<span>
6 Find an exact value. sin 75°
</span>sin(A+B)=sin(A)cos(B)+cos(A)sin<span>(B)
</span>sin(45)=cos(45)=(2^0.5)/2 sin(30)=0.5 cos(30)=(3^0.5)/2
sin(45+30)=sin(45)cos(30)+cos(45)sin(30)=(6^0.5+2^0.5)/4
the answer is the letter d) quantity square root of six plus square root of two divided by four.
<span>
7. Find an exact value. sine of negative eleven pi divided by twelve.
</span>sin(-11pi/12) = -sin(11pi/12) = -sin(pi - pi/12) = -sin(pi/12) = -sin( (pi/6) / 2)
= - sqrt( (1-cos(pi/6) ) / 2) = -sqrt( (1-√3/2) / 2 ) = -(√3-1) / 2√2=(√2-√6)/4
the answer is the letter c) quantity square root of two minus square root of six divided by four.
<span>
8. Write the expression as the sine, cosine, or tangent of an angle. sin 9x cos x - cos 9x sin x
</span>
sin(A−B)=sinAcosB−cosAsinB
sin(9x−x)= sin9xcosx−cos9xsinx= sin(8x)
the answer is the letter c) sin 8x
<span>
9. Write the expression as the sine, cosine, or tangent of an angle. cos 112° cos 45° + sin 112° sin 45°</span>
cos(A−B)=cosAcosB<span>+sinA</span>sinB
cos(112−45)=cos112cos45<span>+sin112</span>sin45=cos(67)
the answer is the letter d) cos 67°
10. Rewrite with only sin x and cos x.
sin 2x - cos 2x
sin2x =
2sinxcosx<span>
cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 -1 = 1- 2(sinx)^2</span>
sin2x- cos2x=2sinxcosx-(1- 2(sinx)^2=2sinxcosx-1+2(sinx)^2
sin2x- cos2x=2sinxcosx-1+2(sinx)^2
<span>
the answer is the letter <span>
b) 2 sin x cos2x - 1
+ 2 sin2x</span></span>
Answer:
20 guitars
Step-by-step explanation:
since 12 guitars is equivalent to 60% of the sales then you would divide the 12 guitars by .6 to get the total number of guitars sold
12/.6 = 20 guitars
Answer:
1) yes
2) No
3) No
4) yes
5) No
Step-by-step explanation:
1) f(0)=0, f(1)=1, f(2)=2, f(3)=3, then ![f[\{0, 1, 2, 3\}]=\{0, 1, 2, 3\}](https://tex.z-dn.net/?f=f%5B%5C%7B0%2C%201%2C%202%2C%203%5C%7D%5D%3D%5C%7B0%2C%201%2C%202%2C%203%5C%7D)
2) f(0)=0, 
, then f(1)=1; 
, then f(2)=0; 
, then f(3)=1
Then ![f[\{0, 1, 2, 3\}]=\{0, 1, 3\}](https://tex.z-dn.net/?f=f%5B%5C%7B0%2C%201%2C%202%2C%203%5C%7D%5D%3D%5C%7B0%2C%201%2C%203%5C%7D)
, this means that f isn't onto.
3.
, then f(1)=0
, then f(2)=2
, then f(3)=2
Then ![f[\{0, 1, 2, 3\}]=\{0, 2\}](https://tex.z-dn.net/?f=f%5B%5C%7B0%2C%201%2C%202%2C%203%5C%7D%5D%3D%5C%7B0%2C%202%5C%7D)
, this means that f isn't onto.
4. ![f[\{0, 1, 2, 3\}]=\{0, 1, 2,3\}](https://tex.z-dn.net/?f=f%5B%5C%7B0%2C%201%2C%202%2C%203%5C%7D%5D%3D%5C%7B0%2C%201%2C%202%2C3%5C%7D)
, then f is onto.
5. ![f[\{0, 1, 2, 3\}]=\{1, 2\}](https://tex.z-dn.net/?f=f%5B%5C%7B0%2C%201%2C%202%2C%203%5C%7D%5D%3D%5C%7B1%2C%202%5C%7D)
, this means that f isn't onto.
Answer:
Step-by-step explanation:
Just trying to get points
Answer:
a) The value of A = 2
b) The value of 
Step-by-step explanation:
a)
Given that:
X should be the random variable that assumes only positive integer values.
The probability function; ![P[X = n] = \dfrac{A}{3^n}](https://tex.z-dn.net/?f=P%5BX%20%3D%20n%5D%20%3D%20%5Cdfrac%7BA%7D%7B3%5En%7D)
for some constant A and n ≥ 1.
Then, let ![\sum \limits ^{\infty}_{n =1} P[X =n] = 1](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bn%20%3D1%7D%20P%5BX%20%3Dn%5D%20%3D%201)
This implies that:
A = 2
Thus, the value of A = 2
b)
Suppose X represents a e constant A (n> 1). Find A.
b) Let X be a continuous random variable that can assume values between 0 and 3
Then, the density function of x is:
where; B is constant.
Then, using the property of the probability density function:
Taking the integral, we have:
![B \Big [\dfrac{x^3}{3} +x \Big ]^3_0 = 1](https://tex.z-dn.net/?f=B%20%5CBig%20%5B%5Cdfrac%7Bx%5E3%7D%7B3%7D%20%2Bx%20%5CBig%20%5D%5E3_0%20%3D%201)
![B \Big [\dfrac{3^3}{3} +3 \Big ]= 1](https://tex.z-dn.net/?f=B%20%5CBig%20%5B%5Cdfrac%7B3%5E3%7D%7B3%7D%20%2B3%20%5CBig%20%5D%3D%201)
![B \Big [\dfrac{27}{3} +3 \Big ] = 1](https://tex.z-dn.net/?f=B%20%5CBig%20%5B%5Cdfrac%7B27%7D%7B3%7D%20%2B3%20%5CBig%20%5D%20%3D%201)
B [ 9 +3 ] = 1
B [ 12 ] = 1
Divide both sides by 12
