Considering there is a function (relationship) and that it is linear, the distance will change proportionally to time constantly. In other words, we are taking the speed to be constant throughout the journey.
If we let:
t = time (min's) driving
d = distance (miles) from destination
Then we can represent the above information as:
t = 40: d = 59
t = 52: d = 50
If we think of this as a graph, we can think of the x-axis representing time and the y-axis representing the distance to the destination. Being linear, the function will be a line, i.e. it will have a constant gradient. If you were plot the two points inferred from the information and connect the two dots, you will get a declining line (one with a negative gradient) representing the inversely proportional relationship or equally, the negative correlation between the time driving and the distance to the destination. The equation of this line will be the linear function that relates time and the distance to the destination. To find this linear function, we do as follows:
Find the gradient (m) of the line:
m = Δy/Δx
In this case, the x-values are t-values and our y-values are d-values, so:
Δy = Δd
= 50 - 59
= -9
Δx = Δt
= 52 - 40
= 12
m = -9/12 = -3/4
Note: m is equivalent to speed with units: d/t
Use formula to find function and rearrange to give it in the desired format:
y - y₁ = m(x - x₁)
d - 50 = -3/4(t - 52)
4d - 200 = -3t + 156
4d + 3t - 356 = 0
Let t = 70 to find d at the time:
4d + 3(70) - 356 = 0
4d + 210 - 356 = 0
4d - 146 = 0
4d = 146
d = 73/2 = 36.5 miles
So after 70 min's of driving, Dale will be 36.5 miles from his destination.
The way it's written it's
Simplify the following:
7 X^3 + 4 X^2 + 2 X^2 + 3 X + X + 2 + 5
Grouping like terms, 7 X^3 + 4 X^2 + 2 X^2 + 3 X + X + 2 + 5 = 7 X^3 + (4 X^2 + 2 X^2) + (3 X + X) + (2 + 5):7 X^3 + (4 X^2 + 2 X^2) + (3 X + X) + (2 + 5)
4 X^2 + 2 X^2 = 6 X^2:
7 X^3 + 6 X^2 + (3 X + X) + (2 + 5)
3 X + X = 4 X:
7 X^3 + 6 X^2 + 4 X + (2 + 5)
2 + 5 = 7:Answer: 7 X^3 + 6 X^2 + 4 X + 7
Answer:
2.28%
Step-by-step explanation:
As this is normally distributed, we can use z scores to find the percentage.
First, find the z-score for 148.
The z-score that you get is:
(148-160)/2=2
As we see that z=2, we can use a calculator or a z-score chart to find the percentage less than a z score of 2.
I used my chart and found: 2.28%
Answer:
8.70%
Step-by-step explanation:
Percentage error = (difference between estimated value and actual value / actual amount spent) x 100
difference between estimated value and actual value = estimated value - actual amount
$250 - $230 = $20
($20 / $230) x 100 = 8.6957%
Answer:
Step-by-step explanation:
We are to find the equation a line that passes through the point (8, 1) and which is perpendicular to a line whose equation is
.
We know that the slope of line which is perpendicular to another line is the negative reciprocal of the slope of the other line so it will be 
.
Then, we will find the y-intercept of the line using the standard equation of a line:
Therefore, the equation of the line will be .
