If the reserve rate is 6% and a bank receives a deposit of $14,000, how much of the $14,000 is the bank free to loan out?

Answers

Answer 1

Apex said $13160 was the right answer

Answer 2

The bank must keep 6% of the $14,000 deposit as a reserve, which amounts to $840. Therefore, it is free to loan out the remaining $13,160.

If the reserve rate is 6% and a bank receives a deposit of $14,000, the bank is required to keep 6% of that deposit as reserves. To calculate the amount the bank needs to keep in reserves, we multiply the total deposit by the reserve rate:

Reserve amount = Total deposit x Reserve rate

Reserve amount = $14,000 x 0.06 = $840

Now, to find out how much the bank is free to loan out, we subtract the reserve amount from the total deposit:

Amount available for loans = Total deposit - Reserve amount

Amount available for loans = $14,000 - $840 = $13,160

The bank can loan out $13,160 of the initial $14,000 deposit.

Related Questions

The daily intakes of milk (in ounces) for ten randomly selected people were: 26.0 13.0 13.5 14.8 19.1 13.6 21.6 30.8 15.8 14.1 find a 99% confidence interval for the population standard deviation σ.

Answers

Final answer:

To establish a 99% confidence interval for the population standard deviation, we first need to calculate the sample standard deviation of the data. We then use the Chi-Square distribution with the appropriate degrees of freedom to get the interval. The formula [√((n-1)*s²/χ²0.995,n-1), √((n-1)*s²/χ²0.005,n-1)] can be applied.

Explanation:

This question refers to constructing a 99% confidence interval for the population standard deviation using the information from a sample. The mentioned sample comprises measures of daily intakes of milk in ounces for ten randomly selected people. To address this, first, we need to calculate the sample standard deviation. After that, we use Chi-Square distribution (χ² distribution) to create the confidence interval for the standard deviation since population standard deviation (σ) is unknown.

Let's denote:

n as number of observations: n=10s as sample standard deviationχ²(α/2,n-1) as the χ² value for α/2 (± z-score for standard normal distribution) with n-1 degrees of freedom

99% confidence interval for the population standard deviation σ can be found using the formula:
[√((n-1)*s²/χ²0.995,n-1), √((n-1)*s²/χ²0.005,n-1)]
Here, χ²0.995,n-1 and χ²0.005,n-1 represent the values from χ² distribution table corresponding to 0.005 and 0.995 (For 99% confidence interval, α=1-0.99=0.01. α/2=0.01/2=0.005) with n-1 degrees of freedom.

Please note that all numbers should be rounded according to the context, and the final values are but estimates that should not be treated as 100% accurate.

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The sum of two numbers is 0.25. their quotient is 0.25. find the numbers.

Answers

[tex]n,\ m-the\ numbers\\\\n+m=0.25\qquad(*)\\\\n:m=0.25\to\dfrac{n}{m}=0.25\to n=0.25m\qquad(**)\\\\\text{Substitute}\ (**)\ \text{to}\ (*):\\\\0.25m+m=0.25\\\\1.25m=0.25\qquad\text{divide both sides by 1.25}\\\\\boxed{m=0.2}\\\\\text{Put the value of }\ m\ \text{to}\ (**):\\\\n=0.25(0.2)\\\\\boxed{n=0.05}\\\\Answer:\ \boxed{0.05\ and\ 0.2}[/tex]

Jamal baked muffins for the school bake sale. He made 12 corn muffins and 15 blueberry muffins. What is the ratio of blueberry muffins to all muffins?

Answers

The answer is 15:27 then simplify it to 5:9
hope it helps! <3

Answer:

5:9

Step-by-step explanation:

A principal of $3900 is invested at 6.5% interest, compounded annually. How much will the investment be worth after 5 years? Use the calculator provided and round your answer to the nearest dollar.

Answers

[tex]3900 \times 0.065 \times 5 = 1267.5 \\ 1267.5 + 3900 = 5167.5[/tex]

Answer:

The answer would to be able to multiply the answers together. For example, the answer for this question would be 5,343 dollars rounded to the nearest tenth.

Step-by-step explanation:

Which of the following sets of possible side lengths forms a right triangle? 12, 35, and 38 11, 60, and 61 9, 40, and 45 6, 12, and 13

Answers

The possible sides of a rectangle triangle are:
11, 60, and 61
Let's check it using the Pythagorean theorem.
We have then:
ROOT ((a) ^ 2 + (b) ^ 2) = c
Where,
a = 11
b = 60
ROOT ((11) ^ 2 + (60) ^ 2) = 61
Answer:
11, 60, and 61

Answer:

11,60, and 61

Step-by-step explanation:

What is the probability of drawing five face cards?

Answers

Total number of cards = 52
Total number of face cards = 12

P( 5 face cards) = (12/52)(11/51)(10/50)(9/49)(8/48) = 33/108290

Answer: 33/108290

A computer salesperson's monthly income depends on the amount of his sales. his monthly income is a salary of $1575 plus 9% of his monthly sales. write a linear equation for his monthly income for sales of x dollars. ( i=mx+b ).

Answers

Fixed salary = $1575

Commission = 9% = 0.09

Monthly Sales = x

Monthly income = 1575 + 0.9x

Answer: Monthly income = 1575 + 0.9x

The solution is, 1575 + 0.9x, is a linear equation for his monthly income for sales of x dollars.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Here, we have,

given that,

A computer salesperson's monthly income depends on the amount of his sales.

his monthly income is a salary of $1575 plus 9% of his monthly sales.

Fixed salary = $1575

Commission = 9% = 0.09

Monthly Sales = x

Monthly income = 1575 + 0.9x

Answer: Monthly income = 1575 + 0.9x

Hence, The solution is, 1575 + 0.9x, is a linear equation for his monthly income for sales of x dollars.

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N a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are: 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. what is the mean?

Answers

The mean would be 70

15 POINTS
What is the equation of the following graph in vertex form?

(parabolic function going down from the left through the point negative four comma zero and turning at the point negative three comma negative one and going up through the point negative two comma zero and then through the point zero comma eight and continuing up towards infinity)

y = (x − 3)2 − 1
y = (x + 3)2 − 1
y = (x − 4)2 − 2
y = (x − 4)2 + 8

Answers

the vertex is at x = -3 so there will be (x + 3)^2 in the answer.
And y coordinate of vertex is -1 so the answer is B.

Answer with explanation:

→The given curve is Quadratic,having two real roots,as it cuts X axis at two distinct points that is at ,-2 and -4.

→Graph is symmetrical about line , x=-3.

→This curve is a Parabola,opening in upward direction ,that is having Y axis as Axis of Symmetry.

→Parabola is defined as locus of all the points such that distance from fixed point called focus, to distance from fixed line called Directrix ,is always Constant.

→Point which divides PARABOLA in two symmetrical parts is called Vertex having coordinates (-3,-1).

Equation of parabola having vertex ,(-3,-1) and opening in Upward Direction,that is in vertical direction, is given by:

General Equation: Equation of parabola passing through point (a,b) and opening in upward direction and having focus (k,h) is

y-b=4 k× (x-a)²

So, the equation of parabola will be

→y-(-1)=4 k[x-(-3)]²

→y+1==4 k(x+3)²-----(1)

This parabola also passes through (-4,0) and (-2,0).

→0+1=4 k×(-4+3)²

→1=4 k×(-1)²

[tex]1=4 k\\\\k=\frac{1}{4}[/tex]

If you will substitute , x=-2 and y=0 in equation 1,you will get same value of k.

Equation of Parabola ,that is equation 1,can be written as

[tex]y+1=4\times\frac{1}{4}(x+3)^2\\\\y+1=(x+3)^2\\\\ y=(x+3)^2-1[/tex]

Option B: y=(x+3)²-1

A family took a trip. They spent $90.71 for gasoline, $153.00 on meals, $197.00 on amusements, and $73.38 on miscellaneous expenses. How much did the trip cost?

Answers

Hello!

Theoretically, the actual TRIP cost $90.71, because the extra money spent was on other things other than the transportation, which is the main part of the trip.

but in total, DURING that trip, they spent $514.09

I hope this helps, and have a nice day!

Make t the subject of the formula

Answers

Move all terms to the left side and set equal to zero.Then set each factor equal to zero.

[tex]t= \frac{4p+3}{p-2} [/tex]

Hopefully i helped, i suppose ill go answer the other one too hehe well mark brainly if possible ^.^

A lion’s heart beats 12 times in 16 seconds.how many heartbeats will it have in 60 seconds?

Answers

Hey there!

Here is your answer:

The proper answer to this question is "44 times".

Reason:

You have to solve it this way:

12 heartbeats=16 seconds

16+16=32
36+16=48
48+16=64
16-12=4
12+12=36+8=44

Therefore lions heart beats 44 times every 60 seconds.

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

how do i answer this question
[tex]7 - 3x = 2x + 7 - 5x[/tex]

Answers

Combine like terms on the right side of the equal sign:

7 - 3x = - 3x + 7

You can rearrange the right side to be:

7 - 3x = 7 - 3x

Because are the same thing, your answer ends up being all real numbers or infinitely many solutions. This means whatever number you plug in for the x-variable, the two sides will always be equal to each other.

The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions of the rectangle.

Answers

Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
[tex]x(2x - 6) = 2 {x}^{2} - 6x[/tex]

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

[tex]2 {x}^{2} - 6x = 108[/tex]
Subtract 108

[tex]2 {x}^{2} - 6x - 108 = 0[/tex]
Divide by 2.

[tex] {x}^{2} - 3x - 54[/tex]
[tex](x - 9)(x + 6) = 0[/tex]
Rule AB = 0, gives A is 0 or B is 0.

[tex]x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6[/tex]

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
[tex]x = 9[/tex]
Width
[tex]2x - 6 = 2 \times 9- 6 = 18 - 6 = 12[/tex]

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!

Which equation can be used to find the volume of this solid?(Please see attached picture)

V=3*5*4
V-3+5+4
V=5*4
V=3*5

Answers

To find the volume of a cube, you have to do length x width x height. So it would be 3 x 5 x 4

V = 3*4*5
Hope that helps

The circle graph shows the portions of the time that Ralph spent playing different games.

Which two types of games did Ralph spend a total of 9/10 of his time playing?

Choose exactly two answers that are correct. exactly two plz!!

A.
Truck Rider

B.
Space Cadet

C.
Trivia Tasks

D.
Wizard Maze

Answers

I would go with letters C and D.

I agree with you C and D

Roll a 5 win 6 dollars roll a 6 win 12 dollars if you play one time what is your expected reward

Answers

2 out of 30 chance fgdfkglhfldk

Based on the information marked in the diagram, ABC and XYZ must be congruent.
Can somebody help ??

A. True
B. False

Answers

Answer: False

There isn't enough info. We have a pair of hypotenuses that are congruent (AB and XY) based on the single tickmarks they share together. Other than that, we don't know anything about any other pairs of sides. We know that angle C = angle Z because of the square angle markers (they're both 90 degrees), but we don't know anything else about the other angles. The triangles could be congruent, or they may not be. There's no way to tell without more information.

Answer: The answer i false

Step-by-step explanation:

If area of a circle measures 16/25 pi cm square, what is the circumference of the circle in terms of pi

Answers

A = pi*r^2

(16/25)*pi = pi*r^2

16/25 = r^2

rt(16/25) = r

r = 4/5

C = 2pi*r
C = 2pi*(4/5)
C = (8/5) pi cm

Marie is buying an ice-cream sundae. There are 3 sizes of sundaes, 15 different ice-cream flavors, and 5 different toppings. How many ways can Marie choose a sundae?

Answers

225 different ways, because 3 x 15 x 5 = 225.

Since each size of sundae has 15 flavor choices, we can find the number of combinations by multiplying the size of sundaes with the different ice cream flavors. The same rule can be applied to the number of different toppings, so you can set up this equation:
[tex]3 \times 15 \times 5 = 225[/tex]
Multiplying them out, you can see that there are 225 different combinations of sundaes

Which linear equation has a slope of 3 and a y-intercept of –2?

Answers

The equation of the line that has a slope of 3 and a y-intercept of -2 is:

Y=3x-2, or B.

Answer:

I believe the answer is A.

Step-by-step explanation:

F(x)=5x^3-2x^2-3x Polynomial factoring

Answers

[tex]f(x)=5x^3-2x^2-3x=x(5x^2-2x-3)\\\\5x^2-2x-3=5x^2-5x+3x-3=5x(x-1)+3(x-1)=(x-1)(5x-1)\\\\f(x)=x(x-1)(5x-1)[/tex]

If you flip 3 coins, what is the probability of landing on heads only 2 times? list your answer as a fraction in simplest form.

Answers

Sample space is HHH HHT HTH THH HTT THT TTH TTT

No. of outcomes with only 2 heads = 3

S0 the Probability of just 2 heads = 3/8

How many dimes in 1898.59

Answers

all you do is divide by 10

there are 189 whole dimes

There are 18,985 dimes in $1,898.59.

Since there are 10 dimes per dollar, you'd multiply $1,898 by 10, to get your final answer (18,985 dimes).

I hope this helps!

What are the solutions of the inequality? 12x – 3x + 11 > 4x – (17 – 9x) a. x > –7 b.x > −1411 c. x < −1411 d.x < 7

Answers

Answer: option d. x < 7

Explanation:

1) given: 12x – 3x + 11 > 4x – (17 – 9x)

2) expand the parenthesis: 12x - 3x + 11 > 4x - 17 + 9x

3) combine like terms on each side: 9x + 11 > 13x - 17

4) subtract 9x and add 17 to both sides:9x - 9x + 11 + 17 > 13x - 9x - 17 + 17

5) combine like terms: 28 > 4x

6) divide both sides by 4: 7 > x

That is x < 7 which is the option d.

How many turning points are in the graph of the polynomial function?

2 turning points
3 turning points
4 turning points
5 turning points

Answers

A point of inflection is that point where the function changes sign.
We then have to look for the slope changes in the given function,
We have inflection points in:
4 points of the given graph.
Answer:
4 turning points

Answer: four turning points.

Explanation:

The turning points are those points where the graph changes direction, i.e. where the function changes from growing to decreasing or from decreasing to growing.

That is the typical behavior of polinomial and it is related with the degree of the polynomial.

In this case, since you have the graph you can directly telling the turning points. Those are near x = - 2, x = -1, x = 1 and x = 2, i.e. four turning points.

Those turning points correspond to local maxima (if the function changes from growing to decreasing) or local minima (if the function changes from decreasing to growing).

If you are examining a triangle with given measurements for one leg and the hypotenuse, how will you determine the measure of the unknown leg? Explain.

Answers

The Pythagorean Theorem.If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse

By using Pythagoras theorem, length of one leg of triangle can be determined.

Given:

A triangle with length of one leg and the hypotenuse

According to question,

Let the length of one leg of triangle which can be base [tex](b)[/tex] or perpendicular [tex](p)[/tex] and hypotenuse represented by [tex](h)[/tex].

Now, using Pythagoras theorem which states that if a triangle is right-angled ([tex]90[/tex] degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

From the figure,

In [tex]\Delta AOB, \;\angle O=90^\circ[/tex]

[tex]\rm{H^2=P^2+B^2}\\\rm{AB^2=AO^2+OB^2[/tex]

[tex]h^2=p^2+b^2[/tex]

[tex]b=\sqrt{h^2-p^2}\\[/tex]

[tex]p=\sqrt{h^2-b^2}\\[/tex]

Therefore, length of one leg of the triangle is determined by using Pythagoras theorem.

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I have a question about the application of definite integrals. I came up with the following integral:

[tex] \int\limits^5_0 {62.5 * 6 * 2 * x} \, dx [/tex]

This is equal to 9780. Unfortunately, 9780 ft-lb is not an answer, but 9375.0 ft-lb is! Can someone tell me what is wrong with my integral and if 9375.0 ft-lb is the answer to my question?

Answers

You have the correct integral set up. I'm not sure how you're getting 9780. The correct answer is 9375.0 foot-pounds

The volume of each slice is 6*2*DeltaX cubic feet. So the force pulling down on each slice is 62.5*6*2*DeltaX pounds as this is the weight of the slice.

The work done to move that slice x feet upward is 62.5*6*2*DeltaX*x or 62.5*6*2x*DeltaX as you wrote for your integrand.

Integrating with respect to x will effectively add up all the horizontal slices to get the total work done

See the attached image for the integral and steps leading to the answer of 9375

At the start of an experiment , there are 30 bacteria dish. The bacteria population is expected to grow at a rate of 180% each day. Which is the best prediction for the bacteria population after 7 years?

A.51,750
B.40,479
C.2682
D.1837

Answers

The problem is stated incorrectly. It should be 7 DAYS and NOT years.

ending amount = beginning amount * (1.8)^days
7 years = 2,555 days
ending amount = 30 * 1.8^7
ending amount = 30 * 61.2220032
ending amount = 1836.660096 or 1,837 (rounded)
answer is D.

A climber is standing at the top of Mount Kazbek, approximately 3.1 miles above sea level. The radius of the Earth is 3959 miles. What is the climber's distance to the horizon?

Answers

I just took a test for K12 with this question. Your answer will be 156.7 miles

The radius of the earth = OC = OB = 3959 miles

Peak of the Mount Kazbek = A = 3.1 miles

OA = OC + CA

OA = 3959 + 3.1 = 3962.1 miles

As OBA is a right triangle,

[tex] OA^{2} [/tex] = [tex] OB^{2} [/tex] + [tex] AB^{2} [/tex]

[tex] 3962.1^{2} [/tex] = [tex] 3959^{2} [/tex] + [tex] AB^{2} [/tex]

15698236.41 = 15673681 + [tex] AB^{2} [/tex]

[tex] AB^{2} [/tex] = 15698236.41 - 15673681

[tex] AB^{2} [/tex] =24555.41

AB = 156.701659

climber's distance to the horizon is 156.7 miles

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