It takes Kay 20 minutes to drive to work traveiling 45 mph. Two minutes after she left home this morning, her husband, Dan, started out with her briefcase, which she had forgotten. If Dan arrived at Kay's office just as she did, how fast did he drive?

Answer:

  Part A:  13.2

  Part B:  see below

Step-by-step explanation:

Part A:

13.245 rounded to tenths is 13.2

Part B:

The rule is ...

  Add 1 in the number place you're rounding to if the digit to its right is 5 or more. Drop (or zero) all digits to the right of the place you're rounding to.

Here, the digit to the right of the tenths place is 4, so no action is taken other than dropping digits to the right of the tenths place.

Answer:

36.25 is equal to the 45.5% of 79.67

Step-by-step explanation:

To solve this you just have to find the value that represents the 100%.

To do this, you can use the Rule of Three that allows you to solve problems of proportions.

In this case, you know that the 45.5% of the magnitude X is 36.25, now you have to find the value which corresponds to the 100%.  

Mathematically it will be:

[tex]\frac{X}{36.25} =\frac{100}{45.5}[/tex]

Then you have to solve the equation to find X:

[tex]X=\frac{100}{45.5}*36.25[/tex]

And finally, the answer is:

[tex]X=79.67[/tex]

This is the set of all integers greater than -2, excluded. So, the elements of the set are

[tex]\{-1,0,1,2,3,4,5,\ldots\}[/tex]

Given:

Set defining the rule → {y | y is an integer and y > -2}

To find:

The set following the given property

Solution:

Set defined by {y | y is an integer and y > -2} where y is the set of integers greater than -2.

Option (1)

{3,4,5,6........}

All the integers are greater than -2, therefore, this set will the answer.

Option (2)

{2, 3, 4, 5, 6.....}

All integers are greater than -2, therefore, this set will be the answer.

Option (3)

{-2, -1, 0, 1, 2, 3....}

There is an element which is equal to -2.

Therefore, given set will not be the answer.

Option (4)

{0, 1, 2, 3.....}

All elements are greater than -2.

Therefore, given set will be the answer.

Options (1), (2), (4) will be the answer.

Learn more about the integers,

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Answer:

120 MW/hour

Step-by-step explanation:

The formula of the average rate of change between two points in a function is:

Average rate of change (ARC) = f(x2) -f(x1)/(x2-x1)

Let's think  the power demad as a function d(x) depending of the hour of the day, so the variable x= hour of the day.

Now we have:

d(5)= 1600

d(8)= 1960

If we apply the mentioned ARC formula = [d(8)-d(5)] MW/(8-5)hour= (1960-1600)MW/3hour= 360/3=120 MW/Hour

Answer:

A)128

B)717

Step-by-step explanation:

In Roman numerals each letter have a numerical value in Hindu-Arabic numerals.

These values are:

I = 1

V = 5

X = 10

L = 50

C =100

D = 500

M = 1000

a) CXXVIII = 100+10+10+5+1+1+1 = 128

b) XCDCCCXXVII = 500+100+100+10+10+7-100-10 = 717

In this question we subtracted the value of XC(-100-10) because it was preceding or appeared before a larger value and hence, we subtract these values from the value of DCCCXXVII(500+100+100+100+10+10+7).

This could be understood with the help of following example: If we calculate the value of CD it would be (500-100) = 400. Now, XCD = (400-10) = 390.

Answer:

[tex]0.950796[/tex]

Step-by-step explanation:

Given that a shuttle launch depends on three key devices that may fail independently of each other with probabilities 0.01, 0.02, and 0.02, respectively.

Required probability =  the probability for the shuttle to be launched on time

= Probability that all three do not fail

Since each key device is independent of the other

we have

prob that all three do not fail = [tex](1-0.01)(1-0.02)(1-0.02)\\=0.99*0.98*0.98\\=0.950796[/tex]

Answer:

[tex]r=5.23\%[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=1\ years\\ P=\$27,580\\I=\$1,442.43\\r=?[/tex]

substitute in the formula above

[tex]1,442.43=27,580(r*1)[/tex]

Solve for r

[tex]r=1,442.43/27,580[/tex]

[tex]r=0.0523[/tex]

convert to percent

[tex]r=0.0523*100=5.23\%[/tex]

Answer:

[tex]z= 5-2i[/tex]

Step-by-step explanation:

Start replacing!

[tex](x+iy) + 4i (x-iy) = -3+18i \\ x+iy +4ix -4i^2 y = -3 + 18i \\\\x + i (4x+y) +4y = -3 + 18i\\x+4y + (4x+y) i = -3 + 18i[/tex]

Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation [tex]\left \{x+4y=-3} \atop {4x+y=18} \right.[/tex]

Pick any method to solve it and you'll get [tex] x=5, y= -2 [/tex]

Answer:

$175 = Cost of single dress

Step-by-step explanation:

It is provided that cost of dress is twice that of a skirt.

Let say, cost of skirt = x

Total things bought 3 dresses and 2 skirts.

Cost of single dress = 2x

Cost of all items = 3 [tex]\times[/tex] 2x + 2 [tex]\times[/tex] x = $1,000 - $300 = $700

6x + 2x = $700

x = 700/8 = $87.50

Cost of single dress = 2x = $87.50 [tex]\times[/tex] 2 = $175

Answer:

  The scale factor is 2/3.

Step-by-step explanation:

When the dilation is about the origin, the ratio of image coordinates to original coordinates is the scale factor:

  4/5 = 6/9 = 2/3

The scale factor is 2/3.

Answer:  B. We are 95% confident that the population parameter is between the lower confidence limit and upper confidence limit.

Step-by-step explanation:

In statistics, we know that the interpretation of [tex](1-\alpha)\%[/tex] level of confidence interval is that we are [tex](1-\alpha)\%[/tex] sure that the true population parameter lies in it.

Therefore, the proper interpretation of a 95% confidence interval is that we are 95% confident that the population parameter is between the lower confidence limit and upper confidence limit.

Final answer:

The correct interpretation of a 95% confidence interval is that we are 95% confident that the population parameter is within the interval. The confidence interval represents the range within which the true population parameter lies, with a certain level of confidence, not the prediction of sample means or point estimates.

Explanation:

The correct interpretation of a 95% confidence interval is B: We are 95% confident that the population parameter is between the lower confidence limit and upper confidence limit. This means that if we were to take many samples from the population and construct a confidence interval from each sample, we would expect about 95% of those intervals to contain the actual population parameter, such as the population mean. It's important to note that the confidence interval does not predict where individual point estimates or sample means will fall. Rather, it expresses the reliability of the estimate of the population parameter based on the sampled data.

Answer:

If it is a simple average, the average is 2.8 points.

If it is a weigthed-by-credits average, the average is 2.86 points.

Step-by-step explanation:

To calculate the simple average of this 5 grades, we sum all the points and divide it by 5:

In Algebra: A = 4 points

In History: B = 3 points

In Sociology: A = 4 points

In English: D = 1 point

In Seminar: C = 2 points

Average = (4+3+4+1+2)/5 = 2.8 points

If the average is weighted by the credits, we must add each score multiplied by the credits and, in total, divide it by the total amount of credits.

[tex]weighted-average = \sum(points_i*credits_i)/\sum(credits_i)\\\\weighted-average = (4*3+3*3+4*3+1*3+2*2)/(3+3+3+3+2)\\weighted-average = 40 / 14 = 2.86[/tex]

Final answer:

To find the student's semester GPA, assign points to each grade based on the grading scale, multiply by the credits for each course, sum these totals, and divide by total credit hours. The student's GPA is approximately 2.86.

Explanation:

To calculate the student's semester grade point average (GPA), we first multiply each grade by its respective credit hours, then sum these numbers, and finally divide by the total number of credit hours. Here is the breakdown:

Algebra: A (4 points) × 3 credits = 12

History: B (3 points) × 3 credits = 9

Sociology: A (4 points) × 3 credits = 12

English: D (1 point) × 3 credits = 3

Seminar: C (2 points) × 2 credits = 4

Next, we add these totals: 12 + 9 + 12 + 3 + 4 = 40. The sum of the credit hours is 3 + 3 + 3 + 3 + 2 = 14. The GPA is calculated as the total points divided by the total credit hours, which is:

GPA = Total Points / Total Credit Hours = 40 / 14 ≈ 2.86

Therefore, the student's semester GPA is approximately 2.86.

Step-by-step explanation:

Consider the provided information.

For the condition statement [tex]p \rightarrow q[/tex] or equivalent "If p then q"

Part (A) If it snows tonight, then I will stay at home.

Here p is If it snows tonight, and q is I will stay at home.

Converse: If I will stay at home then it snows tonight.

[tex]q \rightarrow p[/tex]

Inverse: If it doesn't snows tonight, then I will not stay at home.

[tex]\sim p \rightarrow \sim q[/tex]

Contrapositive: If I will not stay at home then it doesn't snows tonight.

[tex]\sim q \rightarrow \sim p[/tex]

Part (B) I go to the beach whenever it is a sunny summer day.

Here p is I go to the beach, and q is it is a sunny summer day.

Converse: It is a sunny summer day whenever I go to the beach.

[tex]q \rightarrow p[/tex]

Inverse: I don't go to the beach whenever it is not a sunny summer day.

[tex]\sim p \rightarrow \sim q[/tex]

Contrapositive: It is not a sunny summer day whenever I don't go to the beach.

[tex]\sim q \rightarrow \sim p[/tex]

Part (C) When I stay up late, it is necessary that I sleep until noon.

P is I sleep until noon and q is I stay up late.

Converse: If I sleep until noon, then it is necessary that i stay up late.

[tex]q \rightarrow p[/tex]

Inverse: When I don't stay up late, it is necessary that I don't sleep until noon.

[tex]\sim p \rightarrow \sim q[/tex]

Contrapositive: If I don't sleep until noon, then it is not necessary that i stay up late.

[tex]\sim q \rightarrow \sim p[/tex]

The converse, contrapositive, and inverse of each of the specified conditional statements are shown below.

Suppose the conditional statement given is:

[tex]p \rightarrow q[/tex] or 'if p then q'

Then, we get:

For the listed conditional statements, finding their converse, contrapositive, and inverse statements:

This can be taken as: If it is a sunny summar day, then i go to the beach.

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Answer:

The interior angles for this triangle are 80º, 30º and 70º.

Step-by-step explanation:

The sum of a interior angle with it's respective exterior angle is also always 180º.

So, for the exterior angle that is 100º, we can find the first interior angle of the triangle

100º + A1 = 180º

A1 = 180º - 100º

A1 = 80º

The first interior angle of this triangle is A1 = 80º;

For the exterior angle that is 150º, we can find the second interior angle of the triangle.

150º + A2 = 180º

A2 = 180º - 150º

A2 = 30º

The second interior angle of this triangle is A2 = 30º.

From here, to find the third interior angle, we apply the following definition

The sum of the three interior angles of a triangle is always 180º.

So:

A1 + A2 + A3 = 180º

80º + 30º + A3 = 180º

110º + A3 = 180º

A3 = 180º - 110º

A3 = 70º

The third interior angle of this triangle is A3 = 70º.

The interior angles for this triangle are 80º, 30º and 70º.

Answer:

D. 65.7-65.6

(the exact difference is 10.1, which is "about" 10)

The difference that is about 10 is 70.9-58.7. The correct option is B. 70.9-58.7

To determine the difference that is about 10, we will evaluate the given expressions one after the other.

The result that is closest to 10 gives the difference that is about 10

Evaluating this, we get

33.2-28.4 = 4.8

Evaluating this, we get

70.9-58.7 = 12.2

Evaluating this, we get

42.5-16.8 = 25.7

Evaluating this, we get

65.7-65.6 = 0.1

From above, we can observe that from A to D, the answer that is closest to 10 is 12.2

Hence, the difference that is about 10 is 70.9-58.7. The correct option is B. 70.9-58.7

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Answer:

  (a) even: J, K, M, O; odd: L, N

  (b) L and O are connected to J

  (c) N is of degree 3

Step-by-step explanation:

Count the edge ends that intersect each vertex. You get ...

  J-2, K-2, L-3, M-2, N-3, O-4

These numbers are the degree of the vertex.

a) Vertices with even degree are J, K, M, O, since these have degrees of 2, 2, 2, and 4, respectively--all even numbers.

Vertices with odd degree are L and N, since these both have degree 3, an odd number.

__

b) The vertices that are adjacent to J are the ones at the other ends of the edges that intersect vertex J. One of those two edges connects to vertex L; the other to vertex O. J is adjacent to L and O.

__

c) When we counted edges in part (a), we found vertex N to be of degree 3.

Answer:

12,500 units

Step-by-step explanation:

Given:

Selling cost of the pump = $10

Variable cost of producing each unit = 60% of selling cost

or

Variable cost of producing each unit  = 0.60 × $10 = $6

Monthly fixed cost = $50,000

Now,

The profit per unit = Selling cost - Variable cost

or

The profit per unit = $10 - $6 = $4

Therefore,

The breakeven point = [tex]\frac{\textup{Fixed cost}}{\textup{Profit per unit}}[/tex]

or

the breakeven point = [tex]\frac{\textup{50,000}}{\textup{4}}[/tex]

or

the breakeven point = 12,500 units

Answer:

0.25g + 0.05g + 500g = 500.30g

Step-by-step explanation:

The first step is converting everything to grams, by rules of three. Then we add.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

First step: 0.5kg to g

Each kg has 1000g. So

1kg - 1000g

0.5kg - xg

x = 1000*0.5

x = 500g

0.5kg = 500g

Second step: 50mg to g

Each g has 1000mg. So:

1g - 1000mg

xg - 50mg

1000x = 50

[tex]x = \frac{50}{1000}[/tex]

x = 0.05g

50mg = 0.05g

Third step: 2.5dg to g

Each g has 10dg. So:

1g - 10dg

xg - 2.5dg

2.5x = 10

[tex]x = \frac{2.5}{10}[/tex]

x = 0.25g

2.5 dg = 0.25g

Final step: Add

0.25g + 0.05g + 500g = 500.30g

Adding 0.5 kg, 50 mg, and 2.5 dg gives a total of 500.30 grams once all the units are converted to grams.

First, let's convert everything to grams as it's the unit we're asked to report the result in.

To find the total, we just need to add these numbers together: 500 grams + 0.05 grams + 0.25 grams = 500.30 grams. So, when you add 0.5 kg, 50 mg, and 2.5 dg together and convert it to grams, your answer is 500.30 grams.

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Answer:

The person has to invest $5000 at 9% and $7000 at 10%.

Step-by-step explanation:

As stated in the problem, we have an ammount C that the person invest at 9% and an ammount (C+2000) that it is invested at 10%.

To gain $1150 a year, the ammount C needs to satisfy this equation:

[tex]C*0.09+(C+2000)*0.10=1150[/tex]

Applying distributive property,

[tex]0.09C+0.10C+200=1150\\0.19C=1150-200[/tex]

[tex]C=950/0.19\\C=5000[/tex]

So the person has to invest C=$5000 at 9% and (C+2000)=$7000 at 10% to gain $1150 of interest yearly.

Answer:

the range of the relation is 3

Answer:

Units for parameter k would be [tex]minutes^{-1}[/tex].

Step-by-step explanation:

The concentration of CA0 is given in M (moles per liter), which is the unit for CA; if we show units inside parenthesis in the equation, it would be:

[tex]CA (M)=CA0 (M) *(1-e-k(?)*t(minutes))[/tex]

For the concentration units of CA0 not to be affected by the units of the factor (1-e-k*t), this factor would have to be a number without units.

Since 1 is a constant without units, for the constant e to be able to subtract from 1 it would have to be a number without units, which also applies to the factor k*t.

For the factor k*t to be a number without units, k must have units that can be canceled when multiplied by t, which is given in minutes, so k must have units of [tex]\frac{1}{minutes} =minutes^{-1}[/tex]

This can be confirmed by operating the equation using only its units (units of parameter k are noted by a question mark):

[tex]M=M(0-0-?*minutes)[/tex]

[tex]\frac{M}{M} =?*minutes[/tex]

[tex]1=?*minutes[/tex]

[tex]\frac{1}{minutes}=?[/tex]

[tex]minutes^{-1}=?[/tex]

Answer: [tex]6.25\%[/tex]

Step-by-step explanation:

Given: A pharmacist attempts to weigh 0.375 g of morphine sulfate on a balance of dubious accuracy. When checked on a highly accurate balance, the weight is found to be 0.400 g.

i.e. Estimated weight =  0.375 g  and Actual weight = 0.400 g

Now, the percentage of error in the first weighing is given by :-

[tex]\%\text{ Error}=\dfrac{|\text{Estimate-Actual}|}{\text{Actual}}\times100\\\\=\dfrac{|0.375-0.400|}{0.400}\times100\\\\=\dfrac{|-0.025|}{0.400}\times100\\\\=\dfrac{0.025}{0.4}\times100\\\\=\dfrac{25\times10}{4\times1000}\times100=\dfrac{25}{4}=6.25\%[/tex]

Hence, the percentage of error in the first weighing = [tex]6.25\%[/tex]

Answer:

The expected number of women expected to give birth to identical twins is 5.

The calculation is:

[tex]x = \frac{3738*1,000}{804,665}[/tex]

Step-by-step explanation:

This is a proportionality problem, that can be solved by a rule of three. Here, the measures(the number of women that gave birth to identical twins and the nuber of women that gave birth) are directly related. It means that we have a direct rule of three(cross multiplication).

The problem states that of the 804,665 women that gave birth, 3,738 gave birth to identical twins. It asks of 1,000 women, how many are expected to give birth to identical twins? So, 3,738 of 804665 is how much of 1,000?

3,738 - 804,665

x   -  1,000

[tex]804,665x = 3738*1,000[/tex]

[tex]x = \frac{3738*1,000}{804,665}[/tex]

[tex]x = 4.64[/tex]

Rounding up, the expected number of women expected to give birth to identical twins is 5.

Total amount owed by Kyle = $21573

In the question,

Amount of money earned by Kyle in first three months = $94,000

Amount of money earned by Kyle in Remaining months working as a Full Time = $188, 000

Total Money earned by Kyle = $282,000

Now,

We know that the Percent of FICA(Federal Insurance Contributions Act) taxes are,

Social Security tax = 6.2 %

Medicare tax = 1.45 %

So,

Total percent of tax paid = 7.65 %

So,

Total amount paid in taxes = 7.65 % of Total Money earned by Kyle

Therefore,

Total amount paid in tax = 0.0765 x 282000 = $21573

Answer:

312

Step-by-step explanation:

Let the attendance before the drop be x

Now we are given that attendance dropped 4% this year

So new attendance = [tex]x-4\% \times x[/tex]

                               = [tex]x-\frac{4}{100} \times x[/tex]

                               = [tex]\frac{96x}{100}[/tex]

We are also given that attendance dropped 4% this year, to 300

So,  [tex]\frac{96x}{100}= 300[/tex]

[tex]x= 300 \times \frac{100}{96}[/tex]

[tex]x=312.5[/tex]

Hence the attendance before the drop was 312

Answer:

l = 18 - L

Step-by-step explanation:

Since 18 feet board is cut into two pieces L and l.

L + l = 18

Subtracting both sides by L

l = 18 - L

Answer:

3.66

Step-by-step explanation:

Having a 2.9 GPA means there was a certain quantity of points divided by a quantity of credit hours.

In this case 37 hours because of the 20 given to obtain 2.25 and 17 additional hours to get 2.9

So to know the points to get 2.9, we multiply 2.9 by the hours (37)

gpa=[tex]\frac{points}{hours}[/tex]

gpa*hours= points

[tex]2.9*37= 107.3 points[/tex]

Now we need to find out how many points were given in 20 credit hours to get 2.25;

we do a similar calculation by multiplying 2.25 by the credit hours given to obtain that gpa.

gpa*hours=points

[tex]2.25*20=45[/tex]

Then from 45 points to get 107.3 we need to know the difference

[tex]107.3-45=62.3[/tex]

and because those points are needed in 17 additional credit hours, we make a division and we get

[tex]gpa=\frac{points}{hours}[/tex]

[tex]gpa=\frac{62.3}{17}=3.66[/tex]

So the student needs to make a 3.66 gpa minimum in order to improve her current 2.25 gpa to 2.9

The student needs to achieve a minimum GPA of 3.65 over the 17 additional credit hours to reach their goal of a 2.9 overall GPA, showing the importance of planning and effort.

To calculate the minimum GPA needed in the additional 17 hours for the student to achieve an overall GPA of 2.9 after already earning a 2.25 GPA over 20 credit hours, we will use a weighted average formula. Currently, the student has accumulated (2.25 * 20) = 45 quality points from the 20 credit hours. To reach a 2.9 GPA after adding 17 more credit hours, the student will need a total of (20 + 17) * 2.9 = 107.1 quality points.

Subtracting the quality points already earned from the total needed gives us 107.1 - 45 = 62.1 quality points needed over the 17 additional hours. Therefore, the minimum GPA required across these hours is 62.1 / 17 ≈ 3.65. This calculation indicates that, even though the target seems high, clearly understanding the effort needed can help in planning the study strategy accordingly.

Answer: 8 inches

Step-by-step explanation:

We know that the area of a rectangle is given by :-

[tex]A=l\times w[/tex], where l is length and w is width of the rectangle.

Given : The width of rectangle : w=4 inches

The area of rectangle : A =32 inches.

Then substitute these values in the above formula, we have

[tex]32=l\times4\\\\\Rightarrow\ l=\dfrac{32}{4}=8[/tex]

hence, the length of rectangle = 8 inches.

Answer:

Let the growth function that shows the population in millions after x years,

[tex]P=P_0(1+r)^x[/tex]

Where,

[tex]P_0[/tex] = initial population,

r = growth rate per year,

Suppose the population is estimated since 1950,

Thus, if x = 0, P = 2560,

[tex]\implies 2560 = P_0 (1+r)^0\implies P_0 = 2560[/tex]

Now, if x = 10 ( that is, on 1960 ), P = 3040,

[tex]3040=2560(1+r)^{10}\implies r = 0.017[/tex]

Hence, the required function that shows the population after x years,

[tex]P=2560(1.017)^x[/tex]

If x = 42,

The population in 1992  would be,

[tex]P=2560(1.017)^{42}\approx 5196.608365\text{ millions}[/tex]

if x = 80,

The population in 2030 would be,

[tex]P=2560(1.017)^{80}\approx 9860.891929\text{ millions}[/tex]

Final answer:

The world population growth can be modeled using exponential growth with a relative growth rate calculated from given data. The relative growth rate, k, was found to be approximately 0.017355. Using this rate, we can estimate past and predict future populations; however, demographic trends show that actual growth rates are slowing.

Explanation:

To model the world population using a proportional growth rate, we employ the exponential growth model where dP/dt = kP. The world population was 2560 million in 1950 (P(0) = 2560) and 3040 million in 1960 (P(10) = 3040). We will use these data points to find the relative growth rate k.

Finding the Relative Growth Rate

The general solution of the differential equation is P(t) = P(0)e^(kt), where e is the base of the natural logarithm. Inserting our initial conditions:

P(0) = 2560, which implies C = 2560 where C is the initial population.

P(10) = 3040 yields 3040 = 2560e^(10k).

Dividing both sides by 2560 gives 3040/2560 = e^(10k), and then taking the natural logarithm of both sides we find ln(3040/2560) = 10k. Therefore, k ≈ ln(1.1875)/10. By calculating, k ≈ 0.017355 (rounded to six decimal places).

Estimating World Population for 1992 and Predicting for 2030

Using this growth rate, we can estimate the world population for any year t with P(t) = 2560e^(0.017355t):

For the year 1992 (t=42 years since 1950), P(42) ≈ 2560e^(0.017355*42).

For the year 2030 (t=80 years since 1950), P(80) ≈ 2560e^(0.017355*80).

Demographic trends suggest a slowing growth rate. Between 1965 and 1980, the annual rate was 2%, while predictions for 2005-2015 showed a decline to 1.1%. These numbers imply increasing doubling times and changing dynamics in world population growth.

Answer:

(a) Sampling distribution

P(25) = 0,04

P(35) = 0.1 + 0.1 = 0,2

P(42,5) = 0.06 + 0.06 = 0,12

P(45) = 0,25

P(52,5) = 0.15 + 0.15 = 0,3

P(60) = 0,09

(b) E(X) = 45.5 oz

(c) E(X) = μ

Step-by-step explanation:

The variable we want to compute is

[tex]X=(X1+X2)/2[/tex]

For this we need to know all the possible combinations of X1 and X2 and the probability associated with them.

(a) Sampling distribution

Calculating all the 9 combinations (3 repeated, so we end up with 6 unique combinations):

P(25) = P(X1=25) * P(X2=25) = p25*p25 = 0.2 * 0.2 = 0,04

P(35) = p25*p45+p45*p25 = 0.2*0.5 + 0.5*0.2 = 0.1 + 0.1 = 0,2

P(42,5) = p25*p60 + p60*p25 = 0.2*0.3 + 0.3*0.2 = 0.06 + 0.06 = 0,12

P(45) = p45*p45 = 0.5 * 0.5 = 0,25

P(52,5) = p45*p60 + p60*p45 = 0.5*0.3 + 0.3*0.5 = 0.15 + 0.15 = 0,3

P(60) = p60*p60 = 0.3*0.3 = 0,09

(b) Using the sample distribution, E(X) can be expressed as:

[tex]E(X)=\sum_{i=1}^{6}P_{i}*X_{i}\\E(X)=0.04*25+0.2*35+0.12*42.5+0.3*52.5+0.09*60 = 45.5[/tex]

The value of E(X) is 45.5 oz.

(c) The value of μ can be calculated as

[tex]\mu=\sum_{i=1}^{3}P_{i}*X_{i}\\\mu=0.2*25+0.5*45+0.3*60=45.5[/tex]

We can conclude that E(X)=μ

We could have arrived to this conclusion by applying

[tex]E(X)=E((X1+X2)/2)=E(X1)/2+E(X2)/2\\\\\mu = E(X1)=E(X2)\\\\E(X)=\mu /2+ \mu /2 = \mu[/tex]