The legs of a triangle with a hypotenuse that measures 15 units long have lengths that are equal to 15 times the sine or cosine of the given angle.
leg 1 = (15 units) x (cos 19) = 14.18 units
leg 2 = (15 units) x (sin 19) = 4.88 units
The lengths of the legs are 14.18 units and 4.88 units.
There are 14 thirds in 4 2/3
The answer is No because the sample is not representative of the whole population. The standard deviation of the sample is not a good estimate of the variation of the salaries of the TV personalities in general because a single sample is not counted as a whole. Standard Deviation is a quantity that is calculated to indicate the extent of deviation of the population or group as a whole. Standard deviation also represented by the symbol σ means sigma in Greek letter or s in Latin letter. It is also the measurement of a set of data values that are used to quantify the amount of variation.
Answer:
![15x^2+5xy-125=0](https://tex.z-dn.net/?f=15x%5E2%2B5xy-125%3D0)
Step-by-step explanation:
We are give the following in the question:
Dimensions of rectangle:
Length , l =
![l = x\sqrt{100} = 10x](https://tex.z-dn.net/?f=l%20%3D%20x%5Csqrt%7B100%7D%20%3D%2010x)
Width of rectangle, w =
![w = \dfrac{y}{2} +\dfrac{3x}{2}](https://tex.z-dn.net/?f=w%20%3D%20%5Cdfrac%7By%7D%7B2%7D%20%2B%5Cdfrac%7B3x%7D%7B2%7D)
Area of rectangle = 125 square cm.
Area of rectangle =
![A =l\times w](https://tex.z-dn.net/?f=A%20%3Dl%5Ctimes%20w)
Putting values, we get,
![125 = 10x\times (\dfrac{y}{2}+\dfrac{3x}{2})\\\\125 = 5xy+15x^2\\15x^2+5xy-125=0](https://tex.z-dn.net/?f=125%20%3D%2010x%5Ctimes%20%28%5Cdfrac%7By%7D%7B2%7D%2B%5Cdfrac%7B3x%7D%7B2%7D%29%5C%5C%5C%5C125%20%3D%205xy%2B15x%5E2%5C%5C15x%5E2%2B5xy-125%3D0)
is the required equation.
<u>Given</u>:
Given that in a game a player draws and replaces a card from a deck 2 times.
The possible outcomes and payouts are given.
We need to determine the expected value for someone playing the game.
<u>Expected value:</u>
The expected value for someone playing the game can be determined by
![EV=(\frac{26}{52})(\$ 20)+(\frac{52}{52})(\$4)+(\frac{52}{52})(\$ 0)+(\frac{26}{52})(-\$12)](https://tex.z-dn.net/?f=EV%3D%28%5Cfrac%7B26%7D%7B52%7D%29%28%5C%24%2020%29%2B%28%5Cfrac%7B52%7D%7B52%7D%29%28%5C%244%29%2B%28%5Cfrac%7B52%7D%7B52%7D%29%28%5C%24%200%29%2B%28%5Cfrac%7B26%7D%7B52%7D%29%28-%5C%2412%29)
Simplifying the values, we have;
![EV=(\frac{1}{2})(\$ 20)+(1)(\$4)+(1)(\$ 0)+(\frac{1}{2})(-\$12)](https://tex.z-dn.net/?f=EV%3D%28%5Cfrac%7B1%7D%7B2%7D%29%28%5C%24%2020%29%2B%281%29%28%5C%244%29%2B%281%29%28%5C%24%200%29%2B%28%5Cfrac%7B1%7D%7B2%7D%29%28-%5C%2412%29)
Dividing the terms, we get;
![EV=\$ 10+\$4+\$ 0+-\$6](https://tex.z-dn.net/?f=EV%3D%5C%24%2010%2B%5C%244%2B%5C%24%200%2B-%5C%246)
Adding, we have;
![EV=\$ 8](https://tex.z-dn.net/?f=EV%3D%5C%24%208)
Thus, the expected value for someone playing the game is $8