why are the mean and standard deviation used to compaer the center and spread of two symmetrical distributions and why are the five number summary used to compare

The answer of the given question based on the graph is the amplitude of the given sin equation is 2.

Amplitude refers to the maximum displacement of a wave from its equilibrium or rest position. It is a characteristic of a wave that measures the magnitude or strength of its oscillations or vibrations.  The amplitude refers to the distance from the midline (or average value) of the function to its maximum or minimum value. The amplitude is a positive value, and it is half the distance between the maximum and minimum values of the function.

In this case, we can see from the graph that the midline of the function is y = -3, which is the value of the function when sin(Θ) = 0 (since 2sin(Θ) - 3 = 2(0) - 3 = -3).

The maximum value of the function occurs when sin(Θ) = 1 (since the maximum value of sin(Θ) is 1), so the maximum value of 2sin(Θ) is 2. Therefore, the maximum value of 2sin(Θ) - 3 is 2 - 3 = -1.

The distance from the midline (-3) to the maximum value (-1) is 2 units, so the amplitude of the sine function y = 2sin(Θ) - 3 is 2.

Therefore, the amplitude of the given sin equation is 2.

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the ratio of the number of minutes he lifted weights to the total number of minutes of his entire workout is 1:2 option B is correct.

Ratios can be written in three forms:

A to B

A:B

A/B

Ratios are also simplified by reducing to lowest terms like fractions are.

This problem's ratio is:

minutes lifted weights to total minutes workout

The number of minutes lifting weights is in the question: 25.

To find the total minutes of his workout, add the number of minutes he spent for all of the activities:

Total minutes = warm-up + lifting weights + treadmill

Total minutes = 10 + 25 + 15

Total minutes = 50

The ratio before simplifying is 25÷50.

This ratio can be reduced to lowest terms. Both sides are divisible by 25.

[tex]\frac{25}{25}=1[/tex]

[tex]\frac{50}{25} = 2[/tex]

The ratio in the lowest terms is 1/2.

It can also be written as 1 to 2 or 1:2.

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The possible coordinates of the point a is (-4, 11.06) and (-4, -9.06).

Given that point, b has coordinates (5,1) and the distance between point a and point b is 15 units, we can use the distance formula to find the possible coordinates of point a.

The distance formula is given by:

distance = [tex]\sqrt({x_{2}-x_{1 })^{2} } +\sqrt({y_{2}-y_{1 })^{2}[/tex]

If we replace with the point b's coordinates, we obtain:

15 = [tex]\sqrt({5}-(-4)})^{2} } +\sqrt({1-y_{1 })^{2}[/tex]

Simplifying the equation, we get:

225 = [tex](9 + y_{1} ^{2} - 2y_{1} )[/tex]

Rearranging and solving for y1, we get:

y₁² - 2y₁ - 216 = 0

Using the quadratic formula, we get:

y₁ = 11.06

y₁ = -9.06

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The p-value for testing if the proportion who are unemployed differs between the two groups is 0.

To calculate the p-value for testing if the proportion who are unemployed differs between the two groups, we can use a two-sample test of proportions

Let's define

Group 1: High School or Some College

Group 2: Bachelor's or Higher

We want to test if the proportion of unemployed individuals differs between Group 1 and Group 2.

First, we need to calculate the proportion of unemployed individuals in each group

Group 1: 41/601 = 0.06822

Group 2: 14/875 = 0.016

Next, we need to calculate the pooled proportion

Pooled proportion = (41 + 14) / (601 + 875) = 0.043

Now we can calculate the test statistic

Test statistic = (0.06822 - 0.016) / sqrt(0.043 × (1 - 0.043) × (1/601 + 1/875)) = 7.57

Using a two-tailed test with a significance level of 0.05, we can find the critical value from a normal distribution table or calculator. For a two-tailed test with a significance level of 0.05, the critical value is approximately 1.96.

Since the test statistic (7.57) is greater than the critical value (1.96), we reject the null hypothesis that the proportion of unemployed individuals is the same in both groups.

Finally, we can calculate the p-value as the probability of getting a test statistic as extreme or more extreme than the one we observed, assuming the null hypothesis is true. Since this is a two-tailed test, we need to double the area to the right of the test statistic (7.57) under the standard normal curve

p-value = 2 × P(Z > 7.57) = 0

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The given question is incomplete, the complete question is:

The following table is based off a survey of employment from 2018. What is the p- value for testing if the proportion who are unemployed differs between the two groups? Give your answer to three decimal places. Total Unemployed 41 Employed 834 875 High School or Some College Bachelor's or Higher Total 14 587 601 55 1421 1476

The hypotheses being tested are: H0: p = 0.33 versus Ha: p > 0.33.

The test statistic is 1.51.

The p-value is 0.131.

So we have no statistically significant evidence that the population proportion of American women in 2014 who say people can be trusted is different from the proportion of men who feel the same. The p-value of 0.131 is greater than the commonly used alpha level of 0.05, which means that we fail to reject the null hypothesis. However, we cannot conclude that the proportions are equal, only that we do not have enough evidence to say that they are different.

The General Social Survey asked 929 American women in 2014 whether they thought people can be trusted or whether they cannot be too careful in dealing with people. Out of the 929 women sampled, 259 said that most people can be trusted. The hypotheses being tested are whether the proportion of American women who say people can be trusted is different from the proportion of men who feel the same (33%). The null hypothesis (H0) is that the proportion of American women who say people can be trusted is 0.33, while the alternative hypothesis (Ha) is that it is greater than 0.33.

The test statistic for this hypothesis test is 1.51, which is calculated using the sample proportion of women who say people can be trusted (0.28), the hypothesized proportion of men who feel the same (0.33), and the standard error of the sampling distribution. The p-value of the test is 0.131, which is the probability of getting a sample proportion as extreme or more extreme than the observed proportion of 0.28, assuming that the null hypothesis is true.

Since the p-value of 0.131 is greater than the commonly used alpha level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have enough statistical evidence to conclude that the proportion of American women who say people can be trusted is different from the proportion of men who feel the same. However, we cannot conclude that the proportions are equal, only that we do not have enough evidence to say that they are different.

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--The question is incomplete, answering to the question below--

"About a third (33%) of American men feel that, in general, people can be trusted. Is it different for American women? In 2014, the General Social Survey asked its participants: Generally speaking, would you say that most people can be trusted or that you can't be too careful in dealing with people? Out of 929 women sampled, 259 said most people can be trusted.

The hypotheses being tested are: H0: p = 0.33 versus Ha: p [ Select ] ["not =", ">", "<"] 0.33

The test statistic is [ Select ] ["-3.31", "0.279", "-1.51"]

The p-value is [ Select ] ["0.9995", "0.0005", "0.002", "0.001"]

So we have [ Select ] ["very strong", "strong", "some", "no"] statistically significant evidence that the [ Select ] ["population proportion", "sample proportion"] of American women in 2014 who say people can be trusted is different from the proportion of men who feel the same."

Answer:

y>6

Step-by-step explanation:

5y>30

y>6

therefore, y can be any number that is larger than 6 (e.g. 7, 10 etc)

Answer:

25% off

Step-by-step explanation:

Answer It’s Save 20$, cause if u buy Something More then 88$ U could 20% off which the new price will be 68$ (to make sure Take 88 from 20 Which will prob be 68) but 68$ would be the new price if Lacey Picked the “Save $20 one purchased Of $75 or more”

Step-by-step explanation hope this helps

Answer:

18.84 miles

Step-by-step explanation:

Circumference = 2πr

= 2 × 3.14 × 3

= 18.84 miles

The exact circumference of the circle with radius 3 miles is 6π or 18.84 miles (approx).

The radius of a circle is 3 miles. What is the circumference?The formula to calculate the circumference of a circle is given as:

Circumference = 2πr, where r is the radius of the circle and π is a constant value, approximately equal to 3.14. Substituting the given value of r in the formula, we have:

Circumference = 2π(3)

Circumference = 6π

Therefore, the exact circumference of the circle is 6π miles. To simplify this answer in its simplest form, we can use the value of π as 3.14 (approximately).Circumference = 6π = 6(3.14) = 18.84Therefore, the exact circumference of the circle is 18.84 miles (approx).

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Answer:

64°

Step-by-step explanation:

Given:

A complete angle is 360 degrees

A complete angle is 360 degreesOne right angle (90 degrees)

A complete angle is 360 degreesOne right angle (90 degrees)An angle of 154 degrees

A complete angle is 360 degreesOne right angle (90 degrees)An angle of 154 degreesTwo cross angles that are equal

Find: ∠b - ?

.

First, let's find the size of the smaller cross angles:

180° - 154° = 26°

Since there's two of them, we have to multiply this number by 2:

26° × 2 = 52°

Now, we can find ∠b:

∠b = 360° - 90° - 154° - 52° = 64°

To compare the ratios 17:23 and 5:9, you can do it by either finding their decimal equivalents or by cross-multiplying.

Finding decimal equivalents:

Divide each part of the ratio by the sum of its parts.

For 17:23:

17 ÷ (17+23) = 17 ÷ 40 = 0.425

For 5:9:

5 ÷ (5+9) = 5 ÷ 14 = 0.3571

Now compare the decimals:

0.425 > 0.3571

So, the ratio 17:23 is greater than 5:9.

Cross-multiplying:

Cross-multiply the two ratios and compare the products.

For 17:23 and 5:9, multiply 17 by 9 and 23 by 5:

17 * 9 = 153

23 * 5 = 115

Now compare the products:

153 > 115

So, the ratio 17:23 is greater than 5:9.

In both methods, the result is the same: 17:23 is greater than 5:9.

The length that separates the lowest 30% of the means from the highest 70% is between 9.74 cm and 10.26 cm

The mean of the sampling distribution of the mean for a sample size of 15 will also be 10 cm (since the population mean is 10 cm). The standard deviation of the sampling distribution will be:

standard deviation = population standard deviation / sqrt(sample size)

standard deviation = 2 cm / sqrt(15)

standard deviation ≈ 0.5164 cm

We want to find the length that separates the lowest 30% of the means from the highest 70%. We can use the z-score formula to find the corresponding z-scores for these percentiles:

z = (x - μ) / σ

For the lowest 30%, we want to find the z-score that corresponds to a cumulative probability of 0.3. Using a standard normal distribution table or calculator, we can find that this is approximately -0.5244.

-0.5244 = (x - 10) / 0.5164

Solving for x, we get:

x = 9.74 cm

Similarly, for the highest 70%, we want to find the z-score that corresponds to a cumulative probability of 0.7, which is approximately 0.5244.

0.5244 = (x - 10) / 0.5164

Solving for x, we get:

x = 10.26 cm

Therefore, the length that separates the lowest 30% of the means from the highest 70% is between 9.74 cm and 10.26 cm, inclusive.

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The inequality representing the maximum depth permitted for a scuba diver is:
d < 11 meters

To find the inequality representing the maximum depth permitted for a scuba diver, we need to set up an inequality with underwater pressure (consisting of atmospheric pressure and hydrostatic pressure).
Underwater pressure is given by the equation:
Underwater Pressure = Atmospheric Pressure + Hydrostatic Pressure
where:
Atmospheric Pressure = 101 kPa
Hydrostatic Pressure = 101 kPa for every 10 meters of depth (101 kPa/10 m = 10.1 kPa/m)
Depth = d meters
Now, we know the maximum underwater pressure for the scuba diver is 220 kPa.

So, we set up the inequality:
220 kPa > 101 kPa + 10.1 kPa/m * d
Now, we need to solve for d:
220 kPa - 101 kPa > 10.1 kPa/m * d
119 kPa > 10.1 kPa/m * d
Now, divide both sides by 10.1 kPa/m:
119 kPa / 10.1 kPa/m > d
11.7821782... > d
Since we are finding the depth, we can round down to the nearest whole number:
11 > d
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Question: Underwater pressure consists of atmospheric pressure, which is 101 kilopascals (kPa), plus 101 kPa of hydrostatic pressure for every 10 meters (m) of depth under water. Which inequality best represents the depth, d, in meters, that is permitted for a scuba diver who is advised not to exceed 220 kPa of underwater pressure?

101+ 101d≤ 220

101+10.1d ≤ 220

101+10.1d> 220

4

101+101d> 220

The height divides the shape into 2 parts : a trapezoid and a right-angled triangle.

A(trapezoid) = [(a+b)h]/2, where a;b;h are the length, width and height respectively.

-> A(trapezoid) = [(15.3+17.4) x 6]/2 = 98.1 (yd2)

A(triangle) = lh/2, where l is the base.

-> A(triangle) = 2.1 x 6 : 2 = 6.3 (yd2)

So, the area of the figure is 98.1 + 6.3 = 104.4 (yd2)

The probability that the other child is a boy given that the shorter child is a boy is approximately 0.56 or 56%.

The problem can be solved using Bayes' theorem, which states that:

P(A|B) = P(B|A) * P(A) / P(B)

where A and B are events, P(A|B) is the conditional probability of event A given event B has occurred, P(B|A) is the conditional probability of event B given event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

Let A be the event that both children are boys, and B be the event that the shorter child is a boy. We are given that P(B|A') = 1/2, since the gender of the taller child is equally likely to be a boy or a girl.

We are also given that P(A') = 3/4, since there are three equally likely possibilities for the gender of the two children: boy-girl, girl-boy, and girl-girl. Finally, we are given that in 89% of families consisting of one son and one daughter the son is taller than the daughter, which means that P(B|A) = 0.89.

Using Bayes' theorem, we can calculate the probability that the other child is a boy given that the shorter child is a boy:

P(A|B) = P(B|A) * P(A) / P(B)

      = 0.89 * (1/4) / [(1/2) * (3/4) + 0.89 * (1/4)]

      ≈ 0.56

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a) The probability that more than 64% of the sampled adults drinks coffee daily is equals to the 0.2574.

b) The probability that the sample proportion of the sampled adults who drink coffee daily is between 0.59 and 0.67 is equals to the 0.2316.

We have a report data of National Coffee Association related to coffee drinking by adults. Sample proportion that adults drink coffee daily, p = 61% = 0.61

1 - p = 1 - 0.61 = 0.39

A random sample of sample size, n

= 250.

Population proportion= Sample proportion, p = 0.61

So, mean for population, μₚ = population proportion = 0.61

Standard deviations for population is σₚ

= √p( 1 - p)/n = √0.61(1 - 0.61)/250

= 0.0308

The sample proportion is approximately normally distributed, p ~ N(0.62,0.03072).

a) The probability that more than 64% of the sampled adults drinks coffee daily is, P( X > 0.64) = P ( (X - μₚ)/σₚ < (0.64 - 0.61)/0.0308 = 0.974

Using the normal distribution table probability value, P (Z >0.974 ) is equals to 0.2574 so, P( X> 0.64) = 0.2574.

b) The probability that the proportion of the sampled adults who drink coffee daily is between 0.59 and 0.67, P ( 0.59 < p < 0.67) = P[(0.59 - 0.61) / 0.0308 < (p - μₚ)/σₚ < (0.67 - 0.61) / 0.0308]

= P(-0.65 < z < 1.94)

= P(z < 1.94) - P(z < -0.65 )

= 0.4738 - 0.2422

= 0.2316

Hence, required probability is 0.2316.

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Complete question:

Coffee: The National Coffee Association reported that 61% of U.S. adults drink coffee daily. A random sample of 250 U.S. adults is selected. Round your answers to at least four decimal places as needed.

a)find the probability that more than 64% of the sampled adults drinks coffee daily

b)Find the probability that the proportion of the sampled adults who drink coffee daily is between 0.59 and 0.67.

The calculated solution for the ratio given as a : b : c is 1/3 : 1/4 : 1/5

From the question, we have the following parameters that can be used in our computation:

1/a : 1/b : 1/c = 3 : 4 : 5

Take the inverse of both sides

So, we have

a : b : c = 1/3 : 1/4 : 1/5

The above means that the solution for a : b : c is 1/3 : 1/4 : 1/5

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The equation of the given circle is expressed as: x² + y² - 24x + 14y + 112 = 0

The standard form of expression for the equation of a circle is expressed as:

(x - h)² + (y - k)² = r²

where:

(h, k) are coordinates of the center of the circle

r is radius

We are given the parameters:

Coordinates of center = (12, -7)

Diameter = 18

Radius = 18/2 = 9

Thus, equation of circle is:

(x - 12)² + (y - (-7))² = 9²

x² - 24x + 144 + y² + 14y + 49 = 81

x² + y² - 24x + 14y + 112 = 0

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According to the Side-Angle-Side Theorem, the triangles JKL and XYZ are congruent because KL XV, JK VZ, and K V.

Congruent triangles are two triangles that have the same size and shape. They have exactly the same angles and sides. Congruent triangles can be used to prove theorems in geometry, such as the side-angle-side (SAS) theorem and the angle-side-angle (ASA) theorem. Congruence can also be used to find the unknown side length of a triangle when two sides and an angle are known.

How to demonstrate the congruence of two triangles
This is a congruency issue in which we must demonstrate the congruence of two triangles. If two triangles have the same sides in the same order, they are said to be congruent. According to the figure, we discover the following presumptions:

KL XV, JK XV, and K XV

According to the Side-Angle-Side Theorem, which is satisfied by these presumptions, the triangles JKL and XYZ.

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yes both triangles BDC and PNO are congruent by AAS congruency.

Congruent triangles are two triangles that have the same size and shape. They have exactly the same angles and sides. Congruent triangles can be used to prove theorems in geometry, such as the side-angle-side (SAS) theorem and the angle-side-angle (ASA) theorem and the angle-angle-side Congruence can also be used to find the unknown side length of a triangle when two sides and an angle are known.

to demonstrate the AAS congruency of two triangles

for two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in another triangle, then the triangles are congruent.

in triangles BDC and PNO

given that

BD=PN

∠CBD=∠OPN

∠BCD=∠PON

According to the Angle -side -Angle  Theorem, which is satisfied by these presumptions, the triangles BDC and PNO

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Answer:

Ella and her mother bought 8 bananas.

Step-by-step explanation:

There are 16 ounces in 1 pound, so 3 pounds is equal to 3 x 16 = 48 ounces.

If each banana weighs 6 ounces, then they bought 48/6 = 8 bananas.

Answer:

8 Bananas

Step-by-step explanation:

Well for starters we know that 1 pound = 16 ounces, and Ella's mother bought 3 pounds of bananas which is equal to 48 ounces. If each Banana is 6 ounces we simply use the equation of 48/6 = x, and with simple maths we can find that x = 8

9t + 4t can be simplified by combining the like terms (terms with the same variable and exponent). The coefficients of the two terms (9 and 4) are added to get the coefficient of the simplified term:

9t + 4t = (9 + 4)t = 13t

Therefore, the expression that is equivalent to 9t + 4t is 13t.

The odds ratio was for each factor in the table are 2.32, 6.67, 1.64, 1.33, 2.43, 2.33, 1.75 and 8.33 respectively, and the factor with the highest odds ratio is "Pausing at steam iron in hall 4," suggesting that it is the most likely responsible for the outbreak.

To calculate the odds ratio, we need to divide the number of cases with a specific factor by the number of controls with that same factor and then divide that result by the number of cases without that factor divided by the number of controls without that factor. For example, to calculate the odds ratio for pausing at the whirlpool spa in hall 3, we would do:

Odds ratio = (41/101)/(21/119) = 2.32

Using the same formula for the other factors, we get:

Underlying disease: 6.67

A smoker: 1.64

Total hours at exhibition: 1.33

Pausing at bubblemat in hall 3: 2.43

Pausing at electric kettle in hall 3: 2.33

Pausing at whirlpool in hall 4: 1.75

Pausing at steam iron in hall 4: 8.33

Based on these odds ratios, the factor most likely responsible for the outbreak is pausing at the steam iron in hall 4, as it has the highest odds ratio of all the factors considered.

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--The given question is incomplete, the complete question is given

" To measure potential visitor exposure to possible sources of Legionella, a questionnaire and a map of the site was sent to a randomized group of 220 people who had visited the exhibition. A respondent was categorized as a case (n=101) if they had symptoms of a respiratory infection within 20 days of their visit to the exhibition.

Study Population

Cases (n=101)

Controls (n=119)

Male

63

45

Underlying disease

11

2

A smoker

42

31

Total hours at exhibition

4

3

Pausing at whirlpool spa in hall 3

41

21

Pausing at bubblemat in hall 3

37

17

Pausing at electric kettle in hall 3

26

12

Pausing at whirlpool in hall 4

31

20

Pausing at steam iron in hall 4

16

3

Calculate the Odds Ratio for each of the factors considered in Table 2. (You must do this calculation for each factor, but you only need to provide an example calculation for one of them.)

If a larger odds ratio indicates a higher probability that a given factor is the causative mechanism for disease transfer (e.g., the source) which of the last five factors is most likely responsible for the outbreak? "--

the time required for an investment of $5000 to grow to $[tex]7200[/tex] at an interest rate of  [tex]7.5[/tex] percent per year, compounded quarterly, is approximately  [tex]3.79[/tex] years.

o find the time required for an investment of $5000 to grow to $7200 at an interest rate of 7.5 percent per year, compounded quarterly, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

where:

A = the final amount (in this case, $7200)

P = the principal amount (in this case, $5000)

r = the annual interest rate (in decimal form, so 7.5% = 0.075)

n = the number of times the interest is compounded per year (in this case, quarterly, so n = 4)

t = the number of years (which we need to find)

Plugging in the values, we get:

[tex]7200 = 5000(1 + 0.075/4)^(4t)[/tex]

Now we can solve for t by isolating it on one side of the equation.

Dividing both sides by 5000:

Taking the natural logarithm of both sides:

[tex]ln(7200/5000) = ln((1 + 0.075/4)^(4t))[/tex]

Using the property of logarithms that ln(a^b) = b * ln(a):

[tex]ln(7200/5000) = 4t\times ln(1 + 0.075/4)[/tex]

Dividing both sides by [tex]4 \times ln(1 + 0.075/4):[/tex]

[tex]t = ln(7200/5000) / (4 * ln(1 + 0.075/4))[/tex]

Using a calculator, we can find the value of t to be approximately 3.79 years (rounded to two decimal places).

Therefore, the time required for an investment of $5000 to grow to $7200 at an interest rate of 7.5 percent per year, compounded quarterly, is approximately 3.79 years.

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Therefore, the answer is 225 cents.

When an international calling plan charges 45 cents per minute or fraction of a minute for each call, the cost for making a 5-minute call is 225 cents.What is an international calling plan?

An international calling plan is a type of phone plan that allows people to make calls to other countries at lower rates than they would normally be charged. The cost of a call will vary depending on the country and the duration of the call. The per-minute rate may be used to calculate the cost of making an international call when an international calling plan charges 45 cents per minute or fraction of a minute for each call.

If a 5-minute call is made under the given circumstances, the cost of the call will be[tex] 5 x 45 = 225 [/tex]cents.

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This leads to the incorrect conclusion that the food is safe for consumption when it is actually not.

A food inspector's job is to inspect samples of food products to determine if they are safe for consumption. In this context, we can consider this process as a hypothesis test with the following hypotheses:

Null hypothesis (H0): The food is safe.
Alternative hypothesis (H1): The food is not safe.

The statement given - "The sample suggests that the food is safe, but it actually is not safe" - describes a situation where the food inspector incorrectly concludes that the food is safe when it is not. This is an example of an error in hypothesis testing.

There are two types of errors in hypothesis testing: Type I and Type II.

Type I error occurs when the null hypothesis is rejected when it is actually true. In other words, a Type I error leads to the false conclusion that the food is not safe when it actually is safe.

Type II error occurs when the null hypothesis is not rejected when it is actually false. In this case, a Type II error results in the false conclusion that the food is safe when it actually is not safe.

Given the statement, "The sample suggests that the food is safe, but it actually is not safe," we can determine that this is an example of a Type II error. The food inspector failed to reject the null hypothesis (that the food is safe) when it was, in fact, false.

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The car did not travel at a constant speed during the entire trip. Option d is the correct choice.

Option d is the correct answer. The graph shows that the car's velocity is not constant during the trip, indicating that the car did not travel at a constant speed. The car changes its velocity multiple times, which means it either speeds up, slows down or changes direction. Therefore, the car did not travel at a constant speed during the entire trip.

Option a is incorrect because the graph doesn't provide any information about the total time of the trip. Option b is incorrect because the graph clearly shows that the car slows down multiple times during the trip. Option c is also incorrect because the graph doesn't indicate that the car returned to its starting point.

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--The complete question is, The driver of a car completes a trip. the graph displays data about the car's motion during the trip. which of the following statements about the car's motion is true?

a. the total time for the car trip was 50 minutes.

b. the car did not slow down during the trip.

c. the car returned to where it had started the trip at the end of the trip.

d. the car did not travel at a constant speed during the entire trip.--

The frequency table and the probability distribution table have been matched correctly.

The frequency table consists of the number of occurrences of each value of the random variable x.

The probability distribution table consists of the probability of occurrence of each value of the random variable x.

The probability distribution table shows the probability of each value of the random variable x. The value of x can either be 0, 1, 2, 3, or 4. The respective probabilities of each value are 0.1, 0.12, 0.32, 0.16, and 0.6.

The frequency table shows the number of occurrences of each value of the random variable x. The value of x can either be 0, 1, 2, 3, or 4. The respective frequencies of each value are 5, 10, 15, 5, and 15.  

The total of the frequencies in the frequency table is equal to the total of the probabilities in the probability distribution table.

The frequency of each value of the random variable x is equal to the product of the probability of that value and the total number of occurrences in the frequency table.

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226 integers are present between 100 and 999, inclusive, and have the property that some permutation of its digits is a multiple of 11 between 100 and 999. Hence, option A is the correct option.

The problem statement is to find the number of multiples of 11 between 100 and 999 inclusive, where some multiples may have digits repeated twice and some may not.

To solve this problem, we can first count the number of multiples of 11 between 100 and 999 inclusive, which is 81. Some of these multiples may have digits repeated twice, and each of these can be arranged in 3 permutations. Other multiples of 11 have no repeated digits, and each of these can be arranged in 6 permutations. However, we must account for the fact that switching the hundreds and units digits of these multiples also yields a multiple of 11, so we must divide by 2, giving us 3 permutations for each of these multiples.

Thus, we have a total of 81 × 3 = 243 permutations. However, we have overcounted because some multiples of 11 have 0 as a digit. Since 0 cannot be the digit of the hundreds place, we must subtract a permutation for each of these multiples. There are 9 such multiples (110, 220, 330, ..., 990), yielding 9 extra permutations. Additionally, there are 8 multiples (209, 308, 407, ..., 902) that also have 0 as a digit, yielding 8 more permutations.

Therefore, we must subtract these 17 extra permutations from the total of 243, giving us 226 permutations in total. Hence, option A is the correct option.

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Step-by-step explanation:

Yes they are congruent via the S-S-S  triangle theorem.

  triangles are congruent if they have three equal sides ( Side-Side-Side)

the correct answers are:=4, 11, 8, 12, 1, 6, 14 and 14, 10, 6, 9, 11, 8, 1 for the given data

How to solve the data

The box plot represents the distribution of a dataset using quartiles, median, and outliers. In order to create a box plot, we need to have a dataset with numerical values. Based on the options given, the data sets that can be used to create the box plot are:

4, 11, 8, 12, 1, 6, 14: This data set has all the required numerical values to create a box plot. It contains 7 values which are within the range of values shown on the x-axis of the box plot.

14, 10, 6, 9, 11, 8, 1: This data set also contains all the required numerical values to create a box plot. It has 7 values which are within the range of values shown on the x-axis of the box plot.

The remaining data sets listed are either non-numerical or do not contain values within the range shown on the x-axis. Therefore, they cannot be used to create the box plot.

In summary, the correct answers are:

4, 11, 8, 12, 1, 6, 14

14, 10, 6, 9, 11, 8, 1

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The required measures of the acute angles in the given right triangle with side lengths 9, 12, and 15 is equal to 36.87 degrees and 53.13 degrees approximately.

Right triangle with side lengths of 9, 12 and 15.

Check whether Pythagorean theorem holds true,

which states that the sum of the squares of the two shorter sides equals the square of the hypotenuse.

9^2 + 12^2 = 15^2

Simplifying this equation, we get,

⇒81 + 144 = 225

⇒225 = 225

This implies,

Pythagorean theorem holds for this triangle,

And by the converse of the Pythagorean theorem,

Triangle is a right triangle with the right angle opposite the side with length 15.

The acute angles of a right triangle are complementary.

Which means that their sum is 90 degrees.

Calculate the measures of the acute angles in this triangle,

Use trigonometric functions.

Use the sine function to find one of the acute angles,

sin(θ) = opposite/hypotenuse

         = 9/15

         = 0.6

Taking the inverse sine function of both sides, we get,

θ = sin^(-1)(0.6)

⇒ θ ≈ 36.87 degrees.

Sum of the acute angles is 90 degrees, the other acute angle is equals to,

90 - 36.87 = 53.13 degrees.

Therefore, the measures of the acute angles of the triangle are approximately 36.87 degrees and 53.13 degrees.

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