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2 years ago

Cos(90 degrees + theta ) = - sin theta , why?

Mathematics

1 answer:

BigorU [14]2 years ago

3 0

Step-by-step explanation:

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

x = theta

y = 90°

cos(90) = 0

sin(90) = 1

cos(x)×0 - sin(x)×1 = - sin(x)

remember slopes of lines ?

and how the coordinates and the slope changed for a perpendicular line ?

the slope is y/x, and for the perpendicular line this turned into -x/y.

the same happens here.

sin(x) and cos(x) are the x and y coordinates of a point on the circle with the angle x to the horizontal axis.

if you add 90° to the angle, you create a perpendicular line or angle, and the coordinates follow the slope rules : cos turns into sin and vice versa, and the sign has to flip.

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For each of the given situations, write out the alternative hypothesis, being sure to state whether it is one-sided or two-s

tekilochka [14]

Answer:

Null hypothesis: $p\leq 0.3$

Alternative hypothesis: $p > 0.3$

Step-by-step explanation:

1) Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

On this case we want to test is $p>0.3$ since we want to check if the new model has improved the warranty rate, we can express it like this:

$p-0.3$ since are equivalent expressions.

And the alternative hypothesis should be the complement:

Null hypothesis: $p\leq 0.3$ or $p=0.3$

So the correct system of hypothesis for this case would be:

Null hypothesis: $p\leq 0.3$

Alternative hypothesis: $p > 0.3$

The alternative way should be:

Null hypothesis: $p = 0.3$

Alternative hypothesis: $p > 0.3$

3 0

3 years ago

What is the rate of decay, as a percent, for the following function? <br> n(x)=7(0.067)^x

Snezhnost [94]

It is 0.067/=0.67/10=6.7/100=6.7%

answer is 6.7%

8 0

3 years ago

Read 2 more answers

Kim rolls a dice and flips a coin

Dmitry [639]

Answer:

Step-by-step explanation:

a) Calculate the probability that she

b) Work out the probability that she

gets an even number and a tail.

Probability is

4 0

3 years ago

At a football match, there were 250 more men than women. The number of children was twice the number of women and the number of

zlopas [31]

Answer:

450 people were at the match

Step-by-step explanation:

So let's make equation :

W = women

M = Men

C = Children

First equation :

M = W + 250

Second equation :

C = 2W

Third equation :

M = 2(W+C)

Let's substitute the second equation into the third :

M = 2(W + 2W)

M = 2W + 4W

M = 6W

Let's substitute this equation into the first one :

6W = W + 250

5W = 250

W = 50

Now we know that that there were 50 women at the match and can substitute this value for the first equation and then the second :

M = 50 + 250

M = 300

This means that there must have been 300 men at the match.

C = 2(50)

C = 100

This means that there must have been 100 children at the match.

Adding all values together gives us :

50 + 300 + 100 =

450 people were at the match

Hope this helped and have a good day

5 0

2 years ago

Please help me on this question!

kirill [66]

-8 to 8

Step-by-step explanation:

f(x) is the same as y when discussing functions. Therefore we look for the places where the line is above or touching the x axis

4 0

3 years ago