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2 years ago

2. The seniors at our high school decided to play a prank on the principal by completely filling his office with

Mathematics

2 answers:

Kobotan [32]2 years ago

7 0

Answer:

C. 12,600

Step-by-step explanation:

You can try a rough approximation by finding the volume of the room, finding the volume of one basketball, an dividing the first volume by the second one. This method will give a large estimate since there will be empty space between the balls.

volume of room:

V = L * W * H = 15 * 20 * 10 ft^3 = 3,000 ft^3

volume of one ball:

circumference = 29 in.

From the circumference we find the radius.

circumference = 2(pi)r

2(pi)r = 29 in.

r = (29 in.)/(2pi) = 4.61549 in.

Now we convert inches to feet.

4.61549 in. = 4.61549/12 ft = 0.384624 ft

Now we use the radius of a ball in ft to find the volume of a ball in cubic feet.

V = (4/3)(pi)r^3 = (4/3)(3.14159)(0.384624 ft)^3 = 0.23834 ft^3

Now we divide the volume of the room by the volume of a ball.

number of balls = (3,000 ft^3)/(0.23834 ft^3) = 12,587

The closest answer is C. 12,600

melisa1 [442]2 years ago

3 0

Answer:

idk

Step-by-step explanation:

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1 year ago

At a gas station, suppose that 45% of the customers purchase premium grade gas. Assume that these customers decide independently

valkas [14]

Answer:

The answer to the question is

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The probability that a customer would purchase premium grade = 45 %

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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.

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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