Let me research this real quick
<span>8+0.4+0.07+0.008 you basically separate the numbers starting with the largest working down to the smallest.
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Triangle QST is an isosceles triangle. You can tell because two of the legs are congruent. Thus angle T is also an x-variable.
Add all of the degrees together, set them equal to 180 and solve for x.
x + x + 74 = 180
2x + 74 = 180
2x = 180 - 74
2x = 106
x = 53
This rules out options C and D.
Now we have to find angle PQS:
The measurements of triangle PQR are congruent to each other so 180 / 3 = 60 they are all 60 degrees.
Angles PQR, PQS, and SQT are in line with each other so they add up to 180.
60 + PQS + 74 = 180
134 + PQS = 180
PQS = 180 - 134
PQS = 46
Triangle PQS is another isosceles triangle. Thus, the two base angles are the same. We are going to add them together plus y and set it all equal to 180 to solve.
46 + 46 + y = 180
92 + y = 180
y = 180 - 92
y = 88
x = 53, y = 88. Your answer is option B
I think it’s 7 but i’m not sure idk what the shades area is
Answer: ![(-0.2035,\ 0.1235)](https://tex.z-dn.net/?f=%28-0.2035%2C%5C%200.1235%29)
Step-by-step explanation:
The confidence interval for the difference of two population proportion is given by :-
![p_1-p_2\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}](https://tex.z-dn.net/?f=p_1-p_2%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cdfrac%7Bp_1%281-p_1%29%7D%7Bn_1%7D%2B%5Cdfrac%7Bp_2%281-p_2%29%7D%7Bn_2%7D%7D)
Given : ![n_1=100;\ n_2=100](https://tex.z-dn.net/?f=n_1%3D100%3B%5C%20n_2%3D100)
The proportion of students in the first sample replied that they turned to their mother rather than their father for help. =![\dfrac{43}{100}=0.43](https://tex.z-dn.net/?f=%5Cdfrac%7B43%7D%7B100%7D%3D0.43)
The proportion of students in the second sample replied that they turned to their mother rather than their father for help. =![\dfrac{47}{100}=0.47](https://tex.z-dn.net/?f=%5Cdfrac%7B47%7D%7B100%7D%3D0.47)
Significance level : ![\alpha=1-0.98=0.02](https://tex.z-dn.net/?f=%5Calpha%3D1-0.98%3D0.02)
Critical value : ![z_{\alpha/2}=2.326](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D2.326)
Now, the 98% confidence interval for
will be :-
![0.43-0.47\pm(2.326)\sqrt{\dfrac{0.43(1-0.43)}{100}+\dfrac{0.47(1-0.47)}{100}}\\\\\approx-0.04\pm(0.1635)\\\\=(-0.04-0.1635,\ -0.04+0.1635)\\\\=(-0.2035,\ 0.1235)](https://tex.z-dn.net/?f=0.43-0.47%5Cpm%282.326%29%5Csqrt%7B%5Cdfrac%7B0.43%281-0.43%29%7D%7B100%7D%2B%5Cdfrac%7B0.47%281-0.47%29%7D%7B100%7D%7D%5C%5C%5C%5C%5Capprox-0.04%5Cpm%280.1635%29%5C%5C%5C%5C%3D%28-0.04-0.1635%2C%5C%20-0.04%2B0.1635%29%5C%5C%5C%5C%3D%28-0.2035%2C%5C%200.1235%29)
Hence, the 98% confidence interval for
is ![(-0.2035,\ 0.1235)](https://tex.z-dn.net/?f=%28-0.2035%2C%5C%200.1235%29)