Sophia invests $12,500 in an account that earns 4% annual simple interest. Assuming she makes no additional deposits or withdrawals, how much interest will Sophia earn after 3 years?

Answers

Answer 1

[tex]\text{Simple interest formula:}\\\\A=P(1+rt)\\\\\text{Plug in your given values:}\\\\A=12,500(1+0.04(3))\\\\\text{Solve:}\\\\A=12,500(1+0.04(3))\\\\A=12,500(1+0.12)\\\\A=12,500(1.12)\\\\A=14,000\\\\\boxed{\$14,000}[/tex]

Answer 2

Sophia will earn $14, 000 in interests after 3 years.

What is Interest?

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

We have,

Sophia invests $12,500 in an account.

R= 4%

Time= 3 years

So, Amount = P(1+ rt)

A = 12500 (1 + 0.04(3))

A = 12500 ( 1 + 0.12)

A = 12500 + 1.12

A = $14, 000

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Related Questions

In a survey, 15 high school students said they could drive
and 15 said they could not. Out of 60 college students
surveyed, 30 said they could drive. Micah concluded that
knowing that a person is in college means they are more
likely to drive. Is Micah's conclusion correct?

Answers

Answer:

No

Step-by-step explanation:

this is because only 50% of the college students said they could drive there fore it doesn't make sense.

Answer:No, Micah is not correct. Since there are equal numbers in the group that drive and the group that doesn’t drive, the relative frequency for each is 50%. Because the relative frequencies are the same, there is no association between the variables.

Step-by-step explanation: its on e2020

Find the rule of f(2)

Answers

25. 5 x 5 is 25 hope this helps :)

Answer:

f(2) = 25

Step-by-step explanation:

Given

f(x) = [tex](5)^{x}[/tex]

To evaluate f(2) substitute x = 2 into f(x)

f(2) = [tex](5)^{2}[/tex] = 25

5. A bag contains 4 green marbles and 5 white marbles. Suppose a marble is
randomly selected. What are the odds in favor of picking a white marble?
A 4 to 5
OB 5 to 4
c 4 to 9
D
5 to 9

Answers

Answer:

d

Step-by-step explanation:

Taylor is thinking of a three-dimensional object.
All interior angles are right angles.
The object has 8 vertices.
Only 4 of the object's 6 faces are congruent.
Which figure best describes the object that Taylor is thinking of?
A.
cube
B.
rectangular prism
C.
triangular prism
D.
square pyramid
NEED HELPP

Answers

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Name the quadrilateral with the most specific name that will describe it.
A) parallelogram
B) isosceles trapezoid
C) square
D) rectangle

Answers

Answer: a) parallelogram

Step-by-step explanation:

Top side and bottom side are same lengths/parallel

Angles in a quadrilateral add up to 360 degrees

105+75*2=360

Final answer:

The most specific name for the quadrilateral described is a (C) square because it has equal sides and all right angles, which is more specific than a rectangle, isosceles trapezoid, or a parallelogram.

Explanation:

The question asks to name the quadrilateral with the most specific name. The answer is (C) square. A square is a special type of rectangle with all sides of equal length, which is itself a type of parallelogram. A square is more specific than a rectangle, isosceles trapezoid, or a generic parallelogram because a square has all the properties of these shapes but also has equal sides and all right angles.

the fish Casey caught are listed below.
8 8 12 11 10 8 10 9
Casey catches one more fish that is 13 inches long. Which measure will remain the same when the 13-inch fish is included in the list of fish lengths?
(Highlight the correct answer)


Mean
Median
Mode
Range

Answers

Mean- 9.5
Median- 9.5
Mode- 8
Range- 4
Hope I could help you out! I plugged this into a calculator online if you want to double check!
The answer is going to be mean

Find the inner product for 5,2 multiply -3,7 and state whether the vectors are perpendicular.

Answers

Answer:

-1 ; no

Step-by-step explanation:

5 x -3 + 2 x 7 = -1

And since -1 is not zero the vector will not be perpendicular

Answer:

C on edge

Step-by-step explanation:

The rule is applied to ΔFGH to produce ΔF"G"H".
What are the coordinates of vertex F" of ΔF"G"H"?

(4, –1.5)
(4, –0.5)
(–1.5, 4)
(–0.5, 4)

ITS TIMED. I REALLY NEED HELP!!!

Answers

Answer:

(4, –1.5)

Step-by-step explanation:

If r = 4 and ^a8 = 100, what is the first term of the geometric
sequence?

Answers

The first term of the geometric  sequence is 0.0061

Step-by-step explanation:

The general form of geometric  sequence is a, ar, ar²,ar³,.......

where,

a is the first term of the sequence.r is the common ratio. Here, the common ratio r = 4.The 8th term of the sequence is 100. Hence n = 8.

The formula to find the nth term of the geometric sequence is given by :

⇒ [tex]n_{th} term = ar^{n-1}[/tex]

⇒ [tex]8_{th}term = a\times4^{8-1}[/tex]

⇒ [tex]100 = a \times 4^{7}[/tex]

⇒ [tex]100 = a \times 16384[/tex]

⇒ [tex]a = \frac{100}{16384}[/tex]

⇒ a = 0.0061

Therefore, the first term of the geometric  sequence is 0.0061

Answer:

The first term of the geometric  sequence is 0.0061

A carpenter finds that the measure of an angle formed between a vaulted ceiling and one wall is 67°. How many degrees is the supplement of this angle?

Answers

Answer:

113 degrees

Step-by-step explanation:

To find the supplement angle, subtract 67 degrees from 180 degrees

180 - 67 = 113 degrees

If this answer is correct, please make me Brainliest!

Consider the quadratic function fx=x2-8x-4. What is the value of the leading coefficient

Answers

Answer:

1

Step-by-step explanation:

Given

f(x) = x² - 8x - 4

The leading term in the expression is x²

with a coefficient of 1 ← leading coefficient

The leading coefficient of a quadratic function of equation  fx=x2-8x-4 is 1.

The leading coefficient of a quadratic function is the coefficient of the x² term. In the quadratic function f(x) = x² - 8x - 4, the leading coefficient is 1 because the coefficient of x² is always assumed to be 1 when not explicitly shown.

Look at the following graph of the given equation. Determine whether the equation is a function. Explain why or why not.
y = 2 x + 2
On a coordinate plane, points are at (negative 1, 0), (0, 2), (1, 4), (2, 6).

Answers

Answer:

Yes this is a function

Step-by-step explanation:

y = 2x + 2

0 = 2(-1) + 2

0 = -2 + 2

0 = 0

Yes

2 = 2(0) + 2

2 = 0 + 2

2 = 2

Yes

4 = 2(1) + 2

4 = 2 + 2

4 = 4

Yes

6 = 2(2) + 2

6 = 4 + 2

6 = 6

Yes

The equation y = 2x + 2 is a function, because each 'x' value corresponds to a single 'y' value, as per the mathematical definition of a function.

The graph of the equation y = 2x + 2 does indeed represent a function. In mathematics, a function is defined as a relation in which each input (or 'x' value) corresponds to exactly one output (or 'y' value). In the given coordinate pairs, you will notice that each individual 'x' value (such as -1, 0, 1, and 2) corresponds to a single 'y' value. Furthermore, the equation itself, y = 2x + 2, will always yield a single 'y' value for each 'x' value you substitute into it. This aligns with the definition of a function. Hence, the equation y = 2x + 2 is a function.

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A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 1,808.64 square​ feet? Use 3.14 for pi.

Answers

Answer:

The sprinkler can spread water in a radius of 24 feet.

Step-by-step explanation:

Since the sprinkler sends water in a circular pattern in order to find the distance at which it can spread the water we need to find the radius of the circle. The area of the circle is said to be 1808.64 and it's formula is given by:

area = pi*r²

1808.64 = 3.14*r²

r² = 1808.64/3.14 = 576

r = sqrt(576) = 24 feet

The sprinkler can spread water in a radius of 24 feet.

A new statue with a circular base is being unveiled in a downtown park. The statue's base has a radius of 15 feet. What is the area of the base? Round your answer to the nearest whole number. Use 3.14 for π.

Answers

Final answer:

The area of the circular base is 707 square feet, calculated using the formula A = πr², where π is 3.14 and the radius is 15 feet.

Explanation:

The question asks for the area of a circular base of a statue with a given radius. This is a question of geometry, and the formula for the area of a circle is A = πr², where A represents the area and r represents the radius. In this case, the radius given is 15 feet.

To calculate the area, we insert the value of the radius into the formula, so it becomes A = π(15)². Since we are asked to use 3.14 for π, the calculation becomes: A = 3.14 * 15², which equals 706.5 square feet.

However, since we have been asked to round to the nearest whole number, the final answer would be 707 square feet.

To find the area of the circular base of the statue, we can use the formula A = πr^2, where A is the area and r is the radius. In this case, the radius is given as 15 feet. Plugging this value into the formula, we get:

A = 3.14 * 15^2 = 3.14 * 225 = 706.5 square feet

Rounding to the nearest whole number, the area of the base is approximately 707 square feet.

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There are 870 boys and 800 girls in a school.
The probability that a boy chosen at random studies Spanish is 2/3
The probability that a girl chosen at random studies Spanish is 3/5
a) Work out the number of students in the school who study Spanish.
b) What is the probability, as a fraction in its simplest form, that a student
chosen at random from the whole school does not study Spanish?

Answers

Answer: a) 1060, b) [tex]\dfrac{61}{167}[/tex]

Step-by-step explanation:

Since we have given that

Number of boys = 870

Number of girls = 800

Probability that a boy chosen studies Spanish = [tex]\dfrac{2}{3}[/tex]

Probability that a girl chosen studies Spanish = [tex]\dfrac{3}{5}[/tex]

So, the number of boys in the school who study Spanish would be

[tex]\dfrac{2}{3}\times 870=290\times 2=580[/tex]

So, the number of girls in the school who study Spanish would be

[tex]\dfrac{3}{5}\times 800\\\\=3\times 160\\\\=480[/tex]

So, total number of students who study Spanish would be :

[tex]480+580=1060[/tex]

b) What is the probability, as a fraction in its simplest form, that a student

chosen at random from the whole school does not study Spanish?

​Number of students who do not study Spanish would be:

[tex](870+800)-1060\\\\=1670-1060\\\\=610[/tex]

So, the probability of students who does not study Spanish would be :

[tex]\dfrac{610}{1670}=\dfrac{61}{167}[/tex]

Hence, a) 1060, b) [tex]\dfrac{61}{167}[/tex]

Final answer:

There are 1060 students who study Spanish in the school. The probability that a student chosen at random from the whole school does not study Spanish is 610/1670.

Explanation:

To work out the number of students in the school who study Spanish, we need to find the number of boys and girls who study Spanish and add them together. The probability that a boy chosen at random studies Spanish is 2/3. So the number of boys who study Spanish is 870 * (2/3) = 580. The probability that a girl chosen at random studies Spanish is 3/5. So the number of girls who study Spanish is 800 * (3/5) = 480. Therefore, the total number of students who study Spanish is 580 + 480 = 1060.

To find the probability that a student chosen at random from the whole school does not study Spanish, we subtract the probability that a student does study Spanish from 1. The probability that a student does study Spanish is 1060 (students who study Spanish) divided by 1670 (total number of students in the school). Therefore, the probability that a student does not study Spanish is 1 - (1060/1670) = 610/1670, which is already in its simplest form.

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Which of the following are square roots of the number below? Check all that
apply.
64
A. -8
B. 64 1/2
C. 32
D. -(64) 1/2

Answers

Answer:

A

Step-by-step explanation:

Just square all of them to find 64

Final answer:

The square roots of 64 are -8 and 8. Neither 32 nor 64 1/2 are square roots of 64.

Explanation:

The square root of a number is a value that, when multiplied by itself, gives the original number. When dealing with real numbers, remember that a number can have two square roots: a positive root and a negative root.

For the number 64, we know 8 * 8 equals 64, so 8 is a square root. As a negative number multiplied by a negative number results in a positive number, -8 * -8 also equals 64. Therefore -8 is also a square root of 64.

Option A, -8, and B, '(64) 1/2' or -8, are correct. The square root of 64 is not 32 and 64 1/2.

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The roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?

x = –1 and x = ____

Answers

Answer:

x = -1 and x = 3

Step-by-step explanation:

x² – 2x – 3 = (x - 3) (x + 1) = 0

x = 3 or x = -1

Answer:

The roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?

x = –1 and x = 3

Step-by-step explanation:

Which is the best description of the graph of the function f(x)=60(1/3)^x?

Answers

Answer:

what do you mean the best description?

Step-by-step explanation:

Answer:

: the graph has an initial value of 60, and each successive term is determined by multiplying by 1/3

Step-by-step explanation:

f(xequal 6 [1/nitial value x=0, f(x) = 60*[1/3]^0 = 60*1 = 60x=1 ⇒f(1) = 60*[1/3]x=2 f(2) = 60*[1/3]^2 = f(1) * [1/3]x = n  f(n) = 60*[1/3]^n=60*[1/3]^(n-1)*[1/3] = f(n-1)*[1/3]

The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 5 units, then what is the value of k?

Answers

Step-by-step explanation:

k is the variable for the translations on the Y-axis so if u move the graph 5 units down then k would be 5

Answer:

k=5

Step-by-step explanation:

8. What is the maximum number of
right angles a triangle can have?

Answers

Answer:

1

Step-by-step explanation:

180 = 90 + 90 (F)

you must have 3 angles

Answer:

One.

Step-by-step explanation:

A triangle can only have one right angle because all three angles of a triangle MUST add up to be 180 degrees. That means if there are two right angles then the answer would automatically be over 180.

Example:

    90+90+1=181

Therefore, a triangle can only have one right angle

You roll a 6-sided die two times. What is the
probability of rolling a 6 the first time and 2
the second time?
*write your answer as a fraction

Answers

Answer:

First time : 1/6

Second time : 1/6

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Since it is a six-sided die, you will roll every number at least one time, making the answer 1/6

The label on a jacket said it was 80% wool, 14% nylon, and x% other fibers. What is the value of x?

Answers

Answer:

6%

Step-by-step explanation:

80%-14%=x%

every % = %

80%-14%=94%

100%-94%=6%

Answer:

6%

Step-by-step explanation:

80% + 14= 94.

94 is 6 digits away from 100, so the answer is 6%.

The senior class had 100 T-shirts to sell to raise money. They sold 52 T-shirts at $7.75 each. Then they sold the rest for $9.25 each. How much money did they collect overall?

$775.00
$847.00
$925.00
$853.00

Answers

Answer:

$847.00

Step-by-step explanation:

First you multiply 52 by $7.75

This gives you $403

Then you subtract 52 from 100 to find the remainder of shirts

This gives you 48

So then you multiply 48 by $9.25

This gives you $444

Then you add $444 and $403 giving you $847.00

Answer:

The answer is B: 847

Step-by-step explanation:

52 x 7.75 = 403

100 - 52 = 48

48 x 9.25 = 444

444 + 403 = 847

A person invested $690 in an account growing at a rate allowing the money to double
every 7 years. How much money would be in the account after 3 years, to the nearest
dollar?

Answers

Final answer:

The amount of money in the account after 3 years would be $828.

Explanation:

To determine the amount of money in the account after 3 years, we need to find the number of times the money doubles in a period of 3 years, given that it doubles every 7 years. To find this, we divide 3 by 7 to get the number of doubling periods which is approximately 0.4286. Since the money doubles every 7 years, we multiply the initial investment of $690 by 2 raised to the power of 0.4286 to find the final amount.

Using the formula A = P(1+r)^n, where A is the final amount, P is the initial investment, r is the interest rate per period, and n is the number of periods, we have P = $690, r = 100% (as the money doubles), and n = 0.4286. Substituting these values into the formula, we get A ≈ $827.84. Hence, the amount of money in the account after 3 years, to the nearest dollar, would be $828.

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Final answer:

To calculate the future value of an investment that doubles every 7 years after 3 years, we use the exponential growth formula with an annual interest rate determined by the Rule of 70, resulting in approximately $918.

Explanation:

To determine how much money will be in the account after 3 years given that the amount doubles every 7 years, we can use the formula for exponential growth. The formula is A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Since the money doubles every 7 years, the effective annual interest rate 'r' that would cause this can be found using the Rule of 70. The Rule of 70 states that to find the number of years required to double the money at a given interest rate, you divide 70 by the annual interest rate. Here, we have that number already (7 years), so we can rearrange to find the interest rate: rate = 70 / time to double. Therefore, the interest rate is 70 / 7, which equals 10% or 0.10 as a decimal.

However, we are looking for the amount after 3 years, not 7. Thus, we need to adjust our formula to account for this shorter time period:

A = P(1 + r)^t
A = 690(1 + 0.10)^3
A = 690(1.331)
A ≈ $918

So, after 3 years, the investment would grow to approximately $918, to the nearest dollar.

Does coordinate x or coordinate y represent a greater number?

Answers

Answer:

It depends

Step-by-step explanation:

There is no problem attached and it depends on the problem.

Answer:

MOSKAU

Step-by-step explanation:

How many solutions are there to the equation below?
13x + 195 = 13(x+15)
O
A. 1
OB. o
c. infinitely many

Answers

C because there is an exponent... as long as they match up they can go as high up as they want
The answer would be Infinitely Many/ C.

consider the following pair of equations:

x + y = -2
y= 2x + 10

if the two equations are graphed at what point do the lines representing the two equations intersect

Answers

Answer:

The lines representing these equations intercept at the point (-4,2) on the plane.

Step-by-step explanation:

When we want to find were both lines intercept, we are trying to find a pair of values (x,y) that belongs to both equations, which means that it satisfies both equations at the same time.

Therefore, we can use the second equation that gives us the value of y in terms of x, to substitute for y in the first equation. Then we end up with an equation with a unique unknown, for which we can solve:

[tex]x+y=-2\\x+(2x+10)=-2\\x+2x+10=-2\\3x+10=-2\\3x=-2-10\\3x=-12\\x=\frac{-12}{3} \\x=-4[/tex]

Next we use this value we obtained for x (-4) in the same equation we use for substitution in order to find which y value corresponds to this:

[tex]y=2x+10\\y=2(-4)+10\\y=-8+10\\y=2[/tex]

Then we have the pair (x,y) that satisfies both equations (-4,2), which is therefore the point on the plane where both lines intercept.

A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as h=- 16t^2 + 160t until it hits the ground. At what time(s)is it at a height of 9 feet above the ground?

Answers

That means the rocket will take 8 seconds to return to the ground. That means the rocket will be at height = h(t) = 112 at t = 7 and t = 1. That means the rocket will be 112 feet above the ground after 1 second and after 7 seconds.

what is -2(x-5)-4=-22 ??

Answers

Answer:

x = 14

Step-by-step explanation:

-2(x-5)-4=-22

Distribute

-2x +10 -4 = -22

Combine like terms

-2x+6 =-22

Subtract 6 from each side

-2x+6-6 = -22-6

-2x = -28

Divide each side by -2

-2x/-2 = -28/-2

x = 14

what is the slope between the points (4,-1) and (-4,3)?

Answers

The formula for slope is [tex]\frac{rise}{run} = \frac{y2-y1}{x2-x1}[/tex].

Subtract y1 from y2. (y1= -1, y2 = 3)

3 - -1 = 4

Now subtract x1 from x2. (x1 = 4, x2 = -4)

-4 -4 = -8

Divide the difference between the y coordinates by the difference between the x coordinates.

[tex]\frac{4}{-8}[/tex] or 4 ÷ -8 = -0.5

Answer:

The slope between the two points is -0.5.

Hope this helps love :)

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