = 1319 + 0.5 = 1319.5[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1319.5 - 1391.4}{33.36}[/tex]
[tex]Z = -2.16[/tex]
P-value of the test:
The p-value of the test is the probability of 1319 or less people returning the survey, which is the p-value of Z = -2.16.
Looking at the z-table, Z = -2.16 has a p-value of 0.0154.
The p-value of the test is of 0.0154 > 0.01, which means that at the 0.01 significance level, there is not significant evidence that the return rate is less than 20%.
Fine the probability. I NEED THE STEPS IF POSSIBLE
Answer:
1/6x1/2=1/12
Step-by-step explanation:
This is the fourth one !
Answer and Step-by-step explanation:
Angle B' is congruent to Angle B.
The measure of an angle stays the same when dilating, translating, and other transformations.
#teamtrees #PAW (Plant And Water)
Can someone help me with this question
Answer:
The two minimum numbers = 5, 5
Step-by-step explanation:
Let the first number = x
let the second number = y
Their sum: x + y = 10
Sum of their squares: = x² + y²
y = 10 - x
f(x) = x² + (10 - x)²
f(x) = x² + 100 - 20x + x²
f(x) = 2x² - 20x + 100
Find the derivative of f(x), to obtain the critical points;
f'(x) = 4x - 20
4x - 20 = 0
4x = 20
x = 5
The value of y is calculated as;
y = 10 - x
y = 10 - 5
y = 5
The two minimum numbers = 5, 5
A container holds 3.01 grams of
calcium powder for dogs. What is its
weight in centigrams?
Conv
3,010 cg
301 og
30.1 cg
0.0301 og
What is its weight in centigrams
Answer:
ur dog water kid *take the L dance
Step-by-step explanation:
cheese
: A pack of crayon was shared between two friend Shantel and Carl in the ratio 3:5. If Shantel received 27 crayons, how many crayons were in the pack? *
Answer:
72 crayons
Step-by-step explanation:
8/3 × 27 = 72 crayons
The table shows how the time it takes a train to travel between two cities depends on its average speed. The table shows how the time it takes a train to travel between two cities depends on its average speed Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour? What does the number 160 represent in the rational function that models the situation? distance, in miles, between the cities amount of fuel, in gallons, used by the train time, in minutes, needed to travel between the cities
Answer:
Step-by-step explanation:
Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour?
✔ y = 160/x
What does the number 160 represent in the rational function that models the situation?
✔distance, in miles, between the cities
amount of fuel, in gallons, used by the train
time, in minutes, needed to travel between the cities
Answer: NOTE Pictures Are not in order! Make sure you check page number.
Step-by-step explanation:
On page 6 the answers are ”C” and ”5lbs”
On page 7 the answers are “C”, “$ 418”, “ The cat”, and then “ $960”.
On page 8 the answers are : < Just copy paste this below.>
“Based on the calculation, they should purchase the second television as the cost is cheaper.
Based on the information given in the question, the cost of the first television will be:
= $330 + ($14 × 8)
= $330 + $102
= $442
The cost of the second television will be:
= $369 + ($9 × 8)
= $369 + $72
= $441
Therefore, the second television is cheaper.”
^
<Just copy paste this. > [Then check. “A,B,C,”.]
On page 9 the answer is “ D “.
Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______
a) sec sqr Theta
b) Cot theta
c) cot (pie/2-Theta)
d) csc sqr theta
Answer:
[tex](a)\ \sec^2(\theta) = 82[/tex]
[tex](b)\ \cot(\theta) = \frac{1}{9}[/tex]
[tex](c)\ \cot(\frac{\pi}{2} - \theta) = 9[/tex]
[tex](d)\ \csc^2(\theta) = \frac{82}{81}[/tex]
Step-by-step explanation:
Given
[tex]\tan(\theta) = 9[/tex]
Required
Solve (a) to (d)
Using tan formula, we have:
[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]
This gives:
[tex]\frac{Opposite}{Adjacent} = 9[/tex]
Rewrite as:
[tex]\frac{Opposite}{Adjacent} = \frac{9}{1}[/tex]
Using a unit ratio;
[tex]Opposite = 9; Adjacent = 1[/tex]
Using Pythagoras theorem, we have:
[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]
[tex]Hypotenuse^2 = 9^2 + 1^2[/tex]
[tex]Hypotenuse^2 = 81 + 1[/tex]
[tex]Hypotenuse^2 = 82[/tex]
Take square roots of both sides
[tex]Hypotenuse =\sqrt{82}[/tex]
So, we have:
[tex]Opposite = 9; Adjacent = 1[/tex]
[tex]Hypotenuse =\sqrt{82}[/tex]
Solving (a):
[tex]\sec^2(\theta)[/tex]
This is calculated as:
[tex]\sec^2(\theta) = (\sec(\theta))^2[/tex]
[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]
Where:
[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(\theta) = \frac{1}{\sqrt{82}}[/tex]
So:
[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]
[tex]\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2[/tex]
[tex]\sec^2(\theta) = (\sqrt{82})^2[/tex]
[tex]\sec^2(\theta) = 82[/tex]
Solving (b):
[tex]\cot(\theta)[/tex]
This is calculated as:
[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]
Where:
[tex]\tan(\theta) = 9[/tex] ---- given
So:
[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]
[tex]\cot(\theta) = \frac{1}{9}[/tex]
Solving (c):
[tex]\cot(\frac{\pi}{2} - \theta)[/tex]
In trigonometry:
[tex]\cot(\frac{\pi}{2} - \theta) = \tan(\theta)[/tex]
Hence:
[tex]\cot(\frac{\pi}{2} - \theta) = 9[/tex]
Solving (d):
[tex]\csc^2(\theta)[/tex]
This is calculated as:
[tex]\csc^2(\theta) = (\csc(\theta))^2[/tex]
[tex]\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2[/tex]
Where:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin(\theta) = \frac{9}{\sqrt{82}}[/tex]
So:
[tex]\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2[/tex]
[tex]\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2[/tex]
[tex]\csc^2(\theta) = \frac{82}{81}[/tex]
Please help!
An 80% confidence interval is found to be (200,240). What is the margin of error? O A. 32 O B. 20 O C. 40 O D. 16 SUBMIT
Answer:
The margin of error is of 20, option B.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the subtraction between the bounds, divided by 2.
In this question:
Lower bound: 200
Upper bound: 240
Margin of error:
(240 - 200)/2 = 40/2 = 20
The margin of error is of 20, option B.
Help pls it’s urgent. If your able to solve it than I’d really would appreciate you.
Answer:
Step-by-step explanation:
If the radius of the circle is equal to
[tex]\sqrt{\frac{A}{3} }[/tex] and the area is given as 45, then
[tex]r=\sqrt{\frac{45}{3} }[/tex] which simplifies to
[tex]r=\sqrt{15}[/tex] and to the nearest tenth,
r = 3.9
A nurse mixes 90 cc of a 45% saline solution with a 10% saline solution to produce a 20% saline solution. How much of the 10% solution should he use?
Answer:
225cc
Step-by-step explanation:
the solution is attached to the picture.
The amount of the 10% solution should he use if the nurse mixes 90 cc of a 45% saline solution with a 10% saline solution is 225cc
Functions and percentagesLet the amount of 10% solution she should use be x.
If a nurse mixes 90 cc of a 45% saline solution with a 10% saline solution to produce a 20% saline solution, the equivalent equation will be:
90(0.45) + 0.1x = 0.2(90+x)
Simplify the resulting equation for "x"
40.5 + 0.1x = 18 + 0.2x
0.1x = 40.5 - 18
0.1x = 22.5
x = 225cc
Hence the amount of the 10% solution should he use if the nurse mixes 90 cc of a 45% saline solution with a 10% saline solution is 225cc
Learn more on proportion here: https://brainly.com/question/19994681
What is the surface area of the prism shown below?
Your response should show all necessary calculations and diagrams.
Answer:
376 inches squared.
Step-by-step explanation:
a purchasing agent for kelly bread company wants to estimate the mean daily usage of rye flour. she takes a sample for 50 straight days and finds that the sample mean is 180 pounds with a sample standard deviation of 38.5 pounds. State the 90% confidence interval for the mean
Answer:
The 90% confidence interval for the mean is (170.87 , 189.13)
Step-by-step explanation:
Using the calculator we can easily calculate the 90% confidence interval for the mean, the given values are:
mean=180
sx : 38.5
n : 50
c - Level : 0.90
Then the output will be [170.87 , 189.13]
Does anyone know the answer?
Answer:
lx-3l
Step-by-step explanation:
negative in the abs means moving to the right
=========================================================
Explanation:
We start with the parent function y = |x|
Shifting it 3 units to the right will make the equation y = |x-3| and that's the equation of the green curve shown.
The x-3 is because each input is 3 units smaller than it used to be. Imagine the xy axis moved 3 units to the left while the V shaped graph stayed fixed in place. It would give the illusion the V shape moved while the xy axis stay fixed.
The graph doesn't shift up or down, so k = 0
The value of 'a' stays the same at a = 1.
i need help on this one please help! (listing BRAINLIST and giving points) :D
Answer:
tan C is 90
tan B is 60
tan A is 60
What function is represented in the graph
Factor the expression. x2 + 7x+ 10
Answer:
Make me a Brainlist plsStep-by-step explanation:
x²+7x+10=0
ur answer is there in image
An item costs S430 before tax, and the sales tax is $17.20.
Find the sales tax rate. Write your answer as a percentage.
Answer:
Step-by-step explanation:
430
x4%
_________
$17.20+ $430= $447.20
A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation
h =
- 6t2 + 6t where h is the frog's height in meters at any given time, t. Find the maximum height the frog reached
what is the slope of the line that contains the points (-1,2) and (3,3)
Answer:
B
Step-by-step explanation:
Hi there!
We are given the points (-1,2) and (3,3) and we need to find the slope.
The formula for slope calculated from two points is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points
since we have two points, we can substitute them into the formula, but let's label their values to avoid any confusion
[tex]x_{1}[/tex]=-1
[tex]y_{1}[/tex]=2
[tex]x_{2}[/tex]=3
[tex]y_{2}[/tex]=3
now substitute into the formula (m is the slope); remember: we have a negative number in this, so we'll be subtracting a negative.
m=[tex]\frac{3-2}{3--1}[/tex]
simplify
m=[tex]\frac{3-2}{3+1}[/tex]
m=[tex]\frac{1}{4}[/tex]
so B is your answer
Hope this helps! :)
A total of 416 tickets were sold for a school play they were either tickets for adults tickets or student tickets the number of student tickets sold was three times the number of adult tickets sold how many adult tickets were sold
Answer:
let the number of adult tickets = x
Then the number of student tickets = 3x
Total tickets x+3x = 416
4x = 416
x = 416/4
x = 104
Therefore the number of adult tickets sold is 104
Step-by-step explanation:
A tank contains 36,864 L of water. At the end of each subsequent day, half of the water is removed and not replaced. How much water is left in the tank after 11 days
There is approximately L of water left in the tank.
(Round to the nearest whole number as needed.)
Answer:
18 L
Step-by-step explanation:
a = 36,864 * (1/2)^(11)
a = 18
36 L of water will be left after 11 days
What is an Geometric Progression(AP)?
GP is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number .
Constituting an GP according to the question
36,864 , 18432 , 9216 , ...........
In order to find nth term of an GP, formula used will be :
a(n) = a (r^(n-1))
considering above GP ,
a(n) = ? water left after 11 days
a = 36864
r= 18432 /36864 = 1/2
n = 11
a(n) = 36864 ((1/2)^(11-1))
a(n) = 36
Hence 36 L of water will be left after 11 days
Learn more about GP:
https://brainly.com/question/4853032?referrer=searchResults
#SPJ2
A ladder is 74 inches tall. How tall is it in feet and inches?
Answer:1 inch = 0.0833333 feet so 74 x 0.0833333 = 6.16667
Step-by-step explanation:
In the past year, Latoya watched 33 movies that she thought were very good. She watched 60 movies over the whole year. Of the movies she watched, what
percentage did she think were very good?
Answer:
55%
Step-by-step explanation:
Just do 33/60 and multiply by 100
(04.02 MC)
Segment AB falls on line 2x - 4y = 8. Segment CD falls on line 4x + 2y = 8. What is true about segments AB and CD?
Answer:
A
Step-by-step explanation:
A company operates three machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.
Machine
Shift A B C
1 Observed 46 11 13
Expected 40.27933 14.07821 15.64246
2 Observed 37 10 11
Expected 33.3743 11.6648 12.96089
3 Observed 20 15 16
Expected 29.34637 10.25698 11.39665
a. Yes, you can reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.0423
b. Yes, you can reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.9577
c. No, you cannot reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.0423
d. No, you cannot reject the claim that the number of breakdowns is independent of the shift because the p-value = 0.9577
please answer both thanks
Answer:
Question 4 is B and Question 5 is C
Step-by-step explanation:
Question 4 is B because the DIFFERENCE between the two terms is 15 therefore when you subtract the terms it must equal 15 so B could no be an answer. Also since they both equal 24 they both add up to 24
Write an equation of the line containing the point (3,5) and perpendicular to the line 4x-3y=5
The equation of the line is ___
Answer:
Step-by-step explanation:
In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:
[tex]-3y=-4x+5[/tex] and
3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and
[tex]y=\frac{4}{3}x-\frac{5}{3}[/tex] So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):
[tex]y-5=-\frac{3}{4}(x-3)[/tex]* and
[tex]y-5=-\frac{3}{4}x+\frac{9}{4}[/tex] and
[tex]y=-\frac{3}{4}x+\frac{9}{4}+\frac{20}{4}[/tex] so
[tex]y=-\frac{3}{4}x+\frac{29}{4}[/tex]** and, in standard form:
4y = -3x + 29 and
3x + 4y = 29***
* : point-slope form
** : slope-intercept form
*** : standard form
Which of the following is true about the US federal government’s ability to borrow money
o
63°
Please helppppp
Answer:
27
Step-by-step explanation:
180 - 90 - 63 = 27
all angles in a triangle add up to 180 degrees
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval
Answer:
Average rate of change = 5
Step-by-step explanation:
Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,
Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]
From the table,
f(5) = 10
f(4) = 5
Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]
= 5
Answer:
=5
Step-by-step explanation: