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3 years ago

Write sin 33° in terms of cosine

Mathematics

2 answers:

ycow [4]3 years ago

4 0

Answer: $\sin 33^\circ=\cos 57^\circ.$

Step-by-step explanation: We are given to write sin 33° in terms of cosine.

We know that

The sine of any acute angle is equal to the cosine of its complement.

Now, the complement of an acute angle with measurement 33° is given by

$90^\circ-33^\circ=57^\circ.$

Therefore, the sine of an angle with measurement 33° is equal to the cosine of an angle with measurement 57°.

Thus, we can write as follows :

$\sin 33^\circ=\cos 57^\circ.$

Hence, $\sin 33^\circ=\cos 57^\circ.$

Greeley [361]3 years ago

3 0

Cos 57 it has to add up to 90

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A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.6

Angelina_Jolie [31]

Answer:

Step-by-step explanation:

The null hypothesis is

H0 : μ1 ≤ μ2

The alternative hypothesis is

H1 : μ1 > μ2

a) it is a one-tailed and also a right tailed test

b) The decision rule is the basis on which the null hypothesis is rejected or not. If 0.08 > p value, reject H0. If 0.08 < p value, do not reject H0.

c) Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)

z = (x1 - x2)/√σ1²/n1 + σ2²/n2

Where

x1 and x2 represents sample means

σ1 and σ2 represents population standard deviations

n1 and n2 represents number of samples

From the information given,

x1 = 2.67

x2 = 2.59

σ1 = 0.75

σ2 = 0.66

n1 = 65

n2 = 50

z = (2.67 - 2.59)/√0.75²/65 + 0.66²/50

= 0.08/√0.00865 + 0.008712

z = 0.61

From the normal distribution table, the probability value corresponding to the z score is 0.73

d) If 0.08 > 0.73, we would reject H0

e) the p-value is 0.73

3 0

3 years ago

How do you describe the end behavior of a graph?

timofeeve [1]

Answer:

The end behavior of a function [f] describes the behavior of the graph of the function [f] at the ends of the x-axis.

Step-by-step explanation:

I've done this last year and this is what I can come up with

7 0

1 year ago

Suppose a sample of 972972 tenth graders is drawn. Of the students sampled, 700700 read above the eighth grade level. Using the

max2010maxim [7]

Answer:

The 85% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.259, 0.301).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

972 students, 700 read above the eight grade level. We want the confidence interver for the proportion of those who read at or below the 8th grade level. 972 - 700 = 272, so $n = 972, \pi = \frac{272}{972} = 0.28$

85% confidence level

So $\alpha = 0.15$ , z is the value of Z that has a pvalue of $1 - \frac{0.15}{2} = 0.925$ , so $Z = 1.44$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.28 - 1.44\sqrt{\frac{0.28*0.72}{972}} = 0.259$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.28 + 1.44\sqrt{\frac{0.28*0.72}{972}} = 0.301$

The 85% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.259, 0.301).

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3 years ago

The number of cubic feet of water in a curved container can be approximated by v = 0.95h2.9. use a calculator to find the amount

Sati [7]

The first thing we must do for this case is to rewrite the expression of the volume correctly.
We have then:
v = 0.95 * h ^ 2.9
Substituting the value of h we have:
v = 0.95 * (7.5) ^ 2.9
v = 327.6432831
round to the nearest tenth:
v = 327.6 feet ^ 3
Answer:
the amount of water in the container when h = 7.5 feet is:
v = 327.6 feet ^ 3

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3 years ago

For an F distribution, the number of degrees of freedom for the numerator a. must be larger than the number of degrees of freedo

Alecsey [184]

Answer:

b. can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

Step-by-step explanation:

The distribution of all possible values of the f statistic is called an F distribution with various degree of freedom. For an F distribution, the F statistic is greater than or equal to zero and as the degrees of freedom for the numerator and for the denominator get larger, the curve approximates the normal.

For an F distribution, the number of degrees of freedom for the numerator can be larger, smaller, or equal to the number of degrees of freedom for the denominator.

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3 years ago