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lara31 [8.8K]
3 years ago
6

Ambria received flowers for Valentine's Day that were in a vase shaped like a rectangular prism. If the vase measured 12 inches

long, 6 inches wide, and 10 inches high and was filled with water 4 inches from the top, what is the volume of the water that will be in the vase?
Mathematics
1 answer:
ziro4ka [17]3 years ago
5 0

Answer: 432\ in.^3

Step-by-step explanation:

Given

The dimension of a rectangular prism is 12\times 6\times 10\ in.^3

Water is filled 4\ in. from the top i.e. 10-4=6\ in. high

base area for the water is the same i.e.  12\ in.\times 6\ in.

The volume of rectangular prism is l\times b\times h

The volume of water in the vase is given by

\Rightarrow V=12\times 6\times 6=432\ in.^3

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Step-by-step explanation:

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Read 2 more answers
15. Suppose a box of 30 light bulbs contains 4 defective ones. If 5 bulbs are to be removed out of the box.
Naddika [18.5K]

Answer:

1) Probability that all five are good = 0.46

2) P(at most 2 defective) = 0.99

3) Pr(at least 1 defective) = 0.54

Step-by-step explanation:

The total number of bulbs = 30

Number of defective bulbs = 4

Number of good bulbs = 30 - 4 = 26

Number of ways of selecting 5 bulbs from 30 bulbs = 30C5 = \frac{30 !}{(30-5)!5!} \\

30C5 = 142506 ways

Number of ways of selecting 5 good bulbs  from 26 bulbs = 26C5 = \frac{26 !}{(26-5)!5!} \\

26C5 = 65780 ways

Probability that all five are good = 65780/142506

Probability that all five are good = 0.46

2) probability that at most two bulbs are defective = Pr(no defective) + Pr(1 defective) + Pr(2 defective)

Pr(no defective) has been calculated above = 0.46

Pr(1 defective) = \frac{26C4  * 4C1}{30C5}

Pr(1 defective) = (14950*4)/142506

Pr(1 defective) =0.42

Pr(2 defective) =  \frac{26C3  * 4C2}{30C5}

Pr(2 defective) = (2600 *6)/142506

Pr(2 defective) = 0.11

P(at most 2 defective) = 0.46 + 0.42 + 0.11

P(at most 2 defective) = 0.99

3) Probability that at least one bulb is defective = Pr(1 defective) +  Pr(2 defective) +  Pr(3 defective) +  Pr(4 defective)

Pr(1 defective) =0.42

Pr(2 defective) = 0.11

Pr(3 defective) =  \frac{26C2  * 4C3}{30C5}

Pr(3 defective) = 0.009

Pr(4 defective) =  \frac{26C1  * 4C4}{30C5}

Pr(4 defective) = 0.00018

Pr(at least 1 defective) = 0.42 + 0.11 + 0.009 + 0.00018

Pr(at least 1 defective) = 0.54

3 0
3 years ago
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Degger [83]

Answer:

Step-by-step explanation:

\frac{320-160}{40}=\frac{160}{40}=4

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3 years ago
Determine whether the triangles are congruent. Explain your reasoning .
Nookie1986 [14]

Answer:

Step-by-step explanation:

First use the fact that the sum of interior angles of a triangle is 180° to find the measure of the missing angle

in ΔDEF we have 180 -68 -81 = 31°

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the measure of the angles in ΔABC and ΔDEF are different 33°, 68°, 79° ≠81°, 68°, 31°so the two triangles are not congruent.

6 0
3 years ago
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