Step-by-step explanation:
So the Ap will be x,x+10,x+20,x+30
Sum of the angles of a quadrilateral is 360
x+x+10+x+20+x+30=360
4x+60=360
4x=300
x=75
So the angles are 75,85,95,105
Answer: slope = -1
Step-by-step explanation:
Count from point (2,0) to point (0,2)
You get 2/2 which simplifies to 1.
However the line is negative so the slope must be negative, giving you a slope of -1 as your final answer.
Answer: D) 0.438 < p < 0.505
Step-by-step explanation:
We know that the confidence interval for population proportion is given by :-
![\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%5Cpm%20z%5E%2A%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D)
, where n= sample size
= Sample proportion.
z* = critical value.
Given : A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.
i.e. n= 865
![\hat{p}=\dfrac{408}{865}\approx0.4717](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B408%7D%7B865%7D%5Capprox0.4717)
Two-tailed critical avlue for 95% confidence interval : z* = 1.96
Then, the 95 % confidence interval for the true proportion of all voters in the state who favor approval will be :-
![0.4717\pm (1.96)\sqrt{\dfrac{0.4717(1-0.4717)}{865}}\\\\\approx0.4717\pm 0.03327\\\\=(0.4717-0.03327,\ 0.4717+0.03327)=(0.43843,\ 0.50497)\approx(0.438,\ 0.505)](https://tex.z-dn.net/?f=0.4717%5Cpm%20%281.96%29%5Csqrt%7B%5Cdfrac%7B0.4717%281-0.4717%29%7D%7B865%7D%7D%5C%5C%5C%5C%5Capprox0.4717%5Cpm%200.03327%5C%5C%5C%5C%3D%280.4717-0.03327%2C%5C%200.4717%2B0.03327%29%3D%280.43843%2C%5C%200.50497%29%5Capprox%280.438%2C%5C%200.505%29)
Thus, the required 95% confidence interval : (0.438, 0.505)
Hence, the correct answer is D) 0.438 < p < 0.505
(a) Total number of possible ways in which the die can fall = 6
Number of ways of throwing 3 = 1
![P = \frac{ Number \: of \: favourite \: outcomes}{ Total \: number \: of \: possible \: outcomes }](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B%20Number%20%5C%3A%20of%20%5C%3A%20favourite%20%5C%3A%20outcomes%7D%7B%20Total%20%5C%3A%20number%20%5C%3A%20of%20%5C%3A%20possible%20%5C%3A%20outcomes%20%7D%20)
![P (throwing \: 3) = \frac{1}{6}](https://tex.z-dn.net/?f=P%20%28throwing%20%5C%3A%203%29%20%3D%20%5Cfrac%7B1%7D%7B6%7D%20)
(b) Total number of outcomes of throwing a die = 6
Number of outcomes of falling even number, i. e, 2,4,6 = 3
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