Answer: a) Unimodal and symmetric
b) 0.26
c) 0.038
Step-by-step explanation:
Given: Sample size of investors (n)= 131
True proportion of smartphone users(p) =26%
a) Since sampling distribution for the sample proportion is approximately normal when n is larger.
Normal distribution is Unimodal and symmetric.
So correct option : Unimodal and symmetric
b) mean of this sampling distribution = p = 0.26
c) standard deviation of the samplingdistribution = ![\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26\times (1-0.26)}{131}}=\sqrt{0.00146870229008}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%3D%5Csqrt%7B%5Cdfrac%7B0.26%5Ctimes%20%281-0.26%29%7D%7B131%7D%7D%3D%5Csqrt%7B0.00146870229008%7D)
![=0.0383236518364\approx0.038](https://tex.z-dn.net/?f=%3D0.0383236518364%5Capprox0.038)
Answer:
8 square units and
square units
Step-by-step explanation:
The area of the triangle ABC is 24 square units.
1. Triangles ABC and FBG are similar with scale factor
then
![\dfrac{A_{\triangle FBG}}{A_{\triangle ABC}}=\dfrac{1}{9}\Rightarrow A_{\triangle FBG}=\dfrac{1}{9}\cdot 24=\dfrac{8}{3}\ un^2.](https://tex.z-dn.net/?f=%5Cdfrac%7BA_%7B%5Ctriangle%20FBG%7D%7D%7BA_%7B%5Ctriangle%20ABC%7D%7D%3D%5Cdfrac%7B1%7D%7B9%7D%5CRightarrow%20A_%7B%5Ctriangle%20FBG%7D%3D%5Cdfrac%7B1%7D%7B9%7D%5Ccdot%2024%3D%5Cdfrac%7B8%7D%7B3%7D%5C%20un%5E2.)
2. Triangles ABC and DBE are similar with scale factor
then
![\dfrac{A_{\triangle DBE}}{A_{\triangle ABC}}=\dfrac{4}{9}\Rightarrow A_{\triangle DBE}=\dfrac{4}{9}\cdot 24=\dfrac{32}{3}\ un^2.](https://tex.z-dn.net/?f=%5Cdfrac%7BA_%7B%5Ctriangle%20DBE%7D%7D%7BA_%7B%5Ctriangle%20ABC%7D%7D%3D%5Cdfrac%7B4%7D%7B9%7D%5CRightarrow%20A_%7B%5Ctriangle%20DBE%7D%3D%5Cdfrac%7B4%7D%7B9%7D%5Ccdot%2024%3D%5Cdfrac%7B32%7D%7B3%7D%5C%20un%5E2.)
3. Thus, the area of the quadrilateral DFGE is
![A_{DFGE}=A_{\triangle DBE}-A_{\triangle FBG}=\dfrac{32}{3}-\dfrac{8}{3}=8\ un^2.](https://tex.z-dn.net/?f=A_%7BDFGE%7D%3DA_%7B%5Ctriangle%20DBE%7D-A_%7B%5Ctriangle%20FBG%7D%3D%5Cdfrac%7B32%7D%7B3%7D-%5Cdfrac%7B8%7D%7B3%7D%3D8%5C%20un%5E2.)
and the area of the quadrilateral ADEC is
![A_{ADEC}=A_{\triangle ABC}-A_{\triangle DBE}=24-\dfrac{32}{3}=\dfrac{40}{3}\ un^2.](https://tex.z-dn.net/?f=A_%7BADEC%7D%3DA_%7B%5Ctriangle%20ABC%7D-A_%7B%5Ctriangle%20DBE%7D%3D24-%5Cdfrac%7B32%7D%7B3%7D%3D%5Cdfrac%7B40%7D%7B3%7D%5C%20un%5E2.)
Answer:
The amount of gold used in a 200 g 14 gold bracelet is 116 g.
Step-by-step explanation:
Since a 14 karat jewell is stated to have aproximally 58 % of it's weigh in gold we need to take the total weigh of the jewel in question and find that percentage of it's weigh. In order to find that percentage we'll first convert that number into a decimal, we do that by dividing it by 100, so we have 58% = 58/100 = 0.58 we can multiply this value by the weigh of the jewel to find the amount of gold used. So we have:
gold used = total weigh*0.58 = 200*0.58 = 116 g