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3 years ago

Which sum or difference identity would you use to verify that sin (90° + q) = cos q?

Mathematics

2 answers:

Julli [10]3 years ago

8 0

$\hbox{the sum identity:} \\ \sin(\alpha + \beta)= \sin \alpha \cos \beta + \sin \beta \cos \alpha \\ \\
\sin (90^\circ +q)= \\ \sin 90^\circ \cos q+ \sin q \cos 90^\circ= \\
1 \times \cos q + \sin q \times 0= \\
\cos q$

adell [148]3 years ago

8 0

Answer:

Option B is your answer

Step-by-step explanation:

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Katy buys 4 DVDs every 2 weeks. How many DVDs will she buy in 14 weeks?

Lena [83]

Answer:

Step-by-step explanation:

Every 2 weeks 4 DVDs are purchased, so you have to multiply 14 times two, or 7 by 4. And the answer you get either way is 28.

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3 years ago

How many times must we toss a coin to ensure that a 0.95-confidence interval for the probability of heads on a single toss has l

musickatia [10]

Answer:

(1) 97

(2) 385

(3) 9604

Step-by-step explanation:

The (1 - α) % confidence interval for population proportion is:

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

The margin of error in this interval is:

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

The formula to compute the sample size is:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}$

(1)

Given:

$\hat p = 0.50\\MOE=0.1\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.1^{2}}\\=96.04\\\approx97$

Thus, the minimum sample size required is 97.

(2)

Given:

$\hat p = 0.50\\MOE=0.05\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.05^{2}}\\=384.16\\\approx385$

Thus, the minimum sample size required is 385.

(3)

Given:

$\hat p = 0.50\\MOE=0.01\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.01^{2}}\\=9604$

Thus, the minimum sample size required is 9604.

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3 years ago

8 out of ten (Write each decimal)

Marina86 [1]

Eight out of ten as a fraction = 8/10, as a decimal = 0.8

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3 years ago

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Maksim231197 [3]

Answer:

Step-by-step explanation:

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3 years ago

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sveticcg [70]

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3 years ago

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