Answer:
x⁷ = 60
Step-by-step explanation:
Given:-
To Find:-
Solution:-
Given logarithmic equation is ,
⇒ log x⁵ + log x ¹² = 7
⇒ log x ⁵ * ¹² = 7 [ log aⁿ + log aⁿ' = log aⁿ * ⁿ' ]
⇒log x ⁶⁰ = 7
In expotential form we can write it as ,
⇒ x⁷ = 60
No fast food 2310 2295 2280 2340 2235 2265 2315 2291.429 34.8466
food Fast 2579 2160 2165 2580 2558 2591 2614 2518 2583.125 33.0646
Give a 95% confidence interval for the difference of the two means, (Uf - Un), where is the mean calorie intake for teens who typically eat fast food and is that for teens who do not typically eat fast food assuming two normal populations, independent random samples, and equal variances for the two populations
Answer:
Step-by-step explanation:
For "no fast food,
n1 = 9
Mean = (2310 + 2295 + 2280 + 2340 + 2235 + 2265 + 2315 + 2291.429 + 34.8466)/9
Mean, m1 = 2041
Standard deviation, s1 = √summation(x - u)²/n
summation(x - u)² =
(2310 - 2041)^2 + (2295 - 2041)^2 + (2280 - 2041)^2 + (2340 - 2041)^2 + (2235 - 2041)^2 + (2265 - 2041)^2 + (2315 - 2041)^2 + (2291.429 - 2041)^2 + (34.8466 - 2041)^2
= 4533653.14837256
s = √4533653.14837256/9
s = 709.75
For " fast food",
n2 = 10
Mean = (2579 + 2160 + 2165 + 2580 + 2558 + 2591 + 2614 + 2518 2583.125 + 33.0646)/10
Mean,m2 = 2238
summation(x - u)² =
(2579 - 2238)^2 + (2160 - 2238)^2 + (2165 - 2238)^2 + (2580 - 2238)^2 + (2558 - 2238)^2 + (2591 - 2238)^2 + (2614 - 2238)^2 + (2518 - 2238)^2 + (2583.125 - 2238)^2 + (33.0646 - 2238)^2
= 5672294.38379816
s2 = √5672294.38379816/10
s2 = 753.15
For a confidence interval of 95%, z = 1.96
The formula for confidence interval is
m1 - m2 ± z × √(s1²/n1 + s2²/n2)
= 2041 - 2238 ± 1.96 × √(709.75²/9 + 753.15²/10)
= - 197 ± 1.96 × √(55971.6736 + 56723.4923)
= - 197 ± 1.96 × 335.7
= - 197 ± 657.972
The lower end of the interval is
- 197 - 657.972 = - 854.972
The upper end of the interval is
- 197 + 657.972 = 460.972
The proportion of production that is defective and from plant A is
... 0.35·0.25 = 0.0875
The proportion of production that is defective and from plant B is
... 0.15·0.05 = 0.0075
The proportion of production that is defective and from plant C is
... 0.50·0.15 = 0.075
Thus, the proportion of defective product that is from plant C is
... 0.075/(0.0875 +0.0075 +0.075) = 75/170 = 15/34 ≈ 44.12%
_____
P(C | defective) = P(C&defective)/P(defective)
The question required the use of Bayes' theorem to determine the probability of a defective product coming from plant c. Given the probabilities of defectiveness for each plant, the calculation indicated that there is approximately a 54.55% chance that a defective product came from plant c.
The problem described can be solved using Bayes' theorem, which is a principle in Probability that is used when we need to revise/or update the probabilities of events given new data. Since a defective product is received, and we need to determine the probability of it coming from plant c, we apply Bayes' theorem for the probability of events a, b, and c (representative of the products from the respective plants).
The Bayesian formula we will use, given the probabilities of a, b and c respectively and the probability of receiving a nondefective product from these plants, is: P(c|defective) = [P(defective|c) * P(c)] / [P(defective|a) * P(a) + P(defective|b) * P(b) + P(defective|c) * P(c)].
First, calculate the probability of a defective product from each plant (1 minus the probability of a nondefective product): these are 0.25 for plant a, 0.05 for plant b, and 0.15 for plant c.
Then substitute the values: P(c|defective) = [0.15 * 0.50] / [(0.25 * 0.35) + (0.05 * 0.15) + (0.15 * 0.5)] = 0.075 / 0.1375 = 0.5454545.
So, given a defective product, there is approximately a 54.55% chance that it was produced by plant c.
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Answer:
answer is B 64 root 2
Step-by-step explanation:
got it right on edg 2020-2021
Answer:
For a 45 45 90 triangle
leg = hypotenuse / (square root of 2)
leg = 128 / 1.4142135624
leg = 90.5096679902 cm
Step-by-step explanation:
Answer:
no it is equal cause they are the same number
Step-by-step explanation:
Answer:
28π cm²
Step-by-step explanation:
Circumference Formula: C = 2πr
Simply plug in r into the formula:
C = 2π(14)
C = 28π or 87.9646
Answer:
28π cm
Step-by-step explanation:
The circumference of a circle has the formula 2πr.
2 × π × r
Where r is the radius.
2 × π × 14
28 × π
= 28π
The circumference is 28π and the unit is centimeters.
Write the fractions in order from least to greatest.
Answer:
D.
Step-by-step explanation:
Because in negative numbers greater is actually less
Answer:
change into improper fraction , find the common multiple and choose from the biggest because it is a negative fraction