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2 years ago

What are the similarities and differences between these data sets in terms of their centers and their variability?

Mathematics

1 answer:

balu736 [363]2 years ago

3 0

The median of data set A is less that the median in data set B and the range of data set A is greater than the range of data set B

Sorry if I get it wrong; please rate my answer

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A frustum is made by removing a small cone from

irina1246 [14]

Answer:

a similar large cone

Step-by-step explanation:

7 0

2 years ago

What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

lapo4ka [179]

Consider the equation $x^6+6x^3+5=0$ .

First, you can use the substitution $t=x^3$ , then $x^6=(x^3)^2=t^2$ and equation becomes $t^2+6t+5=0$ . This equation is quadratic, so

$D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1$ .

Then you can factor this equation:

$(t+5)(t+1)=0$ .

Use the made substitution again:

$(x^3+5)(x^3+1)=0$ .

You have in each brackets the expression like $a^3+b^3$ that is equal to $(a+b)(a^2-ab+b^2)$ . Thus,

$x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)$

and the equation is

$(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0$ .

Here $x_1=-\sqrt[3]{5} , x_2=-1$ and you can sheck whether quadratic trinomials have real roots:

1. $D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}$ .

2. $D_2=(-1)^2-4\cdot 1=1-4=-3$ .

This means that quadratic trinomials don't have real roots.

Answer: $x_1=-\sqrt[3]{5} , x_2=-1$

If you need complex roots, then

$x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}$ .

6 0

3 years ago

Given the following geometric sequence, find the common ratio:<br><br> {225, 45, 9...}

Tom [10]

Answer:

$\frac{1}{5}$ is the common ratio

Step-by-step explanation:

Common ratio(r) states that the ratio of each term of a geometric sequence to the term preceding it.

$r = \frac{a_2}{a_1} =\frac{a_3}{a_2}........\frac{a_{n+1}}{a_n}$

Given the sequence:

225, 45, 9, .........

Here,

$a_1 = 225$

$a_2 = 45$

$a_3 = 9$ and so on...

Using definition to find r.

$r = \frac{45}{225}=\frac{9}{45}......$

After solving we get;

$r = \frac{1}{5}$

Therefore, the common ratio is, $\frac{1}{5}$

8 0

3 years ago

Read 2 more answers

Mary sells fruit with four of her friends. If the earnings are divided evenly, how

Naya [18.7K]

Answer: 30× 4 = 120

120÷4 = 30

Step-by-step explanation:

8 0

3 years ago

Roselyn is driving to visit her family, which live 150 150150 kilometers away. Her average speed is 60 6060 kilometers per hour.

Sauron [17]

Answer:

She can go 120 km before she runs out of fuel

It will take 2 hours.

Step-by-step explanation:

150 km is the distance

60 km/ h is the speed

The gas tank is 20 liters

We can go 6 km per liter

Fuel costs .60 dollars per liter

We need to determine how far she can go on a tank of gas

20 liters * 6 km / liter = 120 km

She can go 120 km before she runs out of fuel

120 km = 60 km/ h * x hours

Divide each side by 60

120/60 = x

2 hours

8 0

3 years ago