a snack hut is selling fruit smoothies at the beach. the cost of a smoothie is 3 dollars and an additional 1.50 for each fruit you add. your friend writes the equation y=3+1.5x and says the slope of the line that represents this relationship is 3.

When C is the midpoint of AB, D is the midpoint of AC, E is the midpoint of AD, F is the midpoint of ED, G is the midpoint of EF, and H is the midpoint of DB, the length of GH is 77.

How to calculate midpoint for the given problem?

Since D is the midpoint of AC, we know that AD = DC = 56/2 = 28.

Similarly, E is the midpoint of AD, so AE = ED = 28/2 = 14.

Now, F is the midpoint of ED, so EF = ED = 14.

Next, G is the midpoint of EF, so EG = GF = 14/2 = 7.

Finally, H is the midpoint of DB, so DH = HB = AB/2.

Since C is the midpoint of AB, we have AB = 2AC = 2DC = 2*56 = 112.

Therefore, DH = HB = AB/2 = 112/2 = 56.

Now, we can see that GH = GD + DH = (GE + ED) + HB = (7 + 14) + 56 = 77.

Therefore, GH = 77.

The given problem involves a set of line segments and their midpoints. We can use the concept that the midpoint of a line segment divides it into two equal parts. Using this concept, we can determine the lengths of various line segments in terms of the given length DC.

Then we can apply this information to find the length of GH by adding up the appropriate line segments. Specifically, we use the fact that GH is the sum of GD and DH, which in turn are the sum of several mid-segment lengths that can be determined based on the given information. Following this logic, we can calculate that GH is equal to 77.

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1. The length of the fence required to enclose the circular pool with 4 feet of space around it is approximately 125.6 feet.

2.  If he runs around the track once he will still can't complete the goal he needs to run 20 more meters to meet his daily goal. Option A is the correct choice.

1.  To find the length of the fence required to enclose a circular swimming pool with a radius of 20 feet and a 4-foot space around it, we need to first calculate the diameter of the pool plus the space around it.

The diameter of the pool is twice the radius, which is 40 feet.

Adding 4 feet of space on both sides of the diameter gives us a total diameter of 48 feet.

The fence will be installed around the perimeter of this circular area, which is the circumference of the circle.

To calculate the circumference, we use the formula

C = 2πr

where C is the circumference, π is approximately 3.14, and r is the radius of the circle.

Plugging in the values, we get:

C = 2 x 3.14 x 20 feet = 125.6 feet.

2.

To calculate the distance around the swimming pool, we first need to find the total length of the semicircles, which is equal to half the circumference of a circle with a diameter of 35 meters.

The formula for the circumference of a circle is

C = πd

where C is the circumference and d is the diameter.

Plugging in the values, we get:

C = π x 35 meters / 2 = 54.99 meters

The total length of both semicircles is twice the length of one semicircle, which is

2 x 54.99 meters = 109.98 meters.

The length and width of the rectangular part of the pool are 80 meters and 35 meters, respectively.

Therefore, the distance around the rectangular part is

2 x (80 + 35) meters = 230 meters.

Adding the length of the semicircles to the length of the rectangle, we get the total distance around the swimming pool, which is

109.98 meters + 230 meters = 339.98 meters.

Therefore, Kevin needs to run at least 340 meters to meet his daily goal of 320 meters.

Since one lap around the high school track is only 320 meters, Kevin will need to run an additional 20 meters to meet his daily goal.

Thus, the correct answer is: option A "No, he will still need to run 20 more meters."

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Question:

1. A circular swimming pool has a radius of 20 feet. A fence is going to be built so that there is a 4-foot space around the entire pool. What is the length of the fence?

2. A swimming pool is comprised of a rectangle and 2 semicircles. The rectangle has length 80 meters and width 35 meters. The semicircles have diameters of 35 meters. Kevin needs to run 320 meters a day for his training program. He plans on running around the high school track shown. If he runs around the track once, will he meet his daily goal?

A. No, he will still need to run 20 more meters.

B. No, he will still need to run 100 more meters.

C. No, he will still need to run 150 more meters.

D. Yes, he met his daily goal.

The sequence of transformation that makes the shapes congruent is rotation then transformation

From the question, we have the following parameters that can be used in our computation:

The figures

From the figure, we have the shapes to have different orientation but same size

This means that one of the shapes is rotated to form the other

In this case, the rotation is a 90° clockwise

Followed by the rotation is a translation transformation

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Based οn the infοrmatiοn prοvided, we can see that the prοfit earned (p) is prοpοrtiοnal tο the number οf cοοkies sοld (c).

We can write the equatiοn as:

p = 0.25c

This equatiοn means that fοr every cοοkie sοld, the prοfit earned is $0.25. We can alsο write this equatiοn in slοpe-intercept fοrm as:

y = mx + b

where y represents prοfit earned (p), x represents the number οf cοοkies sοld (c), m represents the slοpe (0.25 in this case), and b represents the y-intercept (the value οf y when x is 0, which is 0 in this case).

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Abοut 68% οf sixth-grade students will have heights between 55.7 inches and 60.3 inches.

Mean is the average value οf the set given. It is calculated as:

Mean = Sum οf all the values οf the set given / Number οf values in the set

We have,

The standard deviatiοn is a measure οf hοw tο spread οut a set οf data frοm its mean.

In this case,

The standard deviatiοn is 2.3 inches, which means abοut 68% οf the data.

(in this case, the heights οf sixth-grade students) falls within οne standard deviatiοn οf the mean.

This is knοwn as the empirical rule οr the 68-95-99.7 rule.

Specifically, abοut 68% οf students will have heights between οne standard deviatiοn belοw the mean.

(58 - 2.3 = 55.7 inches).

And οne standard deviatiοn abοve the mean.

(58 + 2.3 = 60.3 inches).

Thus,

Abοut 68% οf sixth-grade students will have heights between 55.7 inches and 60.3 inches.

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Given Data:

Number of miles covered in 25 minutes = 5

To Find:

Number of miles covered in 30 minutes = ?

Solution:

Number of miles covered per minutes = 5/25             (rate=distance/time)                          

                                                                =0.2 miles/minute

Number of miles covered in 30 minutes = 0.2*30

                                                                   =6 miles

We must raise the $1,190 starting rent by 1.7% in order to determine the monthly rent after a year.

We can begin by figuring out how much the rise will be:

Amount of increase: 1.7% of $1,190 multiplied by 0.017 times equals $20.23. (rounded to the nearest cent)

We must multiply the initial rent by this sum in order to determine the new monthly rate:

New rate is $1,190 plus $20.23 per month, or $1,210.23. (rounded to the nearest cent)

As a result, the rate will be $1,210 per month after a year.

When the input parameter value is 0, the output of a function is its starting value, or 0. The first number would be the amount of money you had to start with on day 0 if your function, for instance, was tracking the sum of money you earned over a specific period of time.

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The monthly rent after 1 year will be $1,210.

"Amount" is a general term that refers to the quantity, value, or total of something. It can be used in different contexts to refer to different things.

To calculate the monthly rent after 1 year, we need to find the 1.7% increase and add it to the initial rent.

First, we need to calculate the amount of the increase:

Increase = 1.7% of $1,190

Increase = 0.017 × $1,190

Increase = $20.23 (rounded to two decimal places)

Next, we can find the new monthly rent by adding the increase to the initial rent:

New rent = $1,190 + $20.23

New rent = $1,210.23 (rounded to two decimal places)

Therefore, the monthly rent after 1 year will be $1,210.

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The total number of possible outcomes of 1 spin of the arrow on the spinner and 1 roll of the number cube is 24.

Here's how to find the solution:

First, determine the number of outcomes for spinning the arrow on the spinner. There are four sections labeled W, X, Y, and Z. Therefore, the number of outcomes for spinning the arrow is 4.Next, determine the number of outcomes for rolling the number cube. There are six faces labeled 1, 2, 3, 4, 5, and 6. Therefore, the number of outcomes for rolling the number cube is 6.To find the total number of possible outcomes of 1 spin of the arrow on the spinner and 1 roll of the number cube, multiply the number of outcomes for spinning the arrow by the number of outcomes for rolling the number cube:4 × 6 = 24.Therefore, the total number of possible outcomes of 1 spin of the arrow on the spinner and 1 roll of the number cube is 24.

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Answer:

[tex]f(t) = 4100( {2}^{ \frac{t}{2} }) [/tex]

Answer:

x=40

Step-by-step explanation:

alternate angles are equal so the one of the triangles angles r 50 then 50 plus 90, in a right angled triangle, adds to 140

180 minus 140 is 40

We can use the recursive formula to find each term in the sequence.

From the given formula, we start with:

f(1) = 2

Next, we use the formula to find f(2):

f(2) = -3f(1) = -32 = -6

Using the formula again, we find f(3):

f(3) = -3f(2) = -3(-6) = 18

Now, we find f(4):

f(4) = -3f(3) = -318 = -54

Finally, we can find f(5):

f(5) = -3f(4) = -3(-54) = 162

Therefore, the 5th term in the sequence is 162, or answer (C).

Answer:

The surface area of a cube can be calculated using the formula 6s^2, where s is the length of one of the sides of the cube.

In this case, s = 5 inches, so the surface area would be:

6(5 in)^2 = 6(25 in^2) = 150 in^2

Therefore, the surface area of the cube that measures 5 inches on each side is 150 in^2. So the answer is c) 150 in^2.

Step-by-step explanation:

To find the surface area of a cube, we use the formula:

Surface area = 6s^2

where s is the length of one of the sides of the cube.

In this case, the length of each side of the cube is given as 5 inches.

Substituting this value into the formula, we get:

Surface area = 6 x 5^2

Surface area = 6 x 25

Surface area = 150 square inches

Therefore, the surface area of the cube is 150 square inches.

The area of the polygon is  6. 9m²

From the information given, we have that the regular polygon takes the shape of a triangle.

The formula for calculating the area of a triangle is expressed with the equation;

A = 1/2bh

Such that the parameters in the formula are;

Area of a equilateral triangle is;

= √3/4a²

Then,

= √3/4 (4)²

= √3 × 4

= 6. 9m²

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Therefore , the solution of the given problem of inequality comes out to be  150 units per employee, to satisfy the production demand.

Despite the fact that algebra lacks a comparable symbol, its distinction can be expressed by a pair or collection for numbers. Equilibrium is typically followed by equity. The ongoing disparity in norms is what causes inequality. Disparity and fairness are not synonymous. Even though the components are typically not connected or situated closely together, that was our most popular symbol.

Here,

A) Assume Y is the number of units created and X is the number of employees. The following inequalities represent the circumstances in the issue:

=> 100 ≤ X ≤ 200 (the factory must have at least 100 but no more than 200 workers)

=> Y ≥ 30X (the factory must manufacture at least 30 units per worker)

B) The lines 100, 200, and 30X would form the borders of the darkened area.

C) The following three options meet the set of inequalities:

=> X = 100, Y = 3000

=> X = 150, Y = 4500

=> X = 200, Y = 6000

The factory in the second solution employs 150 people and generates 4500 units, or 150 units per employee, to satisfy the production demand.

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The perimeter of rectangular painting which is 42 cm wide and 51 cm long is 186 cm.

Perimeter of rectangle = 2×(l + b)

Perimeter = 2 × 93

Perimeter = 186 cm

Perimeter is the total length of the boundary of any closed shape. Let’s try and understand this using an example. For example, you have a huge square-shaped farm. Now, in order to save your farm from street animals, you decide to fence it. If you know the length of one side of the farm, you just have to multiply it by 4 in order to find the total length of the boundary of the farm. There are many such instances where we might be using the concept of finding perimeter without even knowing about it.

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a. Based on the chi-squared goodness of fit test, we do not have enough evidence to conclude that mice show a preference towards one paw over the other, with a calculated chi-squared value of 2.5 and a critical value of 3.84 at a significance level of 0.05.

b. The problem with repeating the analysis from part (a) with the new dataset of 480 observations is that the data is no longer independent due to repeated measures. A different statistical test that takes into account repeated measures, such as a repeated measures ANOVA, would need to be used to properly analyze this new dataset.

a. To test whether the data suggests that mice show a preference towards one paw over the other, we can use a chi-squared goodness of fit test. The null hypothesis for this test is that there is no preference towards one paw over the other, while the alternative hypothesis is that there is a preference towards one paw over the other.

The observed frequencies are

Right paw: 18 mice

Left paw: 30 mice

We can calculate the expected frequencies assuming no preference using the formula:

Expected frequency = (total number of observations * probability of right paw use) or (total number of observations * probability of left paw use)

Expected frequency of right paw use = 48 * 0.5 = 24

Expected frequency of left paw use = 48 * 0.5 = 24

We can now calculate the chi-squared test statistic using the formula:

chi-squared = sum((observed frequency - expected frequency)^2 / expected frequency)

Substituting the observed and expected frequencies into the formula:

chi-squared = ((18 - 24)^2 / 24) + ((30 - 24)^2 / 24) = 2.5

Using a chi-squared distribution table with one degree of freedom and a significance level of 0.05, the critical value is 3.84.

Since the calculated chi-squared value (2.5) is less than the critical value (3.84), we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that mice show a preference towards one paw over the other.

b. The problem with repeating the analysis from part (a) with the new dataset of 480 observations is that the data is no longer independent. Since each mouse was observed 10 times, the observations for each mouse are not independent, and treating them as such would violate the assumptions of the chi-squared goodness of fit test. To properly analyze this new dataset, a different statistical test that takes into account repeated measures, such as a repeated measures ANOVA, would need to be used.

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The given question is incomplete, the complete question is:

Do mice show a preference for using one paw over the other? Attempting to answer this question, a researcher tested a random sample of 48 mice and observed which forepaw (right or left) the mice used to retrieve food from a narrow tube. Eighteen of the mice used their right paw, while the rest used their left paw.

a. Does this data suggest that mice show a preference towards one paw over the other? Carry out the appropriate test and include all steps for full credit. Given: critical value = 3.84

b. During the experiment, the researcher noticed that individual mice sometimes switched which forepaw they used to retrieve the food. So she repeated this study on the same 48 mice, but measured each one 10 times and she recorded which forepaw was used each time. What would be the problem with repeating the analysis ran in part (a) with her new dataset of 480 observations? Be specific.

First Convert 15 kg to g

15kg × 1000 = 15000g

15000g - 822g = 14,178g

14178g ÷ 5 = 2,835.6g

Then convert the grams to kilograms

2,835.6g ÷ 1000 = 2.8356kg

2.8356kg × 5 = 14.178kg

Answer: 14.178kg

Answer:

the total weight of the remaining five components in kilograms is roughly 14.178 kg.

Step-by-step explanation:

1. divide the weight of the detergent in grams by 1000 to convert it to kilograms:

822 grams/1000 =  0.822 kilograms  

2 .subtract the weight of the detergent from the total weight of all six things to obtain the weight of the other five items:

15 kilos - 0.822 kilograms = 14.178 kilograms.

As a result, the total weight of the remaining five components in kilograms is roughly 14.178 kg.

The probability that the next vehicle to be rented will be a minivan from all 80 vehicles for rented wheels is equals to the 7/40.

We have, Rent wheels keeps track of the types of vehicles that are rented each week. The above table shows the results from this week and type of vehicle number.

Number of SUV vehicle = 31

Number of truck vehicle = 8

Number of minivan vehicle = 14

Number of sedan vehicle = 27

So, total number of vehicles or outcomes

= 80

Probability is defined as chances of occurrence of an event. It is calculated by dividing the favourable responses to the total number of possible outcomes or responses. Let E be an event that rented vehicle is minivan. The probability that the next vehicle to be rented will be a minivan, P(E) = 14/80

=> P(E) = 7/40

Hence, the required probability is 7/40.

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Complete question:

The above figure completes the question. rent wheels keeps track of the types of vehicles that are rented each week. the table below shows the results from this week. type of vehicle number rented suv 31 truck 8 minivan 14 sedan 27 based on the data, what is the probability that the next vehicle to be rented will be a minivan?

The best way to calculate the periodic interest rate for most credit cards is (a) to divide the annual interest rate by 12.

Interest is a fee charged by a lender to a borrower for the use of borrowed money or assets. It is typically expressed as a percentage of the principal amount borrowed or invested, and it is calculated over a specific period of time. Interest can be charged on loans, credit cards, mortgages, bonds, and other financial instruments. Interest can be positive or negative, depending on whether the borrower or lender is paying or receiving the interest. Positive interest is also known as a return or yield, and it is earned by investors who lend money or invest in financial instruments. Negative interest, on the other hand, is a fee charged by lenders to borrowers, and it is typically associated with negative interest rates or deflationary economic conditions.

Here,

Most credit cards compound interest on a monthly basis, which means that the interest is calculated and added to the balance each month. Therefore, to calculate the monthly or periodic interest rate, we need to divide the annual interest rate by 12.

For example, if the annual interest rate on a credit card is 18%, then the monthly or periodic interest rate would be:

Periodic interest rate = 18% / 12

= 1.5%

Therefore, the correct answer is (a) Divide the annual interest rate by 12.

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Answer:
the translated point A' has coordinates (1,9).
Explanation:
To translate the point A(2,7) by the rule (x,y) → (x-1, y+2), we can apply the rule to the x-coordinate and the y-coordinate separately. Subtracting 1 from the x-coordinate and adding 2 to the y-coordinate will give us the new coordinates of the translated point.

Using this rule, we have: A'(x,y) = (2-1, 7+2) = (1, 9)

Therefore, the translated point A' has coordinates (1,9).

To get the answer, we applied the given rule to the x and y coordinates of the point, separately. In other words, we substituted x = 2 and y = 7 into the expressions x-1 and y+2, respectively, to obtain the new x-coordinate and the new y-coordinate.

So, the sophisticated answer is that to translate a point by a given rule, you apply the rule to each coordinate separately, and then combine the results to form the coordinates of the translated point.

Answer:

Point A' has coordinates (1,9).

Step-by-step explanation:

I did the test

Hope this helps :)

Answer:

The average rate of change of the function h(x) over the interval between 2 points (a , h(a)) and (b ,h(b)) is the

slope of the secant line

connecting the points.

It is found using.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

2

2

h

(

b

)

−

h

(

a

)

b

−

a

2

2

∣

∣

∣

−−−−−−−−−−−−−−−−

h

(

b

)

=

h

(

2

)

=

2

2

+

3

(

2

)

−

1

=

9

h

(

a

)

=

h

(

0

)

=

−

1

⇒

9

−

(

−

1

)

2

−

0

=

10

2

=

5

This means that the average of all the slopes of tangents between (2 ,9) and (0 ,-1) is 5

After answering the presented question, we can conclude that Pythagorean theorem Therefore, the value of x is 15.

The Pythagorean theorem is a fundamental mathematical principle that describes the relationship between the sides of a right triangle. It states that the sum of the squares of the other two sides' lengths equals the square of the hypotenuse's length (the side opposite the right angle). The mathematical theorem is as follows: c2 = a2 + b2 Where "c" denotes the hypotenuse length and "a" and "b" represent the lengths of the other two sides, known as the legs.

Pythagorean theorem

[tex]x^2 = 12^2 + y^2\\y/x = 3/5\\y = (3/5)x\\x^2 = 12^2 + (3/5)^2 x^2\\(1 - (3/5)^2) x^2 = 12^2\\(1 - 9/25) x^2 = 12^2\\(16/25) x^2 = 12^2\\x^2 = (25/16) * (12^2)\\x = (5/4) * 12 = 15\\[/tex]

Therefore, the value of x is 15.

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So, the length of open rectangle box is 4cm, width is 4cm, and height is 2cm, with Surface Area of 48cm^2.

it is an Open box, so there is no top

SA (Surface area) = 2*l*h + 2*w*h + l*w

Volume(V) = l*w*h = 32cm^3

h = 32/(w*l)

SA = 2*l*32/(w*l) + 2*w*32/(w*l) + l*w

SA = 64/w + 64/l + l*w

Find minimum SA: take partial derivatives to get critical point(s)

SAw = -64/w^2 + l

SAl = -64/l^2 + w

Both the partials have to be 0, so...

0 = -64/w^2 + l and 0 = -64/l^2 + w

64/w^2 = l

0 = -64/(64/w^2)^2 + w (plug into second equation)

0 = -w^4/64 + w

0 = w(1-w^3/64)

1 = w^3/64 or 0 = w (impossible answer)

64 = w^3

4 = w

Plug w back into 64/w^2 = l

64/4^2 = l

4 = l

Plug w and l back into h = 32/(w*l)

h = 32/(4*4)

h = 2

The Surface Area:2*l*h + 2*w*h + l*w

SA = 2*4*2 + 2*4*2 + 4*4

SA = 48

So the answer is length = 4cm, width = 4cm, and height = 2cm, with Surface Area of 48cm^2

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Probability equation of P(A/B)=  [tex]\frac{0.31}{0.31+0.17}=0.65[/tex]

let say A and B is not empty set then intersection of A and B is  a set of elements which are common in both two sets A and B .

given that A and B are two events and

probability of A= 0.31+0.30=0.61

probability of B= 0.31+0.17=0.48

probability of intersection of A and B is = 0.31

so,

P(A/B)= is the probability of event A occurring, given that event B occurs.

P(A/B) = intersection of A and B / probability of B

P(A/B) = [tex]\frac{0.31}{0.31+0.17}=0.65[/tex]

therefore , probability of PA/B) = 0.65  

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Answer:

Original angle = 122*

Supplementary angle = 58*

Step-by-step explanation:

Take the formula and do a little algebra.

x + (x + 64) = 180

Subtract 64 from both sides

x + x = 116

Combine the x's

2x = 116

Divide both side by 2

x = 58

Hope this helps!!
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The original number of grapes present in the container was 50.35.

To determine the number of grapes Ariana ate.

then, we'll find the number of grapes Alex ate.

Finally, we'll use the remaining grapes to determine the original number of grapes present in the container.

Let us solve the problem now.

Let the original number of grapes be x. Ariana ate 0.45 of them.

Number of grapes Ariana ate = 0.45x

Alex ate 35% of the remaining grapes after Ariana ate.

Number of grapes Alex ate = 35% of (x - 0.45x)= 35/100(x - 0.45x)= 0.35(0.55x)= 0.1925x

The number of grapes remaining = 18.Number of grapes remaining after both Ariana and

Alex ate = x - 0.45x - 0.1925x= 0.3575x= 18

Hence, we can determine that:0.3575x = 18x = 18/0.3575x = 50.35

The original number of grapes present in the container was 50.35.

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Answer:

A line has slope of zero when it is a horizontal line.

1)
a) the mean is µ = 2.5.

b)  the variance is σ² = 1.25.

c) Standard Deviation σ =  1.12

2)

a) the mean is µ = 6.40.

b)  the variance is σ² = 2.12

c) Standard Deviation σ =  1.46.

1) To find the mean (µ), we can multiply each value of x by its corresponding probability (P(x)), and then add up the products: (See attached table I)

Sum | 1 | 2.5


Therefore, the mean is µ = 2.5.

To find the variance (σ²), we need to find the squared differences between each value of x and the mean, multiply each squared difference by its corresponding probability, and then add up the products:

See table II
Sum | 1 | | 5 | 1.25

Therefore, the variance is σ² = 1.25.

Finally, to find the standard deviation (σ), we can take the square root of the variance:

σ = √(σ²) = √(1.25) ≈ 1.12.


2)
To find the mean (µ), we can multiply each value of x by its corresponding probability (P(x)), and then add up the products: See table III...


Sum | 1.00 | 6.40

Therefore, the mean is µ = 6.40/1.00 = 6.40.

To find the variance (σ^2), we need to find the squared differences between each value of x and the mean, multiply each squared difference by its corresponding probability, and then add up the products: See table IV

Sum | 1.00 | | 40.80 | 2.1200

Therefore, the variance is σ² = 2.1200.

Finally, to find the standard deviation (σ), we can take the square root of the variance:

σ = √(σ²) = √(2.1200) ≈ 1.46.

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Answer: 25%

Step-by-step explanation:

After answering the given question, we can conclude that As a result, the triangle projection's lacking length is 8.

A triangle is a closed, double-symmetrical structure composed of three line segments known as sides that meet at three locations known as vertices. Triangles are distinguished by their edges and angles. Triangles can be equilateral (all groups equal), isosceles, or scalene based on their edges. Triangles are classified as acute (all angles are less than 90 degrees), okay (one angle is identical to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The area of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

Because the initial triangular and its projection are comparable, the sides that correspond to them are proportional. Let x be the length of the initial triangle's side equivalent to n. Then, given that the extension of the length x side has length 8, we can write:

x/n = (initial triangle side length)/(projected triangle side length) = x/8

When we solve for n, we get:

n = (8x)/x = 8

As a result, the projection's lacking length is 8.

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