Evaluate the following expression.
50÷ 5^2×2
In an effort to make children’s toys safer and more tamperproof, toy packaging has become cumbersome for parents to remove in many cases. Accordingly, the director of marketing at Toys4Tots, a large toy manufacturer, wants to evaluate the effectiveness of a new packaging design that engineers claim will reduce customer complaints by more than 10 percentage points. Customer satisfaction surveys were sent to 220 parents who registered toys packaged under the old design and 220 parents who registered toys packaged under the new design. Of these, 86 parents expressed dissatisfaction with packaging of the old design, and 41 parents expressed dissatisfaction with packaging of the new design.
Let p1 represent the population proportion of parents that expressed dissatisfaction with the packaging of the old design and p2 represent the population proportion of parents that expressed dissatisfaction with the packaging of the new design.
A. Specify the null and alternative hypotheses to test for whether the proportion of customer complaints has decreased by more than 5% under the new packaging design.
1. H0 : p1 - p2 < 0.10; HA : p1 - p2 > 0.10
2. H0 : p1 - p2 = 0.10; HA : p1 - p2 is not equal to 0.10
3. H0 : p1 - p2 > 0.10; HA : p1 - p2 < 0.10
B. What is the value of the test statistic and the associated p-value?
C. At the 1% significance level, do the results support the engineers' claim?
D. At the 10% significance level, do the results support the engineers' claim?
Answer:
Explained below.
Step-by-step explanation:
(a)
In this case we need to determine if the proportion of customer complaints has decreased by more than 10% under the new packaging design.
The hypothesis can be defined as follows:
H₀: The proportion of customer complaints has not decreased by more than 10% under the new packaging design, i.e. p₁ - p₂ ≤ 0.10.
Hₐ: The proportion of customer complaints has decreased by more than 10% under the new packaging design, i.e. p₁ - p₂ > 0.10.
(b)
The information provided is:
n₁ = 220
n₂ = 220
X₁ = 86
X₂ = 41
Compute the sample proportions and total proportions as follows:
[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{86}{220}=0.3909\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{41}{220}=0.1864\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{86+41}{220+220}=0.2886[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.3909-0.1864}{\sqrt{0.2886(1-0.2886)\times[\frac{1}{220}+\frac{1}{220}]}}\\\\=\frac{0.2045}{\sqrt{0.0018665}}\\\\=4.733524\\\\\approx 4.73[/tex]
The test statistic value is 4.73.
Compute the p-value as follows:
[tex]p-value=P(Z>4.73)[/tex]
[tex]=1-P(Z<4.73)\\=1-(\approx 1)\\=0[/tex]
The p-value of the test is 0.
(c)
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
p-value = 0 < α = 0.01.
The null hypothesis will be rejected at 1%significance level.
Thus, there is enough evidence at 1% significance level to support the engineers' claim.
(d)
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
p-value = 0 < α = 0.10.
The null hypothesis will be rejected at 10%significance level.
Thus, there is enough evidence at 10% significance level to support the engineers' claim.
how can you work with anybody annoying you white your working at home on a test?
Find the value of x:
What is 200 as a percent?
Answer:
Step-by-step explanation:
So, we know that 200 can also be written as 200.00 which does not change the value of the number. Now, we can turn it into a percentage by moving the decimal point to digits back: 200.00 --> 20000. So, this means that 200 is 20000%.
hello I need help on it please
Answer: Adams heart Beats 1,440 more times than Blake’s in 120 minutes.
Step-by-step explanation:
Adam: 74 x 120 = 8,880
Blake: 62 x 120 = 7,440
8,880 - 7,440 = 1,440
Answer:
1440
Step-by-step explanation: you multiply
74 x 120 and 62 x 120
8,880 7,440 then subtract the two
8,880 - 7,740 = 1,440
Robert and Dora need to write 4,300,000,000 using scientific notation. Robert claims that 4,300,000,000 = 4.3 x 108 and Dora claims that 4,300,000,000 = 4.3 x 109. Which of the following best describes whose number is correct and the reason it is correct?
Answer:
Robert is correct
Step-by-step explanation:
we know in scientific notation a positive number goes to the right and if we do 4.3 and we go back the spaces it would be nine spaces so it would be 4.3 X 109
I NEED THIS NOW! PLZ HELP! 1ST GETS BRAINLIEST! PLZ USE THE 3-READ PROTOCOL
manny has 1/2 of a yard of a fabric with which he intends to make bookmarks. each bookmark is made from 1/8 yard of fabric. how many bookmarks can manny make?
Answer:
Manny can make 4 bookmarks
Step-by-step explanation:
1/2 ÷ 1/8 = ?
(flip the second fraction and multiply)
1/2 x 8/1 = 8/2 = 4
f(x)=2|5x+7|−1, evaluate f(−4)
Answer:
Step-by-step explanation:
f(x) = 2 |5(-4)+7| -1
= 2 |(-20)+7| -1
= 2 | -13 | -1
= 26 - 1
= 25
A function assigns the value of each element of one set to the other specific element of another set. The value of the function f(-4) is 25.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The value of f(-4) can be evaluated by substituting the value of x as -4 in the given function, therefore, the value of f(-4) can be written as,
f(x) = 2|5x+7| − 1
f(-4) = 2|5(-4)+7| − 1
= 2|-20 + 7| - 1
= 2|-13| - 1
= 2(13) - 1
= 26 - 1
= 25
Hence, the value of the function f(-4) is 25.
Learn more about Function here:
https://brainly.com/question/5245372
#SPJ2
HELP!!! Which of the following best describes the slope of the line below?
Answer:
C. Negative
Step-by-step explanation:
A quick reminder: an undefined slope makes the line vertical, a slope of 0 makes the line horizontal, a positive slope makes the line go up as x increases, and a negative slope makes the line go down as x increases.
In this case, the line is going down as x increases, meaning the slope must be negative.
PLEASE HELP!!! ILL GIVE BRAINLIEST
Answer:
118 degrees
Step-by-step explanation:
Answer:
118°
Step-by-step explanation:
62 and angle B are supplementary angles, so they add up to 180. 180-62 is 118, so angle B is 118.
Consider the sequence of steps to solve the equation:
7x
5(x - 3) =
Step 1 = 10(x - 3) = 7x
Step 2 = 10x - 30 = 7x
Step 3 = 3x - 30 = 0
Step 4 = 3x = 30
Step 5 = x= 10
Identify the property of equality which yields Step 5.
A)
Division Property
B)
Addition Property
C)
Subtraction Property
D)
Multiplication Property
How are the different representations of a function used to determine
the relationship between the quantities?
Answer:
Step-by-step explanation:
A function can be represented verbally. For example, the circumference of a square is four times one of its sides.
A function can be represented algebraically. For example, 3x+6 3 x + 6 .
A function can be represented numerically.
A function can be represented graphically.
There are three ways in which representations of a function are used to determine are, algebraic, numerical, and graphical .
Given that,
To explain the way the representation of a function for the relationship between quantities.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
There are three ways in which the representations of a function are used to determine the relationship between the quantities,
(a) algebraic, (b) numerical, and (c) graphical.
Thus, there are three ways, algebraic, numerical, and graphical.
learn more about function here:
brainly.com/question/21145944
#SPJ2
-2x^2-20x-46
How would you solve this?
Answer:
-2x^2-20x-46
Step-by-step explanation:
-2(x^2)-20x-46
-2(x^2) -2(10x)-46
-2(x^2)-2(10x)-2(23)
-2(x^2+10x)-2(23)
-2x^2-20x-46
Bill lent some money to his two brothers. He wrote down the amounts so he would not forget. The list shows the younger brother with −$17.25 and the older brother with $0. Which of the following statements best describes the amounts?
The older brother paid Bill $17.25, and the younger brother does not owe him any money.
The older brother owes Bill $17.25, and the younger brother does not owe him any money.
The younger brother owes Bill $17.25, and the older brother does not owe him any money.
The younger brother paid Bill $17.25, and the older brother does not owe him any money.
Answer:
the younger brother owes bill $17.25, and the older brother dose not owe him anything
Answer:
i got it right on the trst
Step-by-step explanation:
Create a word problem using the math sentence below. Make sure you write in complete sentences. -25 + (-35)
Step-by-step explanation:
john put 25 dollars in a jar and his wife put 35 dollars in the savings jar as well so save for there trip coming up
Answer:
Sally borrowed twenty-five dollars from Alex to buy a movie at the store. Later, she borrowed another thirty-five dollars to buy ride tickets at the state fair. How much money does she owe Alex?
Step by-step explanation:
When you have an even number of negative numbers in an equation, the answer will always be positive. When there's an odd number of negative numbers, the answer will be negative. For a problem like this, you can ignore the negative signs and focus on the numbers. 25+35 is 60, so Sally owes Alex 60 dollars.
Hope this helps!
which set of numbers are equivalent
0.32 , 32% , 1/32
0.45 , 50% ,49/50
0.30, 30% , 30/300
0.15 , 15% , 30/200
i will give you 40 pionts
3+3+3
Please Help....
Answer:
9
Step-by-step explanation:
Please help me I have no idea what the answer is
Answer:
hi
Step-by-step explanation:
A VISA CARD HAS A 3% CASH BACK BONUS FOR GAS AND A 1% CASH BACK FOR EVERYTHING ELSE. THIS MONTH YOU SPENT $1,500. 1/3 WAS FOR GAS.wHAT WAS YOURCASH BACK BONUS?
Answer:
25 Dollars Cashback Bonus
Step-by-step explanation:
Lets determine both Gas CashBack (x) and Non-Gas CashBack (y) first:
x = 500 (1500 times 1/3 is 500) times .03 = 15
y = 1000 (1500 minus 500) times .01 = 10
x (15) + y (10) = 25
In the picture lines AB and CD are parallel. Find the measures of
the following angles. Explain your reasoning.
F
E
D
В.
38 A.
1. BCD
2. ZECF
3. ZDCF
Answer/Step-by-step explanation:
1. <ABC and <BCD are alternate interior angles. Alternate interior angles are equal, therefore, since m<ABC = 38°, then m<BCD = 38°
2. m<ECF = m<BCD (corresponding angles)
m<ECF = 38° (substitution)
3. m<DCF + m<ECF = 180° (linear pair)
m<DCF + 38° = 180° (substitution)
m<DCF = 180° - 38° (Subtraction property of equality)
m<DCF = 142°
6TH GRADE MATH!!
Sheila can ride are bicycle 6,000 meters in 15 minutes. Cal can ride his bicycle 3,400 meters in 8 minutes.Select true or false for the following statement. cal can ride his bicycle 750 meters in 1 minutes.
Answer:
false
Step-by-step explanation:
to get this answer you need to divide 3,400 by 8. Which is 425. So no, he can not go 750 meters, he can only go 425 meters in one minute. hope this helps!!
Find value of x, first gets brain
Answer:
53
Step-by-step explanation:
During the 2005 football season Team Tackle beat Team Sack by 18 points their combined scores totaled 66. the individual team score
1. Team tackles score was ? Points
2. Team sacks score was ? Points
Find the value of x.
(7x + 16)
80°
The value of x is
Which of the following functions has a graph that passes through the origin? Select all that apply.
A. power; y equals x superscript n baseline
B. root; y equals Root Index n Start Root x End Root
C. reciprocal; y equals Start Fraction 1 over x End Fraction
D. exponential; y equals b superscript x baseline
Answer: a and b
power and root
3 new tires for $210; 4 new tires for $250
Tanmayi wants to raise $190 for a school fundraiser. She has raised $140 so far. How much more does she need to reach her goal? Let m be how much more is needed.
Answer:
190 plus x = 140 -140 -140 x=50Write and expression equivalent to - 1/2(6x-8+4x please help
Step-by-step explanation:
I won't say the answer, but will give an explanation. the explanation for solving the expression is above.
the fully simplified expression is 5x - 4. All you need to do now is make an expression that will equal 5x - 4 simplified.
An example is: 20(1/4x-1/5)
if I read the questions wrong and it's just asking to simplify the expression then the answer is 5x - 4.
answer for brainliest ! <3
Answer:
1: p=(2,4) q=(1,1) r=(5,2)
2 I am so sorry. the changing in the shape is not any transformation I've heard of before.
3:90 degree rotation (Counterclockwise.)
4: 180 degree rotation (doesn't matter which way.)
5: 90 degree rotation (clockwise)
6: Up 9 units, over 2 units to the right.
Hope this helps!!