Looking at the destribution sets 1-8 which one seems to be closest to the mean Explain why you choose this data set .

I am answering this during a test, lol.

Answer

C. x > -3

Answer:

THE FOLLOWING MEASURES ARE TRUE FOR THE QUILT:

1. a = 60°

3. The perimeter of the rhombus is 16 inches.

5. The length of the longer diagonal is approximately 7 inches

Step-by-step explanation:

I have attached the picture describing the rhombus.

One by one we will check all the options:

As we can see that:

a+30°=90°

a = 90-30

1) a= 60° which is true

Taking the triangle with the perpendicular x, and using pythagoras theorem, we get:

=16-4 = 12

x= =3.46 ≠3

So option 2, is not true.

The possible lengths for the third side are B. 9, C. 11, and OD. 5.

To determine the possible lengths of the third side of a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Let's analyze the given options:

A. 7: This cannot be the length of the third side since it is equal to one of the given sides, which violates the triangle inequality theorem.

B. 9: This could be the length of the third side. 4 + 7 > 9, and 7 + 9 > 4, satisfying the triangle inequality theorem.

C. 11: This could be the length of the third side. 4 + 7 > 11, and 7 + 11 > 4, satisfying the triangle inequality theorem.

OD. 5: This could be the length of the third side. 4 + 7 > 5, and 5 + 7 > 4, satisfying the triangle inequality theorem.

E. 17: This cannot be the length of the third side since the sum of the two given sides is 4 + 7 = 11, which is less than 17. Therefore, the triangle inequality theorem is violated.

OF. 3: This cannot be the length of the third side since it is less than the length of either of the given sides. Therefore, the triangle inequality theorem is violated.

Based on the analysis, the possible lengths for the third side are B. 9, C. 11, and OD. 5.

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15.3 cm is the diameter of the circle circumscribed about ABC.

In order to determine the diameter of the circle circumscribed about ABC, the formula D = c/sin(C) can be used, where D represents the diameter of the circle, c represents the length of the side opposite the angle in question, and C represents the angle in question.
Therefore, by substituting the values given in the question in the above formula, we get:D = 13.6/sin(63°)D = 15.3 cmHence, the diameter of the circle circumscribed about ABC is 15.3 cm.
The circumcircle of a triangle is a circle that passes through all three vertices of the triangle.

The circumcenter is the point at which the perpendicular bisectors of the sides of the triangle intersect.

The radius of the circumcircle is half of the diameter of the circle. In the given problem, we are required to find the diameter of the circle circumscribed about triangle ABC.
The formula used to find the diameter of the circle circumscribed about the triangle is D = c/sin(C), where D is the diameter of the circle, c is the length of the side opposite to the angle C, and C is the angle for which we are trying to find the diameter of the circle.
The given problem provides us with the value of side AC which is 13.6 cm and the angle at B is 63°. We have to find the diameter of the circle circumscribed about the triangle.

By using the formula D = c/sin(C) and substituting the given values, we get the diameter of the circle circumscribed about triangle ABC which is 15.3 cm.

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The expression, in terms of x and y, for the Total number of sweets in 3 boxes and 2 packets is 3x + 2y.

To find the total number of sweets in 3 boxes and 2 packets, we need to add the number of sweets in the boxes and the number of sweets in the packets.

Let's start by finding the number of sweets in 3 boxes. Since there are x sweets in each box, the total number of sweets in 3 boxes would be 3x.

Next, let's determine the number of sweets in 2 packets. If there are y sweets in each packet, the total number of sweets in 2 packets would be 2y.

To find the total number of sweets in 3 boxes and 2 packets, we can add the two quantities we calculated:

Total number of sweets = 3x + 2y

So, the expression, in terms of x and y, for the total number of sweets in 3 boxes and 2 packets is 3x + 2y.

This expression represents the combined count of sweets from the boxes and packets, accounting for the given variables x and y.

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Answer:

The answer is 692

Step-by-step explanation:

a₁₇ = 72, a₅₁ = 208

aₙ = a + (n-1)d

a₁₇ =a + 16d = 72→ 1

a₅₁ = a + 50d = 208 →2

2-1

34d = 136

d= 4

a₁₇ = a + 16d = 72

72 = a + 64

a = 8

a₁₇₂ = a + (172-1)4

a₁₇₂ = 692

A correct pairing of possible null and alternative hypotheses for this experiment could be:

Null Hypothesis (H0): The new diabetes medication has no effect on the participants' glucose levels.

Alternative Hypothesis (H1): The new diabetes medication has a significant effect on reducing the participants' glucose levels.In hypothesis testing, the null hypothesis (H0) represents the default assumption or the statement of no effect or no difference. In this case, the null hypothesis states that the new diabetes medication has no effect on the participants' glucose levels. It assumes that there is no difference between the placebo group and the group receiving the new drug.

On the other hand, the alternative hypothesis (H1) represents the claim or the statement of an effect or a difference. In this case, the alternative hypothesis states that the new diabetes medication has a significant effect on reducing the participants' glucose levels. It suggests that there is a difference between the placebo group and the group receiving the new drug, indicating that the medication has a measurable impact on glucose levels.

By setting up these null and alternative hypotheses, Martina can conduct statistical tests and analyze the data to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis, providing evidence for the effectiveness of the new diabetes medication.

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The product of (2x + 3) and [tex](4x^2 - 5x + 6) = 8x^3 + 2x^2 - 3x + 18.[/tex]

To find the product of (2x + 3) and (4x^2 - 5x + 6), we need to use the distributive property. We multiply each term in the first binomial by each term in the second binomial and then combine like terms.

Let's go through the steps:

1. Distribute the second binomial to each term in the first binomial:

  (2x + 3)(4x^2 - 5x + 6) = 2x(4x^2 - 5x + 6) + 3(4x^2 - 5x + 6)

2. Multiply each term in the first binomial by each term in the second binomial:

  = [tex](2x * 4x^2) + (2x * -5x) + (2x * 6) + (3 * 4x^2) + (3 * -5x) + (3 * 6)[/tex]

3. Simplify each term:

  = 8x^3 - 10x^2 + 12x + 12x^2 - 15x + 18

4. Combine like terms:

  =[tex]8x^3 + (12x^2 - 10x^2) + (12x - 15x) + 18[/tex]

  = 8x^3 + 2x^2 - 3x + 18

Therefore, the product of (2x + 3) and (4x^2 - 5x + 6) is 8x^3 + 2x^2 - 3x + 18.

In general, to find the product of two binomials, you need to distribute each term from the first binomial to each term in the second binomial and then combine like terms. It's important to pay attention to the signs and simplify the resulting expression.

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Answer:

2/3

Step-by-step explanation:

You set up the formula then come out with 2/3

Its also positive because the arrows are facing to the right.

The possible coordinates for the fountain are (-11/4, -5/2) and (-11/4, 5/2),

To find the possible coordinates for the fountain that is 5 units away from both statues A and B, we can use the concept of distance formula.

The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁))

In this case, the coordinates for statue A are (-2, -1) and the coordinates for statue B are (4, -1).

Let's assume the coordinates for the fountain are (x, y). We want the distance between the fountain and both statues to be 5 units.

Using the distance formula for statue A:

5 = √((-2 - x)² + (-1 - y)²)

Simplifying:

25 = (-2 - x)² + (-1 - y)² (equation 1)

Using the distance formula for statue B:

5 = √((4 - x)² + (-1 - y)²)

Simplifying:

25 = (4 - x)²+ (-1 - y)² (equation 2)

We have a system of equations (equation 1 and equation 2) that represents the conditions for the fountain's coordinates.

By solving this system of equations, we can find the possible coordinates for the fountain.

Note: The solution to this system of equations will provide two sets of coordinates that satisfy the given conditions.

To solve the equations, we can expand and simplify:

From equation 1:

25 = 4 + 4x + x² + 1 + 2y + y²

x² + y² + 4x + 2y - 20 = 0 (equation 3)

From equation 2:

25 = 16 - 8x + x² + 1 + 2y + y²

x² + y² - 8x + 2y - 9 = 0 (equation 4)

Now, we can solve equations 3 and 4 simultaneously.

Subtracting equation 4 from equation 3 we get:

(8x - 4x) + (-9 + 20) = 0

4x + 11 = 0

4x = -11

x = -11/4

Substituting the value of x back into equation 3:

(-11/4)² + y² + 4(-11/4) + 2y - 20 = 0

y² + 2y - 25/4 = 0

Solving this quadratic equation, we can find the possible values of y. Factoring the equation:

(y + 5/2)(y - 5/2) = 0

This gives us two solutions:

y + 5/2 = 0 -> y = -5/2

y - 5/2 = 0 -> y = 5/2

Therefore, the two possible coordinates for the fountain are (-11/4, -5/2) and (-11/4, 5/2).

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The spring constant in this instance would be 3 kilograms per inch.

To obtain the spring constant, we would begin with the slope formula where the change in the y-axis is divided by the change in the x-axis. In the case of the figures above we have a straight line from (0, 0) to (4, 12).

On the y-axis, we would have 12 - 0 and on the x-axis, we would have 4 - 0.

Now, we would divide 12 by 4 to have 3 kilometers per inch which is the constant of proportionality.

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The statements that are true are:

A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).

C. f(-1) = 6

To determine the truth of each statement, we need to analyze the given table of values for the function f(x).

A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).

The x-values listed in the table are -2, -1, 0, 1, 2, 3, 4, 5, and 6. These are the inputs for the function, and therefore, they represent the domain of f(x). Thus, statement A is true.

B. The range for f(x) is all real numbers.

Looking at the y-values listed in the table for f(x), we can see that the range of f(x) is from 5 to 13. It does not include all real numbers, so statement B is false.

C. f(-1) = 6

From the table, we can see that when x = -1, f(x) = 6. Thus, statement C is true.

D. f(5) = -2

There is no entry in the table for f(5), so we cannot determine the value of f(5) from the given information. Therefore, statement D is false.

In conclusion, the true statements are A and C.

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The value of the American put futures option with a strike price of $0.55 and time to maturity of 1 year, using a one-time step tree, is $0.

The following is the one-time step tree for valuing the American put futures option:

Strike Price = $0.55, Volatility = 25%, Time to Maturity = 1 year, Interest Rate = 6% per annum, Current Futures Price = $0.60

The tree will be formed using the following equations:

u = e^(σ√t)

where σ is the volatility, t is the time and u is the up movement factor.

d = 1/u

N is the number of steps

r is the risk-free interest rate.

The values for these are:u = e^(0.25√1) = 1.2840d = 1/u = 1/1.2840 = 0.7787N = 1r = 6% per annum = 0.06First, calculate the futures price at time t=1 using the tree.

This will be used to determine whether to exercise the option or not at time t=1.Futures Price at time t=1:

From the tree:

Futures Price if Up = $0.60 x 1.2840 = $0.7704Futures Price if Down = $0.60 x 0.7787 = $0.4672

Using these values, calculate the risk-neutral probability of the futures price going up and down:

p = (e^(rt) - d) / (u - d)

= (e^(0.06x1) - 0.7787) / (1.2840 - 0.7787)

= 0.5679

The expected futures price at time t=1 is:

E(F) = p x $0.7704 + (1-p) x $0.4672

= 0.5679 x $0.7704 + 0.4321 x $0.4672 = $0.6157

Now we calculate the intrinsic value of the option. If the futures price at time t=1 is less than the strike price, then the option will be exercised. If not, then it will not be exercised.

Therefore, the intrinsic value is:Intrinsic Value = $0.55 - $0.6157 = -$0.0657

As the intrinsic value is negative, the option will not be exercised at time t=1.

Therefore, the option value at time t=0 is the expected value of the option at time t=1, discounted by the risk-free interest rate:

Option Value at t=0 = [pVu + (1-p)Vd] / (1+r)

= [0.5679 x 0 + 0.4321 x 0] / (1+0.06)  = $0.

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The sequence of transformations that proves that the shapes are similar is given as follows:

B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5

First, we have that the orientation of the figure, hence it was reflected.

The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.

The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:

3/2 = 1.5.

Hence option B is the correct option for this problem.

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uhm think you have to move the 2 lined and add the numbers together

Step-by-step explanation:

Answer:

5 units.

Step-by-step explanation:

Given:

[tex]\tt A(x_1,y_1)=(-3,-3)\\D(x_2,y_2)=(0,1)[/tex]

The distance from point A to line  BC, at point D is calculated by using the formula:

distane=[tex]\tt \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

substituting value

distance=  [tex]\tt \sqrt{(0-(-3))^2+(1-(-3))^2}[/tex]

distance =[tex]\tt \sqrt{3^2+4^2}[/tex]

distance =[tex]\tt \sqrt{25}[/tex]

distance = 5

Therefore, the distance from point A to line  BC, at point D is 5 units.

Step-by-step explanation:

Hello please could u re take the picture again

The solution to the inequality x^3 + x^2 ≤ 10x - 8 is x ≤ -2 or -1 ≤ x ≤ 1.

To find the solution to the inequality x^3 + x^2 ≤ 10x - 8, we need to determine the values of x that satisfy this inequality. Let's break down the problem step by step.

First, let's bring all terms to one side of the inequality to get a cubic equation: x^3 + x^2 - 10x + 8 ≤ 0.

To solve this inequality, we can employ various methods, such as graphing, factoring, or using calculus. However, since the degree of the polynomial is relatively low, we can use a simpler approach.

We start by finding the critical points where the polynomial changes its behavior. To do this, we set the equation equal to zero: x^3 + x^2 - 10x + 8 = 0.

Next, we can use synthetic division or long division to find the factors of the polynomial. By performing this calculation, we find that x = -2 is a factor. Using synthetic division again, we can divide the polynomial by (x + 2) to obtain a quadratic equation: (x + 2)(x^2 - x + 4) = 0.

Setting each factor equal to zero gives us two additional solutions: x = 1 ± √15i. However, since we are dealing with a real-valued inequality, we only consider the real solutions. Therefore, x = -2 is the only real root.

Now, we have identified the critical point x = -2. We can plot this on a number line and choose test points within each interval to determine if they satisfy the inequality. By evaluating the inequality for these test points, we find that the solution is x ≤ -2 or -1 ≤ x ≤ 1.

To summarize, the solution to the inequality x^3 + x^2 ≤ 10x - 8 is x ≤ -2 or -1 ≤ x ≤ 1.

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The best answer choice among the given options is O 15 m², as none of the provided options match the correct Ccalculation.

To find the area of a rhombus, we need the lengths of the diagonals. In this case, the lengths of the diagonals are not provided. However, we can use the given information to determine the area based on the side lengths.

A rhombus is a quadrilateral with all sides of equal length, so the given side lengths of 5.5 m and 2 m can help us find the area.

We know that the diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four congruent right triangles. Each side of the rhombus is the hypotenuse of one of these triangles.

Given that the side length is 5.5 m, we can consider one of these right triangles. One leg of the right triangle is half of the side length, which is (5.5 m)/2 = 2.75 m. The other leg of the triangle is the length of the diagonal, which is unknown.

Using the Pythagorean theorem, we can find the length of the diagonal:

(diagonal)^2 = (leg)^2 + (leg)^2

(diagonal)^2 = (2.75 m)^2 + (2 m)^2

(diagonal)^2 = 7.5625 m² + 4 m²

(diagonal)^2 = 11.5625 m²

diagonal ≈ √11.5625 m ≈ 3.4 m (rounded to the nearest tenth)

Since the diagonals of a rhombus are perpendicular bisectors of each other, the length of the other diagonal would also be approximately 3.4 m.

Now, we can calculate the area of the rhombus using the formula: area = (diagonal1 * diagonal2) / 2

area = (3.4 m * 3.4 m) / 2

area = 5.8 m²

The area of the rhombus is approximately 5.8 m².

The best answer choice among the given options is O 15 m², as none of the provided options match the correct area calculation.

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Answer:

I would say D

Step-by-step explanation:

since it already tells you what y equals it makes it easier to substitute the others take more work so the best first step is substituting for y

Answer:

Option D) Substitute for y in the first equation

Step-by-step explanation:

When solving for a system of equation, we always need 1 equation to have x or y already isolated by itself.  This makes it easy to substitute that variable into the other equation, solve, then substitute the other variable into another equation.

This will give us an ordered pair, known as the solution.

In this system, we have 2 equations.  In the first one, we have no variables isolated.  In the second one, we have y isolated on the left side of the equal sign.  This means we can take what y equals (3x+2) and substitute that in for y in the first equation.

Hope this helps! :)

Answer:

The probability of drawing a green marble from the jar is 5/7, since there are 5 green marbles out of a total of 7 marbles.

Since the marbles are replaced after each draw, the probability of drawing 4 green marbles in a row is (5/7) * (5/7) * (5/7) * (5/7) = 625/2401.

Therefore, the probability of selecting 4 green marbles is 625/2401.

The statement accurately describes the behavior of the given curve, indicating a decline through the specified points (-7, 4.9), (-5, 3), (0, 0), (3, -2), and (6, -4).

The statement "A diagonal curve declines through (-7, 4.9), (-5, 3), (0, 0), (3, -2), and (6, -4)" is true.

Based on the given points, we can observe that the y-coordinate decreases as the x-coordinate increases.

This indicates a downward trend or decline along a diagonal curve.

The given points (-7, 4.9), (-5, 3), (0, 0), (3, -2), and (6, -4) satisfy this pattern.

By connecting these points, we can trace a diagonal curve that exhibits a decline.

The curve passes through each of the given points, following a consistent downward slope.  

This is evident from the y-values decreasing as x-values increase.

The curve's behavior suggests a negative correlation between the x and y variables.

As x increases, y decreases, resulting in a diagonal decline.

The specific shape and equation of the curve cannot be determined without further information or additional points, but the given points clearly demonstrate a downward trend along a diagonal curve.

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Answer:

10

Step-by-step explanation:

2x = 2(-10 + 2x)

x = -10 + 2x

-x = -10

x = 10

Answer:

10

Step-by-step explanation:

Multiply the smaller line by 2

which is RS

2x = -20 + 4x

-2x = -20

x = 10

The equation does not have a unique solution for x. It is true for any value of x.

The given equation is:

(5/7)(x + 2) - (3/7)x = (2/7)(x + 5)

To solve for x, we'll first simplify both sides of the equation using the distributive property and combining like terms:

[(5/7)x + (5/7)(2)] - (3/7)x = [(2/7)x + (2/7)(5)]

Simplifying further:

(5/7)x + 10/7 - (3/7)x = (2/7)x + 10/7

Next, we'll collect the x terms on one side and the constant terms on the other side of the equation:

(5/7)x - (3/7)x - (2/7)x = 10/7 - 10/7

Combining like terms:

[(5/7) - (3/7) - (2/7)]x = 0

Simplifying further:

(0/7)x = 0

Any value of x will satisfy this equation since (0/7)x will always be zero.

Therefore, the equation does not have a unique solution for x. It is true for any value of x.

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Answer:

To calculate the probability that the sample mean is 2.5, we need to examine the sampling distribution provided.

Sampling Distribution:

Sample Mean | Probability

1.5 | 1/16

2.0 | 4/16

2.5 | 6/16

3.0 | 4/16

3.5 | 1/16

The probability that the sample mean is 2.5 can be obtained by summing up the probabilities associated with that value:

Probability(sample mean = 2.5) = 6/16 = 3/8 = 0.375

Therefore, the probability that a randomly taken sample from the population will have a sample mean of 2.5 is 0.375 or 37.5%.

Answer:

Both are incorrect

Step-by-step explanation:

In the right triangle ΔABC, ∠ABC = 90 and two angles = 45,

∠ACB = ∠BAC = 45

Therefore, the sides opposite to these angles are equal

⇒ x = z

By  Pythagorean theorem,

x² + z² = y²

⇒ x² + x² = y²

⇒ 2x² = y² -----eq(1)

In the right triangle ΔABD,

∠ADB = 90

∠BAD = 45 (since ∠BAC = 45)

⇒ ∠ABD = 180 - 90 - 45

⇒ ∠ABD = 45

Since ∠BAD = ∠ABD = 45, the sides opposite to these angles are equal

⇒ AD = 3

Also since ΔABC is an isoceles triangle, BD bisects AC

⇒ AD = DC = AC/2 = y/2

⇒ y/ 2 = AD

⇒ y = 2AD

⇒ y = 2(3)

⇒ y = 6

From eq(1)

2x² = y²

⇒ 2x² = 6²

⇒ x² = [tex]\frac{6^2}{2}[/tex]

⇒ [tex]x = \sqrt{\frac{6^2}{2} }[/tex]

⇒[tex]x = \frac{6}{\sqrt{2} }[/tex]

and

[tex]z= \frac{6}{\sqrt{2} }[/tex]

Answer:

Step-by-step explanation:

The next element in the sequence is **-1**.

The sequence {-5, -3} is an arithmetic sequence, which means that the difference between any two consecutive elements is constant. In this case, the difference between -5 and -3 is 2, so the next element in the sequence must be -3 + 2 = **-1**.

The other choices are incorrect because they are not the next element in an arithmetic sequence with a difference of 2.

[tex]P=100\left( \frac{1}{2} \right)^{\frac{t}{30000}} \\\\[-0.35em] ~\dotfill\\\\ \boxed{A}\\\\ t=20000\hspace{5em}P=100\left( \frac{1}{2} \right)^{\frac{20000}{30000}}\implies P=100\left( \frac{1}{2} \right)^{\frac{2}{3}}\implies P\approx 63.0 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\\\\ P=40\hspace{5em}40=100\left( \frac{1}{2} \right)^{\frac{t}{30000}}\implies \cfrac{40}{100}=\left( \cfrac{1}{2} \right)^{\frac{t}{30000}}\implies \cfrac{2}{5}=\left( \cfrac{1}{2} \right)^{\frac{t}{30000}}[/tex]

[tex]\cfrac{2}{5}=\left( \cfrac{1}{2} \right)^{\frac{1}{30000}t}\implies \log\left( \cfrac{2}{5} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{30000}t} \right] \\\\\\ \log\left( \cfrac{2}{5} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{30000}} \right]\implies \cfrac{\log\left( \frac{2}{5} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{30000}} \right]}=t\implies 40000\approx t[/tex]

Answer:

(4 - π)r²

= 0.86 r²

Step-by-step explanation:

The radius of the circle = r

The diammeter of the circle = 2r

Area of circle = πr²

The side of the square = diammeter of the circle = 2r

The area of the square = (2r)² = 4r²

Area of shaded region = ar(square) - ar(circle)

= 4r² - πr²

= (4 - π)r²

= (4 - 3.14)r²

= 0.86 r²

Step-by-step explanation:

To calculate the total cost of the truck including all payments and down payment, we can use the formula for the future value of an annuity due:

FV = PMT × (((1 + r/n)^(n×t) - 1) / (r/n)) + PV × (1 + r/n)^(n×t)

where:

- FV is the future value of the annuity due (the total cost of the truck including all payments and down payment)

- PMT is the monthly payment

- r is the annual interest rate (4%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (3)

- PV is the present value of the annuity due (the amount financed after the down payment)

First, we need to calculate the monthly payment:

PMT = (r/n) × PV / (1 - (1 + r/n)^(-n×t))

PV = $18,000 - $2,000 = $16,000

PMT = (0.04/12) × 16000 / (1 - (1 + 0.04/12)^(-12×3)) = **$470.98**

Now we can calculate the future value of the annuity due:

FV = PMT × (((1 + r/n)^(n×t) - 1) / (r/n)) + PV × (1 + r/n)^(n×t)

FV = 470.98 × (((1 + 0.04/12)^(12×3) - 1) / (0.04/12)) + 16000 × (1 + 0.04/12)^(12×3) = **$19,981.63**

Therefore, the total cost of the truck including all payments and down payment is **$21,981.63**.