Hey there!
No numbers go into a prime number other than one and that number. 9 and 7 go into 63, so it’s not 63. 3 and 17 go into 51, so it’s not 51. 19 and 3 go into 57, so it’s not 57. That leaves 61. Nothing goes into this other than one and 61, so the answer is 61.
I hope this helps!
The mean is the average number meaning that it is all the numbers in a set added together and divided by how many number are in the set. In this case there are 4 numbers (16, 3, whatever number x is, and 5). So, to find out what x is, first you multiple 4 by the known mean which is 9.
4 x 9 = 36
Then you simply subtract 36 from all the known numbers to find x.
36 - 16 - 5 - 3 = 12
So x = 12
The probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.
<h3>How to calculate the probability?</h3>
From the information given, we have to find the probability for each fruit. This will be:
Almond = 12/50 = 0.24
Cashew = 10/50 = 0.2
Mixed = 6/50 = 0.12
Peanut = 14/50 = 0.28
Pecan = 8/50 = 0.16
Therefore, the probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.
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Answer:
The correlation between hour of the day and the speed over the limit at which the motorist is ticketed is weak positive correlation.
Step-by-step explanation:
The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.
The types of correlation coefficient are:
- +1 (-1) : Perfect positive (negative) correlation
- 0 to 0.30(-0.30) : Weak positive (negative) correlation
- 0.30(-0.30) to 0.70(-0.70) : Moderate positive (negative) correlation
- 0.70(-0.70) to 1 (-1) : Strong positive (negative) correlation
The correlation coefficient value between the hour of the day and the speed over the limit at which the motorist is ticketed is:
<em>r</em> = 0.12.
The value of <em>r</em> lies between:
0 < 0.12 < 0.30
Thus, the correlation between hour of the day and the speed over the limit at which the motorist is ticketed is weak positive correlation.
The plane will make an angle 
with the runway.
Explanation:
Given that the plane is flying at an altitude of 11 miles and is 193 miles from the runway, as measured from the ground.
We need to determine the angle that the plane will make with the runway.
From the given measurements, we can see that it is a right angled triangle. Hence, let us use the tangent formula to determine the angle.
The formula for the tangent is given by
Where 
and 
Substituting these values in the above equation, we get,
Dividing, we get,
Taking 
on both sides of the equation, we get,
Simplifying, we have,
Hence, the angle that the plane will make with the runway is
