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The ratio of the number of cups of blue paint to the number of cups of red paint that Lara mixed to make a shade of purple paint

Yuliya22 [10]

Answer:

Part A

The number of cups of blue paint that Lara mixed with each cup of red paint is 3 cups of blue paint

Part B

1/3 cup of red paint is added to 1 cup of blue paint

Part C

The unit price per cup of blue paint is $8 per cup of blue paint

Step-by-step explanation:

The ratio of the number of cups of blue paint to the number of cups of red paint that Lara mixed to make a shade of purple paint is 3: 1

Part A: Write a sentence to describe the number of cups of blue paint that Lara mixed with each cup of red paint (4 points)

The ratio is

Blue paint : Red paint

= 3 : 1

Hence,

The number of cups of blue paint that Lara mixed with each cup of red paint is 3 cups of blue paint

Part B: How many cups of red paint should Lara add to each cup of blue paint to make the shade of purple? Explain your reasoning (4 points)

From Part A , we know that

3 cups of blue paint = 1 cup of red paint

1 cup of blue paint = y

Cross Multiply

3 × y = 1 × 1

y = 1/3

Hence, 1/3 cup of red paint is added to 1 cup of blue paint

Part C: I Lara purchased 6 cups of blue paint for $48, what is the unit price per cup of blue paint? (2 points)

6 cups of blue paint = $48

1 cup of blue paint = x

6 × x = $48 × 1

x = $48/6

x = $8

6 0

4 years ago

n a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of inches and a stand

kotykmax [81]

Answer:

(a) The probability that a study participant has a height that is less than 67 inches is 0.4013.

(b) The probability that a study participant has a height that is between 67 and 71 inches is 0.5586.

(c) The probability that a study participant has a height that is more than 71 inches is 0.0401.

(d) The event in part (c) is an unusual event.

Step-by-step explanation:

The complete question is: In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 71 inches. The probability that the study participant selected at random is between and inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

We are given that the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.

Let X = the heights of men in the 20-29 age group

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean height = 67.5 inches

$\sigma$ = standard deviation = 2 inches

So, X ~ Normal( $\mu=67.5, \sigma^{2}=2^{2}$ )

(a) The probability that a study participant has a height that is less than 67 inches is given by = P(X < 67 inches)

P(X < 67 inches) = P( $\frac{X-\mu}{\sigma}$ < $\frac{67-67.5}{2}$ ) = P(Z < -0.25) = 1 - P(Z $\leq$ 0.25)

= 1 - 0.5987 = 0.4013

The above probability is calculated by looking at the value of x = 0.25 in the z table which has an area of 0.5987.

(b) The probability that a study participant has a height that is between 67 and 71 inches is given by = P(67 inches < X < 71 inches)

P(67 inches < X < 71 inches) = P(X < 71 inches) - P(X $\leq$ 67 inches)

P(X < 71 inches) = P( $\frac{X-\mu}{\sigma}$ < $\frac{71-67.5}{2}$ ) = P(Z < 1.75) = 0.9599

P(X $\leq$ 67 inches) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{67-67.5}{2}$ ) = P(Z $\leq$ -0.25) = 1 - P(Z < 0.25)

= 1 - 0.5987 = 0.4013

The above probability is calculated by looking at the value of x = 1.75 and x = 0.25 in the z table which has an area of 0.9599 and 0.5987 respectively.

Therefore, P(67 inches < X < 71 inches) = 0.9599 - 0.4013 = 0.5586.

(c) The probability that a study participant has a height that is more than 71 inches is given by = P(X > 71 inches)

P(X > 71 inches) = P( $\frac{X-\mu}{\sigma}$ > $\frac{71-67.5}{2}$ ) = P(Z > 1.75) = 1 - P(Z $\leq$ 1.75)

= 1 - 0.9599 = 0.0401

The above probability is calculated by looking at the value of x = 1.75 in the z table which has an area of 0.9599.

(d) The event in part (c) is an unusual event because the probability that a study participant has a height that is more than 71 inches is less than 0.05.

7 0

3 years ago

What is the common ratio of the geometric sequence below?

Lilit [14]

Answer:

The correct answer is A -3.

Step-by-step explanation:

18/(-3)=-6

To get to -6 from 18 you need to divide by -3.

To get to 2 from -6 you will divide by -3.

5 0

3 years ago

What is 352,914 rounded to the nearest hundred thousand?

Orlov [11]

Answer:

40,000

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Toya's dachshund puppy can sprint at a speed up to 15 feet per second. What is this speed in inches per

Andrei [34K]

It would be 180 inches per second

reason: there are 12 inches in a foot so you multiply 12 times 15 and get 180:)

8 0

3 years ago