Set of mathematics questions.

Steps to Solve

Question 6

1. Find the area of the square The area of a square is given by the formula $Area = side \times side = x^2$. Since $x$ is an integer, $x^2$ is a perfect square.

Question 7

1. List all possible pairs of coins Jerry can pick two coins from the following: 3 nickels (N), 1 dime (D), and 1 penny (P). The possible pairs are:

   • N + N = 5 + 5 = 10 cents
   • N + D = 5 + 10 = 15 cents
   • N + P = 5 + 1 = 6 cents
   • D + P = 10 + 1 = 11 cents We have 3 nickels, so the number of ways to pick two nickels is $\binom{3}{2} = 3$. The number of ways to pick a nickel and a dime is $3 \times 1 = 3$. The number of ways to pick a nickel and a penny is $3 \times 1 = 3$. The number of ways to pick a dime and a penny is $1 \times 1 = 1$.

2. Determine the least likely event The possibilities and their likelihoods are:

   • 6 cents (N + P): 3 ways
   • 10 cents (N + N): 3 ways
   • 11 cents (D + P): 1 way
   • 15 cents (N + D): 3 ways Since there is only 1 way to get 11 cents, it is the least likely event.

Question 8

1. Analyze the graph The graph is a parabola that opens upwards, with a vertex at $(-2, 0)$. This suggests a quadratic equation of the form $y = a(x + 2)^2$, where $a$ is a constant. Since the coefficient $a$ is equal to $1$, because the parabola opens upward and we have the vertex at $(-2,0)$, one unit to the right, we go up one unit as well, the equation would be $y = (x + 2)^2$.

Question 9

1. Analyze the data for men Looking at the "Men" column in the data table, the preferences for each package are:
   • Package 1: 25
   • Package 2: 24
   • Package 3: 25
   • Package 4: 26 The numbers are very close to each other. This suggests there is no strong preference among men, and the packaging probably won't influence sales.

Question 10

1. Evaluate the numbers We need to determine which of the listed numbers is a whole number. A whole number is a non-negative integer (0, 1, 2, 3,...). $\sqrt{64} = 8$, which is a whole number. $\sqrt{\pi} \approx \sqrt{3.14} \approx 1.77$, which is not a whole number. $\sqrt{1/4} = 1/2 = 0.5$, which is not a whole number. $\sqrt{6.25} = 2.5$, which is not a whole number.