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3 years ago

Find the binomial coefficient (4 2)

1 answer:

5 0

$\large\begin{array}{l} \mathsf{\dbinom{4}{2}=\dfrac{4!}{2!\cdot (4-2)!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4!}{2!\cdot 2!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4\cdot 3 \cdot \diagup\!\!\!\! 2!}{2!\cdot \diagup\!\!\!\! 2!}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{4\cdot 3}{2\cdot 1}}\\\\ \mathsf{\dbinom{4}{2}=\dfrac{12}{2}}\\\\ \boxed{\begin{array}{c}\mathsf{\dbinom{4}{2}=6}\end{array}}\quad\longleftarrow\quad\textsf{this is the answer.} \end{array}$

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A rectangle has a height of t^2+7t+6t

jek_recluse [69]

Answer:

$2t^3+15t^2+19t+6$

Step-by-step explanation:

Height of the Rectangle $=t^2+7t+6$

Width of the Rectangle $=2t+1$

Area of the Rectangle = Height X Width

$=(2t+1)(t^2+7t+6)\\=2t(t^2+7t+6)+1(t^2+7t+6)\\=2t^3+14t^2+12t+t^2+7t+6\\$Collect like terms\\=2t^3+14t^2+t^2+12t+7t+6\\Area=2t^3+15t^2+19t+6\\$

The area of the rectangle is $2t^3+15t^2+19t+6$

4 0

3 years ago

The mean annual premium for automobile insurance in the United States is $1503 (Insure website, March 6, 2014). Being from Penns

romanna [79]

Answer:

If we compare the p value and the significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean annual premium in Pennsylvania is significantly lower than the national mean annual premium of 1503 at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=1440$ represent the mean annual premium value for the sample

$s=165$ represent the sample standard deviation for the sample

$n=25$ sample size

$\mu_o =1503$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean annual premium in Pennsylvania is lower than the national mean annual premium, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1503$

Alternative hypothesis: $\mu < 1503$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{1440-1503}{\frac{165}{\sqrt{25}}}=-1.909$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=25-1=24$

Since is a one side left tailed test the p value would be:

$p_v =P(t_{(24)}$

Conclusion

7 0

3 years ago

Reina and Sam are multiplying (8^4)^5 (7^3)^9<br><br> Is either of them correct?

PilotLPTM [1.2K]

Answer:

Sam is correct.

Step-by-step explanation:

Exponent rules state that when an number with an exponent is raised to a power, the two exponents multiply. For example, a^2^2=a^4.

6 0

3 years ago

I need help ASAP!!!!

nydimaria [60]

Answer:

17. is 20 18. is 9hours 19. is 60mph

you get this by doing 100 divided by 5 which equals 20 360 divided by 40=9 and 420 divided by 7 =60

5 0

3 years ago

Simplify this answer <br><br> please help!

aliya0001 [1]

Answer:

(hope this helps can I pls have brainlist (crown) ☺️)

Step-by-step explanation:

7^8 x 7^3 x 7^4 / 7^9 7^5

= 7^(8+3+4) / 7^(9+5)

= 7^15 / 7^14

= 7^(15-14)

= 7.

When the bases of the numbers are the same when multiplying numbers with exponents, you can just add the exponents like so:

7^8 x 7^3 x 7^4= 7^15

Now, look at the rest of the simplified equation and do the same to the denominator:

7^15 / 7^9 x 7^5 ⇒ 7^15/ 7^14

When the bases are the same in the fraction, you are allowed to subtract the exponents. This will lead you to the simplified answer = 7^15-14 = 7^1 = 7

5 0

2 years ago