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Maru [420]
3 years ago
9

F(x)= -2x + 2; Find f(5)

Mathematics
1 answer:
adelina 88 [10]3 years ago
7 0
To find f(5),we put 5 into x

f(5) = -2(5) + 2
= -10+2
=-8

Thus,f(5) = -8

hope it helps!
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4. The cosine function can be made to have the same values as the sine function for each angle by including a shifted _______ in
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2 years ago
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

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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.

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Answer:

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