Write an equation that represents the line.

The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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The probability of an earthquake in that magnitude range occurring in next 30 years is 3%.

The probability that the event will not occur for an exposure time of x years is:

\((1-\frac{1}{MRI} )^{x}\)

where, MRI = Mean Recurrence Interval = 1000

                x = Years = 30

Therefore, Probability of not occurring = \((1-\frac{1}{1000} )^{30}\)

                                                                 = \((\frac{999}{1000} )^{30}\)

                                                                 = \((0.999)^{30}\)

                                                                 = 0.97

Probability of occurring = 1 - 0.97

                                       = 0.3

Probability percent = 0.03 * 100

                                = 3 %

Hence, probability is 3%.

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Company B is cheaper if Nabhitha needs to drive 20 miles with the rented truck.

Given that, company A charges an initial fee of $30 for the rental plus $2 per mile driven. Company B charges an initial fee of $55 for the rental plus $1 per mile driven.

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

Let the number of miles Nabhitha drives be x.

Money charged by company A = 30+2x

Money charged by company B = 55+x

If Nabhitha needs to drive 20 miles (x=30) with the rented truck

Then money charged by company A = 30+2(20)

=$70

Money charged by company B = 55+20

=$65

Therefore, company B is cheaper if Nabhitha needs to drive 20 miles with the rented truck.

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The number of people that attended the game in each cost category is Faculty: 7,000,Alumni: 18,000,Public: 18,000,Veterans: 4,000

To determine the number of people that attended the game in each cost category,  to consider the given information and set up a system of equations to solve for the unknowns. Let's break down the problem step by step.

Let's denote the number of people in each cost category as follows:

Faculty: F

Alumni: A

Public: P

Veterans: V

The number of alumni is 11,000 more than the faculty, so we have the equation:

A = F + 11,000

The number of public plus alumni together was 10 times the number of veterans, so  the equation:

P + A = 10V

The number of faculty plus alumni together was the same as the number of veterans, so we have the equation:

F + A = V

The total number of people attending the game is the sum of the people in each category, so  the equation:

F + A + P + V = 100,000

Now, use these equations to solve for the unknowns.

First, substitute equation 1 into equations 2 and 3:

P + (F + 11,000) = 10V

F + (F + 11,000) = V

Simplify these equations:

P + F + 11,000 = 10V

2F + 11,000 = V

Next, substitute these equations into equation 4:

F + (F + 11,000) + P + (2F + 11,000) = 100,000

Simplify and combine like terms:

4F + 22,000 + P = 100,000

Subtract 22,000 from both sides:

4F + P = 78,000

Now a system of two equations:

P + F + 11,000 = 10V

4F + P = 78,000

solve this system of equations to find the values of F, P, and V.

By solving the system,

F = 7,000

P = 18,000

V = 4,000

Finally, substitute these values back into equation 1 to find the value of A:

A = F + 11,000 = 7,000 + 11,000 = 18,000

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The image of vector u under the linear transformation T is [-15, -24, -8], and the image of vector v is [3c, -8a, -4b].

Let's go through the calculation step by step to explain how we arrived at the images of u and v under the linear transformation T.

Given:

A = [0 0 3; -8 0 0; 0 -4 0]

u = [3; 2; -5]

v = [a; b; c]

To find the image of u under the linear transformation T, we need to multiply the matrix A with the vector u.

T(u) = A * u

Multiplying A and u:

[0 0 3; -8 0 0; 0 -4 0] * [3; 2; -5]

= [(0*3 + 0*2 + 3*(-5)); (-8*3 + 0*2 + 0*(-5)); (0*3 + (-4)*2 + 0*(-5))]

= [-15; -24; -8]

Therefore, T(u) = [-15; -24; -8].

To find the image of v under the linear transformation T, we multiply the matrix A with the vector v.

T(v) = A * v

Multiplying A and v:

[0 0 3; -8 0 0; 0 -4 0] * [a; b; c]

= [(0*a + 0*b + 3*c); (-8*a + 0*b + 0*c); (0*a + (-4)*b + 0*c)]

= [3c; -8a; -4b]

Therefore, T(v) = [3c; -8a; -4b].

Hence, the images of u and v under the linear transformation T are:T(u) = [-15; -24; -8]

T(v) = [3c; -8a; -4b].

These vectors represent the transformed coordinates of u and v under the linear transformation T.

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Answer:

2

Step-by-step explanation:

The slope of the line through (-3, 2) and (1,10) can be found by lining up the point's vertically and subtracting then putting 2nd difference on top of first.

(1,10)

Minus

(-3,2)

-------

8/4=2

The slope is 2.

Answer:

purple goes to the first set of points

green goes to the second set of points

blue goes to the third set of points

orange goes to the last set of points

I confirmed with an online calculator

Hope this helped! pls give branliest

Answer: 3x-4

Step-by-step explanation:

If jennifer is x, and Chelsea bought 3 times more than her

then she bought 3x

but since shes giving 4 away to her teacher you subtract 4 from 3x

so the answer is 3x-4

Jennifer bought x books, so let b represent books.

Chelsea bought 3 times more books than Jennifer, so we write b x 3.

She gave 4 books to her teacher, so we write - 4.

The final answer is b x 3 - 4. Hope this helps!

To sketch the solution curves of the given differential equation, analyze the slope field and follow the direction indicated by the slopes at the marked points. Start from each point and draw curves that align with the indicated directions.

Based on the provided differential equation dy/dx = 3y - x + 1, we can analyze the slope field and determine the solution curves through the additional points marked.

To sketch the solution curves, we start by selecting one of the marked points. Let's consider the point (-1, -2) as the starting point for our solution curve.

At the point (-1, -2), the slope field indicates a positive slope. Using this information, we can draw a curve that goes upwards from this point. As we move along the curve, we follow the direction indicated by the slope field, which means the curve should have a positive slope.

Now, let's consider the point (1, 2) as another marked point. At this point, the slope field indicates a negative slope. Therefore, we can draw another curve that goes downwards from this point, following the indicated direction.

Finally, we can draw additional curves through the remaining points, making sure to follow the direction indicated by the slope field at each point.

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The probability of students who took the sat scored less than 350 on the math section is 0.0643

The following can be deduced:

Population Mean,μ = 528

Population Standard Deviation,σ = 117

X follows a normal distribution

I.e X ~ N ( μ = 528 ,σ = 117 )

The formula for z score is:

z = (x - μ) / σ

Subtract the mean and then divide by the standard deviation to turn x into a standard Normal z

X ≤ 350

(x-528)/117 ≤ (350-528)/117

z ≤ -1.52

Now, by using a standard normal distribution table

The area left of -1.52 = 0.0643

Therefore, the required probability is 0.0643.

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The divergence of F is 2xyi - 15(2²-3x) 4+uy³k and the curl of F is -x²yi - 15u³k.

To find the divergence and curl of the vector field F(x, y, z) = x²yi - (2²-3x) 5+uy³k, we can use vector calculus operations.

The divergence of a vector field measures the rate of outward flow from an infinitesimally small region surrounding a point. It is calculated using the divergence operator (∇·F), which is the dot product of the gradient (∇) with the vector field F. In this case, the divergence of F can be found as follows:

∇·F = (∂/∂x)(x²yi) + (∂/∂y)(- (2²-3x) 5+uy³k) + (∂/∂z)(0)

      = 2xyi - 15(2²-3x) 4+uy³k

The curl of a vector field measures the rotation or circulation of the field around a point. It is calculated using the curl operator (∇×F), which is the cross product of the gradient (∇) with the vector field F. In this case, the curl of F can be found as follows:

∇×F = (∂/∂x)(0) - (∂/∂y)(x²yi) + (∂/∂z)(- (2²-3x) 5+uy³k)

      = 0 - x²yi - 15u³k

Therefore, the divergence of F is 2xyi - 15(2²-3x) 4+uy³k and the curl of F is -x²yi - 15u³k.

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The expressions that means "five factors of 3 is \(3^{5}\), option D.

The concept that will be used is the factor: A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

It should be noted that Factors of 3 that can be found are (1 and 3).

Then the  ''Five factors of 3''  can be interpreted as =( 5 times the factor of 3) and this can be written as \(3^{5}\)

Therefore, Five factors of 3  can be expressed as \(3^{5}\)

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Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

Answer:

-60

Step-by-step explanation:

Og problem: x(2x + 2x - 8y + 16)

Substitution: 3(6 + 6 - 48 + 16)

Solve: 3(12 - 48 + 16)

3(-36 + 16)

3(-20) = -60

Answer: x = 3

Step-by-step explanation: 3 + 3 = 6 ; 30 divided by 6 = 5.

Answer:

x = 3

Step-by-step explanation:

\(\frac{30}{3+x}\) = 5 ( models the statement )

multiply both sides by 3 + x

30 = 5(3 + x)

30 = 15 + 5x ( subtract 15 from both sides )

15 = 5x ( divide both sides by 5 )

3 = x

Answer:

x =  1/2 or 0.5

Step-by-step explanation:

Brainliest Please!!

- Hermionia

Answer:

The answer is -1/2

Step-by-step explanation:

5/x = 15/x+20

5/x-15/x=20

-10/x=20

-10=20x

x= -10/20

x= -1/2

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

A

Step-by-step explanation:

12×4=48cm²

12×3=36cm²

12×2×2×2=96cm²

therefore is 270cm² + 65cm² + 65cm²

=370cm²

The inverse of f,  f^-1 = 8x / (x + 3)

To find the inverse function, let's consider the following steps:

Step 1: Replace f(x) with y. y = x/8x - 3

Step 2: Swap the x and y variables. x = y/8y - 3

Step 3: Solve for y. x(8y - 3) = y x 8y - 3x = y y = f⁻¹(x) = 8x / x + 3

Therefore, f⁻¹(x) = 8x / (x + 3)

The domain of f⁻¹ is all real numbers except -3, as it is not defined for x = -3.

Hence the domain is (-∞, -3) U (-3, ∞).

The range of f⁻¹ is also all real numbers except 0, as it is not defined for x = 0. Hence the range is (-∞, 0) U (0, ∞).

Thus, the domain and range of f⁻¹ are (-∞, -3) U (-3, ∞) and (-∞, 0) U (0, ∞) respectively, in interval notation.

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Based on the information, it should be noted the factorization of  4x^5 + 16x³ will be 4x³(x² + 4).

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics. The process of factorization involves dividing mathematical algebraic formulas into the sum of their factors. Once more multiplying the variables will yield the original expression. It should be noted that factorization simply has to do with the writing of a number as a product of the factors that it has.

Based on the information, it should be noted that we want to factor 4x^5 + 16x³

It should be noted that the common factor between 4 and 16 is 4. Also, the common factor between the variables x is x³.

Therefore, based on the information the factor 4x^5 + 16x³ will be : = 4x³(x² + 4).

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Answer:

Hey! Ok so the answers are A.50% B.100% C.80%

Step-by-step explanation:

Just predict the number to what they're next to.

Hoped this helped Im Eve btw. Hope you have a great day and consider marking this brainliest Thank you so much if you do! ✨

Answer:

No solution

Step-by-step explanation:

Substitution method:

(Since y values are defined, make them equal to each other)

y = 152 + 9

y= 22 – 20

152 + 9 = 22 -20

161 ≠ 2

A false statement

The amount she will need to pay is $6.95 .

The amount Anye will need is calculated as follows;

The total cost of the two coffees is 2 x $3.55 = $7.10

The total cost of the coffees and muffin is $7.10 + $2.85 = $9.95

Adding the $2 tip, the total cost becomes $9.95 + $2 = $11.95.

If Anye has a $5 gift card, the amount she will need to pay is calculated as;

= $11.95 - $5

= $6.95

Therefore, Anye will need $6.95 in cash to pay for the rest of the order.

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Answer:

The answer is B) <

Step-by-step explanation:

Just looking at the Base 10 to the power of -5. we can just ignore it since they both have the base.

Now compare 3.2 with 4.6 which one is greater than or less than or equal to.

3.2 < 4.6

Answer: the answer is b . The second choice is correct .

Step-by-step explanation:

the second one is bigger than the fist one . Hopeit helps you .Please give brainliest .thanks .

Roy bought 6 bags of candy at $8 each for a total of $48. To calculate, divide the total amount paid ($48) by the cost per bag ($8) which equals 6. So, Roy bought 6 bags of candy.

Roy purchased some candy for $8 per bag. The total amount he spent was $48. To find out the number of bags he bought, we need to divide the total amount spent by the cost per bag. $48 divided by $8 equals 6.

So, Roy bought 6 bags of candy. This calculation shows us the relationship between the total cost, cost per unit, and the number of units purchased.

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The value of x in the parallelogram is 21.

To find the value of x in the parallelogram, we can equate the lengths of the opposite sides of the parallelogram. In this case, we have side AD equal to 36 and side BC equal to 2x - 6.

Setting these two expressions equal to each other, we have:

36 = 2x - 6

To solve for x, we can isolate it on one side of the equation. Adding 6 to both sides of the equation, we get:

36 + 6 = 2x

To simplify, we have:

42 = 2x

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 42/2

Evaluating the expression on the right side, we find:

x = 21

Therefore, the value of x in the parallelogram is 21.

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