Isaac owes $8,100 on his credit card. The bank charges an annual interest rate of 21.9%, compounded monthly. If Isaac wants to pay off his credit card using equal monthly payments over the next 16 months, what would the monthly payment be, to the nearest dollar?

When estimating the cash flows on a given project, firms should include expenses from previous years, such as research & development costs. (True)

When estimating cash flows for a project, it is important to consider all relevant expenses, including those incurred in previous years. Research and development (R&D) costs are often incurred over an extended period before a project reaches the commercialization stage. Including these expenses in the cash flow estimation provides a more accurate picture of the project's financial performance. R&D costs can be significant and have a direct impact on the project's profitability.

By including these expenses, firms can evaluate the true costs and potential returns associated with the project. Additionally, including past expenses helps in assessing the project's historical performance and provides valuable insights for decision-making.

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Answer:

6,295

Step-by-step explanation:

just add them

The zeros of the function G(t) are given by t = -1 + √(20.25g) and t = -1 - √(20.25g).

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

To find the zeros of the function G(t), we need to find the values of t that make G(t) equal to zero. So, we start by setting G(t) to zero and solving for t:

G(t) = 0

(t+1)2 - 20.25g = 0 [substituting G(t) in place of 0]

(t+1)2 = 20.25g [adding 20.25g to both sides]

t+1 = ±√(20.25g) [taking the square root of both sides]

t = -1 ± √(20.25g) [subtracting 1 from both sides]

So, the zeros of the function G(t) are given by t = -1 + √(20.25g) and t = -1 - √(20.25g).

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cos^2(x) - cos^4(x)

sin^2 (x) cos^2 (x) can be written as sin^2 (x) cos^2 (x) = (1-cos^2(x)) cos^2(x)Expanding (1-cos^2(x)) cos^2(x) gives - cos^4(x) + cos^2(x)Therefore, sin^2 (x) cos^2 (x) in expanded form, with no powers, parentheses or products is cos^2(x) - cos^4(x).

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Answer:  7 Courts

Step-by-step explanation: One US gallon equals for US courts, so 1 3/4 x 4 is seven

Answer: 7

Step-by-step explanation:

3/4 as a decimal is .75

The point at which the line passing through the points p(1, 0, 6) and q(3, −1, 3) intersects the plane given by the equation x y − z = 15. is  (2,0,-1/2)

Given that:

Points are:

p(1, 0, 6) and q(3, −1, 3)

Lets recall the equation of line given 2 point:

\(\frac{x - x_1}{X_2 -x_1} = \frac{y -_1}{y_2 -y_1} = \frac{z - z_1}{z_2 -z_1}\)

Here we have (x₁, y₁, z₁ ) = (1,0,6) and  (x₂ , y₂, z₂) = (3,-1,3)  

We have the equation of line as,

   x - 1/ 3-1 = y - 0/ (-1) - 0 = z - 6/3-6

⇒ x−1/2 = y/-1 = z-6/ -3

Point on the line can be written as (2p+1,−p, -3p+6)

Now to find intersection with xy plane we put z=0,

-3p+6 = 0

⇒ p = 2

2p+ 1 = 0

⇒ p = -1/2

Point of intersection after putting p is (2,0,-1/2).

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Answer:

6.5

Step-by-step explanation:

5.5x5.5= 30.25.        30.25 divide 30 and 25 by 5 then you get 6.5

Answer:

96/45

Step-by-step explanation:

56

847748

38303[

The number of vegetable bearing plants are : 0.45x, where x is the total number of plants.

A fraction in mathematics represents a portion or element of the whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.

Let x be the initial plant population.

Now that 1/10 of plants bear fruit, the quantity of fruit-bearing plants is equal to 0.1x.

Plants remaining then equal x - 0.1x = 0.9x.

Once more, because half of the remaining plants give flowers, the number of flower-bearing plants is equal to 0.5(0.9x) = 0.45x.

As a result, the number of plants left is equal to 0.9x - 0.45x = 0.45x.

Given that all remaining plants produce veggies, the number of plants that do so is equal to 0.45.

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Answer:

darkest shaded- 0.8 times 0.7= 0.56

In the middle- 0.8 times 0.3= 0.24 times 0.2 times 0.7= 0.14  0.24 + 0.14= 0.38

Light- 0.2 times 0.3= 0.06

0.38 + 0.06=0.44

0.56 times 0.44= 0.2464

I hope this helped!

Step-by-step explanation:

There are 35% sixth-graders at Kendrick's school who picked the museum.

Percentage is a part of the whole number.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage.

1 %= 1/100.

Given that,

Total number of sixth-graders at Kendrick's school = 56,

Also,

The number of s sixth-graders that picked the museum = 14.

The percentage of the sixth-graders that picked the museum

= (14/56) x 100

= (1/4) x 100

= 25 %

25 percent of the sixth-graders picked the museum.

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A statement which describes a translation that would produce ΔDEF from the pre-image of triangle ΔABC include the following: A. To the right five units, and up two units.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Next, we would determine the translation rule as follows;

ΔABC → ΔDEF = (2 + 5, 1 + 2) = D (7, 3)

ΔABC → ΔDEF = (4 + 5, 4 + 2) = E (9, 6)

ΔABC → ΔDEF = (4 + 5, 1 + 2) = F (9, 3)

Therefore, the translation rule is given by this mathematical expression ΔABC → ΔDEF = (x + 5, y + 2). This ultimately implies that, triangle ABC (ΔABC) was translated by five units to the right and up two units in order to produce triangle DEF (ΔDEF).

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Answer:

true

Step-by-step explanation:

In 1940, John Atanasoff, a physicist from Iowa State University, wanted to solve a 29 x 29 linear system of equations. To solve this system using Gaussian elimination, it would have required approximately 29^3/3 = 24389 arithmetic operations.

In 1940, John Atanasoff developed the Atanasoff-Berry Computer (ABC), which was the first electronic computer. Atanasoff wanted to use the ABC to solve a 29 x 29 linear system of equations.

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Since the production of y must exceed the production of x by at least 100 units, we can write a second inequality:

Looking at the function P, we can see that the coefficient multiplying y is greater than the coefficient multiplying x, therefore increasing y instead of x will have a bigger increase in P.

But from the inequality x + 2y <= 1400, we can see that the "cost" of producing y is two times the "cost" of producing x, that is, for one y produced, we could have produced 2x instead.

The coefficient of y is greater, but it's not more than 2 times greater, therefore it's better to produce x than y.

Since y needs to be at least 100 more than x, let's choose the minimum amount of y to satisfy the inequalities:

Therefore the values of x and y that give the maximum profit are x = 400 and y = 500.

Graphing the two inequalities, we have:

The feasible region is the intersection region (between red and blue).

The vertices are:

(0, 100), (400, 500), (0, 700).

Calculating the maximum profit (with vertex (400, 500)), we have:

Therefore the production that yields the maximum profit is x = 400 and y = 500, and the maximum profit is P = 15700.

The set of numbers { 9, 12, 14 } could represent the three sides of a right triangle.

In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be expressed as c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

By checking the given sets of numbers, we can calculate the squares of the numbers and see if they satisfy the Pythagorean theorem. For the set { 9, 12, 14 }, we have 9^2 + 12^2 = 81 + 144 = 225, and 14^2 = 196. Since 225 = 196, the set { 9, 12, 14 } satisfies the Pythagorean theorem and can represent the three sides of a right triangle.

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Answer:

70%

Explanation:

The probability can be calculated as the number of free throws that Dylan makes divided by the total number of free throws.

So, if Dylan makes 7 out of 10 free throws, the probability can be calculated as:

Then, to know the probability as a percent, we need to multiply 0.7 by 100% to get:

P = 0.7 x 100% = 70%

Therefore, the answer is 70%

Answer:

The question isn't clear but i try to do for 7-(-1) solution only. 7-(-1) =8 mean that 7+1=8

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

C) x=y

hope it helps.

Solving the algebraic equations given, the missing numbers in the boxes can be known as shown in the steps below.

Given the equation, ⅔(x - 1) = ⅕(2x - 3) + 1

First, apply the distribution property to open the bracket.

Thus:

⅔x - ⅔ = ⅖x - ⅗ + 1

⅔x - ⅔ = ⅖x + ⅖

⅔x - ⅖x - ⅔ = ⅖

4/15x - ⅔ = ⅖

4/15x = ⅖ + ⅔

4/15x = 16/15

x = 16/15 × 15/4

x = 4

Given the equation, 3c - 3 + 2(3c + 1) = - (3c + 1)

3c - 3 + 6c + 2 = -3c - 1

9c - 1 = -3c - 1

9c + 3c - 1 = -1

12c - 1 = -1

12c = -1 + 1

12c = 0

c = 0

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Answer: Linear Function: y = -10x + 15    Exponential Function:  

y = 15(1/3)(to the power of x)

Step-by-step explanation:

Linear Function:

First we need to find the slope by using the slope equation: (y2 - y1)/(x2 - x1)

In which, it should be (5 - 15)/(1 - 0)

So, we know that the slope is -10, and we already know that the y-intercept is 15, so, we are going to plug it in to the slope-intercept formula, which is

y = mx + b,

In which, it would become y = -10x + 15

Exponential Function =

The exponential function is y = ab(to the power of x)

Let's list out the points onto the equation, 15 = ab(0) and 5 = ab(1)

Know let's solve for each variable.

1. 15 = ab(0)

2. 15/b(0) = a

3. 15 = a

Know we know that a is 15, we can solve for b.

1. 5 = (15)b(1)

2. 5/15 = b(1)

3. 1/3 = b

Know we know that b is equal to 1/3, let's plug it into the equation.

y = 15(1/3)(to the power of x)

The value of the probability density function (pdf) at 0 for a uniform random variable between 5 and 15 is 0, because the pdf for a uniform distribution is constant between its minimum and maximum values, and is 0 elsewhere.

To explain further, a uniform distribution is a continuous probability distribution where every value within a certain range has an equal chance of being selected. In this case, the range is between 5 and 15. The pdf for a uniform distribution is constant within the range of the distribution and is 0 outside of it.

Since 0 is not within the range of the uniform distribution, the pdf at 0 is 0. This means that the probability of selecting a value of 0 from this uniform distribution is 0. The area under the pdf curve between 5 and 15 is equal to 1, which means that the probability of selecting a value within this range is 1.

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Here, x value of 8 would be located on the left tail of the normal distribution curve, 3.67 standard deviations below the mean (μ=22.3) and with a very low value in terms of percentile or probability (0.015%).

To indicate where the given x value of 8 would be on the curve, we need to plot it on a normal distribution curve with a mean (μ) of 22.3 and a standard deviation (σ) of 3.9.
First, we need to convert the given x value of 8 into a z-score by using the formula:  z = (x - μ) / σ
Plugging in the values, we get: z = (8 - 22.3) / 3.9 = -3.67
This means that the value of 8 is located 3.67 standard deviations below the mean.
Next, we need to find this point on the normal distribution curve. We can use a z-score table or a graphing calculator to find the corresponding area under the curve.
If we use a z-score table, we can look up the area to the left of -3.67, which is 0.00015. This means that only 0.015% of the data falls below this point.
To plot this on the curve, we can locate the mean (μ) and mark it as the center of the curve. Then, we can count 3.67 standard deviations to the left of the mean and mark this as the point where the value of 8 would be located.

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Answer:

x=-2/3,2

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

2 (3x - 2) - 4x + 1 = 9

Distribute the 2 to 3x and -2

6x - 4 - 4x + 1 = 9

Combine like terms

2x - 3 = 9

Add three to both sides

2x = 12

Divide by 2

x = 6

Answer:

y=f(x)-6 is a vertical translation down by 6 units so draw the same graph but 6 units down with the point at which it crosses the y-axis as (0,-4)