Step-by-step explanation:
since x is in quadrant three,tan theta and cot theta are positive
<h2>
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tan theta= opposite/adjacent
sin theta = opposite /hypotenuese
from triangle ,we know 2 sides hypotenuese and opposite as 5 and 3 respectively,we get third side as 4 using pythagorous theorem
tanx°=3/4
<h2>
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but asked tanx/2
see the attachment now
Answer:
Correct option: (D) <em>H₀</em>: <em>μ</em> = 55 vs. <em>Hₐ</em>: <em>μ</em> < 55.
Step-by-step explanation:
In this case we need to test whether the new high-performance wax price is justifiable or not.
It is provided that the wax needs to be very fast specifically the mean time to finish their standard test course should be less than 55 seconds for a former Olympic champion, for the price to justifiable.
So, to test this a sample of <em>n</em> = 8 champion's times are recorded.
A one-sample <em>t</em>-test will be used to perform the test.
The hypothesis to test this is defined as follows:
<em>H₀</em>: The mean time to finish their standard test course is 55 seconds, i.e. <em>μ</em> = 55.
<em>Hₐ</em>: The mean time to finish their standard test course is less than 55 seconds, i.e. <em>μ</em> < 55.
Thus, the correct option is (D).
Answer:
30
Step-by-step explanation:
Let number of tetras be "t"
number of guppies be "g"
number of minnows be "m"
Ratio of tetras to guppies is 4:2, or reducing, 2:1. Thus we can write:
Ratio of minnows to guppies is 1:3, so we can write:
or, m = g/3
Also, total there are 60 fish, so we can write:
t + g + m = 60
or
2g + g + g/3 = 60
Solving this, we can solve for g. Shown below:
Now, finding t and m:
m = g/3 = 18/3 = 6
m = 6
and
t = 2g
t = 2(18)
t= 36
There are 36 tetras and 6 minnows. So, there are
36 - 6 = 30 more tetras than minnows
Answer:
The prove is as given below
Step-by-step explanation:
Suppose there are only finitely many primes of the form 4k + 3, say {p1, . . . , pk}. Let P denote their product.
Suppose k is even. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
ThenP + 2 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 2 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠2. This is a contradiction.
Suppose k is odd. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
Then P + 4 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 4 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠4. This is a contradiction.
So this indicates that there are infinite prime numbers of the form 4k+3.
In order to calculate the number of loaves Roger can bake, we should calcculate how many times 3/4 (required butter for one loaf of bread) is included in 2 1/2 (amount of butter Roger has).
2 1/2=4/2+1/2=5/2
(5/2)/(3/4)=5*4/2*3=20/6=3,33
Roger can bake 3 loaves of bread.
