16. Critique the reasoning of others. Penny

Explain why the cube root of 64 is rational and the cube root of 1 2 is not.

Ira Lisetskai [31]

$\sqrt[3]{64}=4$ so it's obvious, I guess :)

Now, let's prove $\sqrt[3]{12}$ is not rational number.

Proof by contradiction.

Let assume $\sqrt[3]{12}$ is a rational number. Therefore it can be expressed as a fraction $\dfrac{a}{b}$ where $a,b\in\mathbb{Z}$ and $\text{gcd}(a,b)=1$ .

$\sqrt[3]{12}=\dfrac{a}{b}\\\\12=\dfrac{a^3}{b^3}\\\\a^3=12b^3$

$12b^3$ is an even number, so $a^3$ must also be an even number, and therefore also $a$ must be an even number. So, we can say that $a=2k$ , where $k\in\mathbb{Z}$ .

$(2k)^3=12b^3\\\\8k^3=12b^3\\\\2k^3=3b^3$

Since $2k^3$ is an even number, then also $3b^3$ must be an even number. 3 is odd, so for $3b^3$ to be an even number, $b^3$ must be an even number, and therefore $b$ is an even number.

But if both a and b are even numbers, then it contradicts our earlier assumption that $\text{gcd}(a,b)=1$ . Therefore $\sqrt[3]{12}$ is not a rational number.

7 0

3 years ago

A truck can be rented from Company A for $60 a day plus $0.60 per mile . Company B charges $30 a day plus $0.90 per mile to rent

Mamont248 [21]

x = the number of miles

y = the total cost

Company A:

0.60x + 60 = y [Company A charges $60 plus $0.60 per mile(x)]

Company B:

0.90x + 30 = y [Company B charges $30 plus $0.90 per mile(x)]

To find the number of miles where the costs for both companies are the same, you can set the equations equal to each other as the costs(y) are the same:

y = y Substitute the equations into "y" (substitute (0.60x + 60) and (0.90x + 30) into "y" since y = 0.60x + 60 and y = 0.90x + 30)

0.60x + 60 = 0.90x + 30 To find x, isolate/get the variable "x" by itself. Subtract 30 on both sides

0.60x + 60 - 30 = 0.90x + 30 - 30

0.60x + 30 = 0.90x Subtract 0.60x on both sides to get "x" on one side of the equation

0.60x - 0.60x + 30 = 0.90x - 0.60x

30 = 0.30x Divide 0.30 on both sides to get "x" by itself

100 = x 100 miles

(if you need to find out the cost where both companies cost the same, you can substitute/plug in the value of x into one of the equations.)

0.60x + 60 = y Plug in 100 into "x" since x = 100

0.60(100) + 60 = y

120 = y At 100 miles, both companies cost $120

8 0

3 years ago

Please help with all of these!!! VERY URGENT!!!

nlexa [21]

1. The coefficient is 5
2. The terms are 2x, 4y, and 8
3. The variables are c, cd, d and d
4. The constants are 2 and 14

5 0

3 years ago

Read 2 more answers

Nth term to 4 1 -2 -5 -8

AURORKA [14]

4

4 - 3 = 1

1 - 3 = -2

-2 - 3 = -5

-5 - 3 = -8

It's the arithmetic sequence.

$a_n=a_1+(n-1)d$

$a_1=4,\ d=-3$

substitute

$a_n=4+(n-1)(-3)=4-3n+3=-3n+7$

Answer: $a_n=-3n+7$

7 0

2 years ago

PLEASE HELP W THIS I WILL Give YOU THE BRAINLIEST PLEASE ! - What does it mean to have a skewed distribution? What causes a skew

nata0808 [166]

Answer:

Explained below

Step-by-step explanation:

A) A skewed distribution in a dataset is when the median is not equal to the mean in such a manner that the bell curve is tilted to the left or right.

B) If in a data set, if there are outliers which are extremely large or extremely small in comparison to other values in that same dataset, then we can say that such a curve will be pulled towards the outlier and thus the distribution is skewed.

Also, if the curve is inclined to the left, it means there are few extreme values to the left and it is negatively skewed.

Similarly, if the curve is inclined to the right, it means there are few extreme values to the right and is positively skewed.

C) Example of a research question is;

If in a developed country where the poverty level is about 0%, if we collect the data of income of the households, we will discover majority of people with average income and very few people with extreme high levels of income. This condition means the data is positively skewed.

4 0

2 years ago