5x - 9 ≤ 21
5x ≤ 21 + 9
5x ≤ 30
x ≤ 30 ÷ 5
x ≤ 6
Answer:
undefined
Step-by-step explanation:
To find the slope between two points, we can use the slope formula. The slope formula is:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
where m is the slope and (x₁, y₁) and (x₂, y₂) are two points.
By plugging in (5, 4) and (5, 9) for (x₁, y₁) and (x₂, y₂) respectively, we get:
![m=\frac{9-4}{5-5}=\frac{5}{0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B9-4%7D%7B5-5%7D%3D%5Cfrac%7B5%7D%7B0%7D)
Note, we cannot divide by zero. By using the slope formula, we get that the slope is undefined.
I hope this helps. Happy studying.
Answer:
(a) 0.0833 or 8.33%
(b) 0.40 or 40%
Step-by-step explanation:
Parts line one (n1) = 1,000 parts
Defects line one (d1) = 100 parts
Parts line two (n2) = 2,000 parts
Defects line two (d2) = 150 parts
Total number of parts (n) = 3,000 parts
a. Probability of a randomly selected part being defective:
![P(d) = \frac{d_1+d_2}{n_1+n_2}=\frac{100+150}{1,000+2,000}\\P(d) =0.0833=8.33\%](https://tex.z-dn.net/?f=P%28d%29%20%3D%20%5Cfrac%7Bd_1%2Bd_2%7D%7Bn_1%2Bn_2%7D%3D%5Cfrac%7B100%2B150%7D%7B1%2C000%2B2%2C000%7D%5C%5CP%28d%29%20%3D0.0833%3D8.33%5C%25)
The probability is 0.0833 or 8.33%
b. Probability of a part being produced by line one, given that it is defective:
![P(1|d)=\frac{P(1\cap d)}{P(1\cap d)+P(2\cap d)}\\P(1|d)=\frac{\frac{100}{3,000} }{\frac{100}{3,000}+\frac{150}{3,000}}\\P(1|d)=0.4 = 40\%](https://tex.z-dn.net/?f=P%281%7Cd%29%3D%5Cfrac%7BP%281%5Ccap%20d%29%7D%7BP%281%5Ccap%20d%29%2BP%282%5Ccap%20d%29%7D%5C%5CP%281%7Cd%29%3D%5Cfrac%7B%5Cfrac%7B100%7D%7B3%2C000%7D%20%7D%7B%5Cfrac%7B100%7D%7B3%2C000%7D%2B%5Cfrac%7B150%7D%7B3%2C000%7D%7D%5C%5CP%281%7Cd%29%3D0.4%20%3D%2040%5C%25)
The probability is 0.40 or 40%.
Complete question:
A store sells packages of batteries. The package with the best deal has the highest ratio of number of batteries to total cost.
Packages of Batteries
Number of Batteries
Total Cost
3
$8
5
$8
12
$24
14
$24
Which package offers the best deal?
3 for $8
5 for $8
12 for $24
14 for $24
Answer:
5 for $8
Step-by-step explanation:
Given:
3 batteries sell for $8
5 batteries sell for $8
12 batteries sell for $24
14 batteries sell for $24
To find the package that offers the best deal, find the cost of each battery by dividing each total cost by the number of the batteries. The package with the lowest will be the best package.
Thus:
Package 1: ![\frac{8}{3} = 2.67](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B3%7D%20%3D%202.67%20)
Package 2: ![\frac{8}{5} = 1.60](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B5%7D%20%3D%201.60%20)
Package 3: ![\frac{24}{12} = 2.00](https://tex.z-dn.net/?f=%20%5Cfrac%7B24%7D%7B12%7D%20%3D%202.00%20)
Package 1: ![\frac{24}{14} = 1.71](https://tex.z-dn.net/?f=%20%5Cfrac%7B24%7D%7B14%7D%20%3D%201.71%20)
The best package here is package 2 where 5 batteries sell for $8, because the cost of each battery here is significantly lower than the cost of each battery in other packages.
Answer:
The probability that the sample mean would be greater than 77.21 WPM = 0.9945
Step-by-step explanation:
Mean number of Words per Minute = u = 81
Standard Deviation = s = 17
sample size = n = 130
Target value = x = 77.21
we can find the probability by converting <u>x</u> to z-score.
The formula for z-score = ![\frac{x-u}{\frac{s}{\sqrt{n} } }](https://tex.z-dn.net/?f=%5Cfrac%7Bx-u%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
using given values, z-score = ![\frac{77.21-81}{\frac{17}{\sqrt{130} } }](https://tex.z-dn.net/?f=%5Cfrac%7B77.21-81%7D%7B%5Cfrac%7B17%7D%7B%5Csqrt%7B130%7D%20%7D%20%7D)
=> -2.54
using the z table, we can find the find the probability of -2.54, that is 0.9945.
Therefore, the probability that the sample mean would be greater than 77.21 WPM = 0.9945