Answer:
Step-by-step explanation:
Let x represent the random variable representing the scores in the exam. Given that the scores are normally distributed with a mean of 40 and a standard deviation of 5, the diagram representing the curve and the position of the mean, the mean plus or minus one standard deviation, the mean plus or minus two standard deviations, and the mean plus or minus three standard deviations is shown in the attached photo
1 standard deviation = 5
2 standard deviations = 2 × 5 = 10
3 standard deviations = 3 × 5 = 15
1 standard deviation from the mean lies between (40 - 5) and (40 + 5)
2 standard deviations from the mean lies between (40 - 10) and (40 + 10)
3 standard deviations from the mean lies between (40 - 15) and (40 + 15)
b) We would apply the probability for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 40
σ = 5
the probability that a randomly selected score will be greater than 50 is expressed as
P(x > 50) = 1 - P( ≤ x 50)
For x = 50,
z = (50 - 40)/5 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.98
P(x > 50) = 1 - 0.98 = 0.02
Check out the attached image for the answers.
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Statement 2 is blank, but it has the reasoning "Corresponding angles postulate"
Because BD || AE, we know that the corresponding angles are congruent.
One pair of corresponding angles is angle 1 and angle 4. This is because they are on the same side of the transversal AC and they are both above their parallel line counter-part. Similarly, angle 2 and angle 3 are another corresponding pair.
So you'll have "angle1=angle4, angle3=angle2" in the first blank slot
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Reason 3 is blank. The statement is that triangle ACE is similar to triangle BCD. The reason why the are similar is the AA (angle angle) similarity postulate. This says that if you know two pairs of angles are congruent, then the triangles are similar. The two pairs of angles were mentioned back on the previous line (line 2)
So you'll put "Angle-Angle Similarity Postulate" in the second blank.
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Look at the line just above the last line. Here we have
1 + (BA/CB) = 1 + (DE/CD)
If we subtract 1 from both sides, we end up with,
BA/CB = DE/CD
which is what will go in the last blank space
Side Note: The last statement will always be what you want to prove. So you can just look at the very top of the problem where it says "Prove:" under the "Given" part. Then just copy/paste the statement you want to prove, which in this case is BA/CB = DE/CD
Answer:
A = 2, the number is 3221
Step-by-step explanation:
In order for the number to be divisible by 9, the sum of it's digit has to be divisible by 9.
In our case, 
where k is an integer. the easiest way happens when k=1
Higher values of k will likely most work (with k=2 you get A to be a non-integer, which can't work since it's the digit of a number, and with higher values of K you're not getting a number in base 10.
you can measure the first angle with a protractor and then measure the other one see if there is a different angle
Answer:
C 5a^2 +70a +240
Step-by-step explanation:
We have given these following functions:
h(a+4)
This function is:
f[h(a+4)]
Thus
The correct answer is given by option C.
