Calculate the Total amount that Theo has to pay back if she takes the loan

(a) (f∘g)(x) and the domain of f∘g are defined for real numbers and (b) (g∘f)(x) and the domain of g∘f is defined for real numbers.

The given functions are:f(x) = −x² + 1g(x) = x

Exer. 21-34: To Find

(a) (f ∘ g)(x) and the domain of f ∘ g and (b) (g ∘ f)(x) and the domain of g ∘ f.(a) (f ∘ g)(x) and the domain of f ∘ gTo find the composite of the two functions, substitute the value of g(x) into f(x). Now, (f ∘ g)(x) is given by:f(g(x)) = f(x) = f(x) = f(x) = -x² + 1. The domain of (f ∘ g)(x): Since g(x) is defined for all real numbers, the domain of (f ∘ g)(x) is also defined for all real numbers.

(b) (g ∘ f)(x) and the domain of g ∘ f

To find the composite of the two functions, substitute the value of f(x) with g(x). Now, (g ∘ f)(x) is given by:g(f(x)) = g(-x² + 1) = -x² + 1

The domain of (g ∘ f)(x): The domain of f(x) is defined for all real numbers. However, the domain of g(x) is also defined for all real numbers. Therefore, the domain of (g ∘ f)(x) is defined for all real numbers.

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Answer:

Step-by-step explanation: 55 i think

Answer:

2%?

Step-by-step explanation:

The distance the plane traveled from point A with measures an angle of elevation of 16°, to point B with measures an angle of elevation of 28°, is equals to the 11,728.6feet.

Jaya spots an airplane on radar that is currently approaching in a straight line start from point O in above figure, and that will fly directly overhead.

Altitude that plane maintain,h = 7300 feet

Initially, measure an angle of elevation to the plane at point A = 16°

Measure an angle of elevation to the plane at point B = 28°

Now, Let the distance between point A and point B be equal to 'x feet' and distance between point B and point C ( base) be equal to 'y feet'. So, distance between point A to point C = (x + y ) feet. We have to calculate the distance the plane traveled from point A to point B, i.e., x feet. See the above figure carefully, we see in right angled triangle BOC, tan 28° = 7300/y --(1)

In right angled triangle AOC,

tan 16° = 7300/(x + y) --(2)

Cross multiplication in equation (2)

=> tan 16° ( x + y ) = 7300

=> x + y = 7300/tan 16° --(3)

from equation (1), y = 7300/tan 28°

=> y = 7300/0.5317 = 13,729.55

so, x = 7300/tan 16° - y = 7300/0.287 - 13,729.55

= 25,458.12 - 13,729.55

= 11,728.58 ~ 11,728.6

Hence, required distance is 11,728.6feet.

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The expοnential functiοn fοr the given table is y = 5(2)ˣ.

A functiοn is  relatiοn between  set οf inputs (called  dοmain) and  set οf οutputs (called  range), where each input is assοciated with exactly οne οutput. A functiοn is usually denοted by  symbοl like  f, and is written as f(x), where x is element οf dοmain.

we can use the general fοrm οf an expοnential functiοn, which is:

y = abˣ

where a and b are cοnstants that we need tο determine.

Using the given values οf x and y in the table, we can fοrm fοur equatiοns as fοllοws:

2.5 = ab⁽⁻¹⁾

5 = ab⁰

10 = ab¹

20 = ab²

Dividing the secοnd equatiοn by the first equatiοn, we get:

5/2.5 = (ab⁰)/(ab⁽⁻¹⁾ )

2 = b

Substituting this value οf b in the οther equatiοns, we get:

2.5 = a(2)⁽⁻¹⁾

a = 5

10 = 5(2)¹

10 = 10

20 = 5(2)²

20 = 20

Therefοre, the expοnential functiοn fοr the given table is:

y = 5(2)ˣ.

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Answer: The area of each slice of pizza can be calculated by finding the area of the whole pizza and dividing it by the number of slices.

The radius of the pizza is half of the diameter, so the radius is 20/2 = 10 inches.

The area of the whole pizza can be calculated using the formula for the area of a circle:

Area = π × radius^2

Area = π × 10^2

Area = 100π square inches

Since there are 8 slices, each slice has an area of:

100π square inches / 8 = 12.5π square inches

Therefore, the area of the 5 slices that Chris ate is:

5 × 12.5π square inches = 62.5π square inches

This is approximately equal to 196.35 square inches, when rounded to two decimal places.

Step-by-step explanation:

m = 532 - (57 * h) represents the number of miles remaining after h hours of traveling at an average speed of 57 miles per hour.

The equation m = 532 - (57 * h) is used to represent the number of miles remaining, m, after h hours of traveling at an average speed of 57 miles per hour. The equation works by taking the total distance, 532 miles, and subtracting the product of the average speed, 57 miles per hour, and the amount of hours traveled, h. The result of the equation is the number of miles remaining, m. For example, if the family has been traveling for four hours, the equation would be m = 532 - (57 * 4). Solving the equation, m = 344, meaning the family has 344 miles left to travel. This equation allows the family to easily determine how many miles they have left to travel, given the average speed and amount of time traveled.

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The relationship between the number of times Trevor turns the crank, x, and the height the box has been lifted, y, is a linear equation y = (3/5)x.

What is a linear equation?

A linear equation is an algebraic equation in which each term is either a constant or a product of a constant and a variable raised to the first power (i.e., the variable is not squared or cubed). The general form of a linear equation with one variable, x, is:

ax + b = 0

Now,

We are given that there is a proportional relationship between the number of times Trevor turns the crank, x, and the height the box has been lifted, y. Let k = constant of proportionality.

Then, we can write the equation as:

y = kx

We also know that Trevor turns the crank 5 times to lift a box 3 feet.

Now

3 = k(5)

Solving for k, we get:

k = 3/5

Substituting this value of k in the equation, we get:

y = (3/5)x

Therefore, the equation for the relationship between the number of times Trevor turns the crank, x, and the height the box has been lifted, y, is y = (3/5)x.

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Answer:

3x³- 8x² + 2x +3

Step-by-step explanation:

All you need to do is multiply everything in the second bracket with the first bracket like you would normally do with double brackets.

3x³-3x²-5x²+5x-3x+3=

3x³-8x²+2x+3

Mila should receive 44.44% of the profit.

An equation is a statement that asserts the equality of two expressions, typically with one or more variables. Equations are used to represent relationships between different quantities, such as the relationship between the length and width of a rectangle or the relationship between the time and distance traveled by an object.

Profit is the financial gain that is earned by a business or an individual after all expenses and costs have been subtracted from revenue or income. It is the difference between the amount earned from sales or services and the costs incurred to produce or provide those goods or services.

In the given question,

Let's begin by determining the amount of money each person invested in the project.

Let Sydney's investment be x.

Roy's investment is twice Sydney's, so Roy invested 2x.

Mila's investment is twice Roy's, so Mila invested 2(2x) = 4x.

Taniya's investment is half of Mila's, so Taniya invested 0.5(4x) = 2x.

The total amount invested is x + 2x + 4x + 2x = 9x.

Now, we need to find the percentage of profit Mila should receive. Since the profit is shared in proportion to the amount invested, Mila should receive a fraction of the profit equal to her investment divided by the total investment.

Mila's share = (Mila's investment) / (Total investment) x (Total profit)

Mila's share = (4x / 9x) x 27000

Mila's share = 12000

So Mila should receive $12,000 of the profit. To find the percentage of profit Mila should receive, we can divide her share by the total profit and multiply by 100:

Percentage of profit Mila should receive = (Mila's share / Total profit) x 100%

Percentage of profit Mila should receive = (12,000 / 27,000) x 100%

Percentage of profit Mila should receive = 44.44%

Therefore, Mila should receive 44.44% of the profit.

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Answer: So pretty much what you do is you put a dot on the positive 3 then move over one and put another on the 7 and you just keep doing that with all of them

Step-by-step explanation:

Answer:The coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2).

What do you mean by reflection of coordinates?

A reflection on the coordinate plane is a type of transformation. It takes a geometric figure such as a point, line segment, or shape and transforms it into a congruent geometric figure called the image.

Given is a point (-3, 2) reflected across the y - axis.

Now, when any given coordinate is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.

As given, the coordinates of the point are - P(-3, 2)

Now, after reflection across the y - axis, the new coordinates of the image of this point will be -

x' = - (- 3) = 3

y' = y = 2

P'(3, 2)

Therefore, the coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2)

Answer:

3,2

Step-by-step explanation: Just took the test

1. The sequence is an arithmetic sequence with a common difference of d = -200.

2. The sequence is not an arithmetic sequence.

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

For item 1, each term is the previous term subtracted by 200, hence the sequence is in fact an arithmetic sequence with a common difference of -200.

For item 2, the difference between consecutive terms is difference, hence the sequence is not an arithmetic sequence.

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Therefore , the solution of the given problem of unitary method comes out to be in June 2022, the total amount due to the finance, exclusive of the insurance, was roughly $47,259.52.

The task can be completed by multiplying the data gathered using this type of nanosection along with two variable individuals who utilized the unilateral strategy. In essence, this signifies that perhaps the designated entity is defined or the colour of both mass production is skipped whenever a wanted item occurs. For forty pens, a variable charge of Inr ($1.01) could have been required.

Here,

1.1. The statement omits details about the truck's loan term. Therefore, without more details, we are unable to respond to this query.

1.2. Assume that the truck's loan period is n years and that the contractor borrowed P dollars at an annual interest rate of r to buy the water tanker.

M is calculated as (r * P * (1 + r)n) / ((1 + r)n - 1)

5 years + 60 months Equals n

r = 5% / 12 = 0.004166667 (weekly interest rate) (monthly interest rate)

P = $100,000

=> M = (0.004166667 * $100,000 * (1 + 0.004166667)^60) / ((1 + 0.004166667)^60 - 1)

≈> $1,870.24

As a result, the total monthly payments made for the water tanker, including the insurance protection, came to about $1,870.24.

1.3

(Total Amount Borrowed - Amount Paid) / 2

=>  ($100,000 - $1,870.24 * 6) / 2 = $47,259.52 is the sum that is owed.

Therefore, in June 2022, the total amount due to the finance, exclusive of the insurance, was roughly $47,259.52.

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Answer:

Step-by-step explanation:

2/3*6

6*6

12

Answer:  the answer is that you will have $3630 in the account at the beginning of the 7th year.

Step-by-step explanation:

I = Prt

Using this formula:

I = Prt

I = 3000 x 0.035 x 6

I = $630

Therefore, the total amount in the account at the beginning of the 7th year will be

Total = Principal + Interest

Total = $3000 + $630

Total = $3630

Answer:

8 degrees

Step-by-step explanation:

Given in the picture, hope it helps.

The probability that this whole shipment will be accepted is 0.1813. The company will accept 82.87% of the shipments and will reject 17.13% of the shipments, so the likelihood of a rejected shipment is relatively low.

Probability is essentially the likelihood that something will occur. The entire number of potential outcomes must first be known in order to calculate the likelihood of a particular event.

P(E) = Number of favorable outcomes / Number of total outcomes

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As a result, the Moon orbits the Earth roughly 2.8 billion times while the Sun revolves once around the Milky Way's nucleus.

One cycle of the Sun around the Milky Way's nucleus is thought to take between 225 and 250 million years to complete. The synodic month, or the length of time it takes the Moon to complete one orbit of the Earth, lasts roughly 29.5 days.

We must divide the total time of one orbit of the Sun around the Milky Way by the amount of time it takes for the Moon to orbit the Earth once in order to determine how many times the Moon orbits the Earth during one orbit of the Sun around the Milky Way's centre.

The result is (Total time for one orbit of the Sun around the centre of the Milky Way)/(Time for one orbit of the Moon around the Earth) = (225 million years x 365.25 days per year)/(29.5 days per orbit of the Moon) = around 2.8 billion orbits of the Moon around the Earth.

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The rent of the apartment during the 8th year would be approximately $2491.4.

To calculate the rent of the apartment during the 8th year, we need to apply the 11% increase per year for a total of 7 years (from the 2nd to the 8th year). Here's the calculation:

Rent for the 2nd year:

$1200 + (11% of $1200) = $1200 + ($132) = $1332

Rent for the 3rd year:

$1332 + (11% of $1332) = $1332 + ($146.52) = $1478.52

Rent for the 4th year:

$1478.52 + (11% of $1478.52) = $1478.52 + ($162.64) = $1641.16

Rent for the 5th year:

$1641.16 + (11% of $1641.16) = $1641.16 + ($180.53) = $1821.69

Rent for the 6th year:

$1821.69 + (11% of $1821.69) = $1821.69 + ($200.39) = $2022.08

Rent for the 7th year:

$2022.08 + (11% of $2022.08) = $2022.08 + ($222.43) = $2244.51

Rent for the 8th year:

$2244.51 + (11% of $2244.51) = $2244.51 + ($246.90) = $2491.41

Therefore, the rent of the apartment during the 8th year would be approximately $2491.4.

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Answer:  this equals 100

Step-by-step explanation:

The probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.

A mathematical technique called the Bayes theorem enables us to revise our views or probability regarding an occurrence in light of fresh data or evidence. It has the name of the reverend Thomas Bayes, a statistician and philosopher active in the 18th century. According to the Bayes theorem, the likelihood of an event A given that an event B has already happened is equal to the likelihood of an event B given that an event A has already occurred, multiplied by the prior likelihood of an event A, divided by the previous likelihood of an event B.

The Baye's Theorem is given as:

P(B|A) = P(A|B) × P(B) / P(A)

Here,

P(A) is the probability that a customer ordered a small drink = 0.22.

P(B) is the probability that a customer ordered a hot drink, regardless of whether it was small or medium or large = 0.05.

P(A|B) is the probability that a customer ordered a small drink, given that they ordered a hot drink = 0.2.

Substitute the value we have:

P(B|A) = P(A|B) × P(B) / P(A) = (0.2 × 0.05) / 0.22 ≈ 0.045

Therefore, the probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.

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Thus, to the closest dollar, the total sales revenue included in the master budget for September was as follows: master budget sales income = $11.71 multiplied by 40,000 Sales master budget.

Let's first get the precise variable cost per unit:

Real variable cost is $7.43 per unit.

Let's next determine the revenue from the flexible budget:

$400 000 in flexible budget revenue

Let's now determine the actual sales revenue:

$383,000 was the actual sales revenue.

Let's figure out the overall variance for the flexible budget:

Overall variance for the flexible budget is $17,000.

Given that the flexible-budget variance is unfavourable (U), we can infer that actual revenue was lower than anticipated.

a... a.. a.. a.. a

Variance in sales volume is 40,000 x ($9.58 - $10.00 + $7.43)

Variance in sales volume = 40,000 x $6.01

Variance in sales volume = $240,400

Let's figure out the overall flexible-budget variation for variable costs:

Variance in the flexible budget for all variable costs is $-106,800.

Let's now determine the precise number of units sold using the sales volume variance.

The budgeted amount of units sold that were sold:

With the actual number of units sold compared to the projected amount (34,132.94), we can determine the budgeted price per unit as follows:

$11.71 is the planned price per unit (rounded to nearest cent)

Thus, to the closest dollar, the total sales revenue included in the master budget for September was as follows:

master budget sales income = $11.71 multiplied by 40,000

Sales master budget

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The actual width of the real igloo is 14 feet.

A ratio scale is simply a quantitative scale where there is a true zero and equal intervals between neighboring points.

The given scale tells us that 1 inch on the model igloo represents 2 feet on the real igloo.

If the scale of the model igloo is 1 inch to 2 feet, then we can use this ratio to convert the width of the model igloo (7 inches) to the width of the real igloo:

= 7 inches × 2 feet/inch

= 14 feet

Therefore, the width is 14 feet

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The slope of the linear function that represents the cost of plan B is $0.17.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Since Plan B has the same monthly base charge as plan A, we can logically deduce that the data points (0, 14.45) and (45, 22.10) lie on the linear function.

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (22.10 - 14.45)/(45 - 0)

Slope (m) = $0.17

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Complete Question:

Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table. Monthly Charge for Plan A Minutes used, x Monthly charge ($), y 0 14.45 3 14.84 6 15.23 9 15.62 12 16.01 Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?

Step-by-step explanation:

the given pair (3, 2) is the length of the translation ?

it is really totally simple : you need to add the x value of the translation to the x-cordinate of each point. the same for the y value and the y- coordinates.

A' = (1 + 3, 4 + 2) = (4, 6)

B' = (2 + 3, -2 + 2) = (5, 0)

C' = (-3 + 3, 2 + 2) = (0, 4)

The measures in the circles are calculated as:

2. FD = 22; 4. US = 58

6. MN = 11; 8. YZ = 34

The Intersecting Chords Theorem states that when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

2. 12(3x - 5) = 15(8) [based on the Intersecting Chords Theorem]

36x - 60 = 120

36x = 120 + 60

36x = 180

x = 5

FD = 3x - 5 + 12 = 3(5) - 5 + 12

FD = 22

4. 30(3x + 1) = 42(x + 11) [based on the Intersecting Chords Theorem]

90x + 30 = 42x + 462

90x - 42x = -30 + 462

48x = 432

x = 9

US = 3x + 1 + 30 = 3(9) + 1 + 30 = 58

6. (2x - 7 + 9)(9) = (8 + 10)(10) [based on the intersecting secants theorem]

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 9

MN = 2x - 7 = 2(9) - 7

MN = 11

8. (2x + 12 + 6)(6) = (x + 3 + 10)(10) [based on the intersecting secants theorem]

12x + 108 = 10x + 130

12x - 10x = -108 + 130

2x = 22

x = 11

YZ = 2x + 12 = 2(11) + 12

YZ = 34

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Lorie should deposit $6,986.05 today at 5.25% to have enough money to pay off the loan in 7 months.

To determine the amount that Lorie should deposit today to have enough money to pay off the loan.

We use the simple interest formula for accrued amount.

A = P( 1 + rt )

Where A is total amount, P is initial amount, r is interest rate and t is elapsed time.

Given that;

First, converting R percent to r a decimal

r = R/100

r = 5.25/100

r = 0.0525

Next, we put time into years for simplicity,

t = 7 months / 12 months

t = 7/12 year

Plug the values into the above formula.

A = P( 1 + rt )

P = A / ( 1 + rt )

P = $7,200 / ( 1 + ( 0.0525 × 7/12 ) )

P = $7,200 / ( 1 + 0.030625 )

P = $7,200 /  1.030625

P = $6,986.05

Therefore, the principal or initial amount is $6,986.05.

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The amount she should deposit today to have enough money to pay off the loan would be = $1,060

The cost of the small car that Lorie Reilly needs to buy for college = $7,200.(P)

The number of months that she plans to repay the money = 7 months = 0.58 yr.(T)

The rate at which the money needs to be deposited = 5.25%. (R)

The simple interest = Principal× Time × Rate /100

Simple interest = 7200× 0.58 × 5.25/100

= 21924/100

= $219.24

The amount she is expected to pay after 7 months = 7200+219.24 = 7419.24

The amount she should deposit today to have enough money to pay off the loan = 7419.24/7 = $1,060( approximately)

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Step-by-step explanation:

False, it is 3 units to the left

For any function,

[tex]f(x)[/tex]

the function transformation of

[tex]f(x - h)[/tex]

implies a transformation h units to the left

If h is the positive, this implies a transformation to the right

If h is negative, this implies a transformation to the left.

Here's since

[tex](x + 3[/tex]

can be written as

[tex](x - ( - 3))[/tex]

Our h is negative, therefore we move 3 units to the left