In an effort to make childrenâs 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, 81 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.

Required:
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.
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?

P = principal = 8400

r = interest rate in decimal form = 0.0775

t = time in years = 10/12 = 5/6

i = simple interest

i = P*r*t

i = 8400*0.0775*(5/6)

i = 542.50 dollars is the answer

Answer: 14/18 , 21/27 are ratios equivalent to 7/9's .

Answer:

Step-by-step explanation:

pq = (5-2i)×(-3+7i) = -15 + 35i +6i -14i^2

= -15 +41i -14(-1)

= -15 +41i +14 = -1+41i

Answer:

5.7

Step-by-step explanation:

sine cosine tangent

soh cah toa

sine = opposite/hypotenuse

so sin(35)= x/10

you can multiply 10 to both sides to get rid of the 10 denominator on the right leaving you with 10sin(35)=x

be sure your calculator is in degrees.

put that into a calculator leaving you with 5.7

Answer:

747.3

Step-by-step explanation:

We take 0.06 away from 1

This simulates 100 percent minus 6 percent

0.94

795 * 0.94 = 747.3

Given:

\(f(x)=3x^2-5x-2\); find f(-2/3)

Answer:

\(f(-\frac{2}{3} )=\frac{8}{3}\)

Step-by-step explanation:

1. Insert \(-\frac{2}{3} \\\) as X; \(f(-\frac{2}{3}) = 3 (-\frac{2}{3} )^2 - 5 (-\frac{2}{3}) - 2\)

2. Solve equation; \(f(-\frac{2}{3} )=\frac{8}{3}\)

Answer:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

Step-by-step explanation:

95 percent certainty that the actual percentage of adults  who do not use the Internet in the country is between 12.99 and 17.09 percent.

Probability distributions are widely used to define confidence intervals and to calculate critical regions (eg p-value) for hypothesis testing. It is used in many fields aspiring to informatics.

We can use the following formula to construct a 95% confidence interval estimate for the percentage of adults in countries who do not use the Internet:

CI = p ± z*(√.(p×(1-p)/n))

where:

p = Proportion of non-Internet adults in the sample  

n = sample size

z = z-scores corresponding to the confidence level  (95% in this case)

Combining the values, we get:

p = 752/5000 = 0.1504

n = 5000

z = 1.96 (95% confidence level)

CI = 0.1504 ± 1.96* (√(0.1504*(1-0.1504)/5000))

CI = 0.1299 - 0.1709

Thus, we can say with 95 percent certainty that the actual percentage of adults  who do not use the Internet in the country is between 12.99 and 17.09 percent.

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Answer:

the amount of discount is $210

Step-by-step explanation:

30(.30)

90

90 is 30% of 300

subtract:

300-30= 210

Answer:$210

Step-by-step explanation:

Answer:

95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.

(12.6604 ,19.3396)

Step-by-step explanation:

Step(i):-

Given that mean of the sample = 16

Given that the standard deviation of the sample = 3.81

The standard deviation of the Population = 3.81

Level of significance = 0.05

Step(ii):-

95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.

\((x^{-} - Z_{0.05} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.05} \frac{S.D}{\sqrt{n} } )\)

(\((16 - 1.96 (\frac{3.81)}{\sqrt{5} } , 16 +1.96 (\frac{3.81)}{\sqrt{5} })\)

( 16 - 3.3396 , 16 + 3.3396)

(12.6604 ,19.3396)

Final answer:-

95% confidence interval in order to estimate the average price of the white cotton extra-long twin sheets.

(12.6604 ,19.3396)

Answer:

it would be 9

Step-by-step explanation

The number is 4.5 units away from 6, let x represent said number then you can express it as:

|x-4.5|<6

Solve for x

The determined number is below 1.5

Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

12

Step-by-step explanation:

You simply add the coefficients together.
3 + 4 + 5 = 12

Based on the statistical analysis, there is not enough evidence to conclude that the water from the new source contains unsafe levels of copper at the 0.05 significance level.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves applying mathematical and statistical techniques to extract meaningful insights from data, and to make decisions and predictions based on this information. Statistics is used in a wide range of fields, including business, economics, social sciences, health sciences, engineering, and more. It helps researchers, analysts, and decision-makers to identify patterns, relationships, and trends in data, and to draw conclusions based on statistical evidence.

(a) To test whether the water from this source contains unsafe levels of copper, we need to perform a one-sample t-test with the null hypothesis that the mean copper content in the water is less than or equal to 1.3 mg/l and the alternative hypothesis that the mean copper content in the water is greater than 1.3 mg/l.

The test statistic is calculated as:

t = (x - μ) / (s / √n)

where x is the sample mean (1.36 mg/l), μ is the hypothesized population mean (1.3 mg/l), s is the sample standard deviation (0.18 mg/l), and n is the sample size (30).

Plugging in the values, we get:

t = (1.36 - 1.3) / (0.18 / √30) = 1.47

The degrees of freedom for this test is n - 1 = 29.

Using a t-table or calculator, we find the p-value associated with a t-statistic of 1.47 and 29 degrees of freedom to be approximately 0.076.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence at the 0.05 level to conclude that the water from this source contains unsafe levels of copper.

Conditions for Independence: It is assumed that the water samples are independent of each other. This is because the sample is randomly selected and the size is less than 10% of the population. Also, it is assumed that the copper content in one water sample does not affect the copper content in another water sample.

Conditions for Normality: It is assumed that the distribution of the copper content in the population is approximately normal. We can justify this assumption based on the central limit theorem, which states that the distribution of the sample mean approaches normality as the sample size increases. Since the sample size is 30, we can assume that the sample mean follows a normal distribution. We can also check the normality assumption by creating a histogram or a normal probability plot of the data.

Therefore, based on the statistical analysis, there is not enough evidence to conclude that the water from the new source contains unsafe levels of copper at the 0.05 significance level.

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Answer:

a. Her monthly payment is $1618.786418

b. She will pay $312763.1105 interest over the life of the loan

Step-by-step explanation:

Let us revise the rules of the monthly payments and interest

\(M.P=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}\)

\(I = M.P(nt)- P\)

Where:

∵ Lynn bought a $300,000 house

∵ She was paying 10% down

→ That means the initial amount is 90% of $300,000

∴ p = 90/100 × 300,000 = 270,000

∵ She was financing the rest at 6%

∴ r = 6% = 6/100 = 0.06

∵ There is a monthly payment

∴ n = 12

∵ She was financing the rest for 30 years

∴ t = 30

a.

→ Substitute these values in the first rule to finding the monthly payment

∵ \(M.P=\frac{270,000(\frac{0.06}{12})}{1-(1+\frac{0.06}{12})^{-12(30)}}\)  

→ Let us use the calculator to find the answer

∴ M.P = $1618.786418

∴  Her monthly payment is $1618.786418

b.

→ Substitute these values in the first rule to finding the second rule

   to find the interest

∵ \(I = (1618.786418)(12)(30)-270,000\)

→ Let us use the calculator to find the answer

∴ I = $312763.1105

∴ She will pay $312763.1105 interest over the life of the loan

Answer:

  (c)  x = 4, RS =13

Step-by-step explanation:

You want to find x and RS when RS=3x+1, ST=2x, and RT=21.

As with many multiple-choice problems, the only consistent answer is the correct one.

If x=20, then 3x+1 = RS = 3(20)+1 = 61. This eliminates choices A and D.

If x=4, then 3x+1 = RS = 3(4) +1 = 13. This eliminates choice B and selects choice C.

The correct answer is x=4 and RS=13.

__

Working it out

The sum of segment lengths is the total length.

  RS +ST = RT

  (3x +1) +(2x) = 21

  5x = 20 . . . . . . . . . subtract 1

  x = 4 . . . . . . . . . . . divide by 5

  RS = 3(4) +1 = 13

The experimental probability of choosing a student who walks to school is given by 0.15625 or 15.625%.

Given data ,

The experimental probability of choosing a student who walks to school can be calculated by dividing the number of students who walk to school by the total number of students in Joe's class.

Number of students who walk to school = 5

Total number of students in the class = 32

Experimental probability = Number of students who walk to school / Total number of students

= 5 / 32

P = 0.15625

Hence , the experimental probability of choosing a student who walks is 0.15625 or 15.625%.

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Answer:

\(Ratio = 0.74\)

Step-by-step explanation:

Represent

- Andy with A

- Christopher with C

\(A = 3.5L\)

\(C = 2580mL\)

Required

Determine the ratio of C to A

Ratio is represented as thus:

\(Ratio = C:A\)

Rewrite as fraction

\(Ratio = \frac{C}{A}\)

This gives

\(Ratio = \frac{2580mL}{3.5L}\)

Convert L to mL

\(Ratio = \frac{2580mL}{3.5*1000mL}\)

\(Ratio = \frac{2580mL}{3500mL}\)

\(Ratio = \frac{2580}{3500}\)

\(Ratio = 0.73714285714\)

\(Ratio = 0.74\) --- Approximated

Answer:

-8

Step-by-step explanation:

Slope = (y1-y2) / ( x1-x2)

            = ( f-4) / (-8 - -6)      =  6

                  (f-4) / -2    = 6

                    f-4 = -12

                     f = - 8

Answer:

f = -8

Explanation:

Find slope:

\(\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points\)

Here given:

Inserting into slope formula:

\(\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6\)

\(\sf \rightarrow \dfrac{4-f}{2 } = 6\)

\(\sf \rightarrow 4-f = 12\)

\(\sf \rightarrow -f = 12-4\)

\(\sf \rightarrow -f =8\)

\(\sf \rightarrow f =-8\)

When we evaluate the expression 8x² + 6x - 8 in x = 2, we will get the value 36.

Here we need to evaluate the following expression:

8x² + 6x - 8

in x = 2.

Evaluating means that we need to replace the variable by the given number. Replacing the "x" by 2, we will get:

8*2² + 6*2 - 8

8*4 + 12 - 8

8*3 + 12

24 + 12 = 36

When x = 2, the expression is equal to 36.

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According to the solution we have come to find that, The correct value of x in the given equation is 30.

An equation is a mathematical statement that shows the equality between two expressions, usually containing variables and mathematical operations. In an equation, the expressions on both sides of the equals sign have the same value.

For example, the equation 2x + 5 = 11 is an equation that shows the equality between the expressions 2x + 5 and 11. To solve the equation, we need to find the value of the variable x that makes the equation true.

Martina solved the equation x + 14 = 44 as follows:

x + 14 = 44

x = 44 - 14

x = 30

The error that Martina made is that she forgot to subtract 14 from both sides of the equation. The correct solution should be:

x + 14 = 44

x = 44 - 14

x = 30

Therefore, the correct value of x in the given equation is 30.

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Answer:

The first restaurant is a better deal.

Step-by-step explanation:

First restaurant: Let's say there are 2 people. 28 x 2 = 56. You would have to pay $56 for 2 people.

Second restaurant: Let's say there are 2 people. The graph says that you would have to pay $60 for 2 people.

Therefore, the first restaurant is a better deal.

Answer:

x = 20.6°

using cosine rule:

\(\sf cos(x)= \dfrac{adjacent}{hypotensue}\)

using the formula:

\(\sf cos(61)= \dfrac{10}{x}\)

\(\sf x= \dfrac{10}{cos(61)}\)

\(\sf x= 20.6\)

Answer:

x = 20.6 (nearest tenth)

Step-by-step explanation:

Trigonometric ratios

\(\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}\)

where:

To find the value of x in the given diagram use the cosine ratio.

From inspection of the given diagram:

Substitute the given values into the cosine ratio and solve for x:

\(\implies \cos(61^{\circ})=\dfrac{10}{x}\)

\(\implies x=\dfrac{10}{\cos(61^{\circ})}\)

\(\implies x=20.626653...\)

\(\implies x=20.6\; \sf (nearest\;tenth)\)

Therefore, the value of x to the nearest tenth is 20.6.

Answer:

If the jacket is on sale for 20% off, you are paying 80% of the price.

So, 0.8(250), which is 200 dollars.

Let me know if this helps!

Answer:

$200

Step-by-step explanation:

First you have to figure out how much 20% is. (Its $50) So now, all you have to do it 250-50 which is $200

Answer: 53.333333, 53 1/3

Step-by-step explanation:

The unit rate in this question means how many calories for one ounce.  Thus, you can simply divide 480 by 9 to get 53.3333333

Answer:

Step-by-step explanation:

Calories in a low calorie dinner = 480 calories

Serving at one time = 9 ounce

then,

Unit rate = Amount of calories in one serving

So,

Amount of calorie in 9 serving = 480

Amount of calorie in 1 serving = 480/9

In simple form : 160/3

= 53.33 calories

Hope this helps...

Good luck on your assignment..

Answer:

1/13 chance or roughly 7.7% chance.

Step-by-step explanation:

There are 4 Kings in a standard 52-card deck. If one King was to be pulled out, you'd get a probability of 4/52 chance of pulling a king. Simplified, 4/52 is  1/13 chance.