Answer:
(1) 2π - x² = 0 (2) x = 2.5 cm (3) perimeter = 10 cm
Step-by-step explanation:
(1)The area of the circular coin without the inner square removed is πr² where r = 3 cm is the radius of the coin. So, the area of the coin without the inner square removed is πr² = π(3 cm)² = 9π cm²
The area of the square of x sides removed from its center is x².
The area A of the each face of the coin is thus A = 9π - x²
Since the area of each face of the coin A = 7π cm²,
then
7π = 9π - x²
9π - 7π - x² = 0
2π - x² = 0
(2) Solve the equation 2π - x² = 0
2π - x² = 0
x² = 2π
x = ±√(2π)
x = ± 2.51 cm
Since x cannot be negative, we take the positive answer.
So, x = 2.51 cm
≅ 2.5 cm
(3) Find the perimeter of the square
The perimeter of the square, p is given by p = 4x
p = 4 × 2.51 cm
= 10.04 cm
≅ 10 cm
X=2 is the answer hope it helps
Hello,
Here is your answer:
The proper answer to this question is...."64"!
Here is how:
First translate the problem:
4^3=4×4×4=64
Your answer is 64!
If you need anymore help feel free to ask me!
Hope this helps!
Answer: ![(13.22\%,\ 19.34\%)](https://tex.z-dn.net/?f=%2813.22%5C%25%2C%5C%2019.34%5C%25%29)
Step-by-step explanation:
Given : Sample space : n= 559
Sample proportion : ![\hat{p}=\dfrac{91}{559}=0.162790697674\approx0.1628](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B91%7D%7B559%7D%3D0.162790697674%5Capprox0.1628)
![=16.28\%](https://tex.z-dn.net/?f=%3D16.28%5C%25)
Significance level : ![\alpha= 1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3D%201-0.95%3D0.05)
Critical value : ![z_{\alpha/2}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D1.96)
Confidence level for population proportion:-
![\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.1628\pm (1.96)\sqrt{\dfrac{0.1628(1-0.1628)}{559}}\\\\=0.1628\pm0.030604971367\\\\\approx 0.1628\pm0.0306=(0.1322,\ 0.1934)=(13.22\%,\ 19.34\%)](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%5C%5C%5C%5C%3D0.1628%5Cpm%20%281.96%29%5Csqrt%7B%5Cdfrac%7B0.1628%281-0.1628%29%7D%7B559%7D%7D%5C%5C%5C%5C%3D0.1628%5Cpm0.030604971367%5C%5C%5C%5C%5Capprox%200.1628%5Cpm0.0306%3D%280.1322%2C%5C%200.1934%29%3D%2813.22%5C%25%2C%5C%2019.34%5C%25%29)
Hence, 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.= ![(13.22\%,\ 19.34\%)](https://tex.z-dn.net/?f=%2813.22%5C%25%2C%5C%2019.34%5C%25%29)
E = 2.718281828...
rounded to 3 decimal places
2.718