Enter the coordinates of the
point on the unit circle at the
given angle.
-135°
Type + or -
V2
[? ]
2
12
>
2
![Enter The Coordinates Of Thepoint On The Unit Circle At Thegiven Angle.-135Type + Or -V2[? ]212>2](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/smrCmfBk6sSe5SxHEZci33UZHKuyhQau.png)
Answers
Answer:
It's just negative, just enter this sign -
Step-by-step explanation:
The coordinates of the point on the unit circle at an angle -135° are [tex](-\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} )[/tex]
What are coordinates of point on the circle?"The coordinates of any point on the circle [tex]x^{2}+ y^{2}= r^{2}[/tex] are [tex](r~cos\theta,r~sin\theta)[/tex]"
Formula of sin(A ± B)sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
Formula of cos(A - B)cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
For given question,
We need to find the coordinates of the point on the unit circle at an angle -135°
We know, for unit circle radius = 1
So, the coordinates of any point on the unit circle would be [tex](cos\theta, sin\theta)[/tex]
Here, [tex]\theta=-135^{\circ}[/tex]
Now, we find the the value of [tex]sin(-135^{\circ}),~cos(-135^{\circ})[/tex]
[tex]sin(-135^{\circ})\\\\=-sin(135^{\circ})\\\\=-sin(180^{\circ}-45^{\circ})\\\\=-[sin(180^{\circ})cos(45^{\circ})-cos(180^{\circ})sin(45^{\circ})]\\\\=-[0\times \frac{1}{\sqrt{2} }-(-1)\times \frac{1}{\sqrt{2} } ]\\\\=-(0+\frac{1}{\sqrt{2} } )\\\\=-\frac{1}{\sqrt{2} }\\\\=-\frac{1\times \sqrt{2} }{\sqrt{2} \times \sqrt{2} }\\\\=-\frac{\sqrt{2} }{2}[/tex]
and cos(-135°) would be,
[tex]cos(-135^{\circ})\\\\=cos(135^{\circ})\\\\=cos(180^{\circ}-45^{\circ})\\\\=cos(180^{\circ})sin(45^{\circ})+sin(180^{\circ})sin(45^{\circ})\\\\=((-1)\times \frac{1}{\sqrt{2}} )+(0\times \frac{1}{\sqrt{2} }) \\\\=-\frac{1}{\sqrt{2} }+0\\\\ =-\frac{1}{\sqrt{2}}\\\\=-\frac{1\times \sqrt{2} }{\sqrt{2}\times \sqrt{2}}\\\\=-\frac{\sqrt{2} }{2}[/tex]
Therefore, the coordinates of the point on the unit circle at an angle -135° are [tex](-\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} )[/tex]
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Answer:
B. {2, 5, 6, 9}
Step-by-step explanation:
Mean: the sum of all numbers divided by the amount of numbers.
Median: The number between the two middle numbers
-------------------------------------------------------------------------------------------------
Mean: {2 + 5 + 6 + 9} = 22 ÷ 4 = 5.5.
Median: The median of this data set will be 5.5 because it is in between 5 and 6
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Solve for h.
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Answer:
Step-by-step explanation:
=> h=-341+999
=> h= 658
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Three less than two times a number is 55. What is the number?
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26
step-by-step explanation:
3 - 2n = 55
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Step-by-step explanation:
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Answer:
Solution given:
base of triangle [b]=10in
height of triangle [h]=12in
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[tex]\huge{ \mathcal{ \underline{ Answer }\: \: ✓ }}[/tex]
In the given figure :
[tex] \boxed{ \mathrm{Volume = \dfrac{1}{2} \times 10 \times 12 \times 18}}[/tex]
[tex]1 0\times 12 \times 9[/tex][tex]1080 \: in {}^{3} [/tex]_____________________________
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A roulette wheel has 383838 slots, of which 181818 are red, 181818 are black, and 222 are green. In each round of the game, a ball is tossed in the spinning wheel and lands in a random slot. Suppose we watch 777 rounds of this game, and let RRR represent the number of rounds where the ball lands in a red slot.
Answers
Answer:
Of the 777 rounds of the game in about 368 the ball will land in a red slot.
Step-by-step explanation:
Since a roulette wheel has 383838 slots, of which 181818 are red, 181818 are black, and 222 are green, and in each round of the game, a ball is tossed in the spinning wheel and lands in a random slot, supposing we watch 777 rounds of this game, to determine the approximate number of rounds where the ball lands in a red slot, the following calculation must be performed:
383838 = 100
181818 = X
181818 x 100/383838 = X
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47.3684 = X
47.3684 x 777/100 = X
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Therefore, of the 777 rounds of the game in about 368 the ball will land in a red slot.
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Answer:
C 2 hours
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
Standard Error is increased.
Step-by-step explanation:
Type 2 error is failure to reject a false null hypothesis. This is a 'false negative' result of hypothesis testing, represented by beta 'β'.
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Standard Error increase implies lower level of t statistic , ie = (x - u) / (s / √ n) Lower the t value, higher is the probability of not rejecting null hypothesis, which implies higher chance of type 2 error.
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What is Type I and Type II error?
Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.
The type 1 error occurs if we get false positive conclusion (false positive means we accuse null hypothesis being wrong when it was actually correct).The type 2 error occurs if we get false negative conclusion (false negative means we accept null hypothesis when it was actually false). It is 1 - statistical power of the test. Thus, increasing power of the test decreases this error.How are the type I error and type II error are related to level of significance?The probability of committing the type I error is called the significance level of the hypothesis test.
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Answers
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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dollar?
Answers
Answer:
Robert will have $481 more in his account than Cooper.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Continuous compounding:
Similar to compound interest:
[tex]A(t) = P(1 + r)^t[/tex]
Cooper:
Cooper invested $3,100 in an account paying an interest rate of 2% compounded quarterly. This means that [tex]P = 3100, r = 0.02, n = 4[/tex]
After 12 years is A(12). So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(12) = 3100(1 + \frac{0.02}{4})^{4*12}[/tex]
[tex]A(12) = 3938.5[/tex]
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Robert:
Robert invested $3,100 in an account paying an interest rate of 3 % compounded continuously. So [tex]P = 3100, r = 0.03[/tex].
After 12 years.
[tex]A(t) = P(1 + r)^t[/tex]
[tex]A(12) = 3100(1 + 0.03)^{12}[/tex]
[tex]A(12) = 4419.9[/tex]
Robert will have $4419.9 in his account.
How much more money would Robert have in his account than Cooper, to the nearest dollar?
4419.9 - 3938.5 = 481.4
To the nearest dollar, Robert will have $481 more in his account than Cooper.
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Answer:
Step-by-step explanation:
-37/4
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Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
17 feet
Step-by-step explanation:
a² + b² = c²
a² + 6² = 15²
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a² = 189
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Step-by-step explanation:
Answer:
1 minute and 43 seconds faster
Step-by-step explanation:
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14.5 m
7.3 m
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Answers
Answer:
x= 12.528
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Step-by-step explanation:
7.3 ^2 + x^2 = 14.5^2
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Step-by-step explanation:
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Answers
Answer:
The probability of pulling two of the same types of cookies in a row without replacement is [tex]\frac{51}{105}[/tex].
Step-by-step explanation:
There are a total of 21 * 20 = 420 different outcomes (After you take one cookie out, you aren't replacing it, so there will be 20 cookies in the jar on the second grab). There are a total of 9 * 8 = 72 different combinations of two sugar cookies, and 12 * 11 = 132 different combinations of two snickerdoodle cookies, so the total probability of pulling two of the same types of cookies in a row without replacement is [tex]\frac{132+72}{420} = \frac{204}{420} = \frac{51}{105}[/tex].
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1 pound = 16 ounces
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Answers
Answer:
1
Step-by-step explanation: