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2 years ago

8

Ahmad had 6/7 of a spool of yarn. He used 2/5 of his yarn for a project. What fraction of the spool was used for the project?

1 answer:

GaryK [48]2 years ago

4 0

Answer:

$\dfrac{12}{35}$

Step-by-step explanation:

2/5 ths of 6/7 ths:

$\implies \dfrac67 \times \dfrac25=\dfrac{6\times 2}{7\times5}=\dfrac{12}{35}$

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-3.11666666667

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3 years ago

Suppose you choose a team of two people from a group of n > 1 people, and your opponent does the same (your choices are allow

jonny [76]

Answer:

The number of possible choices of my team and the opponents team is

$\left\begin{array}{ccc}n-1\\E\\n=1\end{array}\right i^{3}$

Step-by-step explanation:

selecting the first team from n people we have $\left(\begin{array}{ccc}n\\1\\\end{array}\right) = n$ possibility and choosing second team from the rest of n-1 people we have $\left(\begin{array}{ccc}n-1\\1\\\end{array}\right) = n-1$

As { A, B} = {B , A}

Therefore, the total possibility is $\frac{n(n-1)}{2}$

Since our choices are allowed to overlap, the second team is $\frac{n(n-1)}{2}$

Possibility of choosing both teams will be

$\frac{n(n-1)}{2} * \frac{n(n-1)}{2} \\\\= [\frac{n(n-1)}{2}] ^{2}$

We now have the formula

1³ + 2³ + ........... + n³ = $[\frac{n(n+1)}{2}] ^{2}$

1³ + 2³ + ............ + (n-1)³ = $[x^{2} \frac{n(n-1)}{2}] ^{2}$

= $\left[\begin{array}{ccc}n-1\\E\\i=1\end{array}\right] = [\frac{n(n-1)}{2}]^{3}$

4 0

3 years ago

Find the reference angle given: t= -5π/3.

Elina [12.6K]

Answer:

The reference angle is $\frac{\pi}{3}$

Step-by-step explanation:

The given angle is $t=-\frac{5\pi}{3}$

The reference angle is the acute angle, that a given angle makes with the x-axis.

First let us make a sketch of the given angle. <em>See diagram in attachment.</em>

Let $\theta$ be the reference angle of $t=-\frac{5\pi}{3}$

Then, from the diagram, we need to subtract $\theta$ from $-\frac{5\pi}{3}$ to get to $-2\pi$ .

We can therefore write the following equation and solve for $\theta$ .

$\Rightarrow -\frac{5\pi}{3}-\theta=-2\pi$

We group like terms to get,

$\Rightarrow -\theta=-2\pi +\frac{5\pi}{3}$

We collect LCM to get,

$\Rightarrow -\theta=\frac{-6\pi+5\pi}{3}$

We simplify to get,

$\Rightarrow -\theta=-\frac{\pi}{3}$

We divide through by $-1$

$\theta=\frac{\pi}{3}$ to get,

The correct answer is D.

4 0

3 years ago