Two actors were rated by 11 casting directors on their audition performance.

A system of inequalities is graphed below. The variable x represents the number of cans someone is buying, and y represents the

8090 [49]

We have that
<span>We will analyze each case to verify the answer
see the attached figure

</span>Point A) 7 cans and 140 bottles------------> (x,y)=(7,140)----> is not solution
Point B) 12 cans and 40 bottles------------> (x,y)=(12,40)----> is not solution
Point C) 8 cans and 120 bottles------------> (x,y)=(8,120)----> is a solution
Point D) 9 cans and 70 bottles------------> (x,y)=(9,70)-------> is a solution

the answer is
the solutions are
<span>8 cans and 120 bottles
9 cans and 70 bottles</span>

6 0

3 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviat

dimulka [17.4K]

As per the concept of normal distribution, the two diameters of the bolt that has separate the top 3% and the bottom 3% are 5.2836 mm and 5.0764 mm respectively .

Normal distribution:

Normal distribution means the 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 and it has the bell shaped curve.

Given,

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviation of 0.07 millimeters.

Here we need to find the two diameters that separate the top 3% and the bottom 3% and these diameters could serve as limits used to identify which bolts should be rejected. we have also round off the result into nearest hundredth.

Here we have the given question with the values of,

The value of Mean is 5.18 millimeters

The value of Standard deviation is 0.07 millimeters.

Here we have to consider the following two cases, they are.

Case 1

We need to find x₁ such that that is P(X > x₁) = 3% when we convert it into decimal then we get P (X > x₁) = 0.03

So, as per the probability,

P (X ≤ x₁) = 1 - 0.03 = 0.97

So, z corresponding to the value of p = 0.97 is 1.48

Apply the given values to the formula of normal distribution then we get,

=> 1.48 = (x₁ - 5.18) /0.07

=> 0.1036 = x₁ - 5.18

Therefore, the value of x₁ is 5.2836

So, the diameter of the both with separate top 3% is 5.2836.

Case 2:

Next we have to take P(X < x₂) = 3% when we convert it into decimal then we get P (X < x₂) = 0.03

So, as per the given probability, the value of

P (X ≤ x₂) = 1 - 0.03 = 0.97

So, z corresponding to but here we have to use the negative because of the less than concept p = 0.97 is -1.48

Apply the values on the formula of normal distribution then we get,

-1.48 = (x₂ - 5.18) /0.07

Move the value to the other side

-0.1036 = x₂ - 5.18

When we simplify it,

x₂ = 5.0764

So, the diameter of the both with separate bottom 3% is 5.0764

To know more about Normal distribution here.

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7 0

1 year ago

Can someone help me ?

prisoha [69]

I’m pretty sure there are infinite solutions as the system of equations are equivalent to each other.

7 0

3 years ago

Read 2 more answers

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with ea

Delicious77 [7]

Answer:

32000000000 bytes are in 32 gigabytes.

Step-by-step explanation:

1e+9 * 32 = 32000000000

7 0

2 years ago

Read 2 more answers

The art teacher has 30 boxes of crayons with 16 cans in each box she gives the students 10 of the boxes to use explain how to fi

Mamont248 [21]

I'm going to assume you meant crayon instead of can:

First step is to find how many boxes she/he has left.

30 - 10 = 20

So the teacher has 20 boxes left;

Now, knowing that each box has 16 crayons, then we simply multiply the 20 by 16 to find the total number of crayons left over:

20 x 16 = 320

So the art teacher has 320 crayons left over.

Hope this helps!

3 0

3 years ago