Answer:
22.39
Step-by-step explanation:
angle D + angle F + angle E = 180 (angle of triangle)
30 +60 + E = 180
E = 180 - 90
E = 90
so triangle DEF is right angled triangle
we know that,
sin 30 = EF /DF
OR, 1/2 = 6/ DF
OR, DF= 12
again,
cos 30 = De/DF
root3 /2 = DE /12
DE= 10.39
hence DF +DE
= 12 + 10.39
= 22. 39
Answer:
a. Fail to reject the null hypothesis.
Step-by-step explanation:
Here we test the claim that proportion of reachers is really 41%
![H_0: p =0.41\\H_a: p \neq 0.41](https://tex.z-dn.net/?f=H_0%3A%20p%20%3D0.41%5C%5CH_a%3A%20p%20%5Cneq%200.41)
(Two tailed test at 1% significance level)
Observed proportion = 0.36
Sample size n = 100
Std error of proportion = ![\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.41*0.59}{100} } \\=0.0492](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D%20%5C%5C%3D%5Csqrt%7B%5Cfrac%7B0.41%2A0.59%7D%7B100%7D%20%7D%20%5C%5C%3D0.0492)
p difference = 0.36-0.41 =- 0.05
Test statistic Z = p diff/std error =-1.0166
p value=0.286
Since p >0.01 we accept null hypothesis.
a. Fail to reject the null hypothesis.
9514 1404 393
Answer:
d. The triangles are not similar
Step-by-step explanation:
The angle between the given sides is the same, so we need to compare the side ratios. In ΔQRS, we have ...
QR/RS = 4/15
In ΔVTU, we have ...
VT/TU = 8/32 = 1/4 ≠ 4/15
The triangles are not similar because corresponding sides are not proportional.
125, 216, 343, 512, 729
the numbers given in the sequence are recognisable as cubes
1 = 1³, 8 = 2³, 27 = 3³, 64 = 4³
the next five terms will be
5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512 and 9³ = 729
In this question we have to find an angle between 0 and 2π that is coterminal with 10pi/3 .
To find the coterminal angle, we need to subtract 2 pi from 10 pi/3. That is
![= \frac{10 \pi }{3} - 2 \pi](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B10%20%5Cpi%20%7D%7B3%7D%20-%202%20%5Cpi)
Multiplying numerator and denominator of 2 pi by 3
![= \frac{10 \pi}{3} -\frac{6 \pi}{3} = \frac{4 \pi}{3}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B10%20%5Cpi%7D%7B3%7D%20-%5Cfrac%7B6%20%5Cpi%7D%7B3%7D%20%3D%20%5Cfrac%7B4%20%5Cpi%7D%7B3%7D)
And that's the required coterminal angle between 0 and 2pi.