The volume of Box A is 2/5
the volume of Box B. What is the height of Box A
if it has a base area of 32 square centimeters?
Box A
32 cm
Box B
10 cm
8cm
16 cm

In this case, both triangles have a side length of 5 units and a side length of 7 units, and they share an angle of 117 degrees. Therefore, they satisfy the ASA criterion, and we can conclude that they are congruent.

Congruent is a mathematical term used to describe two figures or shapes that have the same size and shape. In other words, two figures are congruent if they have exactly the same dimensions and the same angles. When two figures are congruent, they can be superimposed on each other without any overlap or gap between them. Congruent figures are often denoted by the symbol ≅. For example, if two triangles have the same size and shape, we can write them as ∆ABC ≅ ∆DEF, which means that triangle ABC is congruent to triangle DEF. Congruent figures play an important role in geometry and other branches of mathematics.

Yes, the two triangles are congruent.

In Euclidean geometry, if two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles are congruent. This is known as the angle-side-angle (ASA) congruence criterion.

In this case, both triangles have a side length of 5 units and a side length of 7 units, and they share an angle of 117 degrees. Therefore, they satisfy the ASA criterion, and we can conclude that they are congruent.

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The relative frequency of the given students surveyed and prefer to go to Cook Middle School and Energy Flow is equal to 0.4 or 40%.

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow

= (Number of students go to Cook Middle School and prefer Energy Flow) /( total number of students surveyed)

From the given table,

The number of students who go to Cook Middle School and prefer Energy Flow is  equal to 20.

The total number of students surveyed is equal to 50.

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow is,

= 20/50

= 0.4

Therefore, the relative frequency of all students surveyed going to the Cook Middle School and prefer Energy Flow is equal to 0.4 or 40%.

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The above question is incomplete, the complete question is :

Some students at Cook Middle School and Elm Middle School participated in a survey. They were asked which sports drink they prefer: Gym Juice or Energy Flow. The two-way table shows the results.

                       Gym Juice        Energy Flow   Total

Cook                   15                     20                    35

Elm                       5                     10                     15

Total                    20                     30                     50

What is the relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow?

For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.

We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%

The percentage of students win a jump rope = 16%

The percentage of students win a t-shirt

= 6%

The winning amount for stuffed toy game = $ 3.60

The winning amount for jump rope game = $1.20

The winning amount for t-shirt game

= $7.90

The remaining students do not win a prize. Now, total number of students play the game at the booth = 150

So, number of students who win stuffed toy = 22% of 150 = 33

Number of students who win jump rope = 16% of 150 = 24

Number of students who win stuffed toy

= 6% of 150 = 9

For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6

= 218.7

Hence required value is $218.70.

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Answer:

y=4x+5

Step-by-step explanation:

y=mx+b

m=4

b=5

The process time of the system is 32 min/unit.

Here are the given expressions and their respective variables and coefficients:

12s + 4t | Variables: s, t | Coefficients: 12, 4

46rs + 10x | Variables: r, s, x | Coefficients: 46, 10

12q + 14x | Variables: q, x | Coefficients: 12, 14

10x + 10y | Variables: x, y | Coefficients: 10, 10

17rs + 32x | Variables: r, s, x | Coefficients: 17, 32

5x + 7y - 12z | Variables: x, y, z | Coefficients: 5, 7, -12

36ab + 70m | Variables: a, b, m | Coefficients: 36, 70

3r + 19a + 10m | Variables: r, a, m | Coefficients: 3, 19, 10

7k + 16m | Variables: k, m | Coefficients: 7, 16

8r + 5s | Variables: r, s | Coefficients: 8, 5

9h + 120m | Variables: h, m | Coefficients: 9, 120

12k + m | Variables: k, m | Coefficients: 12, 1

7g + 15h + w | Variables: g, h, w | Coefficients: 7, 15, 1

4c - 8d + 12f | Variables: c, d, f | Coefficients: 4, -8, 12

6t + 17r - 35j | Variables: t, r, j | Coefficients: 6, 17, -35

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Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.

The total cost of renting a small car with insurance is:

$465 = $25x + $21x

Simplifying and solving for x, we get:

$465 = $46x

x = 10.11

Since they can't rent for a fraction of a day, the maximum number of days they can rent the small car with insurance is 10 days.

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The triangle is given as equilateral and the length of the perpendicular of the given equilateral triangle is 13.85.

It states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, the longest side of the triangle. This theorem can be used to determine the length of the sides of a right triangle if two sides are known.

The triangle is given as equilateral. As we know he perpendicular in a equilateral triangle divides a line into to equal parts, so

Base= 8+8

= 16

As it is a equilateral triangle, all the sides will be equal.

Now, we can use the Pythagorean theorem to find the length of the perpendicular, which can be found by using the formula:

16²= 8² + x²

x² = 16²- 8²

x = √192

x = 13.85

Thus, the length of the perpendicular of the given equilateral triangle is 13.85.

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In a standard additions method workup the information from the linear regression that is most closely related to the unknown concentration is this:  the intercept of the linear regression line.

In the standard additions method workup, the information that is most closely related to the unknown concentration is the intercept of the linear regression line.

The reason why this is the case is that the intercept represents the y-value of the regression line where the line crosses the y-axis. This y-axis is the value of the dependent variable when the independent variable or concentration is zero. So, by solving for the intercept, we can determine the concentration of the unknown sample.

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The goal of the data analysis stage is to figure out how information is currently flowing and why it isn't flowing properly. The statement is True.

The basic purpose of data analysis is to obtain meaningful insights and information from data by examining it. While knowing how information progresses is an important part of this process, the ultimate goal is to get a better knowledge of the data itself, as well as any patterns or correlations that may exist within it.

The process of troubleshooting and problem-solving is more directly tied to determining why information is not flowing properly. This may entail examining the data to discover any abnormalities, mistakes, or inconsistencies that may be interfering with information flow. Once these concerns have been recognized, efforts may be made to fix them and enhance information flow.

Therefore, the statement is true, the goal of the data analysis stage is to figure out how information is currently flowing and why it isn't flowing properly.

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TRUE. In the data analysis step, the focus is on examining and evaluating data to identify patterns, trends, and insights. The goal is to pinpoint any issues or inefficiencies in the way information flows and to determine the root cause of these problems.

By analyzing the data, organizations can gain a better understanding of their processes and identify areas for improvement.
 In the data analysis step, the goal is to examine and understand the current flow of information. This involves analyzing the data to identify patterns, trends, and any potential issues. By pinpointing the reasons why the information is not flowing properly, you can then work towards implementing solutions to improve the efficiency and effectiveness of the data management process.

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The Area of square is 64 square unit.

We have the coordinates (-3, -3) and (5, -3).

Using distance formula

d = √ (5 + 3)² + (-3 + 3)²

d= √8² + 0

d= 8 units

So, the Area of square

= d x d

= 8 x 8

= 64 square unit

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The explanation of how to convert a general form equation to a standard form equation is given below:

Let's first look at how to convert a general form equation to a standard form equation. Given a general form equation:

x^2 + y^2 + Dx + Ey + F = 0

Complete the square for both x and y:

a. Divide the coefficients D and E by 2, and square the results. Let's call these values Cx and Cy:

Cx = (D/2)^2

Cy = (E/2)^2

b. Add and subtract Cx and Cy on both sides of the equation:

x^2 + Dx + Cx + y^2 + Ey + Cy = -F + Cx + Cy

Rearrange the equation to form the standard form equation:

a. Group the x and y terms and rewrite as perfect squares:

(x + D/2)^2 + (y + E/2)^2 = -F + Cx + Cy

b. Now, compare this to the standard form equation:

(x - h)^2 + (y - k)^2 = r^2

c. Identify the values of h, k, and r:

h = -D/2

k = -E/2

r^2 = -F + Cx + Cy

Now let's see how to convert a standard form equation to a general form equation. Given a standard form equation:

(x - h)^2 + (y - k)^2 = r^2

Expand the squares:

(x^2 - 2hx + h^2) + (y^2 - 2ky + k^2) = r^2

Rearrange the equation to form the general form equation:

x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0

Compare this to the general form equation:

x^2 + y^2 + Dx + Ey + F = 0

Identify the values of D, E, and F:

D = -2h

E = -2k

F = h^2 + k^2 - r^2

Now you can convert equations between the general form and the standard form. If you're missing some variables in the general form equation, just treat them as zero and proceed with the same steps.

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Therefore, the volume of the rectangular prism is 87.5 cubic yards.

A prism is a transparent object, usually made of glass or plastic, that refracts or bends light as it passes through it. It has at least two flat surfaces, called faces, that are usually parallel and rectangular in shape, and two non-parallel faces, called bases, which are usually triangular in shape. When light enters a prism, it is refracted, or bent, as it passes through the prism and is separated into its component colors, creating a rainbow effect. Prisms are often used in optics and science experiments to study the properties of light, such as its wavelength and polarization. They are also commonly used in optical instruments such as binoculars, telescopes, and cameras to help focus and direct light.

The volume V of a rectangular prism is given by the formula:

V = length x width x height

In this case, the length is 5 yards, the width is also 5 yards, and the height is 3- and one-half yard.

To calculate the volume, we can plug this value into the formula:

V = 5 yards x 5 yards x 3.5 yards

Simplifying this expression, we get:

V = 87.5 cubic yards

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Answer:

The volume of a rectangular prism is the product of its length, width, and height. In this case, the length is 5 yards, the width is 5 yards, and the height is 3.5 yards. Therefore, the volume of the prism is 5 * 5 * 3.5 = 87.5 cubic yards.

Here is the calculation:

Volume = length * width * height

= 5 yards * 5 yards * 3.5 yards

= 87.5 cubic yards

Step-by-step explanation:

Number of red counters in the original bag is 3, and the number of green counters is 7.

Let's use algebra to solve the problem. Let U be the number of red counters and G be the number of green counters originally in the bag.

From the first part of the problem, we know that

Probability (selecting a green counter) = G / (U + G) = 3/7

Solving for U in terms of G, we get

U = (7G - 3G) / 3 = 4G/3

So we know that there were 4G/3 red counters and G green counters in the bag originally. But since the number of counters must be a whole number, we can assume that there were 4R red counters and 3G green counters originally, where R and G are both integers and R + G is the total number of counters.

After adding 2 red and 3 green counters, the number of counters in the bag is now R + 2 + G + 3 = R + G + 5.

From the second part of the problem, we know that

P(selecting a green counter) = (G + 3) / (R + G + 5) = 6/13

Solving for R in terms of G, we get

R = (13G - 9G - 15) / 7 = 4G/7 - 15/7

Since R must be an integer, we can try different values of G to see if R is an integer. For example, if G = 7, then R = 3 and the total number of counters is 10.

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The given question is incomplete, the complete question is:

There are only U red counters and G green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7. The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13. Find the number of red counters and the number of green counters that were in the bag originally

The base, lateral area and surface area is B = 96 cm², L = 499.2 cm²,S = 691.2 cm²

The lateral area for the triangular prism is the sum of all three areas. Thus, the formula for lateral area of triangular prism, Lateral surface area of triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h.

To find the lateral area (L) of this solid, we need to calculate the area of the four rectangles that make up the sides of the solid. Since each rectangle has a height of 10.4 cm and a width of 12 cm, the area of one rectangle is:

A = 10.4 cm * 12 cm = 124.8 cm²

Since there are four rectangles, the total lateral area is:

L = 4 * A = 4 * 124.8 cm² = 499.2 cm²

To find the surface area (S) of the solid, we need to add the lateral area to the area of the two circular bases. The base area is given as 96 cm², so the area of both bases is:

A = 2 * 96 cm² = 192 cm²

Therefore, the total surface area is:

S = L + A = 499.2 cm² + 192 cm² = 691.2 cm²

Rounding to the nearest tenth, we have:

B = 96 cm²

L = 499.2 cm²

S = 691.2 cm²

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Answer:  p(θ|x) dθ = 1 − α.

Step-by-step explanation: the critical value is computed based on the given significance level α and the type of probability distribution of the idealized model

Three trigonometric ratios are Sin C=21/29,Cos C=20/29, Tan C=21/20.

Trigonometric ratios, also known as trigonometric functions, are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:

In the given triangle;

AB=21

BC=20

AC=29

Calculating trigonometric ratios;

Sin C=Perpendicular/Hypotenuse

=AB/AC

=21/29

Cos C=Base/Hypotenuse

=BC/AC

=20/29

Tan C=Perpendicular/Base

=AB/BC

=21/20.

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The scientist used 0.786 liters of the liquid for the experiment.

Unit conversion is the process of converting a quantity expressed in one unit of measurement to an equivalent quantity expressed in a different unit of measurement.

To convert between different units of measurement, we need to use conversion factors, which relate to the two units.

In this case, the conversion factor is 1 liter = 1000 milliliters, which allows us to convert from milliliters to liters by dividing by 1000.

Here we have

A scientist used 786 millimeters  

To convert milliliters to liters, we need to divide by 1000 since there are 1000 milliliters in one liter.

So, to convert 786 milliliters to liters, we divide by 1000:

786 milliliters ÷ 1000 = 0.786 liters

Therefore,

The scientist used 0.786 liters of the liquid for the experiment.

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Complete Question:

A scientist used 786 milliliters of a liquid for an experiment. How many liters of the liquid did the scientist use for this experiment?

Answer: See Bellow

Step-by-step explanation:

Juliet's sample may not be valid for several reasons. Firstly, her sample size of 20 students may not represent the entire student population at her school. If her class is not a random sample of the whole student population, her results may not generalize to the entire school. Additionally, the model may suffer from selection bias if she only surveyed students she knew liked short stories or if she conducted the survey in a way that only sure students responded. Therefore, it is essential to have a large and representative sample to ensure the validity of the conclusions drawn from the survey results.

answer

a 17× + 5× + 16 + 7

b 22× + 23

Step-by-step explanation:

the perimeter of a shape is calculated by adding up all the the sides.

part a asks you to use all four lengths so just place them side by side with the addition sign.

in part b you are asked to simplify it so you have to add the like terms. 17× and 15x add up to 22 and 16 and 7 add up to 23.this is the simplest we can go since 22x and 23 are not like terms.

hope this helps :)

[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank A} }{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1810)(0.025)(5) \implies I = 226.25 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{ \textit{\LARGE Bank B} }{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1810\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]

[tex]A = 1810\left(1+\frac{0.025}{12}\right)^{12\cdot 5} \implies A \approx 2050.73~\hfill \underset{ interest }{\stackrel{2050.73~~ - ~~1810 }{\approx 240.73}} \\\\[-0.35em] ~\dotfill\\\\ 240.73~~ - ~~226.25 ~~ \approx ~~ \text{\LARGE 14.48}[/tex]

Answer:

Step-by-step explanation:

C

Answer:

  A

Step-by-step explanation:

You want to know which ball weighs 30 g if balls A, B, C, D, E weigh 30, 50, 50, 50, 80 grams.

The given information does not say what the correspondence is between weights and ball designators. If we assume the given order is the same for designators as for weights, then the first letter corresponds to the first weight, and ...

  Ball A weighs 30 g.

__

Additional comment

If there's more to the question, you'd have to use that additional information to decide.

<95141404393>

the proportion of California college students who currently drink alcohol different from the proportion nationwide p0 = 0.60 (nationwide proportion from CDC)

Information provided; we can determine if the proportion of California college students who currently drink alcohol is different from the proportion nationwide by conducting a hypothesis test. Here are the steps:
The null hypothesis (H0) and alternative hypothesis (H1):
H0: The proportion of California college students who drink alcohol is the same as the nationwide proportion.

(p = 0.60).
H1: The proportion of California college students who drink alcohol is different from the nationwide proportion.

(p ≠ 0.60).
The sample proportion (p-hat), sample size (n), and the population proportion (p0):
p-hat = 0.66 (66% of the 450 California college students surveyed)
n = 450 (sample size)
p0 = 0.60 (nationwide proportion from CDC)
The test statistic (z) using the following formula:
[tex]z = (p-hat - p0) / \sqrt((p0 \times (1 - p0)) / n)[/tex]
A standard normal distribution table or calculator to find the p-value associated with the test statistic.
Compare the p-value to a predetermined significance level (α), usually set at 0.05.
- If the p-value is less than α, reject the null hypothesis (H0), suggesting that the proportion of California college students who drink alcohol is different from the nationwide proportion.
- If the p-value is greater than α, fail to reject the null hypothesis (H0), indicating that there is not enough evidence to suggest a difference between the two proportions.
Determine if the proportion of California college students who drink alcohol is significantly different from the nationwide proportion.

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This data would be considered "paired" data.

The population of ferrets from which our sample was drawn, represented as μd, where μd = μend - μstart, and μ represents the population mean.

       We are dealing with "paired" data since we are comparing the weights of the same ferrets at two different points in time.

      The parameter we are trying to estimate is the mean difference in weight between the start and end of the study for the population of ferrets from which our sample was drawn.

This mean difference in weight can be represented as μd, where μd = μend - μstart, and μ represents the population mean. To estimate this parameter, we would need to calculate the difference in weight for each ferret and then take the average of these differences. This estimate would then provide us with an understanding of how much, on average, the ferrets in the population have gained or lost weight over the course of the study.  

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The area of the sandbox of parallelogram shape is approximately 22.47 square feet. Rounded to the nearest integer, the answer is (a) 24ft².

A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides of a parallelogram are equal in length and parallel to each other. Additionally, opposite angles of a parallelogram are congruent (i.e., have the same measure).

We can choose any side of the parallelogram as the base, and the distance from that side to the opposite side as the height. Let's choose the side between (-4,0) and (-2,6) as the base. The length of this side is the distance between these two points:

√[(-2-(-4))² + (6-0)²] = √40 = 2√10

The height of the parallelogram is the distance between the line containing (-2,6) and (4,0) and the point (2,-6). We can find the equation of the line containing (-2,6) and (4,0) by finding the slope and y-intercept:

Slope: (0-6)/(4-(-2)) = -6/6 = -1

Y-intercept: y = mx + b -> 0 = (-1)(4) + b -> b = 4

Therefore, the equation of the line is y = -x + 4. We can find the distance between this line and the point (2,-6) by substituting x = 2 into the equation and finding the corresponding y-value:

y = -x + 4 = -2

The distance between the line and the point (2,-6) is the absolute value of the difference between the y-coordinate of the point and the y-coordinate of the line:

|(-6) - (-2)| = 4

Therefore, the height of the parallelogram is 4 feet.

The area of the parallelogram is then:

A = base x height = (2√10) x 4 = 8√10

Rationalizing the denominator, we get:

A = 8√10 x √10/√10 = 80/√10 = 80√10/10 = 8√10

Therefore, the area of the sandbox is approximately 22.47 square feet. Rounded to the nearest integer, the answer is (a) 24ft².

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Answer: x^2+2x-7/x-1

The distribution in which variable x has binomial distribution are as follow,

Option A) When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

Option D) When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

This variable X follows a binomial distribution .

Because there are two independent trials two patients.

With a constant probability of success 30%.

And the outcome of one trial doesn't affect the outcome of the other.

When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

This variable X does not follow a binomial distribution.

Because the probability of success is not constant it's the complement of 30%, which is 70%.

Also, the outcome of one trial affects the outcome of the other trials.

As there are only six patients .

Number of patients for whom medicine does not work depends on number of patients for whom it worked.

When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

This variable X follows a binomial distribution.

Because there are six independent trials six patients with a constant probability of success (30%) .

The outcome of one trial doesn't affect the outcome of the other.

When the medicine is tried with two patients, X is the number of doses each patient needs to take.

This variable X does not follow a binomial distribution.

Because it's not a count of successes out of a fixed number of independent trials.

But rather a continuous variable that can take any non-negative value.

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The above question is incomplete, the complete question is:

For a certain type of hay fever, Medicine H has a 30% probability of working.

In which distributions does the variable X have a binomial distribution?

Select EACH correct answer.

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

D. When the medicine is tried with two patients, X is the number of doses each patient needs to take.

For table 14, the table is neither.

Option C is correct.

For table 15, the table is neither.

Option C is correct.

Table 14:

The difference between 22 and 48 is -26

The difference between 39 and 22 is 17

The difference between 40 and 39 is 1

The difference between 42 and 40 is 2

The difference between 42 and 42 is 0

Because  the differences are not constant, the table is neither linear nor quadratic.

For table 15, we check if the difference in y-values is constant:

The difference between 4 and 1 is 3

The difference between 1 and 1 is 0

The difference between 0 and 1 is -1

The difference between 1 and 4 is 3

The difference between 4 and 9 is 5

The difference between 9 and 16 is 7

Because  the differences between y-values are not constant, the table is neither linear nor quadratic.

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The radius of the water bottle which is in cylindrical shape is approximately 2.12 cm.

A cylinder is a three-dimensional shape that consists of two congruent, parallel circular bases that are connected by a curved lateral surface. The lateral surface of the cylinder is formed by a rectangle that is wrapped around the circular bases.

A cylinder can be thought of as a circular prism, where the bases are circles and the lateral surface is curved. The height of a cylinder is the perpendicular distance between the two bases, and the radius is the distance from the center of the base to the edge of the circular base.

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We can rearrange this formula to solve for the radius:

r = √(V/πh)

Substituting the given values, we have:

r = √(150/π(8.9))

r ≈ 2.12 cm (rounded to two decimal places)

Therefore, the radius of the water bottle is approximately 2.12 cm.

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