look at the table below. what is the constant change? ( I put 2 and was marked wrong, and the answer can't be in a fraction for
m).
2 answers:
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Answer:
<em>y=-6</em>
Step-by-step explanation:
<em>Geometric Sequences</em>
Any given sequence is said to be geometric if each term can be obtained as the previous term
by a constant value called the common ratio.
or equivalently
Looking closely at the sequence 2, y, 18,-54, 162 we can try to find out if it's a geometric sequence or not. We compute the possible common ratios
and we see they both result -3. If we use r=-3 and try to find the second term (y), then
y=2*(-3)=-6
Now we compute the third term: (-6)(-3)=18
Since we got the third term as given in the original sequence.
So y=-6
Answer:
a)
Where and
b)
And we can find this probability using the complement rule and with the normal standard table or excel:
c)
d)
e) IQR = 75.13-50.87=24.26
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:
Where and
Part b
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the complement rule and with the normal standard table or excel:
Part c
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel:
Part d
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Part e
Q1
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 25% of data from the top 75% is 50.87.
Q3
Since the distribution is symmetrical we repaeat the procedure for Q1 but now with z= 0.674
And if we solve for a we got
And then the IQR = 75.13-50.87=24.26