Nilo wants to save a total of $500,000 for retirement. How much should they deposit monthly into an account that pays 3.7% interest, compounded monthly, to meet their goal in 22 years? What is their monthly deposit?

The average rate of change of the function g(n) = 10(1.02)ⁿ is 0.25   inches/day.

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing.

To calculate the average rate of change of the function g(n), we use the formula below.

Formula:

Where:

From the question,

Given:

Therefore,

Substitute these values into equation 1

Hence, the average rate of change is 0.25 inches/day.

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The difference between the sum of the first 50 counting numbers and the sum of the first 100 counting numbers is 3775.

Here we have to find the difference between the first 50 counting numbers and first 100 counting numbers.

Formula to find the sum of the number n is:

[tex]S_{n}[/tex] = n/2( 2a + (n-1)d)

a = first number of the series

d = common difference

n = number of series

Sum of first 50 counting numbers:

[tex]S_{50}[/tex] = 50/2( 2× 1 + (50-1) 1)

    = 25 × 51

    = 1275

Sum of first 100 counting numbers:

[tex]S_{100}[/tex] = 100/2 ( 2×1 + (100- 1) 1)

      = 50 × 101

      = 5050

Now the difference between them:

[tex]S_{100}[/tex] - [tex]S_{50}[/tex] = 5050 - 1275

              = 3775

Therefore the difference is 3775.

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The function in the values menu would you use to summarize the data is SUM

Because

I would use the SUM function to figure out how much box office revenue each genre earned. In the pivot table, the SUM function would add the total revenue separately for each genre.

This function, as clear from the name, is used to add all the values provided as arguments and to display the result in the cell-containing function. Argument Type All Numbers Return Type Number. Syntax = SUM(number 1 , number2, ).

The SUM function will sum hardcoded values and numbers that result from formulas. If you need to sum a range and ignore existing subtotals, see the SUBTOTAL function.

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Answer:

[tex]5x {}^{2} - 5y { = }0 [/tex]

Answer:  The correct answer is A) Mrs. Reynolds y = 1/2x + 1/2

Step-by-step explanation:

In the slope-intercept form of y=mx+b, m=the slope of the line

Therefore, y=1/2x + 1/2 has a slope of 1/2

As noted in the graph below, it is the only option listed that also intersects the point (5,3).

The 90% confidence interval is  (5.09% , 5.41%)  and the 99% confidence interval is (52.24% , 52.76%)  .

In the question ,

it is given that ,

number of sample of loans taken = 28

the average of the sample is = 5.25%

the standard deviation of the normally distributed population is 0.5 %

The formula to find the Confidence Interval (CI) for the population mean is written as

[tex]\bar{x}[/tex] ±[tex]t_{n-1} , _{\alpha /2} \frac{\sigma}{\sqrt{n} }[/tex]

it is given that the 30 year fixed mortgage rates are normally distributed .

the sample size (n) = 28

Since sample size is less than 30 , the t - test is applied .

Sample mean ( [tex]\bar{x}[/tex] ) = 0.0525

the standard deviation (σ) = 0.005

the significance level : α = 1 - 0.90 = 0.1

critical value = [tex]t_{n-1} , _{\alpha}[/tex] = [tex]t_{27} , _{0.05}[/tex] = 1.703

So , 90% confidence interval will be :

= 0.525 ± (1.703)×(0.005/√28)

≈ 0.0525 ± 0.0016

= (0.0525 - 0.0016 , 0.0525 + 0.0016)

= (0.0509 , 0.0541)

= (5.09% , 5.41%)

For the 99% confidence interval ,

the significance level : α = 1 - 0.99 = 0.01

critical value = [tex]t_{n-1} , _{\alpha}[/tex] = [tex]t_{27} , _{0.005}[/tex] = 0.2771

So , 99% confidence interval will be :

= 0.525 ± (0.2771)×(0.005/√28)

≈ 0.0525 ± 0.00026

= (0.0525 - 0.00026 , 0.0525 + 0.00026)

= (0.05224 , 0.05276)

≈ (52.24% , 52.76%)

Therefore , The 90% confidence interval is  (5.09% , 5.41%)  and the 99% confidence interval is (52.24% , 52.76%)  .

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The unit rate at which Darrell walks is 1.5 meters per second, so the options with 1.5 meters per second is correct.

Given:

Darrell is walking for a distance of 90 meters in time 60 seconds.

To find out the unit rate we must divide the distance traveled by Darrell by the time taken to travel that distance.

Unit rate = Distance traveled / Time taken

= 90 meters / 60 seconds.

= 1.5 meters per second.

Therefore , The unit rate at which Darrell walks is 1.5 meters per second, so the options with 1.5 meters per second is correct.

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The cost of each bottle of orange juice is 0.78 dollars.

Xavier buys 18 bottles of orange juice at the corner store for a total cost of $14.04. Each bottle costs the same amount.

Therefore, the cost of each bottle of orange juice can be found as follows:

cost of each bottle of orange juice = total cost of the whole orange juice / number of orange juice bought

cost of each bottle of orange juice = 14.04 / 18

Therefore,

cost of each bottle of orange juice = $ 0.78

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Answer:

if i have 19

Step-by-step explanation:

The equation of the parabola is x = -1/16([tex]y^{2}[/tex]+6y-7).

According to the question,

We have the following information:

A parabola can be drawn given a focus of (−3,−3) and a directrix of x=5.

Now, let's take (x,y) to be the points of parabola.

So, we have the following expression:

Distance between (-3,-3) and (x,y) = Distance between (x,y) and x = 5

Distance between (x,y) and x = 5 will be Ix-5I

Now, we will use distance formula to solve this expression further.

[tex]\sqrt{(y+3)^{2}+ (x+3)^{2} }= (x-5)} }[/tex]

Squaring on both sides of the equation:

[tex]{(y+3)^{2}+ (x+3)^{2} }= (x-5)^2} }[/tex]

[tex]y^{2}[/tex]+9+6y+[tex]x^{2}[/tex]+9+6x = [tex]x^{2}[/tex]+25-10x

[tex]y^{2}[/tex]+6y+6x+18-25+10x = 0

[tex]y^{2}[/tex]+6y+16x-7 = 0

16x = [tex]-(y^{2}[/tex]+6y-7)

x = -1/16([tex]y^{2}[/tex]+6y-7)

Hence, the equation of the parabola is x = -1/16([tex]y^{2}[/tex]+6y-7).

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The value of the sinθ is -3/5.

What is the Pythagorean identity?

The Pythagorean trigonometric identity, also known as the Pythagorean identity, is a trigonometric identity that expresses the Pythagorean theorem. It is one of the fundamental relationships between the sine and cosine functions, along with the sum-of-angles formulae.

We have,

cosθ = 4/5

sin θ = ?

We'll use the definition of cos to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

[tex]cos\theta = \frac{Adjacent}{hypotenuse} = \frac{4}{5}[/tex]

We know the hypotenuse and adjacent sides and we'll use the Pythagorean theorem to find the remaining side(opposite side).

opposite = √hypotenuse² − Adjacent²

opposite = √(5)² − (4)²

opposite = √25 - 16

opposite = √9

opposite = 3

[tex]sin\theta = \frac{opposite}{hypotenuse}[/tex]

sin θ = 3/5

In the fourth quadrant, the sine and tangent ratios are negative and the cosine ratio is positive.

Hence, the value of the sinθ is -3/5.

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Step-by-step explanation:

perimeter:

74 + 74 + 48 = 196 yd

area:

48/2=24

√74^2+√24^2 = 77.79 (2dp)

77.79 x 48 = 3734.14

3734.14/2=1867.07yd^2

The equation of the line in Slope-Intercept Form is y = 1/3x - 6

Given,

A line passes through the points (−6,−8) and (−3,−7).

To find the equation of the line in Slope-Intercept Form

Now, According to the question:

Write the slope formula :

[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Substitute x1 = -6 , x2 = -3 and y1 = -8 , y2 = -7 into above slope formula:

Calculate;

[tex]m = \frac{-7-(-8)}{-3-(-6)}[/tex]

Determine the sign :

m = (-7+8)/ (-3+6)

m = 1/3

Substitute m = 1/3 , x = -6 and y = -8 into y = mx + b

Calculate:

-8 = 1/3 x (-6) + b

Reduce the expression:

-8 = -2 + b

-b = 6

b = -6

Again , Substitute

y = 1/3x - 6

m = 1/3  into y = mx +b:

y = 1/3x - 6

Hence, The equation of the line in Slope-Intercept Form is y = 1/3x - 6

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The vertex of your parabola lies at those two coordinates .The axis of symmetry, x is 1, was already discovered.

To locate a parabola's vertex, you must first determine x (or y, if your parabola is sideways) using the axis of symmetry formula. The quadratic equation will then be used to solve for y (or x, if your parabola opens to the side) using that value. The vertex of your parabola lies at those two coordinates.

The axis of symmetry is shown as a line, hence x=1. Since it is the highest or lowest point of the parabola, the vertex of a quadratic equation also serves as its maximum and minimum. We need to do a few things in order to locate the vertex: The axis of symmetry, x=1, was already discovered.

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Equation of the line 'm' is 5x - 6y - 30 = 0.

According to graph,

A(6,0) and B(0,-5) lies on the line m.

Slope-intercept form -> y = mx + c

Putting B(0,-5) in slope-intercept form,

-5 = m(0) + c

 c = -5

Putting A(6,0) in slope-intercept form,

  0 = m(6) - 5

6m = 5

 m = 5/6

Putting the values of m and c in slope-intercept form,

 y = (5/6)x - 5

6y = 5x - 30

5x - 6y - 30 = 0

Hence, equation of the line is 5x - 6y - 30 = 0.

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Ax^2 +Bx + C

x^2 +11x +24

Using the number in place of C gives us what values could be inside the brackets.

For 24 the multiples are

1 and 24

2 and 12

3 and 8

4 and 6

We want the one that can add or subtract to give the number in place of B, which is 11.

The only multiples that add to 11 are 3 and 8

Therefore we know that 8 and 3 need to be in the brackets.

Giving us (x+8)(x+3)

Answer:

Domain: all real numbers >= 4

Range: all real numbers >= 3

The ounces of milk chocolate that the shop sells is 1/27 ounces.

A fraction is a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the chocolate shop sold 1/6 ounces of white chocolate and it sold 2/9 times as much milk chocolate as white chocolate.

The milk chocolate sold will be:

= 1/6 × 2/9

= 2/54.

= 1/27

The ounces is 1/27 ounces.

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Answer:

125

Step-by-step explanation:

150/30=5

25x5=25

Tom saved 14.55% money in this sale.

Given that the sale price of 3 T shirts is $14.50.

And Tom saved in this sale $2.47.

So original selling price of that 3 T shirts is = 14.50+2.47 = 16.97

So the percentage of savings = (2.47/16.97)*100% = 14.55% (approximately)

Hence he saved approximately 14.55% in this sale.

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The probability that she has to pick 5 batteries in order to find one that works is 5/12.

What is probability?

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No of out comes=5

No. of total possible outcome=12

Therefore probability P= 5/12

                                   P=5/12

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Answer:

y=1/4x+4

Step-by-step explanation:

because the slope is 1/4

so k=1/4

y=1/4x+b

put the point into the equation

so

6=1/4*8+b

so

b=4

By using the concept of slope, it is obtained that

Slope of the required trend line is [tex]\frac{22}{9}[/tex]

What is slope of a line?

Slope of the line is the tangent of the angle that the line makes with the positive direction of x axis

If the angle is [tex]\theta[/tex], the slope of the line is given by

[tex]m = tan\theta[/tex]

If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex]), then the slope of the line is given by

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

The line passes through (1, 3) and (10, 25)

[tex]x_1 = 1, y_1 = 3, x_2 = 10, y_2 = 25[/tex]

Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}\\[/tex]

         =  [tex]\frac{25 - 3}{10 - 1}[/tex]

         = [tex]\frac{22}{9}[/tex]

Slope of the required trend line is [tex]\frac{22}{9}[/tex]

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The constant rate of change of the altitude of the Hawk is -10 ft/s. The meaning of the -10 ft/s rate of change in altitude is the hawk is diving vertically down towards the prey with a speed of 10 feet per second

The average rate of change of a function is the rate at which the output values of the function changes with regards to the change in the argument of the function.

A function that has a constant rate of change is a linear function.

The rate of change of a linear function or equation that gives a straight-line graph is found from the slope, m, of the function.

The formula for the slope of a function, using the points (x₁, y₁), and (x₂, y₂), is presented as follows;

[tex]Slope, \, m = \dfrac{y_2-y_1}{x_2- x_1}[/tex]

The points on the graph are; (x₁, y₁) = (3, 60) and (x₂, y₂) = (6, 30)

Which gives;

[tex]Slope, \, m = \dfrac{30\, ft-60 \, ft}{6\, s- 3\, s} = -10 \, ft/s[/tex]

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Answer:

the answer is 3,6 6,0 2,3 4,2 that is the answer :)

Step-by-step explanation:

becuase that is the answer

The statement 'the expected value of a random variable must equal one of the values that the random variable can have.' is False

In this question, we have been given a statement.

We need to state whether given statement is true or false.

Given statement : the expected value of a random variable must equal one of the values that the random variable can have.

We know that the expected value of a random variable is the mean of all possible values of the variable.

It is denoted by E(x).

E(x) can not be one of the values that the random variable have, because it is a average of all values of random variable.

Therefore, the statement 'the expected value of a random variable must equal one of the values that the random variable can have.' is False

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Answer:

1,105

Step-by-step explanation:

since the first digit is 1/5 them the last digit it can only be 1 because if it was 2 then the last digit will be 10 which isn’t possible

So we know the last digit is 5 so we multiply by 2 to get the second and third digit of 10

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60 percent of the sandwiches were not pastrami with work showing.

What do you mean by percentage?

percentage, a comparative figure denoting one-hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified, percentage.

The total number of sandwiches sold by the deli owner is 90

total number of pastrami is 36.

total number of pastrami is 54.

so, the percentage of sandwiches sold that were NOT pastrami is,(54/90)×100

Hence, 60 percent pastrami with work showing.

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A department needs to choose six members consists of 3 women and 3 men from 10 men and 15 women. The number of ways it can be selected is 54,600.

If r persons need to be selected from total n members and the order does not matter, the number of ways it can be selected is calculated using the combination formula:

  ⁿCr = n! / [(n-r)! r!]

Data from the problem:

Total man = 10

Man to be chosen = 3

Total woman = 15

Woman to be chosen = 3

Hence,

The number of ways men can be selected =   ¹⁰C₃ = 10! /(3! 7!)

                                                                       = 120

The number of ways women can be selected =   ¹⁵C₃ = 15! /(3! 12!)

                                                                       = 455

The number of ways men and women selected:

= ¹⁰C₃ x  ¹⁵C₃

= 120 x 455 = 54,600 ways

Hence, the  number of ways the members can be selected =  54,600 ways.

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Answer: 3x-3

Step-by-step explanation: