Answer: 1.460
Step-by-step explanation:
Given : Researchers report that on average freshman who live on campus gain 15 pounds during their first year in college.
Let
represents the population mean .
Then, the set of hypothesis will be:-
![H_0: \mu=15](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu%3D15)
![H_a:\mu\neq15](https://tex.z-dn.net/?f=H_a%3A%5Cmu%5Cneq15)
We assume that this is normal distribution.
Sample size : n = 10, which is a small sample (n<30) ,s o we use t-test.
Sample mean : ![\overliene{x}=16.2\ lbs](https://tex.z-dn.net/?f=%5Coverliene%7Bx%7D%3D16.2%5C%20lbs)
Standard deviation : ![\sigma=2.6](https://tex.z-dn.net/?f=%5Csigma%3D2.6)
The test statistic for population mean for small sample is given by :-
![t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t=\dfrac{16.2-15}{\dfrac{2.6}{\sqrt{10}}}=1.45951276623\approx1.460](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B16.2-15%7D%7B%5Cdfrac%7B2.6%7D%7B%5Csqrt%7B10%7D%7D%7D%3D1.45951276623%5Capprox1.460)
Hence , the value of test statistic = 1.460
C. P+0.085p=$368.90. 1.085p=$368.90. $368.90/1.085=$340. The original cost was $340 :)
A two digit number has a tens digit and a ones digit.
Let's say x = tens digit and y = ones digit
"The sum of the digits is 5"
x + y = 5
The next phrase is "the number multiplied by 3 is 42" but we need to represent the number using the digits. So they need to be multiplied first by their place value and added together. [Example: 34 = 3(10) + 4(1)]
The number is: 10x + y
3(10x + y) = 42
The system of equations: (two equations for two unknowns)
x + y = 5
30x + 3y = 42
Then you can use substitution or elimination to combine and solve.
I'll use elimination, multiply the entire top equation by -3 and add the equations together. y will cancel out
-3x - 3y = -15
30x + 3y = 42
------------------
27x + 0 = 27
x = 1
then plug x = 1 into either equation to find y
1 + y = 5
y = 4
remember the x and y represent digits so the number xy is 14
Answer:
![\huge{ \boxed{ \sf{17.68 \: {cm}^{2} }}}](https://tex.z-dn.net/?f=%20%5Chuge%7B%20%5Cboxed%7B%20%5Csf%7B17.68%20%5C%3A%20%20%7Bcm%7D%5E%7B2%7D%20%7D%7D%7D)
Step-by-step explanation:
![\underline{ \text{Given}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Ctext%7BGiven%7D%7D%20%3A%20)
![\longrightarrow \sf{ \: Length \: of \: a \: rectangle \: = \: 5.2 \: cm}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%20%5Csf%7B%20%5C%3A%20Length%20%5C%3A%20of%20%5C%3A%20a%20%5C%3A%20rectangle%20%5C%3A%20%20%3D%20%20%5C%3A%205.2%20%5C%3A%20cm%7D)
![\longrightarrow{ \sf{Breadth \: of \: \: rectangle \: = \: 3.4 \: cm}}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7BBreadth%20%5C%3A%20of%20%5C%3A%20%20%5C%3A%20rectangle%20%5C%3A%20%20%3D%20%20%5C%3A%203.4%20%5C%3A%20cm%7D%7D)
![\underline{ \text{To \: find} } : \sf{Area \: of \: a \: rectangle}](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Ctext%7BTo%20%5C%3A%20find%7D%20%7D%20%3A%20%20%20%5Csf%7BArea%20%5C%3A%20of%20%5C%3A%20a%20%5C%3A%20rectangle%7D)
![\boxed{ \sf{Area \: of \: a \: rectangle \: = \: Length \: \times \: Breadth}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Csf%7BArea%20%5C%3A%20of%20%5C%3A%20a%20%5C%3A%20rectangle%20%5C%3A%20%20%3D%20%20%5C%3A%20Length%20%5C%3A%20%20%5Ctimes%20%20%5C%3A%20Breadth%7D%7D)
![\mapsto{ \sf{Area \: = \: 5.2 \: cm \: \times \: 3.4 \: cm}}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7BArea%20%5C%3A%20%20%3D%20%20%5C%3A%205.2%20%5C%3A%20cm%20%5C%3A%20%20%5Ctimes%20%20%5C%3A%203.4%20%5C%3A%20cm%7D%7D)
![\mapsto{ \sf{Area \: = \: 17.68 \: {cm}^{2} }}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7BArea%20%5C%3A%20%20%3D%20%20%5C%3A%2017.68%20%5C%3A%20%20%7Bcm%7D%5E%7B2%7D%20%7D%7D)
Hope I helped!
Best regards! :D
~![\text{TheAnimeGirl}](https://tex.z-dn.net/?f=%20%5Ctext%7BTheAnimeGirl%7D)