8. three students scheduled interviews for summer employment at the brookwood institute. in each case the interview results in either an offer for a position or no offer. experimental outcomes are defined in terms of the results of the three interviews. let x equal the number of students who receive an offer. is x continuous or discrete?

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

To learn know more about ellipse, visit:

https://brainly.com/question/14281133

#SPJ1

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°

To know more about equation visit:

https://brainly.com/question/11897796

#SPJ1

We can conclude after answering the provided question that Therefore, diameter m GFH = 21° and m GZH = 116°.

In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either concept can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you consider length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.

We know that angle EGF is a right angle (90°) because EG is a diameter.

Given that m FG = 116°, we can calculate m FGE by subtracting it from 180° (the sum of triangle angles):

m FGE = 180 degrees - m FG = 180 degrees - 116 degrees = 64 degrees

m GFH = 180° - m ZGF - m ZGFH = 180° - 90° - 69° = 21°

Finally, we can calculate m GZH by subtracting m FGE from 180° (the sum of triangle angles):

180° m GZH - 180° m FGE - 64° = 116°

Therefore, m GFH = 21° and m GZH = 116°.

To know more about diameter visit:

https://brainly.com/question/5501950

#SPJ1

Answer:

Step-by-step explanation:

yes

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

To know more about equation,

https://brainly.com/question/28243079

#SPJ1

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?

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

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.

An equation of the line that passes through the points (-7, 7) and (−2, −6) in point-slope form is y - 7 = -13/5(x + 7).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]

Where:

At data point (-7, 7), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 7 = \frac{(-6- 7)}{(-2 -(-7))}(x -(-7))\\\\y - 7 = \frac{(-6- 7)}{(-2 +7)}(x +7)[/tex]

y - 7 = -13/5(x + 7)

y = -13x/5 + 7 - 91/5.

y = -13x/5 - 56/5

In this context, we can reasonably infer and logically deduce that an equation of the line that represents this line in slope-intercept form is y = -13x/5 - 56/5.

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

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.

To know more about budget, visit:

https://brainly.com/question/18803390

#SPJ1

The value of m∠Q is 148°.

What is tangent?

The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

Here, we have

Given: PR is ranger to circle Q at Point R. PS is tangent to circle Q at Point S.

We have to find the value of m∠Q.

We know that PR = PS

In ΔPRS

∠P + ∠R + ∠S = 180°

∴ ∠R = ∠S

∠P + ∠R + ∠R = 180°

38 + 2∠R  = 180°

2∠R  = 180° - 32°

2∠R = 148°

∠R  = 74°

∠S =  74°

∠PRQ = 90°

In ΔSRQ

∠SRQ = 90° - 74° = 16°

∠RSQ = 90° - 74° = 16°

∴ ∠SRQ + ∠RSQ + ∠RQS   = 180°

16° + 16° +∠RQS = 180°

∠RQS = 180° - 32°

∠RQS = 148°

m∠Q = 148°

Hence, the value of m∠Q is 148°.

To learn more about the tangent from the given link

https://brainly.com/question/31048699

#SPJ1

The answer is  option (A)  BC=YZ ,to show that AABC = AXYZ by ASA, we need to know that angle C is congruent to angle ∠Y, angle ∠Z is congruent to angle ∠B, and BC is congruent to ZY.

An angle is a geometric figure formed by two rays with a common endpoint, called the vertex of the angle. The two rays are called the sides of the angle, and they can be named in any order. The measure of an angle is the amount of rotation needed to bring one of the rays into alignment with the other.

To show that AABC = AXYZ by ASA, we need to show that two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle. Since we are given that ZZZC and CB ZY, we know that angle ∠C is congruent to angle ∠Y, and angle ∠Z is congruent to angle ∠B. Therefore, we need to find another piece of information that shows that the included sides are congruent.

Looking at the diagram, we can see that side BC is congruent to side ZY, since they are opposite sides of a rectangle. Therefore, we have BC = ZY, which means that statement A, BC=YZ, is true.

So, to show that AABC = AXYZ by ASA, we need to know that angle ∠C is congruent to angle ∠Y, angle ∠Z is congruent to angle ∠B, and BC is congruent to ZY. Since we have all three of these conditions, we can conclude that AABC = AXYZ by ASA.

To know more about Congruent visit:

https://brainly.com/question/29116501

#SPJ1

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.

To know more about measurement, visit:

https://brainly.com/question/4725561

#SPJ1

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio and the ratio in the given situation is 3a:2b = 6:1.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B).

So, we know that:

a+b/a-b = 5/3

Now, solve as follows:

3 ( a + b) = 5 ( a - b)

3 a + 3 b = 5 a - 5 b

5 b + 3 b = 5 a - 3 a

8 b = 2 a

2 a = 8 b

a = 4 b

3 a = 3 × 4 b

3 a = 12 b

3 a: 2 b = 12 b : 2 b

Then: 3a:2b = 6:1

Therefore, if b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio and the ratio in the given situation is 3a:2b = 6:1.

Know more about ratios here:

https://brainly.com/question/2328454

#SPJ1

Correct question:

A+b/a-b=5/3 what are the following ratios? 3a:2b

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.

Learn more about Standard Deviation here

https://brainly.com/question/30260042

#SPJ4

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?

Answer:

yo moma

Step-by-step explanation:

Answer:

An exponential function can be used to model this situation.

In this case, we know that each hour following the initial dose, 80% of the concentration remains in the body from the preceding hour. This means that the amount of penicillin remaining in the body is decreasing exponentially.

We can use the formula for exponential decay, which is:

A = A0 * e^(-kt)

where A is the amount of penicillin remaining in the body at time t, A0 is the initial amount of penicillin (in this case, 500 milligrams), k is the decay constant, and e is the mathematical constant approximately equal to 2.718.

The decay constant, k, can be calculated using the following formula:

k = ln(0.8)

where ln is the natural logarithm.

So the exponential function that can be used to model this situation is:

A = 500 * e^(-0.2231t)

where t is the time in hours since the initial dose was administered.

This function will give us the amount of penicillin remaining in the body at any time t, based on the initial dose and the rate of decay.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

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 given triangles are  similar by AA~, SSS~, SAS~, or not similar.

What is similar triangles in maths?

Triangles that are similar to one another in terms of shape but not necessarily size are called congruent triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size.

7.  In triangles AEB & BDC

 AE/BD = EB/DC

We can conclude that, the corresponding sides are  in common ratio, so triangles are  similar.

Hence, The given triangles are  similar.

8. Given a figure of two triangles, ΔLKM and ΔLJN

Here,

              LK/LJ = LM/LN

             21 - 6/21 = 10/14

                 15/21 = 10/14

                 5/7 = 5/7

We can conclude that, the corresponding sides are in common ratio, so triangles are  similar.

Hence, The given triangles are  similar.

Learn more about Similar triangles

brainly.com/question/14926756

#SPJ1

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

Learn more about mean here:

https://brainly.com/question/31101410

#SPJ1

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.

Learn more about probability on;

https://brainly.com/question/24756209

#SPJ1

Answer:

5 + 10[tex]\sqrt{3}[/tex]

= 22.3205080757

Step-by-step explanation:

Answer:

≈ 13,7 inches

Step-by-step explanation:

Just use trigonometry (sin or cos) from the right triangles ∆ABC and ∆ADC

After answering the provided question, we can conclude that Therefore, inequality the answer is (D) x > -3 and y > 1.

In mathematics, an inequality is a non-equal relationship between two expressions or values. As a result, imbalance leads to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are used to contrast values. Many simple inequalities can be solved by modifying the two sides until only the variables remain. But a number of things contribute to inequality: Negative values are divided or added on both sides. Trade off the left and right.

domain and range of the inequality

[tex]y - 1 < \sqrt{x + 3}\\(y - 1)^2 < x + 3\\(y - 1)^2 - 3 < x\\[/tex]

Therefore, the answer is (D) x > -3 and y > 1.

To know more about inequality visit:

https://brainly.com/question/29914203

#SPJ1

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.

Find out more on concession sales here: https://brainly.com/question/22982044

#SPJ1

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.

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.

Know more about the proportionality theorem here:

https://brainly.com/question/8160153

#SPJ1

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

Learn more on COLA here: https://brainly.com/question/13277390

#SPJ1

The volume of the sphere is approximately 33.51 cubic centimeters.

The volume of a sphere can be calculated using the formula:

V = (4/3)π[tex]r^{3}[/tex]

where r is the radius of the sphere

V is the volume of the sphere

Since the diameter of the sphere is 4 centimeters, the radius is half of that, or 2 centimeters.

Plugging this value into the formula, we get:

V = (4/3)π([tex]2^{3}[/tex])

V = (4/3)π(8)

V = (32/3)π

So the answer is (a)  32/3π[tex]cm^{3}[/tex]

the volume of the sphere is approximately 33.51 cubic centimeters.

The volume of the sphere is a measure of how much space the sphere occupies. The formula for the volume of the sphere tells us that the volume is proportional to the cube of the radius. This means that as the radius increases, the volume of the sphere increases much more rapidly. This is why a small increase in the radius can result in a much larger increase in the volume of the sphere.

To learn more about volume:

https://brainly.com/question/1578538

#SPJ4

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$

Answer:

16

Step-by-step explanation:

When you square a square root (√1^2) it just cancels out. :)

The dimensions of the box are 30 cm by 50 cm by 25 cm.

Area is a measure of the amount of space enclosed by a two-dimensional object, such as a shape or a surface. It is usually expressed in square units, such as square meters (m²), square inches (in²), or square centimeters (cm²), depending on the unit system used.

Let x be the side length of the squares that are cut out of each corner of the cardboard.

When the squares are cut out and the sides are folded up, the resulting box will have dimensions (80-2x) cm by (100-2x) cm by x cm.

The area of the base of the box is:

(80-2x) cm × (100-2x) cm = 8000 - 360x + 4x² cm²

We know that the area of the base is 4000 cm², so we can set this equal to the expression we just found:

8000 - 360x + 4x² cm² = 4000 cm²

Simplifying and rearranging, we get a quadratic equation:

4x² - 360x + 4000 = 0

Dividing both sides by 4, we get:

x² - 90x + 1000 = 0

This quadratic can be factored as:

(x - 40)(x - 25) = 0

Therefore, the possible values of x are x = 40 cm and x = 25 cm.

If we use x = 40 cm, then the dimensions of the box are:

Length = 80 - 2x = 0 cm (not possible)

Width = 100 - 2x = 20 cm

Height = x = 40 cm

If we use x = 25 cm, then the dimensions of the box are:

Length = 80 - 2x = 30 cm

Width = 100 - 2x = 50 cm

Height = x = 25 cm

Therefore, the dimensions of the box are 30 cm by 50 cm by 25 cm.

To know more about quadratic, visit:

https://brainly.com/question/22364785

#SPJ1