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1 answer:
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Given data is 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22
Arranging it in increasing order:
22 25 34 35 41 41 46 46 46 47 49 54 54 59 60
Number of data items, n=15.
Finding Median, First Quartile, and Third Quartile
22 25 34 35 41 41 46 46 46 47 49 54 54 59 60
Now finding First Quartile from set: 22 25 34 35 41 41 46
Q₁ = middle term i.e. 35
Now finding Third Quartile from set: 46 47 49 54 54 59 60
Q₃ = middle term i.e. 54
So we have Q₁ = 35, M = 46, and Q₃ = 54. Lower bound is 22 and Upper bound is 60.
While drawing the given data on number line and marking First quartile, Median, Third quartile on number line. We can clearly observe that option A matches with given data points.
Hence, option A i.e. Box-plot A is the correct choice.
Answer:
The simplest form is x/(x + 3)
Step-by-step explanation:
* To simplify the rational Expression lets revise the factorization
of the quadratic expression
* To factor a quadratic in the form x² ± bx ± c:
- First look at the c term
# If the c term is a positive number, and its factors are r and s they
will have the same sign and their sum is b.
# If the c term is a negative number, then either r or s will be negative
but not both and their difference is b.
- Second look at the b term.
# If the c term is positive and the b term is positive, then both r and
s are positive.
Ex: x² + 5x + 6 = (x + 3)(x + 2)
# If the c term is positive and the b term is negative, then both r and s
are negative.
Ex: x² - 5x + 6 = (x -3)(x - 2)
# If the c term is negative and the b term is positive, then the factor
that is positive will have the greater absolute value. That is, if
|r| > |s|, then r is positive and s is negative.
Ex: x² + 5x - 6 = (x + 6)(x - 1)
# If the c term is negative and the b term is negative, then the factor
that is negative will have the greater absolute value. That is, if
|r| > |s|, then r is negative and s is positive.
Ex: x² - 5x - 6 = (x - 6)(x + 1)
* Now lets solve the problem
- We have two fractions over each other
- Lets simplify the numerator
∵ The numerator is
- Factorize its denominator
∵ The denominator = x² + 2x - 3
- The last term is negative then the two brackets have different signs
∵ 3 = 3 × 1
∵ 3 - 1 = 2
∵ The middle term is +ve
∴ -3 = 3 × -1 ⇒ the greatest is +ve
∴ x² + 2x - 3 = (x + 3)(x - 1)
∴ The numerator =
- Lets simplify the denominator
∵ The denominator is
- Factorize its denominator
∵ The denominator = x² - 2x
- Take x as a common factor and divide each term by x
∵ x² ÷ x = x
∵ -x ÷ x = -1
∴ x² - 2x = x(x - 1)
∴ The denominator =
* Now lets write the fraction as a division
∴ The fraction = ÷
- Change the sign of division and reverse the fraction after it
∴ The fraction =
* Now we can cancel the bracket (x + 2) up with same bracket down
and cancel bracket (x - 1) up with same bracket down
∴ The simplest form =