You're assuming that this data set represents all of Mrs. Hassaan's pupils. Certain students could be missing from the histogram - for instance, there could be one or two students who missed the test, but for certain reasons will be taking a make-up exam. Their grade would not be recording in this data set, but they still contribute to the class size, and so would be unaccounted for here.
Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.
We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)
N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA
D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA
Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A
This verifies the identity.
Answer:
170,070 residents
Step-by-step explanation:
Original population = 1500 residents
Total population after 6 years is calculated using the formula
A = P(1+r)^t
r is the rate = 120% = 1.2
t is the time = 6 years
P is the original population
A = 1500(1+1.2)^6
A = 1500(2.2)^6
A = 1500(113.379904)
A = 170,069.856
Yes u did get a good deal i think
<h3>5/6 × 3/10</h3>
<em>Multiply 5/6 by 3/10 (to do this,</em><em> multiply the numerator by the numerator </em><em>and the </em><em>denominator by the denominator).</em>
<h3>5 × 3/6 × 10</h3>
<em>Perform the</em><em> multiplications </em><em>in the </em><em>previous fraction.</em>
<h3>15/60</h3>
<em>Reduce the fraction </em><em>15/60</em><em> to its</em><em> lowest expression by extracting</em><em> and canceling 15.</em>
<h3>1/4 ≈ 0.25</h3>
