X= -1
2x+4-x=x+3-x subtract x from both sides
x+4=3
x+4-4=3-4 subtract 4 from both sides
Therefore, x=-1
Answer:
see below
Step-by-step explanation:
f(x)= -0.08x(x^2-11x+18)
Factor
f(x)= -0.08x(x-9)(x-2)
Using the zero product property to find the zeros
0= -0.08x(x-2)(x-9)
-0.8x =0 x-2 =0 x-9 =0
x=0 x=2 x=9
Multiply out
f(x) = -0.08 x^3 + 0.88 x^2 - 1.44 x
The highest power is x^3
f(-∞) = -0.08( -∞)^3 = - ( -∞) = ∞
As x goes to -∞ f(x) goes to +∞
f(∞) = -0.08( ∞)^3 = - ( ∞) = -∞
As x goes to ∞ f(x) goes to -∞
Answer:
14 apples, 10 bananas
Step-by-step explanation:
.07 * 12 = .84 (12 apples at 7 pence/per = 84 pence)
5 - .84 = 4.16 (4.16 pound remaining)
4.16/.4 = 10.4 (you can buy 10 bananas with 4.16 pounds, with .16 pence remaining)
.16 / .7 = 2.3 (you can buy two more apples with 16 pence)
Hope this helps.
Binomial distribution will be used to model situation because all following criteria are satisfied:
1. Bernoulli trials, i.e. exactly two possible outcomes (show up or not)2. Number of trials is known before and constant throughout the experiment, i.e. independent of outcomes (150 booked)3. All trials are independent of each other. (assumed from context)4. Probability of success is known, and remain constant throughout trials. (85%)Since all criteria are satisfied, we can model with binomial distribution, where the probability of x successes out of N trials each with probability of success p is given byP(x)=C(N,x)(p^x)(1-p)^(N-x)and,C(N,x) is number of combinations of selecting x objects out of N.
P(>140)=P(141)+P(142)+...+P(150)
=.00035620+0.00012783+0.00004056+0.00001117+0.00000262+0.00000051+0.00000008+0.00000001+0.00000000
=0.00053907
The above calculation is not very practical unless we have a statistical calculator or a software.
For practical hand calculations, we usually use the binomial approximation.
mean=np=150*0.85=127.5
variance = np(1-p)=150*.85*.15=19.125 (>10, possible to use binomial approximation, but accuracy is marginal).
We also need to use the continuity correction, which means that the portion above 140 is counted as 140.5 to 150 passengers. Then we calculate
Z=(140.5-127.5)/sqrt(19.125)=2.973
P(x>=140.5)
=P(z>=Z)
=1-P(z<Z)
=1-P(z<2.973)
=1-0.99852
=0.00148
The answer is quite a bit off from the exact value of 0.000539, but an approximation is an approximation especially for skew distribution like in the present case (p=0.85 far from 0.5, and x=140 far from mean).
Step-by-step explanation:
An inscribed angle is half the arc angle.
m∠MNQ = 80°/2
m∠MNQ = 40°
The angle between two chords is the average of the arc angles.
m∠AMB = (80° + 85°) / 2
m∠AMB = 82.5°
