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3 years ago

6

Tom is sorting cookies with his little sister Betty. He notices that when he takes a cookie she takes three cookies, when he tak

es two cookies she takes six, and so on. What type of relationship is there between their cookie-taking behaviors?

1 answer:

telo118 [61]3 years ago

3 0

T 1 2 3 4
B 3 6 9 12
This is linear relationships B=3*T (it can be also called directly proportional)

You might be interested in

The process standard deviation is 0.27, and the process control is set at plus or minus one standard deviation. Units with weigh

mr_godi [17]

Answer:

a) $P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.15}) = P(Z>1)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.159+0.159 = 0.318$

And the expected number of defective in a sample of 1000 units are:

$X= 0.318*1000= 318$

b) $P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.05}) = P(Z>3)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.00135+0.00135 = 0.0027$

And the expected number of defective in a sample of 1000 units are:

$X= 0.0027*1000= 2.7$

c) For this case the advantage is that we have less items that will be classified as defective

Step-by-step explanation:

Assuming this complete question: "Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. Calculate the probability of a defect and the expected number of defects for a 1000-unit production run in the following situation.

Part a

The process standard deviation is .15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,0.15)$

Where $\mu=10$ and $\sigma=0.15$

We can calculate the probability of being defective like this:

$P(X$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And if we replace we got:

$P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.15}) = P(Z>1)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.159+0.159 = 0.318$

And the expected number of defective in a sample of 1000 units are:

$X= 0.318*1000= 318$

Part b

Through process design improvements, the process standard deviation can be reduced to .05. Assume the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects.

$P(X$

And for the other case:

tex] P(X>10.15)[/tex]

$P(X>10.15)= P(Z > \frac{10.15-10}{0.05}) = P(Z>3)=1-P(Z$

So then the probability of being defective P(D) is given by:

$P(D) = 0.00135+0.00135 = 0.0027$

And the expected number of defective in a sample of 1000 units are:

$X= 0.0027*1000= 2.7$

Part c What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

For this case the advantage is that we have less items that will be classified as defective

5 0

2 years ago

What is the surface area of the prism in square inches?

Kay [80]

<u>Given</u>:

Given that the triangular prism with height 10 inches.

The side lengths of the base of the triangle are 12 inches, 13 inches and 5 inches.

We need to determine the surface area of the prism.

<u>Surface area of the prism:</u>

The surface area of the prism can be determined using the formula,

$SA=bh+(s_1+s_2+s_3)H$

where b is the base and h is the height of the triangle.

s₁, s₂, s₃ are the side lengths of the triangle and

H is the height of the prism.

Substituting b = 12, h = 5, s₁ = 12, s₂ = 5, s₃ = 13 and H = 10 in the above formula, we get;

$SA=(12)(5)+(12+5+13)(10)$

$SA=60+(30)(10)$

$SA=60+300$

$SA=360 \ in^2$

Thus, the surface area of the triangular prism is 360 square inches.

Hence, Option b is the correct answer.

8 0

3 years ago

-4x-2y=-12 <br>4x+8y=-24

sweet [91]

Answer:

x = 6

y = -6

Step-by-step explanation:

By adding both equations :-

=》-4x -2y + 4x + 8y = -12 + (-24)

=》-4x + 4x + 8y - 2y = -12 - 24

=》6y = -36

=》y = -36 ÷ 6

=》y = -6

putting the value of y in equation 2

=》4x + 8y = -24

=》4x + (8 × -6) = -24

=》4x - 48= -24

=》4x = 48 - 24

=》x = 24 / 4

=》x = 6

6 0

2 years ago

Read 2 more answers

There are 12 bags of apples on a market stall.

Mariana [72]

Answer:

The number of apples in the 12 bag is 96

Solution:

Given that, there are 12 bags of apples on a market stall.

The mean number of apples in each bag is 8.

We have to calculate the number of apples in the 12 bag.

The mean of "n" observations is given as:

Hence, there are 96 apples in 12 bags.

3 0

2 years ago

A teacher writes an inequality x divided by 6 < -2 on the board. Vincent incorrectly solves the inequality and obtains x <

scZoUnD [109]

The error Vincent made was that he only multiplied the left side of the inequality with 6 although he had to multiply on both sides

Step-by-step explanation:

Given inequality that the teacher wrote is:

$\frac{x}{6} -2$

Solving an inequality means that the variable should be isolated on left side of the inequality.

So multiplying both sides by 6

$6* \frac{2}{6} < -2 * 6\\x < -12$

Vincent got the answer is x<-2 = > The error Vincent made was that he only multiplied the left side of the inequality with 6 although he had to multiply on both sides

Keywords: Inequality, solution

Learn more about inequalities at:

#LearnwithBrainly

4 0

3 years ago