Step-by-step explanation:
Since Angle DAE = Angle BCE, lines AD amd BC are parallel (by Z-angles).
This means that Angle ADE = Angle CBE (by Z-angles).
We have 2 congruent angles and 1 congruent side (AD = BC, given).
By ASA congruence, triangles AED and CEB are congruent.
Answer:
No
Step-by-step explanation:
For the adults:
$12 times the 14 adults which is: $168
Then for the kids:
$5 times the 9 kids which is: $45
Add next:
$168 plus the $45 equals $213
A(14)+b(5)=c
Standard deviation is: It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
For example: To find the standard deviation, you have to add up all the numbers in the data set, then divide by how many numbers there are, and that will get you your answer.
Example, Say your data set is: 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4.
The Mean is: 9 + 2 + 5 + 4 + 12 + 7 + 8 + 11 + 9 + 3 + 7 + 4 + 12 + 5 + 4 + 10+ 9 + 6 + 9 + 4. Over 20. That equals: 104 over 20 = 7.
So, the Standard Variance and Mean is: 7 for this problem.
Hope I helped!
- Debbie
Answer:
Dh/dt = 0.082 ft/min
Step-by-step explanation:
As a perpendicular cross section of the trough is in the shape of an isosceles triangle the trough has a circular cone shape wit base of 1 feet and height h = 2 feet.
The volume of a circular cone is:
V(c) = 1/3 * π*r²*h
Then differentiating on both sides of the equation we get:
DV(c)/dt = 1/3* π*r² * Dh/dt (1)
We know that DV(c) / dt is 1 ft³ / 5 min or 1/5 ft³/min
and we are were asked how fast is the water rising when the water is 1/2 foot deep. We need to know what is the value of r at that moment
By proportion we know
r/h ( at the top of the cone 0,5/ 2) is equal to r/0.5 when water is 1/2 foot deep
Then r/h = 0,5/2 = r/0.5
r = (0,5)*( 0.5) / 2 ⇒ r = 0,125 ft
Then in equation (1) we got
(1/5) / 1/3* π*r² = Dh/dt
Dh/dt = 1/ 5*0.01635
Dh/dt = 0.082 ft/min
What you want to do is cross multiply so you get 5(x+4)=7(3x+28) then you distrubute the 5 and then you distribute the 5 and the 7 to the number in the parentheses 5x+20=21x+196
subtract 5x on both sides to get 20=16x+196 then you subtract 196 on both sides to get -176=16x last what you want to do is divide 16 on both sides to get x=-11
