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2 years ago

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In one month, Claudia rides her favorite bike trail 12 times. She travels a total distance of 1,182 km. What is the length of Cl

audia's favorite bike trail? Enter your answer as a simplified MIXED NUMBER in the box.

1 answer:

Svetlanka [38]2 years ago

7 0

98 $98 \frac{1}{2}$

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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.

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

Step-by-step explanation:

The random variable <em>X</em> and <em>Y</em> are defined as follows:

<em>X</em> = amount of ice cream in the box

<em>Y</em> = 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:

<em>X</em> + 3<em>Y</em>.

Compute the expected value of (<em>X</em> + 3<em>Y</em>) as follows:

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

Compute the variance of (<em>X</em> + 3<em>Y</em>) 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 (<em>X</em> + 3<em>Y</em>) 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:

<em>X</em> - <em>Y</em>.

Compute the expected value of (<em>X</em> - <em>Y</em>) as follows:

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

Compute the variance of (<em>X</em> - <em>Y</em>) as follows:

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

Then the standard deviation of (<em>X</em> - <em>Y</em>) 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.

7 0

2 years ago

Which number has a value between -8.423 and -8.395?

pav-90 [236]

Answer:

Step-by-step explanation:

Jmeu eimejrimr

5 0

2 years ago

The accompanying data are lengths (inches) of bears. Find the percentile corresponding to 65.5 in.

Jlenok [28]

Complete question is missing, so i have attached it.

Answer:

Percentile is 74th percentile

Step-by-step explanation:

All the lengths given are;

Bear Lengths 36.5 37.5 39.5 40.5 41.5 42.5 43.0 46.0 46.5 46.5 48.5 48.5 48.5 49.5 51.5 52.5 53.0 53.0 54.5 56.8 57.5 58.5 58.5 58.5 59.0 60.5 60.5 61.0 61.0 61.5 62.0 62.5 63.5 63.5 63.5 64.0 64.0 64.5 64.5 65.5 66.5 67.0 67.5 69.0 69.5 70.5 72.0 72.5 72.5 72.5 72.5 73.0 76.0 77.5

The number of lengths (inches) of bears given are 54 in number.

We are looking for the percentile corresponding to 65.5 in.

Looking at the lengths given, since they are already arranged from smallest to highest, let's locate the position of 65.5 in.

The position of 65.5 in is the 40th among 54 lengths given.

If the percentile is P, then;

P% x 54 = 40

P = (40 × 100)/54

P ≈ 74

3 0

2 years ago

Approximate the area under the curve y = x² from x = 2 to x = 5 using a Right Endpoint approximation with 6 subdivisions.

Tanzania [10]

Answer:

$\text{Area}\,=36.75$

Step-by-step explanation:

Using right estimation point simply means to form a bunch of rectangles between the two limits, x =2 and x = 5. and add the areas of all those rectangles.

There must be 6 subdivisions between 2 and 5. so, to do that:

$\Delta{x}=\dfrac{5-2}{6}=0.5$

the length of each subdivision is 0.5 units. That also means that the 6 rectangles in between the limits will each have the base length of 0.5 units.

So the endpoints of each subdivision from 3 to 5 will be:

$\begin{tabular}{|c|c|c|c|c|}3&3.5&4&4.5&5\\\end{tabular}$

By <em>right </em>endpoint approx<em>, </em>we mean that the height of the rectangles will be determined by the right endpoint of each subdivision, that is, it must be equal to the function value of the first limit.

$\begin{tabular}{|c|c|c|}subdivision&$x$&height($y=x^2$)&3 to 3.5&3.5&12.25&3.5 to 4&4&16&4 to 4.5&4.5&20.25&4.5 to 5&5&25\end$

Note that we have used the right-end-point of the subdivision to determine the height the rectangles.

All that's left to do now is to simply calculate the areas of the each of the rectangles. And add them up.

the base of each of the rectangle is $\Delta{x}=0.5$

and the height is determined in the table above.

$\text{Area}\,=(0.5\times12.25)+(0.5\times16)+(0.5\times20.25)+(0.5\times25)$

$\text{Area}\,=0.5(12.25+16+20.25+25)$

$\text{Area}\,=36.75$

3 0

2 years ago

Lisa the numbers least to greatest -2/5 -2.47 -2 1/2 5 21/4

Paraphin [41]

Answer:

least to greatest are:

-2.5, -2.47, -2/5, 5, 21/4

3 0

2 years ago