So, the best way to do this is translate it to clockwise. 90 degrees counterclockwise is equal to 270 degrees clockwise. So, basically, to rotate, you would follow the following format for each point-
(X,Y) -> (-Y,X)
Now, you do it for each of the points.
A= (-5,5), so A' would be (-5,-5)
B= (-1,5), so B' would be (-5,-1)
C= (-5,4), so C' would be (-4,-5)
D= (-1,4) so D' would be (-4,-1)
Notice, how all the points end up in the square below it. Each quadrant has a specific number. The top right is quadrant 1, the top left is quadrant 2, the bottom left is quadrant 3, and the bottom right is quadrant 4. If you are rotating 270 degrees clockwise, you move to the right, like a clock. That puts the new rectangle in quadrant 3. That is a way to check your work.
Now, just so you know for future reference, the following are also different formats for different problems--
A 90 degree Clockwise rotation about the origin will be (X,Y) -> (Y, -X) *Note, -x just stands for the opposite. Say your original x is a negative number. Then the prime (new) x will be positive.
A 180 degree Clockwise rotation about the origin would be (X,Y) -> (-X,-Y) *Note, -y also stands for the opposite.
A 270 degree clockwise rotation about the origin would be (X,Y) -> (-Y,X).
For translating---
90 degrees Clockwise = 270 degrees Counter
270 degrees Clockwise = 90 degrees Counter
Hope this helped!
Answer:
The lowest time limit in which 95% of the bugs can be found is 11.22 hours.
Step-by-step explanation:
We are given that X is the time in hours required to find a bug in a software system. Assume that X is normally distributed with mean of 3 and standard deviation of 5.
<em>So, X = time in hours required to find a bug in a software system </em>
X ~ N()
The z score probability distribution is given by;
Z = ~ N(0,1)
where, = mean value
= standard deviation
<em>Let the lowest time limit in which 95% of the bugs can be found = </em><em />
Now, we have to find the lowest time limit in which 95% of the bugs can be found, i.e.;
P( < ) = 0.95
P(Z < ) = 0.95
Now, the critical value of in the z table which given an area of less than 95% is 1.6449, which means;
= 1.6449
= 3 + 8.22 = 11.22
Therefore, the lowest time limit in which 95% of the bugs can be found is 11.22 hours.
Let A represents the event that DVD has a video effect.
So,
P(A) = 1.5 %
Let B represents the event that DVD has a audio defect.
So,
P(B) = 0.8 %
A ∩ B represents that DVD has both audio and video defect.
So,
P(A∩B) = 0.4%
Part a)
A ∪ B represents that DVD has a video or audio defect.
P(A∪B) = P(A)+P(B)-P(A∩B) = 1.5 + 0.8 - 0.4 = 1.9%
Thus the probability that the DVD purchased by the customer has a video or audio defect is 1.9%.
Part b)
The complement of P(A∩B) will represent the probability that the DVD does not have video or audio defect.
So, the probability that DVD purchased by customer does not have video or audio defect is 1 - 0.4 = 0.96%
<u>Answer:</u>
- For 15 pens, the cost is $7.2
<u>Step-by-step explanation:</u>
<u>We know that:</u>
<u>Work:</u>
Divide the RHS:
- => 1 pen = 3.84/8
- => 1 pen = 0.48
Multiply the RHS:
- => 15 pens = 0.48 x 1
- => 15 pens = $7.2
Hence, <u>for 15 pens, the cost is $7.2</u>
Hoped this helped.
2.86 gallons
Step-by-step explanation:
If 1/35 gallon of gas = 1 mile
To travel 100 miles,
1/35 * 100
= 0.0286 * 100
= 2.86 gallons
Therefore, the car needs 2.86 gallons of gas to travel 100 miles