Emily is entering a bicycle race for charity. Her mother pledges $0.40 for every 0.25 mile she bikes. If Emily

The sum of rational number and an irrational number

Angelina_Jolie [31]

Answer:

The sum of a rational number and an irrational number is irrational." By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats.

Step-by-step explanation:

However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational. "The product of two irrational numbers is SOMETIMES irrational." Each time they assume the sum is rational; however, upon rearranging the terms of their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.

5 0

3 years ago

398/74 as a mixed number in simplest form

stira [4]

The answer would be 199/37 or 5 14/37

6 0

3 years ago

Read 2 more answers

In 1935, there were 15,295 banks in the United States. In 2003 there were 9,182 banks. What is the percent of the change? Is it

Sati [7]

If it goes from a higher number to a lower number it is a decrease.

(15,295 - 9182) / 15295....x 100
6113 / 15295 = 0.399....x 100 = 39.9% decrease

5 0

3 years ago

Please help me step by step thanks

Gemiola [76]

Left:
180-53 = (8x-9)
127+9 = 8x
136 = 8x
x = 17
Right:
(15x+29) = (26x-4)
29+4 = 26x-15x
33 = 11x
x = 3

7 0

3 years ago

Assume that the helium porosity of coal samples taken from any particular seam is Normally distributed with true standard deviat

riadik2000 [5.3K]

Answer:

a) $4.85-2.33\frac{0.75}{\sqrt{20}}=4.46$

$4.85+2.33\frac{0.75}{\sqrt{20}}=5.24$

b) $4.56-2.33\frac{0.75}{\sqrt{16}}=4.12$

$4.56+2.33\frac{0.75}{\sqrt{16}}=4.99$

c) $n=(\frac{1.960(0.75)}{0.2})^2 =54.02 \approx 55$

Step-by-step explanation:

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$4.85-2.33\frac{0.75}{\sqrt{20}}=4.46$

$4.85+2.33\frac{0.75}{\sqrt{20}}=5.24$

Part b

$4.56-2.33\frac{0.75}{\sqrt{16}}=4.12$

$4.56+2.33\frac{0.75}{\sqrt{16}}=4.99$

Part c

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.4/2 =0.2 we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(0.75)}{0.2})^2 =54.02 \approx 55$

5 0

3 years ago