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Answer:

$7400

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year,

then, solving our equation

I = 5000 × 0.04 × 12 = 2400

I = $ 2,400.00

The simple interest accumulated

on a principal of $ 5,000.00

at a rate of 4% per year

for 12 years is $ 2,400.00.

The total amount due on a simple-interest loan if the principal is $5,000 with a rate of 4% for 12 years is $2400 and this can be determined by using the simple interest formula.

Given :

The total amount due on a simple-interest loan if the principal is $5,000 with a rate of 4% for 12 years.

The total amount due on a simple interest loan can be determined by using the simple interest formula which is given by the equation:

\(\rm I = PRT\)

Given that time, T = 12 years

Rate, R = 4% = 0.04

Principal amount, P = $5000

Now, put the value of P, R, and T in the equation (1).

\(\rm I = 5000\times 0.04 \times 12\)

I = $2400

The total amount due on a simple-interest loan if the principal is $5,000 with a rate of 4% for 12 years is $2400.

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The cost of the labor per hour is 115 hours.

The equation is going to be:

4.25x + 167 = 655.75

your x is going to be:115

The duration was 4.25 hours.

The parts cost 167.

Cost in full: 655.75

so the price per hour is x.

As a result, when you write your equation, the total number of hours (multiplied by the cost per hour) will be added to the cost of the parts, and the sum of these two amounts will be your total cost.

In order to solve the problem, you must deduct the cost of each component from the total cost. This should give you the following result: 4.25x = 488.75

After that, divide 4.25 by each side as you normally would.

The cost of labor per hour follows. 115

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Answer:

x = 1, y = 2

Step-by-step explanation:

Multiply 2x - 8y = -14 ​by 5 to get 10x - 40y = -70

Subtract (10x - 40y = -70) - (10x - 9y = -8)

Solve -31y = -62 for y

y = 2

Plug in y value to get x value

x = 1

Answer:

D. 24 ft

Step-by-step explanation:

Congruent means equal. Since ABCD and PQRS are congruent they are the same.

Answer:

D

Step-by-step explanation:

A distribution in which all the values have the same frequency is called a uniform distribution. This type of distribution is characterized by an equal probability of each value occurring within a given range or interval.

In a uniform distribution, the probability density function is a constant value, indicating that all values have the same chance of occurring.
Uniform distributions are often used in statistical analyses and probability theory, particularly in cases where there is no reason to expect one value to occur more frequently than any other. For example, rolling a fair die would result in a uniform distribution, with each of the six possible outcomes having an equal chance of occurring.
Uniform distributions can be visualized using histograms or probability density functions, which display the frequency or likelihood of each value occurring. In practice, many real-world distributions are not perfectly uniform, but they may approximate a uniform distribution in certain circumstances.
Overall, uniform distribution is an important concept in statistics and probability theory, helping to understand the likelihood and frequency of different values occurring within a given data set or range.

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Answer

A little over 16.

Step-by-step explanation:

If you convert 5 liters to milli-liters, you get 5,000. You then divide 5,000 by 300 and get 16.67.

Hope this helps!

Answer:

If you put two things together it cannot be less than what was originally there.

Step-by-step explanation:

For example if you have two bowls of soup and you add them together you will have more soup.

Alec is incorrect because this inequality of model 1 + 2 < 4 i.e. the sum of two numbers is greater than either number.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Alec says the sum of two numbers can never be less than an either number.

Using a model  a + b < c

Substitute the values a = 1, b = 2, and c = 4 in the inequality of model

1 + 2 < 4

So, the sum of two numbers is greater than either number.

Hence, Alec is incorrect.

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Answer:

  [-2, 2/5] ∪ [2, ∞)

Step-by-step explanation:

You want the solution to the inequality 7x³ -20x +11 ≥ 2x³ +2x² +3.

The inequality can be rewritten to a comparison with zero by subtracting the right-side expression.

  7x³ -20x +11 -(2x³ +2x² +3) ≥ 0

  5x³ -2x² -20x +8 ≥ 0 . . . . . . . simplify

  x²(5x -2) -4(5x -2) ≥ 0 . . . . . . factor pairs of terms

  (x² -4)(5x -2) ≥ 0 . . . . . . . . . . remove common factor

  (x -2)(5x -2)(x +2) ≥ 0 . . . . . factor difference of squares

The values of x that make this product equal to zero are

  x -2 = 0   ⇒   x = 2

  5x -2 = 0   ⇒   x = 2/5

  x +2 = 0   ⇒   x = -2

These x-intercepts divide the domain into 4 intervals where we need to check the sign.

From left to right:

(-∞, -2)

  Using x = -3, we find the product to be ...

  (-3 -2)(5(-3) -2)(-3 +2) = (-5)(-17)(-1) = -85, less than 0

[-2, 2/5]

  Using x = 0, we find the product to be ...

  (0 -2)(5·0 -2)(0 +2) = (-2)(-2)(2) = 8, part of the solution

(2/5, 2)

  Using x = 1, we find the product to be ...

  (1 -2)(5·1 -2)(1 +2) = (-1)(3)(3) = -9, less than 0

[2, ∞)

  Using x = 3, we find the product to be ...

  (3 -2)(5·3 -2)(3 +2) = (1)(13)(5) = 65, part of the solution

The solution to the inequality is [-2, 2/5] ∪ [2, ∞).

__

Additional comment

The function we're comparing to zero is a cubic with a positive leading coefficient. That means the general shape of its graph is /, negative on the left and positive on the right.

The graph changes sign at each of the zeros, so we already know the curve is positive between the left two x-intercepts, and to the right of the rightmost x-intercept. We just need to define the intervals so the zeros themselves are included in the solution set.

9514 1404 393

Answer:

  3x -5y = -38

Step-by-step explanation:

The equation of the perpendicular line can be formed by swapping the coefficients of x and y in the given equation, negating one of them. The new constant will be the one that lets the given point satisfy the equation.

  given: 5x +3y = 5

  perpendicular: 3x -5y = constant

At the given point, the constant is ...

  3(-6) -5(4) = -18 -20 = -38

So, the desired equation is ...

  3x -5y = -38

Answer:

First listen to the video on your left of the screen, and then on the right of your screen, you'll see tests. You click on the button below on the test that says practice and if you 3 out of 4 correct, you can do the other videos and tests.

Step-by-step explanation:

The rate of change and the initial values is solved to be 0.15 and 22 respectively

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem of the service charges of a phone company is represented using linear function as as follows

C(t) = 22 +0.15t,

m = rate of change = $0.15

the rate of change is 0.15

the initial value is the y intercept, value of y(c(t)) when x (t) is zero

C(t) = 22 +0.15 * 0

C(t) = 22

the initial value is 22

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Step-by-step explanation:

The table that is highlighted shows the points of the graphed function.

However we wish to find the inverse. We need to swap the values of x and y for each of the points to get the inverse.

Hence the answer is Option C.

Answer:

X=-3/2

Step-by-step explanation:

1/4+1/2+X=-3/4

X=-3/4-1/4-1/2

X=-3/2

To convert a line integral to an ordinary integral with respect to the parameter, we need to parameterize the curve. In this case, the curve is a helix. Let's assume the parameterization of the helix is given by:
x(t) = a * cos(t)
y(t) = a * sin(t)
z(t) = b * t
Here, a represents the radius of the helix, and b represents the vertical distance covered per unit change in t.

To find the ordinary integral, we need to determine the limits of integration for the parameter t. Since the helix does not have any specific limits mentioned in the question, we will assume t ranges from 0 to 2π (one complete revolution).

Now, let's consider the line integral. The line integral of a function F(x, y, z) along the helix can be written as:
∫[c] F(x, y, z) · dr = ∫[0 to 2π] F(x(t), y(t), z(t)) · r'(t) dt
Here, r'(t) represents the derivative of the position vector r(t) = (x(t), y(t), z(t)) with respect to t.

To evaluate the line integral, we need the specific function F(x, y, z) mentioned in the question.
However, if we assume a specific function F(x, y, z), we can substitute the parameterization of the helix and evaluate the line integral using the ordinary integral. Given the answer value of 11, we can solve for the unknowns in the integral using radicals as needed.

In summary, to convert the line integral to an ordinary integral with respect to the parameter and evaluate it, we need to parameterize the curve (helix in this case), determine the limits of integration, and substitute the parameterization into the integral.

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Answer:

9a^4b^4c^2

Step-by-step explanation:

Area of a  square is expressed using the formula

A =L²

L is the side length of the square

Given that;

L = a²b²c

A = 3²(a²b²c)²

A = 9(a²)²(b²)²c²

A = 9a^4b^4c^2

Hence the area of the square is 9a^4b^4c^2

8y - 2y = 24

a)

The x intercept is when y = 0; if we use the equation when y = 0:

8x - 2(0) = 24 ==> 8x = 24 ==> x = 24/8 ==> x = 3

So the fist answer is TRUE

b)

The y intercept is when x = 0; if we use the equation with x = 0:

8(0) - 2y = 24 ==> -2y = 24 ==> y = 24/(-2) ==> y = -12

So the second answer is FALSE

c)

if we take the equation and solve it for y:

8x - 2y = 24 ==> 8x - 24 = 2y ==> (8x - 24)/2 = y ==> 4x - 12 = y ==> y = 4x -12

So the third answer is TRUE

Answer:

15

Step-by-step explanation:

A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much commission will he earn?

($27,990)*(0.03) = $839.70

The Jones family will pay their insurance broker a commission of $1,750.00.

Commission is an amount of money paid to an employee or company as an incentive to sell more. A straight commission is a percentage of sales.

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Answer:

12 units²

Step-by-step explanation:

The height is 2, and the width is 12.

Now multiply and that gives us 24. But that's not the full answer.

Since a triangle's area is half of a square, we divide by 2, leaving us with 12. (plus the label which is units²)

If people prefer a choice with risk to one with uncertainty, they are said to be averse to uncertainty.

Uncertainty and risk are related concepts in decision-making under conditions of incomplete information. However, they represent different types of situations.

- Risk refers to situations where the probabilities of different outcomes are known or can be estimated. In other words, the decision-maker has some level of knowledge about the possible outcomes and their associated probabilities. When people are averse to risk, it means they prefer choices with known probabilities and are willing to take on risks as long as the probabilities are quantifiable.

- Uncertainty, on the other hand, refers to situations where the probabilities of different outcomes are unknown or cannot be estimated. The decision-maker lacks sufficient information to assign probabilities to different outcomes. When people are averse to uncertainty, it means they prefer choices with known risks (where probabilities are quantifiable) rather than choices with unknown or ambiguous probabilities.

In summary, if individuals show a preference for choices with known risks over choices with uncertain or ambiguous probabilities, they are considered averse to uncertainty.

If people prefer a choice with risk to one with uncertainty, they are said to be averse to uncertainty.

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Answer:

E (The product of seven and the difference of b minus two)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

-4y-3<9

-4y<12

y<-3

==> B

Answer:

5

Step-by-step explanation:

Answer:

I got 350

Step-by-step explanation:

It seems like your doing Pemdas right now.

P: Prenthesies ( )

So I did 8 x 30 = 240

then I added 110 and got 350

I hope this helped. in future reference, Look up what pemdas stands for and go through it step by step. Khan academy has a video on it.

Answer:

see explanation

Step-by-step explanation:

(a)

let the number be x then doubling it is 2x and adding 11 is

2x + 11

(b)

the statement is equal to 25 , then

2x + 11 = 25 ( subtract 11 from both sides )

2x = 14 ( divide both sides by 2 )

x = 7

The intercept (B₀ = 13.8) represents the expected years of completed education for male students, and the coefficient for the dummy variable Female (B₁ = -0.008) represents the average difference in years of education between female and male students, where female students, on average, have 0.008 fewer years of education.

The term "intercept" refers to the location where a line or curve crosses a graph's axis. The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.

In regression (1), the estimated coefficients are as follows:

- B₀ (intercept) = 13.8

- B₁ (coefficient for the dummy variable Female) = -0.008

The interpretation of these coefficients in the context of the given regression equation is as follows:

1. Intercept (B₀ = 13.8):

  The intercept represents the expected value of the dependent variable (Education) when all independent variables (including Female) are equal to zero. In this case, it means that the expected years of completed education for a male student (since Female is a dummy variable where 0 represents male) is 13.8 years.

2. Coefficient for the dummy variable Female (B₁ = -0.008):

  The coefficient for Female indicates the expected change in the dependent variable (Education) associated with a one-unit change in the dummy variable Female, while holding all other variables constant. Since Female is a binary variable (0 for male, 1 for female), a one-unit change refers to the difference between a male and a female student.

  The coefficient value of -0.008 indicates that, on average, female students have 0.008 fewer years of completed education compared to male students. However, note that this coefficient is small, and the standard error associated with it is relatively large (0.06), suggesting that the estimate may not be very precise or reliable.

To summarize, the intercept (B₀ = 13.8) represents the expected years of completed education for male students, and the coefficient for the dummy variable Female (B₁ = -0.008) represents the average difference in years of education between female and male students, where female students, on average, have 0.008 fewer years of education.

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Answer: Z<4

Step-by-step explanation:

Rearrange the equation

-3(z-6) - (2z-2)>0

-3z+18-2z+2>0

-5z +20>0

-5(z-4)>0

divide  both side by -5

z-4<0

z<4

It takes 72 minutes for Nikki to paint the room working alone and 90 minutes for Greg to paint the room working alone given that Greg and Nikki takes a total of 40 minutes to paint a room if they work together and if Greg works alone, he takes 18 minutes longer to paint he room than Nikki takes if she works alone. This can be obtained by using suitable algebraic equation and quadratic formula.

Here in the question it is given that,

⇒  \(\frac{1}{time(Greg)} +\frac{1}{time(Nikki)} =\frac{1}{40}\)

⇒  time(Greg) = time(Nikki) + 18 ⇒ time(Greg) = x + 18

    ⇒    \(\frac{1}{x} +\frac{1}{x+18}= \frac{1}{40}\)

By simplifying the equation we get the quadratic equation,

⇒ \(\frac{x+18+x}{x(x+18)} =\frac{1}{40}\)

⇒ 40(2x + 18) = x(x + 18)

⇒ 80x + 720 = x² + 18x

⇒ x² - 62x - 720 = 0

By using quadratic formula we can find the value of x,

a = 1, b = - 62, c = - 720

⇒ b² - 4ac = (- 62)² - 4(1)(-720)

⇒ b² - 4ac = 3844 + 2880

⇒ b² - 4ac = 6724

√b² - 4ac = √6724

√b² - 4ac = 82

\(x = \frac{-b+\sqrt{b^{2}-4ac} }{2a}\) or \(x = \frac{-b-\sqrt{b^{2}-4ac} }{2a}\)

\(x = \frac{62+82}{2}\) or \(x = \frac{62-82}{2}\)

x = 144/2 or x = - 20/2

x = 72 or x = - 10

Since time taken cannot be negative we take the value of x as 72 min.

That is, time(Nikki) = x = 72 min

time(Greg) = x + 18

time(Greg) = 72 + 18

time(Greg) = 90 min

Hence it takes 72 minutes for Nikki to paint the room working alone and 90 minutes for Greg to paint the room working alone given that Greg and Nikki takes a total of 40 minutes to paint a room if they work together.

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Answer:

See photo #11

Step-by-step explanation:

Answer:

b) It is false

Answer:

30.4

Step-by-step explanation:

12(3.2)-8

38.4-8

30.4