If you invest this money ($7,185.51 ) in an account that compounds monthly with an APR of 2.5%, how much will you have saved i) after 1 year? ii) after 3 years?
Answers
Explanation:
The principal is given below as
\(P=7185.81\)The APR is given below as
\(r=2.5\%=\frac{2.5}{100}=0.025\)Concept:
To figure out the the compund interest, we will use the formula below
\(A=P(1+\frac{r}{n})^{nt}\)For one year, we will have the amount be
\(\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ n=12,t=1 \end{gathered}\)By substituting the values, we would have
\(\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=7185.51(1+\frac{0.025}{12})^{1\times12} \\ A=7,185.51(1+\frac{0.025}{12})^{12} \\ A=7367.22 \end{gathered}\)Hence,
The amount ave after 1 year will be
\(A=7,367.22\)To calculate the amount for three years, we will have
\(\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ n=12,t=3 \\ \end{gathered}\)By substituting the values, we will have
\(\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=7185.51(1+\frac{0.025}{12})^{3\times12} \\ A=7,185.51(1+\frac{0.025}{12})^{36} \\ A=7744.54 \end{gathered}\)Hence,
The amount ave after 3 years will be
\(\begin{equation*} 7744.54 \end{equation*}\)Related Questions
A group of 62 students were surveyed, and it
was found that each of the students surveyed
like at least one of the following three fruits:
apples, bananas, and guavas.
34 liked apples, 30 liked bananas, 33 liked
guavas, 11 like apples and bananas, 15 liked
bananas and guavas, 17 like apples and
guavas, 5 liked three fruits. (20 pts)
• How many students liked apples, but not
bananas and guavas?
. How many students liked bananas only?
• How many students liked apples or bananas
but not guavas?
• How many students liked bananas or guavas
or apples?
• How many students liked like apples and
guavas but not bananas?
Answers
Answer:
\(29\) students liked apples, but not bananas and guavas at the same time. (\(11\) students liked apples and liked neither bananas nor guavas.)
\(9\) students liked bananas only.
\(26\) students liked apples or bananas but not guavas.
\(59\) students liked bananas or guavas or apples, (That is the number of students that liked one or more of the three fruits.)
\(12\) students liked apples and guavas but not bananas.
Step-by-step explanation:
Start by drawing a Venn Diagram. (Refer to the first attachment.)
The outermost rectangle denotes the set of all \(62\) students that were surveyed.The top-left circle denotes the set of surveyed students that liked apples.The top-right circle denotes the set of surveyed students that liked bananas.The other circle denotes the set of surveyed students that liked guavas.Using information from the question, fill in the number of students in each section.
Start with intersection of all three circles denotes the set of surveyed students that liked all three fruits.
The question states that there are \(5\) students in this set. Besides, this set isn't a superset of any other set. Therefore, write the number \(5\!\) in the corresponding place without doing any calculation.
Continue with the intersection of students that liked two fruits only. For example, the question states that \(11\) surveyed students liked apple and bananas. However, that \(11\!\) students also include the \(5\) surveyed students that liked all three fruits (apple, banana, and guava.) Therefore, only \(11 - 5 = 6\) surveyed students liked apple and banana only (but not guava.)
Similarly:
\(15 - 5 = 10\) surveyed students liked bananas and guavas only.\(17 - 5 = 12\) surveyed students liked apples and guavas only.The question states that \(33\) surveyed students liked guavas. However, among that \(33\!\) students:
\(10\) of them also liked banana but not apples (bananas and guavas only.) \(12\) of them also liked apples but not bananas (apples and guavas only.)\(5\) of them also liked apples and bananas (all three fruits.)Therefore, only \(33 - 10 - 12- 5 =6\) surveyed students liked guava but neither apple nor banana (guava only.)
Similarly:
\(34 - 6 - 5 - 12 = 11\) of the surveyed students liked apples but neither guava nor banana (apple only.)\(30 - 6 - 5 - 10 = 9\) of the surveyed students liked bananas but neither apple nor guava (bananas only.)Among the \(62\) surveyed students, \(62 - (11 + 6 + 9 + 12 + 5 + 10 + 6) = 3\) of them liked none of the three fruits.
Refer to the second diagram attached for the Venn Diagram with the corresponding numbers.
Students that liked apples but not bananas and guavas at the same time include:
Students that liked apples only.Students that liked apples and bananas, but not guavas (apple and banana only.)Students that liked apple and guavas, but not bananas (apple and guava only.)These three subsets include \(11 + 6 + 12 = 29\) surveyed students.
It was previously found that \(9\) students liked bananas only.
Students that liked apples or bananas but not guavas include:
Students that liked apples only.Students that liked bananas only.Students that liked apples and bananas, but not guavas (apple and banana only.)That include \(11 + 6 + 9 = 26\) surveyed students.
Among these surveyed students, \(11 + 6 + 9 + 12 + 5 + 10 + 6 = 59\) of them liked at least one of the three fruits.
It was previously found that among these surveyed students, \(12\) of them liked apples and guavas only. That gives the number of students that liked apples and guavas, but not bananas.
look at pic 10 pts will mark brainilest hhhionnia
Answers
I think
Given the function f(x) = 0.5|x - 41-3, for what values of x is f(x) = 7?
x = -24, x = 16
x= -16, x = 24
x=-1, x = 9
x = 1, x = -9
Answers
The values of x for which f(x) = 7 are x = 61 and x = 21.
To find the values of x for which f(x) = 7, we can set up the equation and solve for x.
The given function is f(x) = 0.5|x - 41| - 3.
Setting f(x) equal to 7, we have:
0.5|x - 41| - 3 = 7.
First, let's isolate the absolute value term:
0.5|x - 41| = 7 + 3.
0.5|x - 41| = 10.
To remove the absolute value, we can consider two cases:
Case: (x - 41) is positive or zero:
0.5(x - 41) = 10.
Multiplying both sides by 2 to get rid of the fraction:
x - 41 = 20.
Adding 41 to both sides:
x = 61.
So x = 61 is a solution for this case.
Case: (x - 41) is negative:
0.5(-x + 41) = 10.
Multiplying both sides by 2:
-x + 41 = 20.
Subtracting 41 from both sides:
-x = -21.
Multiplying both sides by -1 to solve for x:
x = 21.
So x = 21 is a solution for this case.
Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.
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Simplify this expression.
(4y^2 - 13y + 3)/ (2y^2 - 5y - 12) • (2y^2 + 9y + 9)/ (16y^2 - 1) • (y^2 + 3y - 28)/ (y^2 - 9)
Answers
Answer:
(y^2+3y-28)/(4y^2-15y-4)
Step-by-step explanation:
(4y-1)(y-3)(2y+3)(y+3)(y+7)(y-3)/(2y+3)(y-4)(4y+1)(4y-1)(y-3)(y+3)
= (y+7)(y-3)/(y-4)(4y+1)
= (y^2+3y-28)/(4y^2-15y-4)
Answer:
(y+7)/(4y+1).
Step-by-step explanation:
If we factor all the polynomials we get:
(4y-1)(y-3) . (2y+3)(y+3) . (y-4)(y+7)
-------------- ---------------- -------------
(2y+3)(y-4) (4y-1)(4y+1) (y-3)(y+3)
we see that (4y-1), (y -3), (2y+3), (y+3) and (y - 4) are in the numerators and denominators so we can cancel them out.
This leaves us with:
(y + 7)
--------
(4y + 1)
2x {3x [40 - (I0 x 2)]} = ?
Answers
the answer its 120 hope helps you
Find the value of the trig function indicated.
3)
tan 0
13
12
0pls help
Answers
The value of the identities are;
1. tan θ = 5/12
2. cot θ = √7/3
How to determine the identitiesTo determine the value of the identities, we need to take note of the different identities;
sinetangentcotangentsecantcosecantcosineFrom the information given, we need to take note that;
tan θ = opposite/adjacent
cot θ = inverse of tangent identity
cot θ = adjacent/opposite
then,
1. tan θ =
Opposite = 5
Adjacent = 12
tan θ = 5/12
2. cot θ = 4√7/12 = √7/3
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I need help! Please show your work, thanks!!
Answers
The amount that should be deposited today is given as follows:
$70,663.15.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
t = 15, A(t) = 115000, r = 0.033, n = 1.
Hence the deposit is obtained as follows:
115000 = P(1.033)^15
P = 115000 x (1.033)^(-15)
P = $70,663.15.
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Which pair of functions are inverses of each other?  A. f(x) = \sqrt[3]{{6x}}f(x)= 3 6x and g(x) = {\left( {\frac{x}{6}} \right)^3}g(x)=( 6 x ) 3  B. f(x) = 10x – 5 and g(x) = \frac{{x + 5}}{{10}}g(x)= 10 x+5 C. f(x) = \frac{4}{x} - 3f(x)= x 4 −3 and g(x) = \frac{{x + 3}}{4}g(x)= 4 x+3 D. f(x) = \frac{x}{8} + 3f(x)= 8 x +3 and g(x) = 8x – 3
![Which pair of functions are inverses of each other? A. f(x) = \sqrt[3]{{6x}}f(x)= 3 6x and g(x) = {\left(](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Ocu4yz8WkkurbTuo4VPpBveJGGaf6QYJ.jpeg)
Answers
Answer:
the answer is B
Step-by-step explanation:
![Which pair of functions are inverses of each other? A. f(x) = \sqrt[3]{{6x}}f(x)= 3 6x and g(x) = {\left(](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/RcYnx4ro0d2lxDNeoxg3kyrOVy7aCXQl.jpeg)
![Which pair of functions are inverses of each other? A. f(x) = \sqrt[3]{{6x}}f(x)= 3 6x and g(x) = {\left(](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/pGAK8O7Uip8F4I2JrRr1uky3xMQUzhap.jpeg)
A box of golf balls contains 10 balls. Each golf ball has a diameter of 3.6 centimeters. What is the total
volume of golf balls in 3 boxes?
about 1465.74 cm
c. about 1221.45 cm
b. about 732.87 cm
d. about 81.43 cm
Answers
Answer:
C
Step-by-step explanation:
the width of a rectangle is 9yds less . The area is 36sq yards
Answers
Answer:
17
Step-by-step explanation:
fhxc. t thug g h y yxhxg yxtzt
Rebecca David earns $427.50 per week as a manager at Marlin Department Store. She is married and claimed 1 allowance last year. She hopes to receive a refund on her next tax return by claiming no allowances this year. How much more in withholdings will be deducted weekly if she claims no allowances?
Answers
The amount that is going to be deducted as per withholdings on a per week basis is 61 dollars.
What is withholding tax?The sum of money that an employer withholds from an employee's gross salary and then sends to the government is referred to as withholding tax. In the United States, tax withholding is required of the great majority of workers. The amount withheld is credited against the employee's yearly income tax obligations.
The amount that is earned = 427.5 dollars
The period is 1 week = 7 days
withholding tax = 427.5 / 7
= 61 dollars.
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Find the equation of the line with the slope 3/2 through the point (-6,2)
Answers
Step-by-step explanation:
y-y1=slope (x-x1)
where x1=-6,y1=2 and slope=3÷2
y-2=3÷2{x-(-6)}
y-2=3÷2(x+6)
y-2=(3x+18)÷2 cross multiply
2y-4=3x+18 collect like terms
2y=3x+18+4
2y=3x+22....ans
A + A =2,A + B =3,A + B × 2 =??..only for geniuses
Answers
Answer: 5
Step-by-step explanation:
HELP!Does the graph represent a function and if so, why? Yes, there is more than one ordered pair in this list. Yes, no two sets of ordered pairs occupy the same location. No, some of the ordered pairs in this list have the same second element. No, some of the ordered pair in this graph have the same first element.
Answers
Answer:
No, some of the ordered pair in this graph have the same first element.
Step-by-step explanation:
A vertical line intersects the graph in as many as 3 places. Each of those has coordinates with the same first element. Because the number of points of intersection with a vertical line can be more than 1, the graph is not a function.
I will mark you brainiest!
Given an equilateral triangle with two vertices located at (-8, -5) and (3, 7), what is its perimeter?
A) 16.2 units
B) 32.4 units
C) 48.9 units
D) 63.2 units
Answers
The correct option is C) 48.9 units. To find the perimeter of the equilateral triangle, we first need to determine the length of one side of the triangle. Since the triangle is equilateral, all three sides are of equal length.
We can use the distance formula to find the length of one side of the triangle. Let's choose the two vertices located at (-8, -5) and (3, 7) to find the distance between them.
Distance between (-8, -5) and (3, 7) = √[(3 - (-8))² + (7 - (-5))²]
= √[11² + 12²]
= √(121 + 144)
= √265
Since the triangle is equilateral, all three sides are of the same length, so the length of one side of the triangle is also √265.
Therefore, the perimeter of the triangle is 3 times the length of one side:
Perimeter = 3 × √265
= 48.91 (rounded to two decimal places)
Therefore, the correct option is C) 48.9 units.
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If tano =
12\5
and coso
5\13
then what is sin ?
1
OA.
12
OB.
5
13
O c.
5
13
OD.
12
13
O E
12
13
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
\( \cos( \alpha ) = \frac{5}{13} \\ \)
\( \tan( \alpha ) = \frac{12}{5} \\ \)
\( \tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ \)
\( \frac{12}{5} = \frac{ \sin( \alpha ) }{ \frac{5}{13} } \\ \)
Multiply sides by 5 / 13
\( \frac{5}{13} \times \frac{12}{5} = \frac{5}{13} \times \frac{ \sin( \alpha ) }{ \frac{5}{13} } \\ \)
\( \frac{5 \times 12}{5 \times 13} = \sin( \alpha ) \\ \)
\( \frac{12}{13} = \sin( \alpha ) \\ \)
\( \sin( \alpha ) = \frac{12}{13} \\ \)
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Graph the line. pllzzzzzzzz
Answers
Answer:
Step-by-step explanation:
X: -2, -1, 0, 1, 2,...
Y: -2, -1, 0, 1, 2,...
(y=x)
problem referred below
Answers
Step-by-step explanation:
since x=0
then the answer is (1-0)(1+0)
= 1×1
=1
I have shown my answer on that picture that I have attached
PLEASE HELP
The table of values represents an exponential function.
What is the y-coordinate of -3f(x-1) when x = 0
Enter your answer in the box.
SEE PHOTO
Answers
The y-coordinate of -3f(x-1) when x = 0 is -63
What is the y-coordinate of -3f(x-1) when x = 0From the question, we have the following parameters that can be used in our computation:
The table of values
So, we have
-3f(x - 1)
When x = 0, we have
y = -3f(0 - 1)
This gives
y = -3f(-1)
From the table, we have
y = -3 * 21
Evaluate
y = -63
Hence, the y-coordinate is -63
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what is 2x+5y+2y+5x?
Answers
Given the initial expression
\(2x+5y+2y+5x\)We can simplify it as shown below
\(\begin{gathered} 2x+5y+2y+5x=2x+5x+5y+2y \\ =7x+7y \\ =7(x+y) \\ \Rightarrow2x+5y+2y+5x=7(x+y) \end{gathered}\)The most simplified expression is 7(x+y)
∠B=angle, B, equals
^\circ
∘
degrees
Round your answer to the nearest hundredth.
Answers
The value of the angle B from the trigonometric ratios is 53.13 degrees
What is the Pythagorean theorem?The Pythagorean theorem is a powerful tool for solving various problems involving right triangles. It allows us to find the length of a missing side in a right triangle when the lengths of the other two sides are known. It is also used to identify whether a triangle is a right triangle or not.
We have that;
TanB = 4/3
B= Tan-1(4/3)
B = 53.13 degrees
Hence we are going to have by the use of tan that the angle is 53.1 degrees
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I already wrote the ordered pair. Just write how the number pairs are related.
Answers
Answer:
it is related by 35 because you are adding 35.
Step-by-step explanation:
Please help!! Algebra!!!
Answers
Answer:
mathanyics it will help a little
Step-by-step explanation:
A woman bought some large frames for $18 each and some small frames for $4 each at a closeout sale. If she bought 16 frames for $148, find how many of each type she bought.
She brought ___ large frames.
She brought ___ small frames
Answers
6 large frames
10 small frames
$108 + $40 = $148
big frames + small frames = total frames
A trawler A is 40km west of another trawler B. A set off at 20kmh travel at 25kmh. What course should trawler B take to intercept trawler A
Answers
Trawler B should take a course that is 18 degrees east of north.
How to explain the angleIn order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.
Here are the steps to find the course that Trawler B should take:
Draw a diagram of the situation.
Label the two trawlers A and B.
Draw a line representing the direction that Trawler A is traveling.
Draw a line representing the direction that Trawler B should travel.
Measure the angle between the two lines.
The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.
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Chemicals A and B react to form one of
two different compounds. When 1 mole of
Chemical A reacts with 1 mole of Chemical
B, the product is 1 mole of a compound with
a molar mass of 72 grams. When 2 moles of
Chemical A react with 3 moles of Chemical
B, the product is 1 mole of a compound with
a molar mass of 160 grams. What is the molar
mass, in grams, of Chemical A? (Note: The
product compound is the only compound
produced by the reaction.)
Answers
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Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
Subtract m + 8 from 5m + 11.
???
Answers
Answer:
=−4m+19
Step-by-step explanation:
Answer:
I think it might be 4m + 19
not sure how to do this
Answers
The new vertices of the figure are (4,8), (16,28), (8,-20).
To find the new vertices of the figure after the transformation with a scale factor of 4, we can multiply the coordinates of each vertex by 4.
(1, 2) → (4, 8)(4, 7) → (16, 28)(2, -5) → (8, -20)Therefore, the new vertices of the figure after the transformation are (4, 8), (16, 28), and (8, -20).
The answer is (B) (4,8), (16,28), (8,-20).
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The perimeter and area of a rectangle are 22 cm
and 30 cm² respectively. Find the length and
breadth of the rectangle
Answers
The perimeter and area of a rectangle are (5,6) and (6,5).
The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.
A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.
The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.
The perimeter of the rectangle:
P=2l+2w=22
divide 2 into both sides
l+w=11 -------------> (1)
w=11-l
Area of the rectangle:
l*w=30
l(11-l)=30
11l-l^2-30=0
l^2-11l+30=0
By factor method,
(l-5)(l-6)=0
l=5,6.
Substitute this value in w,
l=5 implies w=6
l=6 implies w=5
There we have two solutions.
The length and breadth of the rectangle is
(5,6) and (6,5).
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