Supreme cookie dough has 25% chocolate chips. Magic cookie dough has 35% chocolate chips. Samantha mixes 4 cups of Supreme cookie dough with 4 cups of Magic cookie dough. Enter the percent of chocolate chips in the mixture.

Answer:

Step-by-step explanation:

yes

Step-by-step explanation:

To find the vertical asymptotes of the function f(x) = (x^2+3x+6)/(x^2-4), we need to find the values of x that make the denominator equal to zero.

The denominator (x^2-4) factors into (x+2)(x-2). Therefore, the denominator is equal to zero when x = -2 or x = 2.

These values of x give us vertical asymptotes since the function becomes unbounded as x approaches these values. Therefore, the vertical asymptotes of the function are x = -2 and x = 2.

please mark brailest

The tree diagram that list all the possible outcomes with their respective probabilities is given below.

It should be noted that to solve this problem, we can use a tree diagram to represent all the possible outcomes at each step of the selection process. The tree diagram below shows the possible outcomes:

            /   B (6/10)            \   Y (4/10)

       B1 /                            \ Y1

         /                              \

    /   B (5/10)    \   Y (4/10)    /   B (6/10)    \   Y (3/10)

B2 /                  \ Y2         B2 /                  \ Y2

  /                    \           /                    \

 |   B (4/10)   \   Y (4/10)  |   B (5/10)   \   Y (3/10)

B3|                  Y3         |                  Y3

 |                     |       |                     |

  \   B (3/10)   /   Y (4/10)  \   B (4/10)   /   Y (3/10)

    \                  \      /                  \

       \                 \   /                     \

            \   B (2/10)   Y4                     B4 \   Y (2/10)

                 |                                      |

                 |                                      |

                  \   B (1/10)                          \   Y (1/10)

                         |                                     |

                         |                                     |

                          \                                    \

                              B5                                    Y5

The branches in the tree diagram represent the possible outcomes at each selection, and the probabilities are shown next to each branch.

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Using the proportionality theorem we know that the length of the side AE is 28 units respectively.

The intercept theorem often referred to as Thales' theorem, the basic proportionality theorem, or the side splitter theorem is a crucial concept in introductory geometry that deals with the ratios of different line segments produced when two intersecting lines are intercepted by a pair of parallels.

A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.

So, the given proportion is:

= 32/56

= 4/7

Then,

= AE/49

We will be using table 7:

= AE/49

= 7*4/7*7

= 28/49

Therefore, using the proportionality theorem we know that the length of the side AE is 28 units respectively.

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So, the correct answer is: Major Axis: 12[tex]\sqrt{2}[/tex] units, Minor Axis: 24 units.

An ellipse is a closed curve that is symmetrical about two axes, commonly referred to as the major axis and minor axis. It can be described as a stretched circle or a flattened oval. The shape of an ellipse can be defined by two focal points (also known as foci) and the distance between them. Any point on the ellipse is the sum of the distances between that point and each focus. Ellipses have a wide range of applications in mathematics, physics, astronomy, and engineering. They are used to describe the orbits of planets and other celestial bodies, to design reflectors and lenses for telescopes, and to create art and design elements.

The standard equation of an ellipse centered at the origin is given by:

[tex](x^2/a^2) + (y^2/b^2) = 1,[/tex]

where "a" and "b" are the lengths of the semi-major and semi-minor axes, respectively. To find the lengths of the major and minor axes of the given ellipse, we need to first put it in standard form by dividing both sides by 12:

[tex]x^2/72 + y^2/144 = 1[/tex]

Comparing this with the standard form, we see that.[tex]a^2 = 72[/tex]and b^2 = 144. Thus, the lengths of the semi-major and semi-minor axes are:

a = [tex]\sqrt{72}[/tex] = 6[tex]\sqrt{2}[/tex] units

b = [tex]\sqrt{144}[/tex]= 12 units

Therefore, the lengths of the major and minor axes of the ellipse are:

Major Axis: 2a = 2(6[tex]\sqrt{2}[/tex]) = 12[tex]\sqrt{2}[/tex]units

Minor Axis: 2b = 2(12) = 24 units

So, the correct answer is: Major Axis: 12[tex]\sqrt{2}[/tex] units, Minor Axis: 24 units

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Answer:

[tex]y=-4x+7[/tex]

Step-by-step explanation:

According to the formula of the equation of the line passing through two given points

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

where m=slope of the line

[tex]m=(y2-y1)/(x2-x1)[/tex]   ---->eq (II)

where [tex]y2=-5 , y1=3 , x2=1 , x1=-1[/tex]

Substituting the

values in eq(II)

[tex]m=(-5-3)/(1-(-1))=-8/2=-4[/tex]

Substituting the value of m in eq(I)

[tex]y-3=-4(x-(-1))\\= > y=-4x+7[/tex]

So the equation of the line passing through the given points is

[tex]y=-4x+7[/tex]

Answer: y+2x−1=0

Step-by-step explanation: Let's say A is the point (−1,3) and B is the point (3,−5)

The equation of a line that passes through two points is

y−y0=m(x−x0)

Replace x,x0,y and y0

by the coordinates of the two points to find your slope

⇒m

.

It doesn't matter which point you choose to replace

x,x0,y and y0 with as long as you pair xwith yand x0 with

y

0

.

m

=

y

−

y

0

x

−

x

0

=

−

5

−

3

3

−

(

−

1

)

=

−

5

−

3

3

+

1

=

−

2

Now, all you have to do is to choose either the coordinates of

A

or

B

to replace in the equation of a line that passes through two points

⇒

y

−

y

0

=

m

(

x

−

x

0

)

. You are only going to replace

x

0

and

y

0

.

I'm using the point

A

(

−

1

,

3

)

⇒

y

−

y

0

=

m

(

x

−

x

0

)

⇒

y

−

3

=

−

2

(

x

+

1

)

⇒

y

−

3

=

−

2

x

−

2

⇒

y

+

2

x

−

1

=

0

is your line.Let's say

A

is the point

(

−

1

,

3

)

and

B

is the point

(

3

,

−

5

)

The equation of a line that passes through two points is

y

−

y

0

=

m

(

x

−

x

0

)

Replace

x

,

x

0

,

y

and

y

0

by the coordinates of the two points to find your slope

⇒

m

.

It doesn't matter which point you choose to replace

x

,

x

0

,

y

and

y

0

with as long as you pair

x

with

y

and

x

0

with

y

0

.

m

=

y

−

y

0

x

−

x

0

=

−

5

−

3

3

−

(

−

1

)

=

−

5

−

3

3

+

1

=

−

2

Now, all you have to do is to choose either the coordinates of

A

or

B

to replace in the equation of a line that passes through two points

⇒

y

−

y

0

=

m

(

x

−

x

0

)

. You are only going to replace

x

0

and

y

0

.

I'm using the point

A

(

−

1

,

3

)

⇒

y

−

y

0

=

m

(

x

−

x

0

)

⇒

y

−

3

=

−

2

(

x

+

1

)

⇒

y

−

3

=

−

2

x

−

2

⇒

y

+

2

x

−

1

=

0

is your line.

Answer:

54 hours

Step-by-step explanation:

44h=616$

1h=44h divided by 44

=616$ divided by 44

= 14

150% of 14$ = 100% + 50%

= 14$ + 7$

= 21$

826$-616$ = 210$

1h(additional hour rate) =21$

10h= 210$

44h + 10h = 54h = 826$

I think the budget strategy worked because it brought in the necessary amount of money to Vegas and met everyone's needs for the show.

Money Magic is designed to teach basic budgeting principles. The main character, Enzo, represents the human tendency to focus on short-term gratification. This game challenges students to balance immediate desires with long-term plans.

In this free financial game, help magician Enzo get the show to Las Vegas on budget. The player assumes the role of Lord Enzo the magician and his manager. He's tasked with getting him to Vegas for his big break. Along the way, he will raise $50,000 to pay for the venue when he gets there. And it's not an easy task: On their way to the land of neon lights and slots his machine, they reconcile the cost of the hyped show, pay for upkeep such as Enzo's new tricks, fill the tanks of his magic his mobile with gas Have to. And when you're managing a diva like Enzo, this is no easy task.

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Answer: [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

There is a total of 8 + 5 + 7 + 10 = 30 balls. There is 8 + 10 = 18 black or white balls. 18 / 30 simplifies to [tex]\frac{3}{5}[/tex].

Ethernet LANs are usually arranged in a star topology with computers wired to central switching circuitry that is incorporated in modern routers.

Ethernet is a family of computer networking technologies that is used in LAN, metropolitan area networks (MAN), and wide area networks (WAN). It was first introduced in 1980 by Xerox Corporation, and later standardized by the Institute of Electrical and Electronics Engineers (IEEE) as IEEE 802.3.

Ethernet networks can be implemented in different topologies, such as a bus, star, or mesh topology. However, the most common topology for Ethernet LANs is a star topology, in which computers are wired to a central switching circuitry that is incorporated in modern routers. This allows for efficient communication between the computers on the network.In addition to LANs, Ethernet is also used for other networking applications such as Internet access, wireless networking, and broadband access. Overall, Ethernet is a widely used technology that has become an important component of modern computer networking.

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Answer:

D is correct.

Step-by-step explanation:

[tex](x + y + 2)(y + 1)[/tex]

[tex] xy + x + {y}^{2} + y + 2y + 2[/tex]

[tex] {y}^{2} + xy + x + 3y + 2[/tex]

So D is the correct answer.

Answer:

Step-by-step explanation:

Answer:

87.1 degrees

Step-by-step explanation:

First, you know the sum of the angles is 180 degrees. So, 5x+4x+10+10x-5=180.

Then, simplify to 19x+5=180. So, 19x=175. That means by dividing both sides by 19 x is approximately 9.21.

Finally, plug in x into angle 3.

10x9.21-5

=92.1-5

=87.1

So, the third angle is approximately 87.1.

The true statements for a concession sale at a sporting event are:

The following statements are true based on the given data:

7/11 of the people who ordered a hamburger ordered French fries. (252 hamburger orders x 7/11 = 162 orders of French fries with hamburger)

4/11 of the people who ordered French fries ordered a hamburger. (468 French fry orders x 4/11 = 168 orders of hamburgers with French fries)

6/7 of the people who ordered a hot dog ordered French fries. (216 hot dog orders x 6/7 = 186 orders of French fries with hot dog)

2/3 of the people who ordered French fries ordered a hot dog. (468 French fry orders x 2/3 = 312 orders of hot dogs with French fries)

3/7 of the people who ordered a hamburger ordered onion rings. (252 hamburger orders x 3/7 = 108 orders of onion rings with hamburger)

1/3 of the people who ordered a hot dog ordered onion rings. (324 hot dog orders x 1/3 = 108 orders of onion rings with hot dog)

4/7 of the people who ordered onion rings ordered a hamburger. (252 onion ring orders x 4/7 = 144 orders of hamburger with onion rings)

1/2 of the people who ordered onion rings ordered a hot dog. (252 onion ring orders x 1/2 = 126 orders of hot dog with onion rings)

The total number of orders for each item can be calculated by adding up the corresponding row or column totals.

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Image transcribed:

Concession sales at a sporting event are monitored, and the data is recorded in the two-way table below. Which of the following statements are true?

| French fries | Onion rings | Total

Hamburger | 252 | 144 | 396

Hot dog | 216 | 108 | 324

Total | 468 | 252 | 720

7/11 of the people who ordered a hamburger ordered French fries.

4/11 of the people who ordered French fries ordered a hamburger.

6/7 of the people who ordered a hot dog ordered French fries.

2/3 of the people who ordered French fries ordered a hot dog.

3/7 of the people who ordered a hamburger ordered onion rings.

1/3 of the people who ordered a hot dog ordered onion rings.

4/7 of the people who ordered onion rings ordered a hamburger.

1/2 of the people who ordered onion rings ordered a hot dog.

Answer:

[tex]\boxed{706.50}[/tex]

Step-by-step explanation:

You can resolve multiple decimals easily. For this, we need to treat them just like any other number. We can follow the next steps:

[tex]\begin{array}{l}314\times225\\ \cline{0-1}\ \ 1570\\\ \ 628\\\ 628 \\ \cline{0-1}70650\end{array}[/tex]

Finally, we apply step 3:

[tex]\therefore 3.14 \times 225= 706.50[/tex]

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Using some trigonometric relations we can see that x  = 6.72

Here we know that the larger triangle is completely defined, then we can find the angle at X using a trigonometric relation:

Sin(a) = opposite cathetus/hypotenuse

Sin(a) = 7/25

Using the inverse sine function:

a = Asin(7/25) = 16.26°

Now, notice that angle at X is also an angle of the triangle whose x is a side, then we can use the relation:

sin(16.26°) = opposite cathetus/hypotenuse.

This time:

opposite cathetus = x

hypotenuse = 24

Replacing that:

sin(16.26°) = x/24

x = 24*sin(16.26°) = 6.72

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(a) Option A, if its value is a large positive number, statistic A x2 provides strong evidence for the alternative hypothesis.

(b) Option B, the null hypothesis that gender is not related to personal goals and the alternative hypothesis that gender is related to personal goals.

(c) Option B, the variables considered in the chi-square test for the evaluation of contingency table B are categorical variables.

(a) If the x2 statistic is a large positive number, it provides strong evidence for the alternative hypothesis. The x2 statistic is used in hypothesis testing to determine if there is a significant difference between observed and expected frequencies. Large positive values ​​indicate that the observed frequency is significantly different from the expected frequency, supporting the alternative hypothesis.

(b) The hypotheses tested in the chi-square test for the contingency table are the null hypothesis that gender is not related to personal goals and the alternative hypothesis that gender is related to personal goals. personal goals. This test determines whether there is a significant relationship between two categorical variables.

(c) The variables considered in the chi-square test used to evaluate the contingency table are categorical variables. These variables cannot be assumed to be mean or normally distributed. The chi-square test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.

Complete Question:

For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.

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the submarine is approximately 2.236 kilometers from its starting point.

Distance is a numerical measurement of the space between two points. It is the length of the path traveled by an object moving from one point to another, regardless of the direction it takes. Distance is typically measured in units such as meters, kilometers, feet, miles, or any other unit of length.

The submarine is essentially moving in a square pattern, with sides of length 1 km. Each time it moves north or west, it changes its distance from the starting point by 1 km.

Since the submarine moves 1 km north and 1 km west in each "leg" of its journey, it will complete 20 legs before traveling a total of 40 km. At this point, it will be 1 km north and 1 km west of its starting point.

The 21st and final leg of the journey brings the submarine 1 km north, so it ends up 2 km north and 1 km west of its starting point. Using the Pythagorean theorem, we can find the distance between the starting point and the final position of the submarine:

d = √((2 km)² + (1 km)²)

=√(5) km

≈ 2.236 km

Therefore, the submarine is approximately 2.236 kilometers from its starting point.

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If the standard deviation is 12,000 dollars for four electricians, then the standard deviation for the sampling distribution of the sample mean is 6000 dollars.

The standard deviation of the sampling distribution of the sample mean, is also known as the standard error of the mean,

The standard deviation is be calculated using the formula,

⇒ standard-error of mean is = σ/√n,

Where σ = population standard deviation and n = sample size,

In this case, σ = 12,000 dollars and n = 4.

Substituting these values into the standard deviation formula, we get,

⇒ "standard-error" of mean = 12000/√4 = 6,000 dollars.

Therefore, the standard deviation for the sampling distribution of the sample mean is 6,000 dollars.

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The given question is incomplete, the complete question is

Suppose that, on average, electricians earn approximately μ = 54,000 dollars per year in the United States. Assume that the distribution for electrician's yearly earnings is normally distributed and that the standard deviation is σ = 12,000 dollars. Given a sample of four electricians,

What is the standard deviation for the sampling distribution of the sample mean?

The probability that the 39 randomly-selected laptops have a mean "replacement-time" as 3.8 years or less is equal to 0.1058.

The distribution of the sample mean follows a normal distribution with mean (μ) = 3.9 years and standard deviation = σ/√n = 0.5/√39 years, where n = 39 is the sample size.

We want to find the probability that the sample mean replacement time is less than or equal to 3.8 years, which is written as : P(x' ≤ 3.8).

By using the z-score formula, we convert this to a standard normal distribution:

⇒ z = (x' - μ)/(σ/√n) = (3.8 - 3.9)/(0.5/√39) = -1.249,

Using a standard normal distribution table, the probability that a standard normal variable is less than or equal to -1.249,is approximately 0.1058,

Therefore, the required probability is approximately 0.1058.

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The given question is incomplete, the complete question is

Assuming that the laptop replacement times have a mean of 3.9 years and a standard deviation of 0.5 years, find the probability that 39 randomly selected laptops will have a mean replacement time of 3.8 years or less.

The roots f the following polynomial function F(x) = x3 - x2 - 5x - 3 are (A) -1 and (B) 3.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

For instance, the polynomial 2x+5 has an exponent of 1.

f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree.

Polynomials of degrees 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.

So, there is only one true, positive root, according to Descartes' rule of signs. On the list, 3 is the only real number that is positive.

When dividing x3-x2-5x-3 by (x-3), we may use synthetic division to get the quotient and discover that it is x2+2x+1, which we know as (x+1)2.

As a result, 3 is a root and -1 is a root with multiplicity 2.

A and B are the options that need to be checked.

Therefore, the roots f the following polynomial function F(x) = x3 - x2 - 5x - 3 are (A) -1 and (B) 3.

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Complete question:

Which of the following are the roots of the polynomial function? Check all that apply.

F(x) = x3 - x2 - 5x - 3

Answer:

yo moma

Step-by-step explanation:

The average distance between each data value and the data set's mean is represented by the mean absolute deviation of the data set's 3, 7, 10, 12, and 15 values, which is 3.24. It provides a measurement of the variance or departure from the mean of the data values.

The term "absolute" refers to the distance a number is from 0 on a number line. The absolute value of a number is always positive and represents the magnitude of the number regardless of its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

The distance between two points on number line is always the absolute value of the difference between those points. Hence distance a number is from 0 on a number line is always the absolute value of that number.

To deviate means to differ or vary from a standard or expected value. The mean absolute deviation of a data set is the average (mean) distance from each data value to the mean of the data set. It measures how spread out the data values are from the mean.

For example, consider the data set {3, 7, 10, 12, 15}. The mean of this data set is (3 + 7 + 10 + 12 + 15)/5 = 9.4. To calculate the mean absolute deviation, we need to find the absolute deviation of each data value from the mean, then take the mean of those absolute deviations.

The absolute deviations from the mean are:

|3 - 9.4| = 6.4

|7 - 9.4| = 2.4

|10 - 9.4| = 0.6

|12 - 9.4| = 2.6

|15 - 9.4| = 5.6

The mean absolute deviation is the average of these absolute deviations:

(6.4 + 2.4 + 0.6 + 2.6 + 5.6)/5 = 3.24

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The slope of the line is 8, which represents the rate at which the amount of money in the account is increasing per week.

An equation is a mathematical statement that asserts that two expressions have the same value. It typically consists of two parts: the left-hand side, which contains one expression, and the right-hand side, which contains another expression. The two sides are separated by an equal sign. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

Here,

The graph is not shown, but based on the given information, we can determine the slope of the line using the slope-intercept form of a linear equation:

y = mx + b

where y is the amount of money in the account, x is the number of weeks, m is the slope (the rate at which the money in the account is changing), and b is the y-intercept (the initial amount of money in the account). We know that Fred starts with 6 dollars in the account (y-intercept), and deposits 8 dollars each week (slope). Therefore, the equation for the line is:

y = 8x + 6

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Complete question:

Fred starts with 6 dollars in a bank account. He deposits exactly 8 dollars each week, and does not take any money out. The graph below represents the relationship between the number of weeks and the amount of dollars in the account. What is the slope of the line?

The expression for the dimensions of the combined park and bike path in terms of x is length= 200+2x ft and  width = 300+ 2x ft.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given rectangle park length is 200ft and width is 300 ft.

Now in the given diagram , path for bike is expended in both sides of the park.

Length of bike path = x + x = 2x

Width of bike path = x + x = 2x

Then combined dimensions for park and bike path is,

=> length = length of park+ length of path

=> length = 200+2x ft

=> width = width of park + width of bike path

=> width = 300+ 2x ft.

Hence the expression for the dimensions of the combined park and bike path in terms of x is length= 200+2x ft and  width = 300+ 2x ft.

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Therefore , the solution of the given problem of  equation comes out to be for 0 brothers, 78°, for 1 brother, 132°, for two brothers, 66°,for 3 brothers, 42° and for 4 brothers, 42°.

A linear recovery model is founded on the formula: y=mx+b. B is the slope, and m is the y-intercept. The phrase "Bivariate logistic formulas have two components" is frequently used, despite the fact that y and y are two separate elements. When it comes to using linear functions, there are no easy solutions. and. Y=mx+b is the expression, where m stands for slopes and b for the y-intercept.

Here,

(Frequency  Total Frequency) x 360 equals angle (0).

the aggregate of all frequencies is the total frequency.

We can see from the provided chart that:

13 individuals lack relatives.

22 individuals each have one sibling.

11 individuals have two siblings, and 7 people have three.

7 individuals have 4 brothers.

13 + 22 + 11 + 7 + 7 = 60 is the overall frequency.

Using the aforementioned method, we can now determine the angle for each category:

For 0 siblings: Angle = (13 ÷ 60) x 360 = 78°

For 1 sibling: Angle = (22 ÷ 60) x 360 = 132°

For 2 siblings: Angle = (11 ÷ 60) x 360 = 66°

For 3 siblings: Angle = (7 ÷ 60) x 360 = 42°

For 4 siblings: Angle = (7 ÷ 60) x 360 = 42°

The total of all angles ought to

All the angles should total up to 360 degrees, which we can verify by:

78° + 132° + 66° + 42° + 42° = 360°

Therefore, the angles needed to represent the number of siblings among 60 individuals on a pie chart are:

for 0 brothers, 78°

for 1 brother, 132°

For two brothers, 66°

for 3 brothers, 42°

for 4 brothers, 42°

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The probability of renting exactly three apartments in a week using poisson distribution is 0.2107.

A Poisson distribution is a probability distribution that is used to evaluate how many times a particular event is likely to occur during a certain period of time.

The formula for calculating the probability of an event in a poisson distribution is as follows:

where e = 2.71828 (Euler's constant), x = the number of occurrences, μ = the expected value/average number of occurrences.In the given problem, the average number of new apartments rented per week is 2.3. Therefore,μ = 2.3Using the formula for Poisson distribution, we get:

P(3) = e^−2.3 * 2.3^3 / 3!

P(3) = 0.2107Therefore, the probability of renting exactly three apartments in a week is 0.2107.

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The values in the columns which completes the table for the COLA salary adjustments are as follows;

[tex]\begin{tabular}{|c|c|c|c|} \cline{1-4}&Amount & Amount&New Salary\\ \cline{1-4}1& \$1,672&\$1,584&\$47,256 \\ \cline{1-4} 2 & \$1,312&\$3,116&\$45,428 \\ \cline{1-4}3&\$1,483&\$1,425&\$34,408 \\ \cline{1-4}\end{tabular}[/tex]

4. The COLA Increase and New Salaries are presented as follows;

[tex]\begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} & J. Spar&T. Beggins & R. Stokes &D. Garcia& J. Stiles\\ \cline{1-6}COLA Increase & 6.5\%&6.5\%&6.3\%&7.5\%&6.3\% \\ \cline{1-6} New Salary & \$20,430&\$23,925&\$35,480.04&\$15,792.3&\$31,385.64 \\ \cline{1-6} \end{tabular}[/tex]

5. Ron Fortini's weekly salary prior to the increase was about $899.12

What is a COLA?

COLA is an acronym for Cost-Of-Living-Adjustment, which is an increase in salary or income to keep pace with the current inflation rate or trend and increased societal cost of living.

The amount C. North received based on COLA is; $44,000 × 2.80% = $1,232

The amount received as merit is; $44,000 × 3.60% = $1,584

The New Salary amount  = $1,232 + $1,584 + $44,000 = $47,256

The amount N. Vanders received as COLA is; $41,000 × 3.20% = $1,312

The amount received as merit is; $41,000 × 7.60% = $3,116

The New Salary is; $41,000 + $1,312 + $3,116 = $45,428

The amount M. Clark received as COLA is; $31,500 × 4.70% = $1,480.5

The amount M. Clark received as merit is; $31,500 × 4.50% = $1,417.5

M. Clark's New Salary is; $31,500 + $1,480.5 + $1,417.5 = $34,397

Please find above the completed columns that complete the questions 1, 2, and 3 above.

4. The COLA received based on the sliding scale for the cost-of-living adjustment are;

J. Spar; 6.5%

T. Beggins; 6.5%

R. Stokes; 6.3%

D. Garcia; 7.5%

J. Stiles; 6.3%

The New Salaries based on the total increase are;

               [tex]{}[/tex]                                      New Salary

J. Spar; $18,000 + $18,000 × 12.50%  = $20250

T. Beggins; $21,750 + $21,750 × 10.00% = $23,925

R. Stokes; $31,860 + $31,860 × 11.4% = $35,492.04

D. Garcia; $14,615 + $14,615 × 8.20% = $15,813.43

J. Stites; $27,916 + $27,916 × 12.525% = $31,412.479

Please find included the completed rows for the COLA Increase and the New Salary above

5. Let x represents Ron Fortini's prior weekly salary

Ron Fortini's weekly salary after 5.20% merit increase and 2.75% cost-of-living increase, Ron Fortini's new salary is $968.80

Therefore;

New weekly salary =  Prior weekly salary + (Prior weekly salary × (5.20% + 2.75%))

$968.80 = x + x × 0.0775 = 1.0775·x

1.0775·x = $968.80

x = $968.80/1.0775 ≈ $899.12

Therefore, Ron Fortini's weekly salary prior to the increases was $899.12

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