Answer:
p = 1.5 and q = 9
Step-by-step explanation:
Expand the right side then compare the coefficients of like terms on both sides, that is
4(x + p)² - q ← expand (x + p)² using FOIL
= 4(x² + 2px + p²) - q ← distribute parenthesis
= 4x² + 8px + 4p² - q
Comparing coefficients of like terms on both sides
8p = 12 ( coefficients of x- terms ) ← divide both sides by 8
p = 1.5
4p² - q = 0 ( constant terms ), that is
4(1.5)² - q = 0
9 - q = 0 ( subtract 9 from both sides )
- q = - 9 ( multiply both sides by - 1 )
q = 9
2x2-5x-3=0
Two solutions were found :
x = -1/2 = -0.500
x = 3
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x2 - 5x) - 3 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2-5x-3
The first term is, 2x2 its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .
The probability of drawing a green marble is 8/20.
there are 20 marbles total and 8 of them are green.
Answer:
At least 75% of these commuting times are between 30 and 110 minutes
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by 
.
In this question:
Mean of 70 minutes, standard deviation of 20 minutes.
Since nothing is known about the distribution, we use Chebyshev's Theorem.
What percentage of these commuting times are between 30 and 110 minutes
30 = 70 - 2*20
110 = 70 + 2*20
THis means that 30 and 110 minutes is within 2 standard deviations of the mean, which means that at least 75% of these commuting times are between 30 and 110 minutes
