Graph the Inequality.
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Answer:
x ≤ -7
Step-by-step explanation:
There is a filled in circle which means that it is either ≤ or ≥.
The graph is going to the left, which means it is ≤
The starting number is -7.
x ≤ -7
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Suppose that an airline uses a seat width of 16.7 in. Assume men have hip breadths that are normally distributed with a mean of 14.2 in. and a standard deviation of 0.9 in. Complete parts? (a) through? (c) below. A) Find the probability that if an individual man is randomly? selected, his hip breadth will be greater than 16.7 in. B) If the plane is filled with 126 randomly selected men find the the probability that these men have a mean hip breadth greater than 16.7. C) Which results should be considered for any changes in seat design: the result from part a or part b. TI84 use pleaese
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9:44+8:10 = 17.54
Answer : 17 hours and 54 minutes
If you have questions please let me know
I hope that's help !
The solution for \( x \) of the equation \( 8 e^{x}-1=0 \) is
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Answer:
Step-by-step explanation:
The equation \(8e^x - 1 = 0\) can be solved to find the value of \(x\).
To solve for \(x\), we need to isolate the exponential term, \(e^x\).
Here are the steps to solve the equation:
1. Add 1 to both sides of the equation to isolate the exponential term:
\(8e^x = 1\)
2. Divide both sides of the equation by 8:
\(\frac{{8e^x}}{8} = \frac{1}{8}\)
3. Simplify:
\(e^x = \frac{1}{8}\)
4. To solve for \(x\), we can take the natural logarithm (ln) of both sides of the equation:
\(\ln(e^x) = \ln\left(\frac{1}{8}\right)\)
5. Since \(\ln(e^x)\) and \(e^x\) are inverse functions, they cancel each other out:
\(x = \ln\left(\frac{1}{8}\right)\)
6. Use the properties of logarithms to simplify further:
\(x = \ln(1) - \ln(8)\)
7. Simplify:
\(x = -\ln(8)\)
Therefore, the solution for \(x\) in the equation \(8e^x - 1 = 0\) is \(x = -\ln(8)\).
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But you must rearrange this into y=mx+b form
to do this subtract 7x from both sides
y= -7x+5
On the y axis plot a dot on 5 because that is the y intercept.
To find the x intercept let y=0
0= -7x+5
1. Subtract 5 to both sides
-5=-7x
2. Divide by -7 to both sides
x= -5/-7
x=5/7
The x intercept is 5/7, so on the x axis mark a dot on 5/7 which is approximately at 0.7
Once you have marked one dot on the y axis at 5 and another dot on the x-axis at 0.7 then you draw a straight line through these points and you have graphed the function 7x+y=5
For your equation, once you solve it for Y, you get this:
Now, the coefficient of X is a very crucial part of graphing an equation. Once the equation is solved for Y, the coefficient of X is going to be the slope of the line you are graphing. The slope of a line is how much Y goes up every time X is increased by 1.
To graph an equation, you need to put in a number for X and find the matching value for Y and then graph that point. To do this, you will need a coordinate plane. I can't show you what that looks like on here. But, I will do my best to explain how it is done.
Now, for your equation:
Simply chose a number for X and find the matching value for Y. I'll try 0 for an example:
-7 * 0 is 0. Therefore, your new equation looks like this:
Therefore, one "Solution pair" to this equation is (X=0,Y=5)
Simply repeat this process and plot the solution pairs on the coordinate plane and then connect the dots.
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In 26*51! ways we can pick 50 cards from a deck of 52 cards using permutation.
What is Permutation?
Permutation is mathematical technique to get possibiltiy in arrangement with replacement.
We can choose or pick r objects from n objects using permutation in ways.
n! = n*(m-1)*......*3*2*1
We can write n! = n(n-1)!
Total number of matters or cards = 52
We have to pick 50 cards using permutation or replacement.
The required number of ways
Hence we can choose 50 cards from deck of 52 cards in 6*51! ways.
Learn more about Permutation here -
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