Answer: 0.0170
Step-by-step explanation:
Given : The mean amount purchased by a typical customer at Churchill’s Grocery Store is $23.50, with a standard deviation of $5.00.
i.e. ![\mu=23.50](https://tex.z-dn.net/?f=%5Cmu%3D23.50)
![\sigma=5](https://tex.z-dn.net/?f=%5Csigma%3D5)
We assume the distribution of amounts purchased follows the normal distribution.
Sample size : n=50
Let
be the sample mean.
Formula : ![z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
Then, the probability that the sample mean is at least $25.00 will be :-
![P(\overline{x}\geq\25.00)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\geq\dfrac{25-23.50}{\dfrac{5}{\sqrt{50}}})\\\\=P(z\geq2.12)\\\\=1-P(z](https://tex.z-dn.net/?f=P%28%5Coverline%7Bx%7D%5Cgeq%5C25.00%29%3DP%28%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%5Cgeq%5Cdfrac%7B25-23.50%7D%7B%5Cdfrac%7B5%7D%7B%5Csqrt%7B50%7D%7D%7D%29%5C%5C%5C%5C%3DP%28z%5Cgeq2.12%29%5C%5C%5C%5C%3D1-P%28z%3C2.12%29%5C%5C%5C%5C%3D1-0.9830%3D0.0170)
Hence, the likelihood the sample mean is at least $25.00= 0.0170
Answer:
x =
Step-by-step explanation:
If both the triangles ΔABC and ΔBCD are congruent,
Corresponding sides of both the triangles will be proportional.
![\frac{AB}{BD}=\frac{AC}{CD}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BBD%7D%3D%5Cfrac%7BAC%7D%7BCD%7D)
![\frac{5x}{3x+10}=\frac{5x-2}{4x+3}](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B3x%2B10%7D%3D%5Cfrac%7B5x-2%7D%7B4x%2B3%7D)
5x(4x + 3) = (5x - 2)(3x + 10)
20x² + 15x = 15x² + 50x - 6x - 20
20x² + 15x = 15x² + 44x - 20
20x² - 15x² = 44x - 15x - 20
5x² = 29x - 20
5x² - 29x + 20 = 0
5x² - 25x - 4x + 20 = 0
5x(x - 5) - 4(x - 5) = 0
(5x - 4)(x - 5) = 0
![x=\frac{4}{5},5](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%7D%7B5%7D%2C5)
10, because when you use a scientific calculator you get 10.09950494
which would be round to 10 because after the decimal the number is 0 below 5 so 10 stays as 10
Answer:
14
Step-by-step explanation:
3*10=30
5*14=70
30+70=100!!!