A recycling bin in the The shape of a rectangular prism has a volume of 9720 cubic inches. The base area is 324 square inches, what is the height of the recycling bin?

After calculating the cost per square inch for both tiles, the 6x8 tile at $0.026875 per square inch is less expensive than the 4x4 tile at $0.061875 per square inch. Thus, the 6x8 tiles are cheaper.

To determine which tile is cheaper, you need to calculate the cost per square inch for each tile, and then compare them. The 6x8 tile has an area of 48 square inches (6 inches x 8 inches), and it costs $1.29. To find the cost per square inch, divide $1.29 by 48 square inches.

Cost per square inch for 6x8 tile: $1.29 / 48 = $0.026875

The 4x4 tile has an area of 16 square inches (4 inches x 4 inches), and it costs $0.99. To find the cost per square inch, divide $0.99 by 16 square inches.

Cost per square inch for 4x4 tile: $0.99 / 16 = $0.061875

Comparing these two amounts, the 6x8 tile at $0.026875 per square inch is less expensive than the 4x4 tile at $0.061875 per square inch. Therefore, the 6x8 tiles are cheaper than the 4x4 tiles.

Sara's change in elevation is calculated by multiplying 4 hours by -8 meters/hour. This gives a total change in elevation of -32 meters, which shows that Sara descended 32 meters from her starting point.

The subject of your question is math, specifically dealing with the concept of multiplication. To determine Sara's change in elevation, we have to know how much the elevation decreases each hour. It's important to note that the decrease in elevation is the same as saying Sara is descending, thus the change will be represented by a negative number.

In this case, for every hour Sara hiked, her elevation decreased by 8 meters. Therefore, the total change in elevation after 4 hours would be 4 hours multiplied by -8 meters/hour. The calculation for this is:

4 hours * -8 meters/hour = -32 meters

Therefore, Sara hiked down a total of 32 meters from her starting point on the mountain.

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Let [tex] l [/tex] be the length and [tex] w [/tex] be the width of the rectangle.

Given perimeter of the rectangle

[tex] 2(l+w)=34 \; l+w=17[/tex]

Area of the rectangle is

[tex] lw=52 [/tex]

Also length is 5 more than twice its width,

[tex] l=2w+5 [/tex]

From the above equations

[tex] (l-w)^2=(l+w)^2-4lw=17^2-4*52=81\\
l-w=9,\; since \; l>w [/tex]

Now [tex] 2l=9+17=26\;,l=13,w=4 [/tex]

The dimensions of the rectangle are length [tex] l=13 [/tex], and width [tex] w=4 [/tex].

Answer:

7(3n^2-2)

Step-by-step explanation:

=21n^2-14

As the numbers 21 and 14 are multiples of 7, so 7 will be the common factor

=7(3n^2-2)

The length of side CB is 33 unit using Law of Cosines.

Thus, option (D) is correct.

Given:

AB = 28 unit

<A = 81

AC = 17 unit

According to Law of Cosines

the lengths of the sides of a triangle to the cosine of one of its angles.

The Law of Cosines states:

[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]

Where:

c  = side opposite angle C

a and b = lengths of the other two sides

< C= opposite side c

Now, using Law of Cosines

CB² = AC² + AB² - 2 . AC. AB COS (91)

       = (17)² + (28)² - 2 (17)(28) COS (91)

       = 289 + 784 - 476 (-0.01745)

       = 1,081.3062

So, CB = √ (1,081.3062)

CB = 32.883

CB = 33 unit.

Thus, the value of CB is 33 unit.

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Answer:

C

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The number that is equal to 36 more than y is represented as x = y + 36, and is an algebraic expression that adds 36 to the variable y to define another variable x.

The question "A number that is equal to 36 more than y" can be expressed in a mathematical form as x = y + 36. Here, we are defining a new variable x, which represents the number that is 36 more than another variable y. This type of problem is common in algebra, where one variable is defined in terms of another.

To understand this with an example, if y represented someone's final exam history grades and we wanted to find a number that is 36 points higher than their history grade, we would add 36 to their grade y to get x. So, if the history grade was 60, the number x would be 60 + 36, which equals 96.

This relationship between x and y could be part of a larger system of equations or could represent a formula used to transform one set of data to another set, such as adjusting scores or predicting outcomes based on previous data.

Answer:

B

Step-by-step explanation:

Answer:

1. sample space

2. 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The wall, fence and ladder form similar right triangles as pictured

Use the ratio of corresponding sides to solve for x, the fence height

The fence is 10.9 feet tall

The volume of the golf ball, rounded to the nearest tenth, is approximately 13.8 cm^3.

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.

Rounded to the nearest tenth, the volume of the golf ball is approximately 13.8 cm^3.

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Based on the given information, Layla's drawing is a special type of quadrilateral known as a rectangle.

Rectangles are quadrilaterals having four equal vertices and parallel sides that are equal to one another.

A rectangle is defined as a quadrilateral with four right angles and opposite sides that are parallel and congruent (i.e., they have the same length).

In Layla's drawing, she stated that there are two pairs of opposite sides that are parallel, which satisfies this definition.

Furthermore, the fact that all four angles are right angles also fits the definition of a rectangle.

It is important to note that not all quadrilaterals with two pairs of parallel sides and four right angles are rectangles.

For example, a parallelogram with four right angles is a special type of rectangle known as a square, which has all sides congruent.

Therefore, based on the given information, Layla's drawing best describes a rectangle.

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For a probability distribution the expected value is the summation of product of probabilities with their respective data values. Let x be the probability that Jackson goes gym for 2 days and y be the probability that he goes gym for 3 days.

For the given case we have following values and their probabilities:

0 : 0.1

2 : x

3 : y

So the expected value will be = 0(0.1) + 2(x) + 3(y)

Expected value is given to be 2.05. So we can write the equation as:

2x + 3y = 2.05 (Equation 1)

Also for a probability distribution, the sum of probabilities must always equal to 1. So we can set up the second equation as:

0.1 + x + y = 1

x + y = 0.9 (Equation 2)

From Equation 2 we can write the value of x to be x = 0.9 - y. Using this value in equation 1, we get:

2(0.9 - y) + 3y = 2.05

1.8 - 2y + 3y = 2.05

1.8 + y = 2.05

y = 0.25

Using the value of y in equation 2 we get value of x to be 0.65

Therefore we can conclude that:

The probability that Jackson goes to gym for 2 days is 0.65 and the probability that he goes to gym for 3 days is 0.25

He goes to the gym 0, 2, or 3 days per week.  

Let's assume P(0 days)=p, P(2 days)=q, and P(3 days) = r.

So, p+q+r = 1

E(X)= E(x=0)*P(0 days) + E(x=2)*P(2 days) + E(x=3)*P(3 days)

E(X) = 0*p + 2*q + 3*r = 2q + 3r

Given is the value of P(0 days) = p = 0.1

Given is the expected value of number of days is E(X) = 2.05

Therefore, we have 0.1 + q + r = 1 and 2q + 3r = 2.05

Or, q + r = 0.9 and 2q + 3r = 2.05

Solving the two equations :-

(2q+3r)-2*(q+r) = 2.05-2(0.9)

r = 0.25

q = 0.65

Therefore, P(2 days) = 0.65 and P(3 days) = 0.25