77 unicorns, because yesterday the ratio was 6:5 and today it is 3:4. If you add the numbers for both ratios together, you get 11 and 7. Finding the LCM of these two gives 77 (because 7 and 11 are both prime).
You find the LCM of the sums because when you find values based on ratios, you divide value by the sum of the ratio.
e.g. I have 100 fruits. The ratio of apples to oranges is 2:3. How many apples are there?
To solve this you'd add 2 and 3 (5), divide 100 by 5 (20), multiply that by 2 (40) because that's the ratio of apples to oranges.
In this case, you do the reverse. So If I have 77 unicorns, then yesterday there were (77/11 = 7, 7*6= 42, 7*5= 35) 42 green unicorns and 35 yellow. The sum of 42 and 35 is 77. If you do this process with the other ratio you'll get similar results as well.
Answer:
∡TQS = 10x -3
Step-by-step explanation:
∡TQS = ∡RQS - ∡RQT
= 22x - 11 - (12x - 8)
= 10x -3
The value of x when y = -14 is 7
Step-by-step explanation:
Direct variation is a relationship between two variables that can
be expressed by an equation in which one variable is equal to a
constant times the other
If y varies directly with x, then
- y ∝ x
- y = k x, is the equation of variation where k is the constant of variation
∵ y varies directly with x
∴ y ∝ x
∴ y = k x
To find k substitute x and y by their initial values
∵ y = 16 and x = -8
- Substitute y by 16 and x by -8 in the equation above
∴ 16 = k(-8)
- Divide both sides by -8
∴ -2 = k
∴ The value of k is -2
- Substitute the value of k in the equation above
∴ y = -2 x ⇒ equation of variation
∵ y = -14
- To find x substitute y by -14 in the equation of variation
∵ -14 = -2 x
- Divide both sides by -2
∴ 7 = x
∴ The value of x is 7
The value of x when y = -14 is 7
Learn more:
You can learn more about variation in brainly.com/question/10708697
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Answer:
a) (59180,60820)
b) (59020,60980)
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $60,000
Standard Deviation, σ = $5,000
Sample size, n = 100
a) 90% critical values
Putting the values, we get,
b) 95% critical values
Putting the values, we get,
A & C
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