Mathematics College

A bank received an initial deposit of $15,000, kept a percentage of this money in reserve based on a reserve rate of 3%, and loaned out the rest. The amount it loaned out eventually was all deposited back into the bank. If this cycle continued indefinitely, how much money eventually resulted from the initial deposit?
A $50,000
B $45,000
C $500,000
D $19,500

Answers

Answer 1

c 500,000 is the answer for the boys

Answer 2

Answer:

If this cycle continued indefinitely, how much money that eventually resulted from the initial deposit is

500,000 (C is the answer)

Related Questions

A chicken soup recipe calls for 9 cups of chicken stock. How much is this in quarts? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.

Answers

There are 2.25 quarts in 9 cups of chicken stock.

Here's how we can convert cups to quarts:

Since "quarts" are commonly used as whole numbers or mixed numbers, we don't usually express them in decimals.

Conversion factor: Remember that there are 4 cups in 1 quart. This is the conversion factor we'll use.

Calculation: To find the equivalent amount in quarts, we can multiply the number of cups by the conversion factor:

9 cups * (1 quart / 4 cups) = 2.25 quarts

Therefore, 9 cups of chicken stock is equivalent to 2.25 quarts.

Final answer:

To convert 9 cups to quarts, we can use the conversion factor 4 cups = 1 quart. Therefore, 9 cups of chicken stock is equal to 2 1/4 quarts.

Explanation:

To convert cups to quarts, we can use the conversion factor 4 cups = 1 quart.

Given that the recipe calls for 9 cups of chicken stock, we need to determine how many quarts this is.

Using the conversion factor, we can set up the following proportion: 4 cups / 1 quart = 9 cups / x quarts.

Cross-multiplying, we get 4 * x = 1 * 9, which simplifies to x = 9/4 or 2 1/4 quarts.

Therefore, 9 cups of chicken stock is equal to 2 1/4 quarts.

The tempature at 6:00 P.M. was 0°F. At midnight the tempature was 5° lower. By 6:00 A.M., the tempature was 4° lower than it had been at midnight. By noon, the tempature had gone up by 10°. What was the noontime tempature?

Answers

1 degree Fahrenheit your subtracting 0 from 5 and you get -5 then you subtract -4 from -5 and you get -9 then add 10 and you get 1

y – (-5) = -7 can you help me solve this equation

Answers

y - (-5) = -7
y + 5 = -7
y = -12

1.multiply - × -5 = 5 ( negative times a negative = positive

2. subtract 5 to both sides

3. you get y = -12

Use pictures and numbers to show all the ways to take apart 8

Answers

Test if 8 is divisible by all possible numbers. Start by testing the smallest number possible (1) and making your way up to the largest number possible (7). 8/1= 8 8/2=4 8/3= not a whole number 8/4 = 2 8/5 = not a whole number 8/6 = not a whole number 8/7 = not a whole number note we did not try 8/8 because that would not be considered "taking apart". After sorting out our test answers we can conclude that you can take 8 apart in three ways. In 8 groups of 1, in 2 groups of 4, and in 4 groups of 2. You can show this in pictures by illustrating these groups. See Below x x x x x x x x xx xx xx xx xxxx xxxx

Really need help with this, am I on the right track or no?

Answers

[tex]\bf a)\\\\ V=\stackrel{\textit{volume of cone}}{\cfrac{\pi r^2\cdot \boxed{3r}}{3}}+\stackrel{\textit{volume of hemisphere}}{\cfrac{2\pi r^3}{3}}\implies V=\cfrac{3\pi r^3}{3}+\cfrac{2\pi r^3}{3} \\\\\\V=\cfrac{5\pi r^3}{3} \\\\\\ S=\stackrel{\textit{lateral area of cone}}{\pi r\sqrt{r^2+\boxed{3^2r^2}}}+\stackrel{\textit{area of hemisphere}}{2\pi r^2}\implies S=\pi r\sqrt{r^2+9r^2}+2\pi r^2[/tex]

[tex]\bf S=\pi r\sqrt{10r^2}+2\pi r^2\implies S=\pi r^2\sqrt{10}+2\pi r^2 \\\\\\ S=\pi r^2(2+\sqrt{10})\\\\\\ b)\\\\ \stackrel{A=kS}{A=k\cdot \pi r^2(2+\sqrt{10})}\qquad \qquad \stackrel{C=kV}{C=k\cdot \cfrac{5\pi r^3}{3}}[/tex]

[tex]\bf c)\\\\ A\ge C\implies k\cdot \pi r^2(2+\sqrt{10})\ge k\cdot \cfrac{5\pi r^3}{3} \\\\\\ k\pi r^2(2+\sqrt{10})\ge \cfrac{5k\pi r^2r}{3}\implies \cfrac{\underline{k\pi r^2}(2+\sqrt{10})}{\underline{k\pi r^2}}\ge\cfrac{5r}{3} \\\\\\ 3(2+\sqrt{10})\ge 5r\implies 6+3\sqrt{10}\ge 5r\implies \cfrac{6+3\sqrt{10}}{5}\ge r[/tex]

Kyle works 40 hours at a rate of $10.75 per hour. He has total deductions of $87.25. What is his net pay?

Answers

First we need to figure out his total pay. 40hrs*$10.75=$430

He earned $430, but had deductions of $87.25. $430-$87.25=$342.75

Therefore, Kyle's net pay was $342.75.

what is square root of 8 plus square root of 50 minus square root of 72

Answers

The square root of 8 is 3, the square root of 50 is 7, and the square root of 72 is 8. 3+7-8=2.

Answer:

1.41421356237 making it a terminating decimal.

Step-by-step explanation:

2.82842712475

7.07106781187

8.48528137424

Simplified Answer

1.4 or 1.41

I hope this helped :) can you please mark as brainliest?

What property of real numbers is being used in the following (x+a)(x+b)=(x+a)x + (x+a)b ?

Answers

The distributive property. If we expand it, we get (x)(x+a)+b(x+a) by separating the variables in (x+b)

Distributive property. It shows that the first is being multiples the second.

What is the slope of the line passing through points A(−18,24) and B(16,−8)?
Enter your answer as a ratio, in simplest form, like this: 42/53

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -18}}\quad ,&{{ 24}})\quad % (c,d) B&({{ 16}}\quad ,&{{ -8}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-8-24}{16-(-18)}\implies \cfrac{-8-24}{16+18} \\\\\\ \cfrac{-32}{34}\implies -\cfrac{16}{17}[/tex]

How many liters of milk are in 334 gal (1 gal = 4 qt)? enter your answer in scientific notation?

Answers

1 gallon = 3.7854118 liter.

So 334 gallon = 334*3.7854118 = 1264.328 liters.

Now we can write it as
[tex]1264.328 = 1.264328 * 10^{3}[/tex]

So in scientific notation 334 gallon equal to [tex]1.264328*10^{3}[/tex]

1.2643275×10³ litres of milk are in 334 gals.

We need to find out how many litres of milk are in 334 gals (1 gal = 4 qt).

What is scientific notation?

The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.

We know that, 1 gallon=3.785411784 litre

Now, 334 gallon=334×3.785411784

=1,264.3275 litres

=1.2643275×10³

Therefore, 1.2643275×10³ litres of milk are in 334 gals.

To learn more about the scientific notation visit:

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What is: Q=1/2P+15, solve for P?

Answers

Answer:

2 ( Q - 15 ) = P

Step-by-step explanation:

[tex]Q =\frac{1P}{2} + 15[/tex]

First, take 15 to the left side.

[tex]Q -15=\frac{1P}{2}[/tex]

Multiply both sides by 2.

2 ( Q - 15 ) = 1P

Divide both sides by 1.

2 ( Q - 15 ) = P

Now, find the value of 316⋅2574⋅32.don't be intimidated by the complexity of this expression. finding this value consists of simply multiplying twice and then dividing once, tasks that are no more difficult than what you've done before.

Answers

Given
[tex]\frac{3}{16}\cdot\frac{2}{5}\div\frac{7}{4}\cdot\frac{3}{2}[/tex]
we solve the problem by breaking it into two part before we join them and divide.

For the first part, we have
[tex]\frac{3}{16}\cdot\frac{2}{5}=\frac{3}{40}[/tex]

For the second part we have
[tex]\frac{7}{4}\cdot\frac{3}{2}=\frac{21}{8}[/tex]

We now join the first part and the second part to divide as follows:

[tex]\frac{3}{40}\div\frac{21}{8}=\frac{3}{40}\cdot \frac{8}{21} = \frac{1}{35} [/tex]

A house has increased in value by
29%
since it was purchased. If the current value is
$387,000
, what was the value when it was purchased?

Answers

Final answer:

The original value of the house before the 29% increase was approximately $300,000, calculated by dividing the current value of $387,000 by the total percentage value of 129%.

Explanation:

The student's question revolves around the concept of percentage increase in Mathematics. To find the original value of the house before the increase, we need to consider the current value as 129% of the original value (since there was a 29% increase). Let's denote the original value as P.

So, we can set up the equation: 1.29 * P = $387,000. To solve for P, we divide both sides by 1.29: P = $387,000 / 1.29. Upon performing this division, we find that P, or the original purchase price of the house was approximately $300,000.

Final answer:

To find the value when the house was purchased, we set up an equation using the given information and solved for the original value. The value of the house when it was purchased was approximately $300,775.19.

Explanation:

To find the value of the house when it was purchased, we need to determine the original value before the 29% increase.

Let's assume the original value is x. The current value is $387,000, which is 29% higher than x.

We can express this as an equation: x + 0.29x = $387,000.

Combining like terms, we get 1.29x = $387,000.

Dividing both sides by 1.29, we find that x = $300,775.19.

Therefore, the value of the house when it was purchased was approximately $300,775.19.

Sweet T has 2 orange picks for every 5 green. If there are 21 picks in all, how many picks are orange?

Answers

Hello There!

The ratio of orange to green is 2:5
5 + 2 = 7
21/7 = 3
2 x 3 = 6
5 x 3 = 15.
It would be a ratio of 6:15 now.
There are 6 orange picks.

Hope This Helps You!
Good Luck :)

Answer:

The number of picks which are orange is:

Step-by-step explanation:

Sweet T has 2 orange picks for every 5 green.

i.e. if orange picks=2x then green picks=5x

There are 21 picks in all

i.e. 2x+5x=21

⇒ 7x=21

Dividing both sides by 7

⇒ x=3

So, number of orange picks=2×3=6

The number of picks which are orange is:

A car can travel 20 miles on a gallon of gas. Write and solve an inequality to show at least how many gallons of gas are needed to travel 100 miles? let g=gallons of gas

Answers

20g=100

This means 20 miles times the number of gallons needed to equal 100 miles

What is y=-9/2x-11 in standard form?

Answers

y=mx+b is the slope formula
So the equation you have listed follows the standard form of the slope formula
y=-9/2x(slope)-11(y-intersect)

Basically, you don't have to solve an equation that looks something like:
9/2x + y=-11 to put it into the standard form you have presented.

The standard form of the equation y = - 9/2x - 11 is 9x + 2y = - 22.

Given that,

The equation of a line is,

y = - 9/2x - 11

Now we can change the equation into standard form as,

y = - 9/2x - 11

Multiply both sides by 2;

2y = - 9x - 22

Add 9x on both sides,

2y + 9x = - 22

Arrange the equation,

9x + 2y = - 22

Therefore, the standard form is 9x + 2y = -22.

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The length of a rectangle is 9 inches more than twice it's with if the perimeter of the rectangle is 90 inches find its length and width

Answers

perimeter = 2L + 2W

L = 2w+9

90 = 2(2w+9) + 2W

90 = 4W+18 +2W

90 = 6W +18

72 = 6w

w = 72/6 = 12

l = 2*12+9 = 33

2x12 = 24, 2x33 = 66, 66+24 = 90

Length = 33 inches

Width = 12 inches

Write three more equations with integer coefficients and the variable x that have the same solution set {7, -1}. Explain.

Answers

The given values of abscissa and ordinate in the given are that which when substituted to the values of x and y in the equation will make the equation true. This means that the left and right-hand side of the equation will be equal. The established equations should have a basis of,

x + y = c

The equations are,

x + y = 6

Substituting x = 7 and y = -1,

7 + (-1) = 6 ; 6 = 6

The other two equations will be,

2x + y = 13 and,

x + 2y = 5

It is to be noted that countless of equations can be made with the given solution so long as the equation is valid.

what is the value of a laptop that is 1700.00 with a decrease of 35% for 5 years

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1700.00\\ r=rate\to 35\%\to \frac{35}{100}\to &0.35\\ t=\textit{elapsed time}\to &5\\ \end{cases} \\\\\\ A=1700.00(1-0.35)^5[/tex]

Find the cube number that is greater than 50 but less than 100

Answers

The cube number is 64. It is 4 x 4 x 4.

the cube number that is greater than 50 but less than 100 is 64

a central angle θ of a circle with radius 16 inches subtends an arc of 19.36 inches. find θ

Answers

I believe you're going to be working in degrees, there is a different scaling factor for radians (θ/2pi). The arc length formula is just the formula for the circumference of a circle scaled by how many degrees of the circle you have. In this case, radius is 16, arc length is 19.36. Then we have:
[tex]19.36=2 \pi (16)\frac{\theta}{360}[/tex]

Solve for θ.

The required measure of the angle Ф is given as Ф = 69.36°.

As mentioned in the question, a central angle θ of a circle with a radius of 16 inches subtends an arc of 19.36 inches.

What are the angles?

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
Angle = [arc/radius] 180/π
Substitute the values in the above equation,
Ф = [19.36/16]180/3.14
Ф = 69.36°

Thus, The required measure of the angle Ф is given as Ф = 69.36°.

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What is the simplified expression for the expression below?

4(3x – 2) + 6x(2 – 1)

Answers

4(3x – 2) + 6x(2 – 1)12x - 8 + 12x -6x18x - 8
answer is 18x – 8

its ethier 12 (2x-1)
or
24x-12

Brian irons 2/9 of a shirt in 3 3/5 minutes. How long will it take him to iron one shirt? At this rate, how long will it take to iron 5 shirts?

Answers

Alright, so since you can't multiply 2/9 into 1 super easily, we could divide it by 2 and multiply it by 9 then to get 1, so that's what we'll do. Since 3+3/5 is
15/5+3/5=18/5 (since 5 goes into 15 3 times), we can divide that by 2 to get 18/2/5=9/5. Multiplying that by 9, we get 9*9/5=81/5=the amount of minutes it would take to iron 1 shirt. Since 5 goes into 80 16 times, we can write 81/5 as 80/5+1/5=16+1/5. In addition, we need to find how long it would take to iron 5 shirts, and to do that we can multiply 1 shirt's time by 5, getting
81*5/5=405/5=81 minutes since 5 goes into 405 81 times.

Brian takes 16.2 minutes to iron one shirt and 81 minutes to iron five shirts at the rate of ironing 2/9 of a shirt in 3 3/5 minutes.

Brian irons 2/9 of a shirt in 3 3/5 minutes. To determine how long it takes to iron one full shirt, we can set up a proportion. Since 2/9 of a shirt takes 3 3/5 minutes, we can find the time for 1 shirt by multiplying 3 3/5 by 9/2.

First, we convert 3 3/5 to an improper fraction: (3 * 5) + 3 = 18/5. Now, multiply this by 9/2:

(18/5) * (9/2) = 81/5 = 16.2 minutes. Therefore, it takes 16.2 minutes to iron one shirt.

To find the time for 5 shirts, since the rate of ironing is constant, we multiply the time for one shirt by 5:

16.2 minutes * 5 = 81 minutes.

Brian will take 16.2 minutes per shirt, and 81 minutes for 5 shirts, at the given rate.

A car travels 208 miles on 10 gallons of gasoline. Mentally calculate the number of miles that the car travels on 1 gallon of gasoline.

Answers

10 gallons= 208
1 gallon: 208 ÷10= 20.8
(when you divide by 10, the decimal place jumps front 1 place!)
hope this helps!

If country a has 163,950 million more computers than country b and the total number of computers for both countries is 314,250 million, find the number of computers for each country

Answers

Country A = 163,950
Country B = ?
314250= B+[B+163950]
314250-163950= 2B
150300=2B
B=75150 millon
A=239100 millon

Answer:

Country A has 239100 million computers and country B has 75150 computers.

Step-by-step explanation:

Let country A has number of computers = x

and the number of computers in country B = y

By the statement " Country A has 163950 million more computers than country B"

x = y + 163950 ------(1)

Another statement states " Total number of computers in both the countries is 314250 million"

x + y = 314250 --------(2)

Now we place the value of x from equation (1) to equation (2)

y + y + 163950 = 314250

2y = 314250 - 163950

2y = 150300

y = [tex]\frac{150300}{2}[/tex]

= 75150

From equation 1

x = 75150 + 163950

= 239100

Therefore, country A has 239100 million computers and country B has 75150 computers.

How do you write 314,207 in standard form?

Answers

314207 is standard form....

It is already in standard form. If you you like in word form and expanded form then here. Word form: three hundred fourteen thousand, two hundred and seven. Expanded form: 300,000 + 14,000 + 200 + 7. Once again 314,207 is already written in standard form. Hope this helps!

Solve for n. 22 + n - 7 = 8n - 3n + n

Answers

22 + n - 7 = 8n - 3n + n
22-7=8n-3n
15=5n
n=3

hope this helps!

n = 3 because
Combine 22 and 7, and all the numbers in the other side, and you get
15+n=6n
And subtract n from both sides
And you get 15=5n
Divide both sides by 5
And you get 3=n

Find the absolute maximum and minimum values of the function f(x, y) = x2 + xy + y2 on the disc x2 + y2 ≤ 1

Answers

[tex]f(x,y)=x^2+xy+y^2[/tex]
[tex]\dfrac{\partial f}{\partial x}=2x+y[/tex]
[tex]\dfrac{\partial f}{\partial y}=2y+x[/tex]

Critical points occur when both partial derivatives vanish; this happens when

[tex]\begin{cases}2x+y=0\\2y+x=0\end{cases}\implies x=0,y=0[/tex]

The function has Hessian

[tex]\mathbf H(x,y)=\begin{bmatrix}\dfrac{\partial^2f}{\partial x^2}&\dfrac{\partial^2f}{\partial x\partial y}\\\\\dfrac{\partial^2f}{\partial y\partial x}&\dfrac{\partial^2f}{\partial y^2}\end{bmatrix}=\begin{bmatrix}2&1\\1&2\end{bmatrix}[/tex]

which at [tex](0,0)[/tex] has [tex]\det\mathbf H(0,0)=3>0[/tex]. And since [tex]\dfrac{\partial^2f}{\partial x^2}\bigg|_{x=0,y=0}=2>0[/tex], it follows that a local minimum occurs at [tex](0,0)[/tex] with a value of [tex]f(0,0)=0[/tex].

Meanwhile, we can parameterize the boundary by

[tex]\begin{cases}x=\cos t\\y=\sin t\end{cases}[/tex]

with [tex]0\le t\le2\pi[/tex]. So

[tex]f(x,y)=f(x(t),y(t))=F(t)=\cos^2t+\sin t\cos t+\sin^2t=1+\dfrac12\sin2t[/tex]

which has critical points when [tex]F'(t)=0[/tex]:

[tex]F'(t)=\cos2t=0\implies 2t=\dfrac\pi2+n\pi\implies t=\dfrac\pi4+\dfrac{n\pi}2[/tex]

We only have 4 points to worry about: [tex]t=\dfrac\pi4,\dfrac{3\pi}4,\dfrac{5\pi}4,\dfrac{7\pi}4[/tex]

Now,

[tex]F\left(\dfrac\pi4\right)=\dfrac32[/tex]
[tex]F\left(\dfrac{3\pi}4\right)=\dfrac12[/tex]
[tex]F\left(\dfrac{5\pi}4\right)=\dfrac32[/tex]
[tex]F\left(\dfrac{7\pi}4\right)=\dfrac12[/tex]

So we find that an absolute minimum occurs at [tex](0,0)[/tex] with a value of [tex]0[/tex], and two more extrema occur along the boundary when [tex]t=\dfrac\pi4[/tex] and [tex]t=\dfrac{5\pi}4[/tex], i.e at the points [tex]\left(\dfrac1{\sqrt2},\dfrac1{\sqrt2}\right)[/tex] and [tex]\left(-\dfrac1{\sqrt2},-\dfrac1{\sqrt2}\right)[/tex], both with the same maximum value of [tex]\dfrac32[/tex].

a line intersects the points (-23, -17) and (-13, -7). Find the slope of the line.

Answers

The slope of a line through points [tex]A(x_1, y_1)[/tex] and [tex]B(x_2, y_2)[/tex] is :

[tex]\displaystyle{ \frac{y_2-y_1}{x_2-x_1} [/tex]

or

[tex]\displaystyle{ \frac{y_1-y_2}{x_1-x_2} [/tex],

it is the same thing, BUT it it always y's over x's and always in the same order of 1 and 2:

don't write: [tex]\displaystyle{ \frac{y_1-y_2}{x_2-x_1} [/tex]

--------------------------------------------------------------------------------------------------

The slope of the line through the points (-23, -17) and (-13, -7) is :

[tex]\displaystyle{ \frac{-17-(-7)}{-23-(-13)}= \frac{-17+7}{-23+13}= \frac{-10}{-10}=1 [/tex]

Answer: 1

S.O.S I NEED HELP ON THIS QUESTION

What is the recursive formula for the geometric sequence with this explicit formula?

Answers

a(n) = 9.(-1/3)ⁿ⁻¹

for n = 1; a₁ = 9.(-1/3)⁰ = 9.(1) = 9

for n=2 , a₂ = 9.(-1/3)¹ = -9/3 = -3 or a₂ = a₁.(-1/3)¹

for n=3 ; a₃ = 9.(-1/3)² =9/9 =1 or a₃ = a₂.(-1/3)²

so a₁ =9 and

a(n) = a(n-1)(-1/3) (ANSWER A)

Final answer:

To write a recursive formula for a geometric sequence, you need to know the first term and the common ratio. The recursive formula is expressed as each term being a multiple of its preceding term.

Explanation:

The question asks us to find a recursive formula for a geometric sequence when its explicit formula is already known. A recursive formula for a geometric sequence defines each term of the sequence as a multiple of the previous term, typically expressed as an = r × an-1, where r is the common ratio and an is the nth term. The first term, often denoted by a1, must be provided to start the sequence. To obtain a recursive formula, you need to know the first term and the common ratio. The explicit formula normally has the form an = a1 × rn-1. Using this explicit formula, you would need to solve for a1 and r to write the recursive formula.

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