Jim bought dishes for his new apartment. They were $40.87 and there is a 6% sales tax. Calculate the sales tax.

Answer:

120

Step-by-step explanation:

we solve this question by using permutation because the order matters

nPr

5P4 = 120

A) Given the quadratic expression:

First, identify the coefficients of the expression:

a is the coefficient of the quadratic term, in this case, a=1

b is the coefficient of the x-term, in this case, b=10

Second, divide all terms by a=1, since we are dividing by one and the expression will remain the same, you can skip this step.

Third, pass the constant to the right side of the equation by applying the opposite operation to both sides of it:

Forth, complete the square by adding (b/2)²

For this expression b=10 so that:

So you have to add 25 to both sides of the expression:

The simplified expression is:

B)

To solve the expression you have to take the square root to both sides of it:

To determine the possible values of x, you have to solve both options separatelly:

1)

Answer:

63/100

Step-by-step explanation:

0.63 = 63/100

Answer:tinham em cada onibus 55 alunos

Step-by-step explanation:

9 alunos tiveram que viajar de carro ,ou seja apenas 330 alunos foram de onibus , 339-9 igual a 330 .

Depois de conseguir esse resultado divida o numero de alunos (330) por numero de onibus (6) o resultado sera 55.

The remaining amount of the substance with the half life of 64.9 days after 100 days is 2.749.

To calculate the amount that remains  after 100 days, this formular can be used

amount remaining = \(a (0.50)^{\frac{t}{h} }\)

where t is the time that was required for the process to take place, where t is 100 days.

h is the halftime, which is been given as 64.9 days

where a is given as the initial amount that is present which is 8.

Then the values can be substituted to have

\(=a (0.50)^{\frac{100}{64.9} }\)

= 2.749

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According to the text, one result of the large surveys conducted among American college graduates regarding their college experience was that a majority of them felt that their college education helped them develop critical thinking and problem-solving skills.

In fact, around 80% of the respondents agreed that their college experience had helped them develop such skills, which they found useful in their personal as well as professional lives.

This is an important finding, as critical thinking and problem-solving abilities are highly valued in today's job market and are often considered essential for career success.

Moreover, the results suggest that American colleges are doing a good job in imparting these skills to their students. However, these survey also revealed that there were differences in the level of satisfaction with college education across different demographic groups, such as gender and ethnicity.

These findings highlight the need for colleges to ensure that their educational programs are inclusive and accessible to all students, regardless of their background.

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Answer: it is 32.6

Step-by-step explanation:

The orginal number that Gavin was thinking of is 32.60.

Let the orginal number be represented with y

Gavin adds 9 to the original number: 9 + y

The answer is doubled: 2(9 + y)

The answer is 83.2: 2(9+y) = 83.2

In order to determine the value of y, take the following steps:

Divide both sides of the equation by 2

9 + y = 41.60

Subtract 9 from both sides of the equation

y = 41.60 - 9

y = 32.60

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Answer:

See attached

Step-by-step explanation:

Refer to attachment

One relation is a linear function

Second one is a graph of non-functional relation

Answer:

below

Step-by-step explanation:

For the first graph, we can use a linear function as it means "straight" lines so when we use the vertical lines test, it passes it (shown below).

We can use a U shaped line so it when we use the vertical line test, it passes through two points to resemble its not a function (shown below).

Best of Luck!

The present value of the loan is approximately 4. $42,817,078.

The present value of a loan is the current worth of all future cash flows associated with the loan. To calculate the present value of the loan, we need to discount each cash flow to its present value using the market rate of 7% per annum, compounded semi-annually.

Let's break down the cash flows:

1. $11 million is received now and has no discounting since it's already in present value.
2. $22 million is received at the end of month 6. We need to discount it to its present value. Since it's six months in the future, we need to calculate the present value of $22 million in six months at a rate of 7% per annum, compounded semi-annually.
3. $11 million is received at the end of 12 months. We need to discount it to its present value. Since it's one year in the future, we need to calculate the present value of $11 million in one year at a rate of 7% per annum, compounded semi-annually.

To calculate the present value, we can use the formula:

PV = FV / (1 + r/n)^(n*t)

Where:
PV is the present value,
FV is the future value,
r is the interest rate,
n is the number of compounding periods per year, and
t is the number of years.

Let's calculate the present value of each cash flow:

1. PV of $11 million received now = $11 million

2. PV of $22 million received in six months:
PV = $22 million / (1 + 0.07/2)^(2*0.5)
PV = $22 million / (1.035)^(1)
PV ≈ $21,233,298

3. PV of $11 million received in one year:
PV = $11 million / (1 + 0.07/2)^(2*1)
PV = $11 million / (1.035)^(2)
PV ≈ $10,583,780

Now, let's add up the present values of each cash flow to find the total present value of the loan:

Total PV = $11 million + $21,233,298 + $10,583,780
Total PV ≈ $42,817,078

Rounded to the nearest dollar, the present value of the loan is approximately $42,817,078.

Based on the provided answer choices, the closest option to the calculated present value is (4) $42,524,656.

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The function has an inverse that is also a function is g(x)=2x-3

A function that can turn into another function is known as an inverse function or anti function. In other terms, the inverse of a function "f" will take y to x if any function "f" takes x to y. The inverse function is designated by f⁻¹ or F⁻¹ if the function is written by f or F. Here, (-1) should not be confused with an exponent or an inverse.

A function takes in values, applies specific procedures to them, and produces an output. The inverse function works, agrees with the outcome, and returns to the initial function.

The solution in which x and y have been reversed is known as an inverse function.

The vertical line test determines whether a function succeeds or fails when you solve for y once more.

1. Here g(x) = 2x - 3 has inverse x = 2y - 3 which simplifies to;

\(y=\frac{x-3}{2}\)

This is a line and is a function;

\(y=\frac{x}{2} +\frac{1}{2}\)

2. k(x) = -9x² has the inverse x = -9y² which simplifies to;

\(y=\sqrt{x/(-9)}\)

This is a function but only for certain values of x.

3. f(x) = |x+2| is an absolute value function.

Not all absolute value functions have function-based inverses.

4. A function's inverse does not exist for the equation w(x) = -20.

The function therefore has a negative that is also a function, which is

g(x)= 2x – 3.

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The number of distinct initial possible pairings for a single-elimination ping pong tournament involving n players, resulting in distinct tournament brackets, is (n-1)!!..

The double exclamation mark represents the double factorial function.The double factorial is a mathematical notation that generalizes the concept of factorial for even or odd numbers. For even n, the double factorial is calculated by multiplying all even numbers from n down to 2. For odd n, it is calculated by multiplying all odd numbers from n down to 1.

In the context of a single-elimination tournament, each player needs a unique opponent in each round to ensure distinct brackets. The first player can be paired with any of the (n-1) remaining players. The next player can be paired with one of the remaining (n-2) players, and so on. By applying the double factorial, the number of distinct initial pairings can be determined as (n-1)!!.

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Answer:

C

Step-by-step explanation:

Answer:

86.5 inches

Step-by-step explanation:

6228 / 72 = 86.5

I'm pretty sure the answer is 54.4% (D).

Answer:

D

Step-by-step explanation:

Answer:

The irrational numbers from the given options are :-

Step-by-step explanation:

Analyse each option carefully.

1) \(13 + \sqrt{25}\) is a rational number because :-

2) \(17\pi\) is irrational because :-

3) \(0.21475467....\) is irrational because :-

4) \(\sqrt{\frac{9}{16} }\) is rational because :-

5) \(-\frac{4}{5} + \sqrt{\frac{6}{9} }\) is irrational because :-

If you have a good credit rating and can afford monthly payments of $441, you can borrow a certain amount from E-Loan for a 60-month auto loan at an interest rate of 4.8% compounded monthly. The total interest paid and the loan amount can be calculated using the given information.

To determine the loan amount, we can use the formula for the present value of an annuity:

Loan Amount = Monthly Payment * [(1 - (1 + Monthly Interest Rate)^(-Number of Payments))] / Monthly Interest Rate

Here, the monthly interest rate is 4.8% divided by 12, and the number of payments is 60.

Loan Amount = $441 * [(1 - (1 + 0.048/12)^(-60))] / (0.048/12)

Calculating this expression gives the loan amount, which is the amount you can borrow from E-Loan.

To calculate the total interest paid, we can subtract the loan amount from the total payments made over the 60-month period:

Total Interest = Total Payments - Loan Amount

Total Payments = Monthly Payment * Number of Payments

Total Interest = ($441 * 60) - Loan Amount

Calculating this expression gives the total interest paid for the loan.

Note: The precise numerical values of the loan amount and total interest paid can be obtained by performing the calculations with the given formula and rounding to two decimal places.

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Answer:

2 outcomes

Step-by-step explanation

The Roslin has 32 students in her class, of these students, 14 are girlsl number of outcomes are 252.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of outcomes can be found by multiplying the number of options for choosing a boy by the number of options for choosing a girl:

Number of outcomes = number of options for choosing a boy x number of options for choosing a girl

Since Mrs. Roslin has 32 students in her class, there are 32 - 14 = 18 boys in her class.

So the number of options for choosing a boy is 18, and the number of options for choosing a girl is 14.

Therefore, the total number of outcomes is:

18 x 14 = 252

Hence, the total number of outcomes is 252.

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The calculated value of x₁ + x₂ if y = -3 - 8√(x - 2) is 24

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

y = -3 - 8√(x - 2)

Add 3 to both sides

So, we have

- 8√(x - 2) = y + 3

Divide both sides by -8

√(x - 2) = -(y + 3)/8

Square both sides

(x - 2) = (y + 3)²/64

So, we have

x = 2 + (y + 3)²/64

When y = -19, we have

x = 2 + (-19 + 3)²/64 = 6

When y = -35, we have

x = 2 + (-35 + 3)²/64 = 18

So, we have

x₁ + x₂ = 6 + 18

Evaluate

x₁ + x₂ = 24

Hence, the value of x₁ + x₂ is 24

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The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

Let the actual width of the picnic area be x yards.

According to the given question.

Laura measured a picnic area near the river and made a scale drawing.

The scale she used was 3 inches : 2 yards.

⇒ The scale is 3 inches : 2 yards

The width of the picnic area in the drawing is 90 inches.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Thereofore, the acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards is given by

3inches : 2 yards = 90inches : x

⇒ 3x = 180

⇒ x = 60yards

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

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According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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On the number line, if 'A' lies at 7 then 'B' could lie at -2, 16.

What is a number line?

A number line can be stretched in either direction indefinitely and is commonly displayed horizontally.

The numerals on the number line grow as one goes from left to right and drop as one moves from right to left.

Given, AB = 9 and 'A' lies at 7

So, basically 'B' can be at -2 on the number line which makes the distance between 'A' and 'B' 9 units. The same is possible for B at 16 on the number line.

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Answer:

Answer is 18!

Step-by-step explanation:

hope this helps

Answer:

27 degrees

Step-by-step explanation:

SinY = 5/11

Sin^-1(5/11) = y

y = 27.03

to the nearest degree is 27

The correct option is B. 0-9 and 60-69.

For the frequency distribution graph about people who regularly use a specific cell phone app, the two age groups are least likely to use this app is 0-9 and 60-69.

The frequency distribution is a graphical or tabular representation that depicts the number of observations inside a specific interval. The interval size is determined by the data being examined and the analyst's objectives.

Some key features regarding the frequency distribution are-

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The complete question is-

View the frequency distribution graph about people who regularly use a specific cell phone app. Which two age groups are least likely to use this app?

A. 0-9 and 10-19

B. 0-9 and 60-69

C. 10-19 and 20-29

D. 10-19 and 50-59

Sean lives about 15.5 miles from the airport. Number rounds to 15.5

when rounded to the nearest tenth is 15.49.

when we round off this number we have to see the last digit here it is 9 so we have to note whenever the last digit lies between 0-4 we round off it and take the value 0.

when it lies between 5-9 we take the value 0 and add one number t0 the second last digit. so here it is 9 in place of 9 will take zero and in place of 4, we take 4+1=5. so the answer is 15.49.

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The number of different ways of placing 15 balls in a row given that 4 are red, 3 are yellow, 6 are black, and 2 are blue is:

15!/(4!3!6!2!) = 126,126

To find the number of ways of placing the 15 balls, we use the formula for permutations with repetition. There are a total of 15! ways of arranging the balls in a row, but since there are 4 red balls, 3 yellow balls, 6 black balls, and 2 blue balls, we need to divide by the number of permutations of each color.

This gives us the formula: 15!/(4!3!6!2!), which simplifies to 126,126. Therefore, there are 126,126 different ways of placing the 15 balls in a row.

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The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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The perimeter of a rectangle is the sum of twice the width and twice the length

The function that gives the cost of fencing is given from the graph by the following function;

The reason why the above function is correct is as follows:

Question: Please find attached the required diagram used to obtain the function;

The given parameters are;

Area of the square rectangle = 250 m²

Length of the side of the pen wall parallel to the coop = x

Cost of fencing per foot, c = $10

The function for the cost in dollars of fencing, C(x) = 10x + 5000

Solution:

Let y represent the length of the other side, we have;

x × y = 250

Therefore;

\(P = x + 2 \times \dfrac{250}{x} = x + \dfrac{500}{x}\)

The total cost of the fencing, C(x) = c × P

Therefore;

\(\mathbf{C(x)} = 10 \times \left(x + \dfrac{500}{x} \right) = 10 \cdot x + \dfrac{5,000}{x}\)

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