Fator by grouping ab+2a+5b+10
1 answer:
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Answer:
Step-by-step explanation:
We are factoring
So:
((2•5^2x^2) + 485x) - 150
Pull like factors :
50x^2 + 485x - 150 = 5 • (10x^2 + 97x - 30)
Factor
10x^2 + 97x - 30
Step-1: Multiply the coefficient of the first term by the constant 10 • -30 = -300
Step-2: Find two factors of -300 whose sum equals the coefficient of the middle term, which is 97.
-300 + 1 = -299
-150 + 2 = -148
-100 + 3 = -97
-75 + 4 = -71
-60 + 5 = -55
-50 + 6 = -44
-30 + 10 = -20
-25 + 12 = -13
-20 + 15 = -5
-15 + 20 = 5
-12 + 25 = 13
-10 + 30 = 20
-6 + 50 = 44
-5 + 60 = 55
-4 + 75 = 71
-3 + 100 = 97
Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 100
10x^2 - 3x + 100x - 30
Step-4: Add up the first 2 terms, pulling out like factors:
x • (10x-3)
Add up the last 2 terms, pulling out common factors:
10 • (10x-3)
Step-5: Add up the four terms of step 4:
(x+10) • (10x-3)
Which is the desired factorization
Thus your answer is
An interesting twist to a binomial distribution problem.
Given:
p=55%=0.55 for probability of success in solicitation
x=4=number of successful solicitations
n=number of calls to be made
P(x,n,p)>=89.9%=0.899 (from context, it is >= and not =, which is almost impossible)
From context of question, all calls are assumed independent, with constant probability of success, so binomial distribution is applicable.
The number of successes, x, is then given by
where
p=probability of success
n=number of trials
x=number of successes
Here we need n such that
P(x,n,p)>=0.899
given
x>=4, p=0.55, which means we need to find
Method 1: if a cumulative binomial distribution table is available, we can look up n=9,10,11 and find
P(x>=4,9,0.55)=0.834
P(x>=4,10,0.55)=0.898
P(x>=4,11,0.55)=0.939
So she must make (at least) 11 calls to make sure the probability of meeting her quota is 89.9% or more.
Method 2: using technology.
Similar to method 1, we can look up the probabilities directly, for n=9,10,11
P(x>=4,9,0.55)=0.834178
P(x>=4,10,0.55)=0.8980051
P(x>=4,11,0.55)=0.9390368
Method 3: using simple calculator
Here we need to calculate the probabilities for each value of n=10,11 and sum the probabilities of FAILURE S=P(0,n,0.55)+P(1,n,0.55)+P(2,n,0.55)+P(3,n,0.55)
so that the probability of success is 1-S.
For n=10,
P(0,10,0.55)=0.000341
P(1,10,0.55)=0.004162
P(2,10,0.55)=0.022890
P(3,10,0.55)=0.074603
So that
S=0.000341+0.004162+0.022890+0.074603
=0.101995
and Probability of getting 4 successes (or more)
=1-S
=0.898005, missing target by 0.1%
So she will have to make 11 phone calls, bring up the probability to 93.9%. The work is similar to that of n=10.
Given:
p=55%=0.55 for probability of success in solicitation
x=4=number of successful solicitations
n=number of calls to be made
P(x,n,p)>=89.9%=0.899 (from context, it is >= and not =, which is almost impossible)
From context of question, all calls are assumed independent, with constant probability of success, so binomial distribution is applicable.
The number of successes, x, is then given by
p=probability of success
n=number of trials
x=number of successes
Here we need n such that
P(x,n,p)>=0.899
given
x>=4, p=0.55, which means we need to find
Method 1: if a cumulative binomial distribution table is available, we can look up n=9,10,11 and find
P(x>=4,9,0.55)=0.834
P(x>=4,10,0.55)=0.898
P(x>=4,11,0.55)=0.939
So she must make (at least) 11 calls to make sure the probability of meeting her quota is 89.9% or more.
Method 2: using technology.
Similar to method 1, we can look up the probabilities directly, for n=9,10,11
P(x>=4,9,0.55)=0.834178
P(x>=4,10,0.55)=0.8980051
P(x>=4,11,0.55)=0.9390368
Method 3: using simple calculator
Here we need to calculate the probabilities for each value of n=10,11 and sum the probabilities of FAILURE S=P(0,n,0.55)+P(1,n,0.55)+P(2,n,0.55)+P(3,n,0.55)
so that the probability of success is 1-S.
For n=10,
P(0,10,0.55)=0.000341
P(1,10,0.55)=0.004162
P(2,10,0.55)=0.022890
P(3,10,0.55)=0.074603
So that
S=0.000341+0.004162+0.022890+0.074603
=0.101995
and Probability of getting 4 successes (or more)
=1-S
=0.898005, missing target by 0.1%
So she will have to make 11 phone calls, bring up the probability to 93.9%. The work is similar to that of n=10.