True or false
√15 < π
True or false
PART A: At a certain number of visits, both plans will cost the same. At that number, how much will both plans cost, in dollars?
PART B: Which plan is more expensive at the 10th visit?
Write the number of the plan in the box.
After 15 number of visits, both plans cost $55 and at the 10th visit, plan 2 is more expensive than plan 1.
Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Part A :
From the table, we can clearly express both plans as Arithmetic sequence.
Plan 1 : First term, a = 27 and common difference, d = 2
Plan 2 : First term, a = 41 and common difference, d = 1
Let n be the number of visits that both plans costs the same.
27 + 2(n - 1) = 41 + (n - 1)
27 + 2n - 2 = 41 + n - 1
2n + 25 = n + 40
n = 15
Cost = 41 + (15 - 1) = $55
Part B :
We have to find the 10th term.
For plan 1 :
Cost at 10th visit = 27 + 2(10 - 1) = $45
For plan 2 :
Cost at 10th visit = 41 + (10 - 1) = $50
The plan 2 is more expensive at the 10th visit.
Hence at the 10th visit, plan 2 is more expensive.
Learn more about Arithmetic Sequence here :
#SPJ3
Step-by-step explanation:
From the looks of it, Plan A is 25 + 2x and plan B is 40 + x.
Part A:
25 + 2x = 40 + x
x = 15
plug in any: 40 + 15 = $55
Part B:
Plan A = $45
Plan B = $50
Plan B is $5 more expensive.
Let blue counters = x
Red counters would be 3x ( three times as many)
first find the number of red and the number of blue counters:
3x + x = 120
4x = 120
x = 120/4
x = 30
There are 30 blue counters and 90 red counters.
Carl took 1/3 of the red, 90 / 3 = 30, so there were 60 red counters left
Kerry took 80% of the blue, 30 * 0.80 = 24, so there were 6 blue counters left
The ratio of red to blue would be 60: 6 which can be simplified to 10:1.
The ratio of the number of red counters to blue counters now in the box is 10:1.
A ratio is the simplest relation shown between two quantities, in the way x:y, read as "x is to y", and functions as x/y.
In the question, we are said that there are a total of 120 counters in a box, there are only red counters and blue counters in the box. there are three times as many red as blue counters in the box. Carl takes 1/3 of the red counters from the box. Kerry takes 80% of the blue counters from the box.
We are asked to work out the ratio of the number of red counters to blue counters now in the box.
We assume the initial number of blue counters in the box to be x.
Then, the initial number of red counters in the box = 3x {three times as many red as blue}.
Therefore, the initial ratio of red to blue = 3x:x = 3:1.
Now, Carl takes 1/3 of the red counters.
The number of red counters left = 3x - (1/3) of 3x = 3x - (1/3)*3x = 3x - x = 2x.
Also, Kerry takes 80% of the blue counters.
The number of blue counters left = x - 80% of x = x - 0.8x = 0.2x
Therefore, the final ratio of red to blue = 2x:0.2x = 10:1 (Simplest form).
Learn more about ratios at
#SPJ2
The equation of a line that has a slope of 1/2 and passes through point (2, -3) is 2y - x = -8
The standard equation of a line in slope-intercept form is expressed as:
y = mx + b where:
Given the following:
Slope = 1/2
(x0, y0) = (2, -3)
Substitute the given parameters into the formula above:
Hene the equation of a line that has a slope of 1/2 and passes through point (2, -3) is 2y - x = -8
Learn more here: brainly.com/question/21536974
So for this, I will be making the equation using the slope-intercept form, which is y=mx+b (m = slope, b = y-intercept).
Since we have the slope, 1/2, we can just plug in (2,-3) into the equation and solve for b as such:
Putting everything together, our equation is y = 1/2x - 4.