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lisabon 2012 [21]

2 years ago

11

Wendy keeps her hamster, Fluffy, in a cage shaped like a rectangular prism that is 20 inches long, 14 inches wide, and has a vol

ume of 4,340 cubic inches. Kenneth keeps his hamster, Speedy, in a cage that is the same length, but is 15 inches wide and has a volume of 5,250 cubic inches.

1 answer:

Alex17521 [72]2 years ago

5 0

Speedy cage is 2 inches taller than fluffy cage.

<h3>How to find the volume of a rectangular prism?</h3>

The volume of rectangular prism = lwh

where

l =length
h = height
w = weight

Therefore,

height of fluffy cage can be calculate as follows:

4340 = 20 × 14 × h

4340 = 280h

h = 4340 / 280

h = 15.5 inches

height of Kenneth cage can be calculate as follows:

5250 = 20 × 15 × h

5250 = 300h

h = 5250 / 300

h = 17.5 inches

height difference = 17.5 - 15.5 = 2.0 inches

Hence, speedy cage is 2 inches taller than fluffy cage.

learn more on volume here: brainly.com/question/23997886

#SPJ1

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yall its an easy khan academy assignment please help ASAP i needa turn it in by 11:59 pm todayyy so hurry i will give 50 points!

MariettaO [177]

Answer:

The answer is B.

Step-by-step explanation:

6 0

3 years ago

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Layana’s house is located at (2 and two-thirds, 7 and one-third) on a map. The store where she works is located at (–1 and one-t

NeTakaya

We have been given that Layana’s house is located at $(2\frac{2}{3}, 7\frac{1}{3})$ on a map. The store where she works is located at $(-1\frac{1}{3}, 7\frac{1}{3})$ .

We are asked to find the distance from Layana’s home to the store

We will use distance formula to solve our given problem.

Let us convert our given coordinates in improper fractions.

$2\frac{2}{3}\Rightarrow \frac{8}{3}$

$7\frac{1}{3}\Rightarrow \frac{22}{3}$

$-1\frac{1}{3}\Rightarrow -\frac{4}{3}$

Now we will use distance formula to solve our given problem.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Upon substituting coordinates of our given point in above formula, we will get:

$D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}$

$D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}$

$D=\sqrt{0+(\frac{8+4}{3})^2}$

$D=\sqrt{(\frac{12}{3})^2}$

$D=\sqrt{(4)^2}$

$D=4$

Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.

3 0

3 years ago

Read 2 more answers

The diameter of a tire is 2.5 ft. Use this measurement to answer parts a and b. Show all work to receive full credit

Alla [95]

Answer:

The answer is below

Step-by-step explanation:

The diameter of a tire is 2.5 ft. a. Find the circumference of the tire. b. About how many times will the tire have to rotate to travel 1 mile?

Solution:

a) The circumference of a circle is the perimeter of the circle. The circumference of the circle is the distance around a circle, that is the arc length of the circle. The circumference of a circle is given by:

Circumference = 2π × radius; but diameter = 2 × radius. Hence:

Circumference = π * diameter.

Given that diameter of the tire = 2.5 ft:

Circumference of the tire = π * diameter = 2.5 * π = 7.85 ft

b) since the circumference of the tire is 7.85 ft, it means that 1 revolution of the tire covers a distance of 7.85 ft.

1 mile = 5280 ft

The number of rotation required to cover 1 mile (5280 ft) is:

number of rotation = $\frac{5280\ ft}{7.85\ ft\ per\ rotation}=672\ rotations\\\\\\$

4 0

3 years ago

Read 2 more answers

Gary just started a new job as a nurse. he is given a starting salary of $58,550 per year. he is also told that his salary will

IRINA_888 [86]

Firts we need to find the rate of change, or in other words, the slope of the line.

Question 1:

a)

For this we can take two points in the form (years, salary). Then we can define as year 0 the year when Gary starts to work. In this year the salary is $58,550. The first point is (0, $58,550)

The next point we can take is at the year 10, when the salary of Gary will be $71,950. The second point is (10, $71,950)

b) Now that we have the two points, we can use the slope formula to get the rate of change. The slope formula is, for two points A and B:

$\begin{gathered} \begin{cases}A(x_a,y_a) \\ B(x_b,y_b)\end{cases} \\ m=\frac{y_a-y_b}{x_a-x_b} \end{gathered}$

In this case, we can call the points A(0, $58,550) and B(10, $71,950). Using the formula:

$m=\frac{58,550-71,950}{0-10}=\frac{-13400}{-10}=1340$

c) "The rate of change in Gary's salary is $1340 per year."

Question 2:

a) The slope intercept form of a line is:

$y-y_1=m(x_{}-x_1)$

Where:

y is the output of the function.

x is the input of the function. (we provide the function with a value for x and the function give us a value of y)

m is the slope of the line. We calculate it in question 1.

x1 is the x coordinate of a point we choose.

y1 is the y-coordinate of the same point of x1.

In this case, we know:

m = 1340;

And we can take the point (0, $58,550), thus:

x1 = 0

y1 = 58,550

b) Now we need to use all this values and use the slope-intercept form:

$y-58,550=1340(x-0)$

And solve to get:

$y=1340x+58,550$

Question 3:

a) Now we have a equation for the salary, we can use this to find the salary in 13 years. We just need to replace x = 13 in the equation:

$\begin{gathered} \begin{cases}y=1340x+58,550 \\ x=13\end{cases} \\ y=1340\cdot13+58,550 \\ y=75,970 \end{gathered}$

B) The salary of Gary in 13 years will be $75,970.

6 0

1 year ago

In exercises 1 and 2, Find the value of x.

Kruka [31]

From the given picture, we can see that 2 sides are congruen, then the given triangle is an isosceles triangle. In this triangle the base angles are congruent, so we can draw the following picture:

Now, since interior angles of any triangle add up to 180 degrees, we have

$x+\frac{x}{2}+\frac{x}{2}=180$

By combining similar terms, we get

$\begin{gathered} \frac{4}{2}x=180 \\ 2x=180 \end{gathered}$

Then, x is given as

$\begin{gathered} x=\frac{180}{2} \\ x=90 \end{gathered}$

Therefore, the answer is x=90 degrees

4 0

1 year ago