You invested $ 7000 between two accounts paying 3 % and 5 % annual? interest, respectively. If the total interest earned for the year was $ 290 comma how much was invested at each? rate?

Answers

Answer 1

Answer:

In the first account was invested [tex]\$3,000[/tex]  at 3%

In the second account was invested [tex]\$4,000[/tex]  at 5%

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

First account

[tex]t=1 years\\ P=\$x\\ r=0.03[/tex]

substitute in the formula above

[tex]I=x(0.03*1)[/tex]

[tex]I=0.03x[/tex]

Second account

[tex]t=1 years\\ P=\$(7,000-x)\\ r=0.05[/tex]

substitute in the formula above

[tex]I=(7,000-x)(0.05*1)[/tex]

[tex]I=350-0.05x[/tex]

Remember that

The interest is equal to [tex]\$290[/tex]

so

Adds the interest of both accounts

[tex]0.03x+350-0.05x=\$290[/tex]

[tex]0.05x-0.03x=350-290[/tex]

[tex]0.02x=60[/tex]

[tex]x=\$3,000[/tex]

therefore

In the first account was invested [tex]\$3,000[/tex]  at 3%

In the second account was invested [tex]\$7,000-\$3,000=\$4,000[/tex]  at 5%

Answer 2

$3000 was invested at 3% and $4000 was invested at 5%.

To determine how much was invested in each account, follow these steps:

1. Define variables:

  - Let [tex]\( x \)[/tex] be the amount invested at 3% interest.

  - Let [tex]\( y \)[/tex] be the amount invested at 5% interest.

2. Set up the equations:

  - The total amount invested is $7000:

    [tex]\[ x + y = 7000 \][/tex]

  - The total interest earned is $290. The interest from each account is [tex]\( 0.03x \)[/tex] and [tex]\( 0.05y \),[/tex] respectively:

   [tex]\[ 0.03x + 0.05y = 290 \][/tex]

3. Solve the system of equations:

  From the first equation:

  [tex]\[ y = 7000 - x \][/tex]

  Substitute [tex]\( y \)[/tex] into the second equation:

  [tex]\[ 0.03x + 0.05(7000 - x) = 290 \][/tex]

  Distribute and simplify:

  [tex]\[ 0.03x + 350 - 0.05x = 290 \][/tex]

  [tex]\[ -0.02x + 350 = 290 \][/tex]

  [tex]\[ -0.02x = 290 - 350 \][/tex]

  [tex]\[ -0.02x = -60 \][/tex]

  [tex]\[ x = \frac{-60}{-0.02} \][/tex]

  [tex]\[ x = 3000 \][/tex]

  Now find [tex]\( y \)[/tex]:

  [tex]\[ y = 7000 - x \][/tex]

 [tex]\[ y = 7000 - 3000 \][/tex]

  [tex]\[ y = 4000 \][/tex]


Related Questions

The interest rate r required to increase your investment p to the amount a in t years is found by [tex]r=(\frac{a}{p} )^\frac{1}{t} -1[/tex]. Find the interest rate r for p = 2700, a = 6400, and t = 3. Round to the nearest hundredth.

Answers

Final answer:

The interest rate required to increase an investment of $2700 to $6400 in 3 years, using the formula r=(a/p)^(1/t) - 1, is approximately 38.5% per year when compounded annually.

Explanation:

The subject at hand deals with the concept of finding the interest rate on an investment. The provided equation, which represents the interest rate formula, is: r=(a/p)^(1/t) - 1. Here, the variables represent the following: r is the interest rate, a is the amount of money accumulated after t years (the future value of the investment), p is the principle/original amount (the initial value of the investment), and t is the time in years. By inserting the given values (p = 2700, a = 6400, t = 3) into the formula, we get: r = (6400 / 2700)^(1 / 3) - 1.

The next step is to calculate the arithmetic for the values inside the parenthesis first, then raise it to the power of 1/3 (which is the cube root), and finally subtract 1 from the result. Doing these calculations you obtain approximately 0.385, or 38.5% when expressed as a percentage. So, the interest rate that is required to increase your investment of $2700 to $6400 in 3 years is approximately 38.5% per year when compounded annually.

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Please answer this question, will give brainliest!

Answers

m∠H = 50°

∠H is a inscribed angle, and so that the intercepted arc would be twice the amount of the angle.

Arc KI = 100°

Because ∠KGI & ∠HKI share the same arc, the measurement for ∠KGI will be the same as ∠HKI, or 50°

m∠KGI = 50°

Next, find m∠KJI. arcKJI = 2(∠H) = 2(50) = 100

m∠KJI = 100°

~

Given sin theta= 6/11 and sec theta < 0, find cos theta and tan theta.

Answers

Answer: option a.

Step-by-step explanation:

By definition, we know that:

[tex]cos^2(\theta)=1-sen^2(\theta)\\\\tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

Substitute [tex]sin(\theta)=\frac{6}{11}[/tex] into the first equation, solve for the cosine and simplify. Then, you obtain:

[tex]cos(\theta)=\±\sqrt{1-(\frac{6}{11})^2}\\\\cos(\theta)=\±\sqrt{\frac{85}{121}}\\\\ cos(\theta)=\±\frac{\sqrt{85}}{11}[/tex]

As [tex]sec\theta<0[/tex] then [tex]cos\theta<0[/tex]:

[tex]cos(\theta)=-\frac{\sqrt{85}}{11}[/tex]

Now we can find [tex]tan\theta[/tex]:

[tex]tan\theta=\frac{\frac{6}{11}}{-\frac{\sqrt{85}}{11}}\\\\tan\theta=-\frac{6\sqrt{85}}{85}[/tex]

Answer:

a

Step-by-step explanation:

A car travels at an average speed of 48 miles per hour. How long does it take to travel 180 miles?

Answers

Answer:

3 hours and 45 minutes

Step-by-step explanation:

Final answer:

The time to travel 180 miles at an average speed of 48 miles per hour is approximately 3.75 hours. This was calculated using the formula Time = Distance / Speed.

Explanation:

The question is based on time, speed, and distance, all correlating with each other, and to solve, we will use the following frequently used formula:

Time = Distance / Speed

We can substitute the given values into our formula. We know our distance is 180 miles and our speed is 48 miles per hour. So, our equation becomes:

Time = 180 miles / 48 miles per hour

After calculating this equation, we get approximately 3.75 hours.

So, it would take approximately 3.75 hours to travel 180 miles at an average speed of 48 miles per hour.

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many locations require that renters be paid interest on their secuity deposits. If ypu have a security deposit of $1,700, how much interest would you expect to earn per year at 5 percent?

Answers

Answer: $85

Step-by-step explanation: The formula for interest is I = PRT, where I equals interest, P equals principal, R equals rate and T equals time.

I = 1,700 x .05 x 1 = $85

You can expect to earn $85 interest for one year on the security deposit.

A cheesecheese can be classified as either raw dash milkraw-milk or pasteurizedpasteurized. Suppose that 9797​% of cheesescheeses are classified as pasteurizedpasteurized. ​(a) Two cheesescheeses are chosen at random. What is the probability that both cheesescheeses are pasteurizedpasteurized​? ​(b) NineNine cheesescheeses are chosen at random. What is the probability that all ninenine cheesescheeses are pasteurizedpasteurized​? ​(c) What is the probability that at least one of ninenine randomly selected cheesescheeses is raw dash milkraw-milk​? Would it be unusual that at least one of ninenine randomly selected cheesescheeses is raw dash milkraw-milk​?

Answers

Yes. Yes it is. Thanks for the awesome question.

Answer:

chese is th awnser

Step-by-step explanation:

Susan is 60 inches tall. Myra is 6 inches taller than Elaine, who is 4 inches shorter than susan how tall is myra

Answers

62 inchezzzzzzz so 60-4 = 56 --- 56 +6 = 62

So Confused!! Somebody Plz Explain How To Do!!!!!!!

For the following system, use the second equation to make a substitution for y in the first equation.

3x + y = 1
y + 4 = 5x

What is the resulting equation?

A.) 3x + 5x - 4 = 1
B.) 3x + 4 - 5x = 1
C.) 3x + 5x + 4 = 1

Answers

Answer:   A) 3x + 5x - 4 = 1

Step-by-step explanation:

The second equation is y + 4 = 5x.  Solve this equation for y by subtracting 4 from both sides. --> y = 5x - 4

Now replace "y" in the first equation with "5x - 4".

     3x +      y     = 1

-->  3x + (5x - 4) = 1

Identify the area of the rhombus.

Answers

Answer:

[tex]A=240\ m^{2}[/tex]

Step-by-step explanation:

we know that

A rhombus is a parallelogram with four congruent sides, the diagonals are perpendicular bisectors of each other

The area of a rhombus is equal to

[tex]A=\frac{1}{2}(D1*D2)[/tex]

where

D1 and D2 are the diagonals

In this problem we have

[tex]D1=16\ m[/tex]

Applying the Pythagoras Theorem find D2

[tex]17^{2} =(D2/2)^{2}+(16/2)^{2}[/tex]

[tex](D2/2)^{2}=17^{2}-(16/2)^{2}[/tex]

[tex](D2/2)^{2}=225[/tex]

[tex](D2/2)=15[/tex]

[tex]D2=30\ m[/tex]

Find the area of the rhombus

[tex]A=\frac{1}{2}(16*30)=240\ m^{2}[/tex]

Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing intraocular lenses used in the human eye following cataract surgery. 300 lenses were tumble-polished using the first polishing solution, and of this number, 249 had no polishing-induced defects. Another 300 lenses were tumble-polished using the second polishing solution, and 196 lenses were satisfactory upon completion. Is there any reason to believe that the two polishing solutions differ? Use α = 0.01. What is the P-value for this test? There significant difference in the proportion of polishing-induced defects produced by the two polishing solutions at the 0.01 level of significance. The P-value is . Round your answer to three decimal places (e.g. 98.765).

Answers

Final answer:

To determine if there is a significant difference between two polishing solutions, a two-proportion z-test can be used, comparing the proportions of polishing-induced defects. If the p-value is less than the significance level (0.01), the null hypothesis is rejected.

Explanation:

To determine if there is a significant difference between the two polishing solutions used in tumble-polishing intraocular lenses, we can perform a hypothesis test. The null hypothesis (H0) is that there is no difference between the proportions of polishing-induced defects for the two solutions, while the alternative hypothesis (Ha) is that there is a difference.

We can use a two-proportion z-test to compare the proportions of defects. The z-test statistic is calculated as:

z = (p1 - p2) / [tex]\sqrt{(p1q1/n1)[/tex] + (p2q2/n2))

where p1 and p2 are the proportions of defects, q1 and q2 are 1-p1 and 1-p2 respectively, and n1 and n2 are the number of lenses polished with each solution. The p-value for this test can be calculated using a standard normal distribution table or a statistical software.

If the p-value is less than the significance level α (0.01 in this case), we reject the null hypothesis and conclude that there is a significant difference between the two polishing solutions.

The p-value for this test cannot be determined without the actual values of p1, p2, q1, q2, n1, and n2.

Determine if x + 3 is a factor of -3[tex]x^{3}[/tex]+6[tex]x^{2}[/tex]+6x+9. How do you know?

no, because the remainder is 126

yes, because the remainder is 126

no, because the remainder is –108

yes, because the remainder is –108

Answers

Answer:

Option C

no, because the remainder is 126

Step-by-step explanation:

Given the polynomial equation in the question

-3x^{3}+6x^{2}+6x+9

factor =  x + 3 (divisor)

long division

          -3x² + 15x - 39             Quotient

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

x + 3|  -3x³ + 6x² + 6x + 9     Dividend

        |  -3x³ - 9x²

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

                      15x² + 6x + 9

                      15x² + 45x

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

                               -39x + 9

                               -39x - 117

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

                                           126   Reminder

Since reminder is not zero so (x + 3) is not factor of -3x³ + 6x² + 6x + 9.

(x-3) is the factor of  -3x³ + 6x² + 6x + 9.

Evaluate the exponential expression: (2x)2nd power −3y2nd power =___, if x = 5 and y = 3.


A.73
B.125
C.-73
D.-125

Answers

ANSWER

A. 73

EXPLANATION

The given expression is

[tex](2{x})^{2} - 3{y}^{2} [/tex]

We substitute x=5 and y=3 to obtain:

[tex](2 \times 5)^{2} - 3{(3)}^{2} = {10}^{2} - 3 \times 9[/tex]

This simplifies to,

[tex] = 100 - 27[/tex]

[tex] = 73[/tex]

The correct choice is A.

Please help me out with this!

Answers

Answer:

20

Step-by-step explanation:

z=(180-124-16)/2

Here is your answer

[tex]<b>z= 20 degrees</b>[/tex]

REASON:

[tex]<font color="blue" size=5>Concept used</font>[/tex]: The sum of adjacent angles of a parallelogram is 180 degrees.

So, in above given figure

[tex] 2z+16+124=180 [/tex] (measures of adjacent angles)

[tex]2z+140=180 [/tex]

[tex] 2z=180-140 [/tex]

[tex]2z=40 [/tex]

[tex]z= 40/2 [/tex]

[tex]z= 20 [/tex]

HOPE IT IS USEFUL

Please help! I will mark brainliest if it lets me

Answers

The answer you are looking for is the first 1, or a. hope this helps. Please mark me as brainliest.

Answer:

The first line is the correct answer.  because of the ≤ sign it means that circle will be closed and the line will be to the left. A trick is if you picture the sign as an arrow then that will be which way the line will go. ;) Hope this helps!

what is the molariry of a solution that contains 1.22 mol of hydrogen chloride if the total volume of the solution is 1,251 mL?

Answers

Your molarity would be 0.975 M HCl because it’s moles of solute divided by liters of solvent

The answer would be 0.975

Credit cards can only lead to debt that is difficult to eliminate and should be avoided at all costs. Please select the best answer from the choices provided T F

Answers

Answer:

This statement is false.

Step-by-step explanation:

Credit cards can only lead to debt that is difficult to eliminate and should be avoided at all costs. This is false.

This is not a standard statement that credit cards always lead to debt. A person should use his credit card with responsibility. He should pay the bills timely to avoid accumulation of debt and other fines. Only when a person uses his card irresponsibly and does not pay dues timely, can lead to debts.

So, this is a false statements.

Answer:

False

Step-by-step explanation:

Given (x, y ) = (5, 15). Find tan θ.

a.3
b.1/3
c.5
d.1/5

Answers

Answer:

Step-by-step explanation:

You wouldn’t put y over x Which is 15/3 you would divide which gives you five. So your tan theta would be 5

Answer:

it's definitely 3 on odyssey. tan theta= y/x =3.

Step-by-step explanation:

Your cell phone bill just arrived. Your plan only allows you to send and receive 130 texts per month, but you sent and received 268 texts. Your plan charges you $0.05 per text sent on your plan, and then $0.25 for each text you send over your plan limit. How much money do you have to pay for the extra texts that you sent and received? What is your total bill?

Answers

Answer:

$34.5

Step-by-step explanation:

1. 268 - 130 = 138

2. 138 x .25 = 34.5

268 - 130 = 138
138 x .25 = 34.50 Extra Pay
130 x .05 = 6.50
34.50 + 6.50 = $41.00 Total Bill

You want to save ₹1,17,000 to buy your first self-driving magic carpet. You deposit ₹90,000 in a bank at an interest rate of 6 % 6%6, percent per annum. How many years do you have to wait before you can buy your magic carpet?

Answers

Answer:

4.50 yr

Step-by-step explanation:

I assume that this is compound interest.

The compound interest equation is

[tex]A = P(1+ \frac{r }{ n})^{nt}[/tex]

You don't give the frequency of compounding, so I assume that it is once per year.

Data:

A = ₹117 000

P = ₹90 000

r = 6 % = 0.06

n = 1

Calculations:

[tex]117 000 = 90 000(1+ \frac{0.06 }{ 1})^{1 \times t}[/tex]

[tex]117 000 = 90 000(1+ 0.06)^{t}[/tex]

Divide each side by 90 0000

[tex]1.3 = 1.06^{t}[/tex]

Take the logarithm of each side

log1.3 = tlog1.06

0.1139 = 0.025 31t

Divide each side by 0.025 31

t = 4.50 yr

You can buy your magic carpet in 4.50 yr.

Answer: is 5

all you have to do is                          \(^o^)/

(1,17,000−90,000)=27,000

1 year =6%of 90,000

1%of 90,000=900

6% of 90,000=(6*900)

1 year =5400

27,000 u divide that by 5400=5 soooooooooo......

ITs Five 5

Derive these identities using the addition or subtraction formulas for sine or cosine:

a. sin a sin b = 1 / 2(cos(a – b) – cos(a + b))

b. sin a cos b = 1 / 2(sin(a + b) + sin(a – b))

Answers

Answer:

Step-by-step explanation:

cos(a-b)-cos(a+b)=2(sina x sinb)

using formulae of cos (a-b) & cos(a+b)

cos a cos b + sina sinb - cosa cosb + sina sinb=2 sina sinb

2 sina sinb = 2 sina sinb

proved!

A duplex generates $1,400 rent for each of its two units per month. The property has been recently appraised for $350,000. What is this property's GIM? 4.8, 9.6, 10.4, or 20.83??

Answers

Answer:

10.4

Step-by-step explanation:

To get the property's gross income multiplier (GIM), you divide its appraised value by its gross annual rental income.

Rental income = 2 × $1400/1 month × (12 months/1 yr)

= $33 600/yr

GIM = $350 000/$33 600 = 10.4  

The property's GIM is 10.4.

1. Derive this identity from the sum and difference formulas for cosine:


sin a sin b = (1 / 2)[cos(a – b) – cos(a + b)]


Calculation:


1.


2.


3.



Reason:


1.


2.


3.




2. Use the trigonometric subtraction formula for sine to verify this identity:


sin((π / 2) – x) = cos x


Calculation:


1.


2.


3.



Reason:


1.


2.


3.

Answers

Answer:

See below.

Step-by-step explanation:

1.  (1 / 2)[cos(a – b) – cos(a + b)]

= 1/2 ( cosa cosb + sina sinb - (cosa cosb - sina sinb)

= 1/2 ( cosa cosb - cosa cos b + sina sinb + sina sinb)

= 1/2 ( 2 sina sinb)

= sina sinb.

(I  used the 2 identities   cos(a - b) = cosa cosb + sina sinb) and

cos (a + b) = cosa cosb - sina sinb.)

2.  sin (π/2 - x)  = sin (π/2) cos x - cos(π/2) sin x

     =    1 * cos x - 0 * sinx  

     =   cosx - 0

     = cos x.

  (I used the identity sin(a - b) = sina cosb - cosa sinb

 and the fact that  sin(π/2) = 1 and cos (π/2) = 0. )

Answer:

1. sin a sin b = (1 / 2)[cos(a – b) – cos(a + b)]

Calculation:

Taking L.H.S. of above equation

                    (1 / 2)[cos(a – b) – cos(a + b)]

                 = (1 / 2) [ (cos a cos b + sin a sin b) - (cos a cos b - sin a sin b)]

                           {∵ cos(a – b) = cos a cos b + sin a sin b     &    cos(a + b) = cos a cos b - sin a sin b}

                 = (1 / 2) [ cos a cos b + sin a sin b - cos a cos b + sin a sin b]

                 = (1 / 2) [2 sin a sin b]

                 = sin a sin b

2. sin((π / 2) – x) = cos x

Calculation:

sin((π / 2) – x) = sin (π / 2) cos x - cos (π / 2) sin x

                                                      {∵sin(a - b) = sin a cos b - cos b sin a                                                    

                                                       &  sin (π / 2)  =  1   &  cos (π / 2) = 0}

                       = 1 × cos x - 0 × sin x

                       = cos x

Please help with this question, I will give the brainliest if correct! The question is in the picture.

Answers

Answer:

Resolved.

Step-by-step explanation:

Answer:

The Answer is B. I had this a few months ago. Good luck with Apex!

25% of the students at school a got a score greater than 25 but less or an equal to 28

Answers

Answer:

28 >= 0.25x > 25

Step-by-step explanation:

25% of x

1) Greater than 25: 25%x > 25

2) Less than and equal to 28: 25%x <= 28

25%x = 25/100 * x = 0.25x

1 and 2:

28 >= 0.25x > 25

//I hope this is what you are looking for. Not sure it's right

Suppose the side lengths are multiplied by 2. Describe the change in the perimeter.

Answers

Answer:

The perimeter would then be squared

Step-by-step explanation:

Since each length is being multiplied by 2 the you have 2 of the same perimeters. So you just add them together or square it.

How many sums????????????????? EXPLAIN!

Answers

Answer:  7

Step-by-step explanation:

The 1st spinner can land on 2, 3, 4, or 5

The 2nd spinner can land on 2 or 3

The 3rd spinner can land on 6, 7, or 8

1st spinner + 2nd spinner + 3rd spinner:

2 + 2 + 6 = 10,    2 + 2 + 7 = 11,     2 + 2 + 8 = 12    --> 3 different sums

2 + 3 + 6 = 11,     2 + 3 + 7 = 12,     2 + 3 + 8 = 13   --> 1 different sum

This pattern follows where the only new sums are as follows:

                                                       3 + 3 + 8 = 14

                                                       4 + 3 + 8 = 15

                                                       5 + 3 + 8 = 16

This makes a total of 7 different sums.

Solve for x.


mx2 + y

e

= b


A)

x =

be - y

m



B)

x =

be - y

m



C)

x = ±


be - y

m



D)

x = ±


be + y

m

Answers

Answer:

its C

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

Thirty times the square of a non-zero number is equal to eight times the number. what is the number?

Answers

let's say number is x , then

30 × (x)^2 = 8x

subtracting 8x from both side

30x^2 - 8x = 0

taking 2x common

2x( 15x - 4)= 0

one solution is

2x = 0

x= 0

but number is non zero so ignoring it.

next solution is

15x - 4 = 0

adding 4 both side

15x = 4

dividing by 15 both side

x = 4/15

The sophomore class sells tickets to a benefit concert to raise money. Each ticket sells for $15. How much money do they raise?

A. m=15+t
B. m=t/15
C. t=15m
D. m=15t

Answers

Answer:

D.m=15t

Step-by-step explanation:

If the number of tickets is t and the total amount of money collected is m then a product of the price per ticket with the cost of the ticket gives the amount of money collected from the sale of the tickets.

therefore m= t×15

              m=15t

Answer:

D. m = 15t

Step-by-step explanation:

We have to assume that m is supposed to stand for the money (in dollars) that results from the sale of t tickets. Then the sale of t=1 ticket will result in m=15 dollars. Only one of the offered formulas will give this result:

m = 15t

_____

Comment on the problem

Variables need to be defined. We'd prefer to see some discussion of how concert expenses are covered, so we can be assured that ticket sales directly relate to money raised.

Name the rule for each statement: (SSS, ASA, SAS, AAS) Hint: you may use some of the rules more than once. Two triangles are congruent if: a) each pair of corresponding sides is congruent b) two pairs of corresponding angles are congruent and a pair of corresponding sides are congruent c) two pairs of corresponding sides and the angles included between them are congruent d) If three sides of one triangle are congruent to three sides of a second triangle, e) If two angles and a non-included sides of each triangle are congruent

Answers

Answer:

a)SSS b)AAS c)SAS d)SSS e)AAS dont worry i passed this lesson with a 100% if i am wrong then come and kill me :) i am sure it is right

Step-by-step explanation:

Final answer:

The rules for triangle congruence based on the given statements are SSS, ASA, SAS, SSS, and AAS, which are applied when certain combinations of angles and sides are congruent in two triangles.

Explanation:

To name the rule for each statement given for triangle congruence, we can apply the following:

a) SSS (Side-Side-Side) Congruence Postulate: Each pair of corresponding sides is congruent.

b) ASA (Angle-Side-Angle) Congruence Postulate: Two pairs of corresponding angles and one pair of corresponding sides are congruent.

c) SAS (Side-Angle-Side) Congruence Theorem: Two pairs of corresponding sides and the angles included between them are congruent.

d) SSS (Side-Side-Side) Congruence Postulate: Three sides of one triangle are congruent to three sides of a second triangle.

e) AAS (Angle-Angle-Side) Congruence Theorem: Two angles and a non-included side of each triangle are congruent.

These rules are foundational in establishing triangle congruence and are applied based on different combinations of sides and angles of triangles.

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