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3 years ago

2. Mr. Ellis runs an after-school program for nine- and ten-year-olds. Each day the children participate in an

Mathematics

1 answer:

MatroZZZ [7]3 years ago

5 0

Answer:

See explanation

Step-by-step explanation:

Factorize numbers 42 and 56:

$42=2\cdot 3\cdot 7\\ \\56=2\cdot 2\cdot 2\cdot 7$

These two numbers have common factors 2 and 7. So,

A. Mr. Ellis can divide the group into

1 team = 42 ten-year-olds and 56 nine-year-olds (actually this is not dividing only completing 1 team);
2 teams = 21 ten=year-olds and 28 nine-year-olds in each team;
7 teams = 6 ten-year-olds and 8 nine-year-olds in each team;
14 teams = 3 ten-year-olds and 4 nine-year-olds in each team.

So, there are 3 different ways to divide the group of students into teams.

B. The greatest number of teams Mr. Ellis can make so each team has the same number of 9-year-olds and the same number of 10-year-olds is 14 teams.

C. If Mr. Ellis gives a snack to each winner, then he is interested to give the smallest number of snacks, the smallest number of snacks will be when the number of students in the team is the smallest, the smallest number of students will be when the greatest number of teams are created.

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2 years ago

When dividing 592 by 9.25, how many zeros will be placed in the dividend?When dividing 592 by 9.25, how many zeros will be place

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2 years ago

On any given day, mail gets delivered by either Alice or Bob. If Alice delivers it, which happens with probability 1/4 , she doe

Troyanec [42]

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 X denote delivery time of the mail delivered by Alice and Y 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, p = 1/4.

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

The probability density function of a Uniform distribution with parameters [a, b] 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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3 years ago

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Phantasy [73]

3: terms/ 12, 8r, -3, s, -5, 15t coefficients/ 8r, 1s, 15t

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3 years ago