An organization will give a prize to a local artist. The artist will be randomly chosen from among 7 painters, 4 sculptors, and 5 photographers. What is the probability that the artist chosen will be a painter or a photographer?
Write your answer as a fraction in simplest form.
Question 16
An organization will give a prize to a local artist. The artist will be randomly chosen from among 3 painters, 7 sculptors, and 12 photographers. What is the probability that the artist chosen will be a painter or a sculptor? Write your number as a fraction in simplest form.
12/16=3/4
0.75
An organization will give a prize to a local artist. The artist will be randomly chosen from among 7 painters, 4 sculptors, and 5 photographers. What is the probability that the artist chosen will be a painter or a photographer?
Write your answer as a fraction in simplest form.
total number of artist=7+5+4=16
probability of selecting a painter or. photographer=7/16+5/16=12/16=3/4
A spinner with 6 equally sized slices has 2 red slices, 1 blue slice, and 3 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red or blue slice?
Write your answer as a fraction in simplest form.
There are 2 red slices and 1 blue slice, so the total number of favorable outcomes is 2 + 1 = 3.
The total number of possible outcomes is 6 (since there are 6 slices in total).
Therefore, the probability of the dial stopping on a red or blue slice is 3/6, which simplifies to 1/2.
A twelve-sided die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled.
What is the probability of rolling a number less than 12 ?
Write your answer as a fraction in simplest form.
Since there are 12 sides on the die and each number is equally likely to be rolled, the probability of rolling any single number is 1/12.
The probability of rolling a number less than 12 (i.e., rolling any number from 1 through 11) is the sum of the probabilities of rolling each of these 11 numbers, which is:
P(rolling a number less than 12) = P(rolling 1) + P(rolling 2) + ... + P(rolling 11)
P(rolling a number less than 12) = 1/12 + 1/12 + ... + 1/12 (11 times)
P(rolling a number less than 12) = 11/12
Therefore, the probability of rolling a number less than 12 is 11/12.
Lamar borrowed money from a credit union for 5 years and was charged simple interest at an annual rate of 9% . The total interest that he paid was $3600 . How much money did he borrow?
If necessary, refer to the list of financial formulas.
We can use the simple interest formula to solve for the principal amount (the amount Lamar borrowed):
I = Prt
where I is the amount of interest, P is the principal, r is the annual interest rate (as a decimal), and t is the time in years.
We are given that Lamar borrowed money for 5 years and was charged simple interest at an annual rate of 9%, and that the total interest he paid was $3600. Therefore:
$3600 = P(0.09)(5)
Simplifying:
$3600 = 0.45P
Dividing both sides by 0.45:
P = $8000
Therefore, Lamar borrowed $8000.
In a recent year, 34% of all college students were enrolled part-time. If 3.1 million college students were enrolled part-time that year, what was the total number of college students?
Round your answer to the nearest million.
Let's let T be the total number of college students. We know that 34% (or 0.34 as a decimal) of all college students were enrolled part-time, and we know that there were 3.1 million part-time students. We can set up a proportion to solve for T:
0.34 = 3.1 million / T
Multiplying both sides by T, we get:
0.34T = 3.1 million
Dividing both sides by 0.34, we get:
T = 3.1 million / 0.34
T ≈ 9.1 million
Rounding to the nearest million, we get that the total number of college students was about 9 million.
The next model of a sports car will cost 5.9% more than the current model. The current model costs $46,000 . How much will the price increase in dollars? What will be the price of the next model?
Increase in price:
Price of next model:
To find the increase in price, we can start by calculating 5.9% of the current price:
0.059 × 46,000 = 2,714
So the price of the next model will increase by $2,714.
To find the price of the next model, we can add the increase to the current price:
46,000 + 2,714 = 48,714
So the price of the next model will be $48,714.
An item is regularly priced at $79. Josh bought it at a discount of 10% off the regular price.
To find the discount amount, we can start by calculating 10% of the regular price:
0.10 × $79 = $7.90
So the discount that Josh received is $7.90.
To find the sale price, we can subtract the discount from the regular price:
$79 - $7.90 = $71.10
So the sale price that Josh paid is $71.10.
An item on sale costs 95% of the original price. If the original price was $80, what is the sale price?
To find the sale price, we can start by calculating 95% of the original price:
0.95 × $80 = $76
So the sale price is $76.
The wholesale price for a bookcase is $175. A certain furniture store marks up the wholesale price by 39%. Find the price of the bookcase in the furniture store.
Round your answer to the nearest cent, as necessary.
To find the price of the bookcase in the furniture store, we can start by calculating the markup amount:
Markup = 39% × $175 = $68.25
The markup adds $68.25 to the wholesale price, so the retail price is:
$175 + $68.25 = $243.25
Rounding to the nearest cent, the price of the bookcase in the furniture store is $243.25.
A house has increased in value by 24% since it was purchased. If the current value is $403,000, what was the value when it was purchased?
Let's let x be the value of the house when it was purchased. We know that the value of the house has increased by 24%, or 0.24 as a decimal, to reach the current value of $403,000. We can set up an equation to solve for x:
x + 0.24x = $403,000
Simplifying and combining like terms:
1.24x = $403,000
Dividing both sides by 1.24:
x = $324,596.77 (rounded to the nearest cent)
Therefore, the value of the house when it was purchased was about $324,596.77.
This year, a small business had a total revenue of $40,300. If this is 35% less than their total revenue the previous year, what was their total revenue the previous year?
Let's let x be the total revenue of the small business the previous year. We know that the revenue decreased by 35%, or 0.35 as a decimal, to reach the current revenue of $40,300. We can set up an equation to solve for x:
x - 0.35x = $40,300
Simplifying and combining like terms:
0.65x = $40,300
Dividing both sides by 0.65:
x = $62,000
Therefore, the total revenue of the small business the previous year was $62,000.
Jenny wants to buy a new boat but needs money for the down payment. Her parents agree to lend her money at an annual rate of 6%, charged as simple interest. They lend her $4000 for 6 years. She makes no payments except the one at the end of that time.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Jenny have to pay?
(b) What will the total repayment amount be (including interest)?
(a) We can use the simple interest formula to calculate the amount of interest that Jenny will have to pay:
I = Prt
where I is the amount of interest, P is the principal (the amount that was borrowed), r is the annual interest rate (as a decimal), and t is the time in years.
We know that Jenny borrowed $4000 at an annual rate of 6% for 6 years. So:
I = ($4000)(0.06)(6) = $1440
Jenny will have to pay a total of $1440 in interest.
(b) The total repayment amount will be equal to the principal plus the interest:
Total repayment amount = principal + interest = $4000 + $1440 = $5440
Therefore, the total repayment amount (including interest) will be $5440.
A veterinarian estimated the weight of a puppy to be 7 kg . The actual weight of the puppy was 7.8 kg .
Find the absolute error and the percent error of the veterinarian's estimate. If necessary, round your answers to the nearest tenth.
absolute error =
percent error =
The absolute error is the absolute value of the difference between the veterinarian's estimate and the actual weight of the puppy:
|7.8 kg - 7 kg| = 0.8 kg
So the absolute error is 0.8 kg.
The percent error is the absolute error divided by the actual weight, multiplied by 100%:
(0.8 kg / 7.8 kg) x 100% ≈ 10.3%
So the percent error is approximately 10.3%.
To be able to take her dream vacation, Lucy decides to save for 2 years. She opens a savings account with $200 . The account pays simple interest at an annual rate of 5%. She doesn't make any more deposits.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Lucy earn?
(b) What will the total amount in the account be (including interest)?
(a) We can use the simple interest formula to calculate the amount of interest that Lucy will earn:
I = Prt
where I is the amount of interest, P is the principal (the starting balance), r is the annual interest rate (as a decimal), and t is the time in years.
We know that Lucy deposited $200 and will keep the money in the account for 2 years at an annual rate of 5%. So:
I = ($200)(0.05)(2) = $20
Lucy will earn a total of $20 in interest.
(b) The total amount in the account (including interest) will be equal to the starting balance plus the interest:
Total amount = starting balance + interest = $200 + $20 = $220
Therefore, the total amount in the account (including interest) will be $220.
The price of a notebook was $3.75 yesterday. Today, the price fell to $3.50 . Find the percentage decrease. Round your answer to the nearest tenth of a percent.
The original price (yesterday) was $3.75 and the new price (today) is $3.50. To find the percentage decrease, we can use the formula:
percentage decrease = [(original value - new value) / original value] x 100%
Plugging in the values we have:
percentage decrease = [($3.75 - $3.50) / $3.75] x 100%
percentage decrease = ($0.25 / $3.75) x 100%
percentage decrease = 0.0667 x 100%
percentage decrease ≈ 6.7%
Therefore, the percentage decrease is approximately 6.7%.
A veterinarian estimated the weight of a puppy to be 7 kg . The actual weight of the puppy was 7.8 kg.
Find the absolute error and the percent error of the veterinarian's estimate. If necessary, round your answers to the nearest tenth.
absolute error =
percent error =
The absolute error is the absolute value of the difference between the veterinarian's estimate and the actual weight of the puppy:
|7.8 kg - 7 kg| = 0.8 kg
So the absolute error is 0.8 kg.
The percent error is the absolute error divided by the actual weight, multiplied by 100%:
(0.8 kg / 7.8 kg) x 100% ≈ 10.3%
So the percent error is approximately 10.3%.
To be able to take her dream vacation, Lucy decides to save for 2 years. She opens a savings account with $200. The account pays simple interest at an annual rate of 5%. She doesn't make any more deposits.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Lucy earn?
(b) What will the total amount in the account be (including interest)?
(a) We can use the simple interest formula to calculate the amount of interest that Lucy will earn:
I = Prt
where I is the amount of interest, P is the principal (the starting balance), r is the annual interest rate (as a decimal), and t is the time in years.
We know that Lucy deposited $200 and will keep the money in the account for 2 years at an annual rate of 5%. So:
I = ($200)(0.05)(2) = $20
Lucy will earn a total of $20 in interest.
(b) The total amount in the account (including interest) will be equal to the starting balance plus the interest:
Total amount = starting balance + interest = $200 + $20 = $220
Therefore, the total amount in the account (including interest) will be $220.
Jenny wants to buy a new boat but needs money for the down payment. Her parents agree to lend her money at an annual rate of 6%, charged as simple interest. They lend her $4000 for 6 years. She makes no payments except the one at the end of that time.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Jenny have to pay?
(b) What will the total repayment amount be (including interest)?
(a) We can use the simple interest formula to calculate the amount of interest that Jenny will have to pay:
I = Prt
where I is the amount of interest, P is the principal (the amount that was borrowed), r is the annual interest rate (as a decimal), and t is the time in years.
We know that Jenny borrowed $4000 at an annual rate of 6% for 6 years. So:
I = ($4000)(0.06)(6) = $1440
Jenny will have to pay a total of $1440 in interest.
(b) The total repayment amount will be equal to the principal plus the interest:
Total repayment amount = principal + interest = $4000 + $1440 = $5440
Therefore, the total repayment amount (including interest) will be $5440.
If the retail price of a pizza at Tony’s Pizzeria is $14.00, how much is saved by purchasing the pizza when the discount is offered?
We need to know the amount of the discount to calculate how much is saved by purchasing the pizza when the discount is offered. If the discount is given as a percentage, we can calculate the discount amount as follows:
Discount amount = Discount rate × Original price
If we are given the discounted price, we can calculate the discount amount as follows:
Discount amount = Original price − Discounted price
If we are not given the discount amount or rate, we cannot determine the savings.
Assuming we know the discount rate or the discounted price, we can calculate the savings as follows:
Savings = Original price − Discounted price or Savings = Discount amount
1. a) If the retail price of a pizza at Tony’s Pizzeria is $14.00, how much is saved by purchasing the pizza when the discount is offered?
b) What is the discounted price?
We need to know the amount of the discount or the discount rate to calculate the savings and the discounted price.
Assuming we know the discount rate, we can calculate the savings and discounted price as follows:
a) If the discount rate is x%, the discount amount is:
Discount amount = x% × $14.00 = 0.01x × $14.00
The savings is the discount amount:
Savings = 0.01x × $14.00
b) The discounted price is the retail price minus the discount amount:
Discounted price = $14.00 − Discount amount
Discounted price = $14.00 − 0.01x × $14.00
Discounted price = $14.00(1 − 0.01x)
We cannot calculate specific values for the savings or discounted price without knowing the discount rate.