Answer:
Proved!
Step-by-step explanation:
For two functions f(x) and g(x) to be inverses of each other then;
f(g(x)) = x and g(f(x)) = x condition must be satisfied.
<u>Checking: A. f(x) = 7x³ + 10 and g(x) = ∛</u>
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So f(g(x)) = 7(![\sqrt[3]{(x- 10)/7}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%28x-%2010%29%2F7%7D)
)³ + 10
We get; 7() + 10 = x - 10 + 10 = x (*<em>This is correct!)</em>
<em />
So g(f(x)) = ![\sqrt[3]{((7x^3 + 10) - 10)/7}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%28%287x%5E3%20%2B%2010%29%20-%2010%29%2F7%7D)
Ten cancels out and we are left with;
![\sqrt[3]{7x^3/7}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B7x%5E3%2F7%7D)
= ![\sqrt[3]{x^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E3%7D)
= x (* <em>This is also correct!)</em>
Answer:
The percentage of people taking the test who score between 391 and 767 is 95%.
Step-by-step explanation:
The Empirical Rule(68-95-99.7 Rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 579
Standard deviation = 94
391 = 579 - 2*94
So 391 is two standard deviations below the mean.
767 = 579 + 2*94
So 767 is two standard deviations above the mean.
By the Empirical Rule:
The percentage of people taking the test who score between 391 and 767 is 95%.
If we have a number represented by n, we have 20 is equal to, so 20=something. That something is "5 less than twice a number". 5 less than something means something-5, and something-5=20. Since 5 is less than twice a number, and twice a number is n+n=2n, we have 2n-5=20
Actually solving the problem, we can start by adding 5 to both sides, resulting in 2n=25. Next, we can divide both sides by 2 to get n=12.5
Answer: 27,600
Step-by-step explanation:
Ok, there could be two answers to this question. If the question is asking how much he would make if it was .15% more, the total would be 27,600/a year
However, if it's asking .15% <u>of</u> 24,000, your answer would be 3,600 ( as in the extra he would be making)
- To find the answer, you would have to multiply 24,000*.15 (your starting value times how much you would like to multiply it by)
Answer:
see below
Step-by-step explanation:
Small bag
95p / 250 g * 12/12 to get to 3 kg = 1140 p / 3000g =11.40£s/ 3 kgs
Medium bag
1.8£ / 500 g * 6/6 to get to 3 kg = 10.8£ / 3000g =10.80£/ 3 kgs
Large bag
3.7£ / 3 kg *
