Answer:
$7.8
Step-by-step explanation:
$2.6 x 3
= $7.8
Answer:
176.39 inches or
14.70 feet
Step-by-step explanation:
Consider the right triangle made by Kristen, ground and shadow.
This triangle has one leg as 64 inches.
Next consider the right triangle formed by street light, ground upto shadow tip.
The two triangles have common angle of elevation and also another angle as 90 degrees.
Hence the two triangles would be similar
Also if A is the angle made by hypotenuse of both triangles with the ground we have
![tanx=\frac{64}{82}](https://tex.z-dn.net/?f=tanx%3D%5Cfrac%7B64%7D%7B82%7D)
This value also equals by bigger triangle as
![tanx=\frac{h}{82+12(12)}=\frac{h}{226}](https://tex.z-dn.net/?f=tanx%3D%5Cfrac%7Bh%7D%7B82%2B12%2812%29%7D%3D%5Cfrac%7Bh%7D%7B226%7D)
From these two we get
h = height of street light =![\frac{226(64)}{82} =176.39](https://tex.z-dn.net/?f=%5Cfrac%7B226%2864%29%7D%7B82%7D%20%3D176.39)
The sum of the series up to the 12 terms will be 40.5.
<h3>What is the sum of a geometric sequence?</h3>
Let a₁ be the first term, n be the total number term, and r be a common ratio.
Then the sum of the geometric sequence will be
Sₙ = [a₁ (1 - rⁿ)] / (1 - r)
The series is given below.
27 + 9 + 3 + 1 + ... + 1/6561
The first term is 27 and the common ratio is 1/3.
The number of the term will be
1/6561 = 27 · (1/3)ⁿ⁻¹
1/177147 = (1/3)ⁿ⁻¹
(1/3)¹¹ = (1/3)ⁿ⁻¹
11 = n - 1
n = 12
Then the sum of the series will be
![\rm S_{12} = \dfrac{27 \cdot \left [1 - \left (\frac{1}{3} \right )^{12} \right ]}{ \left ( 1- \frac{1}{3} \right )}](https://tex.z-dn.net/?f=%5Crm%20S_%7B12%7D%20%3D%20%5Cdfrac%7B27%20%5Ccdot%20%20%5Cleft%20%5B1%20-%20%20%5Cleft%20%28%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%5E%7B12%7D%20%20%20%5Cright%20%5D%7D%7B%20%5Cleft%20%28%201-%20%5Cfrac%7B1%7D%7B3%7D%20%5Cright%20%29%7D)
Simplify the equation, then we have
S₁₂ = 27 x 0.9999 / 0.6666
S₁₂ = 27 x 1.5
S₁₂ = 40.5
The sum of the series up to the 12 terms will be 40.5.
More about the sum of arithmetic sequence link is given below.
brainly.com/question/25749583
#SPJ1
Answer:
The size of the sample = 1088.90
Step-by-step explanation:
Given that:
The confidence interval level = 0.95
The margin of error = 0.03
Suppose the proportion of the boys and the girls are p₁ and p₂ respectively.
The Standard error S.E of difference is:
![S.E (p_1-P_2) = \sqrt{ \dfrac{p_1(1-p_1) }{n} + \dfrac{p_2(1-p_2)}{n} }](https://tex.z-dn.net/?f=S.E%20%28p_1-P_2%29%20%3D%20%5Csqrt%7B%20%5Cdfrac%7Bp_1%281-p_1%29%20%7D%7Bn%7D%20%2B%20%5Cdfrac%7Bp_2%281-p_2%29%7D%7Bn%7D%20%7D)
Assume p₁ = p₂ = 0.5
![S.E (p_1-P_2) = \sqrt{ \dfrac{0.5(1-0.5) }{n} + \dfrac{0.5(1-0.5)}{n} }](https://tex.z-dn.net/?f=S.E%20%28p_1-P_2%29%20%3D%20%5Csqrt%7B%20%5Cdfrac%7B0.5%281-0.5%29%20%7D%7Bn%7D%20%2B%20%5Cdfrac%7B0.5%281-0.5%29%7D%7Bn%7D%20%7D)
![S.E (p_1-P_2) =\dfrac{0.70711}{\sqrt{n}}](https://tex.z-dn.net/?f=S.E%20%28p_1-P_2%29%20%3D%5Cdfrac%7B0.70711%7D%7B%5Csqrt%7Bn%7D%7D)
The z-critical value at 95% C.I = 1.96
Margin of error = Z_{critical} × S.E
∴
![0.03 = 1.96 \times \dfrac{0.70711}{\sqrt{n}}](https://tex.z-dn.net/?f=0.03%20%3D%201.96%20%5Ctimes%20%5Cdfrac%7B0.70711%7D%7B%5Csqrt%7Bn%7D%7D)
![n =\dfrac{\left(1.96\ \cdot\ 0.70711^{2}\right)}{0.03^{2}}](https://tex.z-dn.net/?f=n%20%3D%5Cdfrac%7B%5Cleft%281.96%5C%20%5Ccdot%5C%200.70711%5E%7B2%7D%5Cright%29%7D%7B0.03%5E%7B2%7D%7D)
n ≅ 1088.90
We'll assume this is an arbitrary triangle ABC.
A) No, the sines of two different angles can be whatever they want
B) sin(B)=cos(90-B)
Yes, that's always true. The "co" in cosine means "complementary" as in the complementary angle, which adds to 90. So the sine of an angle is the cosine of the complementary angle.
C) No, the correct identity is sin(180-B)=sin B. Supplementary angles share the same sine.
D) Just like A, different triangle angles often have different cosines.
Answer: Choice B