If 102y = 25, then 10-y equals: (a) -1/5, (b) 1/625, (c) 1/50, (d) 1/25, (e) 1/5

The volume of a cube is 8 cm'. find th

Usimov [2.4K]

Answer:

side length a = 2 cm

Step-by-step explanation:

side length a = 2 cm

face diagonal f = 2.8284271247462 cm

solid diagonal d = 3.4641016151378 cm

surface area S = 24 cm^2

volume V = 8 cm^3

8 0

4 years ago

Solve. 2x/21= 32/42 a. 8 b. 27.1 c. 32 d. 16

inna [77]

Answer:

a. 8

Step-by-step explanation:

hope this helps

4 0

3 years ago

Read 2 more answers

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. 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.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

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

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

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

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

Y=-3x+9 y=-x-5 what is the solution for the system of equations?

alexandr402 [8]

Our system of equations is:

y = -3x + 9

y = -x - 5

To solve this system of equations, we are going to use substitution. This means that we are going to substitute the second equation into the first equation since both are already solved for y in terms of x.

y = -3x + 9

-x - 5 = -3x + 9

Now, we must simplify by moving all of the constant terms to one side of the equation and all of the variable terms to the other side.

-x - 5 = -3x + 9

2x - 5 = 9

2x = 14

Finally, to undo the multiplication between the coefficient 2 and the variable x, we must divide both sides by 2 to get the variable x alone.

x = 7

Next, we must substitute in this value we have solved for x into one of the original equations to solve for the other variable, y.

y = -3x + 9

y = -3(7) + 9

To simplify, we must multiply through the parentheses and combine like terms by addition.

y = -21 + 9

y = -12

Therefore, your final answer is x = 7 and y = -12, or as an ordered pair (7, -12).

Hope this helps!

6 0

3 years ago

HELPPP ASAPPP!!!!!!!!!!

Veronika [31]

Answer:

c

Step-by-step explanation:

3 0

3 years ago