You would use the Law of Sines here. First realize that if A and B equal 35 and 65 respectively, C=180-65-35=80°. Then from the Law of Sines:

b/sin65=15/sin80

b=15sin65/sin80

b≈13.8 units (to the nearest tenth of a unit)

7 0

3 years ago

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Given that x is a hypergeometric random variable with Nequals10, nequals4, and requals6, complete parts a through d. a. Compu

sergey [27]

Answer:

a. 0.114

b. 0.005

c. 0.381

d. 0.00

Step-by-step explanation:

If x follows a hypergeometric distribution, the probability that x is equal to k is calculated as:

$P(x=k)=\frac{(rCk)*((N-r)C(n-k))}{NCn}$

Where k≤r and n-k≤N-r, Additionally:

$aCb=\frac{a!}{b!(a-b)!}$

So, replacing N by 10, n by 4 and r by 6, we get:

$P(x=k)=\frac{6Ck*((10-6)C(4-k))}{10C4}=\frac{6Ck*(4C(4-k))}{10C4}$

Then, the probability that x is equal to 1, P(x=1) is:

$P(x=1)=\frac{6C1*4C3}{10C4}=0.114$

The probability that x is equal to 0, P(x=0) is:

$P(x=0)=\frac{6C0*4C4}{10C4}=0.005$

The probability that x is equal to 3, P(x=3) is:

$P(x=3)=\frac{6C3*4C1}{10C4}=0.381$

Finally, in this case, x can take values from 0 to 4, so the probability that x is greater or equals to 5 is zero.

6 0

3 years ago

The City Parks Department had 3 2/3 tons of gravel. Then they used 1 1/2 tons to cover the trails in neighborhood parks. How muc

natima [27]

Answer:

2 1/6

Step by step: subtract 1 1/2 from 3 2/3

8 0

2 years ago

How does the graph of g(x) = (x + 4)^3 − 6 compare to the parent function f(x) = x^3?

ANTONII [103]

Answer:

D) g(x) is shifted 4 units to the left and 6 units down

Step-by-step explanation:

When -6 is added to the y-value, it moves the point on the graph down 6 units. Compared to f(x), g(x) is 6 units down.

Transforming the function using f(x -h) shifts its graph h units to the right. Here, we have h=-4, so the graph is shifted 4 units to the left.

5 0

3 years ago