Answer:
30th term is
9(30+3) =270+27=297
to find the first term which is larger than 100
9(n+3) =100
9n=100-27
9n=73
n=73÷9
=8.1
so when n is>8.1 all the terms will be larger than 100 and the first term will be 9 since n can't be fraction as it's an ordinary number
so it's 9th
9(9+3) =81+27=108
the first four terms are
9(1+3) =36
9(2+3) =45
9(3+3) =81
9(4+3) =63
Step-by-step explanation:
n(n-1)
the first four terms are
1(1-1) =0
2(2-1) =2
3(3-1) =6
4(4-1) =12
the 10th term is 10(10-1) =90
to find weather 51 is a term or not
n(n-1) =51
n^2-n-51=0
1-4×1×-51=1+204=205
so it's roots will be fraction
so it's not from its terms because n will
be fraction
to find the term 182
n(n-1) =182
n^2-n-182=0
(n-14) (n+13)=0
so it's the term 14th because n can't be negative
Answer: 0.1854
Step-by-step explanation:
Given : Suppose that a particular candidate for public office is in fact favored by 48% of all registered voters in the district.
Let
be the sample proportion of voters in the district favored a particular candidate for public office .
A polling organization will take a random sample of n=500 voters .
Then, the probability that p will be greater than 0.5, causing the polling organization to incorrectly predict the result of the upcoming election :
![P(\hat{p}>0.5)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.5-0.48}{\sqrt{\dfrac{0.48(0.52)}{500}}})\\\\=P(z>0.8951)\ \ [\because\ z=(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\=1-P(z\leq0.8951)\ \ [\because\ P(Z>z)=1-P(Z\leq z)]\\\\ = 1-0.8146=0.1854](https://tex.z-dn.net/?f=P%28%5Chat%7Bp%7D%3E0.5%29%3DP%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%3E%5Cdfrac%7B0.5-0.48%7D%7B%5Csqrt%7B%5Cdfrac%7B0.48%280.52%29%7D%7B500%7D%7D%7D%29%5C%5C%5C%5C%3DP%28z%3E0.8951%29%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%3D1-P%28z%5Cleq0.8951%29%5C%20%5C%20%5B%5Cbecause%5C%20P%28Z%3Ez%29%3D1-P%28Z%5Cleq%20z%29%5D%5C%5C%5C%5C%20%3D%201-0.8146%3D0.1854)
∴ Required probability = 0.1854
Answer:
feet
Step-by-step explanation:
We will use the Pythagorean Theorem to solve this. Which states that:
One Length^2 + Another Length^2 = Hypotenuse^2
We can take one length as 5 ft and another length as 9 ft and we call the hypotenuse "h", so we have:

Now, let us solve for "h":

The pond's hypotenuse is about 10.3 feet
First solve for y
3x-y-2=1
subtract 3x from each side
-y-2=-3x+1
add 2 to both sides
-y=-3x+3
divide each side by -1
y=3x-3
To graph you could make a table:
x y
0 -3
graph that.... point and use rise over run for slope 3/1 and graph.