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Ira Lisetskai [31]
3 years ago
7

Θ lies in Quadrant II . sinθ=47sinθ=47 What is the exact value of cosθ in simplified form?

Mathematics
1 answer:
Pepsi [2]3 years ago
4 0
I am assuming you mean 4/7 as the sine or cosine cannot be higher than 1.

Lets find <span>θ,
</span>
θ = [sin-1](4/7) = 34.85 °

But lets take into account that this value is the equivalent in Quadrant I.

If Θ lies in Quadrant II , then θ = 180 ° - 34.85 ° = 145.15 °

So cosθ = cos (145.15) = -0.821
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A. Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far
defon

Answer: The addition of the new point alters the previous standard deviation greatly

Step-by-step explanation:

Let the initial five points be : 2 3 4 5 and 6. In order to calculate the standard deviation for this data, we will need to calculate the mean first.

Mean = summation of scores/number of scores.

The mean is therefore: (2+3+4+5+6)/5 = 20/5 = 4.

We'll also need the sum of the squares of the deviations of the mean from all the scores.

Since mean = 4, deviation of the mean from the score "2" = score(2) - mean (4)

For score 3, it is -1

For 4, it's 0

For 5 it's 1

For 6 it's 2.

The squares for -2, -1, 0, 1, and 2 respectively will be 4, 1 , 0, 1, 4. Summing them up we have 10 i.e (4+1+0+1+4=10).

Calculating the standard deviation, we apply the formula:

√(summation of (x - deviation of mean)^2)/N

Where N means the number of scores.

The standard deviation = √(10/5) = 1.4142

If we add another score or point that is far away from the original points, say 40, what happens to the standard deviation. Let's calculate to find out.

i.e we now have scores: 2, 3, 4, 5, 6 and 40

We calculate by undergoing same steps.

Firstly mean. The new mean = (2+3+4+5+6+40)/6 = 60/6 = 10.

The mean deviations for the scores : 2, 3, 4, 5, 6 and 40 are -8, -7, -6, -5, -4 and 30 respectively. The squares of these deviations are also 64, 49, 36, 25, 16 and 900 respectively as well. Their sum will then be 1090. i.e. (64+49+36+25+16+900 = 1090).

The new standard deviation is then=

√(1090/6)

= √181.67

= 13.478.

It's clear that the addition of a point that's far away from the original points greatly alters the size of the standard deviation as seen /witnessed in this particular instance where the standard deviation rises from 1.412 to 13.478

7 0
2 years ago
Kristy makes 5$ per hour babysitting and 12$ per hour giving music lessons. One weekend, she worked a total of 18 hours and made
MariettaO [177]
Let Karen works x hours baby sitting
So, she worked (18-x) hours giving music lessons
So,
According to question
5x + 12(18-x)=139
This gives
7*x=77
x=11
So,
<span>Karen worked <em>11 hours baby sitting </em>and (18-11)=7 hours giving music lessons</span>
3 0
3 years ago
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Just took the test on Edg.

Step-by-step explanation:

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a

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