All categories

3 years ago

What is ∛2197? Explain how you got your answer.

Mathematics

2 answers:

user100 [1]3 years ago

5 0

Answer:

Step-by-step explanation:

We need to write our answer in exponential form. Ask yourself the question, "What times itself 3 times will give you 2197?" Your answer is $13^{3}$ . This will go inside of your cube root. You now have $\sqrt[3]{13^{3} }$ . Since there's a power of 3 and a cube root, those cancel each other out, and your answer is 13.

ZanzabumX [31]3 years ago

4 0

Answer:

$\boxed{13}$

Step-by-step explanation:

=> $\sqrt[3]{2197}$

Factorizing 2197 gives 13 * 13 * 13

=> $\sqrt[3]{13*13*13}$

=> $\sqrt[3]{13^3}$

We know that $\sqrt[3]{} = ^{1/3}$

=> $13^{3 * 1/3}$

=> $13^1$

=> 13

You might be interested in

How do you solve his with working

AlexFokin [52]

Check the picture below.

a)

so the perimeter will include "part" of the circumference of the green circle, and it will include "part" of the red encircled section, plus the endpoints where the pathway ends.

the endpoints, are just 2 meters long, as you can see 2+15+2 is 19, or the radius of the "outer radius".

let's find the circumference of the green circle, and then subtract the arc of that sector that's not part of the perimeter.

and then let's get the circumference of the red encircled section, and also subtract the arc of that sector, and then we add the endpoints and that's the perimeter.

$\bf \begin{array}{cllll}
\textit{circumference of a circle}\\\\ 
2\pi r
\end{array}\qquad \qquad \qquad \qquad 
\begin{array}{cllll}
\textit{arc's length}\\\\
s=\cfrac{\theta r\pi }{180}
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\stackrel{green~circle}{perimeter}}{2\pi(7.5) }~-~\stackrel{\stackrel{green~circle}{arc}}{\cfrac{(135)(7.5)\pi }{180}}~+
\stackrel{\stackrel{red~section}{perimeter}}{2\pi(9.5) }~-~\stackrel{\stackrel{red~section}{arc}}{\cfrac{(135)(9.5)\pi }{180}}+\stackrel{endpoints}{2+2}
\\\\\\
15\pi -\cfrac{45\pi }{8}+19\pi -\cfrac{57\pi }{8}+4\implies \cfrac{85\pi }{4}+4\quad \approx \quad 70.7588438888$

b)

we do about the same here as well, we get the full area of the red encircled area, and then subtract the sector with 135°, and then subtract the sector of the green circle that is 360° - 135°, or 225°, the part that wasn't included in the previous subtraction.

$\bf \begin{array}{cllll}
\textit{area of a circle}\\\\ 
\pi r^2
\end{array}\qquad \qquad \qquad \qquad 
\begin{array}{cllll}
\textit{area of a sector of a circle}\\\\
s=\cfrac{\theta r^2\pi }{360}
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\stackrel{red~section}{area}}{\pi(9.5^2) }~-~\stackrel{\stackrel{red~section}{sector}}{\cfrac{(135)(9.5^2)\pi }{360}}-\stackrel{\stackrel{green~circle}{sector}}{\cfrac{(225)(7.5^2)\pi }{360}}
\\\\\\
90.25\pi -\cfrac{1083\pi }{32}-\cfrac{1125\pi }{32}\implies \cfrac{85\pi }{4}\quad \approx\quad 66.75884$

7 0

3 years ago

A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special c

fredd [130]

Answer:

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

Step-by-step explanation:

Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as

H0 :p 0.5 against Ha: p ≠ 0.5

The significance level is approximately 0.05

The test statistic to be used is number of heads x.

Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution

Heads (x) Probability (X=x) Cumulative Decumulative

0 1/16384 (1) 0.000061 0.000061

1 1/16384 (14) 0.00085 0.000911

2 1/16384 (91) 0.00555 0.006461

3 1/16384(364) 0.02222

4 1/16384(1001) 0.0611

5 1/16384(2002) 0.122188

6 1/16384(3003) 0.1833

7 1/16384(3432) 0.2095

8 1/16384(3003) 0.1833

9 1/16384(2002) 0.122188

10 1/16384(1001) 0.0611

11 1/16384(364) 0.02222

12 1/16384(91) 0.00555 0.006461

13 1/16384(14) 0.00085 0.000911

14 1/16384(1) 0.000061 0.000061

We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).

We observe that P (X≤2) = 0.006461 > 0.025

and

P ( X≥12 ) = 0.006461 > 0.025

Therefore true significance level is

∝= P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122

Hence critical region is (X≤0) and ( X≥14)

Computation x= 12

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

3 0

3 years ago

What should i do now please help me

m_a_m_a [10]

Answer:

x=24

Step-by-step explanation:

Here, you need to make proportion and find x.

12:16=18:x

We multiply 12 by x and 16 by 18:

12x=288

Divide by 12 both sides :

x=24

6 0

3 years ago

What is 288 divided by 8

Tamiku [17]

Answer:

The answer is 36

Step-by-step explanation:

288÷8=36

8 0

3 years ago

Read 2 more answers

Please help me with this question bellow.

Vera_Pavlovna [14]

Answer:

they are just multiplying thr numbers on top for exsample 42÷6=7

Step-by-step explanation:

you should see what numbers dose the bottom numbers have in common and multiply by 15.

3 0

3 years ago