Answer: m∠OPQ + (2x + 16)° = 180°
Step-by-step explanation:
Opposite angles of a cyclic quadrilateral are supplementary.
Answer:The present age of both of them are Christopher = 42 years, and Ishaan = 84 years.
Step-by-step explanation: Solution:
Let present age of:
Christopher =
x
yrs
Ishaan =
2
x
yrs ( given that Ishaan is 2 times as old as Christopher)
35 yrs ago:
Age of Christopher = (
x
- 35)yrs
Age of Ishaan = (
2
x
- 35) yrs
According to question, 35 yrs back, Ishaan was 7 times older than Christopher.
Therefore
7 X (
x
- 35) = (
2
x
- 35)
7
x
- 245 =
2
x
- 35
7
x
-
2
x
= 245 - 35
5
x
= 210
x
= 42
So present age of Christopher =
x
= 42 yrs
&
Present age of Ishaan =
2
x
= 84 yrs
Check your solution:
As 84 is 2 times of 42 so Ishaan is 2 times older than Christopher.
35 yrs ago, Christopher was (42 - 35) = 7 yrs old and Ishaan was (84 - 35) = 49 yrs old so Ishaan was 7 times older than Christopher then.
For the two figures to be similar, the missing length must be 30.
<h3 /><h3>What is the missing length?</h3>
For the two figures to be similar, the dimension of each figures must be proportional to each other.
Let the missing length be x.
Hence,
x/25 = 24/20
We cross multiply
x × 20 = 24 × 25
x × 20 = 600
x = 600/20
x = 30
Therefore, for the two figures to be similar, the missing length must be 30.
Learn more about similarity and congruence here: brainly.com/question/7888063
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Answer:
1) 68%
2) 68%
Step-by-step explanation:
<h2>1) The ages of trees</h2>
We know the mean and the standard deviation.
The mean is:

The standard deviation is:

The Z-score formula is:

For x=20 the Z-score is:

For x=30 the Z-score is:

Then we look for the percentage of the data that is between
deviations from the mean.
According to the empirical rule 68% of the data is less than 1 standard deviations of the mean. This means that 68% of the trees are between 20 and 30 years old
<h2>
2) Pizza delivery </h2>
First we calculate the Z-scores
We know the mean and the standard deviation.
The mean is:

The standard deviation is:

The z-score formula is:

For x=24 the Z-score is:

For x=30 the Z-score is:

Then we look for the percentage of the data that is between
deviations from the mean.
According to the empirical rule 68% of the data is less than 1 standard deviations of the mean. This means that 68% of pizzas are delivered between 24 and 30 minutes
Answer:
110x -200y
Step-by-step explanation:
10(x - 20y) + 100x
Distribute
10x-200y +100x
Combine like terms
110x -200y