The initial amount that Charlie financed to buy his car is approximately $5,364.93. This was calculated using the add-on interest loan formula with the provided monthly payments, interest rates, and number of payments.
Explanation:The question is asking us to find out the initial amount that Charlie financed to buy his car, given that he made monthly payments of $200 at an interest rate of 9% over a total of 30 payments. This is a simple interest loan problem in mathematics, specifically dealing with add-on interest. To determine the original loan amount, we will use the formula for calculating the loan amount in an add-on interest loan. It is calculated by dividing the amount paid in total by the sum of one plus the product of the rate and time: Loan Amount = Total Payment / (1 + (Interest Rate * Time)) .
In this case, the total repayment made by Charlie is $200 * 30 = $6,000. The interest rate is 9% per year, but since he is making monthly payments we need to divide this by 12 to get the monthly interest rate, which is 0.0075. The time is 30 months. Substituting these values into our formula gives: Loan Amount = 6,000 / (1 + (0.0075 * 30)).
Hence, after calculations, the initial amount that Charlie financed to buy his car is approximately $5,364.93.
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Hours worked: 40 Rate: $3.85 Wages: ?
Answer: $154.00
Step-by-step explanation:
I am assuming you are looking for how much the person made.
Multiply 40 hours times $3.85
$154.00
A math teacher gave her class two tests. 27% of the class passed both tests and 51% of the class passed the first test. What percent of those who passed the first test also passed the second test?
Find the half-life of an element which decays by 3.411% each day. Hint: use y = ab^t.
This is about half life of elements with exponential decay.
Half life = 20 years
We are given a decay rate of 3.411% per day.We are given;
y = ab^(t)
Where;
t is the half life
y = a/2 is the amount of substance remaining after decay
a is amount of substance initially
b = 100% - 3.411% = 96.589% = 0.96589
Thus;a/2 = a(0.96589)^(t)
a will cancel out to give;
0.5 = 0.96589^(t)
ln (0.5) = t(ln 0.96589)
t = ln(0.5)/ln(0.96589)
t = 19.968 days
This is approximately 20 days.
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find the coefficient of x^6 in the binomial expression of (2x+3)^9
How are midsegments of trapezoids and triangles alike? How are they different?
In both trapezoids and triangles, midsegments connect the midpoints of two sides. They are parallel to one side and their lengths are determined by the measurements of certain sides. The main difference lies in the number of midsegments each shape can have: a trapezoid can have only one, while a triangle can have three.
Explanation:In both trapezoids and triangles, a midsegment is a line segment that connects the midpoints of two sides. The similarity between these midsegments lies in their properties. In both cases, the midsegments are parallel to one of the sides of the figure (the base for the trapezoids and the third side for the triangles) and their length is equivalent to the average of the two bases in a trapezoid and half the length of the base in a triangle.
However, the main difference between midsegments of trapezoids and triangles is the number of such segments each figure can have. A trapezoid has only one midsegment, that connects the midpoints of the non-parallel sides, while a triangle can have up to three midsegments, one for each side of the triangle.
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Which expression is equivalent to 3(8 + 7)? 24 + 7 24 + 21 11 + 10 11 + 7
Simplify this and show your work :
-2(x-3) = 5x+1
-2x +6 = 5x+1
subtract 5 x from each side
-7x+6 = 1
subtract 6 from each side
-7x = -5
divide both sides by -7
x = -5/-7 = 5/7
x = 5/7
On Saturday, a local hamburger shop sold a combined total of 273 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Final answer:
To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.
Explanation:
The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.
Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.
Felicia invested money at an interest rate of 4%. After six months, she had earned $90.00 interest. How much money did Felicia invest?
Answer:
the answer is 4500 i got it right
Step-by-step explanation:
0.063 written as fraction or a mixed number
6840 round to nearest hundredth
A radio telescope has a parabolic surface, as shown below.
If the telescope is 1 m deep and 12 m wide, how far is the focus from the vertex? (5 points)
For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.
Explanation:For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.
Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.
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Henry recorded the number of miles he biked each day for a week. His miles were 25, 40, 35, 25, 40, 60, and 75. Enter the data into the statistics calculator. What is the standard deviation of the miles Henry biked to the nearest tenth?
The standard deviation of the miles Henry biked to the nearest tenth is 17.1. The standard deviation is calculated following the steps below.
Calculation of standard deviationFirst calculate the mean of the numbers that where given which is = 25 + 40 + 35 + 25 + 40 + 60+ 75/7
= 300/7
= 42.9
Then for each number, subtract the Mean and square the result.
(25 - 42.9)² = −17.9² = 320.41
(40-42.9)² = -2.9²= 8.42
(35-42.9)² = -7.9² = 62.41
(25-42.9)² = −17.9² = 320.41
(40-42.9)² = -2.9²= 8.42
(60-42.9)² = 17.1²= 292.41
(75-42.9)² = 32.1²= 1030.41
Then work out the mean of those squared differences. That is,
320.41+ 8.42+62.41+320.41+8.42+292.41+1030.41/7
= 2042.89/7
= 291.8
Take the square root of 291.8 which is,
√291.8 = 17.08215443
= 17.1 to the nearest tenth.
Therefore, the standard deviation of the miles Henry biked to the nearest tenth is = 17.1
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Answer:
17.1
Step-by-step explanation:
got it right
Which of the following fractions is an equivalent fraction in lowest terms to the fraction ? -276/-540
A. 23/45
B. -23/45
C. 69/135
D. -69/135
Consider a game in which player 1 moves first. the set of actions available to player 1 is a1={a,b,c}. after observing the choice of player 1, player 2 moves. the set of actions available to player 2 is a2={a,b,c,d}. at how many information sets does player 2 move?
a=one half bh solve for b
What are the coordinates of a point on the unit circle if the angle formed by the positive x-axis and the radius is 60?
What are the solutions to the quadratic equation (5y + 6)2 = 24? y = and y = y = and y = y = and y = y = and y =
For this case we have the following quadratic expression:
[tex] (5y + 6) ^ 2 = 24
[/tex]
From here, we must clear the value of y.
For this, we follow the following steps:
1) We clear the square term:
[tex] (5y + 6) =+/-\sqrt{24} [/tex]
[tex] (5y + 6) =+/-2\sqrt{6} [/tex]
2) Pass the value of 6 by subtracting:
[tex] 5y =-6+/-2\sqrt{6} [/tex]
3) Pass the value of 5 to divide:
[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]
Answer:
The solutions to the quadratic equation are:
[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]
[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]
The excluded values of a rational expression are 2 and 5. Which of the following could be this expression?
Answer: d on eng
Step-by-step explanation:
solve these equations fast.
(6 + 3i)(6 − 3i) =
(4 − 5i)(4 + 5i) =
(−3 + 8i)(−3 − 8i) =
Answer:
The correct answers are 45,41,73
Step-by-step explanation:
The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse
Without using a trigonometric ratio, find the distance from the ship to the buoy, B. Round the distance to the nearest tenth of a mile.
What is next number after 2 7 8 3 12 9
The variable Z is directly proportional to X. When X is 5, Z has the value 55.
What is the value of Z when X = 12
Which set of numbers does 8 2/3 belong to
in the final event of a track meet, 6 runners run a 100 meter dash. A) How many possible arrangements are there for the medal winners (gold, silver and bronze)? B) state whether it is a combination or permutation
Answer:
120 possible arrangements.
It is a permutation
Step-by-step explanation:
Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.
Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:
N= Total number possibilities:
[tex]N=6*5*4=120[/tex]
This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.
The permutation can be learnt by the formula:
[tex]N=\frac{p!}{(p-n)!}[/tex]
where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:
[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]
Balcony and orchestra tickets were sold for a Friday night concert last week. The balcony and orchestra tickets sold for $35 and $45, respectively. If 90 tickets were sold, and the total revenue was $3550 for the night, find the number of balcony and orchestra tickets sold.
805 tens in standard form
Evaluate the integral. (use c for the constant of integration.) sin^2(πx) cos^5(πx) dx
if x>2, then x^2-x-6/x^2-4=