Steven has a small business that provides computer application training and data entry support services. He earns $25 per hour for training and $15 per hour for data entry support. Steven can work no more than 40 hours a week. He wants to use linear programming techniques to optimize his income. Part A Construct a model to represent the amount of time Steven can spend on data entry and training. Be sure to define your variables.
Sketch a graph of your model.

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that [tex]\mu = 8, \sigma = 1.1[/tex]

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

[tex]n = 5[/tex] means that [tex]s = \frac{1.1}{\sqrt{5}} = 0.4919[/tex]

This probability is the pvalue of Z when X = 9.3. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{9.3 - 8}{0.4919}[/tex]

[tex]Z = 2.64[/tex]

[tex]Z = 2.64[/tex] has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

[tex]n = 6[/tex] means that [tex]s = \frac{1.1}{\sqrt{6}} = 0.4491[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 9. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{9 - 8}{0.4491}[/tex]

[tex]Z = 2.23[/tex]

[tex]Z = 2.23[/tex] has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

Answer:

y=-1/2x+5/2

Step-by-step explanation:

y-4=-1/2(x-(-3))

y-4=-1/2(x+3)

y-4=-1/2x-3/2

y=-1/2x-3/2+4

y=-1/2x+5/2

Answer:

A C & D

Step-step explanation:

Answer:

83 dz

Step-by-step explanation:

yeahlets bbzkalaamN

Answer:

Area = 80 units²

Step-by-step explanation:

Given that:

a = 19 units

b = 9 units

c = 97°

Find the area of the triangle!

Area = ab(sin(c))/2

Area = [19×9×(sin(97))]/2

Area = 84.86 units²

Area = 80 units² ✅

______________

#IndonesianPride

- kexcvi -

Answer:

4a) The sides are not scaled up equally for the sides. Plus, B is not a right triangle since it does not satisfy the pythogorean theorem.

4b) 6, 8, 10

Answer:

12 / 5 gallons

Step-by-step explanation:

Answer:

y=16/15x-11/3

Step-by-step explanation:

(9--7)/(5--10)

slope = 16/15

y=16/15(x)+b

-9=(16/15)(-5)+b

b=-11/3

Answer:

200

Step-by-step explanation:

I rounded both numbers and multiplayer them.

Answer:

[tex]941 in^{3}[/tex]

Step-by-step explanation:

Answer:

x = 48 (in degrees, I assume)

Step-by-step explanation:

Note that the two horizontal lines have those extra arrowheads on them? The red ones? That notation means those lines are parallel to each other.

In geometry, we learn that when two parallel lines are crossed by a third line (called a 'transversal'), alternate interior angles are congruent.

The two angles with labeled quantities are alternate exterior angles. They are 'alternate' because they are on opposite sides of the transversal line, and 'exterior' because they are above and below the the two horizontal lines, not contained in the interior area between them.

Therefore,       2x + 2 = x + 50

                         -x - 2 = -x -  2

                          x       =    48

Answer:

12.5%

Step-by-step explanation:

Given that,

Initial temperature of a piece of metal = 32°C

Final temperature of the piece of metal = 36°С

We need to find the percentage increase in the temperature of the piece of metal.​ The percentage increase in any value is given by the relation as follows :

[tex]\%=\dfrac{|\text{final value-initial value}|}{\text{initial value}}\times 100\\\\=\dfrac{36-32}{32}\times 100\\\\=12.5\%[/tex]

So, the required percentage increase in the temperature of the piece of metal is equal to 12.5%.

Answer:

attachment plz

Step-by-step explanation:

nothing is being seen

Answer:

{-2, 3, 4, 5}

General Formulas and Concepts:

Math

Algebra I

Step-by-step explanation:

According to our graph, our y-values are 3, 4, 5 and -2. Since they are all closed dots, they are inclusive in the range:

Remember to put it in number line order.

{-2, 3, 4, 5}

Answer: b

Step-by-step explanation: I am 95% sure

Answer:

3.05kilograms to grams

Answer: it’s graph D

:)

Answer: C

Step-by-step explanation:

1 pound is equivalent to 16 ounces. She earned 2 pounds in 1 month, meaning that you have to multiply 16 times 2, which gives 32 ounces. Hope this can help you! Have a great day/night!

Answer:

$365

Step-by-step explanation:

did the math

The formula for the sum of the interior angles of a polygon is (n - 2) * 180. In this formula, N is the number of sides. So, to find the number of sides that a polygon with an interior angle measure of 10080 has, we'll set the formula equal to 10080.

10080 = (n - 2) * 180

Divide both sides by 180

56 = n - 2

Add 2 to both sides

n = 58

Hope this helps!! :)

Answer:

58 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is 10,080°

n = the number of sides

(2n - 4)90 = 10080

2n - 4 = 10080/90 = 112

2n = 116

n = 58.

Answer:

8 bananas

Step-by-step explanation:

4 dozen is equal to 48 and 180 divided by 48 is 3.75 then 30 divided by 3.75 is 8

Answer:

Step-by-step explanation:

From the picture attached,

Segment AB has been divided into four equal parts.

Let each part measures equal length = 1 unit

Point C is 2 units apart from both the points A and B.

Length of AC = Length of BC = 2 units

Therefore, point C will be the mid point of segment AB.

And ratio of AC and BC = 1:1

AC:BC = 1:1

Similarly, AC:AB = 2:4

                           = 1:2

And BC:AB = 2:4

                   = 1:2

Answer:

-9 = Yes

8 = Yes

-8 = Yes

9 = No

Answer:

The answer would be letter D. Valuable.

Answer:

3

Step-by-step explanation:

Answer:

77777777

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

its a because it has a greater base value

Answer:

7:30

Step-by-step explanation:

5:30 + 2:00 = 7:30

Answer:

7:30 p.m.

Step-by-step explanation:

you start babysitting at 5:30 you babysit for 2 hours 5 + 2 equals 7 . 7+.30 equals 7:30 p.m.

Answer:

exact form of n=3/2

decimal form of n=1.5

mixed number form of n= 1 1/2

7

Step-by-step explanation:

10.9-3.7 = 7.2

Therefore, 7 is the best estimate.

Answer:21

Step-by-step explanation: