Answer:
The 95% confidence interval estimate for the population mean force is (1691, 1755).
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally.
The sample selected here is <em>n</em> = 30.
Thus, the sampling distribution of the sample mean will be normal.
Compute the sample mean and standard deviation as follows:
![\bar x=\frac{1}{n}\sum x=\frac{1}{30}\times 51702=1723.4\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{30-1}\times 232561.2}=89.55](https://tex.z-dn.net/?f=%5Cbar%20x%3D%5Cfrac%7B1%7D%7Bn%7D%5Csum%20x%3D%5Cfrac%7B1%7D%7B30%7D%5Ctimes%2051702%3D1723.4%5C%5C%5C%5Cs%3D%5Csqrt%7B%5Cfrac%7B1%7D%7Bn-1%7D%5Csum%20%28x-%5Cbar%20x%29%5E%7B2%7D%7D%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B30-1%7D%5Ctimes%20232561.2%7D%3D89.55)
Construct a 95% confidence interval estimate for the population mean force as follows:
![CI=\bar x\pm z_{\alpha /2}\times\frac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=CI%3D%5Cbar%20x%5Cpm%20z_%7B%5Calpha%20%2F2%7D%5Ctimes%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
![=1723.4\pm 1.96\times\frac{89.55}{\sqrt{30}}\\\\=1723.4\pm 32.045\\\\=(1691.355, 1755.445)\\\\\approx (1691, 1755)](https://tex.z-dn.net/?f=%3D1723.4%5Cpm%201.96%5Ctimes%5Cfrac%7B89.55%7D%7B%5Csqrt%7B30%7D%7D%5C%5C%5C%5C%3D1723.4%5Cpm%2032.045%5C%5C%5C%5C%3D%281691.355%2C%201755.445%29%5C%5C%5C%5C%5Capprox%20%281691%2C%201755%29)
Thus, the 95% confidence interval estimate for the population mean force is (1691, 1755).
The first one is (-2,1)
The other one is 36
The answer to this question is x=3
Sarah bought 3 bracelets and 2 pairs of sunglasses.
Step-by-step explanation:
Total items bought = 5 items
Total spent = $24
Cost of one bracelet = $5
Cost of pair of sunglasses = $4.50
Let,
x be the number of bracelet bought.
y be the number of sunglasses bought.
According to given statement;
x+y=5 Eqn 1
5x+4.50y=24 Eqn 2
Multiplying Eqn 1 by 5
![5(x+y=5)\\5x+5y=25\ \ \ Eqn\ 3](https://tex.z-dn.net/?f=5%28x%2By%3D5%29%5C%5C5x%2B5y%3D25%5C%20%5C%20%5C%20Eqn%5C%203)
Subtracting Eqn 2 from Eqn 3
![(5x+5y)-(5x+4.50y)=25-24\\5x+5y-5x-4.50y=1\\0.50y=1](https://tex.z-dn.net/?f=%285x%2B5y%29-%285x%2B4.50y%29%3D25-24%5C%5C5x%2B5y-5x-4.50y%3D1%5C%5C0.50y%3D1)
Dividing both sides by 0.50
![\frac{0.50y}{0.50}=\frac{1}{0.50}\\y=2](https://tex.z-dn.net/?f=%5Cfrac%7B0.50y%7D%7B0.50%7D%3D%5Cfrac%7B1%7D%7B0.50%7D%5C%5Cy%3D2)
Putting in Eqn 1
![x+2=5\\x=5-2\\x=3](https://tex.z-dn.net/?f=x%2B2%3D5%5C%5Cx%3D5-2%5C%5Cx%3D3)
Sarah bought 3 bracelets and 2 pairs of sunglasses.
Keywords: linear equations, subtraction
Learn more about subtraction at:
#LearnwithBrainly
Answer:orange graph =-2
Blue graph -2 or 2
Step-by-step explanation: