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when applicable.
sin
, given that cos 0. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

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4.Write and solve an equation to find the value of x so that the figures have the same area. The area ...

of a trapezoid is 1/2 h(b1+b2)

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ty distribution:
x 3 5 8 10
pX(x) k k k 2k
i. Determine the constant k and hence write down the probability
distribution of X.
ii. Find E(X), the expected value of X.
iii. Find Var(X), the variance of X.

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y aces or twos, you lose the game immediately. You also lose if you draw picture cards(J,Q,K) more than twice. In this question, you’ll study the probability of winning this game.(a) What is the probability of drawing no aces or twos after thirteen draws?(b) Given you have drawn thirteen times, none of which is aces or twos, what is the probability that you draw at most two picture cards?(c) What is the probability to win this game?
12. Suppose you are tossing an unbiased coin for100times.(a) What is the probability of getting50heads and50tails?(b) LetXbe the random variable counting the number of heads you observe in this exper-iment. What is the expected value ofX? What is the variance ofX? What is thestandard deviation ofX?
13. The following are probability distributions for two random variablesX,Y.
kPr(X=k)
0,0.4
1,0.3
2,0.3
kPr(Y=k)
0,0.5
1,0.3
2,0.2
(a) Construct the probability distribution table for the random variableXY.(b) Find E[X],E[Y] and E[XY]. Is is true that E[XY] =E[X]E[Y]?(c) Find the variances σ2X,σ2Y,σ2XY of X,Y and XY. Is it true that σ2XY=σ2Xσ2Y?
14. The aliens who are fond of gambling came back to play another game with you. In this game, you first toss a coin5times. If you observe3or fewer tails, you roll a die3times. If youobserve4or more tails, you roll a die20times. What is the probability that you end up with at most two6’s in your dice rolls?
15. (Challenge question, worth2points) You have two bags, each of which contains10marbles.Each time you remove a marble from a random bag. What is the probability that after one of the bags is emptied, there are still exactly3marbles in the other bag?

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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- 1); I{x>1}, theta > 1.
(a) Show that log Xi has an exponential distribution with a mean of 1/theta.
(b) Find the form for a UMP test of H_0: theta <= theta_0 vs. H_a : theta > theta_0.
(c) Give formula for nding the rejection region for a given value of alpha.
Hint: use the result from (a) to find the distribution of the test statistic.
(d) Conduct the test in (b) with alpha = 0.05 and theta_0 = 1:5 using the dataset: {1.2, 2.4, 1.3, 1.7, 1.9}.
(e) Find the form of a UMPU test for testing H_0 : theta = theta_0 vs. H_a : theta_0 != theta_0.
(f) Use the data in (d) to conduct the test in (e) with alpha = 0.05 and theta_0 = 1.5.

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13. LetS1 betheareaoftheregionboundedbythecurvey=x2 andthelinesy=ax,(0 ...

ction between the floor and book is µk. Using the information given in the figure:
(a) draw free body diagrams for both the books, and also for the combined system (of mass m1+m2),
(b) find acceleration of the books along horizontal direction, and
(c) find the magnitude and direction of the force exerted by the left book on the right book.
3.A car of mass 1500-kg enters a circular path at point P and leaves at point Q (see the figure) at constant speed of 5.0m/s, and the frictional force acting on its tires is 2500-N.
a) how long it takes to reach point Q from point P, and
b) what should be the minimum value of the coefficient of static friction between the tires and the road?
4)In an elevator which is accelerating downward at 2.5ms−2 , a 25-kg block hangs from a spring attached to the ceiling of the elevator. If spring gets stretched by 0.15m, find its spring constant.

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low, find the value of g(f(-3))
f(x) = 5x + 11
g(x) = x^2 +4x-11

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21.1. Suppose that X0 =100. (a) Find (by hand) the next four terms of the difference equation ...

d by Xn+1 = 2.5Xn + 3n. In other words, find X1, X2, X3 and X4. (Note: Show all of your work. You may enter this difference equation and initial value in your calculator to confirm that you did the calculations correctly.)

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h trigonometric function. (coterminal angle: 2 pts, the value of each trigonometric
function: 2 pts)

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25.By the trial and error method, find a value of the variable (x, y, z or m) so that ...

equal to R. H. S.
Q1= 2x=9-x.

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27.Which of the following equations can be used to find Sx, the value of an annuity after n deposits. ...

S_n=(a_1 (1-r^n))/(1-r)
b. S_n=(a_1 (1-r^n))/r
c. S_n=(a_1 (r^n))/(1-r)
d. S_n=(a_1 (1-r^n))/(1+r)

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lve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
Let f be a twice-differentiable function such that f′(2)=0 . The second derivative of f is given by f′′(x)=x2e2−x−1 for 0≤x≤6 .
(a) On what open intervals contained in 0
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that (3c^3/c^2+2) - c = 3 for some real number c.
2.)Use your calculator to find the value of C, correct to 4 decimal places.

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tal-revenue and total-cost functions, find the total profit, the maximum value of the total profit, and the value of x at which it occurs.
Upper R left parenthesis x right parenthesis equals 1300 x minus x squared, Upper C left parenthesis x right parenthesis equals 3000 plus 30 x
The total profit, P(x)equals
negative x squared plus 1270 x minus 3000.
(Simplify your answer. Do not factor.)

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ulation standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.
H0: μ = 43
H1: μ ≠ 43
find the p value (round z value to 2 decimals and final answer 4 decimal place)

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54.
Which equation can be used to find the number of pennies Ari has?

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01, and 0.01 p. The second row shows Nickels, with the entries, 22 minus p, 0.05, and 0.05 left parenthesis 22 minus p right-parenthesis.
Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54.
Which equation can be used to find the number of pennies Ari has?

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37.Let R be the region bounded by the graph of y=x^4 and the line y=16. There exists a number k, ...

such that when R is revolved about the line y=k, the resulting solid has the same volume as the solid resulting when R is rotated about the x-axis. Write an equation involving integral expressions that can be used to find the value of k, and then solve for k.

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ative of both together.
I then need to use the derivative to find the gradient of the curve at one of its x-intercepts.
I know i need to first need to find a suitable value for t, and then evaluate derivative to obtain a gradient. Also find the corresponding x-coordinate

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40.Given the points on a line below : x (2,4) y (10,16) (i) Find the values of m and c (ii) ...

hat is the equation of the line passing through the points ?
(iii) Using the equation of the line. For a y value of 28, what is the x value?

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41.Find the area of a circle with diameter 8 yd. Use the value 3.14 for \pi , and do not ...

wer. Be sure to include the correct unit in your answer.

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7km/h .
Find the value of x.

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46.2. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value ...

s of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
5. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
9. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
22. What is the greatest value of c for which the roots of the equation x^2 + 4x + c = 0 are real?
24. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
7, 24 and 25
A._________________ (smaller value)
B._________________ (larger value)

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47. 1. What is the greatest value of c for which the roots of the equation x^2 + 4x + ...

2. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
A._______________________ (Smaller Value)
B. _______________________ (Larger Value)
3. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
4. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
5. If 8 ounces of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
6. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value of x?

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ups need one hour in Machine 1; whereas glasses need one hour. The company has exactly ten hours available in Machine 1. Use the method of substitution to find the maximum values of X and Y and the maximum value for the objective function. Show all the steps in the method.

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49.if the scale factor of Figure A to Figure B is 3:8, find the value of x one triangle has an ...

nside, ith an x on the hypotenuse side.
The seond triangle has a B, with a 24 on the hypotenuse side

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points x=2 and x=3 are perpendicular to each other, find the value of k.
b. Given also that the curve passes through (4,9), find the equation of the curve.

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s, you run the following re- gression on a sample of 65 countries for the year 2012:
books = 8.2314 + (1.0329)
+ 0.3149 age (0.4111)
8.1391 (0.5812)
?
income
4.8121 (0.3543)
+
ereaders,
3.4125 educ (0.7314)
where books is the number of paperback novels purchased in 2012, income is per capita GDP in 2012, educ is the average number of years of education for the population in 2012, age is the average age of the population in 2012 and ereaders is the number of electronic readers (e.g. Kindles) sold in 2012. The numbers in parentheses refer to standard errors corresponding to the estimated coefficients. You also find that R2 = 0.7231 and SSR = 1, 231.
(a) Which of the slope coefficients are statistically different from zero at the 5% level of significance? Perform statistical tests to answer this question. [8 marks]
Solution: Each test carries 2 marks. t ratios are: 14.0039, 4.66, 0.7659, -13.5819. The 2.5% critical value for a tn?k=65?5=60 distribution can be seen to be 2.0000, implying that all coefficients except the one on age are significant.
(b) Does the intercept have a plausible interpretation? Explain briefly. [4 marks]
Solution: The intercept indicates that demand for paperback novels equals 8.2314 when income, educ, age and ereaders all equal zero. Clearly this is not plausible.
(c) Construct a 95% confidence interval for the coefficient on age. [8 marks]
Solution: CI is given by [bage

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics