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1 answer:
Given:
The figure of a triangle DEF.
To find:
The coordinate of image of given triangle after reflection over y-axis.
Solution:
The vertices of given triangle are D(1,4), E(4,3), F(2,0).
If a figure is reflected over the y-axis, then the rule of reflection is
Using this rule, we get
Therefore, the coordinates of image are D'(-1,4), E'(-4,3) and F'(-2,0).
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Using the normal distribution, the probabilities are given as follows:
a. 0.4602 = 46.02%.
b. 0.281 = 28.1%.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The parameters are given as follows:
Item a:
The probability is <u>one subtracted by the p-value of Z when X = 984</u>, hence:
Z = 0.1
Z = 0.1 has a p-value of 0.5398.
1 - 0.5398 = 0.4602.
Item b:
By the Central Limit Theorem:
Z = 0.58
Z = 0.58 has a p-value of 0.7190.
1 - 0.719 = 0.281.
More can be learned about the normal distribution at brainly.com/question/4079902
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there are 4 of the 10-nf and 8 of the 100-nf capacitors which is a total of 12 items.
the probability of drawing a 10-nf is: 4 out of 12 =
the probability of drawing a 100-nf is: 8 out of 12 =
(a) "at least two" means: 2 or 3 or 4
Probability of 2 (10's) and 2 (100's): x
x
x
=
Probability of 3 (10's) and 1 (100's): x
x
x
=
Probability of 4 (10's) and 0 (100's): x
x
x
=
2 or 3 or 4: +
+
=
(b) without replacement
Probability of 2 (10's) and 2 (100's): x
x
x
=
Probability of 3 (10's) and 1 (100's): x
x
x
=
Probability of 4 (10's) and 0 (100's): x
x
x
=
2 or 3 or 4: +
+
=
=
=