Carly is saving money. Last month, she saved $120. This month, Carly saved 30% percent more than last month. How much money did
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Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.
<h3>What are the characteristics of each of the three functions?</h3>
a) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(10) = 5 · 10 + 7
f(10) = 57
Case 2
f(10) = 10² + 6
f(10) = 106
Case 3
f(10) = 2¹⁰ + 3
f(10) = 1027
b) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(100) = 5 · 100 + 7
f(100) = 507
Case 2
f(100) = 100² + 6
f(100) = 10006
Case 3
f(100) = 2¹⁰⁰ + 3
f(100) = 1.267 × 10³⁰ + 3
c) In this part we must evaluate each of the three functions at the given value of x:
Case 1
f(1000) = 5 · 1000 + 7
f(1000) = 5007
Case 2
f(1000) = 1000² + 6
f(1000) = 1000006
Case 3
f(1000) = 2¹⁰⁰⁰ + 3
f(1000) = (1.268 × 10³⁰)¹⁰ + 3
f(1000) = 10.744 × 10³⁰⁰ + 3
f(1000) = 1.074 × 10³⁰¹ + 3
e) The <em>third</em> function increases the fastest.
f) In this part we need to compare the <em>third</em> function with respect to the <em>first</em> and <em>second</em> functions:
5 · x + 7 = 2ˣ + 3
2ˣ - 5 · x = 4
The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other <em>first</em> function at x = 4.81.
x² + 6 = 2ˣ + 3
2ˣ - x² = 3
The solution of the equation is x = 4.588. The function will exceed the other <em>second</em> function at x = 4.588.
g) Yes, <em>exponential</em> functions with bases greater than 1 will surpass <em>polynomic</em> function at any point x such that x > 0.
h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:
Case 1
Domain - All <em>real</em> numbers.
Range - All <em>real</em> numbers
Case 2
Domain - All <em>real</em> numbers.
Range - [6, +∞)
Case 3
Domain - All <em>real</em> numbers.
Range - (3, +∞)
To learn more on functions: brainly.com/question/12431044
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Answer:
Margin of error for a 95% of confidence intervals is 0.261
Step-by-step explanation:
<u>Step1:-</u>
Sample n = 81 business students over a one-week period.
Given the population standard deviation is 1.2 hours
Confidence level of significance = 0.95
Zₐ = 1.96
Margin of error (M.E) =
Given n=81 , σ =1.2 and Zₐ = 1.96
<u>Step2:-</u>
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On calculating , we get
Margin of error = 0.261
<u>Conclusion:-</u>
Margin of error for a 95% of confidence intervals is 0.261
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If something isn't clear or you're still confused about, let me know in the comments.
Step-by-step explanation:
Okay, here's my best try.
Suppose you have a bill for $8.45
If you are asked to add, say, 8% tax, you must calculate 8 percent of 8.45 and then add it to 8.45.
Begin by converting 8% to decimals by dividing by 100.
8% is 0.08 in decimal form.
To calculate a percentage of a number, you multiply the decimal percent by the number; example:
8.45 is being multiplied by 0.08. The result is: 0.676. (this is the tax; however you have to round up to two decimal places: $0.68)
After finding the tax amount, if you are asked to add it to the bill, you have to add it to the original bill; in this case, $8.45
This would be: 0.68+8.45=9.13.
Therefore, the total bill after tax is for $9.13
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With tips is the same thing, however, you can have 2 situations.
Situation 1: You are asked to calculate 15% tip of total bill.
In this situation, you can do the same we do to calculate tax.
Convert the percentage to decimal by dividing by 100.
and multiply it by the original bill.
. Rounding up, this would be $1.27 for tip.
If you were to add it to the original bill, simply sum.
The total bill after tips is for $9.72
Situation 2: You are asked to calculate 15% tip of the total bill with a tax of 8% included.
In this situation, you must first calculate the total bill with the tax added, like we did above; we got a bill for $9.13 (Tax included)
Then you can calculate 15% tip of this new bill that has tax included.
Convert
Multiply by the new bill (because this is the one that includes tax)
Round up.... $1.37 for tips.
If you are asked to give a total amount of money including tax and tips, add this to the bill.
9.13+1.37=10.50
This bill would be for $10.50