Question

1. the sail below is in the shape of a triangle. is the sail a right triangle?

(image of a triangle with legs 15 ft, 36 ft and hypotenuse 39 ft)
a. yes, because (15^2 + 36^2 = 39^2)
b. no, because (15 + 36
eq 39)
c. yes, because (15 + 36 > 39)
d. no, because there is no right angle symbol in the triangle.

1. the scatter plot shows the population of bacteria in a controlled environment over time.

(scatter plot with x-axis time (weeks) and y-axis population)
what type of relationship does the scatter plot show?
a. positive correlation with linear association
b. positive correlation with nonlinear association
c. negative correlation with linear association
d. negative correlation with nonlinear association

Explanation:

Question 9

Step1: Recall Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is hypotenuse.

Step2: Calculate \( 15^2 \), \( 36^2 \), \( 39^2 \)

\( 15^2 = 225 \), \( 36^2 = 1296 \), \( 39^2 = 1521 \).

Step3: Check \( 15^2 + 36^2 \)

\( 225 + 1296 = 1521 = 39^2 \). So it's a right triangle.

Question 10

• As time (x - axis) increases, population (y - axis) increases, so it's positive correlation.
• The points do not lie close to a straight line; the trend is curved (nonlinear), so it's nonlinear association.

Answer:

A. Yes, because \( 15^2 + 36^2 = 39^2 \)