2

A factory received a shipment of 11 hammers, and the vendor who sold the items knows there are 2 hammers in the shipment that ar

zhenek [66]

Question:

If a sample of 2 hammer is selected

(a) find the probability that all in the sample are defective.

(b) find the probability that none in the sample are defective.

Answer:

a $Pr = \frac{2}{110}$

b $Pr = \frac{72}{110}$

Step-by-step explanation:

Given

$n = 11$ --- hammers

$r = 2$ --- selection

This will be treated as selection without replacement. So, 1 will be subtracted from subsequent probabilities

Solving (a): Probability that both selection are defective.

For two selections, the probability that all are defective is:

$Pr = P(D) * P(D)$

$Pr = \frac{2}{11} * \frac{2-1}{11-1}$

$Pr = \frac{2}{11} * \frac{1}{10}$

$Pr = \frac{2}{110}$

Solving (b): Probability that none are defective.

The probability that a selection is not defective is:

$P(D') = \frac{9}{11}$

For two selections, the probability that all are not defective is:

$Pr = P(D') * P(D')$

$Pr = \frac{9}{11} * \frac{9-1}{11-1}$

$Pr = \frac{9}{11} * \frac{8}{10}$

$Pr = \frac{72}{110}$

8 0

3 years ago

How would you best describe the two students outside the circles?

ruslelena [56]

Answer:

A. They are boys who are not in sixth grade and don't wear glasses.

Explanation:

5 0

3 years ago

Give an example of a point that is the same distance from (3, 0) as it is from (7, 0). Find lots of examples. Describe the confi

Artist 52 [7]

Supposse that the distance from the point $(x,y)$ to the point $(3,0)$ is equal to the distance from $(x,y)$ to the point $(7,0)$ . Then, by the formula of the distnace we must have

$\sqrt{(x-3)^2 + (y-0)^2}=\sqrt{(x-7)^2 + (y-0)^2}$

cancel the square root and the $(y-0)^2$ 's, and then expand the parenthesis to obtain

$x^2 - 6x + 9 = x^2 - 14x + 49$

then, simplifying we obtain

$8x = 40$

therfore we must have

$x=5$

this means that the points satisfying the propertie must have first component equal to 5. So we can give a lot of examples of such points: $(5,0), (5,7),(5,1/2), (5,-10),...$ . The set of this points give us a straight line and the points (3,0) and (7,0) are symmetric with respect to this line.

3 0

3 years ago

Liquid A and liquid B are mixed to make liquid C.

natta225 [31]

Answer:

Density is defined as:

Density = mass/volume.

We know that:

For liquid A:

Density = 70kg/m^3

Mass = 1400kg

Then the volume is:

Volume = mass/density = (1400kg)/(70kg/m^3) = 20 m^3

For liquid B:

Density = 280 kg/m^3

Volume = 30m^3

We can find the mass of liquid B as:

mass = density*volume = (280kg/m^3)*(30m^3) = 8400 kg

We know that liquid C is a mixture of liquid A and B.

Then the mass of liquid C will be equal to the sum of the masses of liquid A and B, then:

Mass of liquid C = 1400kg + 8400kg = 9800kg

The same happens for the volume, then:

Volume of liquid C = 30m^3 + 20m^3 = 50m^3

Then the density of liquid C is:

Density of liquid C = (9800kg)/(50m^3) = 196 kg/m^3

6 0

3 years ago

What number must you add to complete the square?<br><br> x^2-10x=46

gtnhenbr [62]

X² - 10x = 46
10/2 = 5; 5²+ 25 add 25 to both sides

x² - 10x + 25 = 46 + 25

so the number you have to add to complete the square is 25.

5 0

3 years ago