Determine f(x-1) f(x)=√x+6-8

1. (2 points) The starship Enterprise just picked up a strange creature called a tribble.

koban [17]

Answer:

21 tribbles on the 7th night

Step-by-step explanation:

every night 3 tribbles appear meaning that the tribbles spawn rate is y=3x

y= number of tribbles

x= number of nights

3 0

3 years ago

The age of the children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.8 years old. A fir

Kazeer [188]

Answer:

(1) (c) 5.30 years.

(2) (b) 0.289.

(3) (b) 0.80.

(4) (d) 0.50.

(5) (a) 5.25 years.

Step-by-step explanation:

Let X = age of the children in kindergarten on the first day of school.

The random variable X follows a continuous Uniform distribution with parameters a = 4.8 years and b = 5.8 years.

The probability density function function of X is:

$f_{X}(x)=\left \{ {{\frac{1}{b-a}} ;\ a$

(1)

The expected value of a Uniform random variable is:

$E(X)=\frac{1}{2}(a+b)$

Compute the mean of X as follows:

$E(X)=\frac{1}{2}(a+b)=\frac{1}{2}\times (4.8+5.8)=5.3$

Thus, the mean of the distribution is (c) 5.30 years.

(2)

The standard deviation of a Uniform random variable is:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}=\sqrt{\frac{1}{12}\times (5.8-4.8)^{2}}=0.289$

Thus, the standard deviation of the distribution is (b) 0.289.

(3)

Compute the probability that a randomly selected child is older than 5 years old as follows:

$P(X>5)=\int\limits^{5.8}_{5} {\frac{1}{5.8-4.8}}\, dx\\$

$=\int\limits^{5.8}_{5} {1}\, dx\\=[x]^{5.8}_{5}\\=(5.8-5)\\=0.8$

Thus, the probability that a randomly selected child is older than 5 years old is (b) 0.80.

(4)

Compute the probability that a randomly selected child is between 5.2 years and 5.7 years old as follows:

$P(5.2$

$=\int\limits^{5.7}_{5.2} {1}\, dx\\=[x]^{5.7}_{5.2}\\=(5.7-5.2)\\=0.5$

Thus, the probability that a randomly selected child is between 5.2 years and 5.7 years old is (d) 0.50.

(5)

It is provided that a randomly selected child is at the 45th percentile.

This implies that:

P (X < x) = 0.45

Compute the value of x as follows:

$P (X < x) = 0.45$

$\int\limits^{x}_{4.8} {\frac{1}{5.8-4.8}}\, dx=0.45$

$\int\limits^{x}_{4.8} {1}\, dx=0.45$

$[x]^{x}_{4.8}=0.45$

$x-4.8=0.45\\$

$x=0.45+4.8\\x=5.25$

Thus, the age of the child at the 45th percentile is (a) 5.25 years.

6 0

4 years ago

If a water dispenser pours 2 1/3 gallons a minute. How long does it take to pour 6 gallons in mixed number form?

ahrayia [7]

Answer:

Step-by-step explanation:

3 1/2

4 0

3 years ago

HELP MEEEEEEEEEEEHHHHHHHH (*≧▽≦)ﾉｼ))

Naya [18.7K]

Answer:

1. Point C ( 0; 5 )

2. Point K ( 2; -3 )

3. Point N ( -6; -5 )

Look, here ( A; B ) A is located in x coordinate and B is located in y coordinate

7 0

3 years ago

Read 2 more answers

I WILL GIVE BRAINLIEST PLEASE HELP (picture)

Blizzard [7]

$0.\overline{7}=0.777...\\\\x=0.777...\qquad\text{multiply both sides by 10}\\\\10x=7.777...\\\\\text{Make the difference}\\\\10x-x=7.777...-0.777...\\\\9x=7\qquad\text{divide both sides by 9}\\\\x=\dfrac{7}{9}\\\\Answer:\ \boxed{0.\overline{7}=\dfrac{7}{9}}\\-----------------\\You\ can\ remember\\\\\dfrac{1}{9}=0.\overline{1}\\\\\dfrac{2}{9}=0.\overline{2}\\\\\dfrac{3}{9}=0.\overline{3}\\\\\dfrac{4}{9}=0.\overline{4}\\\vdots\\\\\dfrac{8}{9}=0.\overline{8}$

8 0

3 years ago