Question

1. eden is counting the trees on her property. she knows her grandfather planted four times as many maples trees as oak trees, and they have all survived. she counts six oak trees on the property. how many maple trees are on the property?

a) 24
b) 30
c) 36
d) 42

1. a ladder is leaning against a vertical wall. the base of the ladder is six feet away from the wall, and the ladder itself is ten feet long. how high up the wall does the ladder reach?

a) 3 feet
b) 6.7 feet
c) 7.4 feet
d) 8 feet

1. one section of a zoo has five exhibits: lion, elephant, komodo dragon, penguins, and crocodile. the first two of these animals are mammals, and the remainder are not. each student in a class is randomly assigned to observe one of the exhibits. what is the probability that a particular student will not end up observing a mammal?

a) 20%
b) 40%
c) 60%
d) 80%

1. the perimeter of any regular polygon is given by ( p = n cdot s ), where ( n ) is the number of sides, and ( s ) is the length of any side. if the perimeter of a nine-sided figure is 603, what is the length of one side?

a) 67
b) 74
c) 77
d) 201

1. which of the following lines is parallel to a line passing through the points (2,3) and (4,7)?

a) ( y = 2x - 12 )
b) ( y = -2x + 4 )
c) ( y = (0.5)x - 6 )
d) ( y = -(0.5)x )

1. two clocks ring together at 12:00 am. the first clock rings every 40 minutes. the second clock rings every 60 minutes. at what time will they next ring together?

a) 12:40 am
b) 2:00 am
c) 3:20 am
d) 4:00 am

Explanation:

Question 4

Step1: Identify the relationship

Maple trees = 4 * Oak trees.

Step2: Substitute the number of oak trees

Oak trees = 6, so Maple trees = 4 * 6 = 24.

Step1: Recognize the right triangle

The ladder, wall, and ground form a right triangle. Let \( h \) be the height on the wall, base \( b = 6 \) ft, hypotenuse \( c = 10 \) ft. Use Pythagorean theorem \( a^2 + b^2 = c^2 \), so \( h^2 + 6^2 = 10^2 \).

Step2: Solve for \( h \)

\( h^2 = 10^2 - 6^2 = 100 - 36 = 64 \), then \( h = \sqrt{64} = 8 \)? Wait, no, wait: \( 10^2 - 6^2 = 100 - 36 = 64 \), so \( h = \sqrt{64} = 8 \)? But wait, the options have 8 as D? Wait, no, wait, maybe I miscalculated. Wait, \( 10^2 - 6^2 = 100 - 36 = 64 \), so \( h = 8 \). Wait, but the options: D is 8 feet. Wait, but let me check again. Wait, the ladder is 10 ft, base 6 ft, so height is \( \sqrt{10^2 - 6^2} = \sqrt{64} = 8 \). So the answer is D? Wait, but the options are A)3, B)6.7, C)7.4, D)8. So D.
Wait, maybe I made a mistake. Wait, no, Pythagorean theorem: \( a^2 + b^2 = c^2 \), so \( h^2 + 6^2 = 10^2 \), so \( h^2 = 100 - 36 = 64 \), so \( h = 8 \). So answer is D.

Step1: Apply Pythagorean theorem

Let height be \( h \), \( h^2 + 6^2 = 10^2 \).

Step2: Solve for \( h \)

\( h^2 = 100 - 36 = 64 \), \( h = \sqrt{64} = 8 \).

Answer:

A) 24

Question 5