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3 years ago

Find the 2nd term in the expansion of (a + b)^7 in simplest form

Mathematics

1 answer:

klasskru [66]3 years ago

5 0

Answer:

7a^6b

Step-by-step explanation:

Using the pascal triangle to do this binomial expansion, we find out that the coefficient is 7. The a variables start at the power to which you are expanding and reduce by 1 for every consecutive term. The b variables start at the power of 0 and increase by 1 for every consecutive term. Using this information, we find out that the second term in the binomial expansion (a+b)^7 is 7a^6b

Note that the power of b in the second term is b^1 which is the same as b

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Jenny reaches the corner to clear away spider webs from the room. She is holding the 5 foot pole at top of head level from 45. S

Slav-nsk [51]

Answer:

Height of ceiling = 9.04ft

Step-by-step explanation:

Given:

Length of pole = 5ft

Horizontal angle = $45^{0}$

Jenny's height = 5ft6in = 5ft + (6/12)ft= 5ft + 0.5ft

Jenny's height = 5.5ft

From the attached diagram, we have that

$sin45^{0}= \frac{b}{5}\\ \\b = sin45^{0}*5=0.7071*5\\\\b=3.5355ft$

b ≅ 3.54ft

Height of ceiling = Height of Jenny + b

Height of ceiling = 5.5ft + 3.54ft

Height of ceiling = 9.04ft

7 0

3 years ago

Three teachers handed out math and science textbooks for their classes two teachers had 21 students each and the last teacher ha

Tanya [424]

Answer:

64 textbooks

Step-by-step explanation:

the first two teachers had 21 students each that's 21+21=42

the other teacher had 22 students so apparently all the textbooks handed to the students are,21+21+22=64

8 0

2 years ago

Solve the following equation for F.<br> 2g=n+1/5tf

IceJOKER [234]

9514 1404 393

Answer:

f = 5(2g -n)/t

Step-by-step explanation:

6 0

3 years ago

Find the area of the polygon.

KATRIN_1 [288]

Answer:

8.75 mi

Step-by-step explanation:

well it was quite simple. break the problem into more smaller problems then add when solved

5 0

3 years ago

52. In exploring possible sites for a convenience store in a large neighborhood, the retail chain wants to know the proportion o

kvasek [131]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.1}{1.96})^2}=96.04$

Then the minimum sample size in order to satisfy the condition of 0.1 for the margin of error is 97 and since the sample used is n =100 we can conclude that is sufficient and the best answer would be:

D. Yes.

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. We know that we require a 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

We want a margin of error of $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have prior info for the population proportion we can use as estimator the value of 0.5. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.1}{1.96})^2}=96.04$

D. Yes.

4 0

3 years ago