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3 years ago

11

___ cosb =1/2 sin(a+b)+sin(a-b)?

2 answers:

vodomira [7]3 years ago

8 0

Answer:

That would be sina.

Step-by-step explanation:

sin(a+b) = sinacosb + cosasinb

sin(a-b) = sinacosb - cosasinb

Adding we get sin(a+b) + sin(a-b) = 2sinaccosb

so sinacosb = 1/2sin(a+b) + sin(a-b)

dem82 [27]3 years ago

6 0

Answer:

sina

Step-by-step explanation:

We have

sin(a+b) = sina cosb + cosa sinb ---------------------eqn 1

sin(a-b) = sina cosb - cosa sinb ---------------------eqn 2

eqn 1 + eqn 2

sin(a+b) + sin(a-b) = sina cosb + cosa sinb + sina cosb - cosa sinb

sin(a+b) + sin(a-b) = 2sina cosb

$sina\times cosb =\frac{1}{2}(sin(a+b) + sin(a-b))$

So answer is sina

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Three more than the quotient of a number and 4 is equal to 8

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3+ x/4=8

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3 years ago

26. Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics

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The test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

<h3>What are null hypotheses and alternative hypotheses?</h3>

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

Students who take a statistics course are given a pre-test on the concepts and skills for the first chapter of a statistics course.

Then they are given a post-test once the professor has concluded lecturing on the material.

Pre-test and post-test scores for 4 students in an elementary statistics class are given below.

Then we have

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Then the null hypotheses and alternative hypotheses will be

H₀: $\mu _d = 0$

Hₐ: $\mu _d > 0$

Then the test statistic will be

$\rm \overline{x} _d = \dfrac{\Sigma x_d}{n} = \dfrac{15+12+10+1}{4}\\\\\overline{x} _d = 9.5$

Then

$\rm S_d = 6.02$

The test statistic value is given by

$\rm t = \dfrac{\overline{x} _d }{\dfrac{S_d}{\sqrtn}} \\\\t = \dfrac{9.5}{\dfrac{6.02}{\sqrt4}}\\\\t = 3.16$

Since this is a right-tailed test, so the critical value is given by

$\rm t_{n-1}(\alpha ) = t_3 (0.05) = 2.353$

Since the test statistic value lies to the right of the critical value. So we have sufficient evidence to reject the null hypothesis.

Hence, we can conclude that $\mu _d > 0$ that is test scores have improved.

More about the null hypotheses and alternative hypotheses link is given below.

brainly.com/question/9504281

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7 0

2 years ago

Write the standard equation of the circle with the given center and passes through the given point. Center (7,-2); Point= (1,-6)

vodomira [7]

Answer:

(x - 7)² + (y + 2)² = (2√13)²

Step-by-step explanation:

We already know that the center is at (7, -2), but must find the radius. The radius is the distance between the points (7, -2) and (1, -6):

r = √ [6² + 4²] ) = √(36 + 16) = √52 = √4√13 = 2√13.

Then the desired equation is (x - 7)² + (y + 2)² = (2√13)²

6 0

3 years ago

The 2nd term of an exponential sequence is 9 while the 4th term is 81.find the common ratio,the first term and the sum of the fi

Thepotemich [5.8K]

Answer:

second term: 9

4th term:81

$(3rd \: term)^{2} = 9 \times 81$

=729

$\sqrt{729} = 27$

3rd term=27

${9}^{2} = a1x27 \\ 81 = 27a1$

a1=3 the first term

$81 = 3 \times {q}^{3}$

${q}^{3} = 27$

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3 years ago

HELPP PLEASE!!!!!!<br> (Will give 15 points for right Answer)!!!!

VMariaS [17]

Answer:

12

Step-by-step explanation:

The parallel sides must be the same length.

2x-6 = x+3

2x-x-6-3 = 0

x - 9 = 0

x = 9

x + 3 and 2x - 6 are both 12

8 0

3 years ago