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2 years ago

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Janet set off on a bicycle trip at 7:30 a.m. at an average rate of 24 miles per hour. Her husband John promised to bring her som

e lunch and he set off by Car 2 hours after Janet left driving at an average speed of 40 miles per hour at what time did John catch up with Janet

1 answer:

Gemiola [76]2 years ago

5 0

I believe the answer would be 10:20 am.

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If y=4 when x=16, find y when x=6

timurjin [86]

The answer is 2 I think

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3 years ago

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

2 years ago

F(x)=x^2+10x-12

weqwewe [10]

Answer:

Therefore the two values required are 2.08 and -11.08.

Step-by-step explanation:

i) f(x) = $x^{2}$ + 10x - 12 is a quadratic equation and a quadratic equation will have two roots whose values when substituted in to the given quadratic equation will give the value.

ii) The question is therefore essentially asking us to find the roots of the given quadratic equation.

This can be done by equating the given quadratic equation to zero and then solving the equation for its roots.

∴ $x^{2}$ + 10x -12 = 0 ⇒ x = (-10 ± $\sqrt{10^{2} +(48)}$ ) ÷ 2

= (-10 ± 12.166)÷2 = 2.08, -11.08

Therefore the two values required are 2.08 and -11.08

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3 years ago

What is the slope of this equation (2,-5) (-2,5)

Arisa [49]

Hello!

Here a graph of the slope!

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2 years ago

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What is the number of degrees in an angle whose radian measure is 11pie/12?

Diano4ka-milaya [45]

11pi/12

Note:

2pi = 360°

(11pi/12)(360°/2pi)
330°

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2 years ago

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