Tickets for the school play cost $5 for students and $8 for adults. For one performance, 128 tickets were sold for $751. How many tickets were for adults and how many were for students?

Answers

Answer 1

91 student tickets were sold and 37 adults tickets were sold whose total 128 tickets were sold.

What is elimination method?

The elimination method is a technique for solving a system of linear equations, which involves adding or subtracting the equations to eliminate one of the variables, and then solving for the other variable.

According to question:

Let x be the number of student tickets sold, and y be the number of adult tickets sold. Then we can set up a system of two equations to represent the information given:

x + y = 128 (1) (the total number of tickets sold is 128)

5x + 8y = 751 (2) (the total revenue from ticket sales is $751)

We can solve for one of the variables in terms of the other in the first equation:

x = 128 - y

Substituting this expression into the second equation to eliminate x, we get:

5(128 - y) + 8y = 751

Expanding and simplifying:

640 - 5y + 8y = 751

3y = 111

y = 37

Therefore, 37 adult tickets were sold. Substituting this value back into equation (1) to solve for x, we get:

x + 37 = 128

x = 91

Therefore, 91 student tickets were sold.

To know more about elimination visit:

https://brainly.com/question/30284924

#SPJ1


Related Questions

A+9 as a verbal expression

Answers

Answer:

"9 more than A" is a verbal expression.

A landscaper needs to mix a 80% pesticide solution with 35 gal of a 30% pesticide solution to obtain a 55% pesticide solution. How many gallons of the 80%
solution must he use?

Answers

By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.

What is equation?

In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values ​​of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.  

Let's say a landscaper needs to use x gallons of an 80% pesticide solution.

The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.

After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.

Since we need a 55% pesticide solution, we can set the following formula:

[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]

Therefore, landscapers should use 35 gallons of an 80% pesticide solution.

To know more about equation visit:

brainly.com/question/649785

#SPJ1

Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}

Answers

Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}.

The decision boundary is the line that separates the two classes. When it comes to the nearest neighbour method, the boundary of a class is determined by the closest data point in the other class.What is the nearest neighbour method?The nearest neighbour method (NNM) is a type of lazy learning method in which the data is stored and the computation is deferred until the classification phase.

The goal of the nearest neighbor technique is to use the pattern of the closest data point to classify a new sample. It's also one of the simplest non-parametric classification methods, and it's based on the assumption that the feature spaces used by each class are continuous regions.For Class 1, there are two labeled training data points: (0, 0)T and (0, 1)T. Similarly, for Class 2, there are two labeled training data points: (1, 0)T and (0, 0.5)T.

To generate decision boundaries, follow the steps below:Step 1: Plot the given labeled training data. They are shown in the figure below. Step 2: Label the data points according to their class: Class 1 and Class 2.Step 3: Now, we need to find the nearest neighbors. Find the nearest neighbor for each of the labeled training data points from the opposite class. The distances are calculated as follows:For the Class 1 data points, the nearest neighbor is Class 2's (1, 0)T data point.

For the Class 2 data points, the nearest neighbour is Class 1's (0, 1)T data point.Step 4: Connect the nearest neighbour's labeled training data points with a line. These are the decision boundaries. The red line represents the decision boundary between Class 1 and Class 2. The green line represents the decision boundary between Class 2 and Class 1. The slopes of the decision boundaries are -1 for the red line and 1 for the green line. These slopes are the result of the negative reciprocal of the nearest neighbour's slope. The break point for the red line is 0.5, while the break point for the green line is 0. A break point is the point at which the decision boundary intersects the y-axis.

Learn more about nearest neighbor method:

https://brainly.com/question/29457878

#SPJ11

4. What is the solution to 2 + 3(2a + 1) = 3(a + 2)?

Answers

Answer:

a=1/3

Step-by-step explanation:

First, expand the brackets by doing multiplication:

2+6a+3=3a+6

Then, move the unknown to the left and the numbers to the right:

3a=6-5

3a=1

a=1/3

The solution to the given equation is -1.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 2+3(2a+1)=3(a+2)

2+6a+3=3a+2

6a+5=3a+2

6a-3a=2-5

3a=-3

a=-1

Therefore, the solution to the given equation is -1.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

PLS ANSWER THIS ASAP

In two similar triangles, the ratio of the lengths of a pair of corresponding sides is 7:8. If the perimeter of the larger triangle is 32, find the perimeter of the smaller triangle.​

Answers

The perimeter of the smaller triangle would be = 28.1

How to calculate the perimeter of the smaller triangle?

A triangle can be defined as a three sided polygon that has a total internal angle of 180°.

To calculate the perimeter of the triangle is to find out the scale factor that exists between the two triangles.

The formula for scale factor = original object/new object

Scale factor= 8/7 = 1.14

The perimeter of the smaller triangle = 32/1.14

= 28.1.

Learn more about perimeter here:

https://brainly.com/question/25092270

#SPJ1

Isosceles Trapezoids: Only one pair of opposite sides are _______​

Answers

Answer:

equal

Step-by-step explanation:

A circular flower garden has an area of 314m². A sprinkler at the center of the garden can cover an area of 12 m. Will the sprinkler water the entire garden?

Answers

Step-by-step explanation:

No,

if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular

A=πr2

A=3.142*36

A=113.112 cm3

8hr/2days=28hr/?days

Answers

28/8 = 3.5

2 x 3.5 = 7

? = 7 days

To check your answer,
8/2 = 4
28/7 = 4

find bases for the null spaces of the matrices given in exercises 9 and 10. refer to the remarks that follow example 3 in section 4.2.

Answers

In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.

The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.

The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.

for such more questions on  Gauss-Jordan elimination

https://brainly.com/question/20536857

#SPJ11

Simplify (cos^2a - cot^2a)/(sin^2a - tan^2a)

Answers

Answer:

The simplified expression is sec^2a

Step-by-step explanation:

We can start by using the trigonometric identities:

cot^2 a + 1 = csc^2 a

tan^2 a + 1 = sec^2 a

Using these identities, we can rewrite the expression as:

(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)

= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))

= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)

Now we can use the identity:

sin^2 a + cos^2 a = 1

to rewrite the expression further:

= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)

= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)

= sin^2 a / sin^2 a (1 - cos^2 a)

= 1 / (1 - cos^2 a)

= sec^2 a

Therefore, the simplified expression is sec^2 a.

math question please help

Answers

Answer:

Step-by-step explanation:

only the 1st and 5th statements are true

 choose all the shapes with at least one pair of perpendicular sides

Answers

According to the image, we can infer that the shapes which have at least 1 pair of perpendicular sides are the top leftmost trapezium and the bottom-center rectangle.

What is the definition of perpendicular sides?

Perpendicular sides is a term to refer to a shape with a special characteristic. These shapes have two sides connected through an angle or vertex of 90°. So, to select the correct shapes we have to take into account this feature. According to the above, the correct shapes would be:

The top leftmost trapezium. The bottom-center rectangle.

Learn more about perpendicular in: https://brainly.com/question/11707949

#SPJ1

Write the line equation of (5,-12) and (0,-2)

Answers

Answer:

To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (-2 - (-12)) / (0 - 5)

slope = 10 / (-5)

slope = -2

Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the given points on the line.

Let's use the point (5,-12):

y - (-12) = -2(x - 5)

y + 12 = -2x + 10

y = -2x - 2

Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.

are these equivalent
10-2x -2x10

Answers

No they are not equivalent. 10-2x = -2(x-5) and -2x10 is -20

Schools have different ways of fund raising. The parents and the SGB of Progress High School agree that each learner should donate an amount to the school. The money is payable during the first month of the year. 1.1 Use TABLE 1 to answer the questions that follow. Write down the donation per leamer. 1.2 TABLE 1: INCOME IN RANDS OF FUND RAISING Number of learners that paid Income (R) 1 200 1.3 1.5 Calculate the missing value A. 10 2 000 20 45 215 4 000 9 000 A [Adapted from original school financial books ] Use TABLE 1 and write down the dependent variable. 1.4 Write the income received from 10 leamers to the income received from 45 learners, in a ratio in its simplest form. (3) (2) (2) (2) have The SGB chairperson claims that if 80% of the leamers paid, the school would raised more than R170 000. There are 1 100 learners enrolled at the school. Verify, by showing ALL calculations, whether his statement is valid. (4)

Answers

Answer: 1.1. The donation per learner cannot be determined from the given table.

1.2. TABLE 1: INCOME IN RANDS OF FUNDRAISING

Number of learners that paid Income (R)

1 200

1.3. To calculate the missing value A, we need to add up all the given incomes and subtract it from the total income for 45 learners, which is 45 x A. Then we can solve for A:

Total income = 200 + 150 + 10(2,000) + 20(45) + A + 4,000 + 9,000

Total income = 45A

45A = 25,150

A = 558.89

Therefore, the missing value A is R558.89.

1.4. The dependent variable in the table is the income received from fundraising.

To find the ratio of income received from 10 learners to income received from 45 learners, we need to divide the income received from 10 learners by the income received from 45 learners and simplify the fraction:

Income from 10 learners = R1,100 (since each learner donates R110)

Income from 45 learners = R215

Ratio = Income from 10 learners : Income from 45 learners

= 1,100 : 215

= 20 : 3 (in its simplest form)

The total number of learners enrolled at the school is 1,100. If 80% of the learners paid, then the number of learners who paid is:

80% of 1,100 = 0.8 x 1,100 = 880 learners

The minimum income that the school can raise if 80% of the learners paid is when each of the 880 learners paid the minimum donation, which is R150:

Minimum income = 880 x 150 = R132,000

Since R132,000 is less than R170,000, the SGB chairperson's statement is not valid.

Step-by-step explanation:

the set of all continuous real-valued functions defined on a closed interval (a, b] in ir is denoted by c[a , b]. this set is a subspace of the vector space of all real-val ued functions defined on [a, b]. a. what facts about continuous functions should be proved in order to demonstrate that c [a , b] is indeed a subspace as claimed? (these facts are usually discussed in a calculus class.) b. show that {fin c[a ,b]: f(a )

Answers

Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.

To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.

for such more questions on continuous function
https://brainly.com/question/30089268

#SPJ11

Enter the correct answer in the box.
Write this expression in simplest form.
Don’t include any spaces or multiplication symbols between coefficients or variables in your answer.

Answers

16h^(10/2) *remove the root sign

16h^5 *simplify the exponent

Answer: 16h^5

Step-by-step explanation: im correct

Marcus bought a booklet of tickets to use at the amusement park. He used 25% of the tickets on rides, 1 2 of the tickets on video games, and the rest of the tickets in the batting cage. Marcus says he used 23% of the tickets in the batting cage. Do you agree? Complete the explanation.

Answers

Answer: Do not agree.

Step-by-step explanation:

To determine if we agree with Marcus, we need to verify if the percentages he used on rides, video games, and batting cage add up to 100%.

Marcus used 25% of the tickets on rides and 1/2 on video games. So, the total percentage of tickets he used is:

25% + 1/2 × 100% = 25% + 50% = 75%

This means that Marcus should have used 25% of the tickets in the batting cage. If he said he used 23% of the tickets in the batting cage, then we do not agree with him.

You want to measure the height of an antenna on the top of a 125-foot building. From a point in front of the building, you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°. How tall is the antenna, to the nearest tenth of a foot?

Answers

The antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.

What is an angle of elevation

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

To get the height of the antenna, we subtract the height of the building from the height from the bottom of the building to the top of the antenna.

we shall represent the distance from the point of observation to the building with x and the height from the bottom of the building to the top of the antenna with y. so that;

tan 68° = 125/x {opposite/adjacent}

x = 125/ tan 68° {cross multiplication}

x = 50.5033

tan 71° = y/50.5033

y = 50.5033 × tan 71°

y = 144.6722

height of the antenna = 144.6722 - 125

height of the antenna = 19.6722

Therefore, the antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.

Know more about angle of elevation here:https://brainly.com/question/2096694

#SPJ1

when the expression -3x^5+6x^2-9x^3-x is written with terms in descending order (from highest to lowest), which list represents the coefficients of the term?

a. 6, -9, -3, -1
b. -3, 6, -9, -1
c. 1, 6, -9, -3
d. -3, -9, 6, -1

Answers

To write the expression in descending order, we need to arrange the terms based on the exponent of x, from highest to lowest. So the expression can be written as:

-3x^5 - 9x^3 + 6x^2 - x

Now we can see that the coefficients of the terms in descending order are:

-3, -9, 6, -1

Therefore, the correct answer is option d.

(13-12p) × (13+12p)
...

Answers

Answer:

169 - 144p²

Step-by-step explanation:

(13 - 12p) × (13 + 12p)

each term in the second factor is multiplied by each term in the first factor

13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis

= 169 + 156p - 156p - 144p² ← collect like terms

= 169 - 144p²

Put the steps in correct order to prove that if n is a perfect square, then n + 2 is not a perfect square.1).Lets assume m ≥ 1.2) If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)^2.3) Hence, n + 2 is not a perfect square4) Expand (m + 1)^2 to obtain (m + 1)^2 = m2 + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.5) .Assume n = m2, for some nonnegative integer m

Answers

The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:

Step 1: Assume n = m², for some non-negative integer m.

Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².

Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.

Step 4: Let's assume m ≥ 1.

Step 5: Hence, n + 2 is not a perfect square.

The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.

In the final step, we conclude that n + 2 is not a perfect square.

To know more about the "perfect square": https://brainly.com/question/1538726

#SPJ11

Tamarisk company began operations on january 2, 2019. It employs 9 individuals who work 8-hour days and are paid hourly. Each employee earns 9 paid vacation days and 7 paid sick days annually. Vacation days may be taken after january 15 of the year following the year in which they are earned. Sick days may be taken as soon as they are earned; unused sick days accumulate. Additional information is as follows. Actual hourly wage rate vacation days used by each employee sick days used by each employee 2019 2020 2019 2020 2019 2020 $6 $7 0 8 5 6 tamarisk company has chosen to accrue the cost of compensated absences at rates of pay in effect during the period when earned and to accrue sick pay when earned

Answers

The total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.

To calculate the cost of compensated absences for Tamarisk Company, we need to calculate the number of vacation days and sick days earned by the employees in 2019 and 2020, and then calculate the cost of the days earned but not taken.

Each employee earns 9 vacation days per year. As they can be taken after January 15th of the year following the year in which they are earned, the vacation days earned by the employees in 2019 can be taken in 2020. Therefore, in 2019, no vacation days were taken by any employee.

In 2020, the employees took a total of 8 vacation days. As there are 9 employees, the total vacation days taken in 2020 were 9 x 8 = 72.

Sick Days:

Each employee earns 7 sick days per year, and unused sick days accumulate. In 2019, the employees used a total of 5 sick days. Therefore, the unused sick days at the end of 2019 were 9 x 7 - 5 = 58.

In 2020, the employees used a total of 6 sick days, and the unused sick days at the end of 2020 were 58 + 9 x 7 - 6 = 109.

To find the cost of compensated absences. The unused sick days and vacation days must be multiplied to get the hourly wage rate in effect in a year.

In 2019, the cost of compensated absences was 58 x $6 = $348.

In 2020, the cost of compensated absences was (72 + 109) x $7 = $1,399.

Therefore, the total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.

To know more about the cost of compensated absences

brainly.com/question/12987530

#SPJ4

Juanita’s Social Security full monthly retirement benefit is $2,128. She started collecting Social Security at age 65. Her benefit is reduced since she started collecting before age 67. Using the reduction percents from Example 1, find her approximate monthly Social Security benefit to the nearest dollar.EXAMPLE 1Marissa from Example 2. What will her monthly benefit be, since she did not wait until age 67 to receive full retirement benefits?SOLUTION Age 67 is considered to be full retirement age if you were born in 1945. If you start collecting Social Security before age 67, your full retirement benefit is reduced, according to the following schedule.• If you start at collecting benefits at 62, the reduction is about 30%.• If you start at collecting benefits at 63, the reduction is about 25%.• If you start at collecting benefits at 64, the reduction is about 20%.• If you start at collecting benefits at 65, the reduction is about 13.3%.• If you start at collecting benefits at 66, the reduction is about 6.7%.Marissa’s full retirement benefit was $1,130.40. Since she retired at age 65, the benefit will be reduced about 13.3%.Find 13.3% of $1,130.40, and round to the nearest cent.0.133 x 1,130.40Subtract to find the benefit Marissa would receive.1,130.40 x 150.34Marissa’s benefit would be about $980.06.EXAMPLE 2Marissa reached age 62 in 2007. She did not retire until years later. Over her life, she earned an average of $2,300 per month after her earnings were adjusted for inflation. What is her Social Security full retirement benefit?

Answers

Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

What is social security benefits retirement age?

The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.

Given that, Juanita started collecting benefits at age 65.

Thus, her benefits reduced by 13.3%.

0.133 x $2,128 = $283.10

Deducting the reduction amount from the total:

$2,128 - $283.10 = $1,844.90

Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

Learn more about social security benefits here:

https://brainly.com/question/20911574

#SPJ1

James have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Find how much water is in each tanks

Answers

Answer:

ames have 18 litres of water. He poured unequally into 3 tank

I. Poured three quarter of water from tank one into tank 2

II. Poured half of the water that is now in tank 2 into tank 3

III. Poured one third of water that is now in tank 3 into tank 1

Find how much water is in each tanks

Step-by-step explanation:

Let's start with the amount of water in tank 1 as x liters.

I. Poured three quarter of water from tank one into tank 2, so tank 1 now has 1/4 of x liters and tank 2 has 3/4 of x liters.

II. Poured half of the water that is now in tank 2 into tank 3, so tank 2 now has 3/8 of x liters and tank 3 has 3/8 of x liters.

III. Poured one third of water that is now in tank 3 into tank 1, so tank 3 now has 1/3 * 3/8 * x = 1/8 * x liters and tank 1 has 1/4 * x + 1/8 * x = 3/8 * x liters.

We know that James poured 18 liters of water into the three tanks, so the sum of the water in the three tanks must be 18 liters.

3/8 * x + 3/8 * x + 1/8 * x = 18

Simplifying the equation, we get:

7/8 * x = 18

x = 18 * 8 / 7 = 20.57 (rounded to two decimal places)

Therefore, the amount of water in each tank is:

Tank 1: 3/8 * x = 7.71 liters

Tank 2: 3/8 * x = 7.71 liters

Tank 3: 1/8 * x = 2.57 liters

a credit risk study found that an individual with good credit score has an average debt of $15,000. if the debt of an individual with good credit score is normally distributed with standard deviation $3,000, determine the shortest interval that contains 95% of the debt values.

Answers

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98

How do we calculate the interval values?

Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.

Then the 95% confidence interval can be calculated as follows:

Upper limit: µ + Zσ

Lower limit: µ - Zσ

Where

µ is the mean ($15,000)Z is the z-scoreσ is the standard deviation ($3,000).

The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.

The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.

The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore

Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880

Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.

See more about confidence interval at: https://brainly.com/question/15712887

#SPJ11

Proving Triangle Similarity

Answers

The proof is completed using two column proof as follows

Statement                               Reason

QT ⊥ PT                                   Given

∠ QRP ≅ ∠ SRT = 90              definition of perpendicularity

∠ QPR ≅ ∠ STR                       Given

Δ PQR is similar to Δ TSR       AA similarity theorem

What is AA similarity theorem?

The AA similarity theorem, also known as the Angle-Angle Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.

In the given triangle, the two angles given to be equal are

∠ QRP ≅ ∠ SRT = 90 and ∠ QPR ≅ ∠ STR

Hence the triangles are similar

Learn more about AA similarity theorem at:

https://brainly.com/question/26462153

#SPJ1

Answer:

:)

Hopefully this helps you guys :)

good luck :D

What is the answer to this math problem? I can’t seem to figure it out.

Answers

Answer:

X

Step-by-step explanation:

We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.

Hope this helps!

In each expression below the numbers under the root sign all add to the same number, 10. Determine which expression is greatest. How?

a) √7+ √3
b) √6+ √4
c) √8+ √2

Answers

Answer:

Step-by-step explanation:

I think a calculator is the only way to solve this question:

[tex]\sqrt{7} +\sqrt{3} = 2.96\\\\\sqrt{6} +\sqrt{4} = 2.54\\\\\sqrt{8} +\sqrt{2} =3.07[/tex]

So (c) is the greatest.

Find m ∠ JKL using the picture

Answers

The value of m∠JKL is 34°

How to find the value of m∠JKL?

An angle formed by a tangent and a secant intersecting outside a circle is equal to one-half the difference of the measures of the intercepted arcs.

Based on the theorem above, we can say:

m∠JKL = 1/2 * (159 - 91)

m∠JKL = 1/2 * 68

m∠JKL = 34°

Therefore, the value of m∠JKL in the circle is 34°.

Learn more about tangent-secant theorem on:

https://brainly.com/question/9132922

#SPJ1

Other Questions
in an employer-sponsored defined benefit pension plan, the interest cost included in the pension expense represents: In history,a. evil tends to predominate overgood.b. reason will always win.c. the World Spirit is coming to self-consciousness.d. the individual proves to betriumphant. Ethical conduct is conduct thata. benefits the veterinary staff in some wayb. establishes a VCPRc. fulfills the veterinary staff's moral obligationsd. is specifically outlined in statutory laws Which ideas do the people in the cartoon represent?Select two options.the use of the Internet for everythingthe change from business to casual wearthe young age of internet usersthe benefits of shopping onlinethe shift of retail from storefronts to devices Dividend reinvestment plans (DRIPs) allow shareholders to reinvest their dividends in the company itself by purchasing additional shares rather than being paid out in cash. Understanding how dividend reinvestment plans work dividend reinvestment program invests the dividends in newly issued stock. This type of plan raises new capital for the firm. levels of participation in a dividend reinvestment program suggest that shareholders would be better served if the firm reduced its cash dividends. Why do firms use dividend reinvestment plans? Companies decide to start, continue, or terminate their dividend reinvestment plans for their shareholders based on the firms' need for equity capital. A firm might consider to using DRIPs if it needs additional equity capital. What do both authors show about the everymanarchetype in these excerpts? Eli must motivate the sales force to increase sales in the fourth quarter. If he chooses the wrong medium it could result in which of the following?a. A decrease in the richness of the channelb. A message that is less effective or even misunderstoodc. A message that rewards length over clarityd. A less than systematic writing plan Dust storm blankets in the Midwest and sent deposits as far east and NY and Boston. What happened during 1935? how are animal, plant, and bacterial cells similar? Blastocladiomycetes, neocallimastigomycetes, and chytridiomycetes were originally grouped as a single phylum, based on which of the following feature?Presence of flagella HELP!!Write a quadratic equation in standard form that has solutions of -3 and -4. how many british soldiers were against 100 colonists? Sometimes a liquid can be sitting there and its molecules will become a gas. Thats called___________________________________________. How have African cultures made an impact in Latin American How has oil production affected Southwest Asia? which of the following scenarios illustrates business marketing?A) Molly, a university student buys a book to gift her friendB) tom, the accountant at Martel inc buys a pair of shoes for his daughterC) mark a school student purchases a laptop for his personal useD) Jenny the manager of ikon inc purchases a set of printers for her officeE) none of the above This was an exceptionally dry year for portions of the southwestern United States. Monthly precipitation in Phoenix, Arizona, was recorded in the table and is modeled by y = 0.04088x2 + 0.4485x + 1.862. In what month did Phoenix receive the lowest amount of precipitation? Month (x) Precipitation January 2.27 inches February ? March ? April ? May ? June ? July ? August ? September 2.59 inches October ? November ? December ? Sketch a graph or fill in the table to answer the question. January February November December Education Planning For the past 15 years, an employee of a large corporation has been investing in an employee sponsored educational savings plan. The employee has invested $8,000 dollars per year. Treat the investment as a continuous stream with interest paid at a rate of 4.2% compounded continuously.a. What is the present value of the investment?b. How much money would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the amount found in part a? a. show that the properties of a probability distribution for a discrete random variable are satisfied. During a conversation with his roommate, Brandon realizes that he is not being understood. He notices that he is feeling defensive and becoming angry. What communication variables should Brandon consider in attempting to remedy the situation?