Let
t-------> the time in minutes
y------> the distance from home for an ant in feet
we know that
In this linear equation
the slope m is equal to
The y-intercept is equal to-------->
in this problem the y-intercept is the value of the distance in feet when the value of the time in minutes is zero
so
The y-intercept is equal to-------->
therefore
<u>the answer is the option</u>
D. The ant started out 2 feet from its home
Answer:
102° and 78°
Step-by-step explanation:
let one angle be x then the other angle is
x + 10 ( 10 more than two-thirds the other angle )
A linear pair of angles sum to 180°, hence
x + x + 10 = 180
x + 10 = 180 ( subtract 10 from both sides )
x = 170
multiply both sides by 3 and divide by 5
5x = 510
x = 102
The 2 angles are x = 102° and
x + 10 =
× 102 + 10 = 68 + 10 = 78°
As a check : 102 + 78 = 180 → correct
Answer:
The slope is 17 / 2.
Step-by-step explanation:
The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Find the values of m and b using the form y=mx+b.
m=17 / 2
b=3
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: 17 / 2
y-intercept: 3
Complete question:
The manager of a supermarket would like to determine the amount of time that customers wait in a check-out line. He randomly selects 45 customers and records the amount of time from the moment they stand in the back of a line until the moment the cashier scans their first item. He calculates the mean and standard deviation of this sample to be barx = 4.2 minutes and s = 2.0 minutes. If appropriate, find a 90% confidence interval for the true mean time (in minutes) that customers at this supermarket wait in a check-out line
Answer:
(3.699, 4.701)
Step-by-step explanation:
Given:
Sample size, n = 45
Sample mean, x' = 4.2
Standard deviation = 2.0
Required:
Find a 90% CI for true mean time
First find standard error using the formula:
Standard error = 0.298
Degrees of freedom, df = n - 1 = 45 - 1 = 44
To find t at 90% CI,df = 44:
Level of Significance α= 100% - 90% = 10% = 0.10
Find margin of error using the formula:
M.E = S.E * t
M.E = 0.298 * 1.6802
M.E = 0.500938 ≈ 0.5009
Margin of error = 0.5009
Thus, 90% CI = sample mean ± Margin of error
Lower limit = 4.2 - 0.5009 = 3.699
Upper limit = 4.2 + 0.5009 = 4.7009 ≈ 4.701
Confidence Interval = (3.699, 4.701)