The population of a small town is decreasing at a rate of 6% per year. If the town's population is 12,500 in 2017, what will the population be in 6 years?
8,623 people
8,000 people <--? or D
17,731 people
9,416
Write the equation of the line that passes through the points (-4,2) and (-3,5)
y= -3/7x+16
y= 1/7x+16 <--im not sure
y= 7x-16
y= 7x+26
Tyler rolls a 6-sided die. What is the probability that he rolls an even number of a 5?
1/12 <-- or 5/8?
1/2
2/3
5/8
hmmm
.94^6 * 12500 = 8623
slope = m = (5-2)/(-3+4) = 3
y = 3 x + b
5 = 3(-3) + b
5 = -9 + b
b = 14
so y = 3 x + 14 so none of your answers. You probably have a typo.
even is 2, 4, 6
so 4 of the six sides are even or 5
4/6 = 2/3
To answer the first question about the population of the small town decreasing over 6 years, we need to calculate the population at the end of 2023.
To do this, we'll use the formula for exponential decay: A = P(1 - r/n)^(nt), where:
- A is the final amount (population after 6 years)
- P is the initial amount (population in 2017)
- r is the rate of decrease per year (6% or 0.06)
- n is the number of times the rate is compounded per year (usually 1 for yearly)
- t is the number of years (6)
Plugging in the provided values, we get:
A = 12,500(1 - 0.06/1)^(1*6)
A = 12,500(0.94)^6
A ≈ 12,500(0.5488)
A ≈ 6,860.01
Rounded to the nearest whole number, the population of the small town in 2023 will be 6,860. So the correct answer is 8,623 people (closest option).
Moving on to the second question about the equation of a line passing through the points (-4,2) and (-3,5). To find the equation, we can use the point-slope form: y - y1 = m(x - x1), where:
- (x1, y1) are the coordinates of one of the points on the line
- m is the slope of the line
Using the first point (-4,2) as (x1, y1), we have:
y - 2 = m(x - (-4))
y - 2 = m(x + 4)
y - 2 = mx + 4m <-- (1)
Now we need to find the slope, which is the difference in y-coordinates divided by the difference in x-coordinates:
m = (5 - 2)/(-3 - (-4))
m = 3/-1
m = -3
Substituting -3 for m in equation (1), we get:
y - 2 = -3x + 4m
y - 2 = -3x + 4(-3)
y - 2 = -3x - 12
y = -3x - 10
So the correct equation of the line passing through (-4,2) and (-3,5) is y = -3x - 10.
Finally, in the third question about the probability of rolling an even number or a 5 on a 6-sided die. To find the probability, we need to determine the total number of favorable outcomes (even numbers or a 5) and divide it by the total number of possible outcomes (6 in this case since it is a 6-sided die).
The even numbers on a 6-sided die are 2, 4, and 6. Considering that 5 is also a favorable outcome, we have a total of 4 favorable outcomes (2, 4, 5, and 6) out of 6 possible outcomes.
So the probability of rolling an even number or a 5 is 4/6, which simplifies to 2/3.
Therefore, the correct answer is 2/3 for the probability of rolling an even number or a 5 on a 6-sided die.