The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t.
P = $1000, r = 3.5%, t = 3 months
Answers
The loan's future value A, or the total amount due at time t is $1105.
Given, P = $1000, r = 3.5%, t = 3 months.
We need to find the loan's future value A.
What is Simple interest?Simple interest is computed on the principal amount of a loan or the first deposit in a savings account. Simple interest does not compound, therefore an account holder will only get interest on the principal, and a borrower will never have to pay interest on previously collected interest.
We know that, \(Simple Interest=\frac{P\times\ T \times\ R }{100}\)
Now, \(Simple Interest=\frac{1000\times3\times3.5}{100\times12}\)
\(=\frac{10,500}{100} =105\)
As we know, \(Amount=Principal+Simple Interest\)
\(=1000+105=1105\)
Hence, the loan's future value A, or the total amount due at time t is $1105.
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Related Questions
\(f(x) = {x}^{2} - 4\)
for all instances of
\(x \leqslant 0\)
a) show that f has an inverse function
\( {f}^{- 1} \)
b) find
\(dom( {f}^{ - 1} ) \: and \: ran( {f}^{ - 1} )\)
c) find
\( {f}^{ - 1} (x)\)
Answers
Given function \(f(x)=x^2-4\) find its inverse by substituting x for f(x) and then solving for f(x).
\(x=f(x)^2-4\implies f(x)^{-1}=\sqrt{x+4}\)
Where \(x+4>=0\) for x to be real.
So solve the inequality and you will obtain the domain:
\(x+4>=0\implies x>=-4\implies x\in[-4,+\infty)\).
Range is equal to the range of square root function,
\(y\in[0, +\infty)\).
Hope this helps.
Find the output, y, when the input, x, is -9.
y =
Answers
Answer:
when x=-9, y=1
Step-by-step explanation:
the graph shows when the x is at -9, the y is at 1
When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse?
Answers
when the scale factor is 1, we have:
(side length of side opposite ∠A) / (length of hypotenuse) = sin A
When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.
The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.
In mathematical terms, when the scale factor is 1, we have:
(side length of side opposite ∠A) / (length of hypotenuse) = sin A
It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.
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WILL GIVE BRAINLIEST!!
How do identify which side is the hypotenuse of a right triangle?
Answers
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
(a) Find the probability that at least 13 flights arrive late .
Answers
Answer:
The probability that at least 13 flights arrive late is 2.5196 \(\times 10^{-6}\).
Step-by-step explanation:
We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.
A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
The above situation can be represented through binomial distribution;
\(P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........\)
where, n = number of trials (samples) taken = 18 Southwest flights
r = number of success = at least 13 flights arrive late
p = probability of success which in our question is probability that
flights arrive late, i.e. p = 1 - 0.80 = 20%
Let X = Number of flights that arrive late.
So, X ~ Binom(n = 18, p = 0.20)
Now, the probability that at least 13 flights arrive late is given by = P(X \(\geq\) 13)
P(X \(\geq\) 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)
= \(\binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}\)
= \(\binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}\)
= 2.5196 \(\times 10^{-6}\).
3) A couple will retire in 50 years; they plan to spend about £30,000 a year in
retirement, which should last about 25 years. They believe that they can earn 8
percent interest on retirement savings. If they make annual payments into a
savings plan, how much will they need to save each year? Assume the first
payment comes in one year.
Answers
There are $3,20242.29 will they need to save each year.
what is sinking fund?
The idea of a sinking fund is used in accounting and finance as a way for an individual or business to set aside money for things like retirement, future expenses, or even debt repayment.
A sinking fund is a clever way to set aside a small sum each month to save money for a particular purchase. Sinking funds operate as follows: Each month, you'll set aside money in one or more categories to be used at a later time.
Given:
P = $30,000
r = 8% = 0.08
t = 1
We have to find how much will they need to save each year.
Consider, the formula
\(A = P\frac{(1+r)^n-1}{r(1+r)^t} \\A = 30000\frac{(1+0.08)^2^5-1}{0.08(1 + 0.08)^2^5} \\A = 320243.28565\)
A = 320243.29
Hence, there are $3,20242.29 will they need to save each year.
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Solve for x in both problems
Answers
Answer:
x=3 and x=5
Step-by-step explanation:
its half of the bottom number
At a magazine, the ratio of
• artists to photographers is 3:2.
• photographers to writers is 1:3.
• writers to editors is 2:1.
There are 9 artists. How many
photographers, writers, and
editors does the magazine have?
Answers
Answer: 33
Artists : photographers = 3 : 2, and there are 9 artists, so there are 6 photographers. Then, the ratio of photographers to writers is 1 : 3, so there are 18 writers. Finally, there are half as many editors as writers, so there are 9 editors.
There are 6 + 18 + 9 = 33 photographers, writers and editors total.
i hope this helps! :D
solution of the line y − 2x = 6
Answers
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-2*x-(6)=0
STEP
1
:
Equation of a Straight Line
1.1 Solve y-2x-6 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
Which of the following can be the third side of a
triangle whose two sides are 16cm and 20cm
Answers
-20 cmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
help............................
Answers
Answer: C
Explanation: Anna is running 20 meters in 10 seconds so you divide the numbers by two and that is how you get your answer
What are the coordinates of the image of the point (-4,-5) after reflecting over the y-axis
Answers
So, the coordinates of the image of the point (-4,-5) after reflecting over the y-axis are:
x-coordinate: -4 (remains the same)
y-coordinate: 5 (becomes the opposite of the original y-coordinate, -5)
Therefore, the coordinates of the image are (-4, 5).
Carlos has a box full of 48 brown, 3 yellow, and 2 orange toy blocks. Determine the probability of Carlos randomly selecting an orange block from the box.
A
impossible
B
certain
C
likely
D
unlikely
Answers
Assume the cards are drawn sequentially and without replacement. In how many ways can 5 spades be drawn from a standard deck of 52 cards?
Answers
The number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement = 154440
In this question we have been given a standard deck of 52 cards.
We need to find the number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement.
We use the permutation formula.
We know that the number of ways to choose r elements from a set of n distinct objects where order does matter and replacements are not allowed.
^n(P_r) = n! / (n - r)!
We know that, in a standard deck of 52 cards, there are 13 spade cards.
So, n = 13
5 spades to be drawn
So, r = 5
Using the formula of permutation,
^13(P_5)
= 13! / (13 - 5)!
= 154440
Therefore, the number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement = 154440
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2. If x¹¹+101 is divided by x + 1, then what remainder do we get?
Answers
Answer:
Step-by-step explanation:
To get the remainder of (x-(-1)) we need to evaluate for -1,
\((-1)^{11}+101=-1+101=100\)
So if this is divided by x+1, it means that we can write
\(x^{11}+101=(x+1)P(x)+R\\\\so \ for \ x = -1\\\\(-1)^{11}+101=100=0*P(-1)+R=R\\\\\text{So the remainder is 100 !!}\)
thanks
Suppose you invest $1000 in an account paying 8% interest per year.
a) What is the balance in the account after 3 years? How much of this balance corresponds to ‘interest on interest’?
Answers
Answer:
wasdStep-by-step explanation:
10
Use the cards 1-10. Draw cards without replacing.
A.
B.
CÓ Ư
C.
D.
E.
F.
P(6, then 1)
P(even, then 5)
P(8, then odd)
P(3, then prime)
P(prime, composite)
P(even, then 3, then 5)
4
8
2
6
9
3
10
Answers
A. P(6, then 1) = 1/90
B. P(even, then 5) = 1/18
C. P(8, then odd) = 1/18
D. P(3, then prime) = 2/45
E. P(prime, composite) = 4/15
F. P(even, then 3, then 5) = 1/144
Given:
Total number of cards: 10
A. P(6, then 1):
P(6, then 1) = 1/10 x 1/9
= 1/90
B. P(even, then 5):
Number of favorable outcomes: 5 x 1 = 5
P(even, then 5) = 5/10 x 1/9
= 1/18
C. P(8, then odd):
Number of favorable outcomes: 1 x 5 = 5
P(8, then odd) = 1/10 x 5/9
= 1/18
D. P(3, then prime):
Number of favorable outcomes: 1 x 4 = 4
P(3, then prime) = 1/10 x 4/9
= 2/45
E. P(prime, composite):
Number of favorable outcomes: 4 x 6 = 24
P(prime, composite) = 4/10 x 6/9
= 4/15
F. P(even, then 3, then 5):
Number of favorable outcomes: 5 x 1 x 1 = 5
P(even, then 3, then 5) = 5/10 x 1/9 x 1/8
= 1/144
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A wallet contains 6 five dollar bills and 4 one dollar bills. Two bills are randomly selected (without replacement) and their total is noted. List the possible values for the random variable X = TOTAL value of the two bills you might select. Then determine the probability that each of these totals might occur: Find the expected value (mean) for the total value of the two bills selected: $____________________________ () =μ = ∑( · ()) Gain, x P(x)
Answers
Answer:
See if this works for you
Step-by-step explanation:
A 128 inch board is cut into 3 pieces. The second piece is 33 inches longer than the first piece, and the third is three times as long as the first. Set up an equation and solve it to determine the length of the three pieces.
Answers
Answer:
The first piece is 19 inches, the second is 52, and the third piece is 57.
Step-by-step explanation:
Solve for x using (x) + (x + 33) + (3x) = 128.
Find the midpoint of the segment joining X(6,5) and Y(9,2). I'm lost geomerty
Answers
Answer:
Is there a graph?
Step-by-step explanation:
I need help
I need help fast
Answers
Answer:
<STP=105°
Step-by-step explanation:
two interior angles equal one opposite exterior angle therefore
7x+6+7x+1=15x
group like terms
6+1=15x-7-7
7=15x-14x
7=x
for 15x
15 will multiply 7 and that is 105
Luna is buying food for a dinner party. She is going to buy 2 key lime pies that cost $8.99 each. Shrimp costs $8.50 a pound. She needs to spend less than $45 total. Write and solve an inequality to represent the situation. How many pounds of shrimp she can buy? Round to the nearest whole pound
PLEASE ANSWER WHOLE QUESTION NOT JUST THE SOLUTIONФωФ
Answers
Answer:
x=45- 2*8.99/8.50
x~3.18
3 lbs of shrimp
Approximately 3 pounds of shrimp Luna can buy with $45.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Luna is buying food for a dinner party. She is going to buy 2 key lime pies that cost $8.99 each.
Shrimp costs $8.50 a pound.
Let the number of pounds of Shrimp be x.
She needs to spend less than $45 total.
2×8.99+x×8.50<45
17.98+8.50x<45
Subtract 17.98 on both sides of an inequality, we get
8.50x<27.02
Divide 8.50 on both sides of an inequality, we get
x<3.17
x<3
Therefore, approximately 3 pounds of shrimp Luna can buy with $45.
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Determine whether each ordered pair is a solution of the equation y=2x+6
Answers
The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.
Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.
If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).
Here, x = 1 and y = 8.Substituting these values in the given equation,
we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,
the ordered pair (1, 8) is a solution of the equation y = 2x + 6.
Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12
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the similarly between constant and term
Answers
a constant is a term.
Explanation:A term refers to a number or variable or a combination of number and variable
A constant is a term without variables
For instance:
5x - 8
5x is a term as it is a combination of number and a variable
x is the variable
-8 is a number and a constant as it doesn't have a variable attached to it.
-8 is also a term.
Hence, a constant is a form of a term.
Tell whether the ordered pair is a solution of y=-2x+1.
Answers
the expression is,
y = -2x + 1
a)
the point is (-4,9)
put x = -4 and y = 9
9 = -2(-4) + 1
9 = 8 + 1
9 = 9
both values are same
so this pair is satisfying the equation.
b) the point is (0.5,0)
put x = 0.5 and y = 0
0 = -2(0.5) + 1
0 = -1 + 1
0 = 0
so this pair is satisfying the equation.
c)
the point (1,3)
put x = 1 and y = 3
3 = -2(1) + 1
3 = -2 + 1
3 = -1
so this pair is not satisfying the equation.
Emily's score for a Mathematics test was 5% higher than her score for an English test. If Emily scored 84 points for the Mathematics test, how many points did she score for the English test?
Answers
Answer:
80 points
Step-by-step explanation:
If score in English is x points and score in math is 5% higher then score in math
y = x + 0.05x
where 0.05 = 5% expressed as decimal
0.05x refers to the 5% increase in score
y = math score
y = x(1 + 0.05)
y = 1.05x
Given score in math = 84 this becomes
84 = 1.05x
x = 84/1.05
x = 80
So Emily's score in English was 80 points
gcmf of 25x²y³+55xy³
Answers
Answer: the answer is 5xy^3
5 plus the product of 39 and a number e
Answers
The required solution is 5+39e.
What is arithmetic?
The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications
Given :
Write down the question as an algebra problem, with the unknown as X
The unknown is a number plus 5, so we write it as (X+5). The product is four times (X+5), so we write it as 39(X+5). Set it equal to e, as per the question, 5+39e
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Plzzzz answer witch row is it
Answers
Answer:
The first row I believe, correct me if I'm wrong.
Is 15/0 just 15?
Thank you!
Answers
Answer: 15/0 = 15/0 = 15/0 = 15/0 = 0+15
Step-by-step explanation: 15/0 = 15/0 = 15/0 = 15/0 = 0+15