To determine which loan will have a higher balance at the time of repayment, we need to calculate the future value of both loans. The Stafford Loan will have a higher balance by approximately $234.36.
Explanation:To determine which loan will have a higher balance at the time of repayment, we need to calculate the future value of both loans. Let's start with the Stafford Loan:
Principal: $5,125
Interest Rate: 6.8%
Compounding Period: Monthly
Time: 12 months
Using the formula for future value of an ordinary annuity, we can calculate the balance of the Stafford Loan at the time of repayment:
FV = P * ((1 + r)^n - 1) / r
FV = 5125 * ((1 + 0.068/12)^(12*1) - 1) / (0.068/12)
Calculating this gives us an approximate loan balance of $5,259.35.
Now let's calculate the future value of the PLUS Loan:
Principal: $5,125
Interest Rate: 7.8%
Compounding Period: Monthly
Time: 12 months
Using the same formula, we can calculate the balance of the PLUS Loan at the time of repayment:
FV = P * ((1 + r)^n - 1) / r
FV = 5125 * ((1 + 0.078/12)^(12*1) - 1) / (0.078/12)
Calculating this gives us an approximate loan balance of $5,024.99.
Therefore, the Stafford Loan will have a higher balance at the time of repayment by approximately $234.36. The correct answer is: The Stafford Loan has a higher balance by $234.36.
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A candy store keeps track of its sales during the month of October. Below is the number of sales for the first, second, third and fourth week of the month.
Week 1 ; 2 ; 3 ; 4
Candy Sales 97 ; 168 ; 259 ; 375
Which graph could represent the data shown below?
From the attached diagram you can see that regression that best fits given data is quadratic (not linear).
option 1 is false, because it gives linear regression;option 2 is true, it gives graph, similar to quadratic parabola;options 3 and 4 are false, because graphs are decreasing.Answer: correct choice is B.
The graph of the given values is required.
Option B is correct.
The points are
[tex](1,97)[tex]
[tex](2,168)[/tex]
[tex](3,259)[/tex]
[tex](4,375)[/tex]
Let us find if the points are in the form of a line by finding the slope.
[tex]\dfrac{168-97}{2-1}=71[/tex]
[tex]\dfrac{259-168}{3-2}=91[/tex]
[tex]71\neq 91[/tex]
So, the function is not linear.
Therefore, A and C are incorrect.
Also the function is not decreasing so option D is also eliminated.
Hence, option B is correct.
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B is between A and C, AB = 13.7 and BC = 8.3. Find AC.
What has the sum of 20 but the difference is 8?
I am the number that is divided in a division problem
When you add the number 1, and then add 1, what do you get??
A basketball player is 15 ft horizontally from the center of the basket, which is 10 ft off the ground. At what angle should the player aim the ball if it is thrown from a height of 8.2 ft with a speed of 29 ft/s ?
Which is greater 2 gallons or 8 liters?
richerds checkbook awnsers as of 02/19
At which angle will the hexagon rotate onto itself?
Answer:
The correct answer is: 60°
Step-by-step explanation:
Rotational symmetry is a type of symmetry, in which an object returns back to its original shape after rotation at an angle of 360°/n about a fixed point.
A hexagon is a regular polygon that has six edges and vertices. It has six internal angles, 120° each.
Since there are 6 equal edges, therefore, the hexagon will rotate onto itself after every rotation at an angle of: 360°/n = 360°/6 = 60°
Solve the inequality.
y – 5 ≥ 11
The solution to the inequality y - 5 ≥ 11 is y ≥ 16.
To solve the inequality y - 5 ≥ 11,
we need to isolate the variable y on one side of the inequality sign.
Adding 5 to both sides of the inequality, we have:
y - 5 + 5 ≥ 11 + 5
Simplifying, we get:
y ≥ 16
Therefore, the solution to the inequality y - 5 ≥ 11 is y ≥ 16.
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If f(x) and f^-1(x) are inverse functions of each other and f(x)=2x+5, what is f^-1(8)
Answer:
[tex]\text{The value of }f^{-1}(8)\text{ is }\frac{3}{2}[/tex]
Step-by-step explanation:
Given the function
[tex]f(x)=2x+5[/tex]
[tex]\text{we have to find the value of }f^{-1}(8)[/tex]
First we have to find the inverse
Step 1: Put f(x)=y, the equation becomes
[tex]y=2x+5[/tex]
Step 2: Replace x to y and y to x, we get
[tex]x=2y+5[/tex]
Step 3: Solve for y and then replace it with [tex]f^{-1}x[/tex]
[tex]x-5=2y[/tex]
[tex]y=\frac{x-5}{2}[/tex]
[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
Now substitute x=8, we get
[tex]f^{-1}(8)=\frac{8-5}{2}=\frac{3}{2}[/tex]
[tex]\text{hence, the value of }f^{-1}(8)\text{ is }\frac{3}{2}[/tex]
Suppose that there were a negative correlation between the variables a and b. If b is 90 when a is 8, which of these is most likely to be the value of b when a is 16?
A. 105
B. 120
C. 90
D. 45
Answer:
45 is correct
Step-by-step explanation:
A mall distribution center processes as many as 150,000 pieces of mail each day. The mail is sent via ground and air. Each land carrier takes 2000 pieces per load and each air carrier 1500 pieces per load. The loading equipment is able to handle as many as 200 loads per day.
Let x be the number of loads by land carriers and y the number of loads by air carriers. Which system of inequalities represents the situation?
Options:
1500x+2000y>=150,000 x+y>=200
2000x+1500y>=150,000 x+y>=200
2000x+1500y<=150,000 x+y<=200
1500x+2000y<=150,000 x+y<=200 ...?
Answer: [tex]2000x+1500y\leq150,000[/tex]
[tex]\Rightarrow x+\leq200[/tex]
Step-by-step explanation:
Let x be the number of loads by land carriers and y be the number of loads by air carriers.
Given: A mall distribution center processes as many as 150,000 pieces of mail each day.
Each land carrier takes 2000 pieces per load and each air carrier 1500 pieces per load.
[tex]2000x+1500y\leq150,000[/tex]
The loading equipment is able to handle as many as 200 loads per day.
[tex]\Rightarrow x+\leq200[/tex]
Hence, the system of inequalities represents the situation is
[tex]2000x+1500y\leq150,000[/tex]
[tex]\Rightarrow x+\leq200[/tex]
I am the method of dividing in which multiplies of the divisor are subtracted from the dividend
The polynomial x3 + 8 is equal to
(x + 2)(x2 – 2x + 4).
(x – 2)(x2 + 2x + 4).
(x + 2)(x2 – 2x + 8).
(x – 2)(x2 + 2x + 8)
Answer:
A
Step-by-step explanation:
other guy said it and I got it right.
The slope of a line is 0, and the y-intercept is 6. the equation, written as y = 6, represents a horizontal line. true false
The answer is: true.
Here's why:
A slope of 0 indicates a horizontal line, meaning there's no change in y-value as x changes.
A y-intercept of 6 means the line intersects the y-axis at the point (0, 6).
The equation y = 6 represents a constant y-value for any x, which indeed depicts a horizontal line that intersects the y-axis at (0, 6).
Therefore, both the slope and the equation confirm that the line is horizontal.
A first number plus twice a second number is 13 twice the first number plus the second totals 20 find the numbers
explain how to solve the following system of equations. what is the solution to the system? 2x+2y+z =-5
3X plus 4Y plus 2Z = zero
X plus 3Y plus 2Z= zero
A cyclist rides his bike at a rate of 8 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
miguel is making smoothies out of yogurt and juice to serve his friends, and he needs to make 12 cups. the ratio of yogurt to juice is 2 cups to 1 cup. how much yogurt will he use
Answer:
Eight cups of yogurt will be used.
Step-by-step explanation:
Let cups of yogurt used in 12 cups of smoothies be x
Cups of juice used in 12 cups of smoothies = 12- x
The ratio of yogurt to juice is 2 cups to 1 cup that is:
[tex]\frac{Yogurt}{Juice}=\frac{2}{1}[/tex]
Ratio will be maintained through out 12 cups of smoothies:
[tex]\frac{Yogurt}{Juice}=\frac{2}{1}=\frac{x}{12-x}[/tex]
[tex]2(12-x)=1(x)[/tex]
[tex]24-2x=x[/tex]
[tex]24=3x[/tex]
x = 8
Eight cups of yogurt will be used.
2x+y=3, 5x-2y=12 how to solve this
You know that a certain trait occurs in 30% of the population. You want to know how many individuals you have to draw from the population, on average, to get three subjects with the trait.
To find out how many individuals you have to draw from the population, on average, to get three subjects with the trait, you can use the geometric distribution. The average number of trials until the third success can be calculated by dividing 1 by the probability of success.
Explanation:To find out how many individuals you have to draw from the population, on average, to get three subjects with the trait, you can use the geometric distribution.
The probability of success (finding an individual with the trait) is 30% or 0.30, and the probability of failure is 70% or 0.70.
To calculate the average number of trials until the third success, you divide 1 by the probability of success:
1 / 0.30 = 3.33
Therefore, on average, you would have to draw from the population about 3.33 individuals to get three subjects with the trait.
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10: A bin of bolts at the hardware store contains 7-dozen bolts when full. The stock clerk is supposed to reorder bolts when the bin is 1⁄6 full. How many bolts are in the bin when it’s time to reorder?
Serena drove 40 km on 3 L of gasoline. Which of the following would be an equation to help you find out how far she can travel on a full tank of 50 L? Serena drove 40 km on 3 L of gasoline. Which of the following would be an equation to help you find out how far she can travel on a full tank of 50 L?
AT THANKSGIVING DINNER, EMMA'S FAMILY ATE 1/3 OF A PUMPKIN PIE. WHAT FRACTION OF THE PIE WAS LEFT OVER?
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Total pumpkin in fraction = 1
= 1 - 1/3
= 2/3
The fraction of the pie left over is 2/3
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Amount of pumpkin pie eaten by the family = 1/3
Let the total pumpkin in fraction = 1
Now,
The fraction of the pie left over.
= 1 - 1/3
= (3 -1)/ 3
= 2/3
Thus,
The fraction of the pie left over is 2/3
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whats 3.428571429 into fraction ...?
Which of the following is the expansion of (2m - n)7?
Answer: 128m⁷ - 448m⁶n + 672m⁵n² - 560m⁴n³ + 280m³n⁴ - 84m²n⁵ + 14mn⁶ - n⁷
Step-by-step explanation:
2023 edge
susan wants to buy a paddle boat for $840. She will pay 20% down and pay the rest in six months installments. what will be the amount of each monthly payments?
Susan's down payment for the paddle boat is $168, with the remaining $672 divided into six monthly payments of $112 each.
Susan wants to buy a paddle boat for $840. She will pay 20% down and the rest in six monthly installments. To calculate the down payment, we calculate 20% of $840, which is $168.
The remaining amount after the down payment is $840 - $168 = $672. This remainder will be paid in six monthly installments, so we divide $672 by 6 to get the monthly payment amount.
The amount of each monthly payment will therefore be $672 / 6 = $112 per month.
Therefore, as per the above explaination, the correct answer is $112.
Find the coordinates for the vertex of the graph of the function y = 3x^2- 12x + 12
The Shelby University rose garden is a rectangular shape with an area of 192 square feet. The dimensions of the garden are x^2 feet wide by x^2– 61 feet long. How wide is the garden?
a. 3 feet c. 64 feet
b. 8 feet d. 131 feet
...?