Find the volume for each prism.

Hello there! :)

\(\huge\boxed{g = 2}\)

10g + 8  = 14g

Subtract 10g from both sides:

10g - 10g + 8 = 14g - 10g

8 = 4g

Divide both sides by 4:

8/4 = 4g/4

g = 2.

Hey there!

\(Answer:\boxed{g=2}\)

\(Explanation:\)

\(10g+8=14g\)

In our first step, we will subtract 14g from both sides of the equation.

\(10g+8-14g=14g-14g\\-4g+8=0\)

Now we will have to subtract 8 from both sides of the equation.

\(-4g+8-8=0-8\\-4g=-8\)

In our third/final step, we will divide both sides by -4.

\(\frac{-4g}{-4}=\frac{-8}{-4} \\g=2\)

\(\boxed{g=2}\text{ is your answer.}\)

Hope this helps!

\(\text{-TestedHyperr}\)

Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

Answer: 15cm and 5cm

Step-by-step explanation:

A rectangle's area is the product of the length and width

Given length x and width y, 2x+2y = 40 and x*y = 75.

Verifying my answer:

2(15)+2(5) = 40

30+10 = 40

40 = 40

15*5 = 75

75= 75

This is a week late so I hope this helped.

The length and the width of the rectangle​ are 15cm and 5cm respectively

The given parameters are:

Area (A) = 75

Perimeter (P) = 40

The area of a rectangle is LW, while the perimeter is 2(L + W)

So, we have:

LW = 75

2(L + W) = 40

Divide by 2

L + W = 20

Make L the subject

L = 20 - W

Substitute L = 20 - W in LW = 75

(20 - W)W = 75

Expand

20W - W^2 = 75

Rewrite as:

W^2 - 20W + 75 = 0

Expand

W^2 - 15W - 5W + 75 = 0

Factorize

(W - 15)(W -5) = 0

Split

W - 15 = 0 or W - 5 = 0

Solve for W

W = 15 or W = 5

Recall that:

L= 20 - W

So, we have

L = 20 - 15 or L = 20 - 5

This gives

L = 5 or L = 15

Hence, the length and the width of the rectangle​ are 15cm and 5cm respectively

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A relation that has more than one output of each input. That is not a function. A function only has one output of each input. Function a and function b are linear functions. Function a is represented by the table values. function b is represented by the equation y=3x+4.

Domain, is a term that is used to measure the independent variable’s values. Also known as the “x” values. It tells you what values of “x” are applicable in the function. What values will satisfy the function.

Range, is a term used to measure the dependent variable’s values. Also known as the “y” values. It tells you what values of why does the graph of the function extends till.

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Answer

There are 18 cups of blue paint used for every 27 cups of violet that is mixed.

Step-by-step explanation:

12 + 6 = 18.

Answer: (6, 3)

Step-by-step explanation:

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

total seats = 5000

total revenue = $155600

Step 02:

system of equations:

x = # of $28 tickets

y = # of $40 tickets

equation 1:

x + y = 5000

equation 2:

28x + 40y = 155600

x + y = 5000 * (-28)

28x + 40y = 155600

-28x - 28y = - 140000

28x + 40y = 155600

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

12y = 15600

y = 15600 / 12

y = 1300

y in eq. 1:

x + y = 5000

x + 1300 = 5000

x = 5000 - 13000

x = 3700

The answer is:

x = 3700 of $28 tickets

y = 1300 of $40 tickets

Answer:

x = 4/3

Step-by-step explanation:

First, we cancel the -2 by dividing both sides by -2, so we have

|3x + 2| = -12÷-2

|3x + 2| = 6,

3x + 2 = 6, collecting like terms

3x = 6 - 2

3x = 4

x = 4/3

Required solution of the given equation 3.1 = -0.5 + 0.3x is x = 12.

What is equation?

A mathematical statement that asserts that two expressions are equal is called equation

. It is consist of variables, constants, and mathematical operations such as , subtraction, addition, division, multiplication . We can use equations in mathematics to model real-world situations or to solve problems. It can also be used to express relationships between quantities, to find unknown values, and to test hypotheses. Equations can be written in various forms, such as linear, exponential, trigonometric ,quadratic. Equation depends on the type of relationship being modeled.

Here given equation is 3.1 = -0.5 + 0.3x.

We are Simplifying it,

\(3.1 + 0.5 = 0.3x \\ 0.3x = 3.6 \\ x = \frac{3.6}{0.3} \\ x = 12\)

So, required solution of the given equation is 12.

Therefore, option C is the correct answer.

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Correct question is "What is the solution to this equation? 3.1 = -0.5 + 0.3x A:x=6 B:x=3 C:x=12 D:x=0.8".

Any number between -7 and 7 can be located in the number line.

The number line is a horizontal line that has equally spread number increments.

Given a number line, suppose we plot -5 on it, which is between -7 and 7

Then, its position will be 5 units left of 0 on the number line.

Hence, -5 is the point between -7 and 7 on the number line, which is 5 units left on 0.

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The value of x in this proposition would be the first option i.e. \(-13\frac{1}{4}\)

4/11= -33/x+5,

to get the value of x we need to get the x to the left hand side,

4(x+5)= -33,

4x+20 = -33.

subtracting 20 from both the sides,

4x= -33-20

4x = -53.

dividing both the sides by 4,

x= -53/4

x= \(-13\frac{1}{4}\) ,

which is option A in the given question

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Answer:

\(\mu = x - z(\sigma)\)

\(\mu = 1214.87 - 0.67(116) \\\\\mu = 1214.87 - 77.72 \\\\\mu = \$1137.15\)

Therefore, the mean monthly payment is $1137.15.

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

We are asked to find the mean monthly social security (OASDI) payment.

Mean monthly payment = μ = ?

We are given that the standard deviation is $116

One-fourth of payments are above $1214.87

One-fourth means 25%

\(P(X > x )= P(Z > z ) = 0.25\\\\P(X < x )= P(Z < z) = 1 - 0.25\\\\P(X < x )= P(Z < z) = 0.75\\\\\)

From the z-table, the z-score corresponding to 0.75 is found to be 0.67

\(z = 0.67\)

The mean is found by

\(x = \mu + z(\sigma)\)

\(\mu = x - z(\sigma)\)

Where

x = $1214.87

z = 0.67

σ = $116

\(\mu = 1214.87 - 0.67(116) \\\\\mu = 1214.87 - 77.72 \\\\\mu = \$1137.15\)

Therefore, the mean monthly payment is $1137.15.

Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value of the annuity

PMT = payment (or deposit) made at the end of each compounding period

r = annual interest rate

n = number of compounding periods per year

t = number of years

In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:

Marcia wants to retire in 15 years (when she is 65), so t = 15

The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2

Marcia wants to have $90,000 in her retirement account

Substituting these values into the formula, we get:

$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)

Simplifying the formula, we get:

PMT = $90,000 / [(1.025)^30 - 1] / 0.025

PMT = $90,000 / 19.7588

PMT = $4,553.39 (rounded to the nearest cent)

Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.

Answer:

6

Step-by-step explanation:

To find the mean, you add up all the numbers and divide that by the number of numbers there are.

In this case, the total is \(3+8+7+2+9+6+6+7=48\)

There are 8 numbers.

Thus, the mean is 48 ÷ 8 = 6

Hey there!

When you hear/see the word “mean” in mathematics it usually means “average” or “total”.

Formula: sum of the total numbers ÷ total numbers in the data plot

YOUR EQUATION:

3 + 8 + 7 + 2 + 9 + 6 + 6 + 7 ÷ 8

= 11 + 7 + 2 + 9 + 6 + 6 + 7 ÷ 8

= 18 + 2 + 9 + 6 + 6 + 7 ÷ 8

= 20 + 9 + 6 + 6 + 7 ÷ 8

= 29 + 6 + 6 + 7 ÷ 8

= 35 + 6 + 7 ÷ 8

= 41 + 7 ÷ 8

= 48 ÷ 8

= 6

Therefore, your mean is: 6

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

27

Step-by-step explanation:

Answer:

18Πin3

Step-by-step explanation:

The result after rationalizing is \(\frac{9\sqrt{x+3} }{x+3}\).

Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction.

Here, given fraction

 \(\frac{9}{\sqrt{x+3} }\)

Multiply and divide by \(\sqrt{x+3}\), we get

\(\frac{9}{\sqrt{x+3} } \frac{\sqrt{x+3} }{\sqrt{x+3} }\)  =  \(\frac{9\sqrt{x+3} }{x+3}\)

Thus, the result after rationalizing is \(\frac{9\sqrt{x+3} }{x+3}\).

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Answer:

(2k+3) (k−8)

Step-by-step explanation:

The length of the line segment from a to b is 6.08 units or \(\sqrt{37}\) units.

The length is described as the distance between the two points in a line. The coordinate usually refers to the dimensions of the point with respect to the two dimension graph.

Relation between the coordinates and length:  \(\sqrt{(x_{1} -x_{2}) ^{2} +(y_{1} -y_{2} )^{2} }\)

Now let point a be (\(x_{1},y_{1}\)) and point b be (\(x_{2},y_{2}\))

Thus putting values,

length = \(\sqrt{(3-(-3))^{2}+(4-3)^{2} }\)

length = \(\sqrt{36+1}\)    

length = \(\sqrt{37}\)

Hence the length of ab is \(\sqrt{37}\) or 6.08 units.

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The statement that compares the distribution shapes is (b) East Hills HS is positively skewed, and Southview HS is symmetric.

From the question, we have the following highlights:

Hence, the statement that compares the distribution shapes is (b) East Hills HS is positively skewed, and Southview HS is symmetric.

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Answer:

Step-by-step explanation:

East hills is negative skewed, Southview is symmetric

Explanation-just took the quiz

Answer:

by cancellation method  we can cancel both the y's

so the leftover digits are, 12/3x

when simplifying, we will get 4/x

∴ the final answer is 4/x

hope this answer helps you.....

Simplify the equation.

So correct option is D.

The solution of the integral by variable change is equal to (1 / 6) · √(2 · x + 3)³ - (3 / 2) · √(2 · x + 3).

In this problem we find the definition of an integral, whose solution must be found by variable change, that is, a kind of algebraic substitution. First, write the complete expression:

∫ [x / √(2 · x + 3)] dx

Second, use algebraic substitution to simplify the expression:

u = 2 · x + 3

x = (u - 3) / 2

dx = du / 2

(1 / 2) ∫  [(u - 3) / (2 · √u)] du

(1 / 4) ∫ [(u - 3) / √u] du

(1 / 4) ∫√u du - (3 / 4) ∫ du / √u

Third, solve the integral:

(1 / 6) · √u³ - (3 / 2) · √u

Fourth, revert the algebraic substitution:

(1 / 6) · √(2 · x + 3)³ - (3 / 2) · √(2 · x + 3)

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Answer:

880x+30

880    880

x=29.3 repeating

Step-by-step explanation: Hope this helps