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3 years ago

Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?

1 answer:

7 0

To determine the equation of the line using two points, calculate first the slope with the equation,
m = (y2 - y1)/ (x2 - x1)
In this given,
m = (7 - 1)/ (2 - 0) = 3

Use the point-slope form of the equation where,

y - y2 = m (x - x2)

y - 7 = 3 (x - 2), y = 3x + 1

Thus, the equation of the line is y = 3x + 1

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Debras fish tank 16 liters of water in it. She plans to add 4 liters per minute until the tank has more than 60 liters. What are

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Debras fish tank 16 liters which mean she have 80 liter

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3 years ago

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 $n = 20$

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

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

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

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

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

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

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

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

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 $n = 22$

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

The closest integer to 16.5 is 17.

7 0

3 years ago

If Earth was 10 times farther away from the Sun than it is now, which planet would it be closest to? Compare Earth's new distanc

Phoenix [80]

You need the radius of all the orbits
earth radius is 150 million km
1. 150 million x 10 = 1500 million
From the website below Saturn would be the closest at 1,429 million km
1,500,000,000 - 1,429,000,000 = 71,000,000 km = 7.1 * 10^7 km
I hope this helps :D

8 0

3 years ago

SOME ONE PLS HELP ME ASAP OP THE TEACHER CALLED ON ME AND SHE SAID THAT I HAVE 5 MINS TO FIGURE THIS OUT

ZanzabumX [31]

Answer:

a F

Step-by-step explanation:

Normally when converting to scientific notation, I would count how many digits I have to move the decimal dot to get it in between the number, in this case, 36.

If you start shifting the decimal dot to the right and count one every time you shift one digit and go all the way to between 3 and 6, you would count to 5. Since you are shifting to the right, the power of the 10 should be negative. Thus, the answer should be 3.6 × 10 $^{-5}$ which is F.

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3 years ago

Read 2 more answers

1. BOTANICAL GARDENS One of the displays at a botanical garden is an herb garden planted in the shape of a square. The square me

bija089 [108]

The pathway is 8.46 yards.

<h3>How to find the length of the pathway?</h3>

To find the length of the pathway, it is required to find how long is the diagonal line from one corner of the herb garden to the opposite corner. As shown in the image attached.

The general formula for this is:

d = a√2 or diagonal = side√2

Let's apply this formula:

d= 6 √2
d= 6 x 1.41
d= 8.46 yards

Learn more about yards in: brainly.com/question/14516546

4 0

2 years ago