What ratio can be used to calculate the geometric mean of 6 and 42?

If you place a 24-foot ladder against the top of a 20-foot building, how many feet will the bottom of the ladder be from the bot

LenKa [72]

Answer:

13.3 ft

Step-by-step explanation:

24² - 20² = d²

d = √(576 - 400) = √176 = 13.26649... ≈ 13.3 ft.

6 0

2 years ago

Which of the following is a step in simplifying the expression x multiplied by y to the power of 2 over x to the power of negati

Nat2105 [25]

The simplest form of the algebraic expression is x^-4y^-8/x^12y^-12 (Option B)

<h3>What is simplification?</h3>

The term simplification is mathematics refers to the depiction of the expression in its lowest possible format. In the simplest form, the expression can not be simplified further.

Now we have the original expression as;

(xy^2/x^-3y^3)

The only possible step in the expansion is to open up the bracket by the laws of indices and we get;

x^-4y^-8/x^12y^-12 (Option B)

Learn more about algebraic expression:brainly.com/question/953809

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6 0

2 years ago

one-third of the people from country A claim that they are from country B, and the rest admit they are from country A. One-fourt

In-s [12.5K]

Answer: 3 : 2

Step-by-step explanation:

Let A represents the total population of country A and B represents the total population of country B.

According to the question,

$\text{The population of country A that admit they are from B} = \frac{1}{3}\text{ of }A$

⇒ $\text{ The population of A that admit they are from country A }= A - \frac{1}{3} \text{ of } A$

$= \frac{3-1}{3} A$

$= \frac{2}{3} A$

$\text{The population of country B that admit they are from A} = \frac{1}{4}\text{ of }B$

⇒ $\text{ The total population that claims that they are from A }= \frac{2}{3} A +\frac{1}{4} B$

But, Again according to the question,

The total population that claims that they are from A = one half of the total population of A and B.

⇒ $\frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}(A+B)$

⇒ $\frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}A+\frac{1}{2}B$

⇒ $\frac{2}{3} A - \frac{1}{2}A= \frac{1}{2}B-\frac{1}{4} B$

⇒ $\frac{4}{6} A - \frac{3}{6}A= \frac{2}{4}B-\frac{1}{4} B$

⇒ $\frac{1}{6} A = \frac{1}{4} B$

⇒ $A =\frac{6}{4}B$

⇒ $\frac{A}{B} =\frac{3}{2}$

8 0

3 years ago

Assume the random variable x has a binomial distribution with the given probability of obtaining a success. Find the following.

borishaifa [10]

Answer:

P(x > 10) = 0.6981.

Step-by-step explanation:

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.

In this question:

$n = 14, p = 0.8$

P(x>10)

$P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)$

In which

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

$P(X = 11) = C_{14,11}.(0.8)^{11}.(0.2)^{3} = 0.2501$

$P(X = 12) = C_{14,12}.(0.8)^{12}.(0.2)^{2} = 0.2501$

$P(X = 13) = C_{14,13}.(0.8)^{13}.(0.2)^{1} = 0.1539$

$P(X = 14) = C_{14,14}.(0.8)^{14}.(0.2)^{0} = 0.0440$

$P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.2501 + 0.2501 + 0.1539 + 0.0440 = 0.6981$

So P(x > 10) = 0.6981.

8 0

3 years ago

Decimals equivalent to 7/18

gayaneshka [121]

Answer:

0.388888...

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers