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2 years ago

How would the sum of cubes formula be used to factor x3y3 + 343? Explain the process. Do not write the factorization.

2 answers:

4 0

The sum of cubes formula:
a³ + b³ = ( a + b ) ( a² - a b + b² )
x³ y³ = ( x y )³ and 343 = 7³
x³ y³ + 343 = ( x y )³ + 7³ = ( x y + 7 ) ( x² y² - 7 x y + 49 )

olga_2 [115]2 years ago

3 0

To factor, first identify the quantities that are being cubed. The first term is the cube of xy, and the constant is the cube of 7. Next, use the formula to write the factors. The first factor is the sum of xy and 7. The second factor has three terms: the square of xy, the negative of 7xy, and the square of 7.

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lara [203]

Answer:

(a): 46 degrees

(b): 63 degrees

(c): 27 degrees

(d): 60 degrees

Step-by-step explanation:

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2 years ago

A real estate agent has 19 properties that she shows. She feels that there is a 30% chance of selling any one property during a

netineya [11]

Answer:

$P(X \geq 5)=1-P(X$

We can find the individual probabilities:

$P(X=0)=(19C0)(0.3)^0 (1-0.3)^{19-0}=0.00114$

$P(X=1)=(19C1)(0.3)^1 (1-0.3)^{19-1}=0.0092$

$P(X=2)=(19C2)(0.3)^2 (1-0.3)^{19-2}=0.0358$

$P(X=3)=(19C3)(0.3)^3 (1-0.3)^{19-3}=0.0869$

$P(X=4)=(19C4)(0.3)^4 (1-0.3)^{19-4}=0.1491$

And replacing we got:

$P(X \geq 5) = 1-[0.00114+0.009282+0.0358+0.0869+0.149]= 0.7178$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=19, p=0.3)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X \geq 5)$

And we can use the complement rule:

$P(X \geq 5)=1-P(X$

We can find the individual probabilities:

$P(X=0)=(19C0)(0.3)^0 (1-0.3)^{19-0}=0.00114$

$P(X=1)=(19C1)(0.3)^1 (1-0.3)^{19-1}=0.0092$

$P(X=2)=(19C2)(0.3)^2 (1-0.3)^{19-2}=0.0358$

$P(X=3)=(19C3)(0.3)^3 (1-0.3)^{19-3}=0.0869$

$P(X=4)=(19C4)(0.3)^4 (1-0.3)^{19-4}=0.1491$

And replacing we got:

$P(X \geq 5) = 1-[0.00114+0.009282+0.0358+0.0869+0.149]= 0.7178$

4 0

3 years ago

Four members from a 45-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and

wariber [46]

Answer:

3575880

Step-by-step explanation:

We need to use Permutation method,

$nPr= \frac{n!}{(n-r)!}$

Where n is the sample of size and r the combination considered, so

$n=45\\r=4\\45P4= \frac{45!}{(45-4)!}\\45P4 = 3575880$

There is 3575880 possibilities to make leadership structures in that committee

6 0

3 years ago

The dot plot below shows the number of items in the basket of some shoppers:

scoray [572]

Answer:

The correct answer is A.

Remember summetric means: made up of exactly similar parts facing each other or around an axis; symmetrical. And the peak or highest part is on the 3.

Hope it helps!!

7 0

2 years ago

Read 2 more answers

A rectangular field is two times as long as it is wide. If the perimeter of the field is 450 feet, what are the dimensions of th

lys-0071 [83]

Hi There,

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

We Know:

Total Perimeter = 450 feet

Length is 2 times the width.

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

Solution:

Length = 150

Width = 75

75 x 2 = 150

150 + 150 + 75 + 75 = 450

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

Answer:

Length = 150 feet.

Width = 75 feet.

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

Hope This Helps :)

5 0

3 years ago