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3 years ago

Please help ASAP! Correct answer only! This assignment is due today.

Mathematics

1 answer:

lara31 [8.8K]3 years ago

6 0

Answer:

<em>Probability ≈ 0.0714</em>

Step-by-step explanation:

Consider permutation and combination;

$Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714$

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Round to the nearest hundredth 5/8

Solnce55 [7]

Eighths and their multiples are common fractions which I recommend memorizing, but to actually solve this, you use the literal meaning of a fraction and divide 5 by 8. See the long-division below (it was surprisingly difficult to type, so I hope it helps!).

To round 0.625 to the nearest hundredth, we go to the second decimal place, which is 5, so we round up to 0.63.

3 0

3 years ago

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

3 0

3 years ago

If a number is decreased by 8, the result is -21. What is the

wariber [46]

Answer:

answer = -13

Step-by-step explanation:

number = x

x - 8 = -21

x = -21 + 8

= -13

Recheck :

num = - 13

decreased by 8 = - 13 -8 = -21

4 0

3 years ago

-8+N=15? I can’t find the right answer

Paraphin [41]

Answer:

n = 23

Step-by-step explanation:

-8 + n = 15

-8 + n + 8 = 15 + 8

n = 23

Answer: n = 23

7 0

4 years ago

Read 2 more answers

The product of 5 and a number n is at least 25

Crazy boy [7]

5n≥25
and if you divide 5 on both sides, n≥5 (I don't know if you are supposed to solve or simply put it in the equation form).

Product refers to multiplication. so 5 and n are being multiplied in the equation.
However, instead of using an equal sign, the sign for "greater than or equal to" must be used. "At least" is a term equivalent to "greater than or equal to".

4 0

3 years ago