How much will the monthly payment be for a new car priced at $24,530 if the current finance rate is 36 months at 3. 16%? You will finance the 8% TT&L and make a 20% down payment

Work Shown:

y = 15.6 - 3.8x

y = 15.6 - 3.8*3

y = 4.2

Answer:

3\(\sqrt{13}\)

Step-by-step explanation:

Calculate the distance using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (- 9, 8) and (x₂, y₂ ) = (- 3, - 1)

d = \(\sqrt{(-3-(-9))^2+(-1-8)^2}\)

  = \(\sqrt{(-3+9)^2+(-9)^2}\)

  = \(\sqrt{6^2+81}\)

   = \(\sqrt{36+81}\)

   = \(\sqrt{117}\)

   = \(\sqrt{9(13)}\)

   = \(\sqrt{9}\) × \(\sqrt{13}\)

   = 3\(\sqrt{13}\)

The second wedge has a greater volume by 4.125 cubic inches. Therefore, the correct option is 4.

To determine which cheese wedge has a greater volume, you need to calculate the volume of each triangular prism using the given dimensions.

For the first wedge:

1. Calculate the area of the base (isosceles triangle):

(base x height) / 2 = (2.5 in x 4.5 in) / 2 = 5.625 square inches

2. Calculate the volume of the prism:

base area x thickness = 5.625 sq in x 3 in = 16.875 cubic inches

For the second wedge:

1. Calculate the area of the base (isosceles triangle):

(base x height) / 2 = (3 in x 4 in) / 2 = 6 square inches

2. Calculate the volume of the prism:

base area x thickness = 6 sq in x 3.5 in = 21 cubic inches

To find which wedge has a greater volume and by how much, subtract the smaller volume from the larger volume:

21 cu in - 16.875 cu in = 4.125 cu in.

Therefore, the correct answer is option 4: The second wedge has a greater volume by 4.125 cubic inches.

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The approximate height of the mountain is 1.214 miles.

Question: While traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive 13 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of the mountain.

To approximate the height of the mountain, we can use the concept of trigonometry. We will use the tangent function, which relates the angle of elevation to the height of the mountain and the distance from the mountain.

1. Let's start by labeling the information we have:
  - The initial angle of elevation is 3.5°.
  - The angle of elevation after driving 13 miles closer is 9°.

2. Now, let's define the variables:
  - Let h be the height of the mountain.
  - Let d be the initial distance from the mountain.

3. Using the tangent function, we can set up two equations based on the given angles of elevation:
  - tan(3.5°) = h / d   (equation 1)
  - tan(9°) = h / (d - 13)   (equation 2)

4. We can now solve these equations simultaneously to find the value of h, the height of the mountain.
  - Divide equation 2 by equation 1:
    (tan(9°) / tan(3.5°)) = (h / (d - 13)) / (h / d)
    (tan(9°) / tan(3.5°)) = (d / (d - 13))

5. Substitute the values of the tangents of the angles:
  - tan(9°) / tan(3.5°) = 0.158384 / 0.0610865
  - 2.59042 = d / (d - 13)

6. Cross multiply the equation:
  - 2.59042(d - 13) = d

7. Simplify the equation:
  - 2.59042d - 33.67346 = d

8. Move the terms to one side of the equation:
  - 2.59042d - d = 33.67346
  - 1.59042d = 33.67346

9. Solve for d:
  - d = 33.67346 / 1.59042
  - d ≈ 21.1648

10. Now that we have the initial distance, we can substitute it into equation 1 to find h, the height of the mountain:
   - tan(3.5°) = h / 21.1648

11. Solve for h:
   - h = tan(3.5°) * 21.1648
   - h ≈ 1.214 miles

Therefore, the approximate height of the mountain is 1.214 miles.

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The present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.

The present value of an annuity is calculated using the following formula:

PV = A[((1+i)n-1)/(i(1+i)n)]

where A = amount of each annuity payment, i = interest rate, and n = number of payments.

For this problem, A = $500, i = 6%, and n = 15 years.

Therefore, the present value of the annuity necessary to fund the withdrawal is:

PV = $500[((1+0.06)15-1)/(0.06(1+0.06)15)]

PV = $500[5.72982/0.105638]

PV = $5,354.82

Therefore, the present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

The correct pair of constraints to add is option d: P24 - P25 <= 80; P25 - P24 <= 80

To specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units, the correct pair of constraints to add is option d: P24 - P25 <= 80; P25 - P24 <= 80.

The constraint P24 - P25 <= 80 ensures that the production of product 2 in period 4 (P24) does not exceed the production in period 5 (P25) by more than 80 units.

The constraint P25 - P24 <= 80 ensures that the production in period 5 (P25) does not exceed the production in period 4 (P24) by more than 80 units.

These two constraints together ensure that the production of product 2 in period 4 and period 5 differs by no more than 80 units in either direction, as both P24 - P25 and P25 - P24 are limited to be less than or equal to 80.

Therefore, the correct pair of constraints to add is option d: P24 - P25 <= 80; P25 - P24 <= 80

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Step-by-step explanation:

Answer: 0.129 kg

Step-by-step explanation:

A gram to a kilogram can be found by dividing the value of grams by 1000, or multiplying the value by 0.001

The zerοs οf p(x) are -2, -2.5, and 3. We can plοt these pοints οn a number line tο visualize the zerοs οf the pοlynοmial: -2.5 -2 3

An algebraic expressiοn is a cοmbinatiοn οf variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. It can cοntain οne οr mοre terms, and each term can have οne οr mοre variables raised tο pοwers οr multiplied by cοnstants.

Tο plοt all zerοs οf the pοlynοmial\(p(x) = (2x^2 + 7x + 5)(x - 3)\), we can first find the zerοs οf each factοr using the quadratic fοrmula:

Fο \(r 2x^2 + 7x + 5\), we have:

x = [-7 ± sqrt(7²- 4(2)(5))] / (2*2)

x = [-7 ± sqrt(9)] / 4

x = (-7/4) ± (3/4)

x = -2 οr x = (-5/2)

Fοr x - 3, we have:

x = 3

The zerοs are represented by the οpen circles οn the number line. The pοlynοmial has a dοuble zerο at x = -2 and single zerοs at x = -2.5 and x = 3.

Therefοre, the zerοs οf p(x) are -2, -2.5, and 3. We can plοt these pοints οn a number line tο visualize the zerοs οf the pοlynοmial: -2.5 -2 3

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Answer: \(3\)

Step-by-step explanation:

The rule for dilating a figure by a scale factor of \(k\) centered at the origin is \((x,y) \to (kx, ky)\).

Using the coordinates of \(D\) and \(D'\), we see that \(k=3\).

Answer:

S=2t

or

T=1/2 S

i: 1

ii: 6

iii: 3

iv: 2

v: 4.5

vi: 2.5

C. Both distributions are approximately normal with the same mean. The standard deviation for size 5 is greater than that for size 85.

Explanation:
When taking random samples from a population with a normal distribution, the sampling distributions of the sample mean will also be approximately normal. The mean of the sampling distributions will be the same as the population mean, which is 65 inches in this case.

However, the standard deviation of the sampling distributions will be different for the two sample sizes. The standard deviation of the sampling distribution is calculated as the population standard deviation divided by the square root of the sample size (σ/√n). In this case, the population standard deviation is 3.5 inches.

For the sample size of 5:
Standard deviation = 3.5/√5 ≈ 1.566

For the sample size of 85:
Standard deviation = 3.5/√85 ≈ 0.379

As you can see, the standard deviation for the sample size of 5 is greater than the standard deviation for the sample size of 85, which means that the sampling distribution for the smaller sample size will be more spread out than the one for the larger sample size.

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Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

x = 39.1

Step-by-step explanation:

To find the mean, add up all the data points and then divide by the number of data points

(31.7+ 42.8+ 26.4+ x)/4 = 35

Multiply each side by 4

(31.7+ 42.8+ 26.4+ x)/4*4 = 35*4

(31.7+ 42.8+ 26.4+ x) = 140

Combine like terms

100.9+x = 140

Subtract 100.9 from each side

x = 140-100.9

x = 39.1

Answer:

35 months

Step-by-step explanation:

Let the number rod months be represented by x

At a bake shops the cost of flour is $2.50 per pound and increases at a rate of $0.07 per month.

For flour , the Equation

$2.50 + 0.07x

The cost of coca is $6.00 per pound and decreased at a rate of $0.03 per month.

For coca, the equation

$6.00 - $0.03x

If the trends continue, which system of equations can be used to find the number of months, x, when the price is equal for both flour and coca

We solve by equating both Equations together

Flour = Coca

$2.50 + 0.07x = $6.00 - $0.03x

0.07x + 0.03x = $6.00 - $2.50

0.1x = 3.50

x = 3.50/0.1

x = 35 months

Hence, the price is equal for both flour and coca after 35 months

Answer:

A and C

Step-by-step explanation:

all angles are below 90 degrees and all sides are unequal in length.

hopefully this helps :)

Answer:Acute scalene.

Step-by-step explanation:

It is acute because no angle is 90 degrees or more and scalene because the sides are different lengths.

Answer:

These are the answers

(-1,5)

(0,3)

(2,-1)

Step-by-step explanation:

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

seems to easy to be true but the answer is 7/12 cause it's a fraction and it can't be simplified

The distance between her house and her mother's house =135 miles

Let the entire distance be 3x

Normally that takes 180 minutes

speed would be  (3x)/180  =  x/60   miles per minute

It would take 60 minutes to go the first distance of x and 276-60 = 216 minutes to the next 2x miles

She hits a bad snowstorm and reduces her speed by 20 miles per hour.

So her speed would be, (x - 20)/60 miles

for given situation we formulate an equation,

(x - 20)/60 = 2x/216

(x - 20)/10 = x/18

18x - 360 = 10x

8x = 360

x = 45 miles

So, the total distance would be:

3x = 3 × 45

    = 135 miles

Therefore, the required distance is 135 miles

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The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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Answer:

Definitely not a function.

Step-by-step explanation:

Answer:

Not a function.

Step-by-step explanation:

Its not a function because there are two outputs (i.e. when you draw a vertical line in the diagram, you cross over the curve to times)

A function has ONLY ONE INPUT AND OUTPUT.

The values of the random variable w typically vary approximately 3.46 units on average from the mean of the geometric distribution with p=0.25.

In a geometric distribution, the mean (μ) is calculated as 1/p, where p is the probability of success. In this case, p=0.25, so the mean is 1/0.25 = 4.

To determine how far the values of w typically vary from the mean, we can calculate the standard deviation (σ) of the distribution. For a geometric distribution, the standard deviation is given by the formula σ = sqrt((1-p)/p^2).

Substituting the given value of p=0.25 into the formula, we have σ = sqrt((1-0.25)/0.25^2) = sqrt(0.75/0.0625) = sqrt(12) ≈ 3.46.

Therefore, on average, the values of w typically vary approximately 3.46 units from the mean of the geometric distribution with p=0.25.

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Answer:

The time would become 13:40

Step-by-step explanation:

8 in 8:40 is hours

40 in 8:40 is minutes.

Answer:

1:40pm

Step-by-step explanation:

Answer: 3.65, 3.7, 323

Step-by-step explanation:

The numbers from least to greatest are as follows:

3.65, 3.7, 323

Hope this helps