Jack invests $500 at a certain annual interest rate, and he invests another $2000 at an annual rate that is one-half percent higher. if he receives a total of $85 interest in 1 year, at what rate is the $500 invested?

Answers

Answer 1

Final answer:

The $500 was invested at an annual interest rate of 3%.

Explanation:

Let's assume the interest rate for the $500 investment is x %. Therefore, the interest rate for the $2000 investment would be (x + 0.5) %, since it is one-half percent higher.

The total interest received is $85. So, we can set up the equation:
$500(x/100) + $2000((x + 0.5)/100) = $85

Simplifying and solving the equation, we get:
5x + 20(x + 0.5) = 85
5x + 20x + 10 = 85
25x = 75
x = 3

The $500 was invested at an annual interest rate of 3%.

Related Questions

An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.

Answers

The current rate is simply equal to $175 per month, let us call this as rate A:

A = 175

The new rate is $94 plus $4.50 per devices, let us call this as rate B:

B = 94 + 4.50 x

where x is the number of devices connected to the network

The inequality equation for us to find x which the new plan is less than current plan is:

94 + 4.50 x < 175

Solving for x:

4.50 x < 81

x < 18

So the number of devices must be less than 18.

- From the graph, we can actually see that the new rate intersects the current rate at number of devices equal to 18. So it should really be below 18 devices.

The number of devices connected should be less than 18 (1 to 17 devices) so that the new charges will be less than the old charge.

Given:

The old monthly charge for internet service per household is $175.

The new charges include a fixed pay of $94 plus $4.50 per connected device.

Let x be the number of connected devices.

So, the new charges can be written mathematically as,

[tex]C=94+4.5x[/tex]

Now, the new charge should be less than the old charge. This condition can be written as,

[tex]C=94+4.5x<175\\4.5x<81\\x<18[/tex]

So, the number of devices connected should be less than 18 (1 to 17 devices) so that the new charges will be less than the old charge.

See the attached graph.

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2(x + 7) + 3x = 12
What is the first step in solving this equation for x?

Answers

first step is expand by using distributive property
2(x + 7) + 3x = 12

step 1:
2x + 14 + 3x = 12

First step would be to expand it and make it 2x + 14 + 3x = 12

Second step would be to add 2x + 14 + 3x so it can be 5x + 14

Third step would be to subtract 14 from both sides

Fourth step would be to subtract 12 - 14 so it can be -2

Last step to get your answer would be to divide both sides by 5

Answer to this whole equation: x = -2/5.

1/4x+5/3x-4=2-1/12x what is the answer ??????

Answers

I hope this helps
the answer is x=3

I believe the answer is:

x=3

have a noice day

Monica has saved $735 for a new guitar and lessons. her guitar costs $475, and guitar lessons are $25 per hour. determine how many hours of lessons she can afford.

Answers

475+25h≤735
25h≤260
h≤10.4

10 hours

The vertex of this parabola is at (-4, -1). When the y-value is 0, the x-value is 2. What is the coefficient of the squared term in the parabola's equation?

A. -3
B. 3
C. -6
D. 6

Answers

For this question, we'll need the vertex form of a parabola, which, for a quadratic function, is:

[tex]y=a(x-h)^2+k[/tex]

where (h,k) is the vertex of the parabola. In this case, our parabola is opening horizontally to the right, so we need to swap the x and y in our equation. We have:

[tex]x=a(y-h)^2+k[/tex]

We've been given a the coordinates of the vertex (-4,-1) as well as the coordinates for a point on the parabola (2,0), so we can substitute in the values from both of these coordinates to easily solve for a, the coefficient of the squared term.

[tex]h=-4\\k=-1\\x=2\\y=0\\\\2=a(0-(-1))^2+(-4)\\2=a(1)^2-4\\2=a-4\\6=a[/tex]

So, the coefficient of the squared term for this parabola is 6.

Answer:

the coefficient of the squared term for this parabola is 6

Step-by-step explanation:

2. Your Turn: How many elements are in the sample space for spinning a spinner labeled A, B, C, D? *
1 point
1
4
8
16

Answers

since the spinner is labelled A, B, C, D, there are four possible landing for the spinner.

Thus, the sample space is {A, B, C,D}.

Therefore, the number of elements in the sample space for spinning a spinner labeled A, B, C, D is 4.

Multiply. (−23)⋅(−4) A. −92 B.−27 C.27 D.92

Answers

The answer of this problem is D. 92

the answer is 92 becuase im awesome T_T

Which rectangle is an enlargement of a 5 by 6 rectangle

Answers

Just multiply 5 and 6 by the same number.
Example:
(5 by 2) by (6 by 2) = 10 by 12,
so twelve can be an enlargement of a rectangle that is 5 by 6.

Which rectangle is an enlargement of a 5 by 6 rectangle? B. 15 by 18

A town's population has been growing linearly. In 2003, the population was 25000, and the population has been growing by 1200 people each year.Write an equation for the population
x
years after 2003.

Answers

y=25000*1200x

y would equal the population of the year and x is the amount of years passed.

in year 2003 (starting year) it had 25000 pple
let's say a=25000
so steadily each year it increases by 1200
which means the difference between two consecutive years would be 1200 pple
now this is an arithmetic progression
using Tx=a+(x-1)1200
tx= 25000+(x-1)1200
tx=25000+1200x-1200
tx= 23800+1200x
that's the eqn after X years

Plz help fast will mark brainiest

Determine whether each ordered pair is a solution of y= 2x-4
(3,2)

Yes or No?

Answers

2 x (-4) is -8. So no

Yeah no, I used that solution and I got close to (3,2) yet it wasn't exactly (3,2) yet (2,3).

When a population grows according to the logistic model, what is the value of the instantaneous population growth rate (dn/dt) when the population is stable?
a. dn/dt = 0
b. dn/dt = n
c. dn/dt = r
d. dn/dt = k?

Answers

is c because dn over dt equal r

Answer:

Step-by-step explanation:

If you were a lender, why would employment history or credit reports be important to you?

Answers

Answer:

If I were a lender, the borrower's credit report will be important for me. The credit report should be positive and accurate if a person wants to borrow money from me. Good credit reports generate good credit scores and the higher the credit score, the lower the risk to me or the lender.

Similarly, employment history is a measure to check before lending money. This is because if a person has a good history and is working with good firms and on a regular basis, this develops trust that he will work properly pay off the debt. If a person is not responsible at work place and changes his jobs and cities frequently, then it is not sure if he can pay off the debt.

Banks also check these two things before lending any money. These information about a borrower develops trust among the lenders.

Employment history and credit reports gives an insight of an individual's past financial credibility, hence, they are useful in making a decision on whether to lend such individual and the amount that should be lent.

Employment history gives an account about whether a person is presently employed or not, and it also gives an insight about duration of stay with previous employers.

Credit history gives an account into past financial details, the promptness exercised in repayment and if there are any pending debts.

Therefore, these information are necessary for adequate decision making about the financial capability and integrity of the borrower.

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A cylindrical can is to have volume 1500 cubic centimeters. determine the radius and the height which will minimize the amount of material to be used. note that the surface area of a closed cylinder is s=2rh+2r2 and the volume of a cylindrical can is v=r2h.

Answers

Assuming R and H:
So volume is pir^2 * H = 1500 and H = 1500/(pir^2) while surface area is A= 2pir*H + 2pir^2
A = 2pir(r+h)= 2piR^2 + 2pir*1500/(pir^2)= 2piR^2 + 3000/r
For A to take minimum, get the derivative 4pir - 3000/R^2 and let it be 0
4pir^3 - 3000 = 0
r = cbrt(3000/(4pi)) ≈ 6.20
h = 1500/(pi(6.20)^2) ≈ 12.42

PLEASE HELP FAST!!!

Step 3: Solving real-world problems that involve markups

a) A local shoe store buys shoes at a wholesale price and then marks them up 80% to calculate the retail price. The wholesale price varies, depending on the quantity of shoes purchased. (2 points)

This is the table

Quantity 0-20 pairs 21-40 pairs 41-60 pairs 61-80 pairs 81 or more pairs

Wholesale Price (per pair) $25.00 each $23.00 each $21.00 each $19.00 each $17.00 each

Write an equation that could be used to find the retail price for each range. How do you know the equation will work consistently for each range? (2 points)

Answers

since all the shoes get marked up by 80%

the equation for all of them would be :

y = new price

x = wholesale price

y = 1.8x

ANSWER ASAP 30 POINTS GIVEN

△MNP≅△QST
.
What is
m∠S
?

Enter your answer in the box.

Answers

78 degrees right cuz mnp=qst so n would equal s

Answer:- m∠S=78°.

Explanation:-

Given:- Two congruent triangles ΔMNP and ΔQST which are congruent, where m∠M=66° and m∠N=78°.

⇒The corresponding parts of ΔMNP are congruent to the ΔQST .

Therefore, all the corresponding sides of ΔMNP are congruent to the ΔQST and all the corresponding angles of ΔMNP are congruent to the ΔQST such that

MN=QS , NP=ST and MP=QT.

m∠M=m∠Q, m∠P= m∠T and m∠N=m∠S.

Substitute the value of m∠N=78°, we get

m∠S=78°.

Find the length of the hypotenuse:

Answers

to find the hypotenuse on the given triangle

divide the given height ( 3sqrt(2) ) by the sin of the given angle (45)

3sqrt(2) / sin 45 = 6

answer is B. 6

Method 1:

The sides of a right-angle triangle are equal when the angle = 45°

[tex] a^2 = b^2 + c^2 \\ a^2 = (3 \sqrt{ 2 })^2 + (3 \sqrt{ 2 })^2 \\ a^2 = 9 \times 2 + 9 \times 2 \\ a^2 = 36 \\ a = \sqrt {36} = 6 [/tex]

Method 2:
(Optional)

Using TOA CAH SOH method

Where:

TOA is Tan θ = Opposite/Adjasent
CAH is Cos θ = Adjasent/Hypotenuse
SOH is Sin θ = Opposite/Hypotenuse

You have an angle of 45° and OPPOSITE the angle is a known length.

These are the 2 information we know.

We need to find the third information, which is the HYPOTENUSE.

Notice the capatialised words start with the letter O ans H?

Find in the TOA CAH SOH the corresponding letters, in this case SOH.

SOH is sin θ = opposite/hypotenuse

Simply substitude in the values and find the hypotenuse!

sin 45° = (3√2)/ hypotenuse
hypotenuse = (3√2) / sin 45° = 6

Answer is B.

And there you go! Both methods can be used and gives the same answer.

However the limitations to method 2 are:

1. It must be a right-angle triangle
2. An angle and a side must be given.

If you think method 2 is too confusing, stick to method 1.

Good luck!

1)
The distance traveled in a car varies directly as the amount of gasoline used. If a car travels 520 miles and uses 26 gallons of gas, find the constant of variation or miles per gallon.

A)
18 mpg

B)
20 mpg

C)
22 mpg

D)
24 mpg

Answers

Hello,

520/26=20mpg

That vehicle gets 20 mpg.

Hope this helps

The correct answer is B) 20 mpg
Hope this helps and have a wonderful day!

A ball is thrown upward into the air so that its height, h, in feet, after t seconds is modeled by the function h(t) = 56t – 16t2. What is the velocity, in feet per second, of the ball after 2 seconds?

-32
-8
24
48

Answers

Answer:

Step-by-step explanation:

-32

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

Velocity = Height / Time

The velocity, in feet per second, of the ball after 2 seconds is 24.

Option C is the correct answer.

What is speed?

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

h(t) = 56t - 16t²

h(t) is the height after t seconds.

Now,

Velocity = Height / Time

At t = 2,

h(2):

= 56 x 2 - 16 x 4

= 112 - 64

= 48

Now,

Velocity = 48 / 2

Velocity = 24

Thus,

The velocity, in feet per second, of the ball after 2 seconds is 24.

Option C is the correct answer.

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WILL GIVE A BRAINLIEST SHOW ALL WORK PLEASE!!

A function is graphed on the coordinate plane.

What is the value of the function when x = -4?

Answers

look to see where the line is in the y direction at x=-4

it crosses at y=-3

so the value would be -3

What evidence does the narrator offer for believing in a past life as a bat?

Answers

The narrator of my life as a bat believed in the past life or reincarnation. it believes that it has an impact on the society. The narrator shows her intellect for the human world. Atwood believes that in her past life she was a bat. She considers being a bat is more of a reward than a punishment. Bats can kill without condemnation, but they don't do it out of hate. Whereas human will kill because they hate someone but they sometimes feel condemn or have repentance after.

Final answer:

The narrator's evidence of a past life as a bat can be derived from their understanding of the bat's way of navigating through darkness similar to their pre-literate life, mirroring a bat's perception of the world through sound reflections, and also a subtle hint on a shared evolutionary past with bats.

Explanation:

The narrator of the story hints at the possibility of having a past life as a bat based on their keen sense of understanding and relating to the fundamental traits of a bat. First, the narrator draws parallels between their pre-literate life and a ship lost in the fog, similar to how bats navigate their way in the dark through echolocation, as the figures 17.6 and 14.8 depict. The echoes, in this context, could symbolize the intangible voices of the past, reiterating their bat-like existence.

Secondly, the narrator's reflections on shadows as distorted versions of reality, as narrated in the allegory of the cave, mirrors the bat's perception of the world through sound, making physical visibility a misleading representation. This is also closely connected to the narrator referring to a transcendence that momentarily allows them to live outside social norms, just like bats that occupy the night skies primarily, a time generally regarded as quiet and uninhabited by humans.

Lastly, the narrator’s mention of homologous bat and bird wings as an evidence of common evolutionary past (Figure 20.7) might indicate the belief in being part of the same evolutionary lineage. These instances collectively form the narrator's evidence for the belief in a past life as a bat.

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a contractor finds that 6 gallons of paint will cover 750sq ft of wall area.how much wall area could be covered with 18 gallons of paint

Answers

6*3=18 so it will cover 3 times the area. 750*3=2250 sq ft of wall area

Factor the expression completely over the complex numbers.

y^4+12y^2+36

Answers

y⁴ + 12y² + 36
Now factorize the expression
y⁴ + 6y² + 6y² + 36
= y²(y² + 6) + 6(y² + 6)
= (y² + 6) (y² + 6)
Now 6 is not the perfect square and according to rule, binomial can not be factored as the difference of two perfect squares.
so multiply both.
(y² + 6)² is the answer.

Answer:

the answer given is not in complex form using i variable

Step-by-step explanation:

The first side of a triangle is 2 cm longer than the second side. the third side is 5 cm shorter than twice the second side. the perimeter is 49 cm. find the length of each side.

Answers

Side 1: x+2
Side 2: x
Side 3: 2x-5
Perimeter(sum of the sides)= 49 cm

(x+2)+x+(2x-5)=49
4x-3=49
4x=52
x=13

Side 1=15 cm
Side 2=13 cm
Side 3=21 cm

The sides of the triangles will be 15 cm, 13 cm and 21 cm.

What is a triangle?

A closed polygon with three sides, angles and vertex is called triangle.

Given that, the first side of a triangle is 2 cm longer than the second side. the third side is 5 cm shorter than twice the second side and the perimeter is 49 cm.

Let the second side be x, then the sides will be,

x+2, x and 2x-5

∵ Perimeter = 49 cm

∴ x + 2 + x + 2x - 5 = 49

4x-3 = 49

4x = 52

x = 13

Therefore, side will be =

Side 1 = 15 cm

Side 2 = 13 cm

Side 3 = 21 cm

Hence, the sides of the triangles will be 15 cm, 13 cm and 21 cm.

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How to find the number of sublevels in a principal energy level?

Answers

They are designated by the principal energy level. (# of energy level = # of sublevels)
See attached pic.

Two angles of a triangle have a sum of 110. the sum of all three angles is 180 .what is the measure of the third angle

Answers

Well by the looks of it The missing angle is 70 degrees. I say this because 110 + 70 = 180. If you were asking what were the two angles just divide.

What is the vertex of the absolute value function below?
(4, –1)

(1, –4)

(1, 4)

(4, 1)

Answers

I will work this question for you using the graph attched which belongs to a question with the same statement of yours and whose solution is one of the points of the list of choices.

The vertex is the point where the function changes direction, in this case from growing to decrease.

That is the point wiht x-coordinate 4 and y-coordinate 1, so the point is (4,1).

Answer: (4,1)

Answer:

(4,1) D

Step-by-step explanation:

i got it right on edge

..........

the x value??

Answers

x = 180 - 2(73)
x = 180 - 146
x = 34

answer
x = 34

I think the answer is

x=34

The length of a rectangle is 3 yd less than twice the width, and the area of the rectangle is 65yd . find the dimensions of the rectangle.

Answers

l=2w-3
65=w(2w-3)
65=2w²-3w
2w²-3w-65=0
2w²+10w
2w(w+5)
-13w-65
-13(w+5)
(2w-13)(w+5)
w=13/2
l=13-3
l=10
The width is 13/2 yd, and the length is 10 yd.

Jimmy had $4.52 to spend. He found something he wanted to buy for $6.21. How much would he need to borrow from his friend to make his purchase?

Answers

He would need to borrow $1.69

Answer:

$1.69

Step-by-step explanation:

If he wants to buy something for $6.21 but he only has $4.52, we need to find out the difference between $6.21 and $4.52.

For that, we have to subtract the smallest number from the biggest, that is

$6.21 - $4.52 = $1.69

Therefore, he would need to borrow $1.69 from his friend.

What is the measure of angle C? 25° 30° 60° 75°

Answers

Answer:

75°

Step-by-step explanation:

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