The car needs 14 gallons of gas for the 714 mile trip.
To determine the amount of gas required for a 714-mile trip, we can set up a proportion based on the given information:
We know that the car travels 204 miles on 4 gallons of gas. We need to find the amount of gas needed for 714 miles. Let the gas required for 714 miles be X gallons
First, let us set up the proportion:
204 mi / 4 gal = 714 mi / X galNext, we solve for x (the amount of gas required for 714 miles):
204 mi × X gal = 714 mi × 4 gal204X = 2856X = 2856 / 204X = 14Therefore, the car requires 14 gallons of gas for a 714-mile trip.
Instructions.find the volume and surface area of the rectangular prisms
Use forward or backward substitute to conjecture a closed formula which describes the nth term of the sequence an = an-1 – n, where a0 = 4.
Tripp and Rico are two dogs. Tripp weighs exactly 35 pounds more than Rico. Together, they weigh exactly 49 pounds. How much does each dog weigh? Please use Two-step equations!!!! plz, help!
Using a system of equations, it is found that Tripp weighs 42 pounds and Rico weighs 7 pounds.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Tripp's weight.Variable y: Rico's weight.Tripp weighs exactly 35 pounds more than Rico, hence:
x = 35 + y.
Together, they weigh exactly 49 pounds, hence:
x + y = 49
35 + y + y = 49
2y = 14 -> y = 7
x = 35 + y -> x = 42
Hence, Tripp weighs 42 pounds and Rico weighs 7 pounds.
To learn more about a system of equations, you can check https://brainly.com/question/24342899
Cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 after 3 years. What is the smallest amount, to the nearest pound, she can invest?
Simple steps please ?
housing prices in a certain neighborhood average at 97.86 per square foot. If one house in this neighborhood is 1400 square feet, what should it be priced at?
In a tournament team A won 7 less games than Team B, and Team B won exactly three times as many games as team C. If If Team C won g games, how many games did Team A win?
Team A won 3g - 7 games, where g is the number of games won by Team C. To determine the number of games Team A won, multiply the number of games Team C won by 3 and subtract 7.
Let's denote Team C's number of wins as g. According to the information provided, Team B won three times as many games as Team C, which can be expressed as 3g. It is also stated that Team A won 7 fewer games than Team B. So, if Team B won 3g games, then Team A won 3g - 7 games.
To find the number of games Team A won, simply multiply the number of games Team C won by 3 and subtract 7 from that total. This can be represented by the algebraic expression A = 3g - 7, where A represents the number of games won by Team A and g represents the number of games won by Team C.
An executive invests $22,000, some at 8% and the rest at 6% annual interest. If he receives an annual return of $1,660, how much is invested at each rate?
if a 9 inch pizza serves 4 people, how many people will a 12 inch pizza serve?
Arthur took out a 20 year loan for $60,000 at an APR of 4.4% compounded monthly. Approximately how munch would save if he paid it off 3 years early Apex A. $4516.32,B. $1129.08,C. $376.36,D.$877.96
Answer:
D. $877.96
Step-by-step explanation:
You want the amount saved if a 20 year loan of $60,000 at 4.4% is paid off 3 years early.
PaymentThe monthly payment on the loan can be found from ...
[tex]A=\dfrac{Pr}{12(1-(1+r/12)^{-12t})}[/tex]
where P is the loan amount at rate r for t years.
For the 20 year loan of $60,000 at 4.4%, the payment is calculated as ...
[tex]A=\dfrac{60000(.044)}{12(1-(1+0.044/12)^{-12\cdot20})}=\dfrac{220}{0.584549}=376.3585[/tex]
Balance dueAfter 204 payments on the loan, the remaining balance due is ...
[tex]A=P\left(1-\dfrac{(1+r/12)^n-1}{(1+r/12)^{12t}-1}\right)\\\\\\A=60000\left(1-\dfrac{1.0036667^{204}-1}{1.0036667^{240}-1}\right)=12671.04[/tex]
SavingsThe remaining 36 payments on the loan come to about ...
36 × 376.3585 ≈ 13548.91
So, the savings from early payoff is about ...
13548.91 -12671.04 ≈ 877.86
Choice D, $877.96, is the best match for this value.
__
Additional comment
The actual savings will depend on the details of rounding of intermediate values in the calculation, and on the timing of the early payment. If the loan is amortized over 17 years, so more is paid each month, the savings can be more than $5000.
Here, we have calculated the savings on the assumption that payment number 204 includes the payoff amount.
Using the loan formula, monthly payments are $458.14. Remaining balance after 17 years is approximately $58,214.19. The savings would be approximately $1,785.81. The closest option to this calculation is C. $376.36
To calculate the amount saved by paying off the loan 3 years early, we need to find out the remaining balance of the loan after 17 years (20 years - 3 years). Then, we compare the remaining balance to the original balance to find the savings.
Let's break down the steps:
1. Find the monthly interest rate (r):
[tex]\[ r = \frac{4.4\%}{12} = \frac{0.044}{12} \][/tex]
2. Calculate the total number of payments (n):
[tex]\[ n = 20 \times 12 = 240 \text{ months} \][/tex]
3. Use the formula for the monthly payment (PMT) of a loan:
[tex]\[ PMT = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \][/tex]
where:
P = principal amount (loan amount)
r = monthly interest rate
n = total number of payments
We'll use PMT to find out the monthly payment Arthur has to make.
4. Use the monthly payment (PMT) to find the remaining balance after 17 years (204 months).
5. Finally, calculate the savings by comparing the remaining balance to the original loan amount.
Let's do the calculations:
1. Monthly interest rate:
[tex]\[ r = \frac{0.044}{12} = 0.00367 \][/tex]
2. Total number of payments:
[tex]\[ n = 20 \times 12 = 240 \text{ months} \][/tex]
3. Monthly payment (PMT):
[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot (1 + 0.00367)^{240}}{(1 + 0.00367)^{240} - 1} \][/tex]
[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot (1.00367)^{240}}{(1.00367)^{240} - 1} \][/tex]
[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot 1.937}{1.937 - 1} \][/tex]
[tex]\[ PMT = \frac{429.33}{0.937} \][/tex]
[tex]\[ PMT= 458.14 \][/tex]
4. Remaining balance after 17 years (204 months):
[tex]\[ PV = \frac{PMT \cdot (1 - (1 + r)^{-n})}{r} \][/tex]
[tex]\[ PV = \frac{458.14 \cdot (1 - (1 + 0.00367)^{-204})}{0.00367} \][/tex]
[tex]\[ PV = \frac{458.14 \cdot (1 - 0.533)}{0.00367} \][/tex]
[tex]\[ PV = \frac{458.14 \cdot 0.467}{0.00367} \][/tex]
[tex]\[ PV = \frac{213.94}{0.00367} \][/tex]
[tex]\[ PV = 58214.19 \][/tex]
5. Savings:
Savings = 60000 - 58214.19
Savings ≈ 1785.81
So, Arthur would save approximately $1785.81 by paying off the loan 3 years early.
The closest option to this calculation is C. $376.36
Two corresponding side of similar pentagons are 12 cm and 28 cm.
what is the ratio of the areas of the pentagons?
A. 12/28
B. 27/343
C. 9/49
food costs are expected to rise 6% each month for the next year. Which series correctly depicts the cost (to the nearest cent) for the next three months if the current cost is $150 per month?
a. $150.00 + $159.00 + $168.00
b.$150.00 + $159.00 + $168.54
c.$159.00 + $168.00 + $177.00
d.$159.00 + $168.54 + $178.65
Answer:
the final answer is the last option, D
Step-by-step explanation:
What is value of M in the figure below?
Based on the right-angled triangle, the value of m is equal to: C. [tex]\sqrt{95}[/tex].
What is the geometric mean (leg) theorem?According to the geometric mean (leg) theorem, the length of the leg of a right-angled triangle is the geometric mean between its hypotenuse and the segment of the hypotenuse which is adjacent to that leg.
Mathematically, the geometric mean (leg) theorem can be modeled by the following formula;
Hypotenuse/leg = leg/part
where;
hypotenuse = 14 + 5 = 19
leg = m
part = 5
By applying geometric mean (leg) theorem, the length of the part (x) can be calculated as follows;
19/m = m/5
By cross-multiplying, we have the following:
[tex]m^2=19 \times 5\\\\m^2=95\\\\m=\sqrt{95}[/tex]
Read more on geometric mean here: brainly.com/question/26257841
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A six-sided die is thrown 50 times. the numbers of occurrences of each face are shown below. face 1 2 3 4 5 6 count 12 5 9 11 6 7 can you conclude that the die is not fair?
The gpa at the super university has a normal distribution with a mean 2.29 and standard deviation 1.29 to be an honors student at this university your GPA has to be in the top 20% what is the smallest gpa you need to have to be an honors student?
Identify the function in which Y varies directly with X
If (2 − 3i) + (x + yi) = 6, what is x + yi? 4 + 3i 4 − 3i -4 − 3i -4 + 3i 4x + 3i
Find the length of the arc shown in red. Leave your answer in terms of x.
Sandra is traveling 19 mph on her bicycle. After 2 hours, how far will she have traveled?
what is the factored form of the expression? 4x^2-81y^2
do the scatter plot .........................
Jean gets an allowance of $15 each month plus an extra $2 for each chore she completes around the house. How much allowance will she earn if she does x chores in a month?
a. 15x + 2 dollars
b. 2x dollars
c. 2x + 15 dollars
d. 17x + 15 dollars
How can 52/9 be expressed as a decimal?
For 52/9 to be expressed as a decimal, you need to divide the fraction.
52/9 = 5.78 (rounded by the 1hundreds in the decimals place).
If the perimeter of a rectangle is 52 cm and the area is 165 square cm, then what are the dimensions of the rectangle?
Answer:
11 cm by 15 cm
Step-by-step explanation:
The perimeter is double the sum of length and width, so that sum is 26 cm. The area is the product of length and width, so you want to find two numbers whose product is 165 and whose sum is 26.
165 = 1·165 = 3·55 = 5·33 = 11·15
The numbers in the last factor pair total 26. These are the dimensions.
The dimensions are 11 cm by 15 cm.
what is the minimum value that the graph of y=sin x assumes?
can someone help me 3y-20=8y
which picture justifies wheather -3x(5-4)+3(x-6) is equivalent to -12x-6
Answer:
Your answer would be a. or the first problem.
Step-by-step explanation:
Create a box and whisker plot for the average daily temperatures in Tucson, Arizona, in December: 67, 57, 52, 51, 64, 58, 67, 58, 55, 59, 66, 50, 57, 62, 58, 50, 58, 50, 60, 63
Normal Distributions
I couldn't see the whole graph in the answer above, but using the quartiles, I chose graph A and that was right.
1. b. mean=75.8, median=76.5, mode=63
2. a. dots at 50, 53.5, 58, 62.5, and 67
3. c. 30th percentile=105, 90th percentile=176.
This is a controversial question because some of the numbers repeat, but as of 5/19, answer c is right.
4. d. mean=8, variance=18.3, standard deviation=4.3
5. a. 2
6. b. 22%
7. d. a^6-30d^5+375d^4-2,500d^3+9,375d^2-18,750d+15,625
8. a. 93%
9. b. 16%
10. c. 84%
"a fair coin is tossed 5 times. what is the probability of exactly 4 heads?"
9=7x-13x-21 show step by step
I really really need help with this please.