We have the following general rule for exponents:
then, in this case we have the following:
therefore, the answer is 3
The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.
<h3>Probability</h3>
a. Distribution
X ~ N (20 , 6)
b. P(x ≤24)
= P[(x - μ ) / σ (24 - 20) / 6]
= P(z ≤0.67)
= 0.74857
=0.7486
Hence:
Probability = 0.7486
c. P(21 < x < 26)
= P[(21 - 26)/ 6) < (x - μ ) / σ < (24 - 20) / 6) ]
= P(-0.83 < z < 0.67)
= P(z < 0.67) - P(z < -0.)
= 0.74857- 0.2033
= 0.54527
Hence:
Probability =0.54527
d. Using standard normal table ,
P(Z < z) = 66%
P(Z < 0.50) = 0.66
z = 0.50
Using z-score formula,
x = z× σ + μ
x = 0.50 × 6 + 20 = 23
23 Christmas cards
Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.
Learn more about probability here:brainly.com/question/24756209
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6x - 11 - 2x = -7
4x - 11 - = -7
4x = 11
X= 2
12- 11 -4 -3y = -7
-3 -3y = -7
-3y = -4
Y = -1
It should be 2,-1
Answer:
length : 8 m
width : 13/2 = 6.5 m
Step-by-step explanation:
area of rectangle = l(ength)×w(idth) = 52
l = 2w - 5
=> (2w - 5)×w = 52
=> 2w² -5w - 52 = 0
we know, when transforming this quadratic equation into a multiplication of two expressions of w, that we need to have 2w and w (to make 2w²), and then which 2 numbers multiply to 52 and add to -5 (when one is multiplied by 2 due to 2w) : -13 and 4
=> (2w - 13)×(w + 4) = 0
=> 2 solutions for w :
2w-13 = 0
2w = 13, w = 13/2
w+4 = 0, w = -4
negative values for a side length of a shape do not make sense, so the only usable solution is w = 13/2
=> l = 2w - 5 = 13 - 5 = 8
Step-by-step explanation:
perimeter is 4x+6 +20x-8=20x-2
area is 20x^2+22x-12
