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enot [183]
3 years ago
12

A punch recipe calls for 26 liters of lemon lime soda and 14 gallons of

Mathematics
1 answer:
Darina [25.2K]3 years ago
6 0
13 liters of lemon lime soda.
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On any given day, mail gets delivered by either Alice or Bob. If Alice delivers it, which happens with probability 1/4 , she doe
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Answer:

(a) The value of fₓ (9.5) is 0.125.

(b) The value of fₓ (10.5) is 0.50.

Step-by-step explanation:

Let <em>X</em> denote delivery time of the mail delivered by Alice and <em>Y</em> denote delivery time of the mail delivered by Bob.

It i provided that:

X\sim U(9, 11)\\Y\sim U(10, 12)

The probability that Alice delivers the mail is, <em>p</em> = 1/4.

The probability that Bob delivers the mail is, <em>q</em> = 3/4.

The probability density function of a Uniform distribution with parameters [<em>a</em>, <em>b</em>] is:

f(x)=\left \{ {{\frac{1}{b-a};\ a, b>0} \atop {0;\ otherwise}} \right.

The probability density function of the delivery time of Alice is:

f(X_{A})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[9, 11]} \atop {0;\ otherwise}} \right.

The probability density function of the delivery time of Bob is:

f(X_{B})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[10, 12]} \atop {0;\ otherwise}} \right.

(a)

Compute the value of fₓ (9.5) as follows:

For delivery time 9.5, only Alice can do the delivery because Bob delivers the mail in the time interval 10 to 12.

The value of fₓ (9.5) is:

f_{X}(9.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times0)\\=\frac{1}{8}\\=0.125

Thus, the value of fₓ (9.5) is 0.125.

(b)

Compute the value of fₓ (10.5) as follows:

For delivery time 10.5, both Alice and Bob can do the delivery because Alice's delivery time is in the interval 9 to 11 and that of Bob's is in the time interval 10 to 12.

The value of fₓ (10.5) is:

f_{X}(10.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times\frac{1}{2})\\=\frac{1}{8}+\frac{3}{8}\\=0.50

Thus, the value of fₓ (10.5) is 0.50.

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Find the slope given: (3, -10) &amp; (4, -21)<br> m =
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Answer:

\displaystyle m=-11

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

Point (3, -10)

Point (4, -21)

<u>Step 2: Find slope </u><em><u>m</u></em>

Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>

  1. Substitute in points [Slope Formula]:                                                             \displaystyle m=\frac{-21+10}{4-3}
  2. [Fraction] Add/Subtract:                                                                                 \displaystyle m=\frac{-11}{1}
  3. [Fraction] Divide:                                                                                             \displaystyle m=-11
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The answer to number 7 is 7.5

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