All categories

3 years ago

Question

Mathematics

1 answer:

ella [17]3 years ago

3 0

Answer:

The money invested into bond is $8000

The money invested into stocks is $17,000

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- Vartan wants to invest $25,000

- He wants to put some of the money into a bond that pays 4% annual

interest and the rest into stocks that pay 9% annual interest

- He wants to earn 7.4% annual interest on the total amount

- We need to know how much money he should invest in each account

- Assume that he will put $x into the bond that pays 4% annual interest

- He will put the rest into stocks that pay 9%

- The rest = 25,000 - x

∴ The money earns = (4/100)(x) + (9/100)(25,000 - x)

∴ The money earns = 0.04 x + 2250 - 0.09 x

∴ The money earns = 2250 - 0.05 x ⇒ (1)

∵ He wants to earn 7.4% annual interest on the total amount

∵ Total amount is $25,000

∴ The money earns = (7.4/100)(25,000)

∴ The money earns = 1850 ⇒ (2)

- <u><em>Equate (1) ans (2)</em></u>

∴ 2250 - 0.05 x = 1850

- Add 0.05 x to both sides

∴ 2250 = 0.05 x + 1850

- Subtract 1850 from both sides

∴ 400 = 0.05 x

- Divide both sides by 0.05

∴ x = 8,000

∴ 25,000 - 8,000 = 17,000

∵ x represents the money invested into the bond

∵ 25,000 - x represents the money invested into the stocks

∴ The money invested into bond is $8000

∴ The money invested into stocks is $17,000

You might be interested in

Please answer all 3 questions

Sonja [21]

The residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326, 0.049, -0.286, -0.161, 0.214, 0.429 and 0.059

<h3>How to determine the residuals?</h3>

The regression equation is given as:

y = 0.005x + 3.111

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.005 * 4 + 3.111 = 3.131

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 5 + 3.111 = 3.136

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 8 + 3.111 = 3.151

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 10 + 3.111 = 3.161

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 6 + 3.111 = 3.141

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

y = 3.46 - 3.131 = 0.329

y = 2.78 - 3.126 = -0.346

y = 3.2 - 3.136 = 0.064

y = 2.8 - 3.126 = -0.326

y = 3.2 - 3.151 = 0.049

y = 2.9 - 3.186 = -0.286

y = 3 - 3.161 = --0.161

y = 3.4 - 3.186 = 0.214

y = 3.57 - 3.141 = 0.429

y = 3.2 - 3.141 = 0.059

Hence, the residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326, 0.049, -0.286, -0.161, 0.214, 0.429 and 0.059

See attachment for the residual plot.

The residual plot shows that the linear model from the regression calculator is a good model because the points are not on a straight line

Read more about residuals at:

brainly.com/question/16180255

#SPJ1

3 0

2 years ago

HELP THIS IS DUE BY THURSDAY PLZZ HELP ME (05.03)Bev has to cut her grandma's grass this weekend and wants to know exactly how m

Art [367]

Answer: 220.5 ft^2

That's the answer.

4 0

3 years ago

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

4 years ago

How can you use integers to represent the velocity and the speed of an object?

astraxan [27]

1)The SPEED of an object tells us how fast this object is moving, bit it doesn't indicate the direction of :
Speed = distance/time

2) The VELOVITY of an object tells us how fast this object is moving and in which direction it's moving ( If UP, then it's positive. If DOWN, then it's negative. Same logic for moving right (+) or left (opposite to right, then -)
Velocity = distance/time

In short te absolute value of Velocity = Value of speed:

| Velocity | = Speed

8 0

4 years ago

LenaWriter [7]

An experimental study involves the researcher seeking to affect the results on purpose. The given situation is an observational study.

<h3>What are surveys, experiments, and observational studies?</h3>

Surveys are one type of observational study since the researchers have no control over the results. Statistical surveys collect data from a sample group in order to learn more about the overall population.
The sample population being examined is measured, or surveyed, in observational research. The researcher watches the individuals and measures variables but makes no attempt to influence the population or intervene in the study.
In contrast to an observational study, an experimental study involves the researcher seeking to affect the results on purpose. The objective is to find out what influence a certain therapy has on the result.

Since the researcher needs to find if a certain medicine improves the symptoms of the flu, therefore, the objective is to find out what influence a certain therapy has on the result. Hence, the given situation is an observational study.

Learn more about Observational Studies:

brainly.com/question/15938198

#SPJ1

5 0

2 years ago