Answer: a) 79.10 % b) 7% c)19.85 %
Step-by-step explanation:
a) Z = ( × - μ ) ÷ σ Where μ mean of population σ standard deviation Z is the abscissa to give the area or probability we are looking for associated to the value 10 ounces ( × )
So: Z = ( 10 - 9 ) ÷ 1.2 ⇒ Z = 1/1.2 ⇒ Z = 0.83 it has to be below this value
From Z tables we get P [ Z ≤ 0.82 ] = 0.7910 0r 79.10 %
b) Following the same procedure: We look for
P [ Z > ( x - μ ) ÷ σ ] ⇒ Z = ( 12 -10 ) ÷ 1.2 = 2.5
From Z table we get the area under the curve from the left tail up to the point Z < 2.5 ( 2.5 not included) but we were asked for the area out of that previous so 1- 0.9930 = 0.007 is the area we are looking for
So P (b) = 0.007 or 7 %
Finally between the two points above mentioned ( 10 ≤ Z ≤ 12 ) we use the previous values (taking in consideration the limits, according to the problem statement )
Z ≤ 10 Z ⇒( 10-9 ) ÷ 1.2 Z = 0.7967
Z ≥ 12 Z ⇒ ( 12 - 9 ) ÷ 1.2 Z = 0.9952
The interval is between these two points
0.9952 - 0.7967 = 0.1985 ⇒ or 19.85 %
The attached help in the understanding of the solution
The answer to that question is (5x+3).
To solve this question, we just need to insert 12 into the m position of each question and see if the equation holds true.
a. 4m = 40
4(12) = 40
48 = 40
48 obviously does not equal 40, so it is not choice A.
b. m + 20 = 42
12 + 20 = 42
32 = 42
Again, 32 isn't the same as 42, so not choice B either.
c. 4m = 48
4(12) = 48
48 = 48
It looks like this one is true, but let's solve D also just to make sure.
d. m - 4 = 9
12 - 4 = 9
8 = 9
This is false, since 8 does not equal 9.
Therefore, choice C (4m = 48) is the correct answer.
Hope that helped! =)
<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>
It will be a negative.
for an example: -20 for x would mqke 2x + 1 into -39 and 8x + 5 into -155. that's 116 apart, so maybe -2(8) + 5 = -11
-2(2) + 1 = -3
but that's only 8 apart, so it'd be higher.
-4(2) + 1 = -7
-4(8) + 5 = -27
BOOM
Tadaaaa,
You probably thought positive, but sometimes it's negative, you know what I mean?
