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3 years ago

Can an expert help with this

Mathematics

1 answer:

SVEN [57.7K]3 years ago

7 0

The formula of an area of a circle:

$A_O=\pi r^2$

We have

r = 1.8 m

π ≈ 3.14

Substitute:

$A_O=\pi\cdot1.8^2=3.24\pi\ m^2\approx3.24\cdot3.14=10.1736\ m^2\approx10.17\ m^2$

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2 to the -6 power in expotional form and simplified in fractions

IceJOKER [234]

Answer:

1/64

Step-by-step explanation:

$2 ^{ - 6}$

$1 \div 2 ^{6}$

$1 \div 64$

4 0

2 years ago

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In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal p

skelet666 [1.2K]

Answer:

$\mathbf{P(X=5) =0.0888}$

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

$\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}$

$\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}$

where;

n = 8 and π = 0.36

For x = 5

The probability $\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}$

$\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =0.0887645}$

$\mathbf{P(X=5) =0.0888}$ to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5) $\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})$

${P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +$ $\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )$

P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888

P(x ≤ 5 ) = 0.9707

c. x ≥ 6

The probability of P ( x ≥ 6) = 1 - P( x ≤ 5 )

P ( x ≥ 6) = 1 - 0.9707

P ( x ≥ 6) = 0.0293

4 0

3 years ago

Find the equation of a line that passes through (2,8) and is parallel to the graph of y=2x+6. Write the equation in slope-interc

Rashid [163]

Answer:

The equation of a parallel line would be y = 2x + 4

Step-by-step explanation:

In order to find the equation of this line, we first have to note that paralell lines have same slopes. Therefore, since the original line has a slope of 2, we know the new line will have a slope of 2. Now we can use that information along with the given point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 8 = 2(x - 2)

y - 8 = 2x - 4

y = 2x + 4

3 0

3 years ago

The length of a rectangle is 1 units more than the width. The area of the rectangle is 56 units. What is the width, in units, of

pishuonlain [190]

Answer:

Step-by-step explanation:

$56=8*7\\8-7=1$ The width is smaller, so it is 7.

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3 years ago

24 inches is 250% of what length

Alinara [238K]

The answer is: " 9.6 inches " .
________________________________________________________
Explanation:
________________________________________________________

24 = 250/100 * x ;

24 = 2.5 x ;

↔ 2.5 x = 24 ;

2.5 x / 2.5 = 24/ 2.5 ;

x = 9.6 ;

The answer is: " 9.6 inches <span>" .
</span>_________________________________________________________

4 0

3 years ago

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