Answer:
We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .
Step-by-step explanation:
Given -
The sample size is large then we can use central limit theorem
n = 50 ,
Standard deviation
= 7.1
Mean
= 110
1 - confidence interval = 1 - .98 = .02
= 2.33
98% confidence interval for the mean caffeine content for cups dispensed by the machine = ![\overline{(y)}\pm z_{\frac{\alpha}{2}}\frac{\sigma}\sqrt{n}](https://tex.z-dn.net/?f=%5Coverline%7B%28y%29%7D%5Cpm%20z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Cfrac%7B%5Csigma%7D%5Csqrt%7Bn%7D)
= ![110\pm z_{.01}\frac{7.1}\sqrt{50}](https://tex.z-dn.net/?f=110%5Cpm%20z_%7B.01%7D%5Cfrac%7B7.1%7D%5Csqrt%7B50%7D)
= ![110\pm 2.33\frac{7.1}\sqrt{50}](https://tex.z-dn.net/?f=110%5Cpm%202.33%5Cfrac%7B7.1%7D%5Csqrt%7B50%7D)
First we take + sign
= 112.34
now we take - sign
= 107.66
We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .
Answer:
To sum up, 1683/20 = 84.15. The number has 2 decimal places. As division with remainder the result of 1683 ÷ 20 = 84 R 3.
Answer:
(-3, -7)
General Formulas and Concepts:
<u>Algebra I</u>
Point-Slope Form: y - y₁ = m(x - x₁)
- x₁ - x coordinate
- y₁ - y coordinate
- m - slope
Step-by-step explanation:
<u>Step 1: Define</u>
Point-Slope Form: y + 7 = 4/3(x + 3)
<u>Step 2: Break function</u>
Slope <em>m</em> = 4/3
Point (-3, -7)
The total distance that will be covered is
25 - 3 = 22
If we let x be the head start that Ario will have before Miguel starts, then we have the equation
x / (22 - x ) = 1/4
Solve for x
x = 4.4
Ario will have to travel 4.4 meters before Miguel starts
7 cubes.
imagine that ∆ are the blocks, it should be something like this:
∆
∆∆
∆∆∆
∆∆∆∆
∆∆∆∆∆
∆∆∆∆∆∆
∆∆∆∆∆∆∆
Add up everything 28 comes.