use average rates of change to generate a liner function model.

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer: 6

Step-by-step explanation:

set up a box plot.

To find the interquartile range: 3rd tile value subtracted by the first tile value. Basically: Q3-Q1=IQR

Q= Quartile

3 and 1 is the number

IQR = interquartile range

if you do incorrectly you should get 6 if not add me as a friend and I’ll show you and explain it better!

Answer:

D=2, 3, 5, 6, 7, 8, 9,

Step-by-step explanation:

btw can i js get 1  brainly?

{2,3,5,6,7,8,9}

The union of two sets A and B is defined as the set of all the elements that lie in set A and set B or both the elements in A and B altogether.

$1356.52 is the cost price of the article.

To find the cost price of the article, we can utilize the concept of calculating the original amount based on a percentage increase.

Let's assume the cost price of the article is "x" dollars.

The trader gained a 15% interest, which means the selling price is 115% of the cost price. In other words, the selling price is 115% of "x".

To calculate the selling price, we can set up the following equation:

115% of x = 1560

To convert the percentage to a decimal, we divide it by 100:

1.15 * x = 1560

Now we can solve for x by dividing both sides of the equation by 1.15:

x = 1560 / 1.15

Using a calculator, we find:

x ≈ 1356.52

Therefore, the approximate cost price of the article is $1356.52.

This means that the trader purchased the article for around $1356.52 and then sold it for $1560.00, resulting in a 15% gain.

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The volumes of the figures are

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

V = 22/7 * (32/2)² * 14

Evaluate

Volume = 11264

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

(2r)² = 40² - 32²

(2r)² = 576

So, we have

r = 12

So, we have

V = 22/7 * (12)² * 32

Evaluate

Volume = 14482.28

The rectangular prism

The volume is calculated as

V = lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 8 * 12 * 39

Evaluate

Volume = 3744

The triangular prism

The volume is calculated as

V = 1/2lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 1/2 * 11 * 5.4 * 16

Evaluate

Volume = 475.2

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * (33/2)³

Evaluate

Volume = 18824.14

The sphere

The volume of a sphere is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * 2.8³

Evaluate

Volume = 91.99

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To calculate the area of her rectangular quilt, Mrs. Kuhn needs to multiply the length and width of the quilt in inches. Since each quilt square is 4 inches long, the calculation for the area of the quilt is:

Area of quilt = Length of quilt x Width of quilt x (4 inches) ^2

Therefore, the correct calculation for Mrs. Kuhn to determine the area of her quilt is the product of 4 inches times the sum of the length and width of the quilt.

Answer:

Capital expenditures are typically one-time large purchases of fixed assets that will be used for revenue generation over a longer period. Revenue expenditures are the ongoing operating expenses, which are short-term expenses used to run the daily business operations.

The Eric's time can be represented by the equation t = (d/60) - 2.

To create a second equation showing how long it would take Eric to travel the same distance as Noah, we can use the formula distance = speed x time. Let's call the distance that both Noah and Eric travel "d" (since we don't know the actual distance).

We know that Noah's speed is 135 mph and Eric's speed is 60 mph. We also know that Eric takes two hours longer to travel the same distance as Noah.

So, if we let "t" be the time it takes Noah to travel "d" distance, then Eric's time can be represented as "t + 2" hours. Putting all of this together, we can create the following equation: d = 135t (for Noah) and d = 60(t + 2) (for Eric).

From this second equation, we can solve for Eric's time by dividing both sides by 60, which gives us t + 2 = d/60.

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The term (x - 1) is a factor of both of the given polynomials as;

x² + x - 2

2x² - 5x + 3

Given that (x - a) is a factor of a polynomial p(x), then x = a is a zero of the polynomial, which means that:

p(a) =0.

When x - 1 is a factor of any of the given polynomials, then we need to evaluate them in x = 1 and check if we get zero.

a) x² + x - 2

Evaluate it in x = 1;

1² + 1 - 2 = 0

so (x - 1) is a factor.

b) 2x² - 5x + 3

Evaluating this in x = 1;

2*1² - 5*1 + 3

2 - 5 + 3 = 0

(x - 1) is a factor.

Therefore, the correct option is the last one, it is a factor of both polynomials.

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Answer:

1 is a

2 is c

3 is b

Step-by-step explanation:

The surface area of a three dimensional shape is the total area of all of the faces. To find the surface area of a shape, we find the area of each face and add them together. E.g. The measurements here are in centimetres so the surface area is measured in square centimetres ( c m 2 ) (cm^2) (cm2)

triangle-

Base Surface Area = 112

= 121 feet2

Lateral Surface Area =

2×11× √

( 11 )2 + 72

2

= 195.84943196241 feet2

Total Surface Area = 316.84943196241 feet2

bottom bit-

Surface Area = 2×(15×5 + 15×8 + 5×8) = 470 feet2

12.1 Alternative Hypothesis, 12.2 The level of significance will typically be set at α = 0.05 (5%), 12.3 In terms of tails, we will perform a two-tailed test. 12.4 The rejection region is determined by the critical values corresponding to the significance level α. In a two-tailed test,

To test if there is a significant difference between the survey results and the director's claim, we will perform a hypothesis test using a one-sample proportion test.

12.1 Alternative Hypothesis: The alternative hypothesis would be that the proportion of the workforce supporting the new shift pattern is not equal to 90%. We can express this as H1: p ≠ 0.9.

12.2 The level of significance for testing the difference between the director's claim and the survey results will typically be set at α = 0.05 (5%).

12.3 In terms of tails, we will perform a two-tailed test. This is because we are testing if the proportion is significantly different from the claimed value (90%), which could be either higher or lower.

12.4 The rejection region is determined by the critical values corresponding to the significance level α. In a two-tailed test, we divide α equally between the two tails. So, the rejection region will be split into two parts, one in the left tail and one in the right tail.

12.5 The rejection region is determined by the critical values. In this case, the critical values will be based on the standard normal distribution and the significance level α. The values that indicate the rejection region are the critical values of the standard normal distribution associated with α/2 (in each tail) based on the sample size.

12.6 Let's calculate the test statistic. The sample proportion in favor of the new shift pattern is 85/100 = 0.85. The expected proportion under the null hypothesis is 0.9. The standard error can be calculated using the formula: SE = sqrt(p * (1-p) / n), where p is the expected proportion and n is the sample size. Plugging in the values, we have SE = sqrt(0.9 * 0.1 / 100) ≈ 0.03. The test statistic can be calculated as (sample proportion - expected proportion) / SE, which gives (0.85 - 0.9) / 0.03 ≈ -1.67.

12.7 Referring to the rejection region and the test statistic, if the test statistic falls within the rejection region (i.e., if it is beyond the critical values), we will reject the null hypothesis. If the test statistic is not in the rejection region, we will fail to reject the null hypothesis.

12.8 Based on the calculated test statistic of -1.67 and the critical values associated with α/2, we would compare the test statistic with the critical values to determine if it falls within the rejection region. If it does, we would reject the null hypothesis and conclude that there is a significant difference between the survey results and the director's claim.

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The null hypothesis is given as follows:

[tex]H_0: \mu = 175[/tex]

The alternative hypothesis is given as follows:

[tex]H_1: \mu \neq 175[/tex]

The claim in the context of this problem is given as follows:

"The mean weight of male aerobics instructors in a certain city is equal to 175 lbs".

At the null hypothesis, we test if there is not enough evidence to verify if the claim is false, that is:

[tex]H_0: \mu = 175[/tex]

At the alternative hypothesis, we test if there is enough evidence to verify if the claim is false, that is:

[tex]H_1: \mu \neq 175[/tex]

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Answer:

Yes, (s + t)^2 is equivalent to s^2 + 2st + t^2. This can be shown through the process of expanding the expression (s + t)^2 using the FOIL method (multiplying first, outer, inner, and last terms).

First, we can rewrite (s + t)^2 as (s + t)(s + t).

Now, we do the multiplication and combine like terms:

s*s + s*t + t*s + t*t

s^2 + st + st + t^2

s^2 + 2st + t^2

The number that belongs in the green box is 45.65

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

The triangle

If the number that belongs in the green box is x, then we have

6.78/sin(29) = 10/sin(x)

Take the inverse of both sides

sin(29)/6.78 = sin(x)/10

This gives

sin(x) = 10 * sin(29)/6.78

Evaluate

sin(x) = 0.7151

Take the arc sin of both sides

x = 45.65

Hence, the number that belongs in the green box is 45.65

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Answer:

17.7 degree

Step-by-step explanation:

We can begin by drawing a diagram:

```

C

/|

/ |

/α | 10.5 mi```

A------β------B

\ /

\ /

\/

8.8 mi

```

We can label angles β and α as shown, where β represents the angle from point C to point B and α```

A ------- 9.2 mi -------- B

```

Let's label some angles in the diagram:

- Angle A: the angle between the line from A to C and the line from A to B

- Angle B: the angle between the line from C to A and the line from C to B

- Angle α: the angle at the buoy C

We want to find the measure of angle α. To do that, we can use the law of cosines to find the length of the side opposite angle α:

```

c^2 = a^2 + b^2 - 2ab cos(C)

```

where a = 8.8, b = 10.5, and C = angle B. We can solve for cos(C):

```

cos(C) = (a^2 + b^2 - c^2) / 2ab

```

Since we know a, b, and c (8.8, 10.5, and 9.2 respectively), we can calculate cos(C):

```

cos(C) = (8.8^2 + 10.5^2 - 9.2^2) / (2 * 8.8 * 10.5) ≈ 0.701

```

Now we can find angle B using the inverse cosine function:

```

B = cos^-1(cos(C)) ≈ 45.4°

```

Finally, we can find angle α by subtracting angle A from angle B:

```

α = B - A ≈ 17.7°

```

So the measure of the turn that the ship has to make at the buoy is approximately 17.7 degrees.

The length of the side AB of the given triangle is 210.5cm.

Let us assume that AB = BC, then we can use the Sine Rule to find the length of AB.

Sine Rule states that:

[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{SinC}[/tex]

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.

In this case, we have:

a = BC = c

b = AC = 44

c = AB = x

B = 12°

A + B + C = 180 (sum of angles in a triangle)

but b = c, therefore angle A = angle C

A + 12 + C = 180°

2C + 12 = 180°

C = (180 - 12)/2

C = 84°

Using the Sine rule,

b/SinB = c/SinC

44/Sin 12° = x/Sin 84°

x = (44 Sin 84°)/Sin12

x = (44)(0.9945)/0.2079

x = 43.754/0.2079

x = 210.476

Therefore the side AB = 210.5cm

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Answer:

5376

Step-by-step explanation:

volume of prism = 8 X 6 X 14 = 672.

volume of cube = 1/2 X 1/2 X 1/2 = 1/8.

672 / (1/8)

= 672 X (8/1)

= 5376.

5376 cubes will fit into it

Answer:

The answer is 49

Step-by-step explanation:

We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.

We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:

14/42 = 0.3333

We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:

0.3333 * 147 = 49

Therefore, the best estimate for the number of dogs that suffer from the disease is 49.

The standard deviation of the response time is 1.53 minutes.

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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The value of the length x is 1.5

Using the sine trigonometric identity, we have that;

sin 45 = y/6√2

cross multiply the values, we have that;

y = 1/√2 × 6/√2

Multiply the values, we get;

y = 6/2

Divide the values

y = 3

Then, using the cosine identity, we get;

cos 60 = x/3

Find the cosine value and cross multiply, we get;

x = 0.5(3)

Now, multiply the values, we get;

x = 1.5

Hence, the value of the length is 1.5

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An equation that can be used to find the value of x include the following: 110° + 7x = 180°.

In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are supplementary angles:

110 + 7x = 180°

7x = 180° - 110°

7x = 70°

x = 70°/7

x = 10°

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

5 burgers and 7 milkshakes

Step-by-step explanation:

1.5x5=7.5

2x7=14

7.5+14=21.5

The probability that Jannette in Mr. Alsup's sixth-period English class has not chosen a topic for her writing assignment is approximately c.12%. Therefore, option c.12%.  is correct.

To find the probability that Jannette in Mr. Alsup's sixth-period English class has not chosen a topic for her writing assignment, we need to calculate the proportion of students in that class who have not chosen a topic.

From the table, we can see that in the sixth period, there are a total of 25 students. Out of those, 22 students have chosen a topic, and 3 students have not chosen a topic.

The probability can be calculated by dividing the number of students who have not chosen a topic (3) by the total number of students in the sixth period (25), and then multiplying by 100 to get the percentage:

Probability = (Number of students who have not chosen a topic / Total number of students in the sixth period) × 100

Probability = (3 / 25) × 100

Probability ≈ 12%

Therefore, the probability that Jannette in Mr. Alsup's sixth-period English class has not chosen a topic for her writing assignment is approximately 12%.

The correct answer is c- 12%.

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The appropriate measure of variability for this data is the IQR, and its value is 250.

We have,

The range is not the best measure of variability for this data since it only takes into account the maximum and minimum values and does not consider the other values in the dataset.

The IQR (interquartile range) is a better measure of variability since it gives a measure of the spread of the middle 50% of the data.

To find the IQR, we first need to find the median:

Arranging the data in order, we get:

200, 450, 600, 650, 700, 800

The median is the middle value, which is 650.

The first quartile (Q1) is the median of the lower half of the data:

Q1 = median(200, 450, 600) = 450

The third quartile (Q3) is the median of the upper half of the data:

Q3 = median(700, 800, 650) = 700

The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

= 700 - 450

= 250

Therefore,

The appropriate measure of variability for this data is the IQR, and its value is 250.

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Part A: The table that displays a complete list of possible outcomes would be = Table B, that is option B.

Part B: The probability that the chosen events will take place = 0.3.

To calculate the probability of the given event the formula that should be used is given below. That is;

Probability = possible outcome/sample space

The total number of blues balls = 1

The total number of red balls = 2

The total number of yellow balls = 2

The total number of balls = 5, while total number of colour = 3

For part A: the possible sample outcomes = (H,B), (HR), (HY), (TB), (TR), (TY).

For part B:

Using the formula the possible outcome = 2

Sample space = 7

Probability = 2/7 = 0.3

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