adam has $800 invested in two accounts. one pays 6% annual interest and the other pays 10% interest. the amount of annual interest is the same as he would earn if the entire $800 was invested at 8.25%. How much does he have invested at each rate?

Answers

Answer 1

Adam invested $350 at 6% and $450 at 10%

Amount invested by Adam = $800

Interest paid by one account = 6%

Interest paid by another account = 10%

Let the amount invested in one account be x and the other be y

The formula for simple interest is given by:

Simple interest = (P*R*T)/100

where P = Principal

R = rate of interest

T = number of years amount is invested

Substituting the value in the formula we get:

Simple interest in one account = (x*6*1)/100-------(1)

Simple interest in another account = (y*10*1)/100--------(2)

The question states that interest earned would be the same when $800 is invested at 8.25%, therefore

Simple interest = (800*8.25*1)/100

= 66----(3)

Equating (1), (2) and (3) we get:

x + y = 800-----(4)

6x/100 + 10y/100 = 66

6x + 10y = 6600-----(5)

Multiplying (4) with 6 and equating it with (5)

6x + 6y = 4800

6x + 10y = 6600

4y= 1800

y = 450

x = 350

So, Adam invested $350 at 6% and $450 at 10%

Learn more about simple interest:

https://brainly.com/question/22621039

#SPJ1


Related Questions

Find the sticker price

River City Autos has a pickup truck for sale. Its base price is $22,225. Prices for available options are 6-speed transmission, $2,908; cruise control, $240; trailer towing package, $230; and power windows, $738. Its destination charge is $900.

Answers

The total price of the pick up truck is $27,241.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Base price = $22,225.

Additional options pricing,

6-speed transmission =  $2,908

cruise control = $240

trailer towing package = $230

power windows =  $738

destination charge = $900

All the other charges will be added to the base price if a person chooses all the options available, therefore,

= 22,225 + 2,908 + 240 + 230 + 738 + 900

= $27241

Therefore, The total price of the pick up truck is $27,241.

Read more about  mathematic expression at :

https://brainly.com/question/10413253

#SPJ1

(27/8)-^2/3??????????/

Answers

Answer: 4/9

Step-by-step explanation:

[tex]\displaystyle\\(\frac{27}{8} )^{-\frac{2}{3}} =\\\\(\frac{3*3*3}{2*2*2})^{-\frac{2}{3}}=\\\\ (\frac{3^3}{2^3} )^{-\frac{2}{3}} =\\\\((\frac{3}{2})^3)^{-\frac{2}{3} } =\\\\(\frac{3}{2})^{-\frac{3*2}{3}} =\\\\(\frac{3}{2})^{-2}=\\\\(\frac{2}{3})^2 \\\\\frac{2^2}{3^2} =\\\\\frac{4}{9}[/tex]

(01.01 MC)
Which value of x would make the expression (75)* equal to 5?
a
b
3
12
C 4
5
d 5
4

Answers

Answer: (sidenote, I'm sorry if I answered incorrectly ;-;)

C: 4/5 or D 5/4

Step-by-step explanation:

if you solve the numbers inside the radical symbol you'll get 16807. it's hard for it to be separated into 4 groups since it can only be separated in 5, that being 7*7*7*7*7.

so, by process of elimination i suggest you answer either c or d

Select all the roots of 49?

Answers

Answer:

{2401, {-2401

Step-by-step explanation:

Sorry couldnt type the root symbol on my ipad.

These questions are about calculus, I would greatly appreciate your help on both questions! .
asap , please !

Answers

The 107th derivative of f(x) =cos(x) is sin(x).

What is derivative of a function?

The derivative of y = f(x) function is the rate of change of  y  with respect to the independent variable x.

Derivative is represented by [tex]\frac{d}{dx}[/tex] and

First derivative to y is given by  [tex]\frac{d}{dx}f(x) = \lim_{h\to \00} \frac{f(x+h)-f(x)}{h}[/tex]

Second derivative [tex]\frac{d^{2}y }{dx^{2} } = \frac{d}{dx} (\frac{dy}{dx} )[/tex] and so on higher derivatives can be defined.

[tex]\frac{d(sinx)}{dx} = cosx\\\frac{d(cosx)}{dx} = -sinx[/tex]

Given f(x) = cos(x)

Then the first derivative of cos(x) is [tex]\frac{d(cosx)}{dx} = -sinx[/tex]

The second derivative of cos(x) is [tex]\frac{d^{2}(cosx) }{dx^{2} } = \frac{d}{dx} (\frac{dcosx}{dx} ) = \frac{d(-sinx)}{dx} =-cosx[/tex]

Third derivative [tex]\frac{d^{3}(cosx) }{dx^{3} } = \frac{d }{dx } (\frac{d^{2} cosx}{dx^{2} } ) = \frac{d(-cosx }{dx } = sinx[/tex]

[tex]\frac{d^{4}(cosx) }{dx^{4} } = \frac{d(sinx) }{dx } = cosx\\\frac{d^{5}(cosx) }{dx^{5} } = \frac{d(cosx) }{dx } = -sinx\\\\\frac{d^{6}(cosx) }{dx^{6} } = \frac{d(-sinx) }{dx } = -cosx\\\\\frac{d^{7}(cosx) }{dx^{7} } = \frac{d(-cosx) }{dx } = sinx\\[/tex]

Eighth derivative if cos(x) is  cos(x)

and so on

Therefore , the first , fifth , ninth ,... derivative of f(x) =cos(x)  is -sin(x)

The second, sixth, tenth.... derivative of f(x) =cos(x)  is -cos(x)

The fourth , eighth , 12th,... derivative of f(x) =cos(x)  is cos(x)

We can say that very multiple of fourth derivative of f(x) =cos(x)  is cos(x)

We can write 107 as 104 + 3

As 104 is multiple of 4 therefore 104th derivative of cos(x) is cos(x)

[tex]\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3} }{dx^{3} } (\frac{d^{104} cosx}{dx^{104} } ) \\\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3}(cosx) }{dx^{3} } = sinx[/tex]

Therefore, the 107th derivative of f(x) =cos(x) is sin(x).

Also, learn more about the derivatives from the link below:

https://brainly.com/question/25324584

#SPJ1

true or false 18:5= 5/18

Answers

FALSE because they are two different ratios

Evaluate 11,000,000,000 ÷ 100, write your answer in exponent form.

Answers

Answer :

11 × 10⁹ ÷ 10²

11 × 10⁷

Answer this fraction based Question. I will make you brainliest and provide you 50 points.​

Answers

Part i

6/7 of people are not having a disease, the whole is 1 so the difference is:

1 - 6/7 = 7/7 - 6/7 = 1/7 of the total

Part ii

2/3 of those having a disease is:

1/7*2/3 = 2/21 of the total

Part iii

15 people are the 1/7 fraction of total people referred to quarantine.

The total number is:

15 : 1/7 =  15 * 7 = 105 people

Part iv

3/5 of 105 people are male, that is:

3/5*105 = 63 people

Number of female is:

105 - 63 = 42 people

Answer:

[tex]\sf (i) \quad \dfrac{1}{7}[/tex]

[tex]\sf (ii) \quad \dfrac{2}{21}[/tex]

[tex]\sf (iii) \quad 315\:people[/tex]

[tex]\sf (iv) \quad 126\: females[/tex]

Step-by-step explanation:

Part (i)

If 6/7 of people who are quarantined do not have the disease then the fraction of people that do have the disease is:

[tex]\begin{aligned} \implies 1-\dfrac{6}{7} & =\dfrac{7}{7}-\dfrac{6}{7}\\\\ & =\dfrac{7-6}{7}\\\\ & =\dfrac{1}{7}\end{aligned}[/tex]

Therefore, 1/7 of people in quarantine have the disease.

Part (ii)

We are told that 2/3 of the people who have the disease come from abroad.  Therefore, the fraction of diseased people coming from abroad is 2/3rds of the diseased people:

[tex]\begin{aligned} \implies \dfrac{2}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{2}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{2 \times 1}{3 \times 7}\\\\ & = \dfrac{2}{21}\end{aligned}[/tex]

Therefore, the fraction of diseased people who have come from abroad is 2/21.

Part (iii)

We are told that 15 people who have the disease do not come from abroad.  So if 2/3 of the people who have the disease come from abroad, then 1/3 of the people who have the disease do not come from abroad.  Remember that 1/7 of the total people have the disease.

[tex]\begin{aligned} \implies \dfrac{1}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{1}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{1 \times 1}{3 \times 7}\\\\ & = \dfrac{1}{21}\end{aligned}[/tex]

Therefore, 1/21 of the total number of people have the disease and do not come from abroad.

Therefore, 15 people are equal to 1/21 of the total number of people:  

[tex]\implies \sf Total\:number\:of\:people=15 \times 21 = 315[/tex]

Therefore, the total number of people in quarantine is 315.

Part (iv)

If 3/5 of the total are male, then 2/5 must be female.

[tex]\begin{aligned} \implies \dfrac{2}{5} \textsf{ of }315 & = \dfrac{2}{5} \times 315\\\\ & = \dfrac{2 \times 315}{5}\\\\ & = \dfrac{630}{5}\\\\& = 126 \end{aligned}[/tex]

Therefore, 126 females are in quarantine.

Given m n, find the value of x.

Answers

Answer:

x = 21°

Step-by-step explanation:

180 - 159 = 21

Alternate angles (see image below) are equal, so x = 21

Using corresponding angles and adjacent angles concept, the value of x from the given parallel lines is 21°.

Given that, straight line m parallel to straight line n and t is the transversal.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Here, y°=159°

Now, y°+x°=180° (Adjacent angles on straight line)

159°+x°=180°

x°=21°

Therefore, the value of x from the given parallel lines is 21°.

To learn more about the corresponding angles visit:

brainly.com/question/1597341.

#SPJ7

I’m in need of help with this math problem!!!

Answers

Answer:

Flowers: $19.98Jewelry: $18.92Gift Certificates: $14.52

Step-by-step explanation:

You want the values of three expenditures, given three relations between them.

(The first thing to realize is that the question isn't about averages at all. It is about values that are described as averages.)

Setup

Let f, j, c represent the (average) amounts spent on flowers, jewelry, and gift certificates, respectively. The three given relations are ...

  f + j + c = 53.42

  j = 4.40 + c

  f + c = 15.58 + j

Solution

Using the second equation to substitute for j in the third, we have ...

  f +c = 15.58 +(4.40 +c)

  f = 19.98 . . . . . . . . . . . . . . simplify

Using this and the second equation to substitute into the first, we have ...

  19.98 +(4.40 +c) +c = 53.42

  24.38 +2c = 53.42

  2c = 29.04

  c = 14.52

Then ...

  j = 4.40 +c = 4.40 +14.52 = 18.92

The average expenditures are ...

Flowers: $19.98Jewelry: $18.92Gift Certificates: $14.52

__

Additional comment

This solution is one of many ad hoc methods that could be used. There are also graphing and matrix methods available for solving a set of equations like this. The attachment shows a calculator matrix solution.

The quadrilaterals ABCD and JKLM are similar.
Find the length x of MJ.

Answers

Answer:

x = 4.8

Step-by-step explanation:

since the quadrilaterals are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{MJ}{DA}[/tex] = [tex]\frac{LM}{CD}[/tex] ( substitute values )

[tex]\frac{x}{6}[/tex] = [tex]\frac{2.4}{3}[/tex] ( cross- multiply )

3x = 6 × 2.4 = 14.4 ( divide both sides by 3 )

x = 4.8

Select the 2 values of X that are root of this equation X² + 2X (-6) = 0

Answers

The two values that serves as the root of the equation are  -1-√7 and  -1+√7

Root of quadratic equation

Given the quadratic equation below;

X² + 2X (-6) = 0

x^2 + 2x - 6 = 0

Using the general formula

x = -2±√2²-4(1)(-6)/2(1)

x = -2±√4+24/2

x = -2±√28/2

x =  -2±2√7/2

x = -1±√7

Hence the two values that serves as the root of the equation are  -1-√7 and  -1+√7

Learn more on quadratic equation here: https://brainly.com/question/25841119

#SPJ1

Find the coordinates of the point
7/10 of the way from A to B.

The coordinates of the point
7/10 of the way from A to B are

Answers

Answer:

(4,-4)

is the way from AtoB

Write 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 in exponential form. Write your answer as: base^exponent

Answers

Answer: I could be wrong but I'm pretty sure it's 12^9 but again I could be wrong

Step-by-step explanation:

The total area of Wisconsin
is 65,498 square miles. Of that, about
80% is land area. About how many
square miles of Wisconsin is not land
area?

Answers

Answer:

the other 20%

Step-by-step explanation:

calculate 20% of 65498

Answer:

13,099.6 square miles

Step-by-step explanation:

80%*65,498=

80/100 * 65,498=

4/5 * 65,498=52,398.4 square miles of land area

65,498-52,398.4=       ==> subtract the total area of Wisconsin by the total land area to get the total area that isn't land.

65,498.0-52,398.4=13,099.6 square miles of area that isn't land

In the diagram below, ΔABC ≅ ΔDEF. Complete the statement BC⎯⎯⎯⎯⎯⎯⎯⎯≅ B C ¯ ≅ ___

Answers

Answer:

[tex]\overline{BC} \cong \overline{EF}[/tex]

Step-by-step explanation:

Corresponding parts of congruent triangles are congruent.

Simplify the expression below:

-3/7 ( y-28) - 1/21 y


please show your work and i'll give brainliest :,)

Answers

(-5/7)*(y-28)-((1/21)*y) = 0

(-5/7)*(y-28)+(-1/21)*y = 0

-5/7*(y-28)-y/21 = 0

(-5/7*21*(y-28))/21-y/21 = 0

-5/7*21*(y-28)-y = 0

420-16*y = 0

(420-16*y)/21 = 0

(420-16*y)/21 = 0 // * 21

420-16*y = 0

420-16*y = 0 // - 420

-16*y = -420 // : -16

y = -420/(-16)

y = 105/4

What is the place value of 5 in 62,506,300,782?
A. Hundred thousands
B. Ten thousands
C. Millions
D. Hundred millions

Answers

Answer: D. Hundred millions

Hope this helps!

Simplify the radical √20​

Answers

It would be 4.472 im pretty sure

I think of a number. I add 1090 to the number.
I subtract 450 from the result. The answer is 760.
What is the number I first thought of?

Answers

Answer:

120

Step-by-step explanation:

call the number x,

then x+1090-450

so x+640=760

x=760-640

x=120

hope this works :)

Answer:

120 is the number u thought of first

Step-by-step explanation:

1090-450=640

if we add 120 into 1090

then it will be 1210

so 1210-450=760

Solve the inequality.
6 (x/2+4)>9

Answers

Answer is x > -5

fid comon demoninator

Answer: x>−5

Step-by-step explanation:

[tex]6(\frac{x}{2} +4) > 9[/tex]

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

[tex]\frac{x}{2} +4 > \frac{9}{6}[/tex]

Reduce the fraction    

[tex]\frac{9}{6}[/tex]

 to lowest terms by extracting and canceling out 3.

[tex]\frac{x}{2} +4 > \frac{3}{2}[/tex]

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

x+8>3

Subtract 8 from both sides.

x>3−8

Subtract 8 from 3 to get −5.

x>−5

On Flight #447 if 130 people are on the flight how many can get both headphones and a blanket

Answers

Answer: 106

Step-by-step explanation:

because there is 106 headphones 106 people can get and there is 16 blankets 156 people can get so 106 people can get headphones and blankets  

How do u write Nineteen million three hundred thousand twenty five and twenty two hundredths

Answers

19,300,025.02 hope this helps!

i need this in a hour O_o ​

Answers

Answer:

x= 5/12,y=− 5/4

Step-by-step explanation:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

6x−12y=24,4x+2y=8

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

6x−12y=24

Add 12y to both sides of the equation.

6x=12y+24

Divide both sides by 6.

x= 6/1 (12y+24)

Multiply  6

1 times 24+12y.

x=2y+4

Substitute 4+2y for x in the other equation, 4x+2y=8.

4(2y+4)+2y=8

Multiply 4 times 4+2y.

8y+16+2y=8

Add 8y to 2y.

10y+16=8

Subtract 16 from both sides of the equation.

10y=−8

Divide both sides by 10.

y=− 5/4

​Substitute − 5/4  for y in x=2y+4. Because the resulting equation contains only one variable, you can solve for x directly.

x=2(− 5/4 )+4

Multiply 2 times − 5/4 .

x=− 5/8 +4

Add 4 to − 5/8 .

x= 5/12

what is a - b + 8 = 42

Answers

Answer:

a-b+8=42
a-b=42-8
a-b=36
espero t sirva

Answer:

b=34

Step-by-step explanation:

The line y=kx+4 goes through the point (2,-2)
Find the value of k.

Answers

Answer:

k= -3

Step-by-step explanation:

Since we know the line will go through the point (2,-2), we can plug these values into our x,y variables to solve for k. Our 2 is the x-value and our -2 is the y-value.

y = kx+4

-2 = k(2)+4

To get k by itself, we first have to subtract the 4 from both sides.

-2-4 = k(2)+4-4

-6 = k(2)

Then, we can divide each side by the 2 to get our answer.

-6/2 = k(2)/2

k = -3

Answer:

k=-3

Step-by-step explanation:

                                                                                                               

12.4%of what number is 7.13?

Answers

Answer:57.7

Step-by-step explanation:

Given P(A) = 0.74, P(B) = 0.85 and P(A|B) = 0.84, find the vi P(A and B), rounding to the nearest thousandth, if necessary.

Answers

The value of the given statement rounding to the nearest thousandth = 0.714.

What exactly are dependent events?

Dependent occurrences are ones that are dependent on previous events. The outcomes of prior events have an impact on these occurrences. Dependent events are two or more occurrences that are dependent on one another. If one event is altered by chance, another is most likely to differ.

What exactly is the distinction between dependent and independent?

The independent and dependent factors are the two most crucial variables in a research experiment. The experimental has authority over the independent variable. The variable that varies in reaction toward the independent variable is known as the dependent variable.

According to the information provided:

P(A) = 0.74

P(B) = 0.85

P(A|B) = 0.84

Using  dependent events formula:

P(A∩B) = P(A/B) × P(B)

            = 0.84 X 0.85

            = 0.714

The value of the given statement rounding to the nearest thousandth = 0.714.

To know more about dependent events visit:

https://brainly.com/question/12138721

#SPJ9

what is the value of the sum 1/3 and 2/5

Answers

Answer:11/15

Step-by-step explanation:

you have to change them to common denominators.

i chose 15.

to make the denominator for 1/3 into 15 you have to multiply it by 5 which means you have to multiply the numerator (1) by the same thing which gives you 5/15

to make the denominator for 2/5 into 15 you have to multiply the denominator by 3 so you have to multiply the numerator (2) by the same thing which gives you 6/15

you now have the equation 5/15 + 6/15

to add them together you leave the bottom numbers the same and add the top ones which gives you 11/15

Answer:

0.7333333333333333 = 11/15

Step-by-step explanation:



1/3 = 5/15

2/5 = 6/15


add them, and now you get

(5+6)/15 = 11/15

Graph = 2/3x

Please graph the graph right and answer the ones that apply

Answers

1. Yes, the equation represent the proportionality relationship.

2. Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

3.Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

Given a picture in that we can see a graph and 3 option.

We have to check weather that 3 option satisfy the equation and what are they.

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

1st option: Is the equation represent the proportionality relationship.

Yes, the equation represent the proportionality relationship.

If we see the proportionality rule that is

The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k.

A proportionate relationship exists if an equation in a different form can be rewritten as shown above.

Here, the equation is in the form of y=kx.

Therefore, Yes, the equation represent the proportionality relationship.

2nd option: the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

The amount of change in y for a change of one unit in x is the unit rate of change of y with respect to x.

The slope is [tex]\frac{2}{3}[/tex].

Therefore, Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

3rd option: The slope of the line is [tex]\frac{2}{3}[/tex]

Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

It is possible to simplify the equation of the slope to the form

y=mx+b, where m is the slope of the line and b is constant.

y is the dependent variable and x is the independent variable.

By the equation [tex]y=\frac{2}{3}x[/tex]

Therefore, Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

To learn more about equation visit: https://brainly.com/question/10413253

#SPJ9

Other Questions
how many mm are equal to 4.75x10^-2 m The two caveats of the sullivan principles are first, a company should not obey the apartheid laws in its own south african operations and second, a company should. Samantha works on the weekends doing hair for her classmates.For every head she does ,she charges 26$ complete the table Anorexia can be the result of what?OA. Being sheepishB. Eating healthy foodsC. OvertrainingD. Not sleeping enough Which of the following is an example of a "hidden task"A. A graphic designer is trained to use a new type of design software.B. The office manager maintains an inventory of office supplies because he knows employees need them.C. The office manager proofread marketing material because she has excellent editing skillsD. The human resource manager stays up to date on laws regarding workplace safety. What is the greatest common factor of 16 , 24 , 48 (14+24i)-(26-3i)+10i(11+11i) in standard form Please help due soon. international travel is usually more expensive than domestic travel. a recent survey found that the average per-person cost of a 12-day international vacation is $1,755. this includes transportation, food, lodging, and entertainment. si units are the modern form of the they are working hard. Here the word "hard"is an/n ......... . 10=7-mDo I minus by 10 on each side or do I add minus by 7? There is apeopleliving in the Saudi ArabiaPeninsula.uniteddiversity of Write as a14/11as a decimal.0 0.360.360.036O 0.36 Which disorder might be treated with a dopamine antagonist?major depressive disorderschizophreniaAlzheimers diseaseParkinsons diseasegeneralized anxiety disorder In how many categories did the South hold an advantageover the North? Ms. Rivera has 134 crayons. About how manycrayons does she have? Round to the nearest 100. What immediate challenges did Washington face as commander of the Continental army? Check all of the boxes that apply.No state militiasPoorly trained volunteersShort enlistment termsA small national army A gardener spread 3 4/5 bags of mulch evenly over his 2 equal-sized vegetable beds. Howmuch mulch did he put on each vegetable? The total height of 6 layers of wedding cake is 80 cm 4 mm. What is the height of each layer?