Find the height of the triangle

Mathematics

2 answers:

kotykmax [81]2 years ago

8 0

The given triangle is a right angle. To solve this, we can use;

sin theta = opposite / hypotenuse ; where theta =20 ; h = 10
sin (20) = x / 10
x = 3.42

The answer is the fourth one, 3.42

Paul [167]2 years ago

7 0

There are two -main- approaches to answer this problem. By using the sine identity, or applying law of sines.

We'll do the sine trig. identity, as it is the most effective.

Given an angle ' $\alpha$ ' in a right triangle, ' $sin( \alpha )$ ' is defined as the opposite side of the triangle to the given angle, over the triangle's hypotenuse.

So, for this setup:
$sin(20)= \frac{x}{10}$

Now, we solve for x:
$x=10sin(20)=3.42$

So, answer is 3.4

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6. A bank auditor claims that credit card balances are normally distributed, with a mean of $3570

sergejj [24]

Answer:

Probability that their mean credit card balance is less than $2500 is 0.0073.

Step-by-step explanation:

We are given that a bank auditor claims that credit card balances are normally distributed, with a mean of $3570 and a standard deviation of $980.

You randomly select 5 credit card holders.

Let $\bar X$ = sample mean credit card balance

The z score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean credit card balance = $3570

$\sigma$ = standard deviation = $980

n = sample of credit card holders = 5

Now, the probability that their mean credit card balance is less than $2500 is given by = P( $\bar X$  < $2500)

P( $\bar X$ < $2500) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{2500-3570}{\frac{980}{\sqrt{5} } }$ ) = P(Z < -2.44) = 1 - P(Z $\leq$ 2.44)