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3 years ago

A chest shaped as a rectangular prism can hold 576 wooden cube blocks with edge lengths of 1/4 ft.

2 answers:

eduard3 years ago

4 0

The answer is 9 you have to multiply 1/4 three times which gives you 1/64 then you take 576 and multiply it by 1/64 which gives you 9. Hope this helps.

mario62 [17]3 years ago

4 0

Answer: 9 cubic feet

Step-by-step explanation:

Given: A chest shaped as a rectangular prism can hold 576 wooden cube blocks with edge lengths of $\frac{1}{4}$ ft.

The volume of cube is given by :_

$V=side^3=(\frac{1}{4})^3=\frac{1}{64}$ cubic feet

Then according to the question,

The volume of the rectangular prism = $576\times V$

⇒ The volume of the rectangular prism = $576\times \frac{1}{64}$

⇒ The volume of the rectangular prism =9 cubic feet

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The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a standard deviation of

musickatia [10]

Answer:

By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?

By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.

5 0

3 years ago

After sitting on a shelf for a while, a can of soda at room temperature (73 F) is placed inside a refrigerator and slowly cools.

Alona [7]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling here:

$T(t)=T_s+(T_0-T_s)^{-kt$

where T(t) is the temp of something after a certain amount of time, t, has gone by; Ts is the surrounding temp, and T0 is the initial temp. k is the constant of cooling. We need to first solve for this using the information given. Filling in what we know:

$53=35+(73-35)^{-35k$ which can simplify a bit to

$53=35+(38)^{-35k$ and $18=38^{-35k$

Take the natural log of both sides:

$ln(18)=ln(38)^{-35k$

Taking the natural log allows us to pull that exponent down out front:

$ln(18)=-35k*ln(38)$

and now we can divide both sides by ln(38) to get

-35k = .794585 so

k = -.023

Now that have the value for k, we can go on to solve the rest of the problem which is asking us the temp of the soda after 70 minutes. Filling in using the k value and the new time of 70 minutes:

$T(t)=35+(38)^{70(-.023)$ and

$T(t)=35+(38)^{-1.61$ and

$T(t)=35+.0028612013$ and

T(t) = 35 F, basically the temp of the fridge, which is not surprising!

5 0

3 years ago

Let r be the region in the first quadrant bounded by the graph y=8- x^ (3/2) Find the area of the region R . Find the volume of

Vanyuwa [196]

The boundaries:
x = 0, y = 8; y = 0, √x³ = = 8, x = 4
$A= \int\limits^4_0 {(8- x^{3/2}) } \, dx = \\ =8 x - 2 \sqrt{ x^{5} }/5= \\ 8*4-64/5 =19.2$
$V = \int\limits^4_0 { \pi (8 - x^{3/2}) } \, dx = \\ = \pi \int\limits^0_4 {(64 - 16 * 2 \sqrt{ x^{5} /5} + x^{4}/4) \, dx =$
= π ( 64 x - 16 * 2 *√x^5 + x^4 / 4 ) =
= π ( 320 - 1024/5 + 64 ) = 179.2 π

8 0

3 years ago

X + 4 = -14<br><br> what does x equal?

DaniilM [7]

Answer:

x=-18

Step-by-step explanation:

To move the 4 to the other side you need to subtract both sides by 4 (If you do something to one side you need to do it on the other side)

x+4-4=-14-4

Simplify:

x=-18

Hope this helps!

7 0

3 years ago

Write the word sentence as an equation. Then solve.

scoundrel [369]

Answer:

-1.5-21x

Step-by-step explanation:

6 0

2 years ago