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3 years ago

A six-sided die is rolled three times. what is the probability that all three rolls will be 6?

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

6 0

you have a 1/6 probability of rolling a 6

so for 3 6's it would be

1/6 x 1/6 x 1/6 = 1/216

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Use the equation p=10j to find the value of p when j=6.

lyudmila [28]

Answer:

p=60

Step-by-step explanation:

10(6)=60

p=60

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About 7% of the population has a particular genetic mutation. 400 people are randomly selected. Find the standard deviation for

Deffense [45]

Answer:

5.10 people

Step-by-step explanation:

Calculation to Find the standard deviation for the number of people with the genetic mutation

Using this formula

Standard deviation = √ ( n * p * q)

Where,

n = 400

p = .07

q = 100%-7% = 93% or .93

Let plug in the formula

Standard deviation =√400*07*.93

Standard deviation =√26.04

Standard deviation = 5.10 people

Therefore the standard deviation for the number of people with the genetic mutation is 5.10 people.

5 0

3 years ago

Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 1

belka [17]

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

$F(x) = \int\limits^a_b {f(x)} \, dx$

By using integration formula

$\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c$

Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

$\int\limits^6_^-6} (x^{5} + 8 x^{4} + 2 x^{2} + 5 x + 15) )dx$

On integration , we get

= $(\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}$

$F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)$

= $(\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))$

After simplification and cancellation we get

= $\frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6$

on calculation , we get

= $\frac{124,416}{5} + \frac{864}{3} + 180$

On L.C.M 15

= $\frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}$

= 25 351.2 units²

Conclusion:-

The area of the region between the graph of the given function and the x-axis = 25,351 units²

6 0

3 years ago