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3 years ago

(b) Expand (4 + x)½ up to the forth term using the binomial expansion

Mathematics

1 answer:

Serga [27]3 years ago

4 0

Answer:

2±1\2x

Step-by-step explanation:

[4±x]1\2

we will start by opening the brackets

[4]1\2=2

[x]1\2=1\2x

2±1\2x

hope am right

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A pole casts a 6-foot shadow. If the distance from the top of the pole to the tip of the shadow is

KATRIN_1 [288]

Answer:

8feet high

Step-by-step explanation:

To get the height of the pole, we will use the pythagoras theorem. Let H be the height

H² = 10² -6²

H² = 100 - 36

H² = 64

H = √64

H = 8feet

Hence the pole is 8feet high

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2 years ago

1. (5pt) In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also,

gladu [14]

Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

$\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988$

The combined proportion is:

$\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989$

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

$Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$

$=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78$

Compute the p-value as follows:

$p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075$

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

$=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\$

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

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(b) Expand (4 + x)½ up to the forth term using the binomial expansion​

(b) Expand (4 + x)½ up to the forth term using the binomial expansion