Show two different ways to solve 1/4x-5=3/4x-12

Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive

NeX [460]

Answer:

(a) 0.343

(b) 0.657

(c) 0.189

(d) 0.216

(e) 0.353

Step-by-step explanation:

Let P(a vehicle passing the test) = p

$p = \frac{70}{100} = 0.7$

Let P(a vehicle not passing the test) = q

q = 1 - p

q = 1 - 0.7 = 0.3

(a) P(all of the next three vehicles inspected pass) = P(ppp)

= 0.7 × 0.7 × 0.7

= 0.343

(b) P(at least one of the next three inspected fails) = P(qpp or qqp or pqp or pqq or ppq or qpq or qqq)

= (0.3 × 0.7 × 0.7) + (0.3 × 0.3 × 0.7) + (0.7 × 0.3 × 0.7) + (0.7 × 0.3 × 0.3) + (0.7 × 0.7 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.3)

= 0.147 + 0.063 + 0.147 + 0.063 + 0.147 + 0.063 + 0.027

= 0.657

(c) P(exactly one of the next three inspected passes) = P(pqq or qpq or qqp)

= (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)

= 0.063 + 0.063 + 0.063

= 0.189

(d) P(at most one of the next three vehicles inspected passes) = P(pqq or qpq or qqp or qqq)

= (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7) + (0.3 × 0.3 × 0.3)

= 0.063 + 0.063 + 0.063 + 0.027

= 0.216

(e) Given that at least one of the next 3 vehicles passes inspection, what is the probability that all 3 pass (a conditional probability)?

P(at least one of the next three vehicles inspected passes) = P(ppp or ppq or pqp or qpp or pqq or qpq or qqp)

= (0.7 × 0.7 × 0.7) + (0.7 × 0.7 × 0.3) + (0.7 × 0.3 × 0.7) + (0.3 × 0.7 × 0.7) + (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)

= 0.343 + 0.147 + 0.147 + 0.147 + 0.063 + 0.063 + 0.063

= 0.973

With the condition that at least one of the next 3 vehicles passes inspection, the probability that all 3 pass is,

$= \frac{P(all\ of\ the\ next\ three\ vehicles\ inspected\ pass)}{P(at\ least\ one\ of\ the\ next\ three\ vehicles\ inspected\ passes)}$

$= \frac{0.343}{0.973}$

= 0.353

3 0

4 years ago

Read 2 more answers

Which of the following polygons is not a regular polygon?

Shkiper50 [21]

Answer:

b

Step-by-step explanation:

polygons is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit

6 0

3 years ago

A set of data already has the values 11, 14, 23, and 16. What value would have to be added to the set for the mean of the five n

KonstantinChe [14]

1) Take 18 and multiply it by 5 = 90
2) Then subtract 26 = 64
3) Then subtract 18 = 46
4) Then subtract 12 = 34
5) Then subtract 8 = 26

The answer is 26.

5 0

3 years ago

Ava has a dozen apples of the same size and a dozen watermelons of the same size. Ava uses her juicer to extract 14 ounces of wa

ExtremeBDS [4]

Answer:

85.9%

Step-by-step explanation:

We know that she has a dozen watermelons and apples each. Dozen = 12.

If we can get 14 ounces of watermelon juice from 2 watermelons, that means from 12 watermelons we can get 84 ounces.

12/2 = 6

14 x 6 = 84

If we can get 1 ounce of apple juice from 7 apples, that means from 12 apples we can get 11.9 ounces.

12/7 = 1.7

7 x 1.7 = 11.9

So, we are using an equal number of watermelons and apples. We are using 12 apples and 12 watermelons in this real life equation. The fraction would be: 84/11.9.

To solve the percent of how much watermelon juice is being used in the blend, we just need to:

Divide 84 from 11.9:

11.9/84 = 0.141

I am doing this way because I could not get 84/11.9 into a percent without it going over 100%. Next step is to multiply by 100.

0.141 x 100 = 14.1%

Next, subtract 100% from 14.1%.

100% - 14.1% = 85.9%

Therefore, the answer is 85.9%. I hope this helps.

I rethought this, so if it is asking for a percentage greater than 100, then here is my original answer (which did not make sense to me so i took a different route):

"We know that she has a dozen watermelons and apples each. Dozen = 12.

If we can get 14 ounces of watermelon juice from 2 watermelons, that means from 12 watermelons we can get 84 ounces.

12/2 = 6

14 x 6 = 84

If we can get 1 ounce of apple juice from 7 apples, that means from 12 apples we can get 11.9 ounces.

12/7 = 1.7

7 x 1.7 = 11.9

So, we are using an equal number of watermelons and apples. We are using 12 apples and 12 watermelons in this real life equation. The fraction would be: 84/11.9.

To solve the percent of how much watermelon juice is being used in the blend, we just need to:

Divide 84 from 11.9:

84/11.9 = 7.05

Multiply by 100:

7.05 x 100 = 705

Therefore, the answer is 705%. I have never seen a percentage over 100, but I hope this helps. "

3 0

2 years ago

Write equations for the horizontal and vertical lines passing through the point (8,5)

almond37 [142]

Answers:

Horizontal Line: y = 5

Vertical Line: x = 8

=================================================

Explanation:

All horizontal lines are of the form y = k, for some constant k. We want the horizontal line to pass through (8,5), meaning every point on this horizontal line must have y coordinate 5. Therefore, y = 5 is the equation of the horizontal line. Two such points on this line are (1, 5) and (8, 5). All that matters is the y coordinate is 5. The x coordinate can be anything you want. The slope of any horizontal line is 0.

Flipping things around, all vertical lines will have the x coordinate of each point be the same value. Draw a vertical line through (8,5) and note how each point has x coordinate of 8. Two such points are (8,1) and (8,5). Therefore, the equation of the vertical line is x = 8. The y coordinate can be any value you want. The slope of any vertical line is undefined. Unlike the horizontal line, we cannot write this equation in slope intercept form (namely because the slope isn't defined).

7 0

3 years ago