13. Which relationship would most likely have a positive correlation?
a. The amount of memory in a computer, and the number of keys on the keyboard.
b. The rate at which a train travels, and the time it takes for it to reach its destination.
c. The number of tickets sold for a baseball game, and the number of hotdogs sold at the game.
B?
18. Solve 16(t - 1) + 10 > 8(t + 2) + 4(t - 1) + 4t.
33. Is y = 3x - 10 a linear equation?
a. No
b. Yes
c. Maybe
A?
34. Is y = 3x^2 - 10 a linear equation?
a. No
b. Yes
c. Sometimes
A?
35. If the money Tammy has in an investment doubles every 12 years, does her money grow linearly?
a. No
b. Yes
c. Sometimes
Not sure..
Thanks
-MC
as speed goes up, time goes down, so no
hotdogs go up with number of patrons
16(t - 1) + 10 > 8(t + 2) + 4(t - 1) + 4t.
plug and chug
16 t -16 + 10 > 8 t + 16 + 4 t - 4 +4 t
there is 16 t on both sides so no solution for t
- 6 > 12
simply false
y = 3x - 10
form is y = m x + b
which is a linear equation in slope intercept form
y = 3x^2 - 10
No because there is a quadratic term, x^2
...doubles every 12 years, does her money grow linearly?
No, it grows exponentially
Say it doubled every year
That would be like compound interest at 100%
A = original * 2^n
13. The correct answer is c. The number of tickets sold for a baseball game and the number of hotdogs sold at the game are likely to have a positive correlation. As more tickets are sold, there is a higher likelihood that more hotdogs will be sold as well.
18. Let's solve the equation step-by-step:
16(t - 1) + 10 > 8(t + 2) + 4(t - 1) + 4t
First, simplify both sides of the equation:
16t - 16 + 10 > 8t + 16 + 4t - 4 + 4t
Combine like terms:
16t - 6 > 16t + 16
Since the variable (t) appears on both sides of the inequality, we need to isolate it on one side. Let's subtract 16t from both sides:
-6 > 16
This is a false statement as -6 is not greater than 16. Therefore, there is no solution to this inequality.
33. The correct answer is b. y = 3x - 10 is a linear equation. It is in the form y = mx + b, where m is the slope and b is the y-intercept. The variables x and y are both raised to the first power, and there are no other variables or exponents involved.
34. The correct answer is a. y = 3x^2 - 10 is not a linear equation. It is a quadratic equation because the variable x is raised to the second power (squared), making it a polynomial of degree 2.
35. The correct answer is a. If the money Tammy has in an investment doubles every 12 years, her money does not grow linearly. Linear growth would mean that the money increases by the same amount every year, while in this case, it is doubling every 12 years.
13. To determine which relationship would most likely have a positive correlation, we need to understand what positive correlation means. Positive correlation refers to a relationship between two variables where, as one variable increases, the other variable also increases.
Option (a) The amount of memory in a computer and the number of keys on the keyboard are not directly related. Therefore, this relationship does not have a positive correlation.
Option (b) The rate at which a train travels and the time it takes for it to reach its destination are inversely related. As the train travels faster, the time it takes to reach the destination decreases. Therefore, this relationship does not have a positive correlation.
Option (c) The number of tickets sold for a baseball game and the number of hotdogs sold at the game are likely to have a positive correlation. As more tickets are sold, it is reasonable to assume that more people would be attending the game and buying hotdogs.
Based on this explanation, option (c) would be the most likely relationship to have a positive correlation.
18. Let's solve the given equation step by step:
16(t - 1) + 10 > 8(t + 2) + 4(t - 1) + 4t
Start by simplifying on both sides:
16t - 16 + 10 > 8t + 16 + 4t - 4 + 4t
Combine like terms:
16t - 6 > 8t + 4t + 12
Combine like terms again:
16t - 6 > 12t + 12
Next, move the variables to one side and the constants to the other side by subtracting 12t from both sides:
16t - 12t - 6 > 12t - 12t + 12
Simplify:
4t - 6 > 12
Now, add 6 to both sides of the equation:
4t - 6 + 6 > 12 + 6
Simplify:
4t > 18
Finally, divide both sides of the equation by 4:
4t/4 > 18/4
Simplify:
t > 4.5
Therefore, the solution to the given equation is t > 4.5.
33. The equation y = 3x - 10 is a linear equation because it represents a straight line on a graph. Linear equations have a degree of 1, meaning the highest power of the variable is 1 (in this case, x has a power of 1).
Based on this explanation, the correct answer is option (b) - Yes.
34. The equation y = 3x^2 - 10 is not a linear equation because it has a degree of 2. The variable x is being squared, which makes it a quadratic equation. Linear equations have a degree of 1, as explained in the previous question.
Based on this explanation, the correct answer is option (a) - No.
35. If the money Tammy has in an investment doubles every 12 years, her money does not grow linearly. Linear growth means that the amount increases or decreases by a constant amount over time. In this case, the amount doubles, indicating exponential growth.
Therefore, the correct answer is option (a) - No.
I hope this helps! Let me know if you have any further questions.