The cost of 9 scarves is $65.25. What is the unit price? The unit price is $___

Ice cream usually comes in 1.5-quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v

Troyanec [42]

Answer:

(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c) Because the variance of each variable is dependent on the other.

Step-by-step explanation:

The random variable X and Y are defined as follows:

X = amount of ice cream in the box

Y = amount of ice cream scooped out

The information provided is:

E (X) = 48

SD (X) = 1

V (X) = 1

E (Y) = 2

SD (Y) = 0.25

V (Y) = 0.0625

(a)

The total amount of ice-cream served at the party can be expressed as:

X + 3Y.

Compute the expected value of (X + 3Y) as follows:

$E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54$

Compute the variance of (X + 3Y) as follows:

$V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625$

Then the standard deviation of (X + 3Y) is:

$SD(X + 3Y) =\sqrt{V(X + 3Y)}\\\sqrt{1.5625}\\=1.25$

Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

X - Y.

Compute the expected value of (X - Y) as follows:

$E(X-Y)=E(X)-E(Y)\\=48-2\\=46$

Compute the variance of (X - Y) as follows:

$V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625$

Then the standard deviation of (X - Y) is:

$SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031$

Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

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A carpenter has 10 1/2 feet of wooden plank. He cuts off 4 1/4 feet to replace the slat of a deck and 3 2/3 to repair a Banniste

aalyn [17]

10 1/2-4 1/4= 6 1/4. 6 1/4-3 2/3= 2 7/12. They used 2 7/12 ft or 2ft 7in of wood to fix the stairs.

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1 year ago

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Here is a scale drawing of a window frame that uses a scale of 1 cm to 6 inches.Create another scale drawing of the window frame

Tresset [83]

Answer:

Step-by-step explanation:

Below is the rectangle in the attachment.

Current scale:

1 cm : 6 inches

If the dimensions of the rectangle is:

Length = a cm

Width = b cm

Using the scale:

Length = a × 6 inches

Width = b × 6 inches

Using the same dimensions of the rectangle is:

Length = a cm

Width = b cm

Using the scale:

Length = a × 12 inches

Width = b × 12 inches

Note that there is an enlargement of the rectangle to form the new rectangle. The length and width of new rectangle drawn will be 2 × the length and width of the rectangle seen below.

8 0

1 year ago

Suppose x follows a continuous uniform distribution from 1 to 5. determine the conditional probability p(x >2.5 | x ≤ 4).

Rainbow [258]

Because the random variable x follows a continuous uniform distribution from x=1 to x=5, therefore
p(x) = 1/4, x=[1, 5]
The value of p(x) ensures that the total area under the curve = 1.

The conditional probability p(x > 2.5 | x ≤ 4) is the shaded portion of the curve. Its value is
p(x > 2.5 | x ≤4) = (1/4)*(4 - 2.5) = 0.375

Answer: 0.375

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1 year ago

garrett has one dollar less than three times as much money as liz has. Together they have $179. How much money does Garett have?

jolli1 [7]

Garett has $134 and Liz has $45

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The cost of 9 scarves is $65.25. What is the unit price? The unit price is $____ per scarf.