Move all the logarithms on the left hand side, and all the constants on the other:
Use the rule of logarithms
To rewrite the equation as
Evaluate 2 to the power of each side:
Multiply both sides by 2x:
Two circles, one of radius 5 inches, the other of radius 2 inches, are tangent at point P. Two bugs start crawling at the same t
ime from point P, one crawling along the larger circle at $3\pi$ inches per minute, the other crawling along the smaller circle at $2.5\pi$ inches per minute. How many minutes is it before their next meeting at point P?
1 answer:
Answer:
40 minutes
Step-by-step explanation:
The circumference of the larger circle is ...
C = 2πr = 2π(5 in) = 10π in
The bug navigates the circumference at 3π in/min, so will take
time = distance/speed = (10π in)/(3π in/min) = 10/3 min
to travel once around.
__
The circumference of the smaller circle is ...
C = 2πr = 2π(2 in) = 4π in
The bug navigates this circumference at 2.5π in/min, so will take
(4π in)/(2.5π in/min) = 8/5 min
to travel once around.
__
The bugs will meet at a time that is the least common multiple of these times. Both can be expressed in 15ths of a minute as ...
{50/15, 24/15}
Then the LCM of these will be ...
(1/15)LCM(50, 24) = (1/15)(50×24)/GCD(50, 24) = 1200/30 = 40
It will be 40 minutes before the bugs next meet at point P.
___
A graphing calculator can make use of the mod function to show when the bugs meet at point P (total is displacement of the two bugs from P is zero). It shows the meeting occurs after 40 minutes.
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Answer:
The slope is
Step-by-step explanation:
Take the general equation of a straight line
Here is the slope of the line.
So let's get the equation of the line in the question in the same form.
Add to both sides:
Add to both sides:
Divide by to get it into the general equation:
Now compare it to the general equation to find the value of . The value of
is the coefficient of
which we can see is
Answer:
a) The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.
b)
The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.
c) They are respected, as the upper bound of both intervals is below the new FAA recommendations.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve these questions.
Question a:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 100 - 1 = 99
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of . So we have T = 1.9842
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 183 - 4 = 179 pounds.
The upper end of the interval is the sample mean added to M. So it is 183 + 4 = 187 pounds.
The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.
Question b:
Critical value is the same(same sample size and confidence level).
The margin of error is:
The lower end of the interval is the sample mean subtracted by M. So it is 190 - 4.6 = 185.4 pounds.
The upper end of the interval is the sample mean added to M. So it is 190 + 4.6 = 194.6 pounds.
The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.
c. The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).
They are respected, as the upper bound of both intervals is below the new FAA recommendations.
Answer:
The equation is y= 0,65 x
If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately pays (y) is the original price (x) minus a 35% of this price: y= x -0.35 x . By association: y= (1-0.35) x and then y= 0.65 x.
The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).
Step-by-step explanation:
- The price without discount (or without the coupon) is x.
- The price with discount (or with coupon) is y.
- y and x are both related: y is a percentage of x, specifically, y is 35% smaller than x. This means that y =0.65 x.
