$ 45
multiply 60x.75 = 45
Answer:
;
; ![A = 83](https://tex.z-dn.net/?f=A%20%3D%2083)
Step-by-step explanation:
Given
![A = 2x + 1](https://tex.z-dn.net/?f=A%20%3D%202x%20%2B%201)
![B = x](https://tex.z-dn.net/?f=B%20%3D%20x)
![C = x + 15](https://tex.z-dn.net/?f=C%20%3D%20x%20%2B%2015)
Required
Arrange the angles from smallest to largest
First, we need to determine the value of x.
Since, it is a triangle:
![A + B + C = 180](https://tex.z-dn.net/?f=A%20%2B%20B%20%2B%20C%20%3D%20180)
Substitute values for A, B and C
![2x + 1+ x + x + 15 = 180](https://tex.z-dn.net/?f=2x%20%2B%201%2B%20x%20%2B%20x%20%2B%2015%20%3D%20180)
Collect Like Terms
![2x + x + x = 180 - 15 -1](https://tex.z-dn.net/?f=2x%20%2B%20x%20%2B%20x%20%3D%20180%20-%2015%20-1)
![4x = 164](https://tex.z-dn.net/?f=4x%20%3D%20164)
Solve for x
![x= 164/4](https://tex.z-dn.net/?f=x%3D%20164%2F4)
![x= 41](https://tex.z-dn.net/?f=x%3D%2041)
Solve for A, B and C
![A = 2x + 1](https://tex.z-dn.net/?f=A%20%3D%202x%20%2B%201)
![A = 2 * 41 + 1](https://tex.z-dn.net/?f=A%20%3D%202%20%2A%2041%20%2B%201)
![A = 82 + 1](https://tex.z-dn.net/?f=A%20%3D%2082%20%2B%201)
![A = 83](https://tex.z-dn.net/?f=A%20%3D%2083)
![B = x](https://tex.z-dn.net/?f=B%20%3D%20x)
![B= 41](https://tex.z-dn.net/?f=B%3D%2041)
![C = x + 15](https://tex.z-dn.net/?f=C%20%3D%20x%20%2B%2015)
![C = 41 + 15](https://tex.z-dn.net/?f=C%20%20%3D%2041%20%2B%2015)
![C = 56](https://tex.z-dn.net/?f=C%20%20%3D%2056)
From Smallest to Largest, we have:
;
; ![A = 83](https://tex.z-dn.net/?f=A%20%3D%2083)
Answer:
The 90% confidence interval for the difference in mean (μ₁ - μ₂) for the two bakeries is; (<u>49</u>) < μ₁ - μ₂ < (<u>289)</u>
Step-by-step explanation:
The given data are;
Bakery A
<em> </em>= 1,880 cal
s₁ = 148 cal
n₁ = 10
Bakery B
<em> </em>= 1,711 cal
s₂ = 192 cal
n₂ = 10
![\left (\bar{x}_1-\bar{x}_{2} \right ) - t_{c}\cdot \hat \sigma \sqrt{\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}}}< \mu _{1}-\mu _{2}< \left (\bar{x}_1-\bar{x}_{2} \right ) + t_{c}\cdot \hat \sigma \sqrt{\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}}}](https://tex.z-dn.net/?f=%5Cleft%20%28%5Cbar%7Bx%7D_1-%5Cbar%7Bx%7D_%7B2%7D%20%20%5Cright%20%29%20-%20t_%7Bc%7D%5Ccdot%20%5Chat%20%5Csigma%20%5Csqrt%7B%5Cdfrac%7B1%7D%7Bn_%7B1%7D%7D%2B%5Cdfrac%7B1%7D%7Bn_%7B2%7D%7D%7D%3C%20%5Cmu%20_%7B1%7D-%5Cmu%20_%7B2%7D%3C%20%5Cleft%20%28%5Cbar%7Bx%7D_1-%5Cbar%7Bx%7D_%7B2%7D%20%20%5Cright%20%29%20%2B%20t_%7Bc%7D%5Ccdot%20%5Chat%20%5Csigma%20%5Csqrt%7B%5Cdfrac%7B1%7D%7Bn_%7B1%7D%7D%2B%5Cdfrac%7B1%7D%7Bn_%7B2%7D%7D%7D)
df = n₁ + n₂ - 2
∴ df = 10 + 18 - 2 = 26
From the t-table, we have, for two tails,
= 1.706
![\hat{\sigma} =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}](https://tex.z-dn.net/?f=%5Chat%7B%5Csigma%7D%20%3D%5Csqrt%7B%5Cdfrac%7B%5Cleft%20%28%20n_%7B1%7D-1%20%5Cright%20%29%5Ccdot%20s_%7B1%7D%5E%7B2%7D%20%2B%5Cleft%20%28%20n_%7B2%7D-1%20%5Cright%20%29%5Ccdot%20s_%7B2%7D%5E%7B2%7D%7D%7Bn_%7B1%7D%2Bn_%7B2%7D-2%7D%7D)
![\hat{\sigma} =\sqrt{\dfrac{\left ( 10-1 \right )\cdot 148^{2} +\left ( 18-1 \right )\cdot 192^{2}}{10+18-2}}= 178.004321469](https://tex.z-dn.net/?f=%5Chat%7B%5Csigma%7D%20%3D%5Csqrt%7B%5Cdfrac%7B%5Cleft%20%28%2010-1%20%5Cright%20%29%5Ccdot%20148%5E%7B2%7D%20%2B%5Cleft%20%28%2018-1%20%5Cright%20%29%5Ccdot%20192%5E%7B2%7D%7D%7B10%2B18-2%7D%7D%3D%20178.004321469)
≈ 178
Therefore, we get;
![\left (1,880-1,711 \right ) - 1.706\times178 \sqrt{\dfrac{1}{10}+\dfrac{1}{18}}< \mu _{1}-\mu _{2}< \left (1,880-1,711 \right ) + 1.706\times178 \sqrt{\dfrac{1}{10}+\dfrac{1}{18}}](https://tex.z-dn.net/?f=%5Cleft%20%281%2C880-1%2C711%20%20%5Cright%20%29%20-%201.706%5Ctimes178%20%5Csqrt%7B%5Cdfrac%7B1%7D%7B10%7D%2B%5Cdfrac%7B1%7D%7B18%7D%7D%3C%20%5Cmu%20_%7B1%7D-%5Cmu%20_%7B2%7D%3C%20%5Cleft%20%281%2C880-1%2C711%20%20%5Cright%20%29%20%2B%201.706%5Ctimes178%20%5Csqrt%7B%5Cdfrac%7B1%7D%7B10%7D%2B%5Cdfrac%7B1%7D%7B18%7D%7D)
Which gives;
![169 - \dfrac{75917\cdot \sqrt{35} }{3,750} < \mu _{1}-\mu _{2}< 169 + \dfrac{75917\cdot \sqrt{35} }{3,750}](https://tex.z-dn.net/?f=169%20-%20%5Cdfrac%7B75917%5Ccdot%20%5Csqrt%7B35%7D%20%7D%7B3%2C750%7D%20%3C%20%5Cmu%20_%7B1%7D-%5Cmu%20_%7B2%7D%3C%20169%20%2B%20%5Cdfrac%7B75917%5Ccdot%20%5Csqrt%7B35%7D%20%7D%7B3%2C750%7D)
Therefore, by rounding to the nearest integer, we have;
The 90% C.I. ≈ 49 < μ₁ - μ₂ < 289