⦁ How can a table be used to find the rate of change and the initial value? Describe the process.
1 answer:
1) Table can be used to find the rate of change and the initial value5
x ------> y
0 -------> 3
1 ------> 5
2 ------> 7
Rate of change (Slope) =
=
= 2/1 = 2
Rate of change = 2
Y intercept is the point where x=0
So y = 3 from the table.
2) Attached the graph of a line
Rate of change =
= = 2
3) slope = and a y-intercept = 7
Equation of a line y= mx + b
Where m is the slope and b is the y intercept
Replace slope m and y intercept
m= 2/3, b= 7
Equation of a line : y = x + 7
4) Carson has $450 in his bank account and deposits $70 per month out of his babysitting money.
Initial amount in the bank (y intercept) b= $450
Deposited amount = 70 that is the slope m= 70
So the equation y = mx+ b , where x is the month
y = 70x + 450
Carson’s bank balance f(x) = 70x + 450
5) the graph of straight line is linear. In the graph x<1 that is (-infinity , 1) is linear.
The graph with curved line is non linear.In the graph x>1 that is (1, infinity ,) is non linear.
The graph is attached below.
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Answer:
1) FALSE
2) FALSE
3) TRUE
4) TRUE
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 1
The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively.
The mean and the deviation for the normal standard distribution are:
So then that's FALSE.
Part 2
Using the standard normal curve, the z−score representing the 10th percentile is 1.28.
We are looking for a value a, that satisfy this:
(a)
(b)
We can find a z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.10 and P(Z>-1.28)=0.90
So that's FALSE.
Part 3
Let z1 be a z−score that is unknown but identifiable by position and area. If the symmetrical area between −z1 and +z1 is 0.9544, the value of z1 is 2.0
If we find this probability:
So on this case we can approximate to 0.9544. And that's TRUE.
Part 4
Using the standard normal curve, the z−score representing the 75th percentile is 0.67.
We are looking for a value a, that satisfy this:
(a)
(b)
We can find a z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.67. On this case P(Z<0.67)=0.75 and P(Z>0.67)=0.25
So that's TRUE.