The 4th root of x raised to the 9th power is equivalent to the square root of 8 cubed. What is the value of x?

A petting zoo has a combined total of 16 frogs and chickens with a total of 42 legs. What is the difference between the number of frogs and the number of chickens?

For every 5.75 liters of green paint, a project requires 2.25 liters of black paint and 3.5 liters of orange paint. If Jasmine finished a project that required 22.25 liters of green paint, how many total liters of paint did she use? (Round all intermediate values and the final answer to the nearest hundredth.)

44.50 liters

1212Set up ratios between the green paint volume and the other color volumes:

and

Using these ratios, proportionalities can be set up that enable the unknown liters of black and orange paint to be found.
; solving for the unknown amount gives 8.7 liters of black paint.
Setting up the proportion for orange: ; solving for the unknown amount gives 13.5 liters of orange paint.
Combining each of the amounts used gives: 22.25 + 8.7 + 13.5 = 44.45 liters of paint.

From a pack of 52 cards which includes 4 kings, 4 queens, and 4 jacks. A king, a jack, a queen, and another queen are pulled without replacement. What is the probability of not selecting a queen on the next pull?

0.9583

1212Calculate the probability of selecting a queen from a deck that is missing a king, a jack, and two queens. Because 4 cards have been removed from the deck, and now there are only 2 queens remaining, the probability of selecting a queen is the ratio of the number of queens remaining, 2, to the total number of cards remaining, 48, or . However, the question wants the probability of NOT selecting a queen on the next draw. Recall that the probability of selecting a queen and the probability of not selecting a queen must sum to 1: . Rearrange to solve for :

1212Sally lives in Antarctica. In the afternoon she measures the temperature to be -4 Celsius degree. Eight hours later she measures the temperature to be . Three hours later she measures again and finds it to be . The following morning she measures one last time and finds the temperature to be .
What is the absolute value of the difference between the lowest and highest measured temperatures?

1212

1212The highest measured temperature is . The lowest measured temperature is .
The difference between the lowest and highest temperature is -23 - (-2), and the absolute value of the difference between the lowest and highest temperature is .

Based on the scatterplot, which of these statements must be true?

1212Which of these is equivalent to

1212

1212Apply the rules of exponents to simplify the expression. After multiplying exponents, the given expression becomes: , which becomes , which becomes

Which of the following correctly describes the relationship between the two linear equations: 3y - 2x + 2 = 13x - 19 and x + 5y = 10

perpendicular

1212Rewrite each equation in slope-intercept form and compare their slopes: 3y - 2x + 2 = 13x - 19, adding 2x - 2 to both sides 3y = 15x - 21, dividing by 3 y = 5x - 7 And: x + 5y = 10, subtracting x from both sides 5y = -x + 10, dividing by 5 The slopes are negative reciprocals of each other; the lines are perpendicular to each other.

Joanne is having a pizza party. Each medium pizza costs 8.99 and each large pizza costs 12.99. She does not wish for the total cost to exceed 300, and she wants to order at least 30 total pizzas. If M represents the number of medium pizzas and L represents the number of large pizzas, which of the following systems of inequalities accurately represents her situation?

A circle's area of 280 meters is reduced by 60%. What is the ratio of the reduced radius to the original radius?

0.63

1212When the original area is reduced by 60%, only 40% remains. Find the reduced area by multiplying the original area by 40%: 280 \u00D7 0.4 = 112. Solve for the radius of the original circle: , so . Solve for the radius of the reduced circle: , so . When evaluating the ratio of the reduced radius to the original radius, the π in both denominators will cancel to leave .

Rick scored 85, 88, 62, and 79 on his previous exams. What is the minimum score he must earn on his next exam to have an overall average of at least 80?

86

1212The average of a set of numbers is the sum of the numbers in the set divided by the number of numbers in the set. Use x to represent the last test, and set up the inequality for the average. An inequality is necessary because the question asks for the smallest number that will yield an average larger than 80, not greater than or equal to 80: which becomes 85 + 88 + 62 + 79 + x \u2265 400 or 314 + x \u2265 400, or x \u2265 86

A toy company wishes to earn more than 22,205 dollars in profits for the month. If it is guaranteed to earn 45 dollars, but also earns 8.50 dollars per unit sold, what is the minimum number of units the company must sell in order to meet its goal? (Units can only be sold as whole numbers.)