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2 years ago

An aquarium holds 11.1 cubic feet of water and is 2.8 feet long and is 1.2 feet wide.what is the depth?

Mathematics

1 answer:

just olya [345]2 years ago

8 0

Step-by-step explanation:

the volume of any cube or prism is

length × width × height (or depth)

11.1 = 2.8 × 1.2 × depth

depth = 11.1 / (2.8 × 1.2) = 11.1 / 3.36 = 3.303571429 ft

≈ 3.3 ft

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P^-7 divided by q^-8

UkoKoshka [18]

Answer:

q^8/p^7

Step-by-step explanation:

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8 0

3 years ago

Select the solid whose cross sections are dilations of some two-dimensional shape using a point directly above the shape as a ce

s2008m [1.1K]

Answer:

Cone

Step-by-step explanation:

Options:

a) Cone b) Cube c) Cylinder d) Triangular prism

From the given options (a) to (d), option (a) is true.

This is so, because.

The volume (V) of a cone is:

$V_1 = \frac{1}{3}\pi r^2h$

This is as a result of dilating the cylinder by 1/3 whose volume is:

$V_2 = \pi r^2h$

In other words:

$V_1 = \frac{1}{3}V_2$

i.e. the cross-section of the cylinder (V2) being dilated by 1/3 (which is between 0 and 1) gives the cone (V1)

6 0

3 years ago

The proportion of high school seniors who are married is 0.02. Suppose we take a random sample of 300 high school seniors; a.) F

cricket20 [7]

Answer:

a) Mean 6, standard deviation 2.42

b) 10.40% probability that, in our sample of 300, we find that 8 of the seniors are married.

c) 14.85% probability that we find less than 4 of the seniors are married.

d) 99.77% probability that we find at least 1 of the seniors are married

Step-by-step explanation:

For each high school senior, there are only two possible outcomes. Either they are married, or they are not. The probability of a high school senior being married is independent from other high school seniors. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In this problem, we have that:

$n = 300, p = 0.02$

a.) Find the mean and standard deviation of the sample count X who are married.

Mean

$E(X) = np = 300*0.02 = 6$

Standard deviation

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.02*0.98} = 2.42$

b.) What is the probability that, in our sample of 300, we find that 8 of the seniors are married?

This is P(X = 8).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{300,8}.(0.02)^{8}.(0.98)^{292} = 0.1040$

10.40% probability that, in our sample of 300, we find that 8 of the seniors are married.

c.) What is the probability that we find less than 4 of the seniors are married?

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{300,0}.(0.02)^{0}.(0.98)^{300} = 0.0023$

$P(X = 1) = C_{300,1}.(0.02)^{1}.(0.98)^{299} = 0.0143$

$P(X = 2) = C_{300,2}.(0.02)^{2}.(0.98)^{298} = 0.0436$

$P(X = 3) = C_{300,3}.(0.02)^{3}.(0.98)^{297} = 0.0883$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0023 + 0.0143 + 0.0436 + 0.0883 = 0.1485$

14.85% probability that we find less than 4 of the seniors are married.

d.) What is the probability that we find at least 1 of the seniors are married?

Either no seniors are married, or at least 1 one is. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

From c), we have that $P(X = 0) = 0.0023$ . So

$0.0023 + P(X \geq 1) = 1$

$P(X \geq 1) = 0.9977$

99.77% probability that we find at least 1 of the seniors are married

3 0

3 years ago

Please help ASAP !!!

Ket [755]

I think B..............

6 0

3 years ago

In 2000, the world population 6.08 billion and was increasing at a rate of 1.5% each year.

serg [7]

Answer:

7.8 billion

Step-by-step explanation:

Given:

Initial population = 6.08 billion
Increase rate = 1.5% or 0.015 times per year

Time passed = 2017 - 2000 = 17 years

Population in 2017:

P = 6.08*(1 + 0.015)^17 = 7.8 billion

5 0

3 years ago