Question

a right triangle has legs of length 6 cm and 8 cm. find the hypotenuse.
your answer
a spinner has 10 equal sections, numbered 1 - 10. whats the probability of spinning a number greater than 6?
your answer
the mean of five test scores is 80. four scores are 75, 82, 90, and 79. what is the missing score?
72
74
76
80

Explanation:

First problem:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
where \(a = 6\), \(b=8\)

Step2: Substitute values

$$6^{2}+8^{2}=c^{2}$$
$$36 + 64=c^{2}$$
$$100=c^{2}$$

Step3: Solve for \(c\)

$$c=\sqrt{100}$$
$$c = 10$$

Step1: Determine favorable outcomes

Numbers greater than \(6\) are \(7\), \(8\), \(9\), \(10\). So there are \(4\) favorable outcomes.

Step2: Use probability formula

Probability \(P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}\)
Total outcomes \(n = 10\)
$$P=\frac{4}{10}=\frac{2}{5}$$

Step1: Use mean formula

Mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\)
Given \(\bar{x}=80\), \(n = 5\)
So \(\sum_{i=1}^{5}x_{i}=80\times5=400\)

Step2: Sum of four known scores

\(75 + 82+90 + 79=326\)

Step3: Find missing score

Let missing score be \(x\)
\(x+326 = 400\)
$$x=400 - 326=74$$

Answer:

\(10\) cm

Second problem: