There are 5 children running in a relay race. in a relay race, each person runs part of the race. the next runner starts where the previous runner stops. each runner runs the same distance. in this relay race, each child runs of a mile, then stops so the next , a runner can continue. plot the point on the number line that represents the location where the fourth child will stop running.​

A. Melissa's monthly payment is approximately $146.89.

B. The total amount of the monthly payments over the four-year period is approximately $7,052.72.

C. The finance charge on the loan is approximately $1,052.72.

The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

To calculate the monthly payment, we can use the formula:

Monthly payment = [P x r x (1 + r)ⁿ] / [(1 + r)ⁿ⁻¹]

where P is the principal (the amount of the loan), r is the monthly interest rate, and n is the number of monthly payments.

A. To find the monthly payment, we first need to calculate the values of r and n.

Since the APR is 10%, the monthly interest rate is 10% / 12 = 0.00833 (rounded to 5 decimal places).

The number of monthly payments over four years is 4 x 12 = 48.

Using these values, we can calculate the monthly payment:

Monthly payment = [6000 x 0.00833 x (1 + 0.00833)⁴⁸] / [(1 + 0.00833)⁴⁸⁻¹]

Monthly payment ≈ $146.89

So Melissa's monthly payment is approximately $146.89.

B. To find the total amount of the monthly payments, we can multiply the monthly payment by the number of payments:

Total amount of monthly payments = Monthly payment x Number of payments

Total amount of monthly payments = $146.89 x 48

Total amount of monthly payments ≈ $7,052.72

So the total amount of the monthly payments over the four-year period is approximately $7,052.72.

C. To find the finance charge, we can subtract the original principal from the total amount of the monthly payments:

Finance charge = Total amount of monthly payments - Principal

Finance charge = $7,052.72 - $6,000

Finance charge ≈ $1,052.72

So the finance charge on the loan is approximately $1,052.72.

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Answer:

Problem 8:
Option C)       DE = √21

Problem 9:
Option C)     Perimeter = 30 cm

Step-by-step explanation:

1. Problem 8

Draw a line segment connecting the center of the circle, X, to A. This is the radius of the circle

The points ABX form a right triangle with AX as the hypotenuse and AB, BX as the legs of the right triangle

By the Pythagorean theorem
hypotenuse² = sum of the squares of the two legs

Plugging in line segment references

AX² = AB² + BX²

We are given AC = 8, BX = 3

Since the segment BX intersects AC at right angles, AB = BC = AC/2

So AB = 8/2= 4

Plugging these values into the Pythagorean formula
AX² = AB² + BX²

AX² = 4² +3²

AX² = 16 + 9

AX² = 25

Draw a line connecting X and D
The points DEX form a right triangle with DX as the hypotenuse and EX and DE as the legs

Again, by the Pythagorean theorem

DX² = DE² + EX²

But DX is the radius of the circle so it must be the same as AX

Substitute for DX in terms of AX
DX² = DE² + EX²

=> AX² = DE² + EX²

But AX² = 25 and EX = 2 giving EX² = 4

Therefore

AX² = DE² + EX² becomes
25 = DE² + 4

DE² = 25 - 4

DE² = 21

DE = √21

This is choice C

Problem 9

To find the perimeter, just add up the individual side lengths:

Perimeter = 10 + 8 + 7 + 5 = 30 cm

Option C

Based on the inscribed angle theorem, the measure of angle JKL in the circle is: m<JKL = 121°.

Where an inscribed angle is subtended by an arc it intercepts, the measure of the inscribed angle is equal to half of the the measure of the intercepted arc in the circle, based on the inscribed angle theorem.

Angle JKL is the inscribed angle that is subtended by arc JML. Find the measure of arc JML.

Measure of arc JML = 360 - 53 - 65

Measure of arc JML = 242°

m<JKL = 1/2(measure of arc JML) [inscribed angle theorem]

Substitute:

m<JKL = 1/2(242)

m<JKL = 121°

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The square root of the sample size (n=37), which is approximately 0.820 seconds:

X ~ N(8, 5/√37)

The sample distribution of the mean, denoted as X, is the distribution of all possible sample means of a certain sample size taken from a population. In this case, we have a population of couples in conflict, and we have a sample size of 37. The mean length of time couples in conflict listen to each other is known to be 8 seconds with a standard deviation of 5 seconds.

Since we have a large enough sample size (n=37), we can assume that the sample mean follows a normal distribution according to the Central Limit Theorem. The Central Limit Theorem states that the sample means from a large enough sample size will be approximately normally distributed regardless of the population distribution, given that the samples are independent and randomly selected.

Thus, the sample distribution of X can be represented by a normal distribution with a mean of 8 seconds (same as the population mean) and a standard deviation of 5 seconds divided by the square root of the sample size (n=37), which is approximately 0.820 seconds:

X ~ N(8, 5/√37)

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The particular solution of the given differential equation with the initial condition f(6) = -2.

To find the particular solution of the given differential equation dy/dx = (x-3)/y with the initial condition f(6) = -2, we first need to solve the differential equation. This is a first-order separable equation, so we can rewrite it as:

y dy = (x - 3) dx

Now, integrate both sides:

∫y dy = ∫(x - 3) dx

(1/2)y^2 = (1/2)x^2 - 3x + C

Now, apply the initial condition f(6) = -2:

(1/2)(-2)^2 = (1/2)(6)^2 - 3(6) + C

(1/2)(4) = (1/2)(36) - 18 + C

2 = 18 - 18 + C

C = 2

So the particular solution is:

(1/2)y^2 = (1/2)x^2 - 3x + 2

This is the particular solution of the given differential equation with the initial condition f(6) = -2.

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Answer:

21.5

Step-by-step explanation:

First we can solve for c using the pythagoreom theorem. (probably didn't spell that right)

A squared + B squared =  C squared

9 squared + 3 squared = c squared

81+9= c squared

90=c squared

90 square root is (rounded to the nearest tenth) 9.5

c=9.5

Then we can add 9.5+9+3= 21.5

The solution to the equation is x = 15.

To rewrite the exponential equation using the same base, we need to express both 8 and 32 as powers of the same base. Since both 8 and 32 are powers of 2, we can rewrite the equation as:

[tex](2^3)^(2x) = (2^5)^(x+3)[/tex]

Here, we used the fact that[tex](a^b)^c = a^(b*c)[/tex]to simplify the exponents. We also used the property that 8 is equal to 2 raised to the power of 3, and 32 is equal to 2 raised to the power of 5.

Now that we have rewritten the equation with the same base, we can equate the exponents on both sides of the equation to solve for x:

[tex]2^(6x) = 2^(5x + 15)[/tex]

Since the bases on both sides of the equation are equal, we can equate the exponents and solve for x:

6x = 5x + 15

Subtracting 5x from both sides, we get:

x = 15

Therefore, the solution to the equation is x = 15.

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The surface area of revolution about the x-axis of y=4x+2 over the interval 2 is approximately 88.99 square units.

To find the surface area of revolution about the x-axis of y=4x+2 over the interval 2, we first need to express the equation in terms of x.

Rearranging the equation, we get x = (y-2)/4.

Next, we need to determine the limits of integration.

Since we are rotating about the x-axis, the limits of integration are the x-values, which in this case are 0 and 2.

Using the formula for the surface area of revolution, S = 2π∫(y√(1+(dy/dx)^2))dx, we can plug in the values we have found.

dy/dx for y=4x+2 is simply 4, so we get:

S = 2π∫(4x+2)√(1+16)dx from 0 to 2

Simplifying this, we get:

S = 2π∫(4x+2)√17 dx from 0 to 2

Evaluating this integral using calculus, we get:

S = 32π√17/3

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c. rotate it 90° counterclockwise about point (-3,-3), then translate it 8 units to the right

The correct pair of transformations that moves quadrilateral 1 to quadrilateral 2 is option d: translate it 8 units to the right, then reflect it over the line y = -3.

First, by translating it 8 units to the right, all points of quadrilateral 1 will shift horizontally to the right by 8 units, maintaining their relative positions.

Next, reflecting it over the line y = -3 will result in a vertical flip of the shape. This reflection will change the orientation of the quadrilateral while keeping the translated positions intact.

Together, these two transformations will precisely move quadrilateral 1 to quadrilateral 2. Therefore, option d is the correct choice.

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Declan swims faster than Madison, with a speed of 7/2 miles per hour compared to Madison's speed of 2/5 miles per hour.

Declan swims faster than Madison. While Madison swims 2/5 mile in an hour, which means her speed is 2/5 miles per hour, Declan swims 7/10 mile in 1/5 hour, which means his speed is 7/2 miles per hour. This indicates that Declan's speed is greater than Madison's speed.

In fact, we can see that Declan's speed is almost 4 times faster than Madison's speed. This means that Declan can cover a greater distance in the same amount of time compared to Madison.

Therefore, based on the given information, we can confidently say that Declan swims faster than Madison.

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Answer: 8

Step-by-step explanation:

CF looks like the radius of the circle.

ED looks like the diameter.

.: ED = 2 x CF = 2 x 4 = 8

.: ED = 8

Answer:

The length of ED, or the diameter, is 8

Step-by-step explanation:

As the other person explained, CF is the radius, as the radius is from the centermost point to the edge.  I also see that ED is the diameter, as the diameter is from edge to edge, going through the centermost point.  Therefore, since the diameter is double the radius, we can solve this with the following equation:

2 * r = d, where r is radius and d is diameter.

2 * 4 = d

8 = d

Answer:

Step-by-step explanation:

6.48x1.0e5=x

x/0.35

Answer:

Step-by-step explanation:

60 x 3 = 180

180 miles

Answer:

Step-by-step explanation:

5^2 + x^2 = 8^2

25 + x^2 = 64

x = 6.2

Answer:

The distance between these parallel lines is 2 - (-7) = 9 units.

The total inventory costs consist of two parts: the cost of storing the shoes and the cost of reordering the shoes. The cost of storing the shoes is given by the formula:

Cost of storing = $6 per shoe pair per year x number of shoe pairs

Since the shoes are stored for a year, this cost is incurred annually. The cost of reordering the shoes is given by the formula:

Cost of reordering = $14 per order + $7 per shoe pair x number of shoe pairs

This cost is incurred each time the store places an order with the manufacturer.

Let x be the number of shoe pairs in each order from the manufacturer. The number of orders needed to sell 1750 shoe pairs each year is given by:

Number of orders = 1750 shoe pairs / x shoe pairs per order

The total inventory costs can be expressed as:

Total cost = Cost of storing + Cost of reordering

Substituting the formulas for the two costs and the expression for the number of orders, we get:

Total cost = $6 per shoe pair per year x 1750 shoe pairs + ($14 per order + $7 per shoe pair x x shoe pairs) x (1750 shoe pairs / x shoe pairs per order)

Simplifying this expression, we get:

Total cost = $10,500 + $14(1750/x) + $7(1750)

Total cost = $10,500 + $24,500/x

Therefore, the function that models the total inventory costs as a function of x is:

Total cost(x) = $10,500 + $24,500/x

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With regard to the similar triangles,

In ΔACD

BE ∥ CD

In ΔACD and ΔABE

BE ∥ CD

∠ACD =∠ABE           (corresponding angles)

∠ADC = ∠AEB          (corresponding angles)

∠A = ∠A                    (common angle)

ACD ∼ ΔABE

So,  The corresponding sides are in proportion.

Now, find ED

AB/BC = AE/ED
ED = AE (BC/AB)
ED = 26(5/20)
ED = 6.5cm


For BE

AB/AC = BE/CD
BE = CD (AB/AC)
BE = 18 (20/25)
BE  = 14.4cm

Now, find BE

Therefore, the length of ED is 6.5cm and the length of BE is 14.4 cm.

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The y-intercept of the graph is: C. "the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius."

In mathematical terms, the y-intercept is the point where a line or curve intersects the y-axis on a coordinate plane.

In practical terms, the y-intercept of a situation often represents the starting point or initial value of a variable or function.

In the graph given above that shows the relationship between temperature in degrees Fahrenheit and degrees Celsius, the y-intercept is 32 degrees Fahrenheit, which means: C. "the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius."

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The rate of change of:

total revenue is $500 per day

total cost is $40 per day

total profit is $460 per day

To find the rate of change of total revenue, cost, and profit with respect to time, we need to take the derivative of the given functions with respect to x and then multiply by the rate of change of x with respect to time (dx/dt).

Total revenue (R) = 60x – 0.5x²
dR/dx = 60 – x
When x = 35, dR/dx = 60 – 35 = 25
Rate of change of total revenue = (dR/dx) * (dx/dt) = 25 * 20 = $500 per day

Total cost (C) = 2x+ 10
dC/dx = 2
When x = 35, dC/dx = 2
Rate of change of total cost = (dC/dx) * (dx/dt) = 2 * 20 = $40 per day

Total profit (P) = R - C
dP/dx = (dR/dx) - (dC/dx)
When x = 35, dP/dx = 25 - 2 = 23
Rate of change of total profit = (dP/dx) * (dx/dt) = 23 * 20 = $460 per day

Therefore, the rate of change of total revenue is $500 per day, the rate of change of total cost is $40 per day, and the rate of change of total profit is $460 per day.

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1 hour =60 minutes

Step-by-step explanation:

Let M be the time in minutes . T be temperature in Farhenheit. From 45th min to end of the hour there remains a steady temperature. after that gyms starts to cools down . For time 45≤M≤60, Temperature T=77oF.To find a) Is M a function of T ? we know that Temperature changes with respect to time . So M is independent variable and T is dependent variable . so M cannot be a function of T .

The function f(z) = 1 + 6x + 96x^-1 has one local minimum and one local maximum. This function has a local maximum at x. The function f(x) = 1 + 6x + 96x^(-1) has a local maximum at x = -4.

To find the local maximum of the function f(x) = 1 + 6x + 96x^(-1), we first need to find the critical points. We do this by finding the first derivative of the function and setting it equal to zero.

Step 1: Find the derivative of the function
f'(x) = d/dx (1 + 6x + 96x^(-1))
f'(x) = 6 - 96x^(-2)

Step 2: Set the derivative equal to zero and solve for x
6 - 96x^(-2) = 0

Step 3: Solve for x
96x^(-2) = 6
x^(-2) = 6/96
x^(-2) = 1/16
x^2 = 16
x = ±4

Step 4: Determine which of the critical points is a local maximum. To do this, we will examine the second derivative of the function.

f''(x) = d^2/dx^2 (1 + 6x + 96x^(-1))
f''(x) = 192x^(-3)

Now we will evaluate the second derivative at each critical point:

f''(4) = 192(4)^(-3) = 3 > 0, so x = 4 is a local minimum.
f''(-4) = 192(-4)^(-3) = -3 < 0, so x = -4 is a local maximum.

Therefore, the function f(x) = 1 + 6x + 96x^(-1) has a local maximum at x = -4.

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Answer:

Para comparar las propuestas de los bancos, debemos llevar las tasas de interés a una misma unidad de tiempo. Podemos convertir la tasa del Banco A de bimestral a mensual multiplicándola por 2 (ya que hay 6 bimestres en 1 año):

Tasa del Banco A: 1,5% * 2 = 3% mensual

Tasa del Banco B: 0,5% mensual

Para calcular los intereses que se obtendrán en cada banco, podemos utilizar la fórmula del interés compuesto:

I = C * ((1 + r/n)^(n*t) - 1)

Donde:

I es el interés

C es el capital inicial

r es la tasa de interés en forma decimal

n es el número de veces que se capitaliza al año

t es el tiempo en años

Para el Banco A, como la tasa está en meses, capitalizaremos mensualmente (n=12):

I = 40 000 * ((1 + 0,03/12)^(12*2) - 1) = 4 896,18 soles

Para el Banco B, como la tasa ya está en meses, capitalizaremos mensualmente (n=12):

I = 40 000 * ((1 + 0,005)^(12*2) - 1) = 4 225,48 soles

Por lo tanto, la propuesta más conveniente es la del Banco A, ya que ofrece una tasa de interés mayor y genera un interés total de 4 896,18 soles. En cambio, el Banco B genera un interés total de 4 225,48 soles.

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Step-by-step explanation:

d = a2 - a1

d = 11 - 5

d = 6

[tex]Sn \: = \frac{n}{2} (2a1 + (n - 1)d) \\ S7 = \frac{7}{2} (2 \times 11 + (7 - 1)6) \\ S7 = \frac{7}{2} (22 + 36) \\ S7 = \frac{7}{2} \times 58 \\ S7 = 7 \times 29 \\ S7 = 203[/tex]

The domain of the function f(x) = 1/x - 8 is (-∞, 0) U (0, +∞), and f = 1/x - 8.

The function f(x) is defined as 1/x - 8. The domain of the function is the set of all possible values of x for which the function is defined. Since the function involves division by x, x cannot be equal to zero. Therefore, the domain of f(x) is (-∞, 0) U (0, +∞), which means that x can take any value except 0.

To find f(x), we simply substitute the expression for f(x) in the definition of the function. Therefore, we have:

f(x) = 1/x - 8

This is the final answer. We cannot simplify it any further. The function f(x) represents a hyperbola with a vertical asymptote at x = 0 and a horizontal asymptote at y = -8.

As x approaches 0 from the left, f(x) goes to negative infinity, and as x approaches 0 from the right, f(x) goes to positive infinity. Similarly, as x approaches positive or negative infinity, f(x) approaches 0.

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The first and fourth sequences show a geometric series.

Consequently, the sequences 2, 3, 4.5, 6.75, … and 4, 8, 16, 32, … are the geometric series.

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Complete Question:-

Which of the following show a geometric series? select all that apply.

1) 2 3 4.5 6.75 …

2) 2 2.5 3 3.5 …

3) 6 7 9 12 …

4) 4 8 16 20 …

5) 8 4 2 1 …

Answer:

Step-by-step explanation:

Gray's $3,500 tax-deductible contribution to his IRA will save him $980 on his taxes.

When Gray contributes $3,500 to his individual retirement account (IRA), it is considered a tax-deductible contribution. This means that the amount contributed is deducted from his taxable income, reducing the amount of taxes he owes.

Since Gray is in the 28 percent tax bracket, this means that for every dollar of taxable income, he pays 28 cents in taxes. To calculate the tax savings from his $3,500 IRA contribution, we need to multiply the contribution amount by his tax rate:

$3,500 (contribution) x 0.28 (tax rate) = $980 (tax savings)

In this case, Gray's $3,500 tax-deductible contribution to his IRA will save him $980 on his taxes. By contributing to his IRA, Gray not only invests in his future retirement but also takes advantage of the tax benefits associated with these accounts. In the end, he reduces his taxable income and, consequently, the amount of taxes he needs to pay.

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If a population is normal with a variance of 99, the necessary sample size is 7 (Option B).

To find the necessary sample size for a given confidence level and margin of error, we can use the formula:

n = (Z² * σ²) / E²

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ² is the population variance, and E is the margin of error.

In this case, the population variance (σ²) is 99, the desired confidence level is 68.26%, and the margin of error (E) is 4 units. The Z-score corresponding to a 68.26% confidence level is approximately 1, as it is close to one standard deviation from the mean in a normal distribution.

Now, we can plug the values into the formula:

n = (1² * 99) / 4²
n = (1 * 99) / 16
n = 99 / 16
n ≈ 6.19

Since we cannot have a fraction of a sample, we round up to the nearest whole number, which is 7. So, the necessary sample size is 7 (Option B).

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D (5,2) and (2,5)

This is correct indeed