Write a new equation for the circle (x-3)^2 + (y+8)^2 =25 after it is shifted left 5 units and up 2 units.

The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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Using the Central Limit Theorem, the statement is false, as for the averages of  the data values for a sample group, the standard error is \(s = \frac{\sigma}{\sqrt{n}}\), hence, the formula is:

\(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

While for a single value, it is:

\(Z = \frac{X - \mu}{\sigma}\)

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

Hence, the formulas are different, and for an average of the data values for a sample group it is:

\(Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

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Solve by elimination.

multiply the lower equation by negative 1.

-y=7x-21

-y+y=o

new equation is

7x+6-52=0

6-52 is -46

-7x=-46

divide by -7

x=6.57...

plug it back in

y= 7(6.57)+21

7*6.57= 46

y=46+21

y=67

(might be wrong, I tried)

Answer:

Step-by-step explanation:

its is y=67 or it might be y=7 i

Answer: D

Over the interval [4,7], the local minimum is -7

Answer:

$833

Step-by-step explanation:

Since there are 9 people, we need to determine the cost of accommodation and flights for all 9 people:

9(273) + 9(184) = 2457 + 1656 = 4167 for 9 people

We then subtract that amount from the amount of money she won:

5000 - 4167 = 833

Answer:

Step-by-step explanation:

4/mx

The value of y for the inverse variation when x = -12 is derived to be equal to 1.

Inverse variation is a mathematical relationship between two variables, in which an increase in one variable leads to a proportional decrease in the other variable. Mathematically, inverse variation can be expressed as y = k/x, where y and x are the two variables, k is a constant of proportionality, and the product of y and x is always equal to k.

when x = 6 and y = -2, then k is derived as:

-2 = k/6

k = -12 {cross multiplication}

when x = -12, y is derived as:

y = -12/-12

y = 1

Therefore, the value of y for the inverse variation when x = -12 is derived to be equal to 1.

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The function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

To determine the intervals on which the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.

Let's find the derivative of the function f(x) = x + 10√(9 - x) with respect to x.

f'(x) = 1 + 10 * (1/2) * (9 - x)^(-1/2) * (-1)

= 1 - 5√(9 - x) / √(9 - x)

= 1 - 5 / √(9 - x).

To analyze the sign of the derivative, we need to find the critical points where the derivative is equal to zero or undefined.

Setting f'(x) = 0:

1 - 5 / √(9 - x) = 0

5 / √(9 - x) = 1

(√(9 - x))^2 = 5^2

9 - x = 25

x = 9 - 25

x = -16.

The critical point is x = -16.

We can see that the derivative f'(x) is defined for all x values except x = 9, where the function is not differentiable due to the square root term.

Now, let's analyze the sign of the derivative f'(x) in the intervals (-∞, -16), (-16, 9), and (9, ∞).

For x < -16:

Plugging in a test value, let's say x = -17, into the derivative:

f'(-17) = 1 - 5 / √(9 - (-17))

= 1 - 5 / √(9 + 17)

= 1 - 5 / √26

≈ 1 - 0.97

≈ 0.03.

Since f'(-17) is positive, the function is increasing in the interval (-∞, -16).

For -16 < x < 9:

Plugging in a test value, let's say x = 0, into the derivative:

f'(0) = 1 - 5 / √(9 - 0)

= 1 - 5 / √9

= 1 - 5 / 3

≈ 1 - 1.67

≈ -0.67.

Since f'(0) is negative, the function is decreasing in the interval (-16, 9).

For x > 9:

Plugging in a test value, let's say x = 10, into the derivative:

f'(10) = 1 - 5 / √(9 - 10)

= 1 - 5 / √(-1)

= 1 - 5i,

where i is the imaginary unit.

Since the derivative is not a real number for x > 9, we cannot determine the sign.

Combining the information, we conclude that the function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

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The expression √(7x) × (√x − 7√7) in the simplified form will be x√7 − 49√x.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ √(7x) × (√x − 7√7)

Simplify the expression, then the expression is written as,

⇒ √(7x) × (√x − 7√7)

⇒ x√7 − 7 × 7√x

⇒ x√7 − 49√x

The expression √(7x) × (√x − 7√7) in the simplified form will be x√7 − 49√x.

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Answer:i think its like 40 or sum like that mb-

Step-by-step explanation:

Answer:

(x-2)^2=5 (first option)

Step-by-step explanation:

If you expand (x-2)^2, it equals x^2-4x+4. You then subtract the 5 off the right side and it becomes x^2-4x-1.

I did the work to show you what I mean. Pardon the bad handwriting ^-^'

0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.

Given that,

Standard deviation (σ) = 5.2 oz

mean (μ) = 10 oz

Number of students (n) = 120

As we know,

P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])

                        = P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])

                        = P (z > 1.86)

                        = 1 - P ( z < 1.86)

                        = 1 - 0.862394

                        = 0.137606

Thus, P( z > 12.7 oz.) = 0.137606

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Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

Dog is 2 years old

Step-by-step explanation:

Let dog's age = d

Let friend's age = f

Your dog is 8 years younger than your friend:

d +8 = f

In 2 years, your friend will be three times as old as your dog:

3(d+2) = (f+2)

3d+6 = f+2

3d = f - 4

(sub in f=d+8 from above)

3d = f - 4

3d = d+8 - 4

2d = 4

d = 2

The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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The probability that each guest got one roll of each type is 3/1, which is a fraction with a numerator of 3 and a denominator of 1. Since the numerator and denominator are relatively prime integers, the value of m + n is 3

The equation for the probability that each guest got one roll of each type is m/n, where m and n are relatively prime integers.

We can expand this equation to

m/n

= 3/1.

Since the numerator and denominator are relatively prime integers, we can solve for m + n by multiplying both sides of the equation by 1.

Multiplying both sides of the equation by 1 gives us

m + n = 3.

Therefore, the value of

m + n is 3.

Let m = numerator and n = denominator in the probability of m/n.

Given that each guest got one roll of each type, the probability is m/n.

The numerator and denominator are relatively prime integers, so m and n have no common factors.

Therefore,

m + n = 3.

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Answer:

2x^2 - 6x + 7 - (5x^2 + 2x - 8)

Distributive a -1 to each term in the parentheses.

2x^2 - 6x + 7 - 5x^2 - 2x + 8

Combine like terms.

-3x^2 - 8x + 15 is the expression after being subtracted.

Answer:

Step-by-step explanation:

(2x² − 6x + 7) − (5x²  + 2x +8)

To find the opposite of 5x²  + 2x + 8, find the opposite of each term.

2x²  − 6x + 7 − 5x²  − 2x − 8

Combine 2x²  and −5x²  to get −3x²

−3x²  − 6x + 7 − 2x − 8

Combine −6x and −2x to get −8x.

−3x² − 8x + 7 − 8

Subtract 8 from 7 to get −1.

−3x² − 8x − 1

It looks like you want to find the height of the green region. If so then that would be about 5.2 mL since the top part of the green area is around the first smaller tick above the 5.

Each smaller tickmark is 1/5 = 0.2 of a full unit. Note how there are 5 smaller tickmark spaces to make up a full unit (when we go from 5 to 6, there are 5 smaller tickmark spaces we have to move)

6 cos(π/2 t) is the best model for the position of the weight.

The motion of the weight on the spring can be modeled by a sine or cosine function because it oscillates back and forth around its equilibrium position.

We know that, the weight is initially pulled down 6 inches from its equilibrium position, so the function should have an amplitude of 6.

The time it takes for the spring to complete one oscillation is 4 seconds, so the period of the function is 4 seconds.

The general form of a sine or cosine function with amplitude A and period T is:

f(t) = A sin(2πt/T) or f(t)

= A cos(2πt/T)

Substituting the given values,

we get:

f(t) = 6 sin(2πt/4) or f(t)

= 6 cos(2πt/4)

Simplifying, we get:

f(t) = 6 sin(π/2 t) or f(t)

= 6 cos(π/2 t)

Therefore,

the function that best models the position of the weight is

s(t) = 6 cos(π/2 t).

So, the answer is option (D).

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Answer:

see explanation

Step-by-step explanation:

- 1x + 4y = 12 , that is

- x + 4y = 12 ( add x to both sides )

4y = 12 + x ( divide each term by 4 )

y = 3 + \(\frac{1}{4}\) x

To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

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Answer:

A

Step-by-step explanation:

2p - 5p < 8 + 4

- 3p < 12

-3/-3 p > 12/-3

p  > -4

-2, - 3

Answer:

g = 118

Step-by-step explanation:

Part D

Let g = number of games played

Given:

⇒ 12.75 + 0.95g = 125

Solving the equation:

subtract 12.75 from both sides:

⇒ 12.75 + 0.95g - 12.75 = 125 - 12.75

⇒ 0.95g = 112.25

divide both sides by 0.95

⇒ 0.95g ÷ 0.95 = 112.25 ÷ 0.95

⇒ g = 118.1578947...

⇒ g = 118

We need to round g down to the nearest whole number, since Jose cannot pay for playing part of a game.  Therefore, g = 118.

Part E

*cannot answer as part B has not been provided**

Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

Answer:

1/2, 3/6, 8/16, and 5/10 are all equivalent

Step-by-step explanation:

they all equal 1/2 simplified or .50

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

Answer:

\(\huge\boxed{\sf 38}\)

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

Answer:

Sam workrate 1/5

Lucy workrate 1/3.5 = reciprocal of 7/2 = 2/7

combined workrate: 1/5 + 2/7 = 17/35

they will mow the lawn in  35/17 = 2 and 1/17 hours

2 hours 3 1/2 mins

Step-by-step explanation:

Answer:

B $12.69

Step-by-step explanation:

Divide 84.63 by 100 to get 1% of the bill and then multiply the answer by 15 for 15% and round it:

\($\frac{84.63}{100} \times 15 = 12.6945$\)

The closest answer would be B $12.69.

If a bus company usually transports 12 000 people per day at a ticket price of $1. The ticket price that will maximize revenue is $2 per ticket.

Equation to find the ticket price is:

y = (12000 - 400x)(1 + .1x)

Take the derivative of the function by product rule

y' = (12000 - 400x)(.1) + (-400)(1 + .1x)

y' = 1200 - 40x - 400 - 40x

y' = 800 - 80x

Let y' = 0

0 = 800 - 80x

Solving for x

80x = 800

Divide both side by 80x

x = 800/80

x = 10

Point at x = 10

Substitute x with 10 for 1 + .1x

1 + .1(10)

= 1 + 1

= $2 per ticket

Therefore the ticket price is  $2 per ticket.

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