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A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled

n200080 [17]

Answer:

24000 pieces.

Step-by-step explanation:

Given:

Side lengths of cube = $\frac{1}{4} \ foot$

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

$Volume\ of\ cube =a^{3}$

$=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot$

Length = 8 foot, Breadth = $6\frac{1}{4} =\frac{25}{4} \ foot$ , Height = $7\frac{1}{2} =\frac{15}{2} \ foot$

$Volume\ of\ rectangular\ prism =length\times breadth\times height$

$=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot$

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = $\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube$

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.

7 0

3 years ago

At 107°F, a certain insect chirps at a rate of 92 times per minute, and at 113°F, they chirp 116 times per minute. Write an equa

dsp73

Answer:

The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.

Step-by-step explanation:

A linear equation can be expressed in the form y=m*x + b. In this equation, x and y are coordinates of a point, m is the slope and b is the y coordinate of the y-intercept. Since this equation describes a line in terms of its slope and its y-intercept, this equation is said to be in its slope-intercept form.

When there are two points of a line (x1, y1) and (x2, y2), the slope is determined by the quotient between the difference of the ordinate of these two points and the difference of the abscissa of the same points. This is:

$m=\frac{y2-y1}{x2-x1}$

Having a point on the line, you can substitute the values of m, x and y in the equation y = mx + b and thus find b.

In this case:

(x1, y1): (92, 107)
(x2, y2): (116, 113)

So:

$m=\frac{113-107}{116-92}$

m= 0.25

substituting the values of m, x1 and y1 in the equation y = mx + b you have:

107= 0.25*92 + b

107 - 0.25*92= b

84=b

The equation in slope-intercept form that represents the situation is y=0.25*x + 84 where y represents the temperature in ° F and x the number of chirps per minute.

3 0

3 years ago

The weekend Jerome earned 252.50 in all.what was the dollar amount of the meals that Jerome served? Jerome served worth meals

kobusy [5.1K]

Answer:

im sorry but i need points

Step-by-step explanation:

3 0

2 years ago

Jason knows that the equation to calculate the period of a simple pendulum is , where T is the period, L is the length of the ro

Brrunno [24]

Answer-