Answer:
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative
Step-by-step explanation:
Answer:
(30.09, 32.91)
Step-by-step explanation:
Mean number of pounds of trash = x = 31.5 pounds
Standard deviation = s = 7.8 pounds
Sample size = n = 120
Confidence level = 95%
Since, we are given the sample standard deviation instead of the population standard deviation, we will use t-test to find the confidence interval.
Degrees of freedom = df = n - 1 = 120 - 1 = 119
The t-value associated with 95% confidence interval and df=119 from the t-table comes out to be:
t = 1.98
The formula to calculate the confidence interval is:
Using the values in above expression we get:
Thus, the 95% confidence interval for the mean number of lbs of trash per person per week that is generated in the city is (30.09, 32.91)
Answer:
Question 1:
cos a = 0.2195
tan a = 4.445
Question 2:
sin a = 0.8
tan a = 1.333
Step-by-step explanation:
<h3 /><h3>Question 1:</h3>
Given that;
sin a = 40/41
a = sin ⁻¹ (40/41)
a = 77.32°
Now we have to find the value of cos a and tan a:
a = 77.32°
cos 77.32° = 0.2195
tan 77.32° = 4.445
<h3>Question 2:</h3>
Given that;
cos a = 0.6
a = cos ⁻¹ (0.6)
a = 53.13°
Now we have to find the value of cos a and tan a:
a = 53.13°
sin 53.13° = 0.8
tan 53.13° = 1.333
Answer:
The system if equation that can be used to derive this are
6x + 4y = 69 AND
12x + y = 96
The price of a drink is $7.5
Step-by-step explanation:
The question here says that Taylor and Nora went to the movie theater and purchase refreshments for their friends. Taylor spends a total of $69.00 on 6 drinks and 4 bags of popcorn Nora spends a total of $96.00 on 12 drinks and bag of popcorn.And we are now told to write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations,we should determine and state the price of a drink, to the nearest cent .
Now, Let's assume that the price of a drink is "X" and that of a bag of popcorn to be Y
The first person made a purchase which led to the equation
6x + 4y = 69______ equation 1
And the second person also made a purchase that lead to the equation
12x + y = 96_____ equation 2
We make y the subject of the formula in equation 2 and apply it in 1
Y = 96 - 12x
Now apply the above in equation 1
6x + 4y = 69
6x + 4(96 - 12x)= 69
6x + 384 - 48x = 69
42x = 384 - 69
X = 315/42
X = 7.5
Substitute x= 7.5 in equation 2
12x + y = 96
12(7.5) + y = 96
90 + y = 96
Y = 6
Therefore, the price of a drink is $7.5
