At the city museumy child admission is and admission is $9.30. On Monday four times as many adult tickets as child tickets were sold for a total of sales of $1548.00 . How many child tickets were sold that day.

Answer:No, he doesn't have enough wood for the roof.

Step-by-step explanation:

Total length of Hank's board is 1.75 meters. He used 0.8 meter to build the walls of a birdhouse. This means that the length of the board left would be

1.75 - 0.8 = 0.95 meters

He used 0.4 of what is left for the floor. This means that the length of the board left would be

0.95 - 0.4 = 0.55 meters

He needs 0.6 meter for the roof. Since he has only 0.55 meters left, then, he doesn't have enough wood for the roof.

Answer:The amount of money that you would need to buy the game is $73.324

Step-by-step explanation:

The store buys a video game for the wholesale price of $39.99. There was a markup of 70% on the price of the game. The value of the markup would be

70/100× 39.99 = 0.7×39.99 = $27.993

Cost of the game plus 70% markup would be

39.99 + 27.993 = $67.893

There is sales tax of 8% on the game. This means that the value of the tax would be

8/100 × 67.893 = 0.08 × 67.893 = $5.431

The amount of money that you would need to buy the game would be

67.893 + 5.431 = $73.324

Answer:

Step-by-step explanation:

She has the option for supplying the total of 106 items. This 106 items can be either tacos or burritos or both with a total of 106 items.

If 79 tacos are sold, then it gives [tex]79 \times 3.50 = 276.5[/tex]

She needs to make $470 in total.

She needs to make $(470 - 276.5) = $193.5 more till now.

After selling 79 tacos, she has an option to sell maximum (106 - 79) = 27 burritos.

If she wants to make $193.5, she needs to sell [tex]\frac{193.5}{6.5} = 29.7[/tex] that is 30 burritos.

As she can sell 27 burritos in maximum, so there is no possible solutions.

Answer:

The answer is 6.

Step-by-step explanation:

In the question it is stated that Lisa has designed a "within-group" or "within-subject" experiment using three categories with 2 subject in each category.

Within-group / within-subject experiments mean that every participant is tested for each condition of the experiment, so everyone goes through the same process.

Considering these informations, we can calculate that each participant was in 6 cells because there are 3 categories and 2 subjects for each of the categories.

I hope this answer helps.

Answer:

x ≥ 5

y ≥ 10

3x + 2.3y ≥ 60

Step-by-step explanation:

Lets the number of men's shoes he sells be x and women's shoes be y.

For each men's shoes , he gets a commission of $3 and for each women's shoe, he gets a commission of $2.30 .

He needs to sell atleast 10 women's shoes and 5 men's shoes.

Also he needs to make atleast $60 per week.

x ≥ 5

y ≥ 10

3x + 2.3y ≥ 60

These are are the 3 required inequalities.

Now we will see an example.

If he sells 20 womens shoes and 10 mens shoes , he will meet the requirements.

He will make a total profit = [tex]2.3\times 20 + 3\times 10[/tex] =$76

Answer:

8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid in full, on time, every time.

9. APY means annual percentage yield.

Explanation:

8. A person's credit history tells about the ability of a person to pay and repay his debts. This is very important especially when you want to avail of a credit card from a company because it reflects on how responsible you are when it comes to repaying your debts. However, when you are just starting your credit history, it is important to give a good impression, so you'd have an easier approval in the future.

Usually, for starters with low salary, a low-credit-limit with a high-interest-rate credit card is common. It is very important to pay your debts in full, on time and every time in order to avoid incurring a balance that you will be carrying from one month to the other. If you do this, you will be ending up paying lots of interest charge.

Paying in full, on time and every time will also give you the chance to have an increased credit limit in the future.

9. APY is also known as "Annual Percentage Yield." This is the actual amount (rate of return) that a person could earn while his money is being deposited in the bank in one year. Other than the deposited money, investment that earns a rate of return could also refer to bonds and stock share. APY considers the compounding interest in its computation. This means that the higher your balance, the higher the APY. The value of the asset also increases.

Answer:

Total number of Hardcover books is TWO while the number of Paperback books is FIVE

Step-by-step explanation:

No. of hardcover book = x

No. of paperback book = y

Cost of one hardcover book = $8

Cost of one paperback book = $5

We are given that:

x+y=7 (Equation 1)

8x+5y=41 (Equation 2)

We can find out value of x and y by solving both equations simultaneously.

[tex]Multiplying Equation 1 by 5:\\5x+5y=35\\8x+5y=41\\Subtracting both equations\\-3x=-6\\x=2\\\\According to Equation 1:\\x+y=7\\Putting value of x=2\\2+y=7\\y=5[/tex]

Hence, Total number of Hardcover books is TWO while the number of Paperback books is FIVE

Answer:

b

Step-by-step explanation:

The expression to represent the volume of solid oblique pyramid is (x³+2x²)/3.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x+2) cm.

We know that, the volume of square base pyramid is a²h/3

Now, x²(x+2)/3

= (x³+2x²)/3

Therefore, the volume of solid oblique pyramid is (x³+2x²)/3.

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The volume of the given solid oblique pyramid with a square base of edge length x cm and height (x+2) cm can be calculated using the formula for the volume of a pyramid, 1/3 * (base area) * (height). The volume can thus be represented by the expression 1/3 * x^3 + 2/3 * x^2 cm^3.

The question refers to a solid oblique pyramid with a square base, where the edge length of the base is x, and the height is (x+2) cm. To calculate the volume of the pyramid, you can use the formula for the volume of a pyramid: 1/3 * (base area) * (height). For the given pyramid, the base is a square with side length x, so the area of the base is x*x or x^2. Because the height of the pyramid is (x + 2), we substitute into the formula to get: 1/3 * x^2 * (x + 2). Multiplying it out, the expression representing the volume of the pyramid is: 1/3 * x^3 + 2/3 * x^2 cm^3.

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Answer:

63.21.

Step-by-step explanation:

You have 100 dollars, and there is a dollar bill behind each door. You roll a 100 sided die 100 times, and you take the dollar behind the door on the die roll if the bill has not been taken already (e.g. you roll 16, then you take the dollar behind door 16 if you haven’t already taken it). What is your expected payoff?

X=Σ100i=1   1Ai

where Ai is the event that door i is opened at least once, and 1Ai is the indicator function for event Ai.

Thus the expected payoff is:

E[X]=Σ100  as i=1    Pr[Ai].

to calculate Pr[Ai].

Ai∁ is the probability of the event that after 100 rolls, door i is not chosen, which is:

Pr[Ai∁]=(99/100)^100

Thus:

Pr[Ai]=1−Pr[Ai∁]=1−(99/100)^100.

E[X]=Σ100i=1Pr[Ai]=100×(1−(99/100)^100).

Also based on the following approximation for large n's:

(1−1n)n≈1e

we have:

(99/100)^100=(1−1/100)^100≈1/e.

The expected pay off is

E[X]=100×(1−(99/100)^100)≈100×(1−1/e)≈63.21.

In the scenario where you roll a 100-sided die 100 times to collect a dollar behind each numbered door, the expected payoff is $100, since each number has an equal likelihood of being rolled once.

The question you're asking involves probability and expected value, a concept from mathematics specifically relevant in understanding outcomes in scenarios involving randomness and repetition, like the one described with 100-sided dice and dollars behind doors. When rolling a 100-sided die 100 times for dollars behind 100 doors, your expected payoff is relatively straightforward to calculate. Since each roll has an equal chance to land on any number between 1 and 100 and no number will be chosen more than once, the expected outcome is that you will roll each number once.

Thus, on average, you are expected to open each door exactly once, so the expected payoff would be neatly the sum of all the dollars behind every door. As there are 100 doors, each with a dollar behind it, your expected payoff is simply $100.

Answer:

57

Step-by-step explanation:

The units digit of the quotient (2^1993 + 3^1993)/5 is 9.

The units digit of the sum of two numbers is determined by the units digit of each number. To find the units digit of 2^1993, we can observe the pattern of its units digits: the units digit of 2 repeats every four powers. Therefore, 2^1993 has the same units digit as 2^1, which is 2. Similarly, the units digit of 3^1993 is the same as the units digit of 3^3, which is 7.

Now, we can calculate the units digit of the sum: 2 + 7 = 9. Since the sum is divisible by 5, and the units digit is 9, the quotient (2^1993 + 3^1993)/5 has a units digit of 9 as well.

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Approximately, 2% of the jazz records sold in April were from the new label.To find this, multiply the percentage (2%) by the total jazz records sold, expressing the percentage as a decimal (0.02). The formula is[tex]\( N = 0.02 \times J \),[/tex] where [tex]\( N \)[/tex] is the number of records from the new label, and [tex]\( J \)[/tex]is the total number of jazz records sold.

In order to determine the number of jazz records sold from the new label in April, you need to multiply the percentage by the total number of jazz records sold. Let's denote the total number of jazz records as J. The formula for calculating the number of records from the new label (N) is given by:

[tex]\[ N = (2/100) \times J \][/tex]

This is based on the fact that 2% is equivalent to 0.02 when expressed as a decimal. Therefore, the number of records from the new label is obtained by multiplying 0.02 by the total number of jazz records (J). This calculation provides the direct answer to the question.

Understanding percentages is essential in various fields, and in this scenario, it helps determine the specific quantity of records from the new label in relation to the total jazz records sold. This mathematical approach allows for a precise estimation, providing insights into the market share or performance of the new label within the jazz genre for the specified period, in this case, the month of April.

Answer:

cos x (2 sin x − 1)

Step-by-step explanation:

sin(2x) − cos x

Use double angle formula.

2 sin x cos x − cos x

Factor.

cos x (2 sin x − 1)

Final answer:

The expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).

Explanation:

Given the expression sin 2x - cos x, we can rewrite it using only sin x and cos x. Using the trigonometric identity sin 2x = 2 sin x cos x, we can substitute it into the expression:

sin 2x - cos x = 2 sin x cos x - cos x

Factoring out the common factor cos x, we get:

sin 2x - cos x = cos x (2 sin x - 1)

So, the expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).

Answer:

Step-by-step explanation:

The perimeter of a shape or plane figure is the distance round the shape. The diagram of the circle and the triangle ABC formed is shown in the attached photo.

To determine the length of AC, we would apply the Pythagoras theorem which is expressed as follows

Hypotenuse^2 = opposite ^2 + adjacent ^2

AC = hypotenuse

Opposite = 3

Adjacent = 3

AC^2 = 3^2 + 3^2 = 9 + 9 = 18

AC = √18 = 4.24

BX = AX = 3(they are both radii)

BC = AC = 4.24

The perimeter of triangle ABC would be

3 + 3 + 4.24 + 4.24 = 14.48

Answer:

4.847 cups

Step-by-step explanation:

Let's say x is number of cups of orange juice originally in the container.

The boy takes 1 cup of orange juice out, so there is x−1 cups left out of a total volume of x cups.  So the new concentration in the container is:

(x − 1) / x

Next, he takes another cup out, but this time, it isn't 100% orange juice any more.  So the number of cups of orange juice left in the container is x − 1 − (x − 1) / x.  The total volume is still x cups, so the new concentration is:

[x − 1 − (x − 1) / x] / x

Repeating this logic, after he replaces the third cup with water, the final concentration is:

{x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x

This final concentration is equal to 1/2.

1/2 = {x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x

1/2 x = x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x

1/2 x² = x (x − 1) − (x − 1) − [x − 1 − (x − 1) / x]

1/2 x² = x (x − 1) − (x − 1) − (x − 1) + (x − 1) / x

1/2 x² = x (x − 1) − 2 (x − 1) + (x − 1) / x

1/2 x³ = x² (x − 1) − 2x (x − 1) + (x − 1)

1/2 x³ = x³ − x² − 2x² + 2x + x − 1

0 = 1/2 x³ − 3x² + 3x − 1

0 = x³ − 6x² + 6x − 2

Using a calculator to solve this:

x = 4.847

There are originally 4.847 cups in the container.

Answer:

The cost of a bag of chips is [tex]c=\$0.85[/tex]

Step-by-step explanation:

Let

c ----> the cost of a bag of chips

we know that

The cost of a juice pouch ($2.50) plus the cost of 3 bags of chips must be equal to $5.05

The cost of 3 bags of chips is equal to multiply 3 by its cost c

so

The linear equation that represent this situation is

[tex]2.50+3c=5.05[/tex]

solve for c

Subtract 2.50 both sides

[tex]3c=5.05-2.50[/tex]

[tex]3c=2.55[/tex]

Divide by 3 both sides

[tex]c=2.55/3[/tex]

[tex]c=\$0.85[/tex]

Answer:

26°

Step-by-step explanation:

An obtuse triangle is a triangle that has one obtuse angle. Obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.

An isosceles triangle is a triangle that has two equal sides and angles.  

Therefore, an obtuse isosceles triangle is a triangle with an obtuse angle and two equal sides that have two equal acute angles (angle less than 90° ).

Given:

The three angles of the triangle are given to be x°, x°  and (10x−2) = 128°. The obtuse angle is 128°, the two x° are acute angles. We are not using equation 10x − 2 since the value of the obtuse angle has been given as 128°

The sum of angles in a triangle is 180°

∴  x° + x° + 128° = 180°

2x° = 180° - 128°

2x° = 52°

x° = 52° / 2

x° = 26°

The measurement of one of the acute angles is 26°

Answer:

false

Step-by-step explanation:

Answer:

False!!!!!

Step-by-step explanation:

it is Garnishment, not Bankruptcy! Hope this helps yall.

Answer: The neighbor would be charged $80

Step-by-step explanation:

The dimensions of Mr Jones's yard are 40 feet by 65 feet. This means that the shape of Mr Jones's yard is rectangular. The formula for determining the area of a rectangle is length × width. The area of the yard would be

40 × 65 = 2600 square feet

Mr. Jones was charged $52 for his yard. This means that the amount that he was charged per square foot would be 52/2600 = $0.02

If a neighbor's yard is 50 feet by 80 feet, it means that the area of his yard would be 50 × 80 = 4000 square feet. The amount that the neighbor would be charged is

4000 × 0.02 = $80

The company charges $0.02 per square foot. With the neighbor's yard having an area of 4000 square feet, the total cost would be $80.

To determine how much the neighbor would be charged, we need to find out the price per square foot the landscaping company charges. We start with Mr. Jones's yard. His yard area is 40 feet by 65 feet; multiplying these gives an area of 2600 square feet. Now, the cost for his yard is $52; by dividing this by the area, we get a cost of about $0.02 per square foot. For the neighbor's yard, which is 50 feet by 80 feet, we multiply these values to get an area of 4000 square feet. At a rate of $0.02 per square foot, the total cost for the neighbor's yard would be 4000 square feet * $0.02/square foot = $80.

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Using probability concepts and the information given, it is found that there is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.

The percentages given are:

Hence:

[tex]p = 0.07(0.25) + 0.93(0) = 0.0175[/tex]

There is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.

A similar problem also involving probabilities. is given at https://brainly.com/question/14398287

The probability that a randomly selected student gets a GED is 0.0175, or 1.75%.

To find the probability that a randomly selected student gets a GED, we need to multiply the probability of a student dropping out (0.07) by the probability of a dropout getting a GED (0.25). This can be calculated using the formula:

Probability of getting a GED = Probability of dropping out * Probability of getting a GED if dropped out = 0.07 * 0.25 = 0.0175

Therefore, the probability that a randomly selected student gets a GED is 0.0175, or 1.75%.

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Answer:

Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.

Step-by-step explanation:

Given:

Total pizza = 1

Pizza ate at First time = [tex]\frac{1}{4}[/tex]

Pizza ate at Second time = [tex]\frac{3}{8}[/tex]

Pizza ate at Final time = [tex]\frac{1}{16}[/tex]

We need to find find the amount of pizza left.

Now to find the Amount of Pizza left is equal to Total Pizza minus Pizza ate at First time minus Pizza ate at second time minus Pizza ate at Final time.

Framing in the equation form we get;

Amount of Pizza left = [tex]1- \frac{1}{4} -\frac{3}{8} -\frac{1}{16}[/tex]

Now Taking the LCM we get;

Amount of Pizza left = [tex]\frac{1\times16}{16}- \frac{1\times4}{4\times 4} -\frac{3\times2}{8\times2} -\frac{1\times1}{16\times1}= \frac{16}{16}- \frac{4}{16} -\frac{6}{16} -\frac{1}{16}= \frac{16-4-6-1}{16}= \frac{5}{16}[/tex]

Hence Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.

Answer:

$62.54  

Step-by-step explanation:

     12 cans dog food = 12 × 1.89  = $22.68

2 bags dental chews = 2 × 12.69 =   25.38

                                              1 toy =   10.25

                                       Subtotal =    58.31

         Sales tax = 0.0725 × 58.31 =      4.23

                                         TOTAL = $62.54

Suzie's total cost for June was $62.54.

The complement of 'rain today' is 'no rain today'. Its probability is 1 - the probability of 'rain today', which calculates to 35%.

In probability theory, the complement of any event A represents 'not A'. In this context, the event is 'rain today', therefore the complement of the event would be 'no rain today'.

Probability of an event and its complement always add up to 1. Therefore, you can calculate the probability of the complement by subtracting the probability of the event from 1. So, the probability of the complement of the event 'rain today' is 1 - 0.65 which equals 0.35 or 35%.

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Answer:

The correct option is E: "Unlike most federal tax delinquents, most state tax delinquents fail to pay state tax because of an oversight rather than a decision not to pay."

Step-by-step explanation:

Option A is not the correct answer because it is out of context

Option B is also out of context because what we are looking for is a connection between defaulters at state and federal level

Option C is also wrong because it would lead to the direct opposite of the projection by economists.

Option D is also wrong because once again it is out of context.

Option E is correct

Answer:

Step-by-step explanation:

The standard form for the equation of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

From the info given, we have the center, (h, k) as (5, -3) and the x and y coordinates of (2, 5).  We will use these to solve for r-squared, then plug back in what we need to write the equation.

[tex](2-5)^2+(5-(-3))^2=r^2[/tex] which simplifies to

[tex](-3)^2+(8)^2=r^2[/tex] and

[tex]9+64=r^2[/tex] so

[tex]r^2=73[/tex]

Filling in the equation:

[tex](x-5)^2+(y+3)^2=73[/tex]

Answer: Kelvin has 39 cards

Dustin has 42 cards

Mike has 54 cards

Step-by-step explanation: please see attachment for explanation

Answer:

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The formula for determining the area of a rectangle is expressed

LW^2

The rectangle has an area of 96cm2. This means that

LW = 96 - - - - - - - - - - 1

The width is four less than the length. This means that

L = W + 4

Substituting L = W + 4 into equation 1, it becomes

W(W + 4)= 96

W^2 + 4W = 96

W^2 + 4W - 96 = 0

W^2 + 12W - 8W - 96 = 0

W(W + 12) - 8(W + 12) = 0

(W + 12)(W - 8) = 0

W = 8 or W = -12

Since the width cannot be negative, the W = 8cm

L = W + 4 = 8 + 4 = 12 cm

The formula for determining the perimeter of a rectangle is

Perimeter = 2(L + W)

Perimeter = 2(8 + 12) =2×20

Perimeter of rectangle = 40 cm

.

Final answer:

Perimeter is 40cm.

Explanation:

To find the perimeter of a rectangle with an area of 96 cm2 where the width is four less than the length, we first need to set up equations for the area and the relationship between the sides.

Let the length be represented by L and the width by W.

We know:

We can substitute the second equation into the first to find the length:

A = L × (L - 4 cm) = 96 cm2

L^2 - 4L - 96 = 0

(L - 12)(L + 8) = 0

L = 12

The perimeter (P) of a rectangle is given by 2 × Length + 2 × Width or P = 2L + 2W.

Substituting the values of L and W into this formula will yield the perimeter of the rectangle.

For example, if L = 12 cm (which is a possible solution to the above problem), then W = L - 4 cm = 8 cm.

Therefore, the perimeter would be:

P = 2L + 2W = 2(12 cm) + 2(8 cm) = 40 cm

Answer:

Part A) [tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]  

Part B)  [tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]

Part C) [tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the  median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

L(-3, 6) and P(1, -8)

substitute the values

[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]

[tex]M(-1,-1)[/tex]

step 2

Find the slope of the segment NM

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]  

we have

N(3, 2) and M(-1,-1)

substitute the values

[tex]m=\frac{-1-2}{-1-3}[/tex]

[tex]m=\frac{-3}{-4}[/tex]

[tex]m=\frac{3}{4}[/tex]

step 3

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{3}{4}[/tex]

[tex]point\ N(3, 2)[/tex]

substitute

[tex]y-2=\frac{3}{4}(x-3)[/tex]

step 4

Convert to slope intercept form

Isolate the variable y

[tex]y-2=\frac{3}{4}x-\frac{9}{4}[/tex]

[tex]y=\frac{3}{4}x-\frac{9}{4}+2[/tex]

[tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]  

Part B) Find the equation of the  right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

L(-3, 6) and P(1, -8)

substitute the values

[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]

[tex]M(-1,-1)[/tex]

step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]  

we have

L(-3, 6) and P(1, -8)

substitute the values

[tex]m=\frac{-8-6}{1+3}[/tex]

[tex]m=\frac{-14}{4}[/tex]

[tex]m=-\frac{14}{4}[/tex]

[tex]m=-\frac{7}{2}[/tex]

step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=-\frac{7}{2}[/tex]

so

[tex]m_2=\frac{2}{7}[/tex]

step 4

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{2}{7}[/tex]

[tex]point\ M(-1,-1)[/tex] ----> midpoint LP

substitute

[tex]y+1=\frac{2}{7}(x+1)[/tex]

step 5

Convert to slope intercept form

Isolate the variable y

[tex]y+1=\frac{2}{7}x+\frac{2}{7}[/tex]

[tex]y=\frac{2}{7}x+\frac{2}{7}-1[/tex]

[tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]  

we have

L(-3, 6) and P(1, -8)

substitute the values

[tex]m=\frac{-8-6}{1+3}[/tex]

[tex]m=\frac{-14}{4}[/tex]

[tex]m=-\frac{14}{4}[/tex]

[tex]m=-\frac{7}{2}[/tex]

step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=-\frac{7}{2}[/tex]

so

[tex]m_2=\frac{2}{7}[/tex]

step 3

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{2}{7}[/tex]

[tex]point\ N(3,2)[/tex]

substitute

[tex]y-2=\frac{2}{7}(x-3)[/tex]

step 4

Convert to slope intercept form

Isolate the variable y

[tex]y-2=\frac{2}{7}x-\frac{6}{7}[/tex]

[tex]y=\frac{2}{7}x-\frac{6}{7}+2[/tex]

[tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]

Answer:

If we assume that the deviation is [tex]\sigma=3[/tex] then the solution is:

[tex]P(2.55<X<64.95)=P(-9.15<z<11.65)=P(z<11.65)-P(z<-9.15)[/tex]

f) None of the above

If we assume that the deviation is [tex]\sigma=15[/tex] then the solution is:

[tex]P(2.55<X<64.95)=P(-1.83<z<2.33)=0.956[/tex]

b) 0.956

Step-by-step explanation:

1) 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".  

2) Solution to the problem

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

[tex]X \sim N(30,3)[/tex]  

Where [tex]\mu=30[/tex] and [tex]\sigma=3[/tex]

We are interested on this probability

[tex]P(2.55<X<64.95)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(2.55<X<64.95)=P(\frac{2.55-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{64.95-\mu}{\sigma})=P(\frac{2.55-30}{3}<Z<\frac{64.95-30}{3})=P(-9.15<Z<11.65)[/tex]

And we can find this probability on this way:

[tex]P(-9.15<z<11.65)=P(z<11.65)-P(z<-9.15)[/tex]

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

[tex]P(-9.15<z<11.65)=0.99999[/tex]

If we assume that the deviation is [tex]\sigma=15[/tex] then the solution is:

[tex]P(2.55<X<64.95)=P(\frac{2.55-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{64.95-\mu}{\sigma})=P(\frac{2.55-30}{15}<Z<\frac{64.95-30}{15})=P(-1.83<Z<2.33)[/tex]

And we can find this probability on this way:

[tex]P(-1.83<z<2.33)=P(z<2.33)-P(z<-1.83)[/tex]

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

[tex]P(-1.83<z<2.33)=0.956[/tex]