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3 years ago

What is the product in simplest form? −8/9⋅5/6 A.−1 B.−13/15 C.−20/27 D.−15

2 answers:

8 0

Hello,

-8/9 X 5/6 = -40 / 54. The greatest common factor they both go into is 20.

Divide -40 and 54 by 20, and the answer simplified is -20/27, letter C.

Hope this helps!

May

nalin [4]3 years ago

5 0

The answer is C.
hope this helps!

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What are the steps to solve √(0.2)^(−2)?<br><br>(The answer is 5)

Nimfa-mama [501]

$\bf 0.\underline{2}\implies \cfrac{02}{1\underline{0}}\implies \stackrel{simplified}{\cfrac{1}{5}} \\\\[-0.35em] ~\dotfill\\\\ \left( \sqrt{0.2} \right)^{-2}\implies \left( \sqrt{\cfrac{1}{5}}\right)^{-2}\implies \left( \sqrt{\cfrac{5}{1}}\right)^{+2}\implies \cfrac{(\sqrt{5})^2}{(\sqrt{1})^2}\implies \cfrac{\sqrt{5^2}}{\sqrt{1^2}}\implies 5$

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3 years ago

Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?

OlgaM077 [116]

Answer:

$a_n = 16(\frac{1}{4})^{n - 1}$

Step-by-step explanation:

Given:

Fifth term of a geometric sequence = $\frac{1}{16}$

Common ratio (r) = ¼

Required:

Formula for the nth term of the geometric sequence

Solution:

Step 1: find the first term of the sequence

Formula for nth term of a geometric sequence = $ar^{n - 1}$ , where:

a = first term

r = common ratio = ¼

Thus, we are given the 5th term to be ¹/16, so n here = 5.

Input all these values into the formula to find a, the first term.

$\frac{1}{16} = a*\frac{1}{4}^{5 - 1}$

$\frac{1}{16} = a*\frac{1}{4}^{4}$

$\frac{1}{16} = a*\frac{1}{256}$

$\frac{1}{16} = \frac{a}{256}$

Cross multiply

$1*256 = a*16$

Divide both sides by 16

$\frac{256}{16} = \frac{16a}{16}$

$16 = a$

$a = 16$

Step 2: input the value of a and r to find the nth term formula of the sequence

nth term = $ar^{n - 1}$

nth term = $16*\frac{1}{4}^{n - 1}$

$a_n = 16(\frac{1}{4})^{n - 1}$

3 0

2 years ago

My teacher wrote the answer on the right but he wants me to show how he did it

Airida [17]

865 is the answer of this question...

4 0

2 years ago

What is the volume of the composite figure? (Round to the nearest hundredth. Use 3.14 for Pi.)

Natasha2012 [34]

The volume of composite figure is 385.17 cubic centimeters, if a half sphere and cone have a radius of 4 centimeters and height of 15 centimeters.

Step-by-step explanation:

The given is,

Composite figure is combination of a half sphere and cone

Both have a radius of 4 centimeters

The cone has a height of 15 centimeters

Step:1

Volume of composite figure = Volume of half sphere + Volume of cone

Step:2

Formula for volume of semi sphere,

$Volume of half sphere, V_{Half sphere} = \frac{2}{3} \pi r^{3}$

Where, r - Radius of Half sphere,

From given, r = 4 centimeters

$V_{Half sphere} = \frac{2}{3} \pi 4^{3}$

$= (0.6667) (3.14) (64)$ (∵ $\pi$ = 3.14 )

$V_{Half sphere}$ = 133.9733 cubic centimeters

Formula for volume of cone,

$Volume of cone, V_{cone} = \frac{1}{3} \pi r^{2} h$

where, r - Radius of cone

h - Height of cone

From given,

r = 4 centimeters

h = 15 centimeters

Volume of cone,

$V_{cone} = \frac{1}{3} \pi 4^{2}(15)$

$= (0.333333) (3.14)(16)(15)$ (∵ $\pi$ = 3.14 )

$V_{cone}$ $= 251.1997$ cubic centimeters

Step:3

Volume of composite figure = 133.9733 + 251.1997

Volume of composite figure = 385.17 cubic centimeters

Result:

The volume of composite figure is 385.17 cubic centimeters, if a half sphere and cone have a radius of 4 centimeters and height of 15 centimeters.

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