Answer:
The test statistic is [tex]z = -2.1[/tex]
The p-value of the test is 0.0358 > 0.01, which means that the defective rates of the two suppliers are not significant different at the 1% significance level.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A simple random sample of 400 parts from supplier 1 finds 20 defective.
This means that:
[tex]p_1 = \frac{20}{400} = 0.05, s_1 = \sqrt{\frac{0.05*0.95}{400}} = 0.0109[/tex]
A simple random sample of 200 parts from supplier 2 finds 20 defective.
This means that:
[tex]p_2 = \frac{20}{200} = 0.1, s_2 = \sqrt{\frac{0.1*0.9}{200}} = 0.0212[/tex]
Let p1 and p2 be the proportion of all parts from suppliers 1 and 2, respectively, that are defective. Test whether the defective rates of the parts from two suppliers are significant different at the 1% significance level.
At the null hypothesis, we test if they are equal, that is, if the subtraction of the proportions is 0. So
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternate of the null hypothesis, we test if they are different, that is, if the subtraction of the proportions is different of 0. So
[tex]H_a: p_1 - p_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the sample proportions:
[tex]X = p_1 - p_2 = 0.05 - 0.1 = -0.05[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0109^2 + 0.0212^2} = 0.0238[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.05 - 0}{0.0238}[/tex]
[tex]z = -2.1[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.05, that is, P(|z| < 2.1), which is 2 multiplied by the p-value of Z = -2.1.
Z = -2.1 has a p-value of 0.0179
2*0.0179 = 0.0358.
The p-value of the test is 0.0358 > 0.01, which means that the defective rates of the two suppliers are not significant different at the 1% significance level.
Chau will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $44 and costs an
additional $0.11 per mile driven. The second plan has an initial fee of $49 and costs an additional $0.07 per mile driven.
for what amount of driving to the two plans cost the same amount?
What is the cost when the two plans cost the same?
Answer:
I don't know
Step-by-step explanation:
i don't know
The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.
The density of the material is 1533.3 grams per quarts.
What is density?Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.
Given that, the density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume.
The formula to find the density is Density=Mass/Volume
Density =6900/4.5
Density= 1533.3 grams per quarts
Therefore, the density of the material is 1533.3 grams per quarts.
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NEED HELP LOL
if i have an 80% in a class for the first semester and a 90% in a class for the second semester, what is my grade for the year?
Let x^2+10x=6.
What values make an equivalent number sentence after completing the square?
Enter your answers in the boxes.
x^2+10x+___=___
Answer:
x² + 10x + 25 = 31
Step-by-step explanation:
To complete the square use half the x coefficent (10/2 = 5)
and square it (5² = 25)
Then add it to both sides
x² + 10x + 25 = 6 + 25
x² + 10x + 25 = 31
Answer:
x^2 + 10x + 25 = 31
Step-by-step explanation:
x^2 + 10x + (10/2)^2 = 6 + 25
x^2 + 10x + 25 = 6 + 25
x^2 + 10x + 25 = 31
The first step requires a bit of explanation. The way to complete the square is to take 1/2 the linear term (10x) and square it
1/2 10 = 5
5 squared = 25
That number must be added to the right side to maintain equality.
whats 2+2 pls i have a test tomorrow i need to pass it
A woman bought a number of items for $24. She realized that if she had bought 4 more items for
the same money, she would have pald $8 less per Item. How many Items did she buy?
Answer:
The woman bought 2 items at $12 each.
Step-by-step explanation:
Given that a woman bought a number of items for $ 24, and she realized that if she had bought 4 more items for the same money, she would have paid $ 8 less per item, to determine how many Items did she buy the following calculation must be done:
X = 24
X + 4 = 24
24/2 = 12
24/6 = 4
12 - 4 = 8
Therefore, the woman bought 2 items.
Show how u solved it
Answer:
The surface area of the figure is 412 cm2.
Step-by-step explanation:
To determine the total surface area of a prism, the following formula must be applied: perimeter of the base x height + 2 x area of the base = total surface area. Thus, the calculations of the blue prism must be carried out and then add the sides of the red figure that do not coincide with it:
Blue figure:
(12 x 2 + 2 x 2) x 10 + 2 x (12 x 2) = X
(24 + 4) x 10 + 2 x 24 = X
28 x 10 + 48 = X
280 + 48 = X
328 = X
Red figure:
3 x 8 = 24 x 2 = 48
3 x 6 = 18 x 2 = 36
328 + 48 + 36 = X
376 + 36 = X
412 = X
Therefore, the surface area of the figure is 412 cm2.
Find the equation of the exponential function represented by the table below: 1 4 16 64
Find the inverse of the function.
y = x + 8
Write your answer in the form ax + b. Simplify any fractions.
y =
Answer:
X=y-8................
Do you know how to do this
Answer:
B
C
E
Step-by-step explanation:
PLEASE help test due tonight !!!Use the two-way frequency table to answer questions #14-19
Answer:
14. 1/13
15. 14/15
16. 1/13
17. 15/30=1/2
18. 12/13
19. 12/15
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The solid below is made of eight rectangular prisms, each with dimensions of 14 inches (in.) by 9 inches by 10 inches.
What is the volume, in cubic inches, of the object?
DO NOT ANSWER IF YOU DO NOT KNOW THE ANSWER! Whoever answers correctly will get Brainliest.
Answer:
D
Step-by-step explanation:
Volume of one prism
V = base x width x height = 14 x 9 x 10 = 1260 in^3
Volume of the solid
V = volume of one prims x 8 = 1260 x 8 = 10,080 in^3
FIND C.
Give your answer in the simplest form
Answer:
3
Step-by-step explanation:
[tex] \sin(45) = \frac{a}{7 \sqrt{2} } [/tex]
[tex]a = 7[/tex]
[tex] \tan(30) = \frac{7}{c} [/tex]
[tex]c = 7 \sqrt{ 3} [/tex]
therefore 3 is required in the green box
For the geometric sequence, the common ratio is 2 and the 12th term is a12 =6144. What is the first term?
A. a1=2
B.a1=3
C.a1=4
D.a1=5
Answer:
B. a1 = 3
Step-by-step explanation:
Since we have the comon ratio and 12th term, we could just divide the 12th term (6144) by 2 11 times until we get to the 1st term:
[tex]6144 /2/2/2/2/2/2/2/2/2/2/2 = 3[/tex]
For a better understanding of the question, let's use the formula for geometric equations:
a(r)^(n-1)
1. Let's plug in the values we know
r = common ratio = 2 n = 12a(2)^(12-1)
2. Set equation equal to 6144 (Since we use n = 12) and solve for a
a = 6144/ (2^11) a = 3To confirm this, let's use the formula for geometric equations again:
a(r)^(n-1)
a = first term = 3
r = common ratio = 2
3(2)^(12-1) = 6144
Therefore, a1 = 3
a local park is shaped like a square with sides 6 meters long. A circular splash fountain is being placed in the middle of the park as shown in the image below. How much of the park will still be grass?
Answer: 624 Square meters
Step-by-step explanation:
Identify and write down the keywords in the word problem. (1.) Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3. Evaluate the expression 2g + 3a when g = 4 and a = 8 to find the cost of buying 4 cartons of grape juice and 8 cartons of apple juice. What is the difference in price Missy and Jared paid? Show your work.
The cost of the 4 cartons of grape juice and 8 cartons of apple juice will be $32 and the difference is $12.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3.
The cost of 4 grapes and 8 apples will be,
Cost = 2g + 3a
Cost = ( 2 x 4 ) + ( 3 x 8 )
Cost = 8 + 24
Cost = $32
The difference in the price Missy and Jared paid is,
Difference = $32 - $ 20
Difference = $12
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8. Using the formula C= id, find the circumference of a circle with a
diameter of 9 cm.
A. 28.26 cm B. 28.26 m C. 29.26 cm D. 29.26 m
Answer:
Circumference of a circle, C
[tex]C=\pi d= \pi 9=28.26cm\\Option \ A[/tex]
Germany 3. Guam 24
Greenland -10
Which location is the warmest?
Answer: Guam
Step-by-step explanation:
Guam's location is the warmest because its a higher number than Greenland and Germany
The Barker family just left the local pet store with Lucky, their new family dog. The pet store owner told the Barker family that for the next 6 months, Lucky would grow at an average rate of 9 pounds per month. Currently, Lucky is 2 months old and weighs 3 pounds. Age, in months 2 3 4 5 6 7 8 Weight, in pounds 3 at 2 months old Part A: Complete the given table that represents Lucky's current weight, in pounds, as a function of his age, in months. Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points. Part C: Create a linear model that represents the Lucky's current weight, in pounds, as a function of his age, in months. Part D: If Lucky continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Lucky weigh by the time he is one year old?
The table is given below.
The graph is given below.
The linear model that represents lucky's current weight in pounds as a function of his age in months is
f(x) = 9x - 15.
Lucky's weight in one year is 93 pounds.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Lucky current age and weight = 2 months and 3 pounds.
The growth rate of lucky per month = 9 pounds.
Table of age and weight of lucky.
Age (months) Weight (pounds)
2 3
3 12
4 21
5 30
6 39
7 48
8 57
Now,
The coordinates on the graph from the table are:
(2, 3), (3, 12), (4, 21), (5, 30), (6, 39), (7, 48), and (8, 57).
The graph of the table is given below.
Now,
The function for the weight of the lucky in x months.
f(x) = mx + c
m = 9
(2, 3) = (x, f(x))
So,
3 = 9 x 2 + c
c = 3 - 18
c = -15
So,
f(x) = 9x - 15
Where x is the number of months.
Now,
The weight of lucky in one year i.e 12 months.
This means,
x = 12 months
f(12) = 9 x 12 - 15 = 108 - 15 = 93
Thus,
The table is given above.
The graph is given below.
The function for lucky weight in x months is f(x) = 9x - 15.
The weight of lucky in one year is 93 pounds.
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39➗(2+1) - 2x (4+1)
5/7 - Exit Ticket
Answer:
13 - 10x
= -3x
hope it helps
which expressions are equivalent to 2(-6c + 3) + 4c
A. -8c + 6
B. 3(-4c + 2)+4c
C. None of the Above
Answer:
A and B
Step-by-step explanation:
2(-6c + 3) + 4c
According to PEMDAS, we should evaluate the parentheses first.
However, the parentheses are already simplified completely.
Now we look for exponents. However, there are no exponents.
Next is multiplication. We can see there is a 2 directly outside of the parentheses. Distribute the 2 across each term in the parentheses.
-12c + 6 + 4c
Now combine like terms with addition.
-8c + 6
We can see that A. -8c + 6 is an answer choice.
Let's look at B. 3(-4c + 2) + 4c
Following the same steps, we will move on to multiplication.
-12c + 6 + 4c
Combine like terms with addition.
-8c + 6
This is also an answer choice.
Hope this helps!
explain step by step please thank you! Paco drives an average of 55 miles per hour. Their destination is 274 miles away. wants to arrive at 4:00 p.m. and allow an extra hour for stops. What time should he go out?
Answer:
11:01 am
Step-by-step explanation:
If paco drives 55 miles per hour you must divide 274 by 55 to find the amount of time it will take for him to reach his destination:
274÷55=4.981818...
Now we have 4 hours plus 0.981818.. hours which the latter we multiply by 60 to find out how many minutes are 0.981818 hours:
60×0.981818...=58.9090...
which I will round to 59 as clocks show an hour and a minute so rounding it so it's accurate to the second is unnecassary, this means it will take him 4 hours 59 minutes to reach his destination so we subtract this from 4:00 pm:
4:00 pm-4 hours 59 minutes= 11:01 am
So our answer is 11:01 am
6029-5817 is the correct answer 45
the answer is 212 .... not sure where 45 came from
A recipe for punch requires 20 grams of drink mix for 5 liters.
How many grams of drink mix are needed per liter of water?
Billy is creating a circular garden divided into 8 equal sections. The diameter of the garden is 12 feet.
Billy noticed that several of his carrots had been eaten by some mischievous rabbits. Billy wants to build a fence around his circular garden to keep the rabbits out. How much fence would Billy need? Explain how you determined your answer. Show all your work.
Billy decides that next year he will make his garden a raised-bed garden. He plans to make a short wall of paving bricks all the way around the garden, then fill the space inside with fresh soil. If he makes the wall 1 foot high, what volume of soil will he have to purchase in order to fill the circle to the top of the bricks?
Answer:
Step-by-step explanation:
area=πr^2
so we need to find the area then divide by 8
so
we know that diameter=2radius or diameter/2=radius so
12=diameter
12/2=radius=6
subsitute
area=π(6)^2
area=36π
divide 36π by 8
36π/8=18π/4=9π/2π=4.5π
area of one section is 4.5π square feet or if we aprox pito 3.14159 then we get
4.5(3.14159)=area=14.1372 square feet or 14.14 square feet
Solve for m: m-5/8=-1/4
M-5/8 = -1/4
Add 5/8 to both sides:
M = -1/4 + 5/8
Rewrite the fractions to have a common denominator
-1/4 = -2/8
Now you have m = -2/8 + 5/8
M = 3/8
Answer:
The answer is 0.375 (3/8)
Step-by-step explanation:
Since the M is subtracted by 5/8, you add 5/8 to both sides of the equation to get the M by itself and -1/4+5/8 equals 0.375, or 3/8
Two sides of a parallelogram are 500 feet and 790 feet. The measure of the angle
between these sides is 33°. Find the area of the parallelogram to the nearest square
foot
Answer:
215117 ft²Step-by-step explanation:
Assumed the base is the longer side.
The height of the parallelogram is:
h/500 = sin 33° h = 500 sin 33° h = 272.3 ftThe area is:
A = bh A = 790*272.3 = 215117 ft²Answer:
215132
Step-by-step explanation:
deltamath
multiply the sum by the difference of 19 and 57
Answer:2009#73
Step-by-step explanation:
3939+373
Ie,ek
(please answer)When considering the cost of paying for college, which kind of aid MUST be repaid A) grants B) scholarships 0 student loans D work-study
Answer:
A. grant
that's the answer
does anyone know what this is please help
Answer:
1)2 2)third 3)8
Step-by-step explanation:
So for the first one doubled just means times 2
for the second r³ means to the third power
for the last one all you do is put some values in and calculate the radius volume ratio which is, when the radius is doubled the volume is octupled (times 8)
would be amazing if you Marked this as brainliest