A combined total of $49,000 is invested in two bonds that pay 2% and 6.5%simple interest. The annual interest is $2,5100. How much is invested in each bond?

Answers

Answer 1

let x is the bond pay 2% and y is the pay 6.5%
x + y = 49,000 so x = 49,000 - y
0.02x + 0.065y = 2,510
substitute x = 49,000 - y into 0.02x + 0.065y = 2,510

0.02x + 0.065y = 2,510
0.02(49,000 - y) + 0.065y = 2,510
980 - 0.02y + 0.065y = 2,510
0.045y = 1,530
y = 34,000
x = 49,000 - y = 49,000 - 34,000 = 15,000

answer
invested $34,000 in the bond that pays 6.5% rate and $15,000 in bond that pays 2% rate

Answer 2

Final answer:

The amount invested in the 2% bond is $7,500, and the amount invested in the 6.5% bond is $41,500.

Explanation:

Let's assume that the amount invested in the 2% bond is x dollars. Then, the amount invested in the 6.5% bond is $49,000 - x dollars.

The interest earned from the 2% bond is 0.02x dollars, and the interest earned from the 6.5% bond is 0.065($49,000 - x) dollars.

According to the problem, the sum of these two interests is $2,510. So, we have the equation:

0.02x + 0.065($49,000 - x) = $2,510

Simplifying and solving this equation, we find that x = $7,500. Therefore, $7,500 is invested in the 2% bond, and $41,500 is invested in the 6.5% bond.

Learn more about Calculating Investments here:

https://brainly.com/question/29441992

#SPJ3

Related Questions

you need to count all of the loaves of bread in the front area . there are 22 loaves of white bread, 17 loave of wheat bread, and 19 gourmet breads.what is the total number of loabes?

Answers

19+17=36
36-22=14
the answer is 14

this is a very simple problem if you need to know the amount of loaves of bread in the front area it is a simple addition problem 22+17+19=__ using the formula we find the answer is 58 loaves of bread

How many pounds of peanuts will each person get if 3 people share 1/5 pounds of peanuts equally?

Answers

3 people share 1/5 pound

1 person = 1/5 ÷ 3 = 1/5 x 1/3 = 1/15 pound

Answer: 1 person gets 1/15 pounds of peanuts.

I was sick the day that the class went over how to do this and I don’t know how to do it.

Answers

You first need to know the equation A=pi x r^2. The equation you need for this problem is pi (3.14) x 3^2

Suppose q and r are independent events, and P(Q)= 0.39, P(R)= 0.85. Find P(q and r)

Answers

Answer:
P (q and r) = 0.3315

Explanation:
We are given that:
P (q) = 0.39
P (r) = 0.85

Since the two events are independent, therefore, the formula that we will use to get P (q and r) is as follows:
P (q and r) = P (q) * P (r)

Based on the givens:
P (q and r) = 0.39 * 0.85 = 0.3315

Hope this helps :)

Answer:

0.3315

Step-by-step explanation:

A college entry exam has 38 questions worth 200 points. The test consists of multiple-choice questions, x, worth 4 points each and essay questions, y, worth 10 points each. Which system of equations can be solved to find the number of multiple-choice questions on the test?

Answers

A system of equations is a set of equations to be solved by elimination or substitution.

There are no options listed in the question to choose from, but the equations should look like the following:

x= # multiple choice questions
y= # essay questions

QUANTITY EQUATION:
x + y= 38

VALUE EQUATION:
4x + 10y= 200

If we solved these two equations by elimination or substitution, we would find the number of multiple choice (x) and the number of essay (y) questions on the test.

ANSWER: x + y= 38; 4x + 10y= 200

Hope this helps! :)

Answer:

Let's use the variables x and y to represent the number of multiple-choice and essay questions on the test, respectively.

The total number of questions is 38, so we can write:

x + y = 38

The total number of points is 200, so we can write:

4x + 10y = 200

This gives us a system of equations:

x + y = 38

4x + 10y = 200

We can solve this system of equations to find the number of multiple-choice questions on the test.

The owner of a bookstore predicts that 30% of the books she sells each week are self-help books. To test this prediction, the owner randomly selects 150 books out of the total number of books sold for a week and records the type of each book. The table shows the results of samples taken for 2 separate weeks. Sample Fiction History Cooking Self-help Total week 1 50 29 37 34 150 week 2 55 31 34 30 150 Based on these samples, is the owner's prediction correct? Select from the drop-down menus to correctly answer the question. The owner's prediction is . Based on the samples, about of the books sold each week are self-help books.

Answers

The owner's prediction is incorrect. About 23% of the books sold are self-help books.

34 out of the 150 sold in week 1 were self-help books.
34 out of the 150 sold in week 2 were self-help books.

This gives us 68 self-help books out of 300 books sold.

68/300 = 0.2267 ≈ 0.23 = 23%

Based on the samples, the owner's prediction of 30% is not correct; approximately 21.34% of the books sold each week are self-help books.

The bookstore owner predicts that 30% of the week's book sales are self-help books. To evaluate this prediction, we need to look at the number of self-help books sold in the samples provided for two separate weeks. In week 1, 34 out of 150 books sold were self-help books, which is 22.67%. In week 2, 30 out of 150 books sold were self-help books, which is 20%. To determine the average percentage of self-help books sold over the two weeks, we average these two percentages: (22.67% + 20%) / 2, which gives us 21.34%.

the goalie ate half of a pizza that had a diameter of 20 inches! what was the area of pizza that she ate? what was the length of crust she ate?

Answers

Area= pie • radius square

Since it’s diameter you divide it by 2 so it would 10. 10= radius, now does you multiply it by its self so 10•10= 100. Now multiply it but pie which it 3.14. 100•3.14= 314. 314 should be your answer!

Sorry if you get this wrong :( but I’m learning this and I usually get these right but best of luck! :)

It says in abc, What is m

Answers

The interior angle measures of a triangle add up to 180°.

Make ∠A + B + C = 180.

x + (4x) + (5x - 13) = 180
Add all like terms.

10x - 13 = 180
Add 13 to both sides.

10x = 193
Divide both sides by 10.

x = 19.3

Now plug in x into m∠C, (5x - 13).
5(19.3) - 13 = 83.5

The m∠C is 83.5°.

Jerome bought a book on sale at the store. The sale price of the book was $8.96. Write and solve an equation to determine the regular price of the book to the nearest cent

Answers

Final answer:

The regular price of the book is $8.96.

Explanation:

To determine the regular price of the book, we can set up an equation using the sale price and the regular price. Let's say the regular price is 'x'.

So the equation becomes:

8.96 = x

To solve for 'x', we can simply state that the regular price of the book is $8.96.

Fernando poured water from one-pint bottles into a three-gallon bucket. How many pints of water could the bucket hold?

Answers

24 pints is the answer

24

One gallon holds eight pints. 8 x 3 = 24

A prism is filled with 44 cubes with 1/2 units side lengths. What is the volume of the prism in cubic units?

Answers

The volume would be 5.5 cubic units.

First, we need to find the volume of one cube. It would be LWH.
0.5 x 0.5 x 0.5 = 0.125

Now, just multiply that volume by 44.
0.125 x 44 = 5.5

The mean of 3 consecutive terms in an arithmetic sequence is 10, and the mean of their squares is 394. What is the largest of the 3 terms?

Answers

let the numbers be:
a, a+b, a+2b
mean of the numbers is:
(a+a+b+a+2b)/3=10
(3a+3b)/3=10
a+b=10
thus second term is 10

The sum of square will be:
((10 - b)² + 10² + (10 + b)²) / 3 = 394
(100 - 20b + b² + 100 + 100 + 20b + b²) / 3 = 394
(300 + 2b²) / 3 = 394
(150+b²)=591
b²=441
b=-21,21

thus the numbers will be:
10-21, 10, 10+21
=-11,10,31

A sample of 81 was taken from a population with a standard deviation of 45 kilograms. If the sample mean was 112 kilograms, the mean of any other sample of 81 will be within what range 99.7% of the time?

A. 97 kilograms to 127 kilograms
B. 102 kilograms to 122 kilograms
C. 92 kilograms to 132 kilograms
D. 107 kilograms to 117 kilograms

Answers

Sample size = n = 81
Population Standard Deviation = s = 45
Sample Mean = x = 112

Since, population standard deviation is known, we will use z distribution to find the confidence interval.

The critical z value for 99.7% is 2.968

So, the confidence interval will be:

[tex](112-2.968* \frac{45}{ \sqrt{81} }, 112-2.968* \frac{45}{ \sqrt{81} }) \\ \\ (97.16, 126.84)[/tex]

Rounding of to nearest integers the confidence interval will be 97 to 127.

So, option A gives the correct answer

HELP NEEDED

Use the functions h(x) = 5x − 2 and t(x) = 4x + 6 to complete the function operations listed below.

Part A: Find (h + t)(x). Show your work.

Part B: Find (h ⋅ t)(x). Show your work.

Part C: Find h[t(x)]. Show your work.

Answers

Part A: Find (h + t)(x). Show your work.
h(x) = 5x − 2 and t(x) = 4x + 6
so
(h + t)(x) = 5x − 2 + 4x + 6
(h + t)(x) = 9x +4

Part B: Find (h ⋅ t)(x). Show your work.
h(x) = 5x − 2 and t(x) = 4x + 6
so
(h ⋅ t)(x) = (5x − 2) (4x + 6)
(h ⋅ t)(x) = 20x^2 + 30x - 8x - 12
(h ⋅ t)(x) = 20x^2 + 22x - 12

Part C: Find h[t(x)]. Show your work.
h(x) = 5x − 2 and t(x) = 4x + 6
so
h[t(x)] = 5(4x + 6) − 2
h[t(x)] = 20x + 30 - 2
h[t(x)] = 20x + 28

hope all help.

Find the Distance, d, across the lake

Answers

The answer is 11.25 ft.
You have to use similar figures to work this out.
15 ft / 8 ft has to equal d ft / 6 ft
So, you divide 15 by 8, which equals 1.875
You then times 1.875 by 6 = 11.25

The Distance, d, across the lake is 26.25 feet.

Similar Triangles

When two triangles have all the corresponding angles equal to each other, then their sides are in a ratio.

Given to us,

AB = 8 feet,

BC = 15 feet,

BP = 6 feet,

PQ = d,

AP = AB + BP = 8 + 6 = 14 feet

In the figure, [tex]\triangle ABC \sim \triangle APQ[/tex]

[tex]\dfrac{BC}{AB}=\dfrac{PQ}{AP}[/tex]

[tex]\dfrac{15}{8}=\dfrac{d}{14}[/tex]

[tex]d = \dfrac{15\times 14}{8}[/tex]

[tex]d = 26.25[/tex]

Hence, the Distance, d, across the lake is 26.25 feet.

Learn more about Similar triangles:

https://brainly.com/question/25882965

How can we get the answer for...Decrease £8 by 20%

Answers

multiply by 0.8. do 8×.8

20/100 x 8 = 1.6
8-1.6= 6.4
therefore the answer is £6.40

Through music we can communicate more then what can be expressed with words alone
True or false

Answers

i believe it is true.

I believe it is true because music has many expressions. Like for example, a violin(that’s what I play) can be played that it is singing the songs. I believe music is such a important thing in life.

What is the volume of the triangular prism ?

Answers

The volume of the rectangular pyramid is 640 cm³.

What is the volume of a pyramid?

The volume of a pyramid is [tex]\frac{1}{3} Ah[/tex] where A is the area of the base of the pyramid and h is the height.

Area of the base = area of a rectangle with dimensions 12cm*10cm

Area of the base =12*10 =120 cm²

Height of the pyramid =16cm

So, the volume of the pyramid = [tex]\frac{1}{3}*120*16[/tex] cm³

The volume of the pyramid =640 cm³

Hence, the volume of the rectangular pyramid is 640 cm³.

To get more about pyramids visit:

https://brainly.com/question/12903285

When two six-sided dice are rolled, there are 36 possible outcomes.

a. Find the probability that the sum is not 4. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent.

b. Find the probability that the sum is greater than 5. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent.

Answers

A. 33/36 or 92% B. 26/36 or 72%

A. List the possibilities that do have a sum of 4. (1,3) (3,1) (2,2). 3/36. subtract 3/36 from the whole to get probability it does not have a sum of 4. 36/36-3/36=33/36 or 92%

B. List the possibilities if is less than or equal to 5 because it will be a smaller amount than if it is greater and subtract like we did in the previous problem. (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1). 10 total 36/36-10/36= 26/36 or 72%

Final answer:

The probability that the sum of two six-sided dice is not 4 is 11/12 or 92%. The probability that the sum is greater than 5 is 5/12 or 42%.

Explanation:

The subject of this question is probability, which is a branch of mathematics. When two six-sided dice are rolled, there are indeed 36 possible outcomes.

There are three possible ways to get a sum of 4: (1,3), (2,2), and (3,1). So the probability that the sum is not 4 is 1 - (3/36) = 33/36. This simplifies down to 11/12, and as a percent it rounds to approximately 92%.

There are 15 different combinations that result in a sum that is greater than 5. So the probability is 15/36, which simplifies to 5/12. This roughly translates to 42% when expressed as a percentage.

Learn more about Probability here:

https://brainly.com/question/32117953

#SPJ11

Plzz help me im giving 12 points

Answers

this Is very simple.

30m + 50 = 20m + 100

This is the new equation needed to solve for m.
first we must isolate "m".

30m + 50 = 20m + 100
- 50 - 50

30m = 20m + 50
-20m -20m

10m = 50

divide both sides by 10 to isolate "m".

m = 5

hope this helps!

A diner has a breakfast special. A customer can chose scrambled, fried, or poached eggs. The breakfast comes with a side of bacon, sausage, or fruit salad. The customer can choose coffee, tea, or milk. How many different combinations of eggs, side, and drink does a customer have to choose from?

Answers

3x3x3=27

So, there are 27 combinations.

Solution:

Number of ways the customer can choose eggs=3

Number of ways the customer can choose side=3

Number of ways the customer can choose drinks=3

So, total number of combinations for choosing eggs and side and drinks

=3(for eggs) and 3(for sides) and 3(for drinks)

=3 * 3 *3

=27

A customer has 27 combinations of eggs, side, and drink available.

13 percent of what is 78

Answers

13% of what is 78

"what" is the unknown, so use x for what.
"of" in math usually means a multiplication.
"is" means "="

13% * x = 78

0.13x = 78

x = 78/0.13

x = 600

Answer: the number is 600

i think the answer is 600

which of the following functions is continuous between x=-3 and x=0? choices on attachment

Answers

When we say that a function is continuous between x = -3 and x = 0 it means that it exists for all values of x in between -3 and 0. Let's take a look at each choice individually:

A: f(x) = (-x + 1)/(x + 2)
Now we don't actually need to know what the graph of this function looks like to see which values it is continuous for, instead we should look at which values of x will make this function undefined - in this case that would be x = -2. The reasoning behind this is that a number divided by 0 would be undefined, so when we search for which value of x would make the denominator of the equation 0, we get:
x + 2 = 0
x = -2
Since x = -2 is within the interval [-3, 0] we cannot say the function is continuous over this interval

B: f(x) = -2/(x + 1)
Using the same method as above we get:
x + 1 = 0
x = -1
x = -1 is again within the interval [-3, 0] and so the function is not continuous within this interval

C: f(x) = 3x/(x - 2)
x - 2 = 0
x = 2
x = 2 is outside the interval of [-3, 0] and so the function is continuous within this interval and C is the correct answer.

Just for the sake of it however we can look at D as well:
D: f(x) = 1/(2x + 1)
2x + 1 = 0
x = -1/2
-1/2 is within [-3, 0] and so D is not continuous over this interval

Can please help!
10. Write an inverse variation to model the situation and answer the question. Two rectangular fields have the same area. One measures 75 yd by 60 yd. If the other has a length of 72 yd, what is its width?. Show your work

Answers

Answer:
equation is: width = area / length
width = 62.5 yd

Explanation:
For the first rectangle:
We have:
length = 75 yd and width = 60 yd
Therefore:
area = length * width
area = 75 * 60
area = 4500 yd²

For the second rectangle:
We have:
area = area of first rectangle = 4500 yd²
length = 72 yd
area = length * width
width = area / length ............> The required equation
width = 4500 / 72
width = 62.5 yd

Hope this helps :)

Please help......

1. Write an approximate equation of the line of best fit in slope-intercept form.

2. Use the equation from part B to predict the resting heart rate of a person who exercises 30 minutes per day. Show your work.

3. Explain how you found your answer to part C.

Answers

1. using 2 dots that are on the blue line (0,72) and (6,69)
find the slope:

slope = change in Y over change in x = 69 - 72 / 6-0 = -3 / 6 = -1/2
equation would be y = -1/2x + 72

2. y = -1/2x+72 = -1/2(30) +72 = -15 +72 = 57 beats per minute

3. replaced x in the equation with 30 to find the beats per minute for exercising 30 minutes

You start a business making painted flower containers. You spend 300$ on paint and 5$ on each container. You charge 20$ for each container. How many containers do you have to sell to break even?

Answers

without paint, you're profiting $15 per container with the $5 original cost

300/15 = 20

dividing whole numbers 22 divided by 300

Answers

Answer:

22 divided by 300 will be equal to 0.07333.

Step-by-step explanation:

Dividing 22 by 300

[tex]\frac{22}{300}=\frac{2\times 11}{2\times 2\times 5\times 5\times 3}[/tex]

[tex]\frac{22}{300}=\frac{11}{2\times 5\times 5\times 3}=\frac{11}{150}[/tex]

[tex]\frac{11}{150}=\frac{11}{15}\times \frac{1}{10}[/tex]

The value of [tex]\frac{11}{15}=0.7333[/tex]

[tex]\frac{22}{300}=\frac{11}{150}=0.7333\times \frac{1}{10}=0.07333[/tex]

So, the value of 22 divided by 300 will be equal to 0.07333.

Final answer:

Dividing 22 by 300 gives a quotient of 0.0733, representing the proportion of 22 out of 300.

Explanation:

To perform the division of the whole numbers 22 and 300, you simply divide 22 by 300 using long division or a calculator. However, since 300 is larger than 22, the result will be a decimal or fraction that is less than 1. Mathematically represented as:

22 ÷ 300 = 0.0733

In a real-world scenario, this number could be interpreted as the proportion or percentage of a whole that the number 22 represents out of 300.

Learn more about Division of Whole Numbers here:

https://brainly.com/question/29885808

#SPJ3

give the length and width in whole inches of three different rectangles that each have an area of 48 in. squared

Answers

To find the length and width of 3 different rectangles that have an area of 48 square inches, you can use the factor pairs that result in 48.

The reason is that to find the area of a rectangle you multiply two dimensions.

2 in x 12 in
3 in x 8 in
4 in x 6 in

On all these either one could be the length and the other the width.

Jamelia estimates the square root of 72 in the following way:
√72 = 2√36 = 2*6 = 12

(a) Explain why her reasoning is incorrect.

(b) Estimate the square root of 72 to the nearest tenth. Show your work.

Answers

Part a)
we have that
√72
√72-----> √(2*36)=√2*√36 is not 2*√36------> this is the error
√2*√36=√2*√6²-----> √2*(6)----> 6√2

alternative method
72 is equal to-------> 2³*3²
therefore
√72-----> √[2³*3²]----->√ 2³*√3²-------> (2√2)*(3)-----> 6√2

Part b)Estimate the square root of 72 to the nearest tenth

we know that
√2 is equal to 1.41
so
√72=6√2------> 6*1.41-----> 8.46----> 8.5

the answer Part b) is 8.5

Please help me with this!

Answers

Differences between x-values are 1. Differences between y-values are 2. The y-values are changing 2 times as fast as the x-values, so you are looking for an answer that involves 2x. The appropriate choice is
D. 2x + 3

_____
You can check this result:
for x=1: 2·1 + 3 = 5
for x=4: 2·4 + 3 = 11
These values correspond to those in the table.

Let's just list the coordinats first.
(1,5)
(2,7)
(3,9)
(4,11)

When you see 3 and 9, you sometimes immediately think it is 3x=y, but you have to look at the other coordinates as well. This can be show in option a, 5x=y. This can not be the anser because 3×5=15≠9. We can eliminate that answer. Option B says that you are adding 2, but when you add 2 to 4, it equals 6 and not 11. The same for C, 4 added to 4 equals 8, not 11.

The one left, D, is the answer. When you put each x value in, you do get the corresponding y value as well. To even make sure, I made a graph with 2x+3=y as the function to see if those values/coordinates would pop up.

Other Questions

Lynn has just received a research grant to study the effect of downsizing on morale at a large computer company. lynn is most likely a(n) _____ psychologist. Out of 28 students in a class, 7 have blue eyes. What is the probability a student picked at random from the class does NOT have blue eyes?A) 1/4B) 3/4C) 1/7D) 6/7 Write an inequality for the given statement: The sum of 18 and a number is more than 22. A. 18 n < 22 B. 18 n > 22 C. 18 + n < 22 D. 18 + n > 22 Clauses that stand alone and are complete sentences are called _____.A.subordinate clausesB.independent clauses Read the passage from "Names/Nombres" by Julia Alvarez. Our first few years in the States, though, ethnicity was not yet in. Those were the blond, blue-eyed, bobby-sock years of junior high and high school before the sixties ushered in peasant blouses, hoop earrings, serapes. My initial desire to be known by my correct Dominican name faded. I just wanted to be Judy and merge with the Sallys and Janes in my class. But, inevitably, my accent and coloring gave me away. Which detail best conveys the main idea that Alvarez wants to fit into her new culture? Our first few years in the States, though, ethnicity was not yet in. Those were the blond, blue-eyed, bobby-sock years of junior high and high school . . . . . . before the sixties ushered in peasant blouses, hoop earrings, serapes. I just wanted to be Judy and merge with the Sallys and Janes in my class.....NEED HELP PLEASE Career counselors in private practice require, to a greater extent than those in other settings, the ability to A teacher asks her students to design a game board for a class project. The dimensions of the boards created by four students are shown below. Angelalength: 20 cmwidth: 21 cmdiagonal: 29 cm Bradleylength: 9 in. width: 9 in.diagonal: 9 in. Carltonlength: 25 cmwidth: 30 cmdiagonal: 35 cm Dellalength: 10 in.width: 12 in.diagonal: 15 in. Whose game board could be a rectangle? Johnny flips a coin three times. what is the probability he lands on heads every time Exposure to clostridium tetani causes continuous release of acetylcholine. what effect does this have on particular skeletal muscles? If f(x) = x2 and g(x) = 1 over 2x + 3 , find g(f(-1)). the bill for a meal came to 65.40 plus 15% service charge what was the total bill? Dr. morris believes that it is inadequate for death to be only pain and trauma free. she believes that people suffering from a terminal illness should be able to select the particular style of exit they believe is consistent with their total lifestyle, such as a romantic death, a brave death, or one that integrates and confirms the person's unique identity. dr. morris subscribes to the quest for In which country do citizens have the fewest voting rights A. Iran B. Israel C. Turkey D. Saudi Arabia The source of power in a nuclear power plant comes from The line this disaster swallows up a man and wife together is an example of _____.A) simileB) metaphorC) personificationD) hyperbole What is the mode of the given data set? 65, 45, 79, 56, 63, 45, 71, 69, 65, 53, 45 Which of the following leaders fought for Mexican independence from Spain? When a terminally differentiated cell in an adult body dies, it can typically be replaced in the body by a stock of __________? Describe how you could draw a diagram for a problem about finding the total length for two strings, 15 inches long and 7 inches long Which is a symptom of toxic shock syndrome1.dizziness2.highfever3.depression4.weakness