Answer:
(-1, -1)
Step-by-step explanation:
Let's set these two equations equal to each other to solve the system:
x = 2x + 1
Solving for x, we get x = -1
Plug this value of x back into any of the two equations to get y: y = 2 * (-1) + 1 = -1.
Thus, the point of intersection is (-1, -1).
Hope this helps!
Answer:
- 27 hot dogs
- 13 bags of popcorn
Step-by-step explanation:
Had all received popcorn, the bill would have been 40×$1.75 = $70. The bill was $13.50 more than that. Each hot dog purchased in place of popcorn adds $0.50 to the bill, so the number of hot dogs must be ...
$13.50/$0.50 = 27
Of course, the remainder of the 40 items were popcorn, so 13 bags of popcorn.
27 hot dogs and 13 bags of popcorn were purchased.
Let red marbles = X.
The probability is 1 out of 5, written as 1/5
1/5 in terms of red marbles is equal to the number of red marbles divided by 5x, where 5x is the total number of marbles.
1/5 = x/5x
Now you have 5x total marbles, x red and 4x blue.
Add 5 more red and the new probability is:
(x+5)/(5x+5) = 1/3
Simplify:
3x+15 = 5x+5
Now solve for x:
Subtract 3x from both sides:
15 = 2x +5
Subtract 5 from each side:
2x = 10
Divide both sides by 2:
x = 10/2
X = 5
There were originally 5 red marbles.
Reliable causal inference based on observational studies is seriously threatened by unmeasured confounding.
What is unmeasured cofounding?
- By definition, an unmeasured confounder is a variable that is connected to both the exposed and the result and could explain the apparent observed link.
- The validity of interpretation in observational studies is threatened by unmeasured confounding. The use of negative control group to reduce unmeasured confounding has grown in acceptance and popularity in recent years.
Although they've been utilised mostly for bias detection, negative controls have a long history in laboratory sciences and epidemiology of ruling out non-causal causes. A pair of negative control exposure and outcome variables can be utilised to non-parametrically determine the average treatment effect (ATE) from observational data that is vulnerable to uncontrolled confounding, according to a recent study by Miao and colleagues.
Reliable causal inference based on observational studies is seriously threatened by unmeasured confounding.
Learn more about unmeasured confounding here:
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