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3 years ago

1. What is the volume for the following rectangular prism?

Mathematics

1 answer:

____ [38]3 years ago

8 0

Answer:

2. c) 1050 mm³

3. c) 8 yards.

Step-by-step explanation:

Given the following data;

Length = 25mm

Width = 7 mm

Height = 6 mm

To find the volume of the rectangular prism;

Volume of rectangular prism = base area * height

First of all, we would determine the base area;

Base area = length * width

Base area = 25 * 7

Base area = 175 mm²

Next, we find the volume;

Volume of rectangular prism = 175 * 6

Volume of rectangular prism = 1050 mm³

Question 2.

Given the following data;

Length = 9 yards

Width = 7.5 yards

Volume = 540 cubic yards

To find the height of the rectangular prism, x;

Volume of rectangular prism = length * width * height

540 = 9 * 7.5 * x

540 = 67.5x

x = 540/67.5

Height, x = 8 yards

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Veronika [31]

Answer:

The probability that you lose at most 2 out of your 6 races is 0.54432.

Step-by-step explanation:

We are given that you are running a race. The probability that you win is 3/5.

There are total of 6 races.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6 races

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you lose a race = 1 - (3/5) = 2/5 or 0.4

Let X = Number of races lost

So, X ~ Binom(n = 6, p = 0.40)

Now, the probability that you lose at most 2 out of your 6 races is given by = P(X $\leq$ 2)

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{6}{0} \times 0.40^{0} \times (1-0.40)^{6-0} + \binom{6}{1} \times 0.40^{1} \times (1-0.40)^{6-1} + \binom{6}{2} \times 0.40^{2} \times (1-0.40)^{6-2}$

= $1 \times1 \times 0.60^{6} + 6 \times 0.40^{1} \times 0.60^{5} +15\times 0.40^{2} \times 0.60^{4}$

= 0.54432

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3 years ago