You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $3,650 in interest. If you invest five times the money in the account that pays 4% compared to 3%, how much did you invest in the 4% account?

Answers

Answer 1

Let x = amount invested in the 1st account
y = amount invested in the 2nd account
z = amount invested in the 3rd account

Because the total investment is $100,000, therefore
x + y + z = 100,000 (1)
Interest earned in one year from the accounts is $3,650, therefore
0.04x + 0.03y + 0.02z = 3,650
or
4x + 3y + 2z = 365,000 (2)

Because x = 5y, therefore obtain these 2 equations:
5y +y +z = 100,000
or
6y + z = 100,000 (3)
4*(5y) +3y + 2z = 365,000
or
23y + 2z = 365,000 (4)

Substitute z=1000,000 - 6y from (3) into (4).
23y + 2(100,000 - 6y) = 365,000
23y + 200,000 - 12y = 365,000
11y = 165,000
y = $15,000
Therefore
x = 5y = $75,000
z = 100,000 - 6y = $10,000

Answer:
The amounts invested are
1st account: $75,000
2nd account: $15,000
3rd account: $10,000

Related Questions

for f(x) = x^3-7X^2+8x+16 find f(10) using synthetic division

Answers

[tex]\bf x^3-7x^2+8x+16\qquad f(10)\\\\ -------------------------------\\\\ f(10)=r\implies \begin{cases} x=10\\ remainder=r \end{cases}\\\\ -------------------------------\\\\ \textit{so, let's do the division} \\\\\\ \begin{array}{r|rrrrrrrllll} 10&&1&-7&8&16\\ &&&10&30&380\\ -&&-&--&--&--\\ &&1&3&38&\boxed{396}&\leftarrow remainder \end{array}[/tex]

Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?

Answers

check the picture.

line l is the orange line, intersecting the positive x-axis and the positive y axis.

The angle with measure ∅ is the angle made by the line and the positive x-axis. It is the obtuse (>90° angle) shown in the picture.

the slope of the line l is tan∅

What is 4.76 hours converted to min and sec

Answers

4hr +(.76hr(60min/hr))

4hr + 45.6 min

4hr+45min+(.6min(60sec/min))

4hr+45min+36sec

4:45:36

Oh, if you really only wanted min and sec without hours...

4hr(60min/hr)+45min+36sec

240min+45min+36sec

285min+36sec

4.76 hours times 60 minutes gives 285.6 minutes. We already have 285 minutes. 60% of 1 minute is 36 seconds, so the answer is 285 minutes and 36 seconds. :D

Explain why we need more than one digit to express certain quantities

Answers

We need more than one digit to express certain quantities in order to record more precise values. The significant figure of a measured quantity refers to all the digits known with certainty and the first estimated digit. This will usually differ depending on the quality that is been measured.

Convert 5.6 liters to milliliter
5,600 ml
560 ml
0.056 ml
0.0056

Answers

5,600 ml................

What is the integral of 1/x?

Answers

The indefinite integral is usually written as ln(x) if x>0, as u can see it's undefined for x = 0.

Final answer:

The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.

Explanation:

The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:

[tex]$ \int \frac{1}{x} dx = \ln(|x|) + C $[/tex]

The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.

A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases. If x represents the original price of the jacket, which expression represents the final price of the jacket during this sale? 0.2x – 3 0.8x – 12 0.8x – 15 0.2x – 15

Answers

Answer:

0.8x – 12

Explanation:

The sale price is (x-15). After the 20% discount, the final price is 0.80 times the sale price, so is ...

... final price = 0.80×(x -15) = 0.80x -12

Answer:

The correct option is B.

Step-by-step explanation:

Let the original price of the jacket be x.

A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases.

The price of jacket after $15 off is [tex]x-15[/tex].

Then 20% discount is applied, so the final price of the jacket is

[tex]P=(x-15)(1-\frac{20}{100})[/tex]

[tex]P=(x-15)(1-0.2)[/tex]

[tex]P=(x-15)(0.8)[/tex]

[tex]P=0.8x-12[/tex]

The final price of the jacket during this sale is 0.8x-12. Therefore the correct option is B.

find the equation of a line containing the given point and slope (10,5); m=9/20

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 10}}\quad ,&{{ 5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{9}{20} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-5=\cfrac{9}{20}(x-10)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-5=\cfrac{9}{20}x-\cfrac{9}{2}\implies y=\cfrac{9}{20}x-\cfrac{9}{2}+5\implies y=\cfrac{9}{2}x+\cfrac{1}{2}[/tex]

If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).

Answers

Answer: The required value is

[tex](f-g)(x)=x^2+8.[/tex]

Step-by-step explanation: The given functions are:

[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]

We are given to find the value of [tex](f-g)(x).[/tex]

We know that, if s(x) and t(x) are any two functions of a variable x, then we have

[tex](s-t)(x)=s(x)-t(x).[/tex]

Therefore, we have

[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]

Thus, the required value is

[tex](f-g)(x)=x^2+8.[/tex]

Answer:

3x2 - 6 its the answer

What is after 100,99,07,94,90

Answers

100,99,07,94,91. The ones has to go up one.

please vote my answer brainliest. thanks!

Convert the measurement as indicated.

26ft= _ yd _ ft

Answers

26ft(yd/3ft)

8yd+2yd/3

8yd+(2yd/3)(3ft/yd)

8yd+2ft

8yd 2ft

1 yard is 3 feet, and 26÷3 is 8, and we have 2 left over (3×8=24)

So the correct answer would be 26 ft=8 yd and 2 ft.

The leader of the group brought 8.03 ounces of trail mix. The hikers only ate 5.26 ounces of the trail mix. How much trail mix was left?

Answers

8.03 oz at the start- 5.26 oz eaten= 2.77 oz left

Final answer: 2.77 oz

A motorboat takes 3 hours to travel 108 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answers

recall your d = rt, distance = rate * time.

let's say the boat has a still water rate of "b", and the current has a a rate of "c", ok.... when the boat is going upstream, is not really going "b" fast, is going slower at "b - c", due to the current going in the opposite direction.

when the boat is coming downstream, is not going "b" fast either, is going faster, is going "b + c", due to the current adding speed to it.

we know the trip up was 108 kms, thus the return trip is also 108 kms.

[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ Upstream&108&b-c&3\\ Downstream&108&b+c&2 \end{array} \\\\\\ \begin{cases} 108=3(b-c)\implies \cfrac{108}{3}=b-c\implies 36+c=\boxed{b}\\\\ 108=2(b+c)\\ --------------------\\ 108=2\left(\boxed{36+c} +c \right) \end{cases} \\\\\\ \cfrac{108}{2}=36+2c\implies 54=36-2c\implies \cfrac{54-36}{2}=c[/tex]

and surely you know how much that is.

what's the boat's speed? well, 36 + c = b.

Calculator Reference A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed?

Answers

so he climbed the first 1000ft in 1000/x hours then

the rate of the 5000ft is "10 feet per hour less than twice the first rate", so hmm twice the first rate is 2x, 10 less than that is 2x - 10.

so, the 5000ft were climbed in 5000/(2x-10)

the number of hours it lasted climbing? well, simply add them up.

Answer: The expression that represents the number of hours the mountaineer climbed is given by

[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]

Step-by-step explanation:

Since we have given that

Distance covered by mountaineer = 1000 feet

Speed at which he climbed = x feet per hour

Time taken by him would be

[tex]\dfrac{1000}{x}[/tex]

Additional distance covered by him = 5000 feet

Speed at which he climbed this time = 2x-10

So, Time taken is given by

[tex]\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}[/tex]

Hence, the expression that represents the number of hours the mountaineer climbed is given by

[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]

Please help quick !!

Answers

1) sin(60 degrees)=0.86602540378 (Make sure your calculator is in degrees, not radians)
√3/2
√3=1.73205080757
1.73205080757/2
=0.866025404
1) IS CORRECT
Solve the rest using the same technique.

Hope this helps! A thanks/brainliest answer would be appreciated :)

A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.

Which equation can be used to solve for x, the increase in side length of the square in inches?

x2 + 4x – 81 = 0
x2 + 4x – 65 = 0
x2 + 8x – 65 = 0
x2 + 8x – 81 = 0

Answers

Let x be the "enlargement value" of each side :
Then the enlarged side becomes (x+4) and the square = (x+4)²
The final area should be (x+4)² = 81
Let's expand:
x²+ 8x + 16 = 81
x² + 8x + 16 - 81 = 0
x² + 8x - 65 = 0

Answer:

[tex]x^2+8x-65=0[/tex]

Step-by-step explanation:

Side length of square = 4 inches

Let x be the increase in length

So, New length = x+4

Area of square = [tex]Side^2[/tex]

Area of enlarged square = [tex](x+4)^2[/tex]

Using identity : [tex](a+b)^2=a^2+b^2+2ab[/tex]

Area of enlarged square = [tex]x^2+16+8x[/tex]

We are given that The final area needs to be 81 square inches.

So, [tex]x^2+16+8x=81[/tex]

[tex]x^2+16+8x-81=0[/tex]

[tex]x^2+8x-65=0[/tex]

So, Option C is true

Hence equation can be used to solve for x, the increase in side length of the square in inches is [tex]x^2+8x-65=0[/tex]

what is the value of x in the equation 5(4x-10)+10x=4(2x-3)+2(x-4) ?

-7/4
-1/4
3/20
3/2

Answers

5(4x - 10) + 10x = 4(2x - 3) + 2(x - 4)
20x - 50 + 10x = 8x - 12 + 2x - 8
30x - 50 = 10x - 20
30x - 10x = -20 + 50
20x = 30
x = 3/2 <==

Answer:

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

Step-by-step explanation:

Here, the given expression is,

[tex]5(4x-10)+10x=4(2x-3)+2(x-4)[/tex]

By distributive property,

[tex]20x - 50 + 10x = 8x - 12 + 2x - 8[/tex]

By combining like terms,

[tex]30x -50=10x-20[/tex]

Adding 50 on both sides,

[tex]30x=10x-20+50[/tex]

[tex]30x = 10x + 30[/tex]

Subtracting 10x on both sides,

[tex]20x = 30[/tex]

Divide both sides by 20,.

[tex]x=\frac{3}{2}[/tex]

Hence, LAST option is correct.

In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce?

Answers

1 lb = 16 oz

5.92 / 16 = 0.37 per oz.....37 cents per oz

Answer:

$,37 dollars per ounce of strawberries

Step-by-step explanation:

We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:

5,92/16= ,37

SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.

The Greasy Grab Bag claims that customers can make 20 different meal combinations from the menu items. If the Greasy Grab Bag has 4 sandwiches, 3 sides, and 2 drinks, which of the following is correct?

Answers

The answer is A. The Greasy Grab Bag is understating the number of meal combinations.
4 * 3 * 2 = 24
and 24 > 20

The correct number of different meal combinations that customers can make from the menu items at the Greasy Grab Bag is 24.

To determine the number of different meal combinations, we need to consider that each meal consists of one sandwich, one side, and one drink. Given that there are 4 sandwiches, 3 sides, and 2 drinks to choose from, we can calculate the total number of combinations by multiplying the number of choices for each category together.

The number of sandwich choices is 4, the number of side choices is 3, and the number of drink choices is 2. Therefore, the total number of meal combinations is calculated as follows:

Total combinations = Number of sandwich choices — Number of side choices — Number of drink choices

Total combinations = [tex]$4 \times 3 \times 2$[/tex]

Now, let's calculate the total number of combinations:

Total combinations =[tex]$4 \times 3 \times 2 = 12 \times 2 = 24$[/tex]

Thus, there are 24 different meal combinations that customers can make, which means the Greasy Grab Bag's claim of 20 different meal combinations is incorrect. The correct number is 24.

53 ℃ below zero degrees

Answers

your answer is -53 degrees celsius

hope this helps

The value of y is inversely proportional to the value of x. When y=40, x=5. What is the value of y when x=8

Answers

Since x and y are inversely proportional:

xy = c, where c is a constant

when y = 40 and x = 5 -> c = 40*5 = 200

So xy = 200

Then, when x = 8, y = 200/8 = 25

Answer: 64

Step-by-step explanation:

i put it into math-way

If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?

Answers

Reflection in the y-axis.
g(x) = f(-x); -x has been substituted in for x.

When Sharon began shopping this morning, she had $40.00. She purchased five paperback books and had lunch. The books were all the same price, and lunch cost $3.25. She now has $7.00 left over. What was the price of each of the books? A. $5.95 B. $6.60 C. $7.35 D. $8.75

Answers

The books were bought for $40 - $7 - $3.25 = $29.75

$29.75 divided by 5 books is $5.95, answer A.

40 - 5b - 3.25 = 7
36.75 - 5b = 7
-5b = 7 - 36.75
-5b = - 29.75
b = -29.75 / -5
b = 5.95 <=== 5.95 per book

If f(x)=2x^2sqrt(x-2), complete the following statement f(6)

Answers

f(x) = 2x^2 + 5sqrt (x - 2)....when x = 6
f(6) = 2(6^2) + 5 sqrt (6 - 2)
f(6) = 2(36) + 5 sqrt 4
f(6) = 72 + 5 * 2
f(6) = 72 + 10
f(6) = 82

The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82

How to determine the function value?

The function is given as:

[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]

Substitute 6 for x

[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]

Evaluate the difference

[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]

Evaluate the exponents

f(6)=2 * 36 + 5 * 2

Evaluate the sum of products

f(6) = 82

Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82

Answers

To determine the equation that would be perpendicular with a certain line, we must first know the characteristics of a perpendicular line. This line would have a 90 degrees angle with another line so that the slope of this line would be the negative reciprocal of the slope of the other line. To write the equation, given a certain point we use the point-slope form of a line, y -y1 = m(x - x1).

Original line: -x + 5y= 14
y = x/5 + 14/5
slope = 1/5

Perpendicular line's slope = -5
y - y1 = m (x - x1)
y - (-2) = -5 (x - (-5))
y = -5x - 25 -2
y = -5x -27

Each canvas bag will hold exactly 5 pounds of kings tomatoes. How many bags will be necessary to hold 5 kg worth of these same tomatoes? (1 kg = 2.25 pounds)

Answers

1 kg = 2.25 pounds

5*2.25 = 11.25 pounds

11.25/5 = 2.25 bags

so you would need 3 bags

1 kg = 2.25 lbs....so 5 kg = (5 * 2.25) = 11.25 lbs

at 5 lbs per bag.....2 full bags + 1.25 lbs in the other bag...so it would be 3 bags with 1 bag partially full or 2 bags, leaving out 1.25 lbs

Susan invests
2
times as much money at
8%
as she does at
4%
. If her total interest after
1
year is
$800
, how much does she have invested at each rate?

Answers

Let f=amount invested at 4% and e=amount invested at 8%

0.04f+.08e=800

However, e=2f so the above equation becomes:

0.04f+0.08(2f)=800

0.04f+0.16f=800

0.2f=800

f=$4000, since e=2f

e=$8000

So Susan invested $4000 at 4% and $8000 at 8%.

Final answer:

To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.

Explanation:

Susan has invested $x at 4% interest rate and $2x at 8% interest rate.

Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.

Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.

What is the next number in the series? 71 62 53 44 35 ?

Answers

This is an arithmetic sequence with a common difference of -9, so the next term will be 35-9=26.

If you examine your sequence closely, you can notice that the number in the tens place is decreasing by 1 as the number in the ones place is increasing by 1.
To further prove this;
71 --> 62.
-10 and + 1.
62 --> 53.
-10 and +1
and so on.

However, if that's a little too complicated, there's an alternate method.
All you have to do is subtract 9 from the current number.
To further prove this;
71 - 9 = 62
62 - 9 = 53
53 - 9 = 44
and so on.

So, let's subtract 9 from our most current number, 35.
35 - 9 = 26.

The upcoming number in your sequence is 26.

I hope this helps!

PLEASE HELP!!!!!! The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?
A) -2
B) -1
C) 2

Answers

[tex]y= ax^{2} -8x-3[/tex]

1.

the line of symmetry is x=2, means that the x coordinate of the vertex is x=2.

the point x=2 is the midpoint of the roots [tex]x_1[/tex] and [tex]x_2[/tex].

so
[tex] \frac{x_1+x_2}{2}=2 [/tex]
[tex]x_1+x_2=4[/tex]

Remark: in the x-axis, if c is the midpoint of a and b, then [tex]c= \frac{a+b}{2} [/tex]

2.
since [tex]x_1[/tex] and [tex]x_2[/tex] are roots

[tex]a(x_1)^{2} -8(x_1)-3=0[/tex] and [tex]a(x_2)^{2} -8(x_2)-3=0[/tex]

3.
equalizing:

[tex]a(x_1)^{2} -8(x_1)-3=a(x_2)^{2} -8(x_2)-3[/tex]

[tex]a(x_1)^{2} -8(x_1)=a(x_2)^{2} -8(x_2)[/tex]

[tex]a(x_1)^{2}-a(x_2)^{2} =8(x_1) -8(x_2)[/tex]

in the left side factorize a, in the left side factorize 8:

[tex]a[(x_1)^{2}-(x_2)^{2}] =8(x_1 -x_2)[/tex]

in the right side use the difference of squares formula:

[tex]a(x_1 -x_2)(x_1 +x_2) =8(x_1 -x_2)[/tex]

simplify by [tex](x_1 -x_2)[/tex]

[tex]a(x_1 +x_2) =8[/tex]

substitute [tex](x_1 +x_2)[/tex] with 4:

[tex]a*4 =8[/tex]

a=2

Answer: C)2

If 12 bumper stickers cost $8.64, then how much do 18 cost

Answers

In order to solve this problem, we must first find the GCF of 12 and 18. This would be six. Next, we would need to find out the value of six stickers. This can be done by halving the value of 12, as 6 is one-half of 12. 8.64/2 = $4.32, which is the cost of 6 stickers. Next, we need to multiply the cost of six stickers by 3 in order to get the cost of 18 stickers, because 18 is three times 6. 4.32 x 3 = $12.96. Therefore, the cost of 18 stickers is $12.96.

Hope this helps!

The proportion is solved and the cost of 18 bumper stickers is $ 12.96.

Given data:

To find out how much 18 bumper stickers cost, use a proportion since the cost of bumper stickers is directly proportional to the number of stickers.

Cost of 12 bumper stickers / Number of 12 bumper stickers = Cost of 18 bumper stickers / Number of 18 bumper stickers

On simplifying the proportion:

$8.64 / 12 = x / 18

Now, solve for x (the cost of 18 bumper stickers):

x = ($8.64 / 12) * 18

x = $12.96

Hence, 18 bumper stickers cost $12.96.

To learn more about proportion, refer:

https://brainly.com/question/7096655

#SPJ5

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