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2 years ago

In the following exercises, multiply the binomials. Use any method. 249. (6p + 5)(p + 1)

Mathematics

1 answer:

scoundrel [369]2 years ago

7 0

Answer:

Hence the expression $(6p+5)(p+1)=6p^2+11p+5$

Step-by-step explanation:

Explanation

The given expression is (6p+5)(p+1).
We have to multiply the given expression.
Multiply the (6p+5) by 1 , multiply the (6p+5) by p then add like terms.

$$$\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ \times & {} & p & + & 1 \\ \end{matrix}}$

_____________

${\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ 6{{p}^2} & + & 5p & {} & {} \\ \end{matrix}}{\begin{matrix}6{{p}^2} & + & 11p & + & 5 \\ \end{matrix}}}$$$

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Stolb23 [73]

Answer:

Step-by-step explanation:

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The mean for a month is, $\lambda = \frac{1}{3}$ per month

$E[N(t)]= \lambda t\\\\=\frac{1}{3}(24)\\\\=8$

(Here. t = 24)

For Poisson process mean and variance are same,

$Var[N (t)]= Var[N(24)]\\= E [N (24)]\\=8$

(Poisson distribution mean and variance equal)

The standard deviation of the number of planets is,

$\sigma( 24 )] =\sqrt{Var[ N(24)]}=\sqrt{8}= 2.828$

For the Poisson process the intervals between events(finding a new planet) have independent exponential distribution with parameter $\lambda$ . The sum of $K$ of these independent exponential has distribution Gamma $(K, \lambda)$ .

From the given information, $k = 6$ and $\lambda =\frac{1}{3}$

Calculate the expected value.

$E(x)=\frac{\alpha}{\beta}\\\\=\frac{K}{\lambda}\\\\=\frac{6}{\frac{1}{3}}\\\\=18$

(Here, $\alpha =k$ and $\beta=\lambda$ )

Calculate the probability that she will become eligible for the prize within one year.

Here, 1 year is equal to 12 months.

P(X ≤ 12) = (1/Г (k)λ^k)(x)^(k-1).(e)^(-x/λ)

$=\frac{1}{Г (6)(\frac{1}{3})^6}(12)^{6-1}e^{-36}\\\\=0.2148696\\=0.2419\\=21.49%$

Hence, the required probability is 0.2149 or 21.49%

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3 years ago

Which of the following numbers are greater than or equal to 4/7? Is it 2/5, 0.57, or 2/3. Use explanation why.

Sergeeva-Olga [200]

Answer:

2/3

Step-by-step explanation:

2/5=0.4 and 4/7=0.571428

0.57<0.571428

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2/3=0.6667

which is greater than or equal to 4/7

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3 years ago

I am a multiple of 3 and 5. the sum of my digits is 9. what number am I?

iVinArrow [24]

Answer:

The answer is 45.

Step-by-step explanation:

This number is a multiple of 3 and 5, since it is divisible by both of these numbers.

4 + 5 equals 9, which is what it means by the sum of it's digits.

I hope this helps!

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3 years ago

What is 5% of $30? $150 $35 $1.50 $25

fomenos

Answer:

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Step-by-step explanation:

5% of 30 is 1.5 AKA 1.50

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3 years ago

Read 2 more answers

Water pours into a tank at the rate of 2000 cm3/min. The tank is cylindrical with radius 2 meters. How fast is the height of wat

Gennadij [26K]

Volume of water in the tank:

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(The question asks how the height changes at the exact moment the height is 50 cm, but this info is a red herring because the rate of change is constant.)

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3 years ago