Answer:
3 5/12 cups of flour are needed
Step-by-step explanation:
The flour-sugar total is 3 2/3 cups, of which 1/4 cup is sugar. So, to find the amount of flour used, we subtract 1/4 cup (sugar) from the total (3 2/3 cups):
11 1
----- - ---- where 11/3 is the improper fraction form of 3 2/3
3 4
The LCD is 12. Rewriting this subtraction using the LCD, we get:
44 3
---- - ----- = 41/12 (cups) = 3 5/12 cups
12 12
3 5/12 cups of flour are needed
Answer: 5x-y+6
Step-by-step explanation:
Answer:
Work done in stretching the spring = 7.56 lb-ft.
Step-by-step explanation:
Normal length of the spring = 8 in or
ft
=
ft
If the spring has been stretched to 11 inch then the stretched length of the spring is = 11 in
=
ft
Force applied to stretch the spring = 12 lb
By Hook's law,
F = kx [where k is the spring constant and x = length by which the spring is stretched]
12 = k(
)
k = 18
Work done (W) to stretch the spring by
ft will be
W = ![\int\limits^\frac{11}{12} _0 {kx} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cfrac%7B11%7D%7B12%7D%20_0%20%7Bkx%7D%20%5C%2C%20dx)
= ![\int\limits^\frac{11}{12} _0 {(18x)} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cfrac%7B11%7D%7B12%7D%20_0%20%7B%2818x%29%7D%20%5C%2C%20dx)
= ![18[\frac{x^{2}}{2}]^{\frac{11}{12}}_0](https://tex.z-dn.net/?f=18%5B%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%5D%5E%7B%5Cfrac%7B11%7D%7B12%7D%7D_0)
= 9(
)²
= 7.56 lb-ft
Answer:
The answer is "(0.461 , 7.206)"
Step-by-step explanation:
In the given question some information is missing, that is data. so, the correct answer to this question can be defined as follows:
UnLogged:
![x_1=17.500\\s_1=3.529\\n_1=12](https://tex.z-dn.net/?f=x_1%3D17.500%5C%5Cs_1%3D3.529%5C%5Cn_1%3D12)
Logged:
![x_2=13.667\\ s_2=4.500\\n_2=9\\](https://tex.z-dn.net/?f=x_2%3D13.667%5C%5C%20s_2%3D4.500%5C%5Cn_2%3D9%5C%5C)
formula of std error:
![\ std \ error =\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}](https://tex.z-dn.net/?f=%5C%20std%20%5C%20error%20%3D%5Csqrt%7B%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%7D)
![=\sqrt{\frac{3.529^2}{12}+\frac{4.500^2}{9}}\\\\=\sqrt{\frac{3.529^2\times 3+4.500^2\times 4}{36}}\\\\=1.8133](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5Cfrac%7B3.529%5E2%7D%7B12%7D%2B%5Cfrac%7B4.500%5E2%7D%7B9%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B%5Cfrac%7B3.529%5E2%5Ctimes%203%2B4.500%5E2%5Ctimes%204%7D%7B36%7D%7D%5C%5C%5C%5C%3D1.8133)
Point differential estimation =![x_1-x _2](https://tex.z-dn.net/?f=x_1-x%20_2)
![= 17.500-13.667\\=3.833](https://tex.z-dn.net/?f=%3D%2017.500-13.667%5C%5C%3D3.833)
For 90 percent t= 1.860 Cl & 8 df
error of margin E = ![t\times \ std \ error](https://tex.z-dn.net/?f=t%5Ctimes%20%5C%20std%20%5C%20error)
![= 1.860 \times 1.8133\\= 3.373](https://tex.z-dn.net/?f=%3D%201.860%20%5Ctimes%201.8133%5C%5C%3D%203.373)
Lower bound =mean difference -E=0.461
Upper bound = mean difference+ E=7.206
In the above 90% confidence interval were the population mean= (0.461 , 7.206)