A one story house is 2,200 square feet. 40% of the house has a basement. How many square feet is the basement?

The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

\(y = 20000(0.95)^5\)

Calculating the expression, we find:

\(y ≈ 20000(0.774)\)

Simplifying further, we get:

\(y ≈ 15480\)

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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The equation of the circle with center (-4, 4) and passing through (-2, 4) is \((x + 4)^2 + (y - 4)^2 = 4.\)

We have,

To determine the equation of a circle, we need the center coordinates and the radius. The center coordinates are given as (-4, 4), and we have a point on the circle as (-2, 4).

The distance between the center (-4, 4) and the point on the circle (-2, 4) represents the radius of the circle.

Using the distance formula.

\(radius = √[(x_2 - x_1)^2 + (y_2 - y_1)^2]\\= \sqrt{(-2 - (-4))^2 + (4 - 4)^2}\\= \sqrt{2^2 + 0^2}\\= \sqrt{4}\\= 2\)

Now that we have the center coordinates (-4, 4) and the radius 2, we can write the equation of the circle in standard form:

\((x - h)^2 + (y - k)^2 = r^2\)

Substituting the values:

\((x - (-4))^2 + (y - 4)^2 = 2^2\\(x + 4)^2 + (y - 4)^2 = 4\)

Therefore,

The equation of the circle with center (-4, 4) and passing through (-2, 4) is \((x + 4)^2 + (y - 4)^2 = 4.\)

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Answer:

It is important, because it will determine that size of the house, the amount of equipment needed, shape, design,etc.

Step-by-step explanation:

Answer:5

Step-by-step explanation:

5098

The value of \(7^x = 77\) is C. x = 0.45 obtained by taking log of vase 7 on both sides.

The logarithm is exponentiation's opposite function in mathematics.

This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.

Given, an expression \(7^x = 77\).

Now, \(log_77^x = log_7(77)\).

We have taken log of base 7 on both sides to cancel out log base 7 of 7 to get x explicitly.

\(x = log_777\).

x = 0.4479 Or x = 0.45.

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Answer:

88.889% are right handed, 11.111% are left handed, ~320 people are right handed in a class of 360, ~40 people are right handed.

Step-by-step explanation:

The fraction 8/9 is equal to .88889, or 88.889%

Likewise, the fraction 1/9  (remainder) is equal to .11111, or 11.111%

By multiplying 360 by these fractions to get the number of people who fit these criteria in the sample, you get:

360*8/9 = 320 people right handed.

360*1/9 = 40 people left handed.

Cheers!

For every 1 orange in the fruit bowl there are three bananas.

According to the question,

We have the following information:

In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.

Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:

4 oranges = 12 bananas

Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.

So, we have the following expression:

1 orange = 12/4 bananas

1 orange = 3 bananas

Hence, for every 1 orange in the fruit bowl there are three bananas.

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Answer:

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

Let the radius be r.

Use circumference formula and find the value of r:

Find the area using the circle area formula:

The matching choice is (B).

Answer:

Step-by-step explanation:

a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

\(PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }\)

putting the given values,

⇒ \(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

\(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

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Answer:

Step-by-step explanation:

Answer:

  11

Step-by-step explanation:

The first 12 terms of the sequence are ...

  1 1 2 3  5 8 13 21  34 55 89 144

The first term that is greater than 60 is the 11th term, 89.

  n = 11

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

Answer:

17 - a

Step-by-step explanation:

1. Open parentheses: 25 - 2 x 4-a

2. Follow the Order of Operations to simplify:

-PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction):

- 25-2 x 4 - a

- 25 - 8 - a

- 17 - a

The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

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Dimension of smaller garden :

l = 1/2 ft.

b = 2/3 ft.

Dimension of bigger garden :

L = 4 ft.

Let , breadth be x ft.

We know , area is given by :

Area = L×B.

Area of small garden = \(\dfrac{1}{2}\times\dfrac{2}{3}=\dfrac{1}{3}\ ft^2\)

Area of big garden \(=4\times x=4x\ ft^2\)

Hence, this is the required solution.

Answer:1>-2

1>-2

Step-by-step explanation:

Answer:

1 > -2

Step-by-step explanation:

2/2 = 1

-4/2 = -2

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

There are 48 + 4 = 52 Democrats

Step-by-step explanation:

Let the number of Republicans be

x

.

There are

x

+

4

Democrats.

Thus,

x

+

(

x

+

4

)

=

100

⇒

2

x

=

100

−

4

⇒

x

=

96

2

=

48

There are 48 + 4 = 52 Democrats..

Answer:

there were 43 people in republicans and 57 democrats

Step-by-step explanation:

100-14=86

86/2=

43

43+14=57

Answer:

\(y = x - 10\)

Step-by-step explanation:

Given

Input : x

Rule: Subtract 10 from input

Output: y

Required

Determine the output

The rule implies that: when 10 is subtracted from x, it gives y.

This is represented as:

\(y = x - 10\)

Answer:

Rounding to the nearest foot, the distance from point A to point B is 719 feet.

Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

Answer:48 counters

Step-by-step explanation:8x3=2, 3x8=24, 24+24+48

Answer:

60-24.80=35.20

35.20/2.20=16

16ccf

Step-by-step explanation:

Answer:

3 dollars and 9 cents.

Step-by-step explanation:

From the question given above, the following data were obtained:

Total amount = 20 dollars

Amount for gift A = 9 7/10 dollars

Amount for gift B = 6 2/5 dollars

Amount for gift C =?

The amount of money she has left for gift C can be obtained as follow:

A + B + C = 20

9 7/10 + 6 2/5 + C = 20

Change to improper fraction

97/10 + 32/5 + C = 20

(97 + 64)/10 + C = 20

161/10 + C = 20

Collect like terms

C = 20 – 161/10

C = (200 – 161)/10

C = 39/10

Change to mixed fraction

C = 3 9/10 dollars

C = 3.9

C = 3 dollars and 9 cents

Therefore, Kathy had 3 dollars and 9 cent for gift C

Answer:

they are the same.

Step-by-step explanation:

Answer:

they are equal

Step-by-step explanation:

3/4 is the same thing as 0.75

for blank 1 the answer is "slope" and for blank 2 the answer is y-intercept (slope intercept form is y=mx+b, m=slope and b=y-intercept).