Alex made a $4000 down payment on a car. The total cost of the car was $11000. He made 40 equal monthly payments to pay the car in full. How much did Alex pay per month? Define a variable, write an equation, and solve.​

The present value of Mark's prize, considering the $10,000 annual payments for 10 years and the subsequent $20,000 annual payments for 30 years, with an 8% discount rate, amounts to $171,391.44.

To calculate the present value of Mark's prize, we need to determine the current worth of the future cash flows he will receive. The $10,000 annual payments for 10 years can be considered an annuity, while the subsequent $20,000 annual payments for 30 years can be viewed as a perpetuity starting from the 11th year.

First, we calculate the present value of the annuity using the formula for the present value of an ordinary annuity:

PV_annuity = \(C * [1 - (1 + r)^(-n)] / r\),

where PV_annuity is the present value of the annuity, C is the annual cash flow, r is the discount rate, and n is the number of years. Plugging in the values, we have:

PV_annuity = $10,000\(* [1 - (1 + 0.08)^(-10)] / 0.08\) = $85,394.45.

Next, we calculate the present value of the perpetuity using the formula for the present value of a perpetuity:

PV_perpetuity = C / r,

where PV_perpetuity is the present value of the perpetuity. Plugging in the values, we have:

PV_perpetuity = $20,000 / 0.08 = $250,000.

Finally, we sum up the present values of the annuity and the perpetuity to obtain the total present value:

Total present value = PV_annuity + PV_perpetuity = $85,394.45 + $250,000 = $335,394.45.

Therefore, with an 8% discount rate, the present value of Mark's prize is $171,391.44.

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Answer:

Step-by-step explanation:

This is an application of the distributive property. Begin by putting brackets around the two terms.

(x^2 + 3x)

Now take out the common factor of the two terms.

x^2 = x * x

3x = 3*x

The common factor is x.

x(x + 3)

One of the factors is x

The other one is (x + 3)

Answer:

D- Strong Negative

Step-by-step explanation:

The points have correlation because they form a line. The slope of the line is negative, so the correlation is strong negative. The points would be all over the place if the correlation was weak.

The correlation of the given data is Strong and negative.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

Given, points in a cartesian plane Where all points are on a Straight line that indicates the correlation is strong. Since,

To evaluate the degree of relationships between data variables, correlation coefficients are utilized. The most popular gauge of the strength and direction of a linear link between two variables is known as a Pearson correlation coefficient.

And the given line is decreasing from left to right indicating the slope of the given Data is negative. Thus the correlation of the given points is negative.

Due to the fact that the points form a line, they are correlated. The correlation is strongly negative because the line's slope is negative. If the link was poor, the points would be scattered all over the place.

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If two right triangles have congruent acute angles, then the triangles are similar.

Right Triangle Similarity Theorems are a set of geometric principles that relate to the similarity of right triangles.

Here are two examples of these theorems:

Angle-Angle (AA) Similarity Theorem:

According to the Angle-Angle Similarity Theorem, if two right triangles have two corresponding angles that are congruent, then the triangles are similar.

In other words, if the angles of one right triangle are congruent to the corresponding angles of another right triangle, the triangles are similar.

For example, if triangle ABC is a right triangle with a right angle at vertex C, and triangle DEF is another right triangle with a right angle at vertex F, if angle A is congruent to angle D and angle B is congruent to angle E, then triangle ABC is similar to triangle DEF.

Side-Angle-Side (SAS) Similarity Theorem:

According to the Side-Angle-Side Similarity Theorem, if two right triangles have one pair of congruent angles and the lengths of the sides including those angles are proportional, then the triangles are similar.

For example, if triangle ABC is a right triangle with a right angle at vertex C, and triangle DEF is another right triangle with a right angle at vertex F, if angle A is congruent to angle D and the ratio of the lengths of the sides AB to DE is equal to the ratio of the lengths of BC to EF, then triangle ABC is similar to triangle DEF.

These theorems are fundamental in establishing the similarity of right triangles, which is important in various geometric and trigonometric applications.

They provide a foundation for solving problems involving proportions, ratios, and other geometric relationships between right triangles.

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The probability that both are white is = 4/7 .

Probability is simply the possibility that something will happen. We may talk about the possibility of one result, or the likelihood of numerous outcomes, when we don't know how an event will turn out. The study of events with a probability distribution is known as statistics.

the probability of choosing a white pair of socks = 8/10

the probability of choosing a white t-shirt = 5/7

the probability that both are white = 8/10  *  5/7

                                                         = 8*5 / 70

                                                         = 40 / 70

                                                         = 4/7

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The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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The half-life of U-235 is 704 million years. After one half-life, the amount of U-235 remaining will be 1/2 of the original amount, after two half-lives it will be 1/4, and after three half-lives it will be 1/8.

We can use this information to calculate how much of the sample will remain after three half-lives.

First, we need to calculate how many years have passed in three half-lives.

3 half-lives = 3 x 704 million years = 2,112 million years

So, after 2,112 million years, the amount of U-235 remaining in the sample will be:

(1/2) x (1/2) x (1/2) x 125g = 15.625g

Therefore, the answer is C. 12.5g would remain after 2100 million years had passed.

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Answer:

Q.17  9 2/5

Q.18 5

Q.19  13

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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1)The pdf of U is f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

2)U follows a gamma-distribution with parameter a = 3/2 or a = 1/2.

3)x = (y²/2) and dx = y dy using exponential distribution

We can rewrite the integral as:

I(1/2) = ∫₀^∞ y exp(-y²) dy

       = 1/2 ∫₀^∞ exp(-u/2) du

This is the same as the integral for f(u) when u = 1/2.

Therefore, we have:

I(1/2) = V1

(1) For U = Z², we can use the method of transformations.

Let g(z) be the transformation function such that

U = g(Z)

   = Z².

Then, the inverse function of g is given by h(u) = ±√u.

Thus, we can apply the transformation theorem as follows:

f(u) = |h'(u)| g(h(u)) f(u)

     = |1/(2√u)| exp(-u/2) for u > 0 f(u) = 0 otherwise

Therefore, the pdf of U is given by:

f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

(2) We are given that f(1/2) = VT, where V is a constant.

We can substitute u = 1/2 in the pdf of U and equate it to VT.

Then, we get:VT = (1/(2√(1/2))) exp(-1/4)VT

                            = √2 exp(-1/4)

This gives us the value of V.

Now, we can use the pdf of the gamma distribution to find the parameter a such that the gamma distribution matches the pdf of U.

The pdf of the gamma distribution is given by:

f(u) = (u^(a-1) exp(-u)/Γ(a)) for u > 0 where Γ(a) is the gamma function.

We can use the following relation between the gamma and the factorial function to simplify the expression for the gamma function:

Γ(a) = (a-1)!

Thus, we can rewrite the pdf of the gamma distribution as:

f(u) = (u^(a-1) exp(-u)/(a-1)!) for u > 0

We can now equate the pdf of U to the pdf of the gamma distribution and solve for a.

Then, we get:

(1/(2√u)) exp(-u/2) = (u^(a-1) exp(-u)/(a-1)!) for u > 0 a = 3/2

Therefore, U follows a gamma distribution with parameter

a = 3/2 or equivalently,

a = 1/2.

(3) We need to show that I(1/2) = V1.

Here, I(1) = ∫₀^∞ exp(-x) dx is the integral of the exponential distribution with rate parameter 1 and V is a constant.

We can use the change of variables y = √(2x) to simplify the expression for I(1/2) as follows:

I(1/2) = ∫₀^∞ exp(-√(2x)) dx

Now, we can substitute y²/2 = x to obtain:

x = (y²/2) and

dx = y dy

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Answer:

The addition

Step-by-step explanation:

Peter's contribution to the whole job is the fraction of the job he completed during the second hour, which is 5/12.

So, Peter completed 5/12 of the whole job.

Let's calculate the rate at which each person completes the job.

Tom can complete 1/6 of the job per hour, Peter can complete 1/3 of the job per hour, and John can complete 1/2 of the job per hour.

During the first hour, Tom completes 1/6 of the job.

So, there is 1 - 1/6 = 5/6 of the job left to be done.

When Peter joins Tom, they work together for one hour.

Their combined rate is (1/6 + 1/3) = 1/2 of the job per hour.

So, in that hour, they complete 1/2 of the remaining job, which is (1/2) * (5/6) = 5/12 of the whole job.

Finally, when John joins them, the three of them work together at a combined rate of (1/6 + 1/3 + 1/2) = 11/12 of the job per hour.

Since they work together until the job is completed, the remaining (5/6) of the job is completed in (5/6) / (11/12) = 10/11 of an hour.

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Answer:

d

Step-by-step explanation:

a. (2/5)(-8/9)(-1/3)(-2/7)= - 32/945

b. (-2/5)(8/9)(-1/3)(-2/7) = -32/945

c. 2/5 * 8/9 * 1/3 * - 2/7 = - 32/945

d. -2/5 * - 8/9 * 1/3 * 2/7 = 32/945

Answer:

D

Step-by-step explanation:

32/945 is the final answer

Answer:

Step-by-step explanation:

it would be number 4 please mark brainliest

Answer:

The initial value of the boat was $20,000

The percent decrease per year of the value of the boat is 10%.

The interval on which the value of the boat is decreasing while Harry has it is (0,10)

Step-by-step explanation:

It is given that the boat costs $20,000 in 2010 when x = 0. So, the initial value of the boat was $20,000.

Next, find the percent decrease per year of the value of the boat. Consider the general form of an exponential equation, y = a(b)x, where a is the initial value of the boat, b is the base of the exponent, x is the number of years after 2010, and y is the value of the boat, in dollars.

Consider the point (1 , 18,000) which lies on the graph of this situation. Substitute x = 1, y = 18,000, and a = 20,000 into the exponential equation and isolate b.

Recall that for exponential decay, b = 1 - r where r represents the decay rate. Substitute b = 0.9 into this equation and solve for r.

So, the decay rate is 0.1, and the percent decrease per year of the value of the boat is 10%.

Harry bought the boat in 2010, and plans on selling it after 10 years in 2020. Therefore, the interval on which the value of the boat is decreasing while Harry has it is [0, 10].

The integral ∫ xarcsin(x) dx evaluates to x * arcsin(x) - 2/3 * (1 - x²)^(3/2) + C, where C is the constant of integration.

The integral ∫ xarcsin(x) dx can be evaluated using integration by parts.

∫ xarcsin(x) dx = x * arcsin(x) - ∫ (√(1 - x²)) dx

Let's evaluate the remaining integral:

∫ (√(1 - x²)) dx

To evaluate this integral, we can use the substitution method. Let u = 1 - x², then du = -2x dx.

Substituting the values, we get:

∫ (√(1 - x²)) dx = -∫ (√u) du/2

Integrating, we have:

-∫ (√u) du/2 = -∫ (u^(1/2)) du/2 = -2/3 * u^(3/2) + C

Substituting back u = 1 - x², we get:

-2/3 * (1 - x²)^(3/2) + C

Therefore, the final result is:

∫ xarcsin(x) dx = x * arcsin(x) - 2/3 * (1 - x²)^(3/2) + C

where C is the constant of integration.

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Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

Therefore, the correct answer is c) 3, as there are three F ratios calculated in a 2x2 factorial design.

In a two-way analysis of variance (ANOVA) known as a 2x2

factorial design, there are three F ratios or F statistic values calculated. This design involves two independent variables, each with two levels or categories.

The three F ratios represent the main effects of each independent variable and the interaction between the two variables.The main effects F ratios determine whether there are significant differences between the levels of each independent variable individually, ignoring the other independent variable.

There will be two main effects F ratios, one for each independent variable.The interaction F ratio examines whether there is a significant interaction between the two independent variables. It determines whether the effect of one independent variable differs across the levels of the other independent variable.

This F ratio assesses the joint influence of both independent variables.

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The geometric mean return on the investment over the five-year period is approximately 1.9591%.

To calculate the geometric mean return on the investment over the five-year period, we need to find the average return compounded annually.

The formula for the geometric mean return is:

Geometric Mean Return = \([(1 + r_1) * (1 + r_2) * (1 + r_3) * (1 + r_4) * (1 + r_5)]^{1/n} - 1\)

Where r₁, r₂, r₃, r₄, r₅ are the returns for each year, and n is the number of years.

Using the given returns:

r₁ = 10% = 0.10

r₂ = 3% = 0.03

r₃ = -5% = -0.05

r₄ = 1% = 0.01

r₅ = 2% = 0.02

n = 5 (since we have data for five years)

Plugging in the values, we have:

Geometric Mean Return = \([(1 + 0.10) * (1 + 0.03) * (1 - 0.05) * (1 + 0.01) * (1 + 0.02)]^{1/5} - 1\)

\([(1.10) * (1.03) * (0.95) * (1.01) * (1.02)]^{1/5} - 1\)

\([1.192569]^{1/5} - 1\)

\((1.192569)^{0.2} - 1\)

1.019591 - 1 = 0.019591

Therefore, the geometric mean return on the investment over the five-year period is approximately 0.019591, or 1.9591%.

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Answer:

Step-by-step explanation:

we will need to find the volume of the frosting

V=l*w*h

V=2(13*2*9)= 468 in^2 of frosting for the cake

Answer:

=5

Step-by-step explanation:

have a nice day, please give me brainliest

Answer:

X=5

Step-by-step explanation:

3x-x+2=12

2x+2=12

2x=10

X=5

Correct statements are:

a) A square can be thought of as a special rectangle.

d) Squares, rectangles, and parallelograms are all quadrilaterals.

e) A square is also a parallelogram.

Incorrect statements are:

b) A rectangle cannot be thought of as a special parallelogram. A rectangle is a special type of quadrilateral, but it does not have the same properties as a parallelogram.

c) A square cannot be thought of as a special rhombus. While a square is a special type of rhombus, not all rhombuses are squares.

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The amount of sugar in the entire shipment is 97(1)/(2) tons.

We are given that a shipment of sugar fills 2(1)/(5) containers. If each container holds 3(3)/(4) tons of sugar, we need to find the amount of sugar in the entire shipment.

Step-by-step explanation:

One container of sugar holds 3(3)/(4) tons of sugar. There are 2(1)/(5) containers of sugar in the shipment.

Amount of sugar in one container = 3(3)/(4) tons

Amount of sugar in 2(1)/(5) containers

= 2(1)/(5) × 3(3)/(4) tons

= 13/5 × 15/4 = 195/20

= 97(1)/(2) tons

Therefore, the amount of sugar in the entire shipment is 97(1)/(2) tons.

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Sections taken through the narrow width of an entire building are known as transverse sections.

A building is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory.

Given is a structural analysis blank statement as -

"Sections taken through the narrow width of an entire building are known as __________ sections.

Sections taken through the narrow width of an entire building are known as transverse sections. Those through the long dimension are known as longitudinal sections.

Therefore, Sections taken through the narrow width of an entire building are known as transverse sections.

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Answer:

First one is 142

Secound is 8

Third is 88

Fourth is 242

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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