Patrick is a loan officer at a bank. He has
$2,000,000 to lend out and has two loan programs.
His home equity loan is currently priced at 6% per
annum, and his unsecured personal loan is priced
at 14%. The bank president wants Patrick to earn
a rate of return of 12% on the $2,000,000 available.
How much should Patrick lend out at 6%?

Answers

Answer 1

Answer:

1,500,000 at 14% and 500,000 at 6%

Step-by-step explanation:

x + y = 2,000,000

.14x + .06y = 240,000

[tex]0.14x+0.06\left(2000000-x\right)=240000\quad :\quad x=1500000[/tex]


Related Questions

Solve the following using the order of operations 15+5x8

Answers

Answer:

55

Step-by-step explanation:

Order of operations lists Multiplication before Addition.

So...

8 x 5 = 40

40 + 15 = 55

Answer:

55

Step-by-step explanation:

you have to do 5x8 first and you get 40 and then you add 15

A display case of plastic bracelets are marked 13 for $3. If Nate has $60, how many plastic bracelets can Nate get? (assume no other taxes or fees)

Answers

Answer:

$4

Step-by-step explanation:

We can write a ratio to solve

15 stickers       30 stickers

----------------- = -------------

2 dollars           x stickers

Using cross products

15x = 2*30

15x = 60

Divide by 15

15x/15 = 60/15

x = 4

Solve equation 3.2x=25.6

Answers

Answer:

x=8

Step-by-step explanation:

3.2x=25.6

Divide each side by 3.2

3.2x/3.2=25.6/3.2

x =8

Answer:

[tex]x = 8[/tex]

Step-by-step explanation:

[tex]3.2x = 25.6 \\ \frac{3.2x}{3.2} = \frac{25.6}{3.2} \\ x = 8[/tex]

I have one flat face 1 curved face 1 edge or corner I am aI have 6 equal square faces 12 edges and 8 vertices I am a ​

Answers

Answer:

A . sphere B. Square

Step-by-step explanation:

........

Can you conclude that this parallelogram is a rectangle? Explain.

Answers

Answer:

The answer is B.

Step-by-step explanation:

All parallelograms that have congruent diagonals are rectangles.

its b because it’s b

Find the opposite of: - 4x2 - 4x + 2

Answers

Answer:

4x² + 4x - 2

Step-by-step explanation:

The opposite is the negative value

The opposite of - 4x² - 4x + 2 is

- (- 4x² - 4x + 2) ← distribute parenthesis by - 1

= 4x² + 4x - 2

What is the probability that a normal random variable with mean 6 and standard deviation
3 will fall between 5.7 and 7.5

Answers

Answer:

z-score=7.5-6        1.5

___________=______=0.5

3                                   3

Step-by-step explanation:

Look up -0.1 on a z-table. The result is 0.4602. The means there is a 0.4602 probability the random variable will be below 5.7.

The find the probability the random variable will be between 7.5 and 5.7, simply subtract the two probabilities we found (above) from one another:

0.6915+-+0.4602+=+0.2313

So, there is a 0.2313 probability the random variable will fall between 7.5+and 5.7.

brainiest to whoever right !

Answers

Answer:

m<RST = 32°

m<TSQ = 58°

Step-by-step explanation:

m<RST here, meaning the angle of the whole diagram is 90 degrees as you can see.

m<RSQ + m<TSQ = m<RST

15x — 43 + 8x + 18 = 90

23x — 25 = 90

       +25     +25

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

23x = 115

/23      /23

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

x = 5

Now, plug this into the equation for m<RSQ and m<TSQ to find their values.

m<RSQ = 15x — 43

= 15x - 43

= 15(5) - 43

= 75 - 43

= 32

m<TSQ = 8x + 18

= 8x + 18

= 8(5) + 18

= 40 + 18

= 58

Now, check to see if our values are right or not.

15x — 43 + 8x + 18 = 90

15(5) — 43 + 8(5) + 18 = 90

75 - 43 + 40 + 18 = 90

32 + 40 + 18 = 90

90 = 90 CORRECT

how many inches is in 140 feet?​

Answers

Hey there!

The formula for feet to inches is to simply multiply the length value by 12.

So, multiply 140 by 12.

I believe your answer would be 1680 inches.

Hope this helps!

Have a great day!

Answer:

140 feet is 1680 inches. Don't forget to put your units in; your teacher may dock off points for forgetting to put in the unit.

Step-by-step explanation:

A foot is 12 inches, so you must multiply 140 by 12.

[tex]140\times12=1680[/tex]

Is x^3x^3x^3 equivalent to x^3^3^3

Answers

Answer:

No they aren't equivalent.

Step-by-step explanation:

x^3x^3x^3=x^3^3^3

[tex](x)^{3x^{3x^3[/tex]=[tex]x^{3^{3^3[/tex]

[tex]x^{3x^{9x}[/tex]=[tex]x^{3^{9}[/tex]

[tex]x^{27x^{2} }[/tex]=[tex]x^{27}[/tex]

Apply log on both sides

27[tex]x^{2}[/tex]logx=27logx

27[tex]x^{2}[/tex]logx/27logx=1

[tex]x^{2}[/tex]=1

This is true if x=1 , -1.

The values are equivalent if x=1 and -1 , otherwise no they aren't equivalent.

1 A recipe for sugar cookies requires 2 cups of
flour for every 2/3 cups of sugar.
At this rate, how many cups of sugar should be used if 5 cups of flour is included?

Answers

Answer:

3 cups of sugar should be used if 5 cups of floue is included

Find f(-2) for f(x)=3x^2-8x+7

Answers

Answer:

f(-2) = 35

Step-by-step explanation:

Let x = -2.

[tex]3(-2)^2-8(-2)+7\\\\12+16+7\\\\35[/tex]

write and solve an equation to find the value of X. please explain in details and show your work!

Answers

Answer:175 degrees

Step-by-step explanation: The shape isn't properly drawn.But,I assumed it is a five sided polygon because of the fifth ange

2/3 divided by 3/10

Thanks

Answers

Answer:

[tex] \frac{20}{9} [/tex]

Step-by-step explanation:

[tex] \frac{2}{3} \div \frac{3}{10} [/tex]

➡️ [tex] \frac{2}{3} \times \frac{10}{3} [/tex]

➡️ [tex] = \frac{20}{9} [/tex] ✅

A pattern has 3 blue triangles to every 24
yellow triangles. What is the ratio of blue
triangles to all triangles?

Answers

Answer:

It is 3 : 27

Step-by-step explanation:

Ratio of blue to yellow = 3:24

[tex]{ \sf{total \: ratio = 24 + 3 = 27}}[/tex]

ratio of blue to all triangles:

[tex] = 3 : 27[/tex]



100000-76585 full formula​

Answers

Answer:

Bro it is simple the answer is 23415

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Find the area of this triangle.
8 m
14 m
A = [?] m2

Answers

Answer:

A = 56 m^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 12 (14)(8)

A = 56 m^2

put the bracket in the correct place
10-3x4-2+1=5

Answers

Answer:

10-(3×4)-2+1=5

10-12-3=5

10-15=5

10=5+15

10=20

20-10

10

Answer:

[10 - 3 × (4-2)] +1= 5

.......

a rectangular garden is 3 times as long as it is wide .the perimeter is 32m . find the dimensions of the garden​

Answers

Answer:

Width= 4

length= 12

perimeter= (16+4)×2

3x+3x+x+x=32, let x be the dimensions

8x=32

x=4

so 3(4)=12

for the following geometric sequence find the explicit formula. {12, -6, 3, ...}​

Answers

Answer:

It's geometric sequence where a_1=12, q=-\dfrac{1}{2}a

1

=12,q=−

2

1

So a_n=12\cdot\left(-\dfrac{1}{2}\right)^{n-1}a

n

=12⋅(−

2

1

)

n−1

Answer:

[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex]

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 12 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex] ← explicit formula

What is the correct answer I will give brainlist only if correct answer ASAP

Answers

Answer:

4 tickets left

Step-by-step explanation:

Dividing 276 by 8 gives you a remainder of 4.

Find the value of x if 3(4x+3)

Answers

You can’t actually find x with this equation.
3(4x+3)
12x+9
This is the farthest you can go because there are no like terms.
If it was something like this:
3(4x+3)=3 then you would be able to find the value of x.

Given MP with M(-12, -5) and P(9, -12), if N lies on MP such that the ratio of MN to NP is 3:4, find the coordinates of N.

Answers

Answer:

(-3,-8)

Step-by-step explanation:

MN:Np=3:4   Let m:n=3:4

Use the formula

xN=(xM*n+xP*m)/(m+n)

yN=(yM*n+yP*m)/ (m+n)

xN= ((-12)*4+9*3)/ (4+3)=-3.

yN=((-5)*4+(-12)*3)/(4+3)=-8.

find the measure of angle of ABF​

Answers

Answer: m∠ABF = 120°

Concept:

Here, we need to know the idea of the corresponding angle theorem and linear pair postulate.

The corresponding angle theorem states that if a transversal cuts two parallel lines, their corresponding angles are congruent.

The linear pair postulate states that two angles that form a linear pair are supplementary.

Solve:

Given information

m∠ABF = m∠ABF = 2x + 3x

According to the corresponding angle theorem, ∠ABF is congruent to ∠BCI which is 2x + 4x.

m∠BCH = 3x

Total angle = 180°

∠ABF and ∠BCH are linear pairs which means they form a supplementary angle.

Given equation

m∠ABF + m∠BCH = Total Angle

Substitute values into the equation

2x + 4x + 3x = 180

Combine like terms

9x = 180

Divide 9 on both sides

9x / 9 = 180 / 9

x = 20

m∠ABF = 2x + 4x = 2 (20) + 4 (20) = 40 + 80 = 120°

Hope this helps!! :)

Please let me know if you have any questions

A bag contains 8 red marbles, 4 blue marbles and 7 green marbles. If three marbles
are drawn out of the bag, what is the exact probability that all three marbles drawn
will be red?

Answers

At the start, there are a total of 19 marbles. The chance of pulling one red is 8/19 (because there are 8 red).

Based on the way you stated the questions, I do not assume the red marble that was pulled first would be put back, so there’s only 18 marbles left to choose from and 7 of those are red. So on the second marble, you have 7/18 chance of pulling a red.

Again, since neither of the first two marbles were put back, you now have 17 marbles left and 6 of those are red. So you have a 6/17 chance of pulling a third red marble.

Multiply those together, 8/19 * 7/18 * 6/17 and you’ll have your answer.

Answer:

NO. OF RED =8

NO. OF BLUE=4

NO. OF GREEN=7

THEREFORE,TOTAL MARBLES=19

THEREFORE,PROBABILTY OF RED MARBLES=8/19.

Give the equation of a line that passes
through (9,2) and is parallel to:
y = 3x - 6

Answers

Answer:

y = 3x - 25

Step-by-step explanation:

If the line is parallel, it will have the same slope. So, the line will also have a slope of 3.

Plug in the slope and given point into y = mx + b, and solve for b:

y = mx + b

2 = 3(9) + b

2 = 27 + b

-25 = b

Plug in the slope and y intercept into y = mx + b:

y = mx + b

y = 3x - 25

So, the equation of the line is y = 3x - 25

Identify the pattern for the following sequence. Find the next three terms in the sequence.
-15, -11, -7, -3,
a. Subtract 4; -7, -11, -15
b. Add 4, 2, 6, 10
C. Subtract 4, 1, 5, 9
d. Add 4; 1, 5, 9
Please select the best answer from the choices provided

Answers

Answer:

b. Add 4, 2, 6, 10

Step-by-step explanation:

Let U= {1,2,3,4,5,6,7,8,9,10}, A={2,4,6,8} B={1,2,3,4}, C={5,6,9}

Hello! i need help with these questions

Answers

Answer: 13. is c, 14. is yes and 15 is no

Step-by-step explanation: Try your best and you might succeed

Mr. and Mrs. Samson are planning to build a fence around their garden. They are comparing the different measurements for their plans.
Plan A:
1.Posts are 4 ¼ feet in length
2. Post must be installed 7/8 feet below ground level.
Plan B:
1. Posts are 6 ¾ feet in length.
2. Posts must be installed 1 ½ feet below ground level.


1.What will be the height of the fence in plan A?

2. What will be the height of the fence in plan B?

3. Which fence will be taller and by how much?

4. Which plan would you recommend and why?

5. Mr. And Mrs. Samson decide to go with plan A and purchase the materials. Their total bill is $356.88. If they pay $220 in cash and charge the remainder, how much did they charge?

Answers

The relationship between the heights of the fence, the lengths, the distance below the ground level is an illustration of addition and subtraction.

The height of the fence is [tex]3\frac 38[/tex] in plan A  and [tex]4\frac 34[/tex] in plan BThe fence in plan B is taller by [tex]2\frac{3}{4}[/tex] feet.The fence in plan B is recommended because: It is taller than the fence in plan A, and it goes below the ground level than plan AThey charge $136.88

Plan A

[tex]Length = 4\frac 14[/tex]

[tex]Ground\ Level = \frac 78[/tex]

Plan B

[tex]Length = 6\frac 34[/tex]

[tex]Ground\ Level = 1\frac 12[/tex]

The height of the fence is calculated by subtracting the length below ground level from the length of the fence. So, we have:

[tex]Plan\ A = 4\frac 14 - \frac 78[/tex]                                   [tex]Plan\ B = 6\frac 34 - 1\frac 12[/tex]

[tex]Plan\ A = \frac{17}{4} - \frac 78[/tex]                                   [tex]Plan\ B = \frac{25}{4} - \frac 32[/tex]

                                         Take LCM

[tex]Plan\ A = \frac{17\times 2 - 7}{8}[/tex]                                   [tex]Plan\ B = \frac{25 - 3\times 2}{4}[/tex]

[tex]Plan\ A = \frac{34 - 7}{8}[/tex]                                       [tex]Plan\ B = \frac{25-6}{4}[/tex]

[tex]Plan\ A = \frac{27}{8}[/tex]                                           [tex]Plan\ B = \frac{19}{4}[/tex]

[tex]Plan\ A = 3\frac{3}{8}[/tex]                                           [tex]Plan\ B = 4\frac{3}{4}[/tex]

Hence, the height of fence is [tex]3\frac 38[/tex] in plan A  and [tex]4\frac 34[/tex] in plan B

The fence in plan B is taller because [tex]4\frac 34[/tex] is greater than [tex]3\frac 38[/tex]

The difference (d) in the heights is:

[tex]d = 4\frac 34 - 3\frac 38[/tex]

[tex]d = \frac{19}{4} - \frac{27}{8}[/tex]

Take LCM

[tex]d = \frac{19 \times 2 - 27}{4}[/tex]

[tex]d = \frac{38 - 27}{4}[/tex]

[tex]d = \frac{11}{4}[/tex]

[tex]d = 2\frac{3}{4}[/tex]

Fence in plan B is taller by [tex]2\frac{3}{4}[/tex] feet.

I will recommend the fence in plan B because:

It is taller than the fence in plan AIt goes below the ground level than plan A

For (5), we have:

[tex]Total = \$356.88[/tex]

[tex]Cash = \$220[/tex]

The remainder is the difference in the total amount and the amount they paid:

[tex]Charge = Total - Cash[/tex]

[tex]Charge = \$356.88 - \$220[/tex]

[tex]Charge = \$136.88[/tex]

Hence, they charge $136.88

Read more about addition and subtraction at:

https://brainly.com/question/12361020

Solve the inequality and enter your solution as an inequality in the box below,
using "<=" for sor">=' for if necessary.
-2(5x + 1) > 48​

Answers

Answer:

x < -5

Step-by-step explanation:

-2(5x+1) >48

-10x-2 > 48

-10x-2+2 > 48+2

-10x > 50

p.s : when dividing by a negative number with inequalities, change the sign, i.e. < would then be >....

therefore:

x < -5

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