Since the lines are perpendicular, the slope of the green line has to be the negative reciprocal of the slope of the red line. the negative reciprocal of -1/3 is 3 so C) 3 is your answer.
bearing in mind that, the geometric sequence is "convergent" only when |r|<1, or namely "r" is a fraction between 0 and 1.
Answer: 89 4th grader
Step-by-step explanation:
In a large population, 61% of the people are vaccinated, meaning there are 39% who are not. The problem asks for the probability that out of the 4 randomly selected people, at least one of them has been vaccinated. Therefore, we need to add all the possibilities that there could be one, two, three or four randomly selected persons who were vaccinated.
For only one person, we use P(1), same reasoning should hold for other subscripts.
P(1) = (61/100)(39/100)(39/100)(39/100) = 0.03618459
P(2) = (61/100)(61/100)(39/100)(39/100) = 0.05659641
P(3) = (61/100)(61/100)(61/100)(39/100) = 0.08852259
P(4) = (61/100)(61/100)(61/100)(61/100) = 0.13845841
Adding these probabilities, we have 0.319761. Therefore the probability of at least one person has been vaccinated out of 4 persons randomly selected is 0.32 or 32%, rounded off to the nearest hundredths.
Multiple: 4 * 1
/2 = 4 · 1 = 4
/2 = 2 · 2
1 · 2 1 · 2 = 2
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(4, 2) = 2
Multiple: 7 * 2 = 14
Multiple: 5 * 1
/3 = 5 · 1
1 · 3 = 5
/3
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(5, 3) = 1
Multiple: 3 * 5
/3 = 3 · 5
1 · 3 = 15
/3 = 5 · 3
1 · 3 = 5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(15, 3) = 3
Add: 14 + 5 = 19
Multiple: -3 * 1
/2 = -3 · 1
1 · 2 = -3
/2
= -1.5 · 2
1 · 2
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-3, 2) = 2
Multiple: 1/2 * (-3
/2
) = 2 · (-3)
1 · 2 = -6
/2 = -3 · 2
1 · 2 = -3
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-6, 2) = 2
Add: 19 + (-3) = 16
7(4×1/2) + 3(5×1/3) + 2(-3×1/2) = 16
/1 = 16
