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4 years ago

Simplify (8y)(-3y^2)

Mathematics

2 answers:

podryga [215]4 years ago

8 0

Answer:

$- 24 {y}^{3}$

Step-by-step explanation:

$(8y)( - 3 {y}^{2} )$

$= 8( - 3) {y}^{2} y$

$= - 24 {y}^{2 + 1}$

$= - 24 {y}^{3}$

Ainat [17]4 years ago

3 0

Good evening ,

______

Answer:

-24y⁴

___________________

Step-by-step explanation:

(8y)(-3y^2) = (8y)(-3y²) = -3×8×(y)×y³ = -24y⁴

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URGENT! WILL GIVE BRAINLIEST!!

IgorC [24]

Answer:

Option C) $a_{n}=m-b+m(n-1)$ for $n={\{1,2,3,...}\}$ is not the correct way to define the given infinite sequence

${\{m+b,2m+b,3m+b,4m+b,...}\}$

Step-by-step explanation:

Given infinite sequence is ${\{m+b,2m+b,3m+b,4m+b,...}\}$

Option B) $a_{n}=m-b+m(n-1)$ for $n={\{1,2,3,...}\}$ is not the correct way to define the given infinite sequence ${\{m+b,2m+b,3m+b,4m+b,...}\}$

Now verify $a_{n}=m-b+m(n-1)$ for $n={\{1,2,3,...}\}$ is true for the given infinite sequence

That is put n=1,2,3,.. in the above function

$a_{n}=m-b+m(n-1)$

When n=1, $a_{1}=m-b+m(1-1)$

$=m-b+0$

$a_{1}=m-b\neq m+b$

When n=2, $a_{2}=m-b+m(2-1)$

$=m-b+m$

$a_{2}=2m-b\neq 2m+b$

When n=3, $a_{3}=m-b+m(3-1)$

$=m-b+2m$

$a_{3}=3m-b\neq 3m+b$

and so on.

Therfore $a_{n}=m-b+m(n-1)$ for $n={\{1,2,3,...}\}$ is not the correct way to define the given infinite sequence

${\{m+b,2m+b,3m+b,4m+b,...}\}$

Therefore option C) is correct

5 0

4 years ago

What are the solutions to the system of equations graphed below?

zalisa [80]

Answer:

D.(2,0) and (0,-4)

Step-by-step explanation:

A P E X approved.

4 0

3 years ago

Geologist has collected 10 specimens of basaltic rock and 10th specimens of granite. The geologist instructs a laboratory assist

olya-2409 [2.1K]

Answer:

$p(5)=0.00136$

(a) $p(x)=\frac{(10Cx)*((10)C(15-x))}{20C10}$

(b) $p(10)+p(5)=0.00272$

Step-by-step explanation:

If we have N elements with k elements that we consider success and N-k elements that we consider fail, and we take a sample of n elements, the probability that there are x successes in the sample follows a hypergeometric distribution, so it is calculated as:

$p(x)=\frac{(kCx)*((N-k)C(n-x))}{NCn}$

In this case, N is equal to 20, k is equal to 10 specimens of granite rock, N-k is equal to 10 specimens of basaltic rock and n is 15. So, the probability that there are x specimens of granite rock in the sample or the pmf of the number of granite specimens selected for analysis is:

$p(x)=\frac{(10Cx)*((10)C(15-x))}{20C10}$

Now, the probability of getting exactly 5 granite specimens selected for analysis is:

$p(5)=\frac{(10C5)*((10)C(15-5))}{20C10}=0.00136$

On the other hand, the probability that all specimens of one of the two types of rock are selected for analysis is the probability to select 10 granite specimens or 10 basaltic specimens. Where the probability to take 10 basaltic specimens is equal to the probability to take 5 granite specimens.

Then, the probability that all specimens of one of the two types of rock are selected for analysis is:

$p(10)+p(5)=\frac{(10C10)*((10)C(15-10))}{20C10}+\frac{(10C5)*((10)C(15-5))}{20C10}\\p(10)+p(5)=0.00136+0.00136=0.00272$

For the hypergeometric distribution, the mean E(x) and standard deviation S(x) are:

$E(x)=\frac{nk}{N}=\frac{15*10}{20}=7.5\\S(x)=\sqrt{\frac{nk}{N}*(1-\frac{k}{N})*(\frac{N-n}{N-1})}\\S(x)=\sqrt{\frac{15*10}{20}*(1-\frac{10}{20})*(\frac{20-15}{20-1})}=0.9934$