1 pound is 16 ounces so 3 x 16+6
=
54 ounces
Answer:
Margin of Error = 5.4088 ;
Confidence interval = (30.1 ; 40.9)
Interval estimate are almost the same
Step-by-step explanation:
Given that :
Population standard deviation, σ = 9.3
Sample size, n = 8
Xbar = 35.5
Confidence level = 90%
The confidence interval:
Xbar ± Margin of error
Margin of Error = Zcritical * σ/sqrt(n)
Zcritical at 90% = 1.645
Margin of Error = 1.645 * 9.3/sqrt(8) = 5.4088
Confidence interval :
Xbar ± Margin of error
35.5 ± 5.4088
Lower boundary = (35.5 - 5.4088) = 30.0912 = 30.1
Upper boundary = (35.5 + 5.4088) = 40.9088 = 40.9
(30.1 ; 40.9)
T distribution =. (30.5 ; 40.5)
Normal distribution = (30.1, 40.9)
Answer: y=3x−12
Step-by-step explanation:
Answer:
x = 26, 16
Step-by-step explanation:
( x-21) ^2 = 25
Take the square root of each side
sqrt(( x-21) ^2) = ±sqrt(25)
x-21 = ±5
Add 21 to each side
x-21+21 = 21±5
x = 21±5
x = 21+5 and x = 21-5
x = 26, 16
Answer:
3. C
4. D
Step-by-step explanation:
3.
![x^2+25=0\\x^2=-25\\x=\pm\sqrt{-25}](https://tex.z-dn.net/?f=x%5E2%2B25%3D0%5C%5Cx%5E2%3D-25%5C%5Cx%3D%5Cpm%5Csqrt%7B-25%7D)
Once ![\sqrt{-1}=i](https://tex.z-dn.net/?f=%5Csqrt%7B-1%7D%3Di)
![x=\pm5i](https://tex.z-dn.net/?f=x%3D%5Cpm5i)
4.
A quadratic equation has no real roots when the discriminant (
) is negative.
.
Let's try all the equations:
(A)
![2x^2-7x-9=0\\\\\Delta=\sqrt{\left(-7\right)^2-4\cdot \:2\left(-9\right)}\\\Delta=\sqrt{\left(-7\right)^2+4\cdot \:2\cdot \:9}\\\Delta=\sqrt{121} \\\Delta=11](https://tex.z-dn.net/?f=2x%5E2-7x-9%3D0%5C%5C%5C%5C%5CDelta%3D%5Csqrt%7B%5Cleft%28-7%5Cright%29%5E2-4%5Ccdot%20%5C%3A2%5Cleft%28-9%5Cright%29%7D%5C%5C%5CDelta%3D%5Csqrt%7B%5Cleft%28-7%5Cright%29%5E2%2B4%5Ccdot%20%5C%3A2%5Ccdot%20%5C%3A9%7D%5C%5C%5CDelta%3D%5Csqrt%7B121%7D%20%5C%5C%5CDelta%3D11)
(B)
![2x^2=7x\\2x^2-7x=0\\x(2x-7)=0\\x=0\\\text{or}\\2x-7=0\\2x=7\\\\](https://tex.z-dn.net/?f=2x%5E2%3D7x%5C%5C2x%5E2-7x%3D0%5C%5Cx%282x-7%29%3D0%5C%5Cx%3D0%5C%5C%5Ctext%7Bor%7D%5C%5C2x-7%3D0%5C%5C2x%3D7%5C%5C%5C%5C)
![$x=\frac{7}{2} $](https://tex.z-dn.net/?f=%24x%3D%5Cfrac%7B7%7D%7B2%7D%20%24)
(C)
![2x^2+7x-9=0\\\Delta = \sqrt{7^2-4\cdot \:2\left(-9\right)}\\\Delta = \sqrt{7^2+4\cdot \:2\cdot \:9}\\\Delta = \sqrt{121} \\\Delta= 11](https://tex.z-dn.net/?f=2x%5E2%2B7x-9%3D0%5C%5C%5CDelta%20%3D%20%5Csqrt%7B7%5E2-4%5Ccdot%20%5C%3A2%5Cleft%28-9%5Cright%29%7D%5C%5C%5CDelta%20%3D%20%5Csqrt%7B7%5E2%2B4%5Ccdot%20%5C%3A2%5Ccdot%20%5C%3A9%7D%5C%5C%5CDelta%20%3D%20%5Csqrt%7B121%7D%20%5C%5C%5CDelta%3D%2011)
(D)
![2x^2-7x+9=0\\\Delta = \sqrt{\left(-7\right)^2-4\cdot \:2\cdot \:9}\\\\\Delta=\sqrt{-23} \\\Delta=\sqrt{23i}](https://tex.z-dn.net/?f=2x%5E2-7x%2B9%3D0%5C%5C%5CDelta%20%3D%20%5Csqrt%7B%5Cleft%28-7%5Cright%29%5E2-4%5Ccdot%20%5C%3A2%5Ccdot%20%5C%3A9%7D%5C%5C%5C%5C%5CDelta%3D%5Csqrt%7B-23%7D%20%5C%5C%5CDelta%3D%5Csqrt%7B23i%7D)