Please help with these Statistics and Probability question. The questions are in the attachment.

Constructing probability distributions

1.Which of the following statement is correct from the graph of probability curve?

A.The probability curve is symmetrical.

B.The probability curve is not symmetrical.

C.The given probability curve never happens in trial.

D.The given probability curve shows total probability equal to '1'.

2.From the following graph, identify the correct statement.

A.The probability curve is symmetrical

B.The probability curve is not symmetrical

C.The given probability curve never happens in trial

D.The given probability curve shows total probability equal to '1'

1.Which of the following is more likely to happen?

A.Enteringroom A and room B simultaneously.

B.Sending an e-card to your friend on Uranus.

C.Your height will be reduced by half.

D.Getting a promotion in the next year.

2. What is the probability of a sure event?

A.1

B.0.5

C.0.3

D.zero

3.Team A, B, and C are competing in a basketball tournament. The probability of team A winning is 0.2, the probability of team B winning is 0.45, and the probability of team C winning is 0.35. Anna can join either team A or team B. Elina can join either team B or team C. Nancy can join either team A or team C. Who is most likely to win?

A.Anna

B.Nancy

C.Elena

D.All have an equal probability to win.

4.What is the chance to celebrate the new year on Monday?

A.1/12

B.1/7

C.1/30

D.1/52

5.Which of the following is more likely to occur?

A.Probability of fishing in the sea is 0.45.

B.Probability of fishing in the pool is 0.92.

C.Probability of fishing in the river is 0.35.

D.Probability of fishing in the rill is 0.42.

6.What is the probability of an equally likely event?

A.zero

B.25%

C.50%

D.100%

7.Which of the following is an impossible event?

A.Getting 6 when a die is rolled.

B.Selecting a boy from a class of girls in a school.

C.Getting a card of hearts from a deck of cards.

D.Getting a head on tossing a coin.

1.Multiply: 21 * 3

A.21 + 3

B.21 - 3

C.21*3

D.24

2.Solve the logarithmic equation: log₇ (x - 3) + log₇ (x + 3) = 1

A.3 and -3

B.4

C.7 and -7

D.4 and -4

3.The graph of the logarithmic function is drawn using __________________.

A.table of values

B.relationship between logarithmic and exponential function

C.intercepts

D.all of the choices

4.Solve for x in the following equation: Cos²x = ¹/₁₆

A.75.5 degrees and 104.5 degrees

B.75 degrees and 15 degrees

C.145 degrees and 35 degrees

D.45 degrees and 90 degrees

5.Which one of the following situations could be represented by a linear function?

A.The price of a car depreciates at a certain rate every year.

B.Number of bacteria in a petri dish triples every hour.

C.A ball rebounds to half the previous height upon every collision with floor.

D.Morgan walks at a constant rate and covers 4 miles every hour.

6.Using the graph of f(x) = x² - 12x + 28, find the global minimum of the function f(x).

A.0

B.3

C.-8

D.8.5

7.Find the approximate value of x if ln 45 3.8066.

7e^4x = 315

A.0.95165

B.1.52264

C.9.5165

D.15.2264

8.Find the relationship between the given two triangles.

A.Similar right triangles

B.Not similar

C.Equilateral triangles

D.Isosceles triangles

9.Assuming that the two right triangles are similar, find the height of the tower from the given measurements.

A.3 m

B.5 m

C.6 m

D.10 m

10.Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)

A.14.76 units

B.218 units

C.13.1 units

D.7.62 units

11.A park is 5 miles east of Roxana's home. A library is 4 miles north of the park. How far is Roxana's home from the library?

A.3 miles

B.4.3 miles

C.5. 7 miles

D.6.4 miles

12.The measure of an angle formed by a tangent and a chord on a circle is ____ the measure of the intercepted arc.

two times

A.two times

B.3/4

C.1/2

D.1/4

13.Find the length of PS from the following figure:

A.3

B.4

C.6

D.8

21.Find the 7^th term of the geometric sequence using a₆ = -¹/₁₈ and r = ¹/₃.

A.-1/54

B.-1/52

C.-1/36

D.-1/9

14.A circle and a point outside the circle are given. What would be the first step to draw a tangent line to the circle from that point?

A.Draw the radius of the circle.

B.Draw a chord on the circle.

C.Draw the line between the point and the center of the circle.

D.Draw a secant of the circle through the given point.

15.A building is 150 feet high. An observer at a distance away from the building notices that the angle of elevation to the top of the building is 80. How far is the observer from the base of the building?

A.152.30 ft

B.867.05 ft

C.30 ft

D.26.45 ft

16.Find the value of (sin.cos)/cosec, when = 45.

A.2/2

B.1/2

C.1/22

D.2/2

18.Find the value of -4[g(2)] if g(x) = x² - 5x.

A.24

B.20

C.-20

D.21

19.The area of a circle is given as A(r) = r², find A(2).

A.12

B.12.6

C.13

D.13.4

17.The vertices of a quadrilateral are A(-2, 1), B(0, 3), C(-3, 4), and D(-4, 2). Identify the reflected image across the y-axis.

A B

_CD

20.Assume a worm covered a distance of 18 mm in the first minute, 46 mm in the next minute, 74 mm in the third minute, and so on. What is the distance the worm would have covered in the 5th minute?

A.276 in.

B.260 in.

C.170 in.

D.130 in.