Response:
Step-by-step explanation:
Shift the decimal points in both the divisor and the dividend.
Transform the divisor (the number you're dividing by) into a whole number by moving its decimal to the furthest right. Simultaneously, adjust the dividend's decimal (the number being divided) the same number of places to the right.
In the quotient (the result), place a decimal point directly over where the decimal point is now located in the dividend.
Proceed with the division as normal, ensuring proper alignment so the decimal point appears correctly.
Align each digit in the quotient directly over the last digit of the dividend utilized in that step.
Since m∠abe = 2b, and angle abe consists of angles abf and ebf, we can write:
m∠abe = m∠abf + m∠ebf
To find m∠ebf, rearrange:
m∠ebf = m∠abe - m∠abf
Substitute the given expressions:
m∠ebf = 2b - (7b - 24)
Simplify:
m∠ebf = 2b - 7b + 24
m∠ebf = -5b + 24.
Response:
Detailed explanation:
Hello!
Stratified sampling involves the categorization of the population into subgroups based on pre-established criteria for the study. These subgroups consist of homogeneous units concerning the relevant characteristics. In this instance, individuals in the groups will represent only one of the two potential opinions (support or not support) and not both.
The researcher determines the sample size desired, considering several factors such as finances, material availability, and accessibility to experimental subjects (for instance, if they are endangered species, larger sample sizes may not be feasible).
One might conduct proportionate stratified sampling by selecting a proportion of respondents who answered "yes" along with those who answered "no."
In this sampling method, taking a specific proportion from each subgroup allows for a more straightforward extrapolation of results to the overall populations. For example, if you needed a sample size of n = 20, each stratum would ideally contain half, meaning 10 from the “yes” group and 10 from the “no” group.
I hope this is helpful!
Assuming arcs are measured in degrees, let S represent the following sum:
S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°
By rearranging, S can be reformulated as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] +... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] +... + [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
However, for any real k,
sin(360° – k) = – sin k
Thus,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°
S results in 0 + 0 +... + 0 + 0 + 0 (... since sine of 180° and 360° are both equal to 0)
Therefore, S equals 0.
Each pair within the brackets negates itself, leading the sum to total zero.
∴ sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0. ✔
I hope this clarifies things. =)
Tags: sum summatory trigonometric trig function sine sin trigonometry
<span><span>Center coordinates: (x0, y0, z0)</span></span> and radius r.
<span>The equation of the sphere is:</span>
<span>(x - x0)^2 + (y - y0)^2 + (z - z0)^2 = r^2</span>
