Quiz about Mu Alpha Theta In-School Competition April 15th, 2024

Question 1

A family has 3 children. You know that 2 of the children are boys. What is the probability that the third child is also a boy?

Accepted Answer

$$\frac{1}{4}$$

Answer

$$\frac{1}{2}$$

Answer

$$\frac{1}{6}$$

Answer

$$\frac{1}{5}$$

Answer

$$\frac{1}{3}$$

Question 2

The GDP per capita for 6 countries are:

$252

$122,451

$6,592

$12,129

$12,171

$23,472

Determine the mean, median, and mode of this data set.

Accepted Answer

Mean: $29,511.17

Median: $12,150

Mode: No mode

Answer

No mean, median, or mode

Answer

Mean: $32,983.40

Median: $12,129

Mode: No mode

Answer

Mean: $29,511.17

Median: $12,171

Mode: $12,2451

Answer

Mean: $27,486.17

Median: $12,150

Mode: No mode

Question 3

A streaming service tracks the length (in minutes) of various movies in its library. Here are the lengths of a random sample of 5 movies:

98 minutes
125 minutes
150 minutes
172 minutes
201 minutes
Calculate the range and interquartile range of the movies.

Accepted Answer

Range = 103 minutes, Interquartile Range = 47 minutes

Answer

Range = 47 minutes, Interquartile Range = 103 minutes

Answer

Range = 150 minutes, Interquartile Range = 172 minutes

Answer

Range = 201 minutes, Interquartile Range = 125 minutes

Answer

Range = 98 minutes, Interquartile Range = 201 minutes

Question 4

Describe the correlation of the points on the scatter plot.

Accepted Answer

Strong, linear, positive

Answer

Strong, linear, negative

Answer

Moderate, quadratic, positive

Answer

Weak, linear, positive

Answer

Strong, logarithmic, positive

Question 5

Imagine a company manufactures lightbulbs, and the lifespans of these lightbulbs are normally distributed with an average lifespan of 10,000 hours and a standard deviation of 500 hours. What percentage of lightbulbs can be expected to last between 9,000 and 11,000 hours?

Accepted Answer

95%

Answer

99.7%

Answer

34%

Answer

68%

Answer

49.85%

Question 6

A right triangle has legs measuring 6 cm and 8 cm. Calculate the length of the hypotenuse.

Accepted Answer

10 cm

Answer

18 cm

Answer

16 cm

Answer

14 cm

Answer

12 cm

Question 7

Write the equation of a circle centered at (3, -1) with a radius of 4.

Accepted Answer

(x - 3)² + (y + 1)² = 16

Answer

(x - 3)² + (y - 1)² = 16

Answer

(x + 3)² + (y - 1)² = 16

Answer

(x - 3)² + (y + 1)² = 4

Answer

(x + 3)² + (y + 1)² = 4

Question 8

A bag contains 5 red marbles, 3 blue marbles, and 2 yellow marbles. What is the probability of drawing all 3 blue marbles from the bag without replacement in the first 3 draws?

Accepted Answer

$$\frac{1}{120}$$

Answer

$$\frac{3}{500}$$

Answer

$$\frac{3}{80}$$

Answer

$$\frac{27}{1,000}$$

Answer

$$\frac{3}{10}$$

Question 9

Solve the inequality -11x + 9 > 25.

Accepted Answer

x < $$-\frac{16}{11}$$

Answer

x > $$\frac{16}{11}$$

Answer

x > $$-\frac{16}{11}$$

Answer

x < $$\frac{16}{11}$$

Answer

x = $$-\frac{16}{11}$$

Question 10

Solve for the solutions of 2x² - 7x - 15 = 0.

Accepted Answer

x = $$-\frac{3}{2}$$ , x = 5

Answer

x = -1, x = 4

Answer

x = -4, x = 7

Answer

x = $$\frac{5}{2}$$ , x = -3

Answer

x = -2, x = 3

Question 11

Factor the polynomial: x² + 6x - 7 = 0

Accepted Answer

(x + 7)(x - 1) = 0

Answer

(x + 7)(x + 1) = 0

Answer

(x - 7)(x + 1) = 0

Answer

(x - 7)(x - 1) = 0

Answer

(x + 7)(x - 2) = 0

Question 12

Consider $$y\ =\ \frac{2x+5}{\left(x-1\right)\left(x+2\right)}$$ . Solve for A and B when $$y\ =\ \frac{A}{x-1}+\frac{B}{x+2}$$ .

Accepted Answer

A = $$\frac{7}{3}$$

B = $$-\frac{1}{3}$$

Answer

A = 1

B = -2

Answer

A = $$-\frac{1}{3}$$

B = $$\frac{7}{3}$$

Answer

A = -2

B = 1

Answer

A = $$-\frac{7}{3}$$

B = $$\frac{1}{3}$$

Question 13

A ball is thrown vertically upwards from ground level. It reaches a maximum height of 20 meters and then falls back down, bouncing repeatedly. With each bounce, the ball reaches 75% of its previous height. Find the total distance traveled by the ball.

Accepted Answer

160 meters

Answer

130 meters

Answer

80 meters

Answer

30 meters

Answer

70 meters

Question 14

Find the area of the sector of a circle where the radius is 5 meters and the angle of the sector is 47 degrees (round to the nearest hundredth).

Accepted Answer

10.25 square meters

Answer

4.10 square meters

Answer

2.05 square meters

Answer

41.02 square meters

Answer

20.51 square meters

Question 15

The Sun is spherical shaped and has a radius of about 695,700 kilometers. Determine the approximate volume in cubic kilometers.

Accepted Answer

Approximately 1.41 x 10¹⁸ cubic kilometers

Answer

Approximately 2.82 x 10¹⁸ cubic kilometers

Answer

Approximately 7.05 x 10¹⁷ cubic kilometers

Answer

Approximately 2.03 x 10¹² cubic kilometers

Answer

Approximately 9.81 x 10²³ cubic kilometers

Question 16

Find x.

Accepted Answer

8.00

Answer

8.26

Answer

8.10

Answer

7.90

Answer

7.50

Question 17

Write the equation of the line that passes through points (2, 3) and (-1, 4) in slope-intercept form.

Accepted Answer

y = -x/3 + 5

Answer

y = 2x + 1

Answer

y = -3x + 7

Answer

y = 0.5x + 2

Answer

y = -2x + 3

Question 18

Given the function f(x) = x² - 4x + 3, find the vertex and axis of symmetry.

Accepted Answer

The vertex is (2, -1) and the axis of symmetry is x = 2.

Answer

The vertex is (2, -1) and the axis of symmetry is y = -1.

Answer

The vertex is (1, 0) and the axis of symmetry is x = 1.

Answer

The vertex is (0, 3) and the axis of symmetry is y = 3.

Answer

The vertex is (-2, 15) and the axis of symmetry is x = -2.

Question 19

Solve the following system of equations:
6x + 9y = 43

4y + 2x = 19

Accepted Answer

x = $$\frac{1}{6}$$

y = $$\frac{14}{3}$$

Answer

x = $$\frac{1}{3}$$

y = $$\frac{14}{3}$$

Answer

x = $$\frac{14}{3}$$

y = $$\frac{1}{6}$$

Answer

x = $$3$$

y = $$\frac{3}{14}$$

Answer

x = $$6$$

y = $$\frac{8}{3}$$

Question 20

The 3rd and 5th term of a geometric sequence is 48 and 768, respectively. Find the 6th term.

Accepted Answer

3072

Answer

6144

Answer

1536

Answer

384

Answer

12288

Question 21

In the figure above, the radius of circle A is $$\frac{1}{3}$$ the radius of circle B. Starting from the position shown in the figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of circle first reach its starting point?

Accepted Answer

4

Answer

$$\frac{3}{2}$$

Answer

$$\frac{7}{2}$$

Answer

3

Answer

6

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