Ruth borrowed $2000, part from each of two different sources, for a 6-month period. One charged 6% interest and the other 8% interest. When she paid them off, she paid a combined total of $68 in interest. How much did she borrow at each rate? Show how you got it

Answers

Answer 1
X is 6% interest
Y is 8% interest

X+Y=2000 or 0.08X+0.08Y=160
0.06X+0.08Y=68*2
Subtract the two equations:
0.08X-0.06X+0.08Y-0.08Y=160-68*2
0.02X=92
X=1200
Y=800

Related Questions

how to simplify 6/35

Answers

well if you think about it you can evenly divide both the denominator and numerator by 6. when you do this the fraction becomes 1/5.

Romeo and Juliet headed north at 8.a.m by noon Romeo was 80 miles ahead of Juliet what was romeos speed if Juliet's speed was 30 miles per hour? Will give brainlest for help!!!

Answers

He was going at 50mph

Suppose that a department contains 8 men and 16 women. how many different committees of 6 members are possible if the committee must have strictly more women than men

Answers

the committees will consist of 5 women and 1 man  OR 4 women and 2 men.

Number of committees of 5 W and 1 M = 16C5 * 5 =  4368
Number with 4 W and 2 M  =  16C4* 5C2 =  1820 * 10 = 18200

Answer is 18200 + 4368 =  22,568

Begin by writing out all possible ways that women are more than men. 

6 women, 0 men 
5 women, 1 man 
4 women, 2 men <-- 3 men and 3 women would be equal so this is the last one

Now find out the combinations for each (knowing you need to choose 6 people from the group)

(16C6) OR (16C5)(8C1) OR (16C4)(8C2) 
= (16C6) + (16C5)(8C1) + (16C4)(8C2) 
=8008+34944+50960
=93912

Therefore, there should be 93912 ways of arranging this.

Hope I helped :) 

First step to solve the equation 9h-21=99

Answers

9h-21=99
+21 +21 add 21 to both sides
9h= 180
/9 /9 divide 9 by both sides
h= 13.3~

What is the solution to 3x+2.4≥3.0

Answers

3x  ≥3.0 - 2.4
3x ≥ 0.6
x ≥ 0.6/3
x ≥ 0.2 is your answer 

Answer:

A

Step-by-step explanation:

Which graph represents the division of -12 / 4 ?

Answers

The top graph represents the division of -12/4

Sakura speaks 150 words per minute on average in Hungarian and 190 words per minute on average in polish she once gave cooking instructions in polish Sakura spent 5 minutes total giving both instructions and spoke 370 more words in polish than Hungarian

Answers

let  p   time in minutes speaking Polish
let  h   time in minutes speaking Hungarian

p  +   h   =  5    equation 1 

190 p - 150 h = 370          equation 2

multiply eq. (1) by 150 (both sides) 

15 0p + 150 h = 750 

190p -150 h = 370 

add the two eqiations we get :

190 p + 150p = 370 + 750

340 p = 1120

p= 1120/ 340 =  3.29 

3 minutes speaking Polish and 2 minutes speaking Hungarian.


make sure if the  number 370 ?? i think it is wrong , it can be 270  because i get a point in the answer 

When two lines intersect to form a 90 degree angle, these lines are called ________ lines?

Answers

When two lines intersect to form a 90 degree angle, these lines are called perpendicular lines.

Answer:

perpendicular lines.

Step-by-step explanation:

Answers to question 5 and 6 please xx

Answers

5a) a
5b) 3a
5c) b
5d) a²/b
5e) 4ab
5f) a           (take out the a, from both (bring to outside) cancel the rest
6a)8a^5
6b)15b^7
6c)24a^4b^2
6j)18a^4b^9


hope this helps

2/3 + y - 1/9 = 7/9 Solve for Y
2 1/2x - 3/4(2x + 5) = 3/8 Solve for X
0.9 (x + 1.4) - 2.3 + 0.1x = 1.6 Solve for X

Answers

A. Y = 2/9
B. X =  11/24
C. X = 2.64

Answer:

A. Y = 2/9

B. X =  11/24

C. X = 2.64

how do you solve this equation?

216=-4(8n-6)

Answers

You would first apply the Distributive Property to get rid of the parentheses:
216 = -32n + 24
You would then subtract 24 from both sides:
192 = -32n
Then you would divide each side of the equation by -32:
-6 = n

Hope this helps.
216=-32n+24
192=-32n
-6=n

Let f(x) = x2 and g(x) = x − 3.

Evaluate (f ∘ g)(−2).


1


25


−7


20 My guess

Answers

Answer:

[tex]25 = f(g(-2))[/tex]

Step-by-step explanation:

[tex]g(-2) = -2 - 3 = -5 \\ \\ f(-5) = {[-5]}^{2} = 25 \\ \\ 25 = f(g(-2))[/tex]

I am joyous to assist you anytime.

For the geometric sequence 3, 12, 48, 192 find the indicated term

Answers

768

3x4= 12
12x4= 48
48x4= 192
192x4=768

rewrite d= 2r in function notation

Answers

Final answer:

The equation d = 2r can be rewritten in function notation by replacing 'd' with 'f(r)', giving the function f(r) = 2r.

Explanation:

To rewrite the equation d = 2r using function notation, we first need to understand that function notation is a way to represent a function that is derived from a certain equation. Here, the equation given is d = 2r, where d is in terms of r.

To translate this into function notation, we would change d to f(r). The letter f stands for 'function', and the (r) is the variable that the function is dependent upon. Therefore, the equation d = 2r would be rewritten in function notation as f(r) = 2r.

Learn more about Function Notation here:

https://brainly.com/question/5025688

#SPJ12

Why did Benjamin Franklin use the pseudonym “Richard Saunders” when writing Poor Richards Almanac?

Answers

The name Richard Saunders was inspired by the name of a London almanac writer named Richard Saunders who was an English physician and astrologist.

The naming of “Poor Richard’s Almanac” was based on a another almanac called Poor Robin. There is some humor behind the naming of his almanac too: Poor Richard’s sounds like an oxymoron (Poor Rich).

Hope this helps, and May the Force Be With You!

-Jabba

If you know the density and volume of a substance, how could you find its mass?

Answers

Since D=MV, we can infer that M=D/V
That is your equation----------------^

what is the numerical sum of angle DEA (X+25) and angle AEB (9x+10) ?

Answers

10x + 35
If it is just the sum then it is this.

An iron fence reacts with the oxygen in the air to form rust. The formation of rust is an oxidation-reduction reaction and a _____ reaction.
A. decomposition
B.combustion
C. synthesis
D. single-replacement

Answers

Final answer:

The formation of rust on an iron fence is a synthesis reaction, where iron combines with oxygen in the air to create iron oxide. During this process, iron is oxidized and oxygen is reduced, making it an oxidation-reduction (or redox) reaction.

Explanation:

The formation of rust is an oxidation-reduction reaction and a synthesis reaction. Rusting occurs when iron reacts with oxygen in the air, typically in the presence of water, to form iron oxide.

The process can be summarized as iron (Fe) being oxidized to iron(II) ions (Fe2+) which react further with oxygen and water to produce a hydrated iron(III) oxide, commonly known as rust (Fe2O3·xH2O).

This process is classified as a synthesis reaction because it involves the combination of simpler substances - iron and oxygen - to form a more complex compound, namely iron oxide.

In comparison to other types of reactions, decomposition refers to a single compound breaking down into two or more simpler compounds or elements.

Combustion reactions involve fuel (often a hydrocarbon) reacting with oxygen to produce carbon dioxide and water.

Lastly, single-replacement reactions occur when an element replaces another element in a compound. Since the reaction of iron with oxygen adds oxygen to create a new product, rather than decomposing, combusting, or substituting, it is indeed a synthesis reaction.

If you are given the height and base of a pyramid, how would you get the slope of one of the triangular faces?

Answers

by using the Pythagorean theorem

 use the height and half the base dimension for the 2 edges of a triangle and the slope ( slant height) would be the hypotenuse

 so:  SQRT(height ^2 + half of base^2) = hypotenuse ( Slant height)


Is it true that a continuous function that is never zero on an interval never changes sign on that​ interval? give reasons for your answer?

Answers

Yes it is true that a continuous function that is never zero on an interval never changes sign on that interval. This is because of ever important Intermediate Value Theorem.

Yes, It is true that a continuous function that is never zero on an interval never changes its sign on that​ interval.

What is a continuous function?

In mathematics, a continuous function is a function such that a continuous variation of the argument causes a continuous variation of the value of the function. This indicates that there aren't any discontinuities or sudden changes in value.

Unchanged sign is a property of continuous functions that are never zero on an interval, hence this is true. This is due to the perennially significant Intermediate value theorem.

Therefore, It is true that a continuous function that is never zero on an interval never changes its sign on that​ interval.

To know more about continuous function follow

https://brainly.com/question/18102431

#SPJ2

You make skateboard ramps by cutting pieces from a board that is 12 1/2 feet long.
a. your friend estimates you can cut 6 ramps from the board. is her estimate reasonable? explain. how many ramps can you cut from the board? how much wood is left over?

Answers

The length of the ramp is unknown. 
If 6 ramps were cut from a board that is 12 1/2 feet long, the ramps would be about 2 feet long each which seems like a reasonable answer. The questions regarding how many boards are cut would need the length of the ramps. Lets say that the length is x. You can get 12 1/2 divided by x boards. In order to find out how much is left over, take the number of boards made, multiply it by how long they are. This product is then subracted from 12 1/2. 
Final answer:

The estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable. Each ramp will have a length of 2 1/12 feet, and no wood will be left over.

Explanation:

To determine if the estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable, we can calculate the length of each ramp by dividing the total length of the board by the number of ramps.

12 1/2 feet is equivalent to 12 + 1/2 feet. To divide by a fraction, we can multiply by the reciprocal. So, when we divide 12 1/2 by 6, we get (12 + 1/2) / 6 = 12/6 + 1/2 / 6 = 2 feet + 1/12 feet = 2 1/12 feet.

Therefore, each ramp will have a length of 2 1/12 feet. Since 6 ramps multiplied by 2 1/12 feet is 12 1/2 feet, the estimate is reasonable. No wood will be left over.

Identify the function that has a vertex of (2,-1) and is stretched vertically by a factor of 3.

f(x) = ⅓|x - 2| - 1
f(x) = |x - 2| + 4
f(x) = ⅓|x + 2| - 1
f(x) = 3|x - 2| - 1

Answers

f(x) = 3|x - 2| - 1
is the function 


Answer:

[tex]f(x)=3|x-2|-1[/tex]

Step-by-step explanation:

Identify the function that has a vertex of (2,-1) and is stretched vertically by a factor of 3.

The option are absolute function, So the parent function is y=|x|

Vertex form of absolute function is

[tex]y=|x-h|+ k[/tex] where (h,k) is the vertex

vertex of (2,-1) h=2, k =-1

the function becomes

[tex]f(x)=|x-2|-1[/tex]

function is stretched vertically by a factor of 3

when f(x) is vertically stretched by a factor of 'a'.We multiply the factor with f(x)

[tex]f(x)=3|x-2|-1[/tex]

A trainer gives his horse, Caballo, 7 gallons of water every day from a 57 - gallon container. How many days will Caballo receive his full portion of water from the container? On which number day will the trainer need to refill the container of water?

Answers

The trainer gives his horse, Caballo water 7 gallons of water a day out of a 57 gallon container, so for eight days the horse gets his full portion of water, on day 9 the trainer must add more water to the container.

A bag contains 4 red marbles, 5 yellow marbles, and 6 blue marbles. three marbles are to be picked out randomly (without replacement). what is the probability that exactly two of them have the same color

Answers

A 50 50 percent , I think

A population grows with an annual growth rate of 16.5 % per year. (a) what is the monthly growth rate

Answers

the monthly growth rate would be 16.5% divided by 12 which is 1.3%

A line parallel to a triangle's side splits AB into lengths of x - 7 and x - 3. The other side, AC, is split into lengths of x and x + 12. What is the length of AC?

Answers

Given: x – 7 and x – 3 &  AC is split into lengths of x and x + 12.

Solution:

(x – 7) / (x – 3) = x / (x + 12)

(x – 7) (x + 12) = x (x – 3)

x^2 + 5x – 84 = x^2 -3x

8x = 84

x = 10.5
Thus,

AC = x + x + 12

= 10.5 + 10.5 + 12

= 33 would be the length of AC

33

[tex]\frac{x-7}{x} = \frac{2x-10}{2x+12}[/tex] → x = [tex]\frac{21}{2}[/tex]

AC = x + x + 12 = [tex]\frac{21}{2} + \frac{21}{2}[/tex] +12 = 33

Bill spends two days driving from point a to point
b. on the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. if during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?

Answers

Answer: his average speed on the second day is 35 miles per hour

Step-by-step explanation:

Bill spends two days driving from point a to point b

Let x = his speed on the first day.

Let y = his speed on the second day

Speed = distance / time

Time = distance / speed

Total time spent on the trip is 18 hours

Let time that he spent on the first day be t hours

Time that he spent on the second day will be 18 - t

Bill drove 2 hours longer on the second day than on the first day. This means

t = 18 - t + 2

t+t = 18+2

2t = 20

t = 10

He spent 10 hours on the first day.

He spent 18-10 = 8hours on the second day.

Bill drove at an average speed of 5 miles per hour faster than he drove on the second day. This means that

x = y + 5 - - - - - - - -- 1

Distance travelled on the first day = speed on the first day × time spent. This becomes

10 × x = 10x miles

Distance travelled on the second day = speed on the second day × time spent. This becomes

8 × y = 8y miles

He drove a total of 680 miles over the course of the 18 hours. This means that

10x + 8y = 680 - - - - - - - - 2

Substituting equation 1 into equation 2, it becomes

10(y + 5) + 8y = 680

10y + 50 + 8y = 680

10y + 8y = 680 - 50

18y = 630

y = 630/18 = 35 miles per hour

x = y + 5 = 35 + 5

x = 40 miles per hour

If w||v, solve for x.

Answers

The two angles are alternate exterior angles, so they have the same measure.

5x+42=8x-15
5x+57=8x
57=3x
x=19

Evaluate f(x)= 1.8 X 2^x for x=6

A: 115.2

B: 2176.78

C: 21.6

Answers

by substitution
f(6) = 1.8×2^(6)
= 1.8×64
= 115.2

Question:

Evaluate f(x)= 1.8 X 2^x for x=6

Answer choices:

A: 115.2

B: 2176.78

C: 21.6

Answer:

A:115.2

Step-by-step explanation:

F(x) F(6)

=1 . 8 • 2 • 1

=1 . 8 • 261

=1 . 8 • 64115.2

=115.2

Hence, your answer is A:

Two events e and f are​ __________ if the occurrence of event e in a probability experiment does not affect the probability of event f.

Answers

Two events e and f are​ independent if the occurrence of event e in a probability experiment does not affect the probability of event f. And if it opposite to that and affect the probability of event f, then two events are dependent.
When we collect the possible outcomes from a probability experiment, this is called an event and it may consist of one or more than one outcomes.
Final answer:

Two events are independent if the occurrence of one event does not affect the probability of the other event.

Explanation:

Two events are independent if the occurrence of one event does not affect the probability of the other event. This means that the outcomes of the two events are not related and the probability of one event happening does not change based on whether the other event occurred or not.

For example, if you flip a coin and roll a die, the outcome of the coin flip does not affect the probability of getting a certain number on the die roll. The two events are independent.

Learn more about independent events here:

https://brainly.com/question/32716243

#SPJ12

Other Questions
Which act is also known as the anti-injunction act?a. conflict-reduction actb. cooperative labor-management actc. norris-laguardia actd. landrum-griffin act? What is the property of 2x32x5=2x5x32= Think of someone in your life who is a leader. Your teacher? Your coach? Your parent? In 50 words or less, provide an example of how this person demonstrates leadership characteristics. Which of the following is a physiological adaptation? a. group hunting b. hyoid bone adapted for roaring c. dark coloration d. migration Which of the following works helped to redefine the symphony as a genre? identify the terms and like terms in the expression - x - 9x*2 + 12x*2 + 7 Who makes up most of the workforce in the food services industry? busserschefs managers supervisors servers simplify the expression (5-5i)-(-6-3i)How do I solve this? Either teach me how, or help me with a few other simmilar ones. What is the equation of the line (8,-6) 8x-3y=7 A pattern of fat thats predominantly distributed around the hips and thighs, and is more common in women, is known as _______ obesity. Jasmine opened a bank account. She deposited $84.50 into her account every month for 20 months. She used $50.50 every month to pay for dance lessons. After 20 months, she used 1 over 4 of the total money left in her account to go to a music camp. What is the total amount of money Jasmine spent to go to the music camp? $115.00 $135.00 $155.00 $170.00 During renaissance, churches that grew out of protests against the power abuses of the Roman Catholic Church were called You are on an elevator that is plummeting toward the ground at 30 m/s and you jump up right before it hits the ground. you jump upward with a velocity of 5 m/s. at what speed do you hit the ground? Which of these is a renewable resource?a)coalb)geothermalc)petroleumd)potash? What was the motto which became popular as the result of unjust acts? An important function of the regional federal reserve banks is Will give brainliest! How long will it take the tool to fall to the ground?The function for objects dropped from a height where t is the time in seconds, h is the height in feet at time t, and h0 is the initial height is h(t)=-16t^2+h0. The building I already figured to be 162 feet.Thank You!! I need help to figure out n Which command is used to combine two or more cells together into one cell Why did Europeans of the 1400s want to send explorers to East Asia? a.to find places where Europeans could settle b.to take over the land and people there c.to find the secrets of Asian wealth d.to get spices, gold, silk, and jewels? Steam Workshop Downloader