The standard conversion toolbox:
x=rcos(θ)
y=rsin(θ)
Here r=7csc(θ)
so
x=7csc(θ)*cos(θ)=7cos(θ)/sin(θ)=7cot(<span>θ)
y=7csc(</span>θ)*sin(θ)=7sin(θ)/sin(<span>θ) = 7
therefore the rectangular coordinates are (7cot(</span><span>θ), 7)</span>
Yes, 23 has an inverse mod 1000 because gcd(23, 1000) = 1 (i.e. they are coprime).
Let <em>x</em> be the inverse. Then <em>x</em> is such that
23<em>x</em> ≡ 1 (mod 1000)
Use the Euclidean algorithm to solve for <em>x</em> :
1000 = 43×23 + 11
23 = 2×11 + 1
→ 1 ≡ 23 - 2×11 (mod 1000)
→ 1 ≡ 23 - 2×(1000 - 43×23) (mod 1000)
→ 1 ≡ 23 - 2×1000 + 86×23 (mod 1000)
→ 1 ≡ 87×23 - 2×1000 ≡ 87×23 (mod 1000)
→ 23⁻¹ ≡ 87 (mod 1000)
Answer:
Step-by-step explanation:
given that on a six-question multiple-choice test there are five possible answers for each question, of which one is correct and four are incorrect
By mere guessing probability for choosing correct answer = p = 0.2
also each question is independent of the other
Hence if X is the number of correct questions then
X is binomial with p = 0.2 and n = 6
a) being correct on three questions,
=
(b) being correct on four questions,
= 
(c) being correct on all six questions
=
<h2>
Answer:</h2>
<u><em>As a percent, the odds of having an allergic reaction would be 2%.</em></u>
This is because 1 in 50 of a chance, is equal to 1/50, and to make this a percent out of 100, just multiply both parts of the fraction by 2.
None of the choices equal 1/50, so let's just make it a percentage anyway.
1/50 ---> 0.02
0.02 ---> 2%
<em>The answer is 2%, or 1/50 as a fraction.</em>
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