Please help, I don't understand

Mathematics

1 answer:

MaRussiya [10]4 years ago

7 0

Answer:

sin(θ) = (2/5)√6

Step-by-step explanation:

The sine and cosine are related by the formula ...

$\sin{(\theta)}^2+\cos{(\theta)}^2=1\\\\\sin{(\theta)}=\pm\sqrt{1-\cos{(\theta)}^2}$

Filling in the given value for cos(θ), we find the sine to be ...

$\sin{(\theta)}=\pm\sqrt{1-\left(\dfrac{1}{5}\right)^2}=\pm\dfrac{\sqrt{24}}{5}=\pm\dfrac{2}{5}\sqrt{6}$

The cosine function is positive for angles in both the first and fourth quadrants. The restriction on θ tells us this is a first-quadrant angle. The sine is positive in the first quadrant, so the desired value is ...

sin(θ) = (2/5)√6

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3 years ago

Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with μ=10

Tju [1.3M]

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Step-by-step explanation:

Given : Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with $\mu=106$ and $\sigma=15$ .

Let x denotes the scores on a certain intelligence test for children between ages 13 and 15 years.

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$P(x>92)=1-P(x\leq92)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{92-106}{15})\\\\=1-P(z\leq })\\\\=1-P(z\leq-0.93)=1-(1-P(z\leq0.93))\ \ [\because\ P(Z\leq -z)=1-P(Z\leq z)]\\\\=P(z\leq0.93)=0.8238\ \ [\text{By using z-value table.}]$