Find the volume of the prism.


The volume is cubic meters.

Answer:

The table represents a linear function.

The graph of linear function y = 3x is attached below.

Step-by-step explanation:

Given the table

Number of Hours           1             3                 5

Number of Tents             3            9                15

Given that the slope is 3.

Finding the slope between (1, 3) and (3, 9)

Slope = (y₂-y₁) / (x₂-x₁)

          = [9-3] / [3-1]

           = 6 / 2

           = 3

Finding the slope between (3, 9) and (5, 15)

Slope = (y₂-y₁) / (x₂-x₁)

          = [15-9] / [5-3]

           = 6 / 2

           = 3

As the value of slope remains constant i.e. slope = m = 3.

Using the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 3 and the point (1, 3)

\(y - 3 = 3 (x-1)\)

\(y-3 = 3x-3\)

\(y = 3x-3+3\)

\(y = 3x\)

Comparing with the slope-intercept form of a linear function of line

y = mx+b     where m is the slope and b is the y-intercept

slope = 3 and y-intercept b = 0

Therefore, the table represents a linear function.

The graph of linear function y = 3x is attached below.

The point that is not included in the solution set for the inequality in the graph is (-1, 3).

In the information given, (h, k) is the vertex point. In the graph, the vertex point will be (1, 2). The equation will be:

y = a(x + 1)² + 2

By the point of the graph(0, 3) the value of a will be:

3 = a(0 - 1)² + 2

3 = a + 2

a = 3 - 2

a = 1

The equation this becomes:

y = 1(x - 1)² + 2.

y = x² - 2x + 1 + 2

y = x² - 2x + 3

Therefore, the point that is not included in the solution set for the inequality is (-1, 3).

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Answer:

(-∞,19)

Definition: The domain of a function is the set of input or argument values for which the function is real and defined

Answer:

(-∞, 19]

Step-by-step explanation:

The domain of this function is only true for all real values of f(x).

That means the lower limit of the function is -∞ as the values are positive, and the upper limit is 19, because that is the greatest value it can become before becoming negative.

The domain is : (-∞, 19]

Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

\(\frac{a}{b}\) = \(\frac{8}{5}\) ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = \(\frac{5}{8}\) a

also

\(\frac{b}{c}\) = \(\frac{3}{4}\) ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = \(\frac{4}{3}\) b = \(\frac{4}{3}\) × \(\frac{5}{8}\) a = \(\frac{5}{6}\) a

Then

a : b : c

= a : \(\frac{5}{8}\) a : \(\frac{5}{6}\) a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Answer:

From the image below

Hence,

Using the method of division below, we will have

Hence,

By applying the principle, we will have

Hence,

The complete statement is

Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

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Answer: <AOB= 180°

<ZOB= 15 °

<XOY=25 °

<AOY=92°

<YOZ=73°

Step-by-step explanation:

<AOB=180 Because angle on a straight line is 180 degrees it<s kinda like a fact or rule.

<XOY=25°As it says in the question , b=25° and <XOY is b

<ZOB=15° As <ZOB represent b

<AOY=67° + 25°= 92°

a=67 and b=25, <AOY is simply a+b as that is what is between A and Y

<YOZ=73°

The reason is because X is between< YOZ

since an angle in a straight line is 180° therefore a+b+x+c=180°

TO FIND X (<YOZ)

x=180-a-b-c

a=67°

b=25°

c=15°

therefore,

180-67-25-15=73°

Substitute the x and y coordinate into both equations and check to see if they work is a best way to determine whether a given point is a solution to a system of equations.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

The best way to determine whether a given point is a solution to a system of equations is to substitute the  x and y coordinate into both equations and check to see if they satisfy the equation.

And if the solutions do not satisfy the equation that means given x , y are not the solutions.

And if the unknowns are the solutions of system of the equation that

means the pair of point lies in the graph.

Therefore the answer is option C.

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Answer:

(x+1)(x-5)

Step-by-step explanation:

The correct order of the assumptions used in the derivation is: A, B, C, D, E. A states that the population is large, B: random, C: representative, D: large, and E states that the sampling is done without replacement.

The derivation of the Central Limit Theorem was based on five assumptions: (a) The population is large, (b) The sample is random, (c) The sample is representative, (d) The sample size is large, and (e) The sampling is done without replacement. The first assumption used in the derivation is that the population is large, which means that the number of individuals in the population is much greater than the sample size. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases. The second assumption used is that the sample is random, which means that each individual in the population has an equal chance of being selected for the sample. This helps to ensure that the sample is representative of the population as a whole. The third assumption is that the sample is representative, which means that the characteristics of the sample are similar to those of the population. This is important because it allows us to make generalizations about the population based on the sample. The fourth assumption is that the sample size is large. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases.

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Answer:

y = 2x -16

Step-by-step explanation:

two parallel lines have the same slope (2)

the other equation es:

\(y-(-6)=2(x-5)\)

\(y+6=2x-10\)

\(y=2x-10-6\)

\(y=2x-16\)

Hope this helps

The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)

1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)

2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).

3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).

4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)

5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)

6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)

7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)

8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)

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Answer:

He must sell 24 computes

Step-by-step explanation:

100 + 15x = 450

15x = 350

x = 23.33

Answer: I think its 118 feet per hour

Step-by-step explanation: Sorry if im wrong

Answer:

c

Step-by-step explanation:

c. j = a + 5

such that 7 = 2 +5

Answer: The initial cost on rent on your first year living there is 1100. Supposing you live there for another 11 years your rent would be 2200 per month.

Step-by-step explanation:110x11=1100 1100+1100=2200

Answer: I think it's 1,100

Step-by-step explanation: We know that the apartment costs $1100 per month during the first year but if it goes up 110 dollars per year how much would total be in 11th year?

First we need to multiply 1100 and 110 which equals 121,000

Secondly, of course we need to make sure that our anwser is correct, now we divide 121,000 with 11 years (which equals 1100)

But of course if it is not correct, I'm very sorry. But Have a nice day/night!

Hope it helped!

-GreenteaStudys

Answer:

Step-by-step explanation:

\(6\dfrac{7}{9}=\dfrac{(6*9)+7}{9}=\dfrac{54+7}{9}\\\\\\=\dfrac{61}{9}\)

Answer:

y = 98

z = 21

Step-by-step explanation:

in the picture, y and 82 are supplementary angles because the are same side interior angles. This means that we can create this equation:

y = 180 - 82

we get y = 98

<Y and <4z + 14 are vertical angles, so we can also say that they are equal to each other. So we can create this equation:

4z + 14 = 98

subtract 14 from both sides:

4z = 84

divide both side by 4 to find z:

z = 21

Answer:

y = 82

z  = 21

Step-by-step explanation:

You can get y almost immediately.

82 and y are supplementary. Interior angles on the same side of the transversal = 180

82 + y = 180              Subtract 82 from both sides

y = 180 - 82

y = 98

y and 4z + 14 are equal.

y = 4z + 14                Substitute for y    

98 = 4z  +  14           Subtract 14 from both sides.

98-14 = 4z

84 = 4z                     Divide by 4

84/4 = 4z/4

21 = z

"Define variables"

→ The number of student's tickets = a

→ The number of non-student tickets = b

→ the total cost represented = y

"Create an equation that models this situation"

→ y = $5 × a + $10 × b

"Rewrite the equation in slope intercept form"

→ y = $5 × a + $10 × b

→ y = 5a + 10b

→ 250 = 5a + 10b

Answer:

Option D

Step-by-step explanation:

\(6\dfrac{3}{5}*\dfrac{5}{8}=\dfrac{5}{8}*6\dfrac{3}{5}\)

Poperty : Commutative property of multiplication.

When two numberes are multiplied, changing the order of numbers  will not change the result.

Answer:

I don’t even know

Step-by-step explanation:

The maximum value of the original data set is 109.

To determine the maximum value of the original data set from the given stemplot, we need to look at the rightmost digits in each stem and identify the highest value.

Looking at the stemplot:

O 10 | 0 0 8 9 8 9 0 0 0

0 20 | 5 4 7 9 6

0 30 | 1 4 6 7 7 9 7

0 40 | 0 0 2 5 5 7 7 9 9 8

0 50 | 1 2 2 2 3 4 5 5 7 8 9 9

0 60 | 0 0 0 3 3 3 3 6 8

The rightmost digits in each stem represent the original data values. We can see that the highest value occurs in the stem "10" with a rightmost digit of "9".

Therefore, the maximum value of the original data set is 109.

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Answer:

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

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

Answer:

8 {m},{a},{t},{m,a},{m,t},{a,t},{m,a,t},{}

The amount of cake has been eaten is, 3/4.

What is parts of number?

A decimal fraction can be used to represent decimal numbers. It consists of a whole number and a decimal. In the decimal number 3.25, for instance, 3 is the whole number portion, and 25 is the decimal portion.

Given:

Todrick eats one fourth of lemon cake.

Roberta eats one third of the same cake.

Latasha comes home from work and eats one sixth of the same cake.

Let x be the amount of cake has been eaten.

So from the given information,

\(\frac{1}{4}+\frac{1}{3}+\frac{1}{6} = x\\ \frac{3 + 4 + 2}{12} = x\\ \frac{9}{12} = x \\x = \frac{3}{4}\)

Hence, the amount of cake has been eaten is, 3/4.

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Answer:

263,870

Step-by-step explanation:

Answer:

263,870

Step-by-step explanation:

You have 26,387 then you will multiply it by 10 and you'll get 263,870

Answer:

The height is 6 feet, and the length of the ramp is the hypotenuse of a right triangle with angle 28 degrees with the ground

Step-by-step explanation:sin

28=6/x

x*sin 28=6

x=6/sin 28=12.78 ft.

Answer:

$180

Step-by-step explanation:

If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180