Ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles. What fraction of those who were cast got major roles? Write your answer as a decimal
One-third of the students who auditioned were cast, meaning that 1/3 * 90 = <<1/3*90=30>>30 students were cast.
Of those who were cast, 6 received major roles, so the fraction of those who were cast that got major roles is 6/30 = 1/5.
As a decimal, this fraction is equal to 1/5 = 0.2. Answer: \boxed{0.2}.
One-third of the campers at Rosewood Performing Arts Camp play an instrument, so if we let the total number of campers be represented by the fraction 1, then the fraction of campers that play an instrument is 1/3.
Of those campers that play an instrument, two-fifths play the guitar. Hence, we need to multiply 1/3 by 2/5 to find the fraction of campers that play the guitar.
(1/3) * (2/5) = (2/15).
Therefore, 2/15 of the campers at Rosewood Performing Arts Camp play the guitar. Answer: \boxed{\frac{2}{15}}.
Apologies for the confusion. Let's correct the solution.
If we let the length of the Beginner's Trail be 1 unit, then the Medium Trail is 1.2 times as long, or 1.2 units long.
And since the Advanced Trail is 3.6 times as long as the Medium Trail, it is 3.6 * 1.2 = 4.32 units long.
Therefore, the Advanced Trail is 4.32 times as long as the Beginner's Trail.
Written as a decimal, the answer is \boxed{4.32}.
To find out how much sugar Ms. Johnson used, we need to multiply the fraction of sugar used (1/2) by the total amount of sugar in the canister (7/8).
The expression for the amount of sugar used is: (1/2) * (7/8).
To multiply fractions, we multiply the numerators (top numbers) together to get the new numerator and the denominators (bottom numbers) to get the new denominator.
So, (1/2) * (7/8) = (1 * 7) / (2 * 8) = 7/16.
Therefore, Ms. Johnson used 7/16 of a cup of sugar. Answer: \boxed{\frac{7}{16}}.
At Point Pleasant Park, the Advanced Trail is 3.6 times as long as the Medium Trail, and the Medium Trail is 1.2 times as long as the Beginner's Trail. How many times as long as the Beginner’s Trail is the Advanced Trail? Write your answer as a decimal.
wrong
There are 7/8
cups of sugar in a canister in the kitchen. Ms. Johnson used 1/2
of the sugar when she was preparing dessert for her daughter's birthday cake. How much sugar did she use?
How much did Mr. Romanov pay for 9.3 gallons of gas at $3.30 a gallon?
To find out how much Mr. Romanov paid for the gas, we need to multiply the number of gallons purchased (9.3) by the price per gallon ($3.30).
The expression for the total cost of the gas is: 9.3 * $3.30.
To multiply decimals, we multiply the numbers as if they were whole numbers and then adjust the decimal point in the final answer.
So, 9.3 * $3.30 = $30.69 (rounded to the nearest cent).
Therefore, Mr. Romanov paid $30.69 for 9.3 gallons of gas. Answer: $30.69.
One-third of the campers at Rosewood Performing Arts Camp play an instrument. Two-fifths of those campers play the guitar. What fraction of the campers at Rosewood Performing Arts Camp play the guitar?
The altitude of an airplane is decreasing at a rate of 43 feet per second. What is the change in altitude of the airplane over a period of 31 seconds?
To find the change in altitude of the airplane over a period of 31 seconds, we need to multiply the rate of decrease (43 feet per second) by the duration (31 seconds).
The expression for the change in altitude is: 43 feet per second * 31 seconds.
To multiply, simply multiply the numbers together:
43 * 31 = 1333.
Therefore, the change in altitude of the airplane over a period of 31 seconds is 1333 feet. Answer: \boxed{1333 \text{ feet}}.
Use properties of rational numbers to multiply the following.
-8 × (-32)
To multiply two negative numbers, we can use the property that states that the product of two negative numbers is positive.
Therefore, -8 * (-32) is equal to the positive value of the product of 8 and 32, which is 8 * 32 = 256.
So, -8 * (-32) = 256.
Answer: \boxed{256}.
Multiply : 2 4/5 x -4/5
To multiply mixed numbers, we first need to convert them to improper fractions.
2 4/5 can be written as (5 * 2 + 4) / 5 = 14/5.
-4/5 remains the same.
Now, we can multiply the two fractions:
(14/5) * (-4/5).
When multiplying fractions, we multiply the numerators and the denominators separately:
(14 * -4) / (5 * 5).
This simplifies to:
-56/25.
Therefore, 2 4/5 multiplied by -4/5 is equal to -56/25.
Answer: \boxed{-\frac{56}{25}}.
-7/8 x -2/5
To multiply two fractions, we multiply the numerators together and multiply the denominators together.
Using this rule, we have (-7/8) * (-2/5) = (7 * 2) / (8 * 5) = 14/40.
The fraction 14/40 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
Dividing 14 by 2 yields 7, and dividing 40 by 2 yields 20.
Therefore, -7/8 multiplied by -2/5 equals 7/20.
Answer: \boxed{\frac{7}{20}}.
IS THAT RIGHT?
Apologies for the incorrect response. Let's correct the solution.
To multiply -7/8 by -2/5, we multiply the numerators and the denominators:
(-7/8) * (-2/5) = (7 * 2) / (8 * 5) = 14/40.
The fraction 14/40 is not in simplest form. We can simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 2.
Dividing 14 by 2 yields 7, and dividing 40 by 2 yields 20.
Therefore, -7/8 multiplied by -2/5 equals 7/20.
Answer: \boxed{\frac{7}{20}}. The previous response was correct.
-3.3 x (-2.6)
1 2/5 x 5/6
-3/7 x -3 1/9
-12 x (3.4) 3 x (-2 1/3)
solve all
Let's solve each of the given multiplications step by step:
1. -3.3 x (-2.6):
When multiplying two negative numbers, the product is positive. Therefore, -3.3 x (-2.6) = 3.3 x 2.6 = 8.58.
2. 1 2/5 x 5/6:
First, convert the mixed number to an improper fraction:
1 2/5 = (5 * 1 + 2) / 5 = 7/5.
Then, multiply the fractions:
(7/5) x (5/6) = (7 * 5) / (5 * 6) = 35/30.
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5:
35/30 = (7/5) * (1/6) = 7/6.
3. -3/7 x -3 1/9:
First, convert the mixed number to an improper fraction:
-3 1/9 = (9 * -3 - 1) / 9 = -28/9.
Then, multiply the fractions:
(-3/7) x (-28/9) = (3 * 28) / (7 * 9) = 84/63.
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 21:
84/63 = (4/3) * (1/3) = 4/9.
4. -12 x 3.4:
Multiply the numbers:
-12 x 3.4 = -40.8.
5. 3 x (-2 1/3):
Convert the mixed number to an improper fraction:
-2 1/3 = (3 * -2 - 1) / 3 = -7/3.
Multiply the numbers:
3 x (-7/3) = -21/3 = -7.
Final answers:
-3.3 x (-2.6) = 8.58
1 2/5 x 5/6 = 7/6
-3/7 x -3 1/9 = 4/9
-12 x (3.4) = -40.8
3 x (-2 1/3) = -7.
solve 6.15 x (-3.11)
To solve 6.15 x (-3.11), we multiply the two numbers:
6.15 x (-3.11) = -19.1165.
Therefore, 6.15 x (-3.11) equals approximately -19.1165.
Which expression represents another method of computing the product given below?'
6.15 x (-3.11)
ANSWERS;
(-1)(6.15 - 3.11)
(-1)(6.15 - 3.11)
(-1)(6.15 × (-3.11))
(-1)(6.15 × (-3.11))
(6 × (-3.11)) + (0.15 × (-3.11))
(6 × (-3.11)) + (0.15 × (-3.11))
(-1)(6.15 + 3.11)
The expression that represents another method of computing the product 6.15 x (-3.11) is:
(-1)(6.15 × (-3.11))
This expression involves multiplying the absolute values of the numbers (6.15 and 3.11) and then multiplying the product with -1 to account for the negative sign.
A number is multiplied by 70. The result is zero.
Which of these was multiplied by 70?(2 points)
Responses
a number less than zero
a number less than zero
zero
zero
a number greater than one
a number greater than one
a number between zero and one
The correct response is "zero".
When any number is multiplied by zero, the result is always zero.
Use properties of rational numbers to multiply the following.
81 × (-28.54)
(2 points)
a x b
To multiply 81 by -28.54, simply multiply the two numbers together:
81 × (-28.54) = -2307.74.
Therefore, 81 multiplied by -28.54 equals approximately -2307.74.
the correct answer is -2311.74
Apologies for the mistake. You're correct.
81 multiplied by -28.54 equals -2311.74.
Thank you for pointing out the error.
Mr. Anderson decides to visit a childhood friend. His car gives him 24.6 miles to the gallon. Mr. Anderson has 7 gallons of fuel. Which of the following is true?(2 points)
Mr. Anderson can travel 86.1 miles.
Mr. Anderson can travel 86.1 miles.
Mr. Anderson can travel 123.2 miles.
Mr. Anderson can travel 123.2 miles.
Mr. Anderson can travel 221.2 miles.
Mr. Anderson can travel 221.2 miles.
Mr. Anderson can travel 172.2 miles.
To calculate the total distance Mr. Anderson can travel, we need to multiply the number of gallons of fuel (7) by the car's fuel efficiency (24.6 miles per gallon).
The expression for the total distance is: 7 gallons * 24.6 miles per gallon = 172.2 miles.
Therefore, Mr. Anderson can travel 172.2 miles.
The statement "Mr. Anderson can travel 172.2 miles" is true.
Use properties of rational numbers to multiply the following.
-7/9 x 162
(2 points)
Responses
-148
-148
-208.29
-208.29
-126
-126
-3,773
To multiply -7/9 by 162, we multiply the numerators and the denominators:
(-7/9) * 162 = -7 * 162 / 9 = -1134/9.
The fraction -1134/9 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 9:
-1134/9 = -126.
Therefore, -7/9 multiplied by 162 equals -126.
The correct answer is: \boxed{-126}.
Let's assume the length of the Beginner's Trail is 1 unit.
Then, the Medium Trail is 1.2 units long (1 unit * 1.2).
And, the Advanced Trail is 3.6 units long (1.2 units * 3.6).
Therefore, the Advanced Trail is 3.6 times as long as the Beginner's Trail.
Converted to a decimal, the answer is \boxed{3.6}.