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3 years ago

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Calculate the volume of a rectangular prism with a length of 4.4 cmcm, a width of 3.1 cmcm, and a height of 6.3 cmcm. (As before

, you do not need to enter the units since they are provided to the right of the answer box.)

1 answer:

sergeinik [125]3 years ago

8 0

Answer: 85.93 cm³ .

Step-by-step explanation:

We know that the volume of the rectangular prism is given by :-

$V=\text{length x width x height}$

Given : A rectangular prism has

length =4.4 cm, width = 3.1 cm, and a= height =6.3 cm.

Then, the volume of the rectangular prism will be :

$V=4.4\times3.1\times6.3=85.932\approx85.93\ cm^3$

Hence, the volume of a rectangular prism is 85.93 cm³ .

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The perimeter of a rectangle is 34 units. Its width is 6.5 point, 5 units.

12345 [234]

<h3><u>Question:</u></h3>

The perimeter of a rectangle is 34 units. Its width W is 6.5 units.

Write an equation to represent the perimeter in terms of the length L, and find the value of L

<h3><u>Answer:</u></h3>

The length of rectangle is 10.5 units

<h3><u>Solution:</u></h3>

Given that,

Perimeter of rectangle = 34 units

Width of rectangle = 6.5 units

Let "L" be the length of rectangle

<em><u>The perimeter of rectangle is given by formula:</u></em>

Perimeter = 2(length + width)

<em><u>Substituting the values we get,</u></em>

$34 = 2(L + 6.5)$

Thus the equation is found

<em><u>Solve for "L"</u></em>

$L + 6.5 = \frac{34}{2}\\\\L + 6.5 = 17\\\\L = 17 - 6.5\\\\L =10.5$

Thus length of rectangle is 10.5 units

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3 years ago

After a bride has interviewed 7 DJs to play at her wedding, her fiance tells her she needs to narrow it down to 4 DJs. In how ma

Alex17521 [72]

Answer:

840

Step-by-step explanation:

Given

$DJs = 7$

$To\ pick = 4$

Required

Determine the number of rankings

The term "ranking" as used in this question implies permutation and the required is calculated using:

$^nP_r = \frac{n!}{(n-r)!}$

Where

$n = 7$

$r = 4$

So:

$^nP_r = \frac{n!}{(n-r)!}$

$^7P_4 = \frac{7!}{(7-4)!}$

$^7P_4 = \frac{7!}{3!}$

$^7P_4 = \frac{7 * 6 * 5 * 4 * 3!}{3!}$

$^7P_4 = 7 * 6 * 5 * 4$

$^7P_4 = 840$

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3 years ago

James trained for the Boston marathon for 3 1/2 hours every day how many hours did he train in the month of June?

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3 years ago

Please answer! I crossed out the ones you don’t have to complete.

Nina [5.8K]

Answer:

1. Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: $\mathbf{5^3a^2b^4c}$

5. $x^-6 = \frac{1}{x^6}$

6. $5^{-3}.3^{-1}=\frac{1}{5^3.3^1}$

7. $a^{-3}b^0c^4=\frac{c^4}{a^3}$

Step-by-step explanation:

Question 1:

We need to rewrite the expression using exponents

5.a.b.b.5.c.a.b.5.b

We will first combine the like terms

5.5.5.a.a.b.b.b.b.c

Now, if we have 5.5.5 we can write it in exponent as: $=5^{1+1+1}=5^3$

a.a as $a^{1+1}=a^2$

b.b.b.b as: $b^{1+1+1+1}=b^4$

So, our result will be:

$5^3a^2b^4c$

Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: $\mathbf{5^3a^2b^4c}$

Question:

Rewrite using positive exponent:

The rule used here will be: $a^{-1}=\frac{1}{a^1}$ which states that if we need to make exponent positive, we will take it to the denominator.

Applying thee above rule for getting the answers:

5) $x^{-6} = \frac{1}{x^6}$

6) $5^{-3}.3^{-1}=\frac{1}{5^3.3^1}$

7) $a^{-3}b^0c^4=\frac{b^0c^4}{a^3}$

We know that $b^0=1$ so, we get

$a^{-3}b^0c^4=\frac{b^0c^4}{a^3}=\frac{c^4}{a^3}$

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