Tutor profile: Stephanie C.
A researcher is studying the effects of a new anti-depressant. The researcher is testing the drug on people diagnosed with depression, people diagnosed with borderline personality disorder, and people who have not been diagnosed with any mental illness. Participants are randomly assigned to either receive the new anti-depressant or a placebo. What is the independent variable of the study? What is the dependent variable of the study? Is this a between-subjects or within-subjects design?
The independent variable of the study is the anti-depressant/placebo. The dependent variable is the effect of the anti-depressant The study is a between-subjects design because no one is taking both the anti-depressant and the placebo
What is the equation, in slope-intercept form, of the tangent line of the function f(x)=x^2+3x+2 at x = 2?
Okay, remember that slope-intercept form equation is y = mx +b Since the question is asking for the tangent line of the function, we know we are going to be taking the derivative of the function to find the slope of the tangent line. So, let's take the derivative of f(x) first. f(x)=x^2+3x+2 f'(x) = 2x+3 (remember the shortcut to finding the derivative, multiply the integer by the exponent, and subtract the exponent value by 1) We know the question is asking for the value at x = 2. So let's plug in x=2 into f'(x) f'(2) = 2(2)+3 = 4+ 3 = 7 Now we know that f'(2)= 7, so our slope (m) is 7 Back to our slope intercept form equation, we know y = 7x + b. We need to find the y intercept. We know that the equation asks for the slope at x = 2. Let's find the y coordinate from f(x) f(2) = 2^2 + 3(2) + 2 = 4+6+2 = 12 The coordinate is (2,12). Let's plug in this coordinate in the y=mx+b equation we have so far. x = 2, y =12 y = 7x+b -> 12=7(2)+b (multiply 7 by 2) 12 = 14+b (subtract 14 from both sides) -2 = b -> b = -2 So, now we can finish the equation y = 7x - 2 And that's our answer
Dan has dimes and nickels. He has a total of 22 coins. The value of the coins is $1.70. How many dimes and nickels does he have?
Here we have a system of equations. We know we have a total of 22 coins. So, we can set up the first equation to be the sum of nickels and dimes is 22, d+n=22, where d is dimes and n is nickels. Next, we know that the total value of the coins together is $1.70. We know dimes are $0.10 each and nickels are $0.50 each, but we don't know how many we have. So, the equation would be $0.10d+$0.05n=$1.70. Does that make sense? Do you have any questions? So our two equations are: n + d = 22 0.10d + 0.05n = 1.70 What can we do next?... That's right, substitution. Let's work substitute n. So with our first equation let's move d over to the other side by subtracting it from both sides. Now we have n = 22 - d In our second equation, let's plug in 22 - d for n. 0.10d + 0.05(22-d) = 1.70 Now, let's simplify the equation. Following PEMDAS, we do the multiplication first. 0.10d + (.05*22) - (0.05*d) = 1.70 0.10d + 1.1 - 0.05d = 1.70 Now, let's combine our like terms (d). (0.10d - 0.05d) + 1.1 = 1.70 0.05d + 1.1 = 1.70 Subtract 1.1 from both sides of the equation (1.70-1.10 = 0.60) 0.05d = 0.60 Divide both sides by 0.05. 0.05d = 0.60 /0.05 /0.05 d = 12 Okay, now let's plug d = 12 back into one of our first equations, n = 22 - d n = 22 -12 = 10 Remember, d is for dimes and n is for nickels. And there we go! Dan has 10 nickels and 12 dimes
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