Answer:
d = 9
Step-by-step explanation:
Calculate the slope m of line AB and equate the result to 3
m = 
with (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(d, 21)
m = 
= 
= 3 ( multiply both sides by d - 4 )
15 = 3(d - 4), that is
15 = 3d - 12 ( add 12 to both sides )
27 = 3d ( divide both sides by 3 )
9 = d
Answer:
a) .033 b) .4678 c) 100
Step-by-step explanation:
Distribution of miraculin produced is normal. To answer question we need to find the z-score of 100g, 110g and 120g miraculin
General formula for z score is given by
z=
where
- X is the miraculin produced (120,110,100)
- M is the mean miraculin produced for a partucilar tomato plant, which is 105.3
- s is the standard deviation of the sample, which is 8.0
a)
z-score for 120 g miraculin is 
=1.8375 then
P(x > 120) = P(z>1.8375) = 0.033
b)
z-score for 110 g miraculin is 
= 0.5875
z-score for 100 g miraculin is 
= -0,6625
P(100 < x < 110) = P(x>100) - P(x>110) =0.7462 - 0,2784 = 0.4678
c)
if P(x < a) = 0.25 then corresponding z score for a is -0.6745. From the above formula we can calculate a:
=-0.6625 which gives a= 100
Answer:
Ed Moura invest $64000 in certificates of deposit paying 3%
Step-by-step explanation:
Ed Moura has $32000 invested in stocks paying 6%.
Additional money in certificates of deposit paying 3% =x
so that the average return on the two investments is 4%.
32000*6% +3%*x = 4%(32000+x)
32000*0.06 +0.03*x = 0.04(32000+ x)
1920 + 0.03x = 1280 +0 .04x
1920 - 1280 = 0.04x - 0.03x
0.01x = 640
x = 64000
x = $64000
x= $64000 in certificates of deposit paying 3%
Thank you.
integrate to get
![[ln|t|]^{3x}_x=ln|3x|-ln|x|=ln| \frac{3x}{x}| =ln |3|=ln(3)](https://tex.z-dn.net/?f=%5Bln%7Ct%7C%5D%5E%7B3x%7D_x%3Dln%7C3x%7C-ln%7Cx%7C%3Dln%7C%20%5Cfrac%7B3x%7D%7Bx%7D%7C%20%3Dln%20%7C3%7C%3Dln%283%29)
this only is true when x>0
when x turns negative, we get -ln(3) because of math
