An object with total mass m_total = 14.8 kg is sitting at rest when it explodes into three pieces. One piece with mass m₁ = 4.8 kg moves up and to the left at an angle of θ₁ = 22° above the –x axis with a speed of v₁ = 27.6 m/s. A second piece with mass m₂ = 5.1 kg moves down and to the right an angle of θ₂ = 27° to the right of the -y axis at a speed of v₂ = 20.5 m/s.

What is the x-component of the velocity of the third piece?

What is the y-component of the velocity of the third piece?

What is the magnitude of the velocity of the center of mass of the pieces after the collision?

Calculate the increase in kinetic energy of the pieces during the explosion？

Are these bionomial? If not, explain why.

A.)Approx 5% of a school district's 1000 seniors have no siblings. A random sample of 300 seniors is taken from that district, and X counts the number with no siblings.

B.) Approx 5% of high school seniors have no siblings. A random sample of 200 high school seniors is taken and X counts the number with no siblings.

C.) Approx 5% of high school seniors have no siblings, 29% have one, 27% have two and the remaining 39% have three or more. A random sample of 100 high school seniors is taken and the random variable X counts the number of siblings for each of the sampled seniors.

There are three hospitals in the Tulsa, Oklahoma, area. The following data show the number of outpatient surgeries performed on Monday, Tuesday, Wednesday, Thursday, and Friday at each hospital last week. At the 0.05 significance level, can we conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week?

Number of Surgeries performed:

Day      St. Luke      St. Vincent      Mercy

Mon       24                 26                     22

Tues      21                 22                     20

Wed        20              32                    28

Thur       19                  22                 27

Fri           29                 22                   14

A.) Complete the ANOVA Table:(round to 2 decimal places)

Treatments, blocks,error total. SS, DF, MS, F

Six names will be drawn from a group of H+2 freshmen, F+L sophomores, 2*(H-1) juniors, and 2*H seniors. Calculate (rounding your answers to three decimal places) the probability that:

a. freshmen, sophomores and juniors are equally represented. Ans.___________

b. the number of freshmen drawn equates the number of sophomores and juniors drawn. Ans.___________

c. the ratio of drawn seniors to drawn sophomores is 3:1. Ans.___________

d. the ratio of drawn juniors to drawn freshmen is at least 3:1. Ans.___

H = 6

T = 27

F = 3

L = 7

S = 47

Please do it correctly and need to show steps

Bruin Inc. will have earnings of $15 million next year and is projected to grow at a constant rate of 6 percent forever. All earnings are paid out as dividends to shareholders.

The company plans to launch a new project three years from now that will cost $10 million. The project will increase the firm's annual earnings by a constant $8.3 million every year forever starting one year later (i.e. 4 years from now).

What is the market value of the company stock? The discount rate is 16 percent.

Select one:

a. $192 million

b. $65 million

c. $121 million

d. $27 million

e. $177 million

The following are advertised sale prices of color televisions at an electronics store.

Calculate the least squares line. Put the equation in the form of:

ŷ = a + bx

Find the correlation coefficient r.

Find the estimated sale price for a 33-inch television. (Use your equation from part (d). Round your answer to two decimal places.)
$

Find the estimated sale price for a 47-inch television

What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.)

The following description applies to the next three problems.

Air enters steadily an electrical hair dryer at 100 kPa and 27 C. It leaves the hairdryer at a temperature of 80 C, an exit velocity of 10 m/s, and at the same pressure. The exit and inlet areas are 20 cm² and 40 cm² respectively.

(Assume properties of air cp= 1.007 kJ/kg.K, cv = 0.72 kJ/kg.K, and R= 0. 287 kJ/kg.K )

The mass flow rate of air entering the hairdryer, in kg/s, is closer to

The velocity of the air at the inlet of the hairdryer, in m/s, is closer to

The total power the hairdryer needs to operate at the stated conditions, in kW, is closer to:

GFC’s balance sheet shows a total of $25 million long-term debt with a coupon rate of 8.50%. The yield to maturity on this debt is 8.00%, and the debt has a total current market value of $27 million. The company has 10 million shares of stock, and the stock has a book value per share of $5.00. The current stock price is $20.00 per share, and stockholders' required rate of return, r_s, is 12.25%. The company recently decided that its target capital structure should have 35% debt and 65% common equity. The tax rate is 40%. Calculate WACCs based on book, market, and target capital structures. What is the sum of these three WACCs?

1. For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
   1. 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, ...
   2. 7,11,15,19,23,27,31,35,39,43,...
   3. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .
   4. 0, 2, 8, 26, 80, 242, 728, 2186, 6560, 19682, ...
   5. 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, ...
   6. 2, 4, 16, 256, 65536, 4294967296, ...

You are considering how to invest part of your retirement savings.You have decided to put $400,000

into three​ stocks: 64% of the money in GoldFinger​ (currently 27​/share), 25%

of the money in Moosehead​ (currently $99​/share), and the remainder in Venture Associates​ (currently

$4​/share). Suppose GoldFinger stock goes up to $32​/share,

Moosehead stock drops to $51​/share, and Venture Associates stock rises to $15

per share.

a. What is the new value of the​ portfolio?

b. What return did the portfolio​ earn?

c. If you​ don't buy or sell any shares after the price​ change, what are your new portfolio​ weights?