Round 452,906 to the nearest hundred thousand

There is a basketball with a diameter of 9 in. and a softball with a diameter of 4 in.. Find how many times greater the volume o

Nata [24]

The basketball has a volume of 113 inches .

8 0

4 years ago

What is the best Estimation for the product of 1.09 times 5.4 A.0x5=0 B.10x5=50 C.11x5=55 D.1x5=5

OLga [1]

Answer: D) 1*5=5

Step-by-step explanation: 1.09*5.4=5.5 so the closest number to that is 5.The rest of the answer choices are not possible.

8 0

4 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

3 years ago

4^3 · 4-^6 Simplified A) 4-3 B) 4-9 C) 4-18 D) 43

Triss [41]

4^3 · 4-^6

= 4^(3 + (-6))

= 4^-3

Answer

A) 4^-3

8 0

3 years ago

Read 2 more answers

Which rational number is equivalent to 0 . ¯¯¯¯¯¯ 36 ?

11Alexandr11 [23.1K]

The rational number is equivalent to 0.36 is 9/25

<h3>How to determine the equivalent rational number?</h3>

From the question, we have the following decimal number that can be used in our computation:

Decimal number = 0.36

To start with, we need to express the decimal number as a fraction

This is represented as follows:

So, we have the following representation

Decimal number = 36/100

Change the label of the above representation to rational number

Rational number = 36/100

Simplify the rational number (divide the numerator and the denominator by 2)

Rational number = 18/50

Simplify the rational number (divide the numerator and the denominator by 2)

Rational number = 9/25

Hence, the equivalent rational number is 9/25