Answer: The number is 26.
Step-by-step explanation:
We know that:
The nth term of a sequence is 3n²-1
The nth term of a different sequence is 30–n²
We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.
we get:
3n²- 1 = 30–m²
Notice that as n increases, the terms of the first sequence also increase.
And as n increases, the terms of the second sequence decrease.
One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.
if m = 1, then:
3n²- 1 = 30–1²
3n²- 1 = 29
3n² = 30
n² = 30/3 = 10
n² = 10
There is no integer n such that n² = 10
now let's try with m = 2, then:
3n²- 1 = 30–2² = 30 - 4
3n²- 1 = 26
3n² = 26 + 1 = 27
n² = 27/3 = 9
n² = 9
n = √9 = 3
So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.
the number is:
3*(3)² - 1 = 26
30 - 2² = 26
The number that belongs to both sequences is 26.
Step-by-step explanation:
7 - 3b-2(0 + 3 - 2b)
To simplify the expression in the box, Fatua used
these steps:
Step 1:7 - 3b-2(3 - 3b)
Step 2:7 - 3-6-36-
Step 3: -13 - 66
Did Fatua calculate correctly? if nnot, in what step
did she make her FIRST mistake?
Answer:
11.25
Step-by-step explanation:
Step 1:
4/5 = 9/x Proportion
Step 2:
4x = 45 Multiply
Step 3:
45 ÷ 4 Divide
Answer:
x = 11.25
Hope This Helps :)
Answer:
Because of the presence of an outlier (30), an extremely higher value when compared to others. Outliers affects the value of mean, thereby mean should not be used for data with outliers.
Step-by-step explanation:
For the set of data above, it would be misleading to use the mean as the center of measure for the number of points that she scored in each game because of the presence of outliers, the presence of extremely lower or extremely higher value makes the use of mean as a measure of central tendency inaccurate because the mean take into consideration all the values in a data including the outliers for its calculation, and the mean would tend to shift towards the outliers thereby misinterpreting the data. The presence of outlier which is 30 in the data given would shift the mean to the right towards 30, thereby misleading to represent the measure of central tendency. 30 is an outlier because it is extremely higher than the rest of the data (10,8,9,8,30).
In the presence of outliers it's best to use median or mode as an acceptable measure of central tendency.
Answer:
x2
Step-by-step explanation:
If the graph has a gap at the x value c, then the two-sided limit at that point will not exist.
If the graph has a vertical asymptote and one side of the asymptote goes toward infinity and the other goes toward negative infinity, then the limit does not exist.
