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3 years ago

Find all solutions in the interval [0, 2π). sec2 x - 2 = tan2 x PLZ HELP!!!

1 answer:

4 0

The equation is equivalent to 1/cos(2x)-2=sin(2x)/cos(2x).
Make the denominator cos(2x) for all terms, we get
1-2cos(2x)=sin(2x).
Since cos^2(2x)+sin^2(2x)=1,
let cos(2x)=a,
substitute sin(2x) by
+-\sqrt(1-a^2),
and solve the equation with only one variable a.
We get a=4/5 or 0,
but cos(2x) cannot be 0,
otherwise sec(2x) is undefined.
2x=36.9 degrees,
so x=18.9 degrees
in radians we have
x=(18.9/180)*pi=0.33
answer
0.33 (it is between [0, 2π))

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A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored

pickupchik [31]

Answer:

We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.

Step-by-step explanation:

The complete question is: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:

Number sampled: 1,000 (republican) , 800 (democrats)

Number in favor: 200 (republican) , 168 (democrats)

At the 0.02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.

Let $p_1$ = proportion of Republicans in favor of lowering the standards.

$p_2$ = proportion of Democrats in favor of lowering the standards.

SO, Null Hypothesis, $H_0$ : $p_1 \geq p_2$ {means that there is an equal or larger proportion of Republicans in favor of lowering the standards}

Alternate Hypothesis, $H_A$ : $p_1 < p_2$ {means that there is a larger proportion of Democrats in favor of lowering the standards}

The test statistics that would be used here Two-sample z-test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of Republicans in favor of lowering the standards = $\frac{200}{1000}$ = 0.20

$\hat p_2$ = sample proportion of Democrats in favor of lowering the standards = $\frac{168}{800}$ = 0.21

$n_1$ = sample of Republicans = 1000

$n_2$ = sample of Democrats = 800

So, the test statistics = $\frac{(0.20-0.21)-(0)}{\sqrt{\frac{0.20(1-0.20)}{1000}+\frac{0.21(1-0.21)}{800} } }$

= -0.52

The value of z test statistics is -0.52.

Now, P-value of the test statistics is given by the following formula;

P-value = P(Z < -0.52) = 1 - P(Z $\leq$ 0.52)

= 1 - 0.6985 = 0.3015

Now, at 0.02 significance level, the z table gives a critical value of -2.054 for left-tailed test.

Since our test statistic is more than the critical value of z as -0.52 > -2.054, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.

7 0

3 years ago

In order to test whether the average waiting time this year differs from last year, a sample of 25 data were collected this year

irina [24]

Answer:

True

Step-by-step explanation:

Confidence interval for banking service in a given confidence level can be calculated as M±ME where

M is the mean banking service in the sample and
ME is the Margin of Error

margin of error (ME) is calculated using the formula

ME= $\frac{t*s}{\sqrt{N} }$ where

t is the corresponding statistic in the given confidence level

s is the standard deviation of the sample(or of the population if it is known)

N is the sample size

t-statistic for 99% confidence level is always bigger than 95% confidence level which makes Margin of Error bigger and thus confidence interval wider.

6 0

4 years ago

A club offers me membership for a fee of 20$ plus a monthly fee of 18 b club offers a fee of 14$ and a monthly fee of 20 after h

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Answer:

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Step-by-step explanation:

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3 years ago

9 times the quantity of 12 less than a number x is 24. Write in an algebraic expression.

kiruha [24]

Answer:

9(x-12)=24

Step-by-step explanation:

5 0

3 years ago

Write a rule for each pattern. Then use your rule to find the next two terms in the pattern. The numbers are: 1, 3, 6, 10, 15, 2

Leya [2.2K]

Triangular Number Sequence

This is the Triangular Number Sequence:

1, 3, 6, 10, 15, 21, 28, 36, 45, ...

This sequence comes from a pattern of dots that form a triangle:

By adding another row of dots and counting all the dots we can
find the next number of the sequence.

A Rule

We can make a "Rule" so we can calculate any triangular number.

First, rearrange the dots (and give each pattern a number n), like this:

Then double the number of dots, and form them into a rectangle:

The rectangles are n high and n+1 wideand xn is how many dots in the triangle (the value of the Triangular Number n)

And we get (remembering we doubled the dots):

2xn = n(n+1)xn = n(n+1)/2

Rule: xn = n(n+1)/2

Example: the 5th Triangular Number is

x5 = 5(5+1)/2 = 15

Example: the 60th is

x60 = 60(60+1)/2 = 1830

Wasn't it much easier to use the formula than to add up all those dots?

5 0

4 years ago

Read 2 more answers