Lines j and k are intersected by line m. At the intersection of lines j and m, the uppercase left angle is 93 degrees. At the in
tersection of lines k and m, the bottom right angle is 93 degrees. Given the information in the diagram, which theorem best justifies why lines j and k must be parallel? a) alternate interior angles theorem b) alternate exterior angles theorem c) converse alternate interior angles theorem d) converse alternate exterior angles theorem
2 answers:
Answer:
b) alternate exterior angles theorem
Step-by-step explanation:
When two lines are cut by a transversal, the alternate exterior angles are congruent. In the first diagram:
- x and y are congruent
- a and b are congruent
Comparing with our given lines, j, k and m.
We can see that the two given angles are in the same position as in the first image. Therefore, lines j and k are parallel by the alternate exterior angles theorem.
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Answer:
1) 22.66%
2) 20
Step-by-step explanation:
The scores of a test are normally distributed.
Mean of the test scores = u = 22
Standard Deviation = = 4
Part 1) Proportion of students who scored atleast 25 points
Since, the test scores are normally distributed we can use z scores to find this proportion.
We need to find proportion of students with atleast 25 scores. In other words we can write, we have to find:
P(X ≥ 25)
We can convert this value to z score and use z table to find the required proportion.
The formula to calculate the z score is:
Using the values, we get:
So,
P(X ≥ 25) is equivalent to P(z ≥ 0.75)
Using the z table we can find the probability of z score being greater than or equal to 0.75, which comes out to be 0.2266
Since,
P(X ≥ 25) = P(z ≥ 0.75), we can conclude:
The proportion of students with atleast 25 points on the test is 0.2266 or 22.66%
Part 2) 31st percentile of the test scores
31st percentile means 31%(0.31) of the students have scores less than this value.
This question can also be done using z score. We can find the z score representing the 31st percentile for a normal distribution and then convert that z score to equivalent test score.
Using the z table, the z score for 31st percentile comes out to be:
z = -0.496
Now, we have the z scores, we can use this in the formula to calculate the value of x, the equivalent points on the test scores.
Using the values, we get:
Thus, a test score of 20 represent the 31st percentile of the distribution.
Answer:
The triangular prism shown has 2 triangular face(s) and 3 lateral face(s).
The area of one triangular face is 7.5 mm²
The surface area of the triangular prism is 135 mm²
Step-by-step explanation:
A triangular face of the prism is the face that has a three sided figure while the lateral faces are faces with four-sided figure. As seen from the triangular prism, it has 2 triangular faces since it is made up of 2 right angled triangles and has 3 lateral faces since it is made up of 3 rectangles which are 4 sided each.
Area of one triangular face =
Given base = 2.5 mm and height = 6 mm
Area of one triangular face =
Surface area of triangular prism = bh + pH
b= base of the triangle = 2.5 mm
h- height of the triangle = 6 mm
p= perimeter of the triangle = base + height + slant height = 2.5+6+6.5
p = 15 mm
H= height of the prism = 8mm
Surface area of triangular prism = 2.5(6)+15(8)
Surface area of triangular prism = 15 + 120
Surface area of triangular prism = 135mm²
Answer:
Step-by-step explanation:
The following formula is used to compute the Proportion of error-free units given the sigma level in Excel.
<em> The proportion of error-free units = NORMSDIST(Sigma Level - 1.5) </em>
Suppose that a process is currently operating at a 3.5-sigma quality level.
The proportion of error-free units for this process is
NORMSDIST(3.5 - 1.5) = 0.977250
Therefore, the rejection rate is equal to
or 22750 PPM.
Now, consider a 6-sigma level process.
The proportion of error-free units equals
NORMSDIST(6.0 - 1.5) = 0.9999966
and the rejection rate is
Hence, reduction is PPM required per year , that is
reduction per year