Answer:
-7/(x-5) - 3
Step-by-step explanation:
First off, to reflect an equation in the y axis, just multiply by -1. Now that it is reflected, to stretch an equation by a factor of 7, multiply it by 7. Now we have -7/x.
Then, to move an equation down by 3 units, simply subtract it by 3. Now we have -7/x - 3.
Lastly, since you want to translate it 5 units to the left, you want the equation to be undefined at x = 5 (because originally it is undefined at x = 0). To do that, set the denominator to x - 5. We arrive at our answer: -7/(x-5) - 3.
Answer:
And we can find this probability using the normal standard table or excel and we got:
The figure shows the calculation for this case.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the hardness of a population, and for this case we know the distribution for X is given by:
Where 
and 
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel and we got:
The figure shows the calculation for this case.
Given P(E) = 0.24 and P(F ∩ E) = 0.17
It says to find conditional probability of F given E has occurred.
We know the formula of conditional probability is given by :-
P(F ║ E) = 
P(F ║ E) = 
= 0.708333
P(F ║ E) = 0.71
Hence, option C i.e. 0.71 is the final answer.
Answer/Step-by-step explanation:
1. The figure is composed of a triangle and a rectangle.
Area of the triangle = ½*base*height
base = 4 ft
height = 12 - 8 = 4ft
Area of triangle = ½*4*4 = 8 ft²
Area of rectangle = length * width
Length = 8 ft
Width = 4 ft
Area of rectangle = 8*4 = 32 ft²
✔️Area of the figure = 8 + 32 = 40 ft²
2. The figure is composed of a semicircle and a triangle
Area of the semicircle = ½(πr²)
radius (r) = 3 cm
π = 3
Area = ½(3*3²) = 13.5 cm²
Area of triangle = ½*base*height
base = 3*2 = 6 cm
height = 6 cm
Area = ½*6*6 = 6 cm²
✔️Area of the figure = 13.5 + 6 = 19.5 cm²
Answer:
0.2231 (22.31%)
Step-by-step explanation:
defining the event F = the marketing company is fired, then the probability of being fired is:
P(F)= probability that the advertising campaign is cancelled before lunch * probability that marking department is fired given that the advertising campaign was cancelled before lunch + probability that the advertising campaign is launched but cancelled early * probability that marking department is fired given that the advertising campaign is launched but cancelled early .... (for all the 4 posible scenarios where the marketing department is fired)
thus
P(F) =0.10 * 0.74 + 0.18 * 0.43 + 0.43 * 0.16 + 0.29*0.01 = 0.2231 (22.31%)
then the probability that the marketing department is fired is 0.2231 (22.31%)
