HELP!
Jeff volunteers his time by working at an animal shelter. Each year he works for a total of 240 hours. So far this year, he has worked 97 hours. Which equation will solve for how many more hours (h) Jeff will volunteer for?

A) 97 = 240 + h
B) 97 = 240h
C) 240 = 97 + h
D) 240 = 97 - h

A survey asked a group of students to choose their favorite type of sport from the choices of soccer, softball, basketball, and others. The results of the survey are shown in the graph.

Based on the graph, how many students in a class of 84 students would be expected to choose a sport other than soccer, softball, or basketball as their favorite type of sport?

A) 3
B) 12
C) 24
D) 72

You're the banker at HappyBank.com. Identify the two borrowers you would MOST likely offer a loan based on their credit scores.

A) F. Lutts and B. Parker
B) F. Lutts and K. Teller
C) A. Fulbright and K. Teller
D) A. Fulbright and B. Parker

What is the prime factorization of 240?

A) 23 · 3 · 5
B) 23 · 5 · 7
C) 24 · 3 · 5
D) 24 · 3 · 7

Answer:

It is a rhombus.

Step-by-step explanation:

To identify the type of polygon, we will first determine if the opposite sides are parallel.  To do this, we find the slope of each line segment.  (Parallel lines have the same slope.)

For WX, m = (5-2)/(1-5) = 3/-4 = -3/4

For XY, m = (2--1)/(5-1) = 3/4

For ZY, m = (2--1)/(-3-1) = 3/-4 = -3/4

For ZW, m = (2-5)/(-3-1) = -3/-4 = 3/4

Since the slopes of WX and ZY are the same, these two sides are parallel.  Since the slopes of XY and ZW are the same, these two sides are parallel.  Since opposite sides are parallel, the figure is a parallelogram.

In order to be a rectangle, the angles would have to be right angles.  Since perpendicular lines have slopes that are negative reciprocals of each other, the slopes of adjoining sides would have to be opposite signs and flipped.  This is not the case, so the angles are not right; this means it is not a rectangle.

The only other option for a parallelogram without right angles would be a rhombus.  This is the case if the length of each side is the same.  We will use the distance formula for this:

[tex]WX=\sqrt{(5-2)^2+(1-5)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\XY=\sqrt{(2--1)^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\YZ=\sqrt{(2--1)^2+(-3-1)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\ZW=\sqrt{(2-5)^2+(-3-1)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

Since the length of each side is the same, this figure is a rhombus.

y = k/x

Step-by-step explanation:

The volume of the pencil is approximately 4.05 cm³.

To determine the volume of the pencil, we need to calculate the volumes of the cylindrical body and the conical tip separately and then add them together.

Volume of the cylindrical body:

The formula for the volume of a cylinder is [tex]V = \pi r^2h[/tex], where r is the radius and h is the height.

[tex]V_{cylinder} = \pi (0.5 cm)^2 * 15 cm[/tex]

Volume of the conical tip:

The formula for the volume of a cone is [tex]V = (1/3)\pi r^2h[/tex], where r is the radius and h is the height.

[tex]V_{cone} = (1/3) * \pi (0.5 cm)^2 * 2 cm[/tex]

Now, we can calculate the volumes:

[tex]V_{cylinder} = \pi * (0.5 cm)^2 * 15 cm = 3.53 cm^3\\\\V_{cone} = (1/3) * \pi * (0.5 cm)^2 * 2 cm = 0.52 cm^3[/tex]

Finally, we can add the volumes of the cylindrical body and the conical tip to get the total volume of the pencil:

[tex]Total\ volume = V_{cylinder} + V_{cone} = 3.53 cm^3 + 0.52 cm^3 = 4.05 cm^3[/tex]

Therefore, the volume of the pencil is approximately 4.05 cubic centimeters ([tex]cm^3[/tex]).

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Answer:

7 years

Step-by-step explanation:

An initial investment of $200 is now valued at $350.

The annual interest rate is 8% compounded continuously.

Formula:

[tex]A=Pe^{rt}[/tex]

Where,

A is amount, A=350

P is principle, P=200

R is rate of interest, r=0.08

t is time, t=?

Substitute the value into formula

[tex]350=200e^{0.08\cdot t}[/tex]

[tex]e^{0.8t}=1.75[/tex]

Taking ln both sides

[tex]0.08t = ln(1.75)[/tex]

[tex]t=6.99\approx 7[/tex]

Hence, 7 years ago money was invested.

Answer:

Its 7 years

Step-by-step explanation:

Answer:

11.18

Step-by-step explanation:

Answer:

A) [tex]24\text{ m}^3[/tex].

Step-by-step explanation:

We have been given an image of a square pyramid and we are asked to find the volume of our given pyramid.

[tex]\text{Volume of square pyramid}=\frac{a^2*h}{3}[/tex], where,

a = Base length of square,

h = height of pyramid.

Upon substituting our given values in above formula we will get,

[tex]\text{Volume of square pyramid}=\frac{\text{(3 m)}^2*\text{ 8 m}}{3}[/tex]

[tex]\text{Volume of square pyramid}=\frac{9\text{ m}^2*\text{ 8 m}}{3}[/tex]

[tex]\text{Volume of square pyramid}=\frac{72\text{ m}^3}{3}[/tex]

[tex]\text{Volume of square pyramid}=24\text{ m}^3[/tex]

Therefore, the volume of our given square pyramid is 24 cubic meters and option A is the correct choice.

Answer:

A. 24 m3.

Step-by-step explanation:

Number of chicken = 26

And, Number of dogs = 17

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A farmer has a collection of chickens and dogs.

And, all together there are 120 legs and 43 heads.

Hence, Number of chicken = x

And, Number of dogs = y

Thus, We get;

⇒ x + y = 43  

⇒ x = 43 - y .. (i)

⇒ 2x + 4y = 120

⇒ x + 2y = 60 .. (ii)

Substitute value of x from (i) to (ii);

⇒ x + 2y = 60

⇒ 43 - y + 2y = 60

⇒ y = 60 - 43

⇒ y = 17

And, From (i);

⇒ x = 43 - y

⇒ x = 43 - 17

⇒ x = 26

Thus,  Number of chicken = 26

And, Number of dogs = 17

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[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

Step-by-step explanation:

Given :

[tex]\dfrac {c-4}{c-2} = \dfrac {c-2}{c+2} - \dfrac{1}{2-c}[/tex]                   --------- (1)

Calculation :

[tex]\dfrac {c-4}{c-2} = \dfrac {(c-2)^2+(c+2)}{(c+2)(c-2)}[/tex]

[tex]c-4 = \dfrac {(c^2-4c+4)+(c+2)}{(c+2)}[/tex]

[tex](c-4)(c+2) = (c^2-3c+6)[/tex]

[tex](c^2-2c-8) = (c^2-3c+6)[/tex]

[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

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Answer:

14 and Zero

Step-by-step explanation:

Answer:

If you wanted to predict the value of the y variable when the x variable is 15, you would be extrapolating the data.

Step-by-step explanation:

If you wanted to predict the value of the y variable when the x variable is 15, you would be Extrapolating the data.

Extrapolation means, estimating the value of a variable beyond its given range.

The expression that can be simplified by combining like terms is 16 c^2 + 8cd + 7c - 8d, where 8cd and -3dc are like terms and can be combined to simplify the expression to 16c^2 + 5cd + 7c - 8d.

The expression 16 c2 + 8cd + 7c - 8d can be simplified by combining like terms. Like terms in an algebraic expression are terms that have the same variable raised to the same power. Here, the terms 8cd and -3dc are like terms and can be combined.

Here's the step-by-step simplification:

This process of combining like terms helps in simplifying algebraic expressions, making them easier to work with.

After combining like terms, it's important to always check the answer to see if the simplification is reasonable and if there are any other like terms that can be combined.

So, the simplified expressions are:

1. [tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]

2. [tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]

3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]

4. [tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]

Let's simplify each expression by combining like terms:

1. [tex]\(6d^2 + 5cd - 3dc + 8\)[/tex]

  Combine like terms:

  [tex]\(6d^2 + (5cd - 3dc) + 8\)[/tex]

 [tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]

2. [tex]\(12c^2 - 8d^2c + 3dc + 4\)[/tex]

  Combine like terms:

[tex]\(12c^2 - (8d^2c - 3dc) + 4\)[/tex]

  [tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]

3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]

  No like terms to combine.

4. [tex]\(16c^2 + 8cd + 7c - 8d\)[/tex]

  Combine like terms:

  [tex]\(16c^2 + (8cd + 7c) - 8d\)[/tex]

  [tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]

General Idea:

There are few exponent rules that need to be used to simplify the rational exponent to get to the answer.

Exponent rules:

[tex] Rule\; 1: a \cdot a \cdot a \cdot a =a^4\\ \\ Rule\; 2: (a^m)^n=a^{m \times n} [/tex]

Applying the concept:

Rewriting 81 as a number with an exponent using prime factorization.

[tex] 81=3 \times 3 \times 3 \times 3 = 3^4\\ \\ Applying \; Rule \; 1, \; we\; get\; \\\\81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}} \\ \\ Applying \; Rule \; 2,\; we\; get\\ \\ 3^{4 \times\frac{3}{4} } = 3^{\frac{12}{4} }=3^3=3 \times 3 \times 3 = 27 [/tex]

Conclusion:

The above explanation explains why [tex] 81^{\frac{3}{4}} =27 [/tex]

I'm assuming that the 1/3 is an exponent.

If so, then  

Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.