Which of the following is an example of a rational number that is not an integer?<br> 4 , 0 , 1/5

The mass of earth is 5.9 x 10^24. The mass of Pluto is 13,000,000,000,000,000,000,000 kg. Compared to Pluto, how much greater is

nadya68 [22]

5.9 × 10^24 = 5,900,000,000,000,000,000,000,000 minus
13,000,000,000,000,000,000,000 equals
5,887,000,000,000,000,000,000,000 kg
which is the amount greater that Earth's mass is. you could write this problem as
5.9 × 10^24 - 13 × 10^21 = 5.887 × 10^21

7 0

4 years ago

What is a factor? _____________________________________________

andriy [413]

Answer: What is a factor?

A factor is a a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

Step-by-step explanation: Why can’t certain expressions be factored?

Because there are no common factors other than 1 the constants cannot be factored. And, because there is no x in the second term (10), we cannot factor an x out of the two terms.

4 0

3 years ago

Read 2 more answers

In the figure, AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. Prove that △AEB ≅ △DEC

Makovka662 [10]

Answer:

From top to bottom:

A, J, E, B, I, C, D, G, F, H

See below for more clarification.

Step-by-step explanation:

We are given that AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. And we want to prove that ΔAEB ≅ ΔDEC.

Statements:

1) XY is perpendicular to AB.

Definition of perpendicular bisector.

2) XY ⊥ CD.

In a plane, if a transveral is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

3) m∠AXE = 90°, m∠DYE = 90°.

Definition of perpendicular lines.

4) ∠AXE ≅ ∠DYE.

Right angles are congruent.

5) XE ≅ YE

Definition of a midpoint.

6) ∠A ≅ ∠D.

Alternate Interior Angles Theorem

7) ΔAEX ≅ ΔDEY

AAS Triangle Congruence*

(*∠A ≅ ∠D, ∠AXE ≅ ∠DYE, and XE ≅ YE)

8) AE ≅ DE

Corresponding parts of congruent triangles are congruent (CPCTC).

9) ∠AEB ≅ ∠DEC

Vertical Angles Theorem

10) ΔAEB ≅ ΔDEC

ASA Triangle Congruence**

(**∠A ≅ ∠D, AE ≅ DE, and ∠AEB ≅ ∠DEC)

3 0

3 years ago

An insurance company has 25,000 automobile policy holders. If the yearly claim of a policy holder is a random variable with mean

telo118 [61]

Answer:

$P(T>8300000)=1-P(T$

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Data given

n = 25000 represent the automobile policy holders

$\mu= 320$ represent the population mean

$\sigma =540$ represent the population standard deviation

Let T the variable that represent the total of interest on this case. We can assume that the random variable for an individual policy holder is given by:

$X\sim N(\mu = 540, \sigma=540)$

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

Solution to the problem

First we need to find the distribution for the random variable T like this:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}$

And the total T is given by:

$T=\sum_{i=1}^n X_i =n \bar X$

We can find the expected value, variance and deviation for this random variable like this:

$E(T)= n E(\bar X) = n \mu = 25000*320=8000000$

$Var(T)= Var(n\bar X)= n^2 Var(\bar X) = n^2 \frac{\sigma^2}{n}=n \sigma^2 =25000*(540^2)=7290000000$

$Sd(T)=\sqrt{7290000000}=85381.497$

And we are interested on this probability:

$P(T>8300000)$

And we can use the Z score formula given by:

$Z=\frac{T-E(T)}{\sigma_T}$

$P(T>8300000)=1-P(T$

6 0

3 years ago

Could someone help me please

Alexxx [7]

1. 3x+9-9=18-9

3x=9

x=3

2. 4x-12=20

4x-12+12=20+12

4x=32

x=8

3. x+0-0

x=0

4. x/2-2+2=9+2

x/2=11

(2)(x/2)=11(2)

x=22

5. 12x-21=3

12x-21+21=3+21

12x=24

x=2

6. 3x-15=18

3x-15+15=18+15

3x=33

x=11

7. 3x-25=14

3x-25+25=14+25

x=13

8. 3x+16=22

3x+16-16=22-16

x=2

9. 2x-8=2

2x-8+8=2+8

2x=10

x=5

10. 9x-18=9

9x-18+18=9+18

9x=27

x=3

11. x+0=0

x=0

12. 9x-8=19

9x-8+8=19+8

9x=27

x=3

If you want to check my answers

use substitution method by using the x into for each equation.

7 0

3 years ago

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Which of the following is an example of a rational number that is not an integer? 4 , 0 , 1/5