Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he
has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.

a. What will the new principal be when he begins making loan payments?

b. How much interest will he pay over the life of the loan?

The solution to the algebraic equation 8x - 8 = 4x is x = 2

Algebra: This is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

8x - 8 = 4x

8x - 4x = 8

4x = 8

x = 8/4

x = 2

Check:

8x - 8 = 4x

substitute x = 2 into the equation

8(2) - 8 = 4(2)

16 - 8 = 8

8 = 8

Other examples of algebraic equation

3x + 5 = 11

substract 5 from both sides

3x = 11 - 5

3x = 6

divide both sides by 3

x = 6/3

x = 2

Therefore, the value of x from the equation is given by 2

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The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.

The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.

constant of proportionality = 2.5

Given  :  y = 2.5x.

To find : What is constant of Proportionality in the equation.

Solution : We have given

y = 2.5x.

On comparing with equation of proportionality : y = kx,

Where,   k is the constant of proportionality.

On comparing y = 2.5 x  by y = kx .

We get  k = 2.5

So, constant of proportionality = 2.5

Therefore, constant of proportionality = 2.5

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The value of constant proportionality is 2.5. The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.

The constant of proportionality is a term that is defined as the rate or the ratio of two proportional values which are known to be at the same value.

constant of proportionality = 2.5

Given  :  y = 2.5x.

To find : What is constant of Proportionality in the equation.

Solution : We have given

y = 2.5x.

On comparing with equation of proportionality : y = kx,

Where,   k is the constant of proportionality.

On comparing y = 2.5 x  by y = kx .

We get  k = 2.5

So, constant of proportionality = 2.5

Therefore, constant of proportionality = 2.5

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Answer:

11

Step-by-step explanation:

Distance formula is square root of (x2-x1)^2+(y2-y1)^2

square root of (6-(-5))^2+(7-7)^2

square root of (11)^2+(0)^2

square root of 121+0

square root of 121

11

distance is 11

The required expression of the reflection of the point is (-x, y).

Given that,
A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4) is to be determined.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
A line segment has endpoints at (–4, –6) and (–6, 4) and an image with endpoints at (4, –6) and (6, 4) is produced the equation of the reflection is given as,
(x, y) ----> (-x, y)

Thus, the required expression of the reflection of the point is (-x, y).

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3[tex]x^{2}[/tex]+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3*[tex]3^2[/tex] + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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Answer:

5

Step-by-step explanation:

The only way I know how to go about this is to multiply 2 until it becomes 32

2x2=4

4x2=8

8x2=16

16x2=32

Now just count how many 2 I used and I used 5 so the missing exponent is 5

Hopes this helps please mark brainliest

The probability that at most 25 tails occur is 0.99999848.

We know that,

P(x = x) = ⁿCₓ × pˣ × [tex]q^{n-x}[/tex]

p = probability of success = 0.5

n = number of trials = 28

q = 1 - p = 0.5

The probability of the tail occurring at most 25 times can be written as

P(X ≤ 25) = P (X = 0) + P(X = 1) + ..... + P(X = 25)

Using a binomial probability calculator,

P(X ≤ 25) = 0.99999848

Therefore the probability that at most 25 tails occur is 0.99999848

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a) The margin of error associated with a 95% confidence interval is 4.

b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)

a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.

The formula for margin of error is Z  = zα/2 σ √ n

Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96

So, the value of error margin is  zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04

= 4

b) We know from part a that margin of error is 4.

Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77

The value of confidence interval for population mean is,

x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)

Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)

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The require angle, angle ABD = 40 degrees

A bisector has two primary characteristics:

Any point along an angle's bisector is equally - spaced from the angle's sides.

The angle bisector divides the other side of a triangle in proportion to the other two sides.

Given : ∠ ABC is bisected by a ray BD

∠ ABC = 80°

Since the angle ABC is being bisected this means that the angles are equal

Let the bisected angle be x

thus we can write it mathematically as

x + x = 80

2x = 80

dividing both the sides as 2 we would get

x = 40 degrees

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Answer: $84.80

Step-by-step explanation:

The actual sales tax was 4.80 because 6% of 80 is 4.80

Then add the 4.80 to the 80 to get your total

Hope this helped :)

For the given figure, angle 3 will be equal to angle 2.

According to the question,

We have the following information:

We have a figure where some angles are marked in form of numbers and  the measure of angle 3 is equal to the sum of the measures of angle 6.

Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.

(More to know: the sum of three angles of a triangle is equal to 180°.)

Hence, for the given figure, angle 3 will be equal to angle 2.

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The demand function for a certain is given by the equation p=−0. 01x2−0. 1x+21 then the determined values will be −50.905557, −0.427737,41.333295.

From the given values,

R=px

9 = (−0. 01x2−0. 1x+21) x

0.01x3+0.1x2−21x−9=0

By reducing the equation,

X = −50.905557, −0.427737,41.333295.

Therefore, the determined values will be −50.905557, −0.427737,41.333295.

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We have to prove (cosA−sinA+1)/(cosA-sinA-) = cotA+cosecA using Trigonometric Functions

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

L.H.S=(cosA−sinA+1)/(cosA-sinA-)

dividing by sinA

=cotA+1−cosecA/cotA−1+cosecA

​=(cotA−1+cosecA)(cotA+1+cosecA)/(cotA+1)²-cosec²A

=(cotA+cosec)²-1/2cotA

=cotA+cosecA(R.H.S)

​Hence the above trigonometric function is proved.

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There are 18 students who like snickers but not twix or reese's peanut butter cups.

Given, that 500 high school students was taken to determine their favorite chocolate candy.

118 like snickers, 185 like twix, 179 like reese's peanut butter cups,

60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups,

and 17 like all three kinds of chocolate candy.

Let A = Set of students like snickers

B = Set of students like twix

C = Set of students like reese's peanut butter cups

Now, we have to find the number of students like snickers but not twix or reese's peanut butter cups i.e. A - A∩B - A∩C + A∩B∩C

A - A∩B - A∩C + A∩B∩C = 118 - 60 - 57 + 17

A - A∩B - A∩C + A∩B∩C = 135 - 117

A - A∩B - A∩C + A∩B∩C = 18

Hence, there are 18 students who like snickers but not twix or reese's peanut butter cups.

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11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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Answer:

Step-by-step explanation:

a=apples

a/7

The linear functions representing the systems of equations in each case are given as follows:

8. (D) 6x − y = 8 3x + 2y = 9

9. (C) a + o = 72 a = o + 8.

10. (C) 4x + 3y = −12 2x − 5y = 10.

The slope-intercept representation of a linear function is presented by the rule as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:

m = 36/6 = 6.

Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:

b = 4 - 2 x 6 = -8.

Hence the equation is:

y = 6x - 8.

6x - y - 8.

Thus option d is correct.

For item 9, we use the variables a and o. The total is of 72, hence:

a + o = 72.

Suppose that a crate has 8 more apples than oranges, hence:

a = o + 8.

Thus option c is correct.

For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:

m = -4/3.

When x = 0, y = -4, hence the intercept is:

b = -4.

Thus the equation is:

y = -4x/3 - 4

3y = -4x - 4.

4x + 3y = -12.

Meaning that option c is correct.

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Answer:

The guy under me is correct

Step-by-step explanation:

Answer:

x - 5

Step-by-step explanation:

Factor the expressions that are not already factored

(x^2 - 9x + 20) / (x - 4)

Cancel out x - 4 in both numerator and denominator

[tex]\frac{(x-5)(x-4)}{x-4}[/tex]

x - 5

Answer:

14.5 feet

Step-by-step explanation:

     To make the subject as 'w', isolate w.

              2L + 2W =P

                      2W = P - 2L

                        [tex]\sf W = \dfrac{P-2L}{2}\\\\W =\dfrac{P}{2}-\dfrac{2L}{2}\\\\ \boxed{W = \dfrac{P}{2}-L}[/tex]

   P = 37 feet

   L = 4 feet

           [tex]\sf W =\dfrac{37}{2}-4\\\\[/tex]

                = 18.5 - 4

           W = 14.5 feet

Answer:

D

Step-by-step explanation:

The domain of this function is all real numbers because you can see that there are no endpoints on the graph. The function is going off of the graph, which means it is continuing aka never-ending.

(-∞,∞) aka all real numbers

Answer: [tex]x^{26}[/tex]

Step-by-step explanation:

The [tex]x^2[/tex] appears 13 times. Using the exponent rule [tex]x^a x^b=x^{a+b}[/tex], we get that:

[tex]x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2=x^{2(13)}=x^{26}[/tex]

Answer:

1: x^2+y^2-6x-4y-3=0

2: x^2+y^2-10x+4y=0

3: x^2+y^2-10x+2y+1=0

First, break down the problem.  

Someone can skate 3 miles in 9 minutes.

What is their speed?  How far would they go if they did that speed for 1 minute?

To find speed given time and distance, divide distance by time.

3/9 = 1/3

Speed is 1/3 mile per minute

if they travel one minute, they will travel 1/3 of a mile

hope this helps :)

The solution of the double-ended inequality is -7/2 < x < -5/2

From the question, we are to solve the doubled ended inequality.

The given inequality is

2x - 5 < 4x + 2 < 2x -3

From the inequality, we can write that

2x - 5 < 4x + 2 and 4x + 2 < 2x - 3

Now, we will solve each of the inequalities separately

Solving 2x - 5 < 4x + 2

Add 5 to both sides

2x - 5 + 5 < 4x + 2 + 5

2x < 4x + 7

Subtract 4x from both sides

2x - 4x < 4x - 4x + 7

-2x < 7

Divide both sides by -2 and reverse the sign

x > -7/2

-7/2 < x

Solving 4x + 2 < 2x - 3

Subtract 2x from both sides of the equation

4x - 2x + 2 < 2x - 2x -3

2x + 2 < -3

Subtract 2 from both sides

2x + 2 -2 < -3 - 2

2x < -5

Divide both sides by 2

x < -5/2

Putting the two solutions together, we get

-7/2 < x and x < -5/2

-7/2 < x < -5/2

Hence, the solution is -7/2 < x < -5/2

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The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.

In the given question,

The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;

C(x) = 3x^2-1500x+199,000

(a) In the given question we have to find the number of bicyles that must be  manufactured to minimize the cost.

The given function is

C(x) = 3x^2-1500x+199,000

To find the maximum or minimum value we firstly find the value of f'(x).

C'(x) = 6x-1500

Now put f'(x)=0

6x-1500=0

Add 1500 on both side, we get

6x=1500

Divide by 6 on both side we get

x=250

Hence, the number of bicycles that must be manufactured to minimize the cost of 250.

(b) Now finding the value of function at x=250

C(250) = 3(250)^2-1500*250+199,000

C(250) = 3*62,500-375,000+199,000

C(250) = 187,500-375,000+199,000

C(250) = 11,500

The minimum cost is $11,500.

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El interés junto con el préstamo de $ 200,000 tiene un monto de $ 8,080.

En este problema tenemos el caso de una persona que pide prestado $ 200,000 a una tasa de interés anual de 36 %, cuyo pago se realiza tras un plazo de dos años de realizarse el préstamo. Asumimos, que la deuda se genera por interés compuesto, esto es, un interés acumulativo. El interés compuesto es descrito mediante la siguiente fórmula:

I = C' · [(1 + r / 100)ⁿ - 1]

Donde:

Si sabemos que C' = 200,000, r = 36 y n = 2, entonces el interés a pagar al final del plazo es:

I = 200,000 · [(1 + 2 / 100)² - 1]

I = 8080

El interés a pagar es $ 8080, además del préstamo de $ 200,000.

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