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2 years ago

11

An advertising agency notices that approximately 1 in 50 potential buyers of a product sees a given magazine ad, and 1 in 8 sees

a corresponding ad on television. One in 100 sees both. One in 4 actually purchases the product after seeing the ad, 1 in 10 without seeing it. What is the probability that a randomly selected potential customer will purchase the product

1 answer:

zheka24 [161]2 years ago

7 0

Answer:

Probability = 0.12025

Step-by-step explanation:

P (Am) = 1/50 = 0.02 {Magazine ad}

P (At) = 1/8 = 0.125 {Television ad}

P (Am ∩ At ) = 1/100 = 0.01 {Both ads}

P (Am U At) = P (Am) + P (At) - P (Am ∩ At )

= 0.02 + 0.125 - 0.01

P (Am U At) = 0.135 {Person sees either ad}

P (Am' ∩ At') = 1 - P (Am U At)

P (Am' ∩ At') = 1 - 0.135 = 0.865 {Person sees none ad}

Prob (Purchase) = Prob (Purchase with ad) + Prob (purchase without ad)

P (P/ A) = 1/4 = 0.25 , P (P / A') = 1/10 = 0.1

P (P) = (0.25) (0.135) + (0.1) (0.865)

= 0.03375 + 0.0865

0.12025

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Find the slope of the line that passes through (-37, 47) and (26, 32).

stiks02 [169]

(x1,y1) = (-37,47)
(x2,y2) = (26,32)

Now, m = (47-32) / (26+37)
m = 15 / 63
m = 5/21
So, the slope would be 5/21

Hope this helps!

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2 years ago

The employees of a firm that manufactures insulation are being tested for indications of asbestos in their lungs. The firm is re

balandron [24]

Answer:

0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.

Step-by-step explanation:

For each employee, there are only two possible outcomes. Either they test positive, or they do not. The probability of an employee testing positive is independent of any other employee, which means that the binomial probability distribution is used 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.

40% of the employees have positive indications of asbestos in their lungs

This means that $p = 0.4$

Find the probability that fifteen employees must be tested in order to find three positives.

2 during the first 14(given by P(X = 2) when n = 14).

The 15th is positive, with 0.4 probability. So

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

$P(X = 2) = C_{14,2}.(0.4)^{2}.(0.6)^{12} = 0.0317$

0.0317*0.4 = 0.013.

0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.

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2 years ago

5. Three people are planting tomatoes in a community garden. Marta takes

SCORPION-xisa [38]

The time it will take for Tyler to finish planting tomatoes alone is; 75 minutes

<h3>Understanding Work Proportion</h3>

We are told that three people are planting tomatoes in a community garden. The time each alone takes to plant are;

Marta = 50 minutes

Benito = x minutes

Tyler = x + 15 minutes

Thus, their individual rates are;

Marta = 1/50

Benito = 1/x

Tyler = 1/(x + 15)

Since together, they take 20 minutes, then it means that;

1/50 + 1/x + 1/(x + 15) = 1/20

Multiply through by x(x + 15) to get;

(x² + 15x)/50 + (x + 15) + x = (x² + 15x)/20

Multiply through by 100 to get;

2(x² + 15x) + 100(x + 15) + 100x = 5(x² + 15x)

100x + 1500 + 100x = 5(x² + 15x) - 2(x² + 15x)

200x + 1600 = 3x² + 45x

3x² - 155x - 1600 = 0

Solving this using quadratic formula calculator online gives;

x ≈ 60

Thus, the time it will take tyler alone to finish is;

60 + 15 = 75 minutes

Read more about Work Proportion at; brainly.com/question/1781657

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2 years ago

The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televis

Shalnov [3]

Answer:

The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.

Step-by-step explanation:

35-inch television is a television whose screen has an hypotenuse ( $l$ ) of 35 inches and the aspect ratio of 4 : 3 means that 4 inches width per each 3 inches height. And by Pythagorean Theorem:

$r_{l} =\sqrt{r_{w}^{2}+r_{h}^{2}}$

Where:

$r_{l}$ - Hypotenuse rate, dimensionless.

$r_{w}$ - Width rate, dimensionless.

$r_{h}$ - Height rate, dimensionless.

If $r_{w} = 4\,in$ and $r_{h} = 3\,in$ , the hypotenuse rate is:

$r_{l} = \sqrt{4^{2}+3^{2}}$

$r_{l} = 5$

The width and height of the old television can be found with the help of trigonometric functions:

Width of 35-inch old television ( $w$ )

$w = l\cdot \cos \theta$

$w = l\times\left(\frac{r_{w}}{r_{l}} \right)$

Height of 35-inch old television ( $h$ )

$h = l\cdot \sin \theta$

$h = l\times\left(\frac{r_{h}}{r_{l}} \right)$

Where $\theta$ is the direction of the hypotenuse with respect to width, measured in sexagesimal degrees.

If $r_{w} = 4$ , $r_{h} = 3$ and $r_{l} = 5$ and $l = 35\,in$ , the width and height of the old 35-inch television:

$w = (35\,in)\times \left(\frac{4}{5} \right)$

$w = 28\,in$

$h =(35\,in)\times \left(\frac{3}{5} \right)$

$h = 21\,in$

The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.

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3 years ago

What is the volume of this<br> pyramid?

babunello [35]

Answer:

There is not pictutre.

Step-by-step explanation:

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3 years ago