To calculate how long it takes for an investment to earn a certain amount in simple interest, use the formula T = I / (PR), where I is the interest, P is the principal, R is the rate of interest, and T is the time. For a $2000 investment at 4.5% interest to earn $495, it would take approximately 5.5 years.
Explanation:The subject of this question is Simple Interest. The formula for calculating simple interest is I = PRT, where I is the interest, P is the principal (the initial amount of money), R is the rate of interest per time period, and T is the time. In this case, we know the interest ($495), the principal ($2000), and the rate (4.5% or 0.045 as a decimal). We're trying to find out the time, so we rearrange the formula to T = I / (PR).
Substituting our known values, we get T = 495 / (2000 * 0.045). Doing the math, the time it takes for the investment to earn $495 is approximately 5.5 years.
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Find the area of a circle with a diameter of 10 units. Round answer to the nearest hundredth of a square unit.
Answer:
Step-by-step explanation:
The area of a circle is given by A = π*r²
If diameter is 10 units, the radius is 5, so:
A = π * 5² = 78,54units²
A wallet contains 23 bills. All the bills are $1 bills and $5 bills. There are 7 more $1 bills than 5 bills. How much money does the wallet contain
Final answer:
The wallet contains a total of $55, given that there are 8 $5 bills and 15 $1 bills.
Explanation:
The student's question involves determining the total amount of money in a wallet given a specific mix of $1 bills and $5 bills. According to the information provided, there are 23 bills in total, with 7 more $1 bills than $5 bills.
Let's denote the number of $5 bills as x. Therefore, there are x + 7 $1 bills. The total number of bills is the sum of the number of $1 bills and the number of $5 bills, which gives us the equation:
x + (x + 7) = 23
Solving the equation for x will give us the number of $5 bills:
2x + 7 = 23
2x = 23 - 7
2x = 16
x = 8
Now, since there are 8 $5 bills, and 7 more $1 bills than $5 bills, we have:
Number of $1 bills = 8 + 7 = 15
Thus, the total amount of money in the wallet is:
($5 × 8) + ($1 × 15) = $40 + $15 = $55
Therefore, the wallet contains $55.
Megan is checking her tax bill for the last year.
The tax rates were as follows;
-no tax on the first £11 000 of earnings
Final answer:
Marginal tax rate refers to the tax rate applied to each additional dollar of income. Individuals pay according to the bracket their income falls into, with higher rates applying only to income that exceeds certain thresholds. An example includes a single taxpayer earning $35,000 a year being in the 15% marginal tax rate bracket.
Explanation:
The student's question relates to understanding marginal tax rates and how they apply to an individual's income. Marginal tax rate is the tax rate incurred on each additional dollar of income, meaning as you earn more, you generally pay a higher tax rate on your incremental earnings beyond certain thresholds. However, it's important to note that lower tax rates apply to lower income brackets, meaning individuals pay progressively more only on the income that falls within higher brackets.
For instance, consider the marginal tax rate structure where the first $9,075 of income is taxed at 10%, the income from $9,075 to $36,900 at 15%, and income beyond $36,900 at 25%. If a single taxpayer earns $35,000 a year, their marginal tax rate is 15% because their last dollar earned falls into the 15% tax bracket. However, not all their income is taxed at 15%; the income up to $9,075 is taxed at 10%, and only the income over $9,075 up to $35,000 is taxed at 15%.
Write an equation in point-slope form of the line having the given slope that contains the given point. m=34m=34, (36,24)
What is the value of X? Make sure to show all of your work!
Deniz had a full gallon of milk. She poured out 4 cups of milk. There are 16 cups in 1 gallon. About what percent of the original volume is left?
Answer:
75% of the original volume is left.
Step-by-step explanation:
Deniz had a full gallon of milk, or 16 cups of milk, and then she poured out 4 cups of milk. That is:
[tex]\\ A_{full-gallon} = \frac{16}{16}[/tex] cups of milk, since [tex]\\ \frac{16}{16} = 1[/tex] or [tex]\\ 1 * 100\% = 100\%[/tex] of the original volume.Deniz poured out 4 cups of milk from the 16 available (or [tex]\\ \frac{4}{16}[/tex]).Then,
The total left is:
[tex]\\ Total_{left} = \frac{16}{16} - \frac{4}{16} = \frac{12}{16} = \frac{3}{4}[/tex], since we are dealing here with fractions with the same denominator.
In other words, [tex]\\ \frac{3}{4} = 0.75[/tex] is the amount of milk left in the container.
In terms of percentage, [tex]\\ \frac{3}{4} = 0.75[/tex] is equivalent to [tex]\\ 0.75*100\% = 75\%[/tex] of the original volume, because Deniz poured out [tex]\\ \frac{4}{16} = \frac{1}{4} = 0.25[/tex] or [tex]\\ 0.25*100\% = 25\%[/tex] from the original volume.
So, Deniz left 75% of the original volume of milk after pouring out 25% of it.
This can be represented in the graph below.
Answer:
75%
Step-by-step explanation:
Jennifer figures that she uses 2 pens per month. she started the year with 10 pens. how do i write the equation that represents the number of pens, y, she will have after x months
operations absolute value
|4 - 9| =
|4| -9 =
Scores on a test have a mean of 70 and q3 is 83. the scores have a distribution that is approximately normal. find p90. (you will need to first find the standard deviation.)
a. 94.84
b. 85.08
c. 85.31
d. 83.7
The value corresponding to the 90th percentile (p90) is 94.84. Option A is correct.
To find the value corresponding to the 90th percentile (p90), we first need to find the standard deviation of the scores.
We know that the third quartile (Q3) is 83, which corresponds to the 75th percentile (p75). Since the distribution is approximately normal, we can use the properties of the normal distribution to find the standard deviation.
In a standard normal distribution, the value corresponding to the p75 is approximately 0.6745 standard deviations above the mean. So, we can set up the following equation:
70 + 0.6745 * standard deviation = 83
Now, solve for the standard deviation:
standard deviation = (83 - 70) / 0.6745 ≈ 19.3047
Next, to find the value corresponding to the p90, we use the properties of the normal distribution again. The value corresponding to the p90 is approximately 1.2816 standard deviations above the mean.
Now, calculate p90:
p90 = 70 + 1.2816 * standard deviation
≈ 70 + 1.2816 * 19.3047
≈ 94.84
Rounding to two decimal places, we get p90 ≈ 94.84. So, the answer is (a) 94.84.
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To find p90 in a normally distributed set of scores, we need to find the standard deviation. Using the mean and q3, we can find the IQR and estimate the standard deviation. Finally, we can use the standard deviation to find the value corresponding to the 90th percentile.
Explanation:To find the value of p90 in a normally distributed set of scores, we need to first find the standard deviation of the scores. We know that the mean is 70 and q3 (the third quartile) is 83. Using the formula for the interquartile range (IQR = q3 - q1), we can calculate the value of q1. Subtracting q1 from q3 gives us the IQR. Since the distribution is approximately normal, we can assume that the IQR is approximately 1.35 times the standard deviation. Dividing the IQR by 1.35 gives us the standard deviation. Finally, we can use the standard deviation to find the z-score corresponding to the 90th percentile and then find the corresponding value in the original distribution using the mean and standard deviation. The correct answer is option (a) 94.84.
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How many six-letter passwords are there that use only lowercase letters with no letter repeated?
What happened to the glass blower who inhaled
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The function graphed is f(x). What is f(2)?
when x is on 2
y is on -3
answer is y=-3
180=2x+y which equation is used to find x
The value of x would be equal to (180-y)/2
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
To solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We are given the equation as- 180=2x+y
Now solving;
180=2x+y
180=2x+y
180-y=2x
(180-y)/2=x
x = (180-y)/2
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In the xy-plane, if the parabola wiry equation y=ax^2+bx+c, where a, b, and c are constants, passes through the point (-1,1), which of the following must be true?
2/3 is what percent of 1/4?
To determine what percent 2/3 is of 1/4, convert both fractions to percent form, where 1/4 is 25%. Converting 2/3 to a percent gives approximately 66.67%, and dividing this by 25% gives 266.68%. Thus, 2/3 is 266.68% of 1/4.
To find out what percent 2/3 is of 1/4, you first need to express the fractions in a way that allows comparison. A standard way of expressing a fraction as a percent involves having a denominator of 100. Since you know 1/4 equals 25 percent, you can use this as a basis for comparison with 2/3.
To convert 2/3 to a decimal, divide the numerator by the denominator: 2 divided by 3 equals approximately 0.6667. To then convert that decimal to a percent, multiply by 100, getting approximately 66.67 percent. To find what percent 2/3 is of 1/4, divide 66.67 by the percent value of 1/4, which is 25, and then multiply by 100 to get the percentage. This gives you (66.67 / 25) x 100 = 266.68 percent. So, 2/3 is 266.68 percent of 1/4.
This figure is a rectangle Select the three statements that describe all rectangles.
Given triangle XP’s is congruent to triangle dnf, find the values of x and y.
x = 3
y = 15
Let's establish the proportion below to find the value of x and y
XP / DN = XS / DF = PS / NF
Since only 2 sides of XPS is given, then
4y - 3 = 5717x + 3 = 54Therefore,
4y = 60
y = 60 / 4
y = 15
17x = 57
x = 57 / 17
x = 3
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Write an equation in point-slope form of the line having the given slope that contains the given point. y= 3 4 ,(5 1 3 ,2 7 8 )
John Tucker is interested in purchasing stock. He wants to determine the costs.
Answer: a0 =$97.5 ; a1 =$87.96 ; a2=$282.48; a3=$1,722.5 ; a4=$1,553.96 ; a5=$4,990.48
Step-by-step explanation:
Hi, to solve this problem we have to multiply each total by the commission in decimal form (6 / 100= 0.06).
So:
$1625 x 0.06 = $97.5
$1,466 x 0.06 =$87.96
$4,708 x 0.06 =$282.48
And finally, to obtain the total costs we have to add to each total the commission of the total.
$1625 + $97.5 = $1,722.5
$1,466 +$87.96 = $1,553.96
$4,708 +$282.48 = $4,990.48
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1.8 as a fraction????
According to one web page on the resale value of cars, a BMW that cost $71,000 in 2003 depreciates in value about 15% a year. How much was it worth in 2013?
71,000 *(1-0.15)^10 =
71,000*0.85^10 =
$13,978.08
we apply the exponential decay formula leading to an estimated worth of approximately $13,978.37 in 2013.
To calculate the value of a BMW that cost $71,000 in 2003 and depreciates at a rate of about 15% per year for 10 years, we will use the formula for exponential decay, which is:
V = [tex]P(1 - r)^t[/tex]
Where:
V is the final value after depreciation
P is the principal amount ($71,000)
r is the rate of depreciation (15%, or 0.15)
t is the time in years (2013 - 2003 = 10 years)
So, our calculation will be:
V = $71,000 *[tex](1 - 0.15)^{10}[/tex]
V = $71,000 * [tex](0.85)^{10}[/tex]
V = $71,000 * 0.19687
V ≈ $13,978.37
Therefore, the BMW would be worth approximately $13,978.37 in 2013.
The length of the side of a square is 8 radical 12 in. What is the area of the square?
The sum of two numbers is 47 and the difference is 1 . what are the numbers?
Can you create a rule relating library fines for new books to the number of days the book is kept? Write your rule in symbolic form, using F for the fine and d for number of days the book is kept.
total of the fine = C
you would need to multiply the amount of the fine by the number of days
so the equation would be C=Fd
what is the greatest possible whole number remainder if you divide any number by 41?
Which is bigger 4 kilometers or 4400 meters?
tim earns $150 a week plus $15.50 for each desk he assembles. write an inequality to represent how many desks he needs to assemble to make $400 in one week.
x = number of desks needed to make
equation: 150 +15.50x >= 400
solution:
150 +15.50x >=400
15.50x = 250
x = 250/15.50 = 16.129
he needs to assemble 17 desks
15.50*17 = 263.50 +150 = $413.50
There were 91 books on a shelf. Twenty-eight of the books were nonfiction, 13 of the books were poetry books, and the rest were fiction books. How many books were fiction?
Find the plane containing the points S, X, and V. Which statement is true?
Point Y is noncoplanar with points S, X, and V.
Point U is coplanar with points S, X, and V.
Point Z is coplanar with points S, X, and V.
Point C is coplanar with points S, X, and V.
Devon Price is a clerk typist. His annual salary is 18,720. What is his biweekly salary?
Answer:
Biweekly salary is $ 720.
Step-by-step explanation:
Given,
Annual salary = 18,720,
Number of weeks in a year = 52,
Thus, the number of bi weeks in a year = [tex]\frac{52}{2}[/tex] = 26,
Hence, the biweekly salary = [tex]\frac{\text{annual salary}}{\text{Number of bi weeks in a year }}[/tex]
[tex]=\frac{18720}{26}=\$ 720[/tex]