Mathematics College

PLEASE HELP
You invested $10,000 in two accounts paying 7% and 8% annual interest, respectively. If the total interest earned for the year was $780, how much was invested at each rate?
The amount invested at 7% is $0

PLEASE HELPYou Invested $10,000 In Two Accounts Paying 7% And 8% Annual Interest, Respectively. If The

Answers

Answer 1

Using simple interest, it is found that:

The amount invested at 7% is $2,000.The amount invested at 8% is $8,000.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The interest after t years in is modeled by:

[tex]I(t) = Prt[/tex]

In which:

P is the initial amount.r is the interest rate, as a decimal.

In this problem:

A total of $10,000 was invested, hence [tex]P_1 + P_2 = 10000[/tex].Two accounts paying 7% and 8% annual interest, respectively, hence [tex]r_1 = 0.07, r_2 = 0.08[/tex].The total interest earned for the year was $780, hence [tex]t = 1, I_1 + I_2 = 780[/tex]

Then:

[tex]I_1 = 0.07P_1[/tex]

[tex]I_2 = 0.08P_2[/tex]

Considering [tex]P_1 + P_2 = 10000 \rightarrow P_2 = 10000 - P_1[/tex]:

[tex]I_2 = 0.08(10000 - P_1)[/tex]

Considering [tex]I_1 + I_2 = 780 \rightarrow I_2 = 780 - I_1[/tex]:

[tex]780 - I_1 = 0.08(10000 - P_1)[/tex]

Considering [tex]I_1 = 0.07P_1[/tex]:

[tex]780 - I_1 = 0.08(10000 - P_1)[/tex]

[tex]780 - 0.07P_1 = 0.08(10000 - P_1)[/tex]

[tex]0.01P_1 = 20[/tex]

[tex]P_1 = \frac{20}{0.01}[/tex]

[tex]P_1 = 2000[/tex]

And:

[tex]P_1 + P_2 = 10000[/tex]

[tex]2000 + P_2 = 10000[/tex]

[tex]P_2 = 8000[/tex]

Then:

The amount invested at 7% is $2,000.The amount invested at 8% is $8,000.

You can learn more about simple interest at https://brainly.com/question/25296782

Related Questions

NO LINKS!!! Fill in the blanks of this sheet. Part 1​

Answers

Problem 1

Answer:

The square root of the   expression   of the   difference   of   x^2    and 11.The   quotient   of   2   times a number and -1The   sum   of the   square root   of two times a number and 11.

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

Explanation:

The term "difference" is the result of subtraction. We're subtracting the x^2 and 11. Then applying the square root to the result.

Question 2 has the blanks filled correctly.

For the last sentence, we have a sum of the terms [tex]\sqrt{2x}[/tex] and 11.

===========================================================

Problem 2

Answer:

The value of an algebraic expression depends on its   variables  

Substitute the known value for each variable.Simplify using the   order   of   operations   Use the work to answer any word problems related to the expression.

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

Explanation:

The variables are placeholders for numbers

So for instance, saying x+5 is like saying "some unknown number plus 5".

We could replace it with something like x = 10 to get x+5 = 10+5 = 15

Once the variable is replaced, you use the order of operations PEMDAS (some books refer to it as BODMAS).

The depth of Lake Carl is about 1 1/8 miles. Lake Susan is 3 times as deep as Lake Carl. Lake Wayne is 2 times as deep as Lake Susan. How much deeper is Lake Wayne than Lake Susan?

Answers

Answer:

[tex]3\frac{3}{8}[/tex]

Step-by-step explanation:

Let LC be Lake Carl, LS be Lake Susan, and LW be Lake Wayne

First, find a way to denote all the lakes using one lake depth

LC = 1 1/8

LS = 3LC

LW = 3LS or 6LC

Then write an equation.

LW - LS = 6LC - 3LC = 3LC

Substitute LC and calculate.

3 * 1 1/8 = 3 3/8

Hope this helps :)

Have a great day!

graph the following function in picture

Answers

Answer:

You already have the equations ready so I will just explain

Step-by-step explanation:

The first equation: place a point on the y-axis on -5. then proceed to place points by going down 2 and right 1 or by going up 2 and left 1. that will make your first line.

second equation: on the y-axis place a point on -1 then proceed to go up 1 right 1 or down 1 left 1. that makes your second line

Part A: Describe how you can decompose this shape into triangles. (2 points)
Part B: What would be the area of each triangle? (5 points)
Part C: Using your answers above, determine the area of the table's surface. (25 points)

Answers

Answer:

I don't really know the answer, but I think that the answer for b is 6.

Step-by-step explanation:

Three kids, Alberto, Bernadette, and Carlos, decide to share 11 cookies. They wonder how many ways they could split the cookies up provided that none of them receive more than 4 cookies (someone receiving no cookies is for some reason acceptable to these kids

Answers

Answer:

Each kid can get 3 cookies and split up the remaining 2 cookies into thirds so each kid gets the same amount of cookies.

Step-by-step explanation:

15 feet of edging costs $24.98. How much will 28 yards cost?

Answers

Answer:

  139.888 $

Step-by-step explanation:

Data :

   15 ft = 24.98$

   So

  1 yard = 3 ft

15ft / 3 ft = 5 yard

So  

   5 yard  = 24.98$

28 yd / 5yd = 5.6

    5.6 × 24.98 =  139.888

Name 3 integers greater than -3.

Answers

Answer:

0,3,6

hope I helped you

What value of b will make the expressions −12.8x+b and −3.2(4x−2.1)+2.4 equivalent?

Answers

Solution:

Note that:

[tex]-12.8x+b = -3.2(4x-2.1)+2.4[/tex]

Simplifying the distributive property.

[tex]-12.8x+b = -3.2(4x-2.1)+2.4[/tex]

[tex]-12.8x+b = -12.8x + 6.72+2.4\\[/tex]

Simplifying the RHS.

[tex]-12.8x+b = -12.8x + 9.12[/tex]

Canceling out -12.8x.

[tex]b = 9.12[/tex]

Graph the parabola. y=-2x^2 Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right ​

Answers

Answer:

1 tama 2Mali 3 Mali 4 tama 5 mali

Find the smallest non-zero whole number that is
divisible by 315, 378 and 392.

Answers

Answer:

  52920

Step-by-step explanation:

You have described the Least Common Multiple (LCM) of the three numbers. That can be found by considering their unique factors. The LCM is the product of the unique factors, 2³, 3³, 5, 7².

  315 = 3×3×5×7

  378 = 2×3×3×3×7

  392 = 2×2×2×7×7

The LCM will be ...

  2×2×2×3×3×3×5×7×7 = 52920

The smallest natural number divisible by 314, 378, and 392 is 52920.

please help me and take a picture and show your work​

Answers

Answer:

D

Step-by-step explanation:

Your rule is 1x is 5y

5 * 100 is 500

Your answer is D.

Answer:

$500

Step-by-step explanation:

Consider the values shown, what you should notice is that the ratio remains the same as you would expect;

The money per raffle sold will be the same ordinarily so this is recognisable logically;

The first pair of corresponding x and y values are 5 and 25, representable as the ratio:

5 : 25

Which simplifies to (by dividing each part of the ratio by 5):

1 : 5

The second pair is 15 and 75:

15 : 75

Which simplifies to (by dividing each part of the ratio by 15):

1 : 5

The same applies to the third pair (by dividing each part of the ratio by 25)

This translates to 1 raffle raising $5;

We want to find y when x = 100;

If we use the ratio, we can find out how x and y values are related;

The way to understand this is think what do we multiply or divide the left number (x part of the ratio) to get the number on the right (y part of the ratio);

Well, 1 multiplied by 5 would give 5;

This means y = 5x;

So, if x = 100, then:

y = 5(100)

y = 500

Jinfa, upon receiving his paycheck, spent four-fifths of it on car repairs and then bought a $40 gift for his mother. He had $64 left. How much was his paycheck?

Answers

you’ll do it in reverse here so
$64 + $40 = $104
if he spent 4/5 on car repairs then had a remaining $104, the 1/5 is equal to $104.
multiply $104 by 5 and it gives you $520

his paycheck was $520

Algebra 1 Question Math (Will Give Brainliest)

Answers

Question:

2(5x-1) = 3(x+11)

x=?

You need 2 cups of flour for every 10 dog biscuits you make. How many cups of flour are required to make 35 dog biscuits?

Answers

7 cups because 10 divided by 2 is 5, so 1 cup of flour for 5 biscuits would make it easier. 35 divided by 5 is 7, so that means there would be 7 cups used for 35 dog biscuits. hope this helps

how to round 831,756 nears hundred thousand

Answers

Answer:

800,000

Step-by-step explanation:

If the number was above 850,000 it would round up. If the number was 849,999 or below it would round down. In other words, you look at the number to the right of the hundred thousands place, or the number in the tens of thousands place, and if it is 5 or above you round up. 4 and below you round down.

1) Identify the coefficients.
4a + 6 + 24b + 3 + c3

Answers

4,6,24,3,3 I think only bc




8x+3=4x-1 solve the equation and check your solution

Do not do it like its set up in the picture​

Answers

it is 2000000 couse when u ad all together u geth 20000000

80 points!!

A.What does tangent mean? Select all that apply.

a straight line or segment that touches a curve at a point 90 degrees to the radius of the circle it touches

to touch

the tangent of an angle is the comparison of the opposite side to the adjacent side when a right triangle is given

a straight line or segment that touches a curve and matches the curve's slope at that point

Answers

It would be D the last one

Which of the following is the solution to the equation 25^(z-2)=25

Answers

Answer:

z=3

Step-by-step explanation:

work out the value of x​

Answers

Answer:

x = 74°

Step-by-step explanation:

360 = x - 17 + 2x - 67 + 3x

360 = 6x - 84

360 + 84 = 6x

444 = 6x

x = 444 : 6

x = 74°

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

check

2 * 74 - 67 + 74 - 17 + 3 * 74 = 360°

the answer is good

What are they? I don’t quite understand it

Answers

The answers are:

Top Left - equilateral triangle (all three sides are equal)

Top Right - scalene triangle (no sides are equal)

Bottom Left - right angle triangle (one right angle)

Bottom Right - obtuse angle triangle ( one obtuse angle)

The table below represents a function.

x
1
2
3
4
5
y
1
16
64
256
1,024

Which statement would best describe the graph of the function?

Answers

1024 y axis and 4 X axis best describe the graph function

The square root for 160

Answers

Answer:

12.6 maybe? Thats what it most likely is

collect like terms

-3b cubed subtract 2b cubed

Answers

Answer: -5b cubed

Step-by-step explanation:

-3b^2 minus -2b^2 = -5b^2

first, collect like terms (-3-2)b^2

then, calculate the difference which makes
-5b^2

Statement True False HELP ME please guys
:l​

Answers

Answer:

Step-by-step explanation:

False

False

False

True

Find the smallest non-zero whole number that is
divisible by 315, 378 and 392.

Answers

Answer:

The smallest nonzero whole number that is divisible by 315,378 & 392 is the LCM of these 3 numbers. This can be found out by factorization method. Thus,the smallest nonzero whole number that is divisible by 315,378 & 392 is 52,920.

plz help me with this ​

Answers

Answer:

Idek that is a weird question

Step-by-step explanation:

Sorry that it isn't a real answer but how is that a question at your school

4 and 9 are the composite numbers and they do not have any common prime factor Their L.C.M. is 4×9 = 36 Find the L.C.M. of 9,10​

Answers

Answer: 90

Step-by-step explanation:

9 and 10 do not have a common factor either, so their lcm is 9*10 = 90.

REAL CASE SCENARIO) - A client of yours comes to you wondering about overtime. They are working regular 45 hour weeks and not receiving overtime. Without actual specific information on certain necessities, you know your client is a hourly vet tech (does not require a degree) at a local Veterinary office with 4 veterinarians and approx. 10 total staff. Explain your answer using reasonable rational assumptions about information you will need to answer your client.

Does this EE deserve overtime pay? This problem is worth 5 POINTS! A detailed answers citing specific law requirements is required.

In your answer you should address if this employee would be exempt or not (give specific reasons) and if the EE would typically be covered by FLSA (give your reasons and provide logical assumptions when needed).

Answers

The vet tech and his colleagues should be getting overtime pay because they are working more than 40 hours per week.

What is an extra hour?

An overtime is a term that refers to the extra time that a worker works in a company. Usually this time is paid in addition to her salary.

What does FLSA stand for?

FLSA stands for the Fair Labor Standards Act. This law establishes the parameters and guidelines that an employer must follow to pay their employees' salaries.

A very important aspect of this law is that it establishes exceptions for those employees who must receive overtime pay.

According to these guidelines, the veterinary technician must receive overtime pay because a weekly shift of more than 40 hours is required.

When must overtime be paid?

According to the Fair Labor Standards Act (FLSA) the employer must pay their employees overtime once they are required to work more than 40 hours per week. Once the employee works more than that time, he must start counting the hours he worked extra to collect an additional cost.

In this case, the vet tech's employer should pay him for the 5 hours of overtime he is doing. Adicionalmente,

Learn more about overtime pay in: https://brainly.com/question/17043970

Plz help need right now

Answers

Answer:

the value of x is 3 I know it

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