Question

a grove has 6 rows of birch trees and 5 rows of maple trees. each row of birch trees has 8 trees 20 feet or taller and 6 trees shorter than 20 feet. each row of maple trees has 9 trees 20 feet or taller and 7 trees shorter than 20 feet. a tree from one of these rows will be selected at random. what is the probability of selecting a maple tree, given that the tree is 20 feet or taller?
a) 9/164
b) 3/10
c) 15/21
d) 9/17
question 8
each year, the value of an investment increases by 0.49% of its value the previous year. which of the following functions best models how the value of the investment changes over time?
a) decreasing exponential
b) decreasing linear
c) increasing exponential
d) increasing linear

Explanation:

Question 1

Step1: Calculate total tall birch trees

Number of birch - tree rows is 6, and each row has 8 trees 20 feet or taller. So total tall birch trees = 6×8 = 48.

Step2: Calculate total tall maple trees

Number of maple - tree rows is 5, and each row has 9 trees 20 feet or taller. So total tall maple trees = 5×9 = 45.

Step3: Calculate total tall trees

Total tall trees = total tall birch trees+total tall maple trees = 48 + 45=93.

Step4: Calculate the conditional probability

The probability of selecting a maple tree given that the tree is 20 feet or taller is $\frac{\text{total tall maple trees}}{\text{total tall trees}}=\frac{45}{93}=\frac{15}{31}$.

The general form of an exponential growth function is $y = a(1 + r)^t$, where $a$ is the initial amount, $r$ is the growth rate as a decimal, and $t$ is the time. Here, the value of the investment increases by 0.49% or 0.0049 each year. So the function representing the value of the investment over time is of the form $y=a(1 + 0.0049)^t$, which is an increasing exponential function.

Answer:

C. $\frac{15}{31}$

Question 2