Answer:
a)
b)
c)
Step-by-step explanation:
There are total three groups say A, B and C.
Lets suppose I am assigned to be a part of group C
a) neither has studied calculus
P(Group A neither studied calculus) P(Group A neither studied calculus)
b) both have studied at least one semester of calculus
Probability of studying one or more than one semesters of calculus
P(Group A has studied calculus) P(Group A has studied calculus)
c) at least one has had more than one semester of calculus
Answer:
Length of the Rectangle = 10 inches
and Width = 25 inches
Step-by-step explanation:
Let the width of the rectangle = k inches
So, the Length of the rectangle = (3k - 5) inches
Perimeter = 70 inches
Now, Perimeter of the Rectangle = 2(Length + Width)
= 2 (k + (3k-5))
⇒ 2 (k + (3k-5)) = 70
or, 2(k + 3k -5) = 70 ⇒ 2(4k - 5) = 70
⇒ 8k - 10 = 70
or, 8k = 70+ 10 = 80
or, k = 80/8 = 10
So, the Length = 10 inches
Hence, Width = 3k - 5 = 3(10) - 5 = 30 - 5 = 25 inches
So, Length of the Rectangle = 10 inches
and Width = 25 inches
Answer:
n = 15
Step-by-step explanation:
For inputs of the value of n, the running time for the algorithm A is 100n^2 and that of B is 2^n.
If A is to run faster than B, 100n^2 must be smaller than 2^n.
Let's check from n = 1 to know the value of n that fits
n = 1
100(1)^2 > 2^1
100 > 2
n = 2
100(2)^2 > 2^2
400 > 4
n = 4
100(4)^2 > 2^4
1600 > 16
n = 8
100(8)^2 > 2^8
6400 > 2^8
n = 16
100(16)^2 < 2^16
25600 < 2^16
This implies that between n = 8 and 16, A starts to run faster than B
n = (8+16)/2 = 12
100(12)^2 > 2^12
14400 > 2^12
n = (12+16)/2 = 14
100(14)^2 > 2^14
19600 > 2^14
n = (14+16)/2
n = 15
100(15)^2 < 2^15
22500 < 2^15
At n= 15, A starts running faster than B
y=40⁰
x=35⁰
Step-by-step explanation:
y⁰=40⁰ (because they are vertically opposite.)
2 of the triangles are isosceles triangle, in isosceles triangle the 2 bottom angles are the same.
The sum of a triangle is 180⁰,
180⁰=2x+2x+40⁰
180⁰=4x+40⁰
180-40=4x
140⁰=4x
140/4=x
x=35⁰
To check your answer,
2(35)+2(35)+40=180⁰
brianlist me??
Answer:
every point will be 4 tons lower than it was
Step-by-step explanation:
26 is 4 less than 30, so the new function g(x) is ...
g(x) = f(x) -4
It is shifted down 4 units (tons) from the original function.