How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) =
2 answers:
The transformed equation , the graph is shifted 4 units to the left and 6 units down.
Explanation:
The parent equation is
The transformed equation is
By using the function transformation rules, we can see that the parent function is transformed into the function
Since, from the function transformation rules, we know that,
shifts the function b units to the left.
Thus, the transformed function is shifted 4 units to the left.
Also, from the function transformation rules, we know that,
shifts the function b units downward.
Thus, the transformed function is shifted 6 units down.
Thus, the transformed equation , the graph is shifted 4 units to the left and 6 units down.
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Notice the picture below
so.. whatever the parabola y= -3x²+k is, will pass over (3,-2) and (-3,-2)
so.. .let us pick say hmmm 3,-2
thus
solve for "k"
so.. whatever the parabola y= -3x²+k is, will pass over (3,-2) and (-3,-2)
so.. .let us pick say hmmm 3,-2
thus
solve for "k"
You haven't provided the series, therefore, I can only help with the concept.
<u><em>For an infinite geometric series, we have two possibilities for the common ratio (r):</em></u>
for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series
<u><em>In an infinite series with r < 1, the summation can be found using the following rule:</em></u>
sum =
where:
a₁ is the first term in the series
r is the common ratio
<u>Example:</u>
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum =
Hope this helps :)
<u><em>For an infinite geometric series, we have two possibilities for the common ratio (r):</em></u>
for r > 1, the terms in the series will keep increasing infinitely and the only possible logic summation of the series would be infinity
for r < 1, the terms will decrease, therefore, we can formulate a rule to get the sum of the infinite series
<u><em>In an infinite series with r < 1, the summation can be found using the following rule:</em></u>
sum =
where:
a₁ is the first term in the series
r is the common ratio
<u>Example:</u>
For the series:
2 , 1, 0.5 , 0.25 , ....
we have:
a₁ = 2
r = 0.5
Therefre:
sum =
Hope this helps :)
Answer:
b. 0.864
Step-by-step explanation:
Let's start defining the random variables.
Y1 : ''Number of customers who spend more than $50 on groceries at counter 1''
Y2 : ''Number of customers who spend more than $50 on groceries at counter 2''
If X is a binomial random variable, the probability function for X is :
Where P(X=x) is the probability of the random variable X to assume the value x
nCx is the combinatorial number define as :
n is the number of independent Bernoulli experiments taking place
And p is the success probability.
In counter I :
Y1 ~ Bi (n,p)
Y1 ~ Bi(2,0.2)
With y1 ∈ {0,1,2}
And P( Y1 = y1 ) = 0 with y1 ∉ {0,1,2}
In counter II :
Y2 ~ Bi (n,p)
Y2 ~ Bi (1,0.3)
With y2 ∈ {0,1}
And P( Y2 = y2 ) = 0 with y2 ∉ {0,1}
(1Cy2) with y2 = 0 and y2 = 1 is equal to 1 so the probability function for Y2 is :
Y1 and Y2 are independent so the joint probability distribution is the product of the Y1 probability function and the Y2 probability function.
With y1 ∈ {0,1,2} and y2 ∈ {0,1}
P( Y1 = y1 , Y2 = y2) = 0 when y1 ∉ {0,1,2} or y2 ∉ {0,1}
b. Not more than one of three customers will spend more than $50 can mathematically be expressed as :
when Y1 = 0 and Y2 = 0 , when Y1 = 1 and Y2 = 0 and finally when Y1 = 0 and Y2 = 1
To calculate we must sume all the probabilities that satisfy the equation :