The solution of the given equation is -6 and 1.
<h3>What is Quadratic Equation?</h3>
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Here, given equation:
(x+2)(x+3) = 12
x(x+3)+2(x+3) = 12
x² + 3x + 2x + 6 = 12
x² + 5x + 6 - 12 = 0
x² + 5x - 6 = 0
x² + 6x - x - 6 = 0
x(x+6) -1(x+6) = 0
(x+6)(x-1) = 0
Now, x + 6 = 0 or x - 1 = 0
x = -6 or x = 1
Thus, the solution of the given equation is -6 and 1.
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4/7 of the children in the pool are girls
3/7 of the children in the pool are boys
4/7:3/7
4:3 is the ratio of girls to boys
Answer:
Infinite solution
Step-by-step explanation:
There is 3 possible solutions to a system of linear equations:
- One solution - two distinct lines that do not share y-intercept or slop intersect at a point
- No solution - two distinct lines that share the same slope but not the same y-intercept never intersect and are parallel
- Infinite solution - one distinct function represented two ways which in simplest form share the same slope and y-intercept
The first equation is in simplest form y=2x+3.
The second equation 2y=4x+6 when simplified becomes y=2x+3.
These are the same lines with the same slope and y-intercept. Therefore, they have infinite solutions.
Answer:
a) sample of size n from the population has an equal chance of being selected.
b) Every member of the population has an equal chance of being included in the sample.
Step-by-step explanation:
Simple random sampling:
- It is a type of probabilistic sampling.
- It is an unbiased representation of population.
- The probability of selection is equal for every observation.
- A sample is taken in such a way that each member has an equal probability of being selected.
- A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
- Thus,the correct interpretation is given by,
a) sample of size n from the population has an equal chance of being selected.
b) Every member of the population has an equal chance of being included in the sample.
- c) The simplest method of selection is used to create a representative sample.
The statement is false.
There is no pattern or technique used for selection. The selection is purely random.
- d) Each subset of the population has an equal chance of being included in the sample.
The statement is false.
Each object of the population has an equal chance of being included in the sample. and not each subset.
- e) Every sample of size n from the population has a proportionally weighted chance of being selected.
The given statement is false.
