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3 years ago

Use the Binomial Theorem to expand each binomial (5x-4y)^3

1 answer:

5 0

You should know that:

(a+b)(a+b)(a+b)

=a(a+b)(a+b)+b(a+b)(a+b)

=a(a²+2ab+b²)+b(a²+2ab+b²)

=a³+2a²b+ab²+a²b+2ab²+b³

=a³+3a²b+3ab²+b³

-----------------

If a=5x and b=-4y

(5x+(-4y))³

=(5x-4y)³

=(5x)³+3(5x)²(-4y)+3(5x)(-4y)²+(-4y)³

=125x³+3(25x²)(-4y)+15x(16y²)-64y³

=125x³+75x²(-4y)+240xy²-64y³

=125x³-300x²y+240xy²-64y³

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The population of bacteria in a petri dish doubles every 24 h. The population of the bacteria is initially 500 organisms. How lo

liberstina [14]

Answer:

16.34 hours

Step-by-step explanation:

According to the given information we can see that the case is of exponential growth

Hence, we will use the formula

$A=P(2)^\frac{t}{24}$

Here A =800 is the amount that is needed to reach

P is the initial amount that is 500

We have to find the time it will take to reach 800 that is we need to find t

On substituting the values in the formula we get

$800=500(2)^\frac{t}{24}$

On simplification we get

$\Rightarrow\frac{8}{5}=(2)^\frac{t}{24}$

Taking log on both sides we get

$\Rightarrow\log\frac{8}{5}=\log(2)^\frac{t}{24}$

using $\log\frac{m}{n}=\log m-\log n$

And $\log a^m=m\log a$

$\Rightarrow\log{8}-\log{5}=\frac{t}{24}\log2$

Now substituting values of log 8=0.903, log 5=0.698 and log 2=0.301 we get

$\Rightarrow 0.903-0.698=\frac{t}{24}0.301$

$\Rightarrow 0.205=\frac{t}{24}0.301$

$\Rightarrow \frac{0.205}{0.301}\cdot 24=t$

$\Rightarrow t=16.34$

8 0

3 years ago

Read 2 more answers

The vertex angle of an isosceles triangle measure 40.whats the measure of the base angle?

Eddi Din [679]

I don't know if my answer is completely correct, but I think it's 100. All triangles add up to 180, and an isosceles triangle has 2 equal sides. 40 would be the 2 sides, and 180 subtracted from 80 equals 100.

7 0

3 years ago

Read 2 more answers

A hat contains marbles. Of them, are red and are green. If one marble is randomly selected out of this hat, what is the probabil

maksim [4K]

Answer:

Step-by-step explanation:

4 0

3 years ago

What exponent goes with the area of a triangle

user100 [1]

Answer:

its just 1/2 times base times height

Step-by-step explanation:

7 0

3 years ago

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Nu

Tasya [4]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Answer:

a. Cumulative Probability Distribution

Grade P(X ≤ x)

F 0.145

D 0.310

C 0.670

B 0.910

A 1

b. P(at least B) = 0.330

c. P(pass) = 0.855

Step-by-step explanation:

Professor Sanchez has been teaching Principles of Economics for over 25 years.

He uses the following scale for grading.

Grade Numerical Score Probability

A 4 0.090

B 3 0.240

C 2 0.360

D 1 0.165

F 0 0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

The cumulative probability distribution is given by

Grade = F

P(X ≤ x) = 0.145

Grade = D

P(X ≤ x) = 0.145 + 0.165 = 0.310

Grade = C

P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670

Grade = B

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910

Grade = A

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1

Cumulative Probability Distribution

Grade P(X ≤ x)

F 0.145

D 0.310

C 0.670

B 0.910

A 1

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

At least B means equal to B or greater than B grade.

P(at least B) = P(B) + P(A)

P(at least B) = 0.240 + 0.090

P(at least B) = 0.330

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Passing the course means getting a grade of A, B, C or D

P(pass) = P(A) + P(B) + P(C) + P(D)

P(pass) = 0.090 + 0.240 + 0.360 + 0.165

P(pass) = 0.855

Alternatively,

P(pass) = 1 - P(F)

P(pass) = 1 - 0.145

P(pass) = 0.855

4 0

2 years ago