short leg: x
long leg: 5x + 19
hypotenuse: 5x + 20
(short leg)² + (long leg)² = hypotenuse
(x)² + (5x + 19)² = (5x + 20)²
x² + 25x² + 190x + 361 = 25x² + 200x + 400
x² - 10x - 39 = 0 <em>subtracted 25x², 200x, and 400 from both sides</em>
(x - 13)(x + 3) = 0
x - 13 = 0 , x + 3 = 0
x = 13 x = -3 <em>length cannot be negative so disregard -3</em>
long leg: 5x + 19 = 5(13) + 19 = 65 + 19 = 84
hypotenuse: 5x + 20 = 5(13) + 20 = 65 + 20 = 85
Answer: short leg = 13, long leg = 84, hypotenuse = 85
Answer:
The correct option is (a) 0.9780.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
![\mu_{\hat p}=p](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%3Dp)
The standard deviation of this sampling distribution of sample proportion is:
![\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}](https://tex.z-dn.net/?f=%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
As the sample selected is quite large, i.e. <em>n</em> = 110 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:
![\mu_{\hat p}=p=0.70\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.70(1-0.70)}{110}}=0.044](https://tex.z-dn.net/?f=%5Cmu_%7B%5Chat%20p%7D%3Dp%3D0.70%5C%5C%5C%5C%5Csigma_%7B%5Chat%20p%7D%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%3D%5Csqrt%7B%5Cfrac%7B0.70%281-0.70%29%7D%7B110%7D%7D%3D0.044)
Compute the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 as follows:
![P(0.60](https://tex.z-dn.net/?f=P%280.60%3C%5Chat%20p%3C0.80%29%3DP%28%5Cfrac%7B0.60-0.70%7D%7B0.044%7D%3C%5Cfrac%7B%5Chat%20p-%5Cmu_%7B%5Chat%20p%7D%7D%7B%5Csigma_%7B%5Chat%20p%7D%7D%3C%5Cfrac%7B0.80-0.70%7D%7B0.044%7D%29)
![=P(-2.27](https://tex.z-dn.net/?f=%3DP%28-2.27%3CZ%3C2.27%29%5C%5C%5C%5C%3DP%28Z%3C2.27%29-P%28Z%3C-2.27%29%5C%5C%5C%5C%3D0.98840-0.01160%5C%5C%5C%5C%3D0.9768%5C%5C%5C%5C%5Capprox0.9780)
*Use a <em>z</em>-table.
Thus, the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 is approximately equal to 0.9780.
The correct option is (a).
To rearrange you must first simplify
aq-ac=d
add ac to each side:
aq=d+ac
then divide by a:
q=(d/a)+c and this is your answer
Answer:
The total change was 8*C
Step-by-step explanation:
If the unit rate is 2/1 ~2 degrees per every 1 hour~ than you would need to multiply 2 by the amount of hours given to get the total change in temperature, which would be 8*C.
This is exponential growth...
F=ar^t
F=25(1.15^t) so in six weeks...
F=25(1.15^6)
F≈57.82
F≈58 words per minute (to nearest whole word per minute)