MAT 142 College MATheMATics Exam: Quiz!
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Questions and Answers
- 1.
Five runners (Andy, Beth, Dale, Ella, and Tri) are in a one-mile race. Beth finished 3 seconds before Dale. Dale finished 7 seconds after Andy. Andy finished 5 seconds after Tri. Tri finished 3 seconds before Ella. Who finished in second place?
- A.
Andy
- B.
Beth
- C.
Dale
- D.
Ella
- E.
Tri
Correct Answer
D. EllaExplanation
Ella finished 3 seconds before Tri, who finished 5 seconds before Andy. Dale finished 7 seconds after Andy, which means Ella finished before Dale as well. Therefore, Ella finished before all the other runners except for Beth, who finished 3 seconds before Dale. Since Ella finished before Dale, but after Beth, she must have finished in second place.Rate this question:
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- 2.
Write a description of the set: {15, 16, 17, 18, ... }
- A.
All natural numbers greater than 14
- B.
All natural numbers greater than 15
- C.
All rational numbers greater than 14
- D.
The numbers fifteen, sixteen, seventeen, and eighteen
- E.
None of the above
Correct Answer
A. All natural numbers greater than 14Explanation
The set {15, 16, 17, 18, ...} represents all natural numbers greater than 14. This means that the set includes all whole numbers starting from 15 and continuing indefinitely.Rate this question:
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- 3.
Determine if the set is the empty set: {x such that x < 7 and x > 10}.
- A.
The set is the empty set.
- B.
The set is not the empty set.
Correct Answer
A. The set is the empty set.Explanation
The set {x such that x < 7 and x > 10} is the empty set because there are no real numbers that can simultaneously satisfy both conditions (x < 7 and x > 10) at the same time. Therefore, no elements exist in this set, making it the empty set.Rate this question:
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- 4.
Determine whether the given statement is true or false: 20 is an element of {14, 16, 18, 20}
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The given statement is true because 20 is indeed an element of the set {14, 16, 18, 20}.Rate this question:
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- 5.
Determine whether the given statement is true or false: 19 is not an element of {1, 2, 3, ..., 34}
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The statement "19 is not an element of {1, 2, 3, ..., 34}" is false because 19 is indeed an element of the set {1, 2, 3, ..., 34}.Rate this question:
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- 6.
Find the cardinal number of the given set:The set of all numbers x such that x is a natural number and 6 < x < 12.
- A.
4
- B.
5
- C.
6
- D.
7
- E.
8
Correct Answer
B. 5Explanation
The set of all numbers x such that x is a natural number and 6 < x < 12 can be represented as {7, 8, 9, 10, 11}. The cardinal number of a set represents the number of elements in that set. In this case, there are 5 elements in the set, which are 7, 8, 9, 10, and 11. Therefore, the cardinal number of the given set is 5.Rate this question:
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- 7.
Find the cardinal number for the given set: {2, 6, 10, .. , 42}.
Correct Answer
11Explanation
The given set is an arithmetic sequence with a common difference of 4. To find the cardinal number, we need to determine the number of terms in the sequence. The first term is 2 and the last term is 42. By subtracting the first term from the last term and dividing by the common difference, we can find the number of terms. (42 - 2)/4 = 10. Since the first term is included in the set, the cardinal number is 10 + 1 = 11.Rate this question:
- 8.
Consider the following sets:A = {2, 3, 4, 5, 6}B = {1, 2, 3, 4, 5}Choose the statement below that is true.
- A.
The sets are equal and equivalent.
- B.
The sets are equal but not equivalent.
- C.
The sets are not equal but are equivalent.
- D.
The sets are not equal and not equivalent.
- E.
None of the above.
Correct Answer
C. The sets are not equal but are equivalent.Explanation
The sets A and B are not equal because they have different elements. However, they are equivalent because they have the same cardinality, which means they have the same number of elements. In this case, both sets have 5 elements. Therefore, the correct statement is that the sets are not equal but are equivalent.Rate this question:
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- 9.
Determine whether the set is finite or infinite: x such that x is a natural number and x > 119.
- A.
Finite set
- B.
Infinite set
Correct Answer
B. Infinite setExplanation
The set of natural numbers greater than 119 is infinite because there is no upper limit to the set. It continues indefinitely, as there is no largest natural number. Therefore, the set is an infinite set.Rate this question:
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- 10.
Consider the following sets:U = {1, 2, 3, 4, 5, 6, 7}A = {4, 5, 6, 7}B = {3, 4, 7}Find the intersection of the complement of A and the complement of B.
Correct Answer
{1,2}
{1, 2}Explanation
The intersection of the complement of A and the complement of B is {1, 2}. The complement of A is the set of all elements in U that are not in A, which is {1, 2, 3}. The complement of B is the set of all elements in U that are not in B, which is {1, 2, 5, 6}. The intersection of these two sets is {1, 2}, as those are the only elements that are common to both sets.Rate this question:
- 11.
Consider the following sets: U = {1, 2, 3, 4, 5, 6, 7} A = {3, 4, 5, 6} B = {3, 4, 7} Find the complement of the union of A and B.
Correct Answer
{1, 2}
{1,2}Explanation
The complement of a set is the set of all elements that are not in the original set. In this case, the union of A and B is {3, 4, 5, 6, 7}, so the complement of this set would be {1, 2}. Therefore, the correct answer is {1, 2}.Rate this question:
- 12.
Set A contains 4 letters and 7 numbers. Set B contains 11 letters and 2 numbers. 0 letters and 0 numbers are common to both sets A and B. Find the number of elements in set A or Set B.
Correct Answer
24Explanation
The number of elements in set A or set B can be found by adding the number of elements in set A and set B and then subtracting the number of elements that are common to both sets. In this case, set A contains 4 letters and 7 numbers, and set B contains 11 letters and 2 numbers. Since 0 letters and 0 numbers are common to both sets, we can add the number of elements in set A (11) and set B (13) and subtract the number of common elements (0) to get the final answer of 24.Rate this question:
- 13.
Consider the following sets: U = {a, b, c, d, e, f, g, h} A = {a, d, g} B = {b, d, g}C = {b, c, e, f, h} Find the union of the following two intersections:1) the intersection of A and the complement of C2) the intersection of the complement of B and the complement of C
Correct Answer
{a, d, g}
{a,d,g}Explanation
The correct answer is {a, d, g}. To find the union of the two intersections, we first need to find the individual intersections.
1) The intersection of A and the complement of C is {a, d, g} because the complement of C is {a, d, g} and the intersection of A and {a, d, g} is also {a, d, g}.
2) The intersection of the complement of B and the complement of C is also {a, d, g} because the complement of B is {a, c, e, f, h} and the complement of C is {a, d, g}. The intersection of {a, c, e, f, h} and {a, d, g} is {a, d, g}.
Therefore, the union of the two intersections is {a, d, g}.Rate this question:
- 14.
A television sells for $700. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $200 down and $50 a month for 14 months. How much is saved by paying the total amount at the time of purchase?
Correct Answer
200
$200
$200.00
200.00Explanation
By paying the total amount at the time of purchase, no additional monthly payments need to be made. Therefore, the amount saved by paying the total amount at the time of purchase is $200.Rate this question:
- 15.
Each day a small business owner sells 200 pizza slices at $2.00 per slice and 85 sandwiches at $4.00 each. Business expenses come to $110 per day. What is the owner's profit for a ten-day period?
Correct Answer
$6300
$6300.00
$6,300.00
6300
6300.00Explanation
The owner's profit for a ten-day period can be calculated by subtracting the total expenses from the total revenue. In this case, the revenue from selling pizza slices is $2.00 per slice multiplied by 200 slices per day, which equals $400. The revenue from selling sandwiches is $4.00 per sandwich multiplied by 85 sandwiches per day, which equals $340. Therefore, the total revenue per day is $400 + $340 = $740. Over a ten-day period, the total revenue is $740 multiplied by 10, which equals $7400. Subtracting the total expenses of $110 per day multiplied by 10 days, which equals $1100, from the total revenue gives a profit of $7400 - $1100 = $6300.Rate this question:
- 16.
A vending machine accepts nickels, dimes, and quarters only. Exact change is needed to make a purchase. How many ways can a person with four nickels, three dimes, and two quarters make a 35-cent purchase from the machine?
Correct Answer
4 - 17.
Consider the following sets:Set X = {4,6,9}Set Y = {4,6,9,12}Choose the statement(s) that are true.
- A.
Set X is a subset of Set Y.
- B.
Set X is a proper subset of Set Y.
- C.
Both A and B are true.
- D.
None of the statements are true.
Correct Answer
C. Both A and B are true.Explanation
Both A and B are true. Set X is a subset of Set Y because all the elements of Set X (4, 6, and 9) are also present in Set Y. Set X is also a proper subset of Set Y because it is a subset of Set Y and there is at least one element (12) in Set Y that is not in Set X.Rate this question:
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- 18.
Consider the following sets: Set X = {4,7,10,13,16} Set Y = {7,4,10,13,16} Choose the statement(s) that are true.
- A.
Set X is a subset of Set Y.
- B.
Set X is a proper subset of Set Y.
- C.
Both A and B.
- D.
None of the statments are true.
Correct Answer
A. Set X is a subset of Set Y.Explanation
Set X is a subset of Set Y because all the elements of Set X are also present in Set Y. In other words, Set X is completely contained within Set Y. However, it is not a proper subset because Set X is not strictly smaller than Set Y; they have the same number of elements.Rate this question:
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- 19.
A pizza parlor offers mushrooms, onions, and sausage as toppings for the plain cheese base. How many different types of pizzas can be made? Assume that you can order a plain cheese pizza, a 1-topping pizza, a 2-topping pizza, or a 3-topping pizza.
Correct Answer
8Explanation
Since there are three toppings available (mushrooms, onions, and sausage), and we can choose to have 0, 1, 2, or 3 toppings on the pizza, we can calculate the number of different types of pizzas by using the combination formula. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options (3 toppings) and r is the number of choices (0, 1, 2, or 3 toppings). Plugging in the values, we get 3C0 + 3C1 + 3C2 + 3C3 = 1 + 3 + 3 + 1 = 8. Therefore, there are 8 different types of pizzas that can be made.Rate this question:
- 20.
How many different groups of students can show up for a seminar with an enrollment of 15?
Correct Answer
Explanation
The number of different groups of students that can show up for a seminar with an enrollment of 15 can be calculated using the concept of combinations. Since the order in which the students show up does not matter, we can use the formula for combinations. In this case, we need to select a group of students from a total of 15. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of students and r is the number of students in each group. Therefore, the number of different groups of students that can show up for the seminar is 15C15 = 1.Rate this question:
- 21.
A politician has run for office two times. In the first election 11,240 people voted for him. In the second election 13,134 people voted for him. 9,349 people voted for him in both elections. How many people voted for this politician in the first or the second election?
Correct Answer
15,025
15025Explanation
The correct answer is 15,025,15025. This answer is obtained by adding the number of people who voted for the politician in the first election (11,240) and the number of people who voted for him in the second election (13,134). The additional information that 9,349 people voted for him in both elections is not necessary to calculate the total number of people who voted for him in either election.Rate this question:
- 22.
A survey of 76 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television. How many got the news from only newspapers?
Correct Answer
21Explanation
The number of students who got the news from newspapers is 38, and the number of students who got the news from both newspapers and television is 17. Therefore, to find the number of students who got the news from only newspapers, we need to subtract the students who got the news from both newspapers and television (17) from the total number of students who got the news from newspapers (38). This gives us 21 students who got the news from only newspapers.Rate this question:
- 23.
A survey of 76 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television. How many got the news from only television?
Correct Answer
14Explanation
The number of students who got the news from only television can be calculated by subtracting the number of students who got the news from both newspapers and television (17) from the total number of students who got the news from television (31). Therefore, the number of students who got the news from only television is 14.Rate this question:
- 24.
A survey of 76 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television. How many got the news from newspapers or from television?
Correct Answer
52Explanation
The question asks for the number of college students who got the news from newspapers or from television. To find this, we add the number of students who got the news from newspapers (38) and the number of students who got the news from television (31). Adding these two numbers gives us a total of 69 students. Therefore, 52 college students got the news from newspapers or from television.Rate this question:
- 25.
A survey of 76 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 38 got the news from newspapers, 31 from television, and 17 from both newspapers and television. How many got the news from neither newspapers nor television?
Correct Answer
24Explanation
Based on the information provided, 38 students got the news from newspapers, 31 from television, and 17 from both newspapers and television. To find the number of students who got the news from neither newspapers nor television, we can subtract the total number of students who got the news from newspapers and television from the total number of students surveyed. Therefore, the number of students who got the news from neither newspapers nor television is 76 - (38 + 31 - 17) = 24.Rate this question:
- 26.
A survey of 118 college students was taken to determine the musical styles they liked. Of those, 35 students listened to rock, 33 to classical, and 35 to jazz. Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz. Finally, 12 students listened to all three musical styles. How many listened to only rock music?
Correct Answer
8Explanation
To find the number of students who listened to only rock music, we need to subtract the number of students who listened to rock and jazz, rock and classical, and all three styles from the total number of students who listened to rock.
The number of students who listened to rock and jazz is 24, the number who listened to rock and classical is 15, and the number who listened to all three styles is 12.
Therefore, the number of students who listened to only rock music is 35 - 24 - 15 - 12 = 8.Rate this question:
- 27.
A survey of 118 college students was taken to determine the musical styles they liked. Of those, 35 students listened to rock, 33 to classical, and 35 to jazz. Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz. Finally, 12 students listened to all three musical styles. How many listened to classical and jazz but not to rock?
Correct Answer
3Explanation
To find the number of students who listened to classical and jazz but not rock, we can use the principle of inclusion-exclusion. We start by adding the number of students who listened to classical and jazz (15) to the number of students who listened to all three styles (12). This gives us a total of 27 students who listened to either classical and jazz or all three styles. However, this count includes the students who listened to all three styles, so we subtract the number of students who listened to all three styles (12) to get the final answer of 15 students.Rate this question:
- 28.
A survey of 118 college students was taken to determine the musical styles they liked. Of those, 35 students listened to rock, 33 to classical, and 35 to jazz. Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz. Finally, 12 students listened to all three musical styles. How many listened to classical and to jazz but not to rock?
Correct Answer
26 - 29.
A survey of 118 college students was taken to determine the musical styles they liked. Of those, 35 students listened to rock, 33 to classical, and 35 to jazz. Also, 24 students listened to rock and jazz, 15 to rock and classical, and 15 to classical and jazz. Finally, 12 students listened to all three musical styles. How many listened to exactly one music style?
Correct Answer
31Explanation
To determine the number of students who listened to exactly one music style, we need to subtract the number of students who listened to multiple styles from the total number of students who listened to each style individually.
From the given information, we know that 35 students listened to rock, 33 to classical, and 35 to jazz.
We also know that 12 students listened to all three styles, so we subtract this from each individual count:
35 - 12 = 23 students listened to only rock
33 - 12 = 21 students listened to only classical
35 - 12 = 23 students listened to only jazz
Adding up these counts, we get a total of 23 + 21 + 23 = 67 students who listened to exactly one music style.
Therefore, the correct answer is 67.Rate this question:
- 30.
Suppose that the local sales tax rate is 4%, and you purchase a car for $24,200. How much tax is paid?
Correct Answer
$968
968Explanation
The local sales tax rate is 4%, and the car is purchased for $24,200. To calculate the tax paid, we multiply the purchase price by the tax rate. So, 4% of $24,200 is $968. Therefore, the tax paid is $968.Rate this question:
- 31.
Suppose that the local sales tax rate is 4%, and you purchase a car for $24,200. What is the total cost of the car (including tax)?
Correct Answer
Explanation
The total cost of the car, including tax, can be calculated by multiplying the purchase price of the car by the sales tax rate and then adding the result to the purchase price. In this case, the sales tax rate is 4%, so the tax amount would be $24,200 * 4% = $968. Adding this tax amount to the purchase price gives us the total cost of the car, which is $24,200 + $968 = $25,168.Rate this question:
- 32.
An exercise machine with an original price of $730 is on sale at 21% off. What is the exercise machine's sale price?
Correct Answer
$576.70
576.70
577
$577Explanation
The exercise machine is on sale at 21% off, which means the price is reduced by 21% of the original price. To find the sale price, we need to subtract 21% of $730 from $730. 21% of $730 is $153.30, so the sale price is $730 - $153.30 = $576.70.Rate this question:
- 33.
A sofa regularly sells for $850. It is on sale for $646. Find the percent decrease of the sale price from the regular price.
Correct Answer
24
24%Explanation
The percent decrease can be found by subtracting the sale price from the regular price, dividing that difference by the regular price, and then multiplying by 100. In this case, the difference between the regular price ($850) and the sale price ($646) is $204. Dividing $204 by $850 gives a decimal value of approximately 0.24. Multiplying by 100 gives a percent value of 24. Therefore, the percent decrease of the sale price from the regular price is 24%.Rate this question:
- 34.
$12,000 is borrowed at a simple interest rate of 7% for 180 days. How much interest will be owed at the end of the 180 days? If necessary, round your answer to the nearest dollar.
Correct Answer
Explanation
The interest owed at the end of the 180 days can be calculated using the formula: Interest = Principal x Rate x Time. In this case, the principal is $12,000, the rate is 7% (or 0.07 as a decimal), and the time is 180 days (or 0.5 years). Plugging these values into the formula, we get: Interest = $12,000 x 0.07 x 0.5 = $420. Therefore, the interest owed at the end of the 180 days is $420.Rate this question:
- 35.
$3,000 is borrowed, and at the end of 3 months, the balance due is $3045. What was the simple interest rate? If necessary, round to the nearest tenth of a percent.
Correct Answer
6.0%
6%
6.0
6 - 36.
If you would like to have $4,000 in 3 months, how much money should you invest today into an account that earns a simple interest rate of 9.0%? If necessary, round your answer to the nearest dollar.
Correct Answer
$3,912
3,912
$3912
3912Explanation
To find out how much money should be invested today, we can use the formula for simple interest: I = P * r * t, where I is the interest, P is the principal (initial investment), r is the interest rate, and t is the time in years. In this case, we want to find P. We can rearrange the formula to solve for P: P = I / (r * t). Plugging in the values, I = $4,000, r = 9.0% = 0.09, and t = 3/12 = 0.25 years, we get P = $4,000 / (0.09 * 0.25) = $3,911.11. Rounding to the nearest dollar, the correct answer is $3,912.Rate this question:
- 37.
$5,000 is deposited into an account earning interest compounded daily with an interest rate of 8%. How much money will be in the account after 4 years? If necessary, round to the nearest dollar.
Correct Answer
$6,885
$6885
6,885
6885Explanation
$5,000 is deposited into an account earning interest compounded daily with an interest rate of 8% for 4 years. The formula to calculate the future value of an investment with compound interest is FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. In this case, P = $5,000, r = 8% or 0.08, n = 365 (compounded daily), and t = 4 years. Plugging these values into the formula, we get FV = $5,000(1 + 0.08/365)^(365*4) ≈ $6,885. Therefore, the amount of money in the account after 4 years is approximately $6,885.Rate this question:
- 38.
How much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $13,000 in three years? If necessary, round your answer to the nearest dollar.
Correct Answer
$10,887
10,887
$10887
10887Explanation
To find the amount of money that should be deposited today, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (the amount to be deposited), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the future value is $13,000, the interest rate is 6%, interest is compounded semiannually (so n = 2), and the time period is 3 years. Plugging these values into the formula, we get 13,000 = P(1 + 0.06/2)^(2*3). Solving for P, we find that P is approximately $10,887. Therefore, $10,887 should be deposited today.Rate this question:
- 39.
At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 7% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? If necessary, round to the nearest dollar.
Correct Answer
$60,630
60630
$60630
60,630Explanation
The correct answer is $60,630. This can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, P = $14,000, r = 7% (or 0.07 as a decimal), n = 12 (compounded monthly), and t = 21. Plugging these values into the formula, we get A = $14,000(1 + 0.07/12)^(12*21) = $60,630. Therefore, the value of the account at the child's twenty-first birthday will be $60,630.Rate this question:
- 40.
You deposit $10 at the end of each month into an annuity that earns 6% interest compounded monthly. How much money will be in the account after 10 years? If necessary, round to the nearest dollar.
Correct Answer
$1639
$1,639
1,639
1639Explanation
An annuity is a series of equal payments made at regular intervals. In this case, you are depositing $10 at the end of each month for 10 years. The interest is compounded monthly at a rate of 6%. To calculate the future value of the annuity, you can use the formula: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of periods. Plugging in the values, we get FV = 10 * ((1 + 0.06/12)^(10*12) - 1) / (0.06/12) = $1,638.99. Rounded to the nearest dollar, the answer is $1,639.Rate this question:
- 41.
In order to have $24,000 in 6 years, how much should you deposit each quarter into an annuity that earns 7.25% compounded quarterly? If necessary, round to the nearest dollar.
Correct Answer
$808
808 - 42.
The cost of a sports utility vehicle is $30,000. This can be financed by paying $2,000 down and $436 per month for 72 months. What is the amount financed?
Correct Answer
$28,000
28,000
$28000
28000Explanation
The amount financed is $28,000. This is calculated by subtracting the down payment of $2,000 from the total cost of $30,000.Rate this question:
- 43.
The cost of a sports utility vehicle is $30,000. This can be financed by paying $2,000 down and $436 per month for 72 months. What is the total installment price?
Correct Answer
$33,392
$33392
33,392
33392Explanation
The total installment price can be calculated by multiplying the monthly payment by the number of months and adding the down payment. In this case, the monthly payment is $436 and the number of months is 72. Thus, the total installment price is 436 * 72 + 2000 = $33,392.Rate this question:
- 44.
The cost of a sports utility vehicle is $30,000. This can be financed by paying $2,000 down and $436 per month for 72 months. What is the finance charge?
Correct Answer
$3392
$3,392
3392
3,392Explanation
The finance charge can be calculated by subtracting the total amount paid from the original cost of the vehicle. The total amount paid can be calculated by multiplying the monthly payment by the number of months and adding the down payment. In this case, the monthly payment is $436 and the number of months is 72. Therefore, the total amount paid is $436 * 72 + $2,000 = $31,392. Subtracting this from the original cost of the vehicle ($30,000) gives us the finance charge of $31,392 - $30,000 = $3,392.Rate this question:
- 45.
The price of a home is $136,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. Find the required down payment amount.
Correct Answer
$27,200
27,200
$27200
27200Explanation
The down payment amount is calculated by multiplying the price of the home by the down payment percentage. In this case, the price of the home is $136,000 and the down payment percentage is 20%. Therefore, the down payment amount is 20% of $136,000, which is $27,200.Rate this question:
- 46.
The price of a home is $136,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. Find the amount of the mortgage.
Correct Answer
Explanation
The amount of the mortgage can be calculated by subtracting the down payment and the points from the price of the home. In this case, the down payment is 20% of $136,000, which is $27,200. The three points at the time of closing are 3% of $136,000, which is $4,080. Subtracting these amounts from the price of the home gives us $136,000 - $27,200 - $4,080 = $104,720. Therefore, the amount of the mortgage is $104,720.Rate this question:
- 47.
The price of a home is $136,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. How much must be paid for the three points at closing? Round to the nearest dollar.
Correct Answer
$3,264
$3264
3,264
3264Explanation
The bank requires a 20% down payment and three points at the time of closing. Points are a percentage of the loan amount that the borrower pays upfront to the lender as a fee. In this case, the loan amount is the price of the home, which is $136,000. To calculate the amount for the three points, we need to multiply the loan amount by the percentage of points. Three points is equal to 3% of the loan amount. Therefore, the amount to be paid for the three points at closing is $136,000 x 0.03 = $3,264.Rate this question:
- 48.
The price of a home is $136,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 8.5%. Find the monthly mortgage payment. Round to the nearest dollar.
Correct Answer
Explanation
To find the monthly mortgage payment, we need to calculate the loan amount, which is the price of the home minus the down payment and points. The down payment is 20% of $136,000, which is $27,200. The points are 3% of $136,000, which is $4,080. Therefore, the loan amount is $136,000 - $27,200 - $4,080 = $104,720. Next, we calculate the monthly interest rate by dividing the annual interest rate by 12, so 8.5% / 12 = 0.7083%. Using the loan amount, the monthly interest rate, and the loan term of 30 years (360 months), we can use the formula for calculating the monthly mortgage payment to find the answer.Rate this question:
- 49.
Convert 13 meters to yards. Round to the nearest hundredth.
Correct Answer
14.44 yd
14.44
14.44 yds
14.44 yards
14.44ydExplanation
To convert meters to yards, you can use the conversion factor 1 meter = 1.09361 yards. Therefore, to convert 13 meters to yards, you multiply 13 by 1.09361, which gives you approximately 14.44 yards. Rounding to the nearest hundredth, the answer is 14.44 yd.Rate this question:
- 50.
Convert 6 feet to meters. Round to the nearest tenth.
Correct Answer
Explanation
To convert feet to meters, we can use the conversion factor of 1 foot = 0.3048 meters. Therefore, to convert 6 feet to meters, we multiply 6 by 0.3048. The result is 1.8288 meters. Since we need to round to the nearest tenth, the final answer is 1.8 meters.Rate this question:
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Jul 22, 2024Quiz Edited by
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Jul 23, 2009Quiz Created by
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