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Constance is planning to pay for part of her college using a $12,000 student loan. She is comparing the total costs of two loan options. Option A is to borrow the $12,000 for 5 years at 4.75% annual compound interest. Option B is to borrow the $12,000 for 4 years at 5% annual compound interest. Which of the following is closest to the difference in total cost of Option A compared to Option B?

A. $450.00
B. 867.72
C. $529.87
D. $547.84

Answer:

y = 24x

Step-by-step explanation:

In a direct variation, we have

output = k * input, with k being a positive number.

Therefore, with the output being the number of water bottles and the input being the number of cases, we have y = kx. We know that the output is y and the input is x because the question states that the number of water bottles (y) is directly proportional to the number of cases (x), so x must be multiplied by something to obtain y.

We have 120 water bottles as one output and 5 cases as its corresponding input.

120 = k(5)

divide both sides by 5 to isolate k

k = 24

y = 24x

Answer:

38.0067567568 hours

Step-by-step explanation:

x = +7 or -7

a = +3 or -3

x = +19 or -5

n = -5 or -7

p = +4 or -2

x = +11 or +1

a = -11 or -7

k = +16 or 0

m = -1 or 0

r = +6 or +1    

: Answer:

Step-by-step explanation:

|3a|=9

a=3

2- |x–7|=12

For the Negative case we'll use -(x-7)  

For the Positive case we'll use (x-7)  

Solve the Negative Case

     -(x-7) = 12  

 Multiply

     -x+7 = 12  

    rearrange and Add up

     -x = 5  

    Multiply both sides by (-1)

     x = -5  (for negative)

Solve the Positive Case

     (x-7) = 12  

     x = 19  

 Which is the solution for the Positive Case

Wrap up the solution

x=-5             ,x=19

 4- |n+6|=1

The Absolute Value term is |n+6|

 For the Negative case we'll use -(n+6)  

For the Positive case we'll use (n+6)  

Solve the Negative Case

     -(n+6) = 1  

    Multiply

   -n-6 = 1  

  -n = 7  

  Multiply both sides by (-1)

     n = -7  

  Which is the solution for the Negative Case

Solve the Positive Case

     (n+6) = 1  

     n = -5  

Which is the solution for the Positive Case

Wrap up the solution

n=-7

n=-5

5-   |1–p|=3

The Absolute Value term is |-p+1|

 For the Negative case we'll use -(-p+1)  

For the Positive case we'll use (-p+1)  

Solve the Negative Case

     -(-p+1) = 3  

  Multiply

   p-1 = 3  

   Rearrange and Add up

     p = 4  

Solve the Positive Case

     (-p+1) = 3

Rearrange and Add up

   -p = 2  

 Multiply both sides by (-1)

p = -2

Which is the solution for the Positive Case

Wrap up the solution

p=4                             , p=-2

6 - |6–x|=5    

The Absolute Value term is |-x+6|

For the Negative case we'll use -(-x+6)  

For the Positive case we'll use (-x+6)  

Solve the Negative Case

   -(-x+6) = 5  

  Multiply

   x-6 = 5

 Rearrange and Add up

     x = 11  

Solve the Positive Case

     (-x+6) = 5  

 Rearrange and Add up

     -x = -1

  Multiply both sides by (-1)

  x = 1  

   Which is the solution for the Positive Case

Wrap up the solution

x=11              ,   x=1

7-

The Absolute Value term is |a+9|

 For the Negative case we'll use -(a+9)  

For the Positive case we'll use (a+9)  

Solve the Negative Case

     -(a+9) = 2  

  Multiply

     -a-9 = 2  

    Rearrange and Add up

     -a = 11  

  Multiply both sides by (-1)

   a = -11  

   Which is the solution for the Negative Case

Solve the Positive Case

     (a+9) = 2  

    Rearrange and Add up      a = -7  

 Which is the solution for the Positive Case

Wrap up the solution

a=-11    a=-7

8-  |k–8|=8

The Absolute Value term is |k-8|

For the Negative case we'll use -(k-8)  

For the Positive case we'll use (k-8)  

Solve the Negative Case

     -(k-8) = 8  

    Multiply

     -k+8 = 8  

    Rearrange and Add up

     -k = 0  

    Multiply both sides by (-1)

   k = 0  

  Which is the solution for the Negative Case

Solve the Positive Case

     (k-8) = 8  

  Rearrange and Add up

     k = 16  

    Which is the solution for the Positive Case

Wrap up the solution

k=0  k=16

Solutions on the Number Line

Two solutions were found :

k=16

k=0

9-|2m+1|=1

The Absolute Value term is |2m+1|  

For the Negative case we'll use -(2m+1)  

For the Positive case we'll use (2m+1)  

Solve the Negative Case

     -(2m+1) = 1  

    Multiply

     -2m-1 = 1  

Rearrange and Add up

     -2m = 2  

    Divide both sides by 2

     -m = 1  

    Multiply both sides by (-1)

     m = -1  

    Which is the solution for the Negative Case

Solve the Positive Case

     (2m+1) = 1  

Rearrange and Add up

  2m = 0  

  Divide both sides by 2

   m = 0  

 Which is the solution for the Positive Case

Wrap up the solution

m=-1

m=0

Solutions on the Number Line

Two solutions were found :

m=0

m=-1

9- |7–2r|=5

The Absolute Value term is |-2r+7|

For the Negative case we'll use -(-2r+7)  

Solve the Negative Case

     -(-2r+7) = 5  

    Multiply

     2r-7 = 5  

    Rearrange and Add up

     2r = 12  

    Divide both sides by 2

     r = 6  

Solve the Positive Case

     (-2r+7) = 5  

   Rearrange and Add up

   -2r = -2  

  Divide both sides by 2

   -r = -1  

 Multiply both sides by (-1)

   r = 1  

  Which is the solution for the Positive Case

Wrap up the solution

r=6

r=1

Answer:  5.22 seconds

Step-by-step explanation:

t represents time and y represents the height.

Since we want to know when the ball hits the ground, find t when y = 0

Ball 1 starts at a height of 109 --> h = 109

0 = -16t² + 109

16t² = 109

   \(t^2=\dfrac{109}{16}\\\)

   \(t=\sqrt{\dfrac{109}{16}}\)

   \(t=\dfrac{\sqrt{109}}{2}\)

   t = 5.22

=> H = 109

=> 0 = -16t² + 109

=> 16t² = 109

=> t² = 109/16

=> t = 109/2

=> t = 5.22 sec

Therefore, 5.22 second is the answer.

Select all expressions that are equivalent to (2n + 6)(n + 3)

we have

(2n + 6)(n + 3)

apply distributive property

2n^2+6n+6n+18

2n^2+12n+18

Verify each option

option A

2(n^2 + 6n +9)=2n^2+12n+18 -------> is ok

option B

is not correct

option C

is correct

option D

is not correct

option E

2(n + 3)(n + 3)= (2n + 6)(n + 3) ------> is correct

option F

2(n + 3)^2=2(n^2+6n+9)=2n^2+12n+18 -----> is ok

therefore

You have this ordered pair:

You can identify that its coordinates are:

Given the first equation:

Substitute the value of "x" and the value of "y" into the equation and then evaluate (If the ordered pair is a solution of the System of linear equations, the value on the right side of the equation and the value on the left side must be equal):

Apply the same procedure in the second equation. Then:

The answer is: The ordered pair is the solution of the System of linear equations.

Answer:

1.-Then we p-value indicates that we are in the rejection region we reject H₀

We support the claim of the garbage collector the average picking up more than 4 tn of garbage

2.- p  = 75 %

3.-3.-t(s) is in the rejection region we accept H₀ we have not evidence to support Marc´s claim

Step-by-step explanation:

1.- If p-value is 0,04   and significance level α = 5 %  or  α = 0,05 then p-value < α

Test hypothesis should be    ( x the average of garbage)      

Null hypothesis          H₀           x = 4 Tn

Alternative Hypothesis     Hₐ    x  > 4 Tn

Then  alternative hypothesis suggests a one tail-test to the right  and

p-value <  0,05

Then we p-value indicates that we are in the rejection region we reject H₀

We support the claim of the garbage collector the average picking up more than 4 tn of garbage

2.- As we are dealing with a normal distribution the CI  95 % is symmetrical with respect to the mean, therefore the proportion of student living in Brooklyn is:  

(0,73 + 0,77) /2

p = 0,75     p  = 75 %

Test hypothesis:

Null Hypothesis            H₀            μ    =  26

Alternative Hypothesis      Hₐ      μ   <  26

Alternative hypothesis tells us the test is a one-tail test to the left

Sample size   n = 25

Sample mean   μ  =  24,4

Sample Standard deviation  =  9,2

We assume normal distribution, and as n < 30 we use t-student table

with  24 degree of freedom

Significance level is 0,05  and df = 24  we find t (c)  in t- student table

t(c) = 1,7109      test to the left   t(c) = -1,7109

To calculate  t(s)

t(s)  =  (  24,4 - 26 ) / 9,2 / √25

t(s) =  - 1,6 * 5 / 9,2

t(s) = - 0,87

Comparing t(s)  and t(c) we have

t(s) > t(c)

t(s) is in the rejection region we accept H₀ we have not evidence to support Marc´s claim

The Sum S of the infinite series is 5/4.

A series of terms is referred to as a geometric progression if each next term is produced by multiplying each previous term by a fixed amount. (GP), whereas the common ratio is the name given to the constant value.

Given:

1, 1/5, 1/25, 1/125

now, let s= 1+ 1/5+ 1/25+ 1/125+ ....

Then, Divide by 5 both side

s/5 = 1/5 + 1/25 + 1/125+ 1/625

Now, add 1 on both side

1+ s/5 = 1 +1/5 + 1/25 + 1/125+ 1/625..

1+ s/5 = s

s - s/5 = 1

4s/5 = 1

s= 5/4

Hence, the Sum S of the infinite series is 5/4.

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Answer:

Most of the mens shoes in the data sets cost more than the womens shoes

Step-by-step explanation:

i did this and got it correct

Answer:

6.729

Step-by-step explanation:

Integers only include plsitive and negative numbers and zero. 6.729 is a number alright but it is a fractional or decimal number.

Answer:

X-intercept: \((\frac{14}{3}, 0)\).

Y-intercept: (0, 7) ⇒ Option B.

Step-by-step explanation:

I'm not certain whether the question asks for either the x-intercept or the y-intercept, but I will provide the answers for both since none of the given options matches the coordinates of the x-intercept.  

The x-intercept is the point on the graph where it crosses the x-axis, with coordinates of (a, 0).  The x-intercept is the value of x when y = 0.

Given the linear equation in standard form, 3x + 2y = 14, set y = 0 to solve for the x-intercept:

3x + 2y = 14

3x + 2(0) = 14

3x + 0 = 14

3x = 14

Divide both sides by 3 to solve for x:

\(\frac{3x}{3} = \frac{14}{3}\)

\(x = \frac{14}{3}\)

Therefore, the x-intercept is \((\frac{14}{3}, 0)\).   None of the given option matches the value of the x-intercept.

The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). It is the value of y when x = 0.

Set x = 0, and substitute into the given equation.

3x + 2y = 14

3(0) + 2y = 14

0 + 2y = 14

2y = 14

Divide both sides by 2 to solve for y:

\(\frac{2y}{2} = \frac{14}{2}\)

y = 7

Therefore, the y-intercept is (0, 7), which matches Option B.

Cara's first error was not 7 - 13, leading to an incorrect result of -32.

Cara's first error was that she did not evaluate (Negative 4) squared.

The expression in question is not provided, so let's assume it is "6 - 2 × (-4)² + 7 - 13".

According to the order of operations (PEMDAS/BODMAS), we evaluate operations inside parentheses first, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

To evaluate the expression correctly, we follow the order of operations:

Evaluate the exponent (-4)².

Since (-4) squared is positive, (-4)² = 16.

Multiply 2 and 16.

2 × 16 = 32.

Evaluate the addition and subtraction from left to right.

6 - 32 + 7 - 13.

At this point, we see that Cara did not evaluate 7 - 13.

Therefore, her first error was not evaluating the subtraction correctly.

Continuing the evaluation:

6 - 32 + 7 - 13 = -32.

So, Cara's first error was not evaluating 7 - 13, leading to an incorrect result of -32.

It's important to carefully follow the order of operations to ensure accurate evaluations of mathematical expressions.

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The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.

The correct answer choice is option D.

Cost of 16-pound bag of Kitty Kibbles = $20.80

Unit price of kitty kibbles = Price / number of pounds

= $20.80 / 16

= $1.30 per pound.

Cost of 8-pound bag of Feline flavor = $11.20

Unit price of feline flavor = Price / number of pounds

= $11.20 / 8

= $1.40 per pound

Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.

Complete question:

A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?

A. Feline Flavor has a lower unit price of $1.40/pound.

B. Feline Flavor has a lower unit price of $1.30/pound.

C. Kitty Kibbles has a lower unit price of $1.40/pound.

D. Kitty Kibbles has a lower unit price of $1.30/pound.

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Answer:

27/6, 4 3/6, or simplified version 4 1/2

Step-by-step explanation:

Always convert the mixed numbers into an improper fraction before you solve, this makes it easier to solve.

2 4/6 = 16/6

1 5/6 = 11/6

3 4/6 = 22/6

Now we solve. Remember, you do NOT add the denominator, leave it as 6 not 12. You only add the numerator.

16/6 + 11/6 = 27/6, 4 3/6 or simplified as 4 1/2

22/6 + 5/6 = The same as above.

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is  nλe^(-nλx)

Given fx (x) = λe^λx

Fx (x) = 1 – e^-λx      x…0

To find distribution of Min (X1,….Xn)

By applying the equation

fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)

For minimum j = 1

[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx

= ne^[(n-1) λx] λe^(λx)

= nλe^(-λx[1+n-1])

= nλe^(-nλx)

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Answer:

Step-by-step explanation:

h(t)=-5t²+10t+80=-5(t²-2t+1-1)+80

=-5(t²+2t+1)+5+80

=-5(t-1)²+85

maximum height reached=85 ft

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer: 150 percent.

Step-by-step explanation:

The problem asks for the percent increase in the annual student fees from 2000 to 2014.

First, we need to know how to find a percent increase.

The percentage change formula is

(Increase in amount) / (Original amount) * 100

Using this formula, we can solve this problem.

Since the fee in 2000 was $6000 and the fee in 2014 was $15000, we can find the increase in fees.

Increase in fees = 15000-6000 == 9000

Next, let's use the formula to find the answer.

Percentage Increase = (Increase in fees) / (Original amount) * 100

= 9000 / 6000 * 100

= 150

Therefore, the answer is 150 percent.

The fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

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Answer: 160

Step-by-step explanation:

I divided 144/9 to see how many students are their per 10% of the 90% of students and got the answer 16. I then added 16 as the other missing 10% to 144 and got the answer 160.

The rate at which her daily revenue is currently changing and the direction of the change is; Her revenue is currently increasing at $12 per day

The rate of change of a function is the rate at which the output of the function changes per unit change in the input of the function.

Let x represent the number of days, therefore;

The number of T-shirts Dorothy sells, y = 40 - 4·x

The price at which she sells the T-shirts = 7 + x

Therefore, Dorothy's daily revenue, R(x) = (40 - 4·x) × (7 + x) = 12·x - 4·x² + 280

The rate of change of her daily revenue can be obtained from the derivative of the revenue function as follows;

The rate at which her daily revenue is therefore;

R'(x) = d(R(x))/dx = 12 - 8·x

The rate at which her revenue is changing currently can be obtained from the rate function by plugging in x = 0, as follows;

R'(0) = 12 - 8×0 = 12

Her revenue is changing at a rate of $+12 per day.

The positive value of the rate, 12, indicates that her revenue is increasing at $12 per day

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Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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Answer:

x=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Desmos Graphing Calculator

Answer:

x = 0

Step-by-step explanation:

\(\sqrt{x+4}\) = 2 - x ( square both sides to clear the radical )

x + 4 = (2 - x)² ← expand using FOIL

x + 4 = 4 - 4x + x² ( subtract x + 4 from both sides )

0 = x² - 5x ← factor out x from each term

0 = x(x - 5)

equate each factor to zero and solve for x

x = 0

x - 5 = 0 ⇒ x = 5

As a check

substitute these values into the equation and if both sides are equal then they are the solutions

x = 0

left side = \(\sqrt{0+4}\) = \(\sqrt{4}\) = 2

right side = 2 - 0 = 2

then x = 0 is a solution

x = 5

left side = \(\sqrt{5+4}\) = \(\sqrt{9}\) = 3

right side = 2 - 5 = - 3 ≠ 3

then x = 5 is an extraneous solution

Answer: \(x=\Large\boxed{0}\)

Step-by-step explanation:

Given expression

\(\sqrt{x+4} =2-x\)

Square both sides of the equation

\(\sqrt{x+4}^2 =(2-x)^2\)

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

Subtract x on both sides

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

\(4=x^2-5x+4\)

Subtract 4 on both sides

\(4-4=x^2-5x+4-4\)

\(0=x^2-5x\)

Factorize the quadratic expression

\(0=x(x-5)\)

\(x=\Large\boxed{0} \text{ or }x=5~(reject)\text{ }\)

Check the answer

\(\text{When x = 0:}\)

\(\sqrt{(0)+4} =2-(0)\)

\(\sqrt{4}=2\)

\(2=2\)   \(\boxed{TRUE}\)

\(\text{When x = 5:}\)

\(\sqrt{(5)+4} =2-(5)\)

\(\sqrt{9}=-3\)

\(3\neq -3\)  \(\boxed{FALSE}\)

Hope this helps!! :)

Please let me know if you have any questions

Since it is a rectangular window, we can find its area using the following formula:

Let's make a conversion first:

48in = 4ft

24in = 2ft

The list of counting numbers less than or equal to 9, is:

We can write it in set notation with the listing method as:

A descriptional method using set notation is also possible. Let x be a counting number, then this set is given by: