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3 years ago

Which trigonometric ratios are correct for triangle DEF?

Mathematics

1 answer:

ziro4ka [17]3 years ago

3 0

Sin(D) = 24/25
tan(D) = 24/7
sin(E) = 7/25

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8 ^ x * 16 ^ x - 1 equals 1

Lana71 [14]

Answer:

${8}^{x} \times {16}^{x } - 1 = 1 \\ {2}^{3x} \times {2}^{4x} = 1 + 1 \\ {2}^{7x} = {2}^{1} \\ 7x = 1 \\ x = \frac{1}{7}$

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2 years ago

The temperature in Vancouver is -8ºC, in Montreal it is -4ºC , in Seattle it is -6ºC, and in Buffalo it is -10ºC. Which city is

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3 years ago

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2 years ago

25 10^6 in standard form

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3 years ago

The sodium content of a popular sports drink is listed as 200 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sample me

julia-pushkina [17]

Answer:

The sample does not contradicts the manufacturer's claim.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 200 mg

Sample mean, $\bar{x}$ = 211.5 mg

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = 18.5 mg

a) First, we design the null and the alternate hypothesis for a two tailed test

$H_{0}: \mu = 200\\H_A: \mu \neq 200$

We use Two-tailed t test to perform this hypothesis.

b) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$ Putting all the values, we have

$t_{stat} = \displaystyle\frac{211.5 - 200}{\frac{18.5}{\sqrt{20}} } = 2.7799$

c) Now,

$t_{critical} \text{ at 0.05 level of significance, 19 degree of freedom } = \pm 2.0930$

Since, the calculated t-statistic does not lie in the range of the acceptance region(-2.0930,2.0930), we reject the null hypothesis.

Thus, the sample does not contradicts the manufacturer's claim.

d) P-value = 0.011934

Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis.

Yes, both approach the critical value and the p-value approach gave the same results.

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3 years ago