What is 2(8+1)(4v+7) URGENT !!!

Susan purchased company ABC's stock and invested the balance in her money market account. ABC's stock yielded 13% last year and

garri49 [273]

$4,000 is invested in ABC's stock and $11,000 is invested in her market account

Step-by-step explanation:

Susan purchased company ABC's stock and invested the balance in her money market account

ABC's stock yielded 13% last year and her money market account yielded 5% last year
Susan's initial investments amount to $15000, and the annual income is $1070

We need to find how much money is invested in stock and how much is invested in her money market account

Assume that she invested $x in ABC's stock and $y in her money market account

∵ She invested $x in ABC's stock

∵ She invested $y in her market account

∵ Her initial investments amount is $15000

∴ x + y = 15000 ⇒ (1)

The interest formula is I = Prt, where P is the initial investment, r is the rate of interest in decimal and t is the time

In ABC's stock:

∵ She invested $x

∴ P = x

∵ The rate is 13%

∴ r = 13% = 13 ÷ 100 = 0.13

∵ t = 1

- Substitute all of these values in the formula of interest above

∴ $I_{ABC}$ = x(0.13)(1)

∴ $I_{ABC}$ = 0.13x

In her market account:

∵ She invested $y

∴ P = y

∵ The rate is 5%

∴ r = 5% = 5 ÷ 100 = 0.05

∵ t = 1

- Substitute all of these values in the formula of interest above

∴ $I_{market}$ = y(0.05)(1)

∴ $I_{market}$ = 0.05y

∵ Her annual income is $1070

- Add the interest of ABC's stock and the interest of her market

account, equate the sum by 1070

∴ 0.13x + 0.05y = 1070 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -0.05 to eliminate y

∵ -0.05x - 0.05y = -750 ⇒ (3)

- Add equations (2) and (3)

∴ 0.08x = 320

- Divide both sides by 0.08

∴ x = 4000

- Substitute value of x in equation (1) to find y

∵ 4000 + y = 15000

- Subtract 4000 from both sides

∴ y = 11000

$4,000 is invested in ABC's stock and $11,000 is invested in her market account

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

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3 years ago

Convert the rational number below to a decimal. Round to the nearest hundredth when necessary. 3/5

Gekata [30.6K]

Answer: 0.6

Explanation: You need to divide 3 by 5 and it will give you the answer of 0.6

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2 years ago

Soccer practice began at 2:30 PM and stopped at 3:00 PM because of the rain during this time through what fraction of a circle d

ICE Princess25 [194]

The hand turn 1 quarter of a circle (1/4). it turned 90 degrees

7 0

3 years ago

The Institute of Management Accountants (IMA) conducted a survey of senior finance professionals to gauge members’ thoughts on g

DochEvi [55]

Answer:

(1) The probability that the sample percentage indicating global warming is having a significant impact on the environment will be between 64% and 69% is 0.3674.

(2) The two population percentages that will contain the sample percentage with probability 90% are 0.57 and 0.73.

(3) The two population percentages that will contain the sample percentage with probability 95% are 0.55 and 0.75.

Step-by-step explanation:

Let X = number of senior professionals who thought that global warming is having a significant impact on the environment.

The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.65.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of p if the following conditions are satisfied:

np ≥ 10
n(1 - p) ≥ 10

Check the conditions as follows:

$np= 100\times 0.65=65>10\\n(1-p)=100\times (1-0.65)=35>10$

Thus, a Normal approximation to binomial can be applied.

So, $\hat p\sim N(p, \frac{p(1-p)}{n})=N(0.65, 0.002275)$ .

(1)

Compute the value of $P(0.64$ as follows:

$P(0.64$

$=P(-0.20$

Thus, the probability that the sample percentage indicating global warming is having a significant impact on the environment will be between 64% and 69% is 0.3674.

(2)

Let $p_{1}$ and $p_{2}$ be the two population percentages that will contain the sample percentage with probability 90%.

That is,

$P(p_{1}$

Then,

$P(p_{1}$

$P(\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$P(-z$

The value of z for P (Z < z) = 0.95 is

z = 1.65.

Compute the value of $p_{1}$ and $p_{2}$ as follows:

$-z=\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}\\-1.65=\frac{p_{1}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{1}=0.65-(1.65\times 0.05)\\p_{1}=0.5675\\p_{1}\approx0.57$ $z=\frac{p_{2}-p}{\sqrt{\frac{p(1-p)}{n}}}\\1.65=\frac{p_{2}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{2}=0.65+(1.65\times 0.05)\\p_{1}=0.7325\\p_{1}\approx0.73$

Thus, the two population percentages that will contain the sample percentage with probability 90% are 0.57 and 0.73.

(3)

Let $p_{1}$ and $p_{2}$ be the two population percentages that will contain the sample percentage with probability 95%.

That is,

$P(p_{1}$

Then,

$P(p_{1}$

$P(\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$P(-z$

The value of z for P (Z < z) = 0.975 is

z = 1.96.

Compute the value of $p_{1}$ and $p_{2}$ as follows:

$-z=\frac{p_{1}-p}{\sqrt{\frac{p(1-p)}{n}}}\\-1.96=\frac{p_{1}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{1}=0.65-(1.96\times 0.05)\\p_{1}=0.552\\p_{1}\approx0.55$ $z=\frac{p_{2}-p}{\sqrt{\frac{p(1-p)}{n}}}\\1.96=\frac{p_{2}-0.65}{\sqrt{\frac{0.65(1-0.65)}{100}}}\\p_{2}=0.65+(1.96\times 0.05)\\p_{1}=0.748\\p_{1}\approx0.75$

Thus, the two population percentages that will contain the sample percentage with probability 95% are 0.55 and 0.75.

7 0

4 years ago

Marco and Drew stacked boxes on a shelf. Marco lifted 9 boxes and Drew lifted 14 boxes. The boxes that Drew lifted each weighed

belka [17]

If m = the weight of boxes that marco lifted, and each box that drew lifted was 8 lbs less than marcos boxes, then you would multiply the total number of boxes that drew lifted by the weight of marcos total boxes - 8 or 14(m-8)

3 0

3 years ago

Read 2 more answers