Elijah ran around the quarter mile track at the school seven times. Approximately how many kilometers is this?

djyliett [7]

The answer is the first option: I, II and III.

The explanation is shown below:

1. By definition, there is a joint variation when a variable depends on two or more different variables. Therefore, you can express it as following:

$y=kxz$

Where $x,y$ and $z$ are the variables and $k$ is the constant of proportionality.

As you can see, $y$ is directly proportional to $x$ and $z$ .

2. Keeping the information above, you have:

I) $V=lwh$ ( $V$ varies jointly with $l$ , $w$ and $h$ .

II) $V=\frac{1}{3}r^{2}h\pi$ (If $\frac{\pi}{3}$ is the constant of proportionality, $V$ varies jointly with $r^{2}$ and $h$ ).

III) $V=Bh$ ( $V$ varies jointly with $B$ and $h$ .

8 0

3 years ago

Read 2 more answers

Nia answered 80% of the 40 questions on a test correctly. How many correct answers did she have?

Step2247 [10]

Nia answered correct answers = 80% of the 40 questions

When we remove % sign from a number, we divide that number by 100

= $\frac{80}{100}$ of 40

= $\frac{80}{100} \times 40$

Cancelling the two zeroes from numerator and denominator,

= $8 \times 4$

= 32.

Total correct answers answered by Nia = 32

3 0

3 years ago

Read 2 more answers

Is the circle inside the hexagon or hexagon inside the circle?

nexus9112 [7]

It could be either, we need more info. How big are each? If it doesn't say, then it's a trick question. Throw Schrodinger's cat at it or something.

8 0

3 years ago

Find the sum of the geometric series 512+256+ . . .+4

mario62 [17]

$\bf 512~~,~~\stackrel{512\cdot \frac{1}{2}}{256}~~,~~...4$

so, as you can see above, the common ratio r = 1/2, now, what term is +4 anyway?

$\bf n^{th}\textit{ term of a geometric sequence}\\\\a_n=a_1\cdot r^{n-1}\qquad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\a_n=+4\end{cases}$

$\bf 4=512\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{4}{512}=\left( \cfrac{1}{2} \right)^{n-1}\\\\\\\cfrac{1}{128}=\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{1}{2^7}=\left( \cfrac{1}{2} \right)^{n-1}\implies 2^{-7}=\left( 2^{-1}\right)^{n-1}\\\\\\(2^{-1})^7=(2^{-1})^{n-1}\implies 7=n-1\implies \boxed{8=n}$

so is the 8th term, then, let's find the Sum of the first 8 terms.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\n=8\end{cases}$

$\bf S_8=512\left[ \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right]\implies S_8=512\left(\cfrac{1-\frac{1}{256}}{\frac{1}{2}} \right)\implies S_8=512\left(\cfrac{\frac{255}{256}}{\frac{1}{2}} \right)\\\\\\S_8=512\cdot \cfrac{255}{128}\implies S_8=1020$

7 0

3 years ago

Which value is a solution to the inequality 2x − 5 < −12?

aleksandr82 [10.1K]

The correct answer would be -4

explanation:
2x-5<-12, add 5 to both sides so then you get 2x<-8, then divide by two, x<-4.

8 0

3 years ago