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Svetllana [295]
2 years ago
15

Maisie has saved up $50 to buy concert tickets, but the tickets cost $125. She is able to earn $15 per day by walking her neighb

or’s dogs. How many days will Maisie have to walk the dogs to earn enough money to buy the tickets? Let d = the number of days worked. What equation will you use to solve this word problem? What equivalent equation can you write after combining like terms? How many days will Maisie have to walk the dogs?
Mathematics
1 answer:
Greeley [361]2 years ago
5 0

Answer:

15d + 50 = 125

15d = 75

5 days

Step-by-step explanation:

Her total must equal $125.

She has $50 so far.

50 + _____ = 125

In the blank, we will put what she will earn by walking the dogs.

Each day she will earn $15. In d number of days, she will earn 15d.

The equation is:

50 + 15d = 125

15d + 50 = 125

We can subtract 50 from both sides to get

15d = 75

Now we solve the equation to find the number of days.

We divide both sides by 15.

15d/15 = 75/15

d = 5

She will need to walk the dogs for 5 days.

Guest
1 year ago
Your wrong about the first answer its's: 50+15d=125
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A credit card issuer charges an APR of 13.99%, and its billing cycle is 30 days long. What is its periodic interest rate?
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The CEO of Millennium Dairy Product, a small venture among 10 partners each having 100,000 shares, sought to raise an additional
klemol [59]

Answer:

Millennium Dairy Product

a) Share of the company that SBI Caps should require today to get a required rate of return of 50%.

= 50%

b) If the company had 1,000,000 (100,000 x10) shares outstanding before the private placement, SBI Caps should purchase

1,000,000 shares = 50% of (1,000,000 + 1,000,000) shares

Assuming the founding promoters are not giving up their shares, instead, new equity shares are being issued.

c) The price per share SBI Caps should agree to pay, if her required return was 50% is

Rs.50 per share, which will provide the required additional equity financing of (Rs.50 million) since Rs.50 x 1,000,000 equals Rs.50 million.

d) Pre money and post money valuations:

These are based on the calculated Market Price of Rs.1,000 per share from the Price/Earnings Ratio.

Pre money valuation will be Rs.1,000 x 1,000,000 shares = Rs.1 billion

Post money valuation will be Rs.1,000 x 2,000,000 shares = Rs.2 billion

e) Carried interests of the VC and the promoters

VC's carried interest = share of profits = 50% xRs.50 million = Rs.25 million

Promoters' carried interest = Rs.25 million

Step-by-step explanation:

a) Calculation of share in the company:

SBI Cap's required rate of return is 50%

If she invests Rs.50 million today, her expected return will be equal to Rs.50 million x 50% = Rs.25 million

Since rate of return = Net Income/Initial Investment or (Current value of investment - Initial Investment)/Initial Investment.

This return will be equal to 50% of the total net income of Rs.50 million

b) Price/Earnings P/E ratio = Market price per share/Earnings per share (EPS)

Since P/E ratio of similar companies = 20 times,

The company's P/E = 20 times x EPS

With calculated EPS = Rs.50 million /1,000,000 = Rs.50

Therefore, price per share = 20 x Rs.50 = Rs.1,000

Pre money valuation = Rs.1,000 x 1 million shares = Rs.1 billion

Post money valuation = Rs.1,000 x 2 million shares = Rs.2 billion

c) The carried interest is the share of profits to which the promoters and the Venture Capitalists are entitled.  Their respective shares are 50% of the net income = Rs.25 million each.

d) The pre money and post money valuations:  The pre money valuation is the valuation of the company before the additional equity financing.  The post money valuation is the valuation of the company after the additional equity financing.  There are many ways to value a company.  In this case, we have used the P/E ratio as a basis for the valuation.  However, we did not dilute the earnings per share post money, for simplicity.

3 0
2 years ago
Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three number
Dmitry [639]

Answer:

Part a) 2,50,18

Part b) When Jenny divides the square root of her favorite positive integer by \sqrt{2}, she gets an integer

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For x=2

\sqrt{2}*\sqrt{2}=\sqrt{4}=2 -----> the product is an integer

so

The number x=2 could be Jenny favorite positive integer

2) For x=50

\sqrt{50}*\sqrt{2}=\sqrt{100}=10 -----> the product is an integer

so

The number x=50 could be Jenny favorite positive integer

3) For x=18

\sqrt{18}*\sqrt{2}=\sqrt{36}=6 -----> the product is an integer

so

The number x=18 could be Jenny favorite positive integer

Part B)

1) For x=2

\sqrt{2}/\sqrt{2}=\sqrt{1}=1 -----> the result is an integer

2) For x=50

\sqrt{50}/\sqrt{2}=\sqrt{25}=5 -----> the result is an integer

3) For x=18

\sqrt{18}/\sqrt{2}=\sqrt{9}=3 -----> the result is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by \sqrt{2} , she gets an integer

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2 years ago
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Scrat [10]

Answer:

a. dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. πa² ≥ k/∝

Step-by-step explanation:

a.

The rate of volume of water in the pond is calculated by

The rate of water entering - The rate of water leaving the pond.

Given

k = Rate of Water flows in

The surface of the pond and that's where evaporation occurs.

The area of a circle is πr² with ∝ as the coefficient of evaporation.

Rate of volume of water in pond with time = k - ∝πr²

dV/dt = k - ∝πr² ----- equation 1

The volume of the conical pond is calculated by πr²L/3

Where L = height of the cone

L = hr/a where h is the height of water in the pond

So, V = πr²(hr/a)/3

V = πr³h/3a ------ Make r the subject of formula

3aV = πr³h

r³ = 3aV/πh

r = ∛(3aV/πh)

Substitute ∛(3aV/πh) for r in equation 1

dV/dt = k - ∝π(∛(3aV/πh))²

dV/dt = k - ∝π((3aV/πh)^⅓)²

dV/dt = K - ∝π(3aV/πh)^⅔

dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. Equilibrium depth of water

The equilibrium depth of water is when the differential equation is 0

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k - ∝π(3a/πh)^⅔V^⅔ = 0

∝π(3a/πh)^⅔V^⅔ = k ------ make V the subject of formula

V^⅔ = k/∝π(3a/πh)^⅔ -------- find the 3/2th root of both sides

V^(⅔ * 3/2) = k^3/2 / [∝π(3a/πh)^⅔]^3/2

V = (k^3/2)/[(∝π.π^-⅔(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝π^⅓(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝^3/2.π^½.(3a/h))]

V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. Condition that must be satisfied

If we continue adding water to the pond after the rate of water flow becomes 0, the pond will overflow.

i.e. dV/dt = k - ∝πr² but r = a and the rate is now ≤ 0.

So, we have

k - ∝πa² ≤ 0 ---- subtract k from both w

- ∝πa² ≤ -k divide both sides by - ∝

πa² ≥ k/∝

5 0
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