Step 1: Simplify both sides of the equation.
Step 2: Subtract 6x from both sides.
- 65x²+390x+585−6x=6x−6x
- 65x²+384x+585=0
For this equation: a=65, b=384, c=585
Step 3: Use quadratic formula with a=65, b=384, c=585
- x=−b±√b2−4ac/2a
- x=−(384)±√(384)2−4(65)(585)/
- 2(65)
- x=−384±√−4644/130
Therefore, There are no real solutions.
Probability =
(number of ways it can come out the way you want it to)
divided by
(total number of ways it can come out).
Total number of ways it can come out =
number of bottles in the cooler
= (10 + 15 + 13) = 38 .
Number of ways it can come out the way you want it to =
(soda + lemonade)
= (10 + 15) = 25 .
Probability of coming out the way you want it to =
25 / 38 = about 65.8 % .
The given function is:

The parents functions of g(x) will be:

The domain of g(x) and its parent function is the same i.e. Set of all Real numbers except 0.
The range of g(x) and its parent function is the same i.e. set of all real numbers except 0.
g(x) and its parent function only decrease. They do not increase over any interval. However, the interval in which they decrease is the same for both.
So, the correct answers are:The domain of g(x) is the same as the domain of the parent function.
<span>The range is the same as the range of the parent function.
</span><span>The function g(x) decreases over the same x-values as the parent function.</span>
Answer:
The value is 
Step-by-step explanation:
From the question we are told that
The population proportion is 
The sample size is n = 563
Generally the population mean of the sampling distribution is mathematically represented as

Generally the standard deviation of the sampling distribution is mathematically evaluated as

=>
=>
Generally the probability that the proportion of persons with a college degree will differ from the population proportion by less than 5% is mathematically represented as

Here
is the sample proportion of persons with a college degree.
So
![P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 )) = P(\frac{[[0.05 -0.52]]- 0.52}{0.02106} < \frac{[\^p - p] - p}{\sigma } < \frac{[[0.05 -0.52]] + 0.52}{0.02106} )](https://tex.z-dn.net/?f=P%28%20-%20%280.05%20-%200.52%20%29%20%3C%20%20%5C%5E%20p%20%3C%20%20%280.05%20%2B%200.52%20%29%29%20%3D%20P%28%5Cfrac%7B%5B%5B0.05%20-0.52%5D%5D-%200.52%7D%7B0.02106%7D%20%3C%20%5Cfrac%7B%5B%5C%5Ep%20-%20p%5D%20-%20p%7D%7B%5Csigma%20%7D%20%20%3C%20%5Cfrac%7B%5B%5B0.05%20-0.52%5D%5D%20%2B%200.52%7D%7B0.02106%7D%20%29)
Here
![\frac{[\^p - p] - p}{\sigma } = Z (The\ standardized \ value \ of\ (\^ p - p))](https://tex.z-dn.net/?f=%5Cfrac%7B%5B%5C%5Ep%20-%20p%5D%20-%20p%7D%7B%5Csigma%20%7D%20%20%3D%20Z%20%28The%5C%20standardized%20%5C%20%20value%20%5C%20%20of%5C%20%20%28%5C%5E%20p%20-%20p%29%29)
=> ![P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 )) = P[\frac{-0.47 - 0.52}{0.02106 } < Z < \frac{-0.47 + 0.52}{0.02106 }]](https://tex.z-dn.net/?f=P%28%20-%20%280.05%20-%200.52%20%29%20%3C%20%20%5C%5E%20p%20%3C%20%20%280.05%20%2B%200.52%20%29%29%20%3D%20P%5B%5Cfrac%7B-0.47%20-%200.52%7D%7B0.02106%20%7D%20%20%3C%20%20Z%20%20%3C%20%5Cfrac%7B-0.47%20%2B%200.52%7D%7B0.02106%20%7D%5D)
=> ![P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 )) = P[ -2.37 < Z < 2.37 ]](https://tex.z-dn.net/?f=P%28%20-%20%280.05%20-%200.52%20%29%20%3C%20%20%5C%5E%20p%20%3C%20%20%280.05%20%2B%200.52%20%29%29%20%3D%20P%5B%20-2.37%20%3C%20%20Z%20%20%3C%202.37%20%5D)
=> 
From the z-table the probability of (Z < 2.37 ) and (Z < -2.37 ) is

and

So
=>
=>
=> 
Answer:
11
Step-by-step explanation:
There are more than eleven cards in a deck but there can only be one outcome because there are only 11 letters in the word PERSONALITY.