Jim and Joan Miller are borrowing $120,000 at 6.5% per annum compounded monthly for 30 years to purchase a home. Their monthly payment is determined to be $758.48.


You need to present Jim and Joan with a report detailing the following:


A recursive formula for their balance after each monthly payment has been made.

A determination of Jim and Joan's balance after the first payment.

Use a spreadsheet or graphing utility to create a table showing their balance after each monthly payment.

Determine when the balance will be below $75,000.

Determine when the balance will be paid off.

Determine the interest expense when the loan is paid.


You will form an accurate recursive formula.

You will accurately determine the balance after the first payment.

You will accurately and completely construct a chart showing balances after each monthly payment.

You will accurately determine when the balance will be below $75,000 and when it will be paid off.

You will accurately determine the total interest expense incurred

Answer:

She will have a total of 17 pounds.

Step-by-step explanation:

You could simply put the question is slop intercept form to figure it out from there.

y = m(x) + b

y = 3(x) + 8

y = 3(3) + 8

y = 9 + 8

y = 17

Pls mark Brainliest with the crown

Answer:

NO

1,2,3,6

Step-by-step explanation:

THOSE ARE CORRECT

√8=2.8

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

All the factors of 12

So 1, 2, 3, 4, 6 and 12 are factors of 12.

Answer:

answer is 2×2×3×5= 4×15=60 im srry if you did not mean this but anyways have nice day

Step-by-step explanation:

12,10| 2

6,5| 2

3,5| 3

1,5| 5

1,1

The x-intercepts with multiciplity greater than 1 is x = 0

The number of distinct intercepts is 3 and the number of zeros is 4

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

f(x) = x²(x + 2)(x - 7)

The x-intercepts with multiciplity greater than 1 is the factor that has a power greater than 1

So, we have

x² = 0

This gives

x = 0

The number of distinct intercepts is the number of factors i.e. 3

The number of zeros is the sum of powers

i.e. Zeros = 2 + 1 + 1

Zeros = 4

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Since both are neutral, we know that each has 6 electrons as well. The sum of protons plus neutrons equals the mass number 12 in 12-C, so carbon-12 has 12 – 6 protons = 6 neutrons. The sum of protons plus neutrons equals the mass number 13 in 13-C, so carbon-13 has 13 - 6 protons = 7 neutrons.

am sorry i forgot the first but the second is transformation and the third is rotation

1) corresponding

2) translation

3)rotation

Hope this helps a lil I'm not for sure tho

Answer:

Mean: 85

Median: 90

Step-by-step explanation:

The triangle has an area of  13 square units.

We can use the formula for the area of a triangle given its vertices:

\(\text{Area} = \frac{1}{2}|\vec{AB}\times\vec{AC}|\)

where \(\vec{AB}\) and \($\vec{AC}$\)are vectors representing two sides of the triangle.

First, we need to find the vectors \($\vec{AB}$\) and \($\vec{AC}$\):

\(\vec{AB} = \begin{pmatrix}5-2 \\ 4-5\end{pmatrix} = \begin{pmatrix}3 \\ -1\end{pmatrix}\)

\(\vec{AC} = \begin{pmatrix}8-2 \\ 13-5\end{pmatrix} = \begin{pmatrix}6 \\ 8\end{pmatrix}\)

Next, we can calculate the cross product:

\(\vec{AB}\times\vec{AC} = \begin{pmatrix}3 \\ -1 \\ 0\end{pmatrix}\times\begin{pmatrix}6 \\ 8 \\ 0\end{pmatrix} = \begin{pmatrix}0 \\ 0 \\ 26\end{pmatrix}\)

The magnitude of this vector is\(|\vec{AB}\times\vec{AC}| = 26,\) so the area of the triangle is:

\(\text{Area} = \frac{1}{2}|\vec{AB}\times\vec{AC}| = \frac{1}{2}(26) = 13\)

Therefore, the area of triangle ABC is 13 square units.

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72 millimeters is equal to 2.83 inches.

Length is a measure of the distance between two points. There are different units of measurement for length, one of which is millimeters (mm) and another is inches (in). In order to convert from one unit to another, we use a conversion factor.

Here's how you convert 72 millimeters to inches:

1 inch = 25.4 millimeters

So, to convert 72 millimeters to inches, we divide by the conversion factor:

72 mm / 25.4 mm/in = 2.83 in

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Answer:

by Translation.

Using the photo it is (5/-8)

Answer: C. 90ᴼ

Step-by-step explanation:

This is an equilateral triangle because all three sides are congruent. Equilateral triangles also have 3 congruent angles.

The sum of each angle of a triangle equals 180ᴼ and there are 3 congruent angles.

180 / 3 = 60

Each angle measures 60ᴼ

The probability that the sample mean will be between 8 and 14 is approximately 0.785 or 78.5%. The 15th percentile of the population is 2.57.

To find the probability that the sample mean will be between 8 and 14, we need to calculate the standard error of the mean (SEM) first. The SEM is the standard deviation of the sampling distribution of the mean, and it is given by the formula SEM = σ/√n, where σ is the population standard deviation and n is the sample size.

In this case, σ = 12 and n = 75, so SEM = 12/√75 ≈ 1.386.

Next, we need to standardize the sample mean using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We do this by calculating the z-score for each endpoint of the interval:

z1 = (8 - 10) / 1.386 ≈ -1.441

z2 = (14 - 10) / 1.386 ≈ 2.882

We then use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. Alternatively, we can use the formula for the cumulative distribution function (CDF) of the standard normal distribution:

P(-1.441 < Z < 2.882) ≈ Φ(2.882) - Φ(-1.441) ≈ 0.985 - 0.204 ≈ 0.785

So, the probability that the sample mean will be between 8 and 14 is approximately 0.785 or 78.5%.

To find the 15th percentile of the population, we use the inverse of the CDF of the standard normal distribution. That is, we find the z-score that corresponds to a cumulative probability of 0.15:

Φ(z) = 0.15

z ≈ -1.036

Finally, we use the formula for the sample mean in terms of the standard normal distribution to find the corresponding value in the original units:

X = μ + z(σ/√n)

X = 10 + (-1.036)(12/√75)

X ≈ 2.57

Therefore, the 15th percentile of the population is 2.57

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Answer:

21 windows

Step-by-step explanation:

colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answer: Let the number of window Colleen father would paint be x while that of her mother be y. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father x = 2y

Let the number of windows each painted by Colleen and her 2 brothers be z since they would paint the same number of windows. The total number of windows to be painted = 2y + y + z + z + z = 3y + 3z = 3(y + z).

Then number of windows needed to be painted by Colleen and her mother is given as z + y. Since Colleen painted 7 windows as her share and her mother share i.e. y + z = 7

Therefore the total number of windows = 3(y + z) = 3(7) = 21 windows

The x and y are of t, if y = x4 5x and dx/dt = 4, when x = 3, the rate of change of y with respect to t is 436

Using the chain rule, we can find the derivative of y with respect to t as:

dy/dt = (dy/dx) * (dx/dt)

We are given that dx/dt = 4 and y = x^4 + 5x. Taking the derivative of y with respect to x, we get:

dy/dx = 4x^3 + 5

Substituting x = 3, we get:

dy/dx (at x=3) = 4(3)^3 + 5 = 109

Now, substituting dx/dt = 4 and dy/dx = 109 into the chain rule formula, we get:

dy/dt = (dy/dx) * (dx/dt) = 109 * 4 = 436

Therefore, when x = 3, the rate of change of y with respect to t is 436

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Answer:

5x

Step-by-step explanation:

We can use a theoreom to help us here.

Theorom of extereor angles. It would be 5x.

===========================================================

Explanation:

Angle 3 and the 100 degree angle are corresponding angles. They are both in the southeast quadrant of their four-corner angle configuration. Assuming the lines that look horizontal are parallel, this would mean angle 3 is 100 degrees. Recall that corresponding angles are congruent when we have parallel lines.

Once we know that angle 3 = 100, we will use this to find angle 4.

Angles 3 and 4 add to 180. They form a straight angle or straight line.

(angle3)+(angle4) = 180

(100) + (angle4) = 180

angle4 = 180-100

angle4 = 80 degrees

Answer:

10

Step-by-step explanation:

The image vertices of N'M'O' after reflecting triangle NMO over x = -2 are N'(1, 2), M'(-2, 1), and O'(-1, 3).

What is meant by vertices?

Vertices (singular: vertex) are the points where two or more edges meet in a geometric shape or object. They are also known as corners and are a defining feature of many shapes, including polygons, polyhedra, and graphs.

What is meant by a triangle?

A triangle is a geometric shape with three sides and three angles. It is a fundamental shape in geometry and has many practical applications in mathematics, science, and engineering.

According to the given information

In this case, the line of reflection is x = -2. The distance from N's x-coordinate to the line of reflection is |-5 - (-2)| = 3. So the x-coordinate of N' is -2 + 3 = 1. The y-coordinate of N' remains the same as N's y-coordinate, so N' = (1, 2).

The distance from M's x-coordinate to the line of reflection is |-2 - (-2)| = 0. So the x-coordinate of M' is -2 + 0 = -2. The y-coordinate of M' remains the same as M's y-coordinate, so M' = (-2, 1).

The distance from O's x-coordinate to the line of reflection is |-3 - (-2)| = 1. So the x-coordinate of O' is -2 + 1 = -1. The y-coordinate of O' remains the same as O's y-coordinate, so O' = (-1, 3).

So the image vertices of N'M'O' after reflecting triangle NMO over x = -2 are N'(1, 2), M'(-2, 1), and O'(-1, 3).

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Using the properties of remainder theorem we calculate that Luisa can get 8 toys and 5 coupons will be left over.

The Remainder Theorem is a method for dividing polynomials in Euclidean space. According to this theorem, reducing a polynomial P(x) by a factor (x - a) that is not an ingredient of the polynomial results in a smaller polynomial and a remainder.

Luisa has 85 coupons.

Each toy can be traded for 10 coupons .

So number of toys that can be bought = 85 ÷ 10

This given 8 quotient and 5 remainder.

This deduced remainder is a magnitude of P(x) at x = a, more precisely P (a). When and only when P(a) = 0, x -a is thus a component of P(x). It is used to factor polynomials of any degree in a visually appealing manner.

Hence we calculate that Luisa can get 8 toys and 5 coupons will be left over.

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Answer:

2st

Step-by-step explanation:

because only 34 can be divided by 17 and there arent enough of s and ts

To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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Answer:

A

Step-by-step explanation:

23 x 2 = 46

i) April's gross wages for last week were $515.20.

ii) The overtime premium is $67.20.

To calculate April's gross wages for last week, we need to consider the regular pay for 40 hours and the overtime pay for the additional hours worked.

i. Gross wages for last week:

Regular pay = 40 hours * $11.20 per hour = $448

Overtime pay:

April worked 44 hours in total, which means she worked 4 hours of overtime (44 - 40).

Overtime rate = 1.5 * regular pay rate = 1.5 * $11.20 = $16.80 per hour

Overtime pay = 4 hours * $16.80 per hour = $67.20

Total gross wages = Regular pay + Overtime pay = $448 + $67.20 = $515.20

Therefore, April's gross wages for last week were $515.20.

ii. Overtime premium:

The overtime premium refers to the additional amount paid for the overtime hours worked.

Overtime premium = Overtime pay - Regular pay = $67.20 - $448 = -$380.80

However, since the overtime premium is typically considered a positive value, we can interpret it as the additional amount earned for the overtime hours.

Therefore, the overtime premium is $67.20.

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Answer:

x has a value of 14.

Step-by-step explanation:

In addition to the information provided in the question, we are also told that the rectangle has a length x+1 and a width x-4.  This is all we need to know.

To work this out, we simply need to plug those numbers into the equation for the perimeter of a rectangle.  That would be p = 2l + 2w, where p is perimeter, l is length, and w is width.

We know that the resulting area (p) is equal to 54 units.  We are also given variable values for the length and width.  With that we can simply plug them into that equation and solve it for x:

\(p = 2l + 2w\)

\(54 = 2(x + 1) + 2(x - 4)\)

\(54 = 2x + 2 + 2x - 4\)

\(54 = 4x - 2\)

\(56 = 4x\)

\(x = 56 / 4\)

\(x = 14\)

a. The alternative hypothesis (H1) specifies that is greater than 26, indicating a directed alternative, this is a one-tailed test.

b. The alternative hypothesis is one-sided and argues that > 26, hence the critical value is 1.645.

c. The value of the test statistic (z-score) is z ≈ 3.82.

d. We reject the null hypothesis (H0) because the test statistic (z = 3.82) is higher than the crucial value (1.645).

In this case, the p-value is the probability of observing a sample mean of 28 or greater, assuming the population mean is 26.

a. This is a one-tailed test because the alternative hypothesis (H1) states that μ is greater than 26, indicating a directional alternative.

b. The decision rule for a one-tailed test at a significance level of 0.05 is to reject the null hypothesis (H0) if the test statistic is greater than the critical value. In this case, the critical value is 1.645 because the alternative hypothesis is one-sided and states that μ > 26.

c. The value of the test statistic (z-score) can be calculated using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case:

x = 28

μ = 26

σ = 4

n = 34

Substituting the values into the formula:

z = (28 - 26) / (4 / √34) ≈ 3.82

d. Since the test statistic (z = 3.82) is greater than the critical value (1.645), we reject the null hypothesis (H0).

e-1. To calculate the p-value, we need to find the area under the standard normal distribution curve to the right of the test statistic (z = 3.82). We can use a standard normal distribution table or a calculator to find this area.

The p-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis.

e-2. Interpreting the p-value: The p-value represents the probability of obtaining a sample mean as extreme as the one observed (or more extreme) if the null hypothesis is true.

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Imagine that a survey of randomly selected people finds that people who used sunscreen were more likely to have been sunburned in the past year.

There are several possible explanations for the finding that people who used sunscreen were more likely to have been sunburned in the past year.

However, without additional context or data, it is difficult to determine the most likely explanation definitively. Here are a few possible explanations to consider:

1. Ineffective or improper use of sunscreen: It is possible that the individuals who reported using sunscreen did not apply it correctly or did not reapply it as recommended.

Inadequate application or failure to follow proper sunscreen usage guidelines could result in insufficient protection from the sun's harmful rays, leading to sunburn.

2. Self-selection bias: It is possible that individuals who have previously experienced sunburns may be more likely to use sunscreen. They may be more aware of the potential risks and take precautions, including using sunscreen.

This could create an association between sunscreen use and sunburn, even though sunscreen itself is intended to prevent sunburn.

3. Recall bias: The survey responses may be subject to recall bias, where individuals may inaccurately remember or report their sunscreen use and sunburn experiences.

Memory limitations or subjective perceptions of sunburn severity could influence the reported data and the observed association between sunscreen use and sunburn.

4. Confounding factors: There may be other factors or variables at play that are related to both sunscreen use and sunburn. For example, individuals who engage in activities that increase sun exposure or who have certain skin types may be more likely to both use sunscreen and experience sunburn.

It is important to note that further investigation, including more detailed surveys, data collection and statistical analysis, would be necessary to determine the most likely explanation for the observed association between sunscreen use and sunburn.

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Answer:

P = A/1+rt

Step-by-step explanation:

Given: A = P + Prt

Applying the distributive principle: A = P( 1 + rt)

Dividing both sides by (1 + rt):

A/1 + rt = P