According to the number line, what is the distance between points A and B? 6 units 7 units 12 units 14 units

What is the slope of any line parallel to line containing (-5,2)&(1,8)

borishaifa [10]

Slope = (8 -2) / (1 + 5) =6/6 = 1

Parallel lines, slope is the same

So the slope of any line parallel to the line containing (-5,2) & (1,8) is also equal 1

7 0

2 years ago

The manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.8

Ber [7]

Answer:

0.85

Step-by-step explanation:

Given two events A and B, the probability that either A or B occurs is given by:

$p(A\cup B) = p(A)+p(B)-p(A\cap B)$

where

$p(A)$ the probability that A occurs

$p(B)$ is the probability that B occurs

$p(A\cap B)$ is the probability that both A and B occur at the same time

In this problem, we know the following facts:

$p(o) = 0.83$ is the probability that the car requires an oil change

$p(b)=0.17$ is the probability that the car requires a brake repair

$p(o\cap b) = 0.15$ is the probability that the car requires both an oil change and brake repair

Therefore, the probability that either o (car requiring oil change) or b (car requiring brake repait) occur is:

$p(o\cup b)=p(o)+p(b)-p(o\cap b)=0.83+0.17-0.15 = 0.85$

4 0

3 years ago

Write a polynomial function in standard form with zeros at −3, −1, and 1.

Annette [7]

Answer:

$f(x) = {x}^{3} + 3 {x}^{2} - x -3$

Step-by-step explanation:

The given polynomial has zeros at:

x=−3, x=−1, and x=1.

This means that:

x+3, x+1, and x-1 are all factors of this polynomial.

The factored form of this polynomial is :

$f(x) = (x + 3)(x + 1)(x - 1)$

We expand the last two factors using difference of two squares.

$f(x) = (x + 3)( {x}^{2} - 1)$

$f(x) = x ( {x}^{2} - 1) + 3( {x}^{2} - 1)$

$f(x) = {x}^{3} - x+ 3 {x}^{2} -3$

$f(x) = {x}^{3} + 3 {x}^{2} - x -3$

This is the standard form because it is now in decreasing powers of x.

8 0

3 years ago

I totally blanked and forgot how to do this. Can anyone help

neonofarm [45]

Answer:

The answer is 82 unit total

Step-by-step explanation:

You can take the entire shape and break it down to normal shapes such as squares and triangles. Then you can use the formula of these shapes to find the area. Last you add all the unit together and that's the answer

8 0

3 years ago

Read 2 more answers

Suppose on a certain planet that a rare substance known as Raritanium can be found in some of the rocks. A raritanium-detector i

aleksandrvk [35]

Answer:

0.967 = 96.7% probability the rock sample actually contains raritanium

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive reading

Event B: Contains raritanium

Probability of a positive reading:

98% of 13%(positive when there is raritanium).

0.5% of 100-13 = 87%(false positive, positive when there is no raritanium). So

$P(A) = 0.98*0.13 + 0.005*0.87 = 0.13175$

Positive when there is raritanium:

98% of 13%

$P(A) = 0.98*0.13 = 0.1274$

What is the probability the rock sample actually contains raritanium?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1274}{0.13175} = 0.967$

0.967 = 96.7% probability the rock sample actually contains raritanium

7 0

2 years ago