Your favorite breakfast cereal contains a fidget toy in each box. There are three different fidget toys in the complete collection (spinner, pop strip, squishy ball) and each toy has an equal chance of being in each box.
You want to figure out what the probability is that you will get more than one squishy ball if you buy four boxes of the cereal. Which experiment could be used to simulate this situation?
Responses
A You flip a coin 4 times and record the number of times you get tails. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more tails.
B You put 10 each of 4 different colored marbles in a bag for a total of 40 marbles. You draw 3 marbles out without replacing them and record how many are red. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more red marbles.
C You have a spinner equally divided into 3 sections, with each section colored red, blue, or green. You spin the spinner 4 times and record how many times you get a red. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more red spins.
D You draw 4 cards from a standard deck of cards and record how many hearts you get. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more hearts.
C You have a spinner equally divided into 3 sections, with each section colored red, blue, or green. You spin the spinner 4 times and record how many times you get a red. You do 10 trials of the experiment, then calculate the percentage of trials that resulted in 2 or more red spins.
This experiment simulates the situation of buying four boxes of the cereal that each contain a fidget toy with equal probability of being one of three different types. In this case, we are interested in finding the probability of getting more than one squishy ball, which is similar to the scenario of getting more than one red spin from the spinner.
Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.
The distance from their home to Yellowstone National Park is 1,701 miles.
On average the RV gets 10.5 miles per gallon.
On average the cost of a gallon of gasoline is $3.60.
Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?
Responses
A $583.20$583.20
B $2,480.63$2,480.63
C $1,166.40$1,166.40
D $64,297.80
C $1,166.40
To find the total cost of gas for the round trip, we first calculate the total gallons of gas needed for the trip.
Total miles for the round trip = 2 * 1,701 = 3,402 miles
Total gallons of gas needed = Total miles / Average gas mileage = 3,402 / 10.5 = 324 gallons
Cost of gas for the round trip = Total gallons * Cost per gallon = 324 * $3.60 = $1,166.40
Therefore, Clinton and Stacy will spend $1,166.40 on gasoline for the round trip to Yellowstone National Park and back home.
Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
Responses
A purchase price: $117, advertised price: $293purchase price: $117, advertised price: $293
B purchase price: $120, advertised price: $300purchase price: $120, advertised price: $300
C purchase price: $130, advertised price: $325purchase price: $130, advertised price: $325
D purchase price: $108, advertised price: $270
D purchase price: $108, advertised price: $270
To find the purchase price, we know that the dresser was sold for 250% of the purchase price. So, if the sale price was $255, the purchase price can be found by dividing $255 by 250% (or 2.5).
Purchase price = $255 / 2.5 = $102.
The advertised price was 15% higher than the sale price, so the advertised price can be found by adding 15% of the sale price to the sale price.
Advertised price = $255 + 0.15 * $255 = $255 + $38.25 = $293.25.
Since we're looking for the nearest whole dollar, the purchase price is $108 and the advertised price is $270. So, the correct answer would be purchase price: $108, advertised price: $270 (Closest option is $108 and $270).
Briona mixed up 3 1/2 pounds of homemade hot chocolate powder to give as gifts. She is going to put the hot chocolate powder in 3/4-pound bags.
How many 3/4-pound bags will Briona have?
bags
To find the number of 3/4-pound bags Briona will have, you can divide the total amount of hot chocolate powder by the amount each bag can hold.
3 1/2 pounds is the same as 7/2 pounds.
Number of bags = (7/2) / (3/4)
Number of bags = (7/2) * (4/3)
Number of bags = 28 / 6
Number of bags = 4 2/3 or 4.67 bags
Therefore, Briona will have 4 2/3 (or 4.67) bags. However, since she cannot have a fraction of a bag, she will have to round down to the nearest whole number. Briona will have 4 bags.
Which expression is equivalent to 3.2 (x-2)+7.2(x-1)
?
Responses
A
negative 4 x plus 0 point 8
B
10 point 4 x minus 13 point 6
C
negative 4 x minus 13 point 6
D
The given expression is 3.2(x-2) + 7.2(x-1).
To simplify, distribute the terms inside the parentheses:
= 3.2x - 6 + 7.2x - 7.2
Combine like terms:
= (3.2x + 7.2x) + (-6 - 7.2)
= 10.4x - 13.2
So, the simplified expression is 10.4x - 13.2, which corresponds to answer choice B:
B. 10.4x - 13.2
The sum of a number, w, and 9 is multiplied by -3, and the result is -15.
What is the number?
Responses
A
w is equal to negative 14
B
w is equal to negative 4
C
w is equal to 4
D