<span>There are 24 who like both rock and country. There are 8 who like all 3 types, and these eight have been counted under the 24. This means that the number who like rock and country but not jazz is 24 - 8 = 16.
We are given a total of 155 who like country. We subtract the 16 who like both rock and country, and are left with 139 people who like country but not rock. (It does not matter whether they like jazz or not).
The probability is 155 out of the total of 500, so 155/500 = 31/100 = 0.31.
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Remember that an extraneous solution of an equation is a solution that emerges from the algebraic process of solving the equation but is not a valid solution of the equation.
First, we are going to solve our equation algebraically:
Step 1 simplify the equation:


Step 2 subtract 5 from both sides of the equation:


Step 3 square both sides of the equation:


Next, we are going to replace our solution in our original equation and check if it is a valid solution:




Since 9 is not equal to 1,
is not valid solution of the equation; therefor it is an extraneous solution.
We can conclude that the correct answer is: x = 16, solution is extraneous
Answer:
A on edge
Step-by-step explanation:
i just took the quiz
When you think about it. It's actually quite easy.
The number are the amount of miles, and the variables are the amount of hours. So we would just have to multiply them. So, by putting the number together we would be able to multiply them once we have the numbers for the variables. Since we dont have them, we can just make the inequality. It says that car 1 traveled at LEAST that of car 2. Showing that car 1 may have traveled farther. SOOOOO........ the inequality should look like this:
165x <span>≥ 175y</span>
Answer:
a) distance halfway = 16.49 [m], displacement halfway = 10.5 [m]
b) distrance traveled increases when the child completes one circuit of the track.
Step-by-step explanation:
a) Distance is a scalar quantity that tells you how much space a body has covered when moving. Displacement is a vector quantity that tells you how far from its initial position and object is after moving.
In this case, the child goes around the track only halfway from point 1 to point 2. We know the circunference or perimeter of a circle to be 2*PI*radius. We also know the child only when halfway, so we need to divide the perimeter by 2, thus we get distance = PI*radius
- distance halfway = (PI)*(5.25) = 16.49 [m]
And now that we know the definition of displacement, we can easily see that the child went from point 1 to point 2 which is located at a distance of 1 diameter from point 1:
- displacement halfway = D = 2*radius = 2(5.25) = 10.5 [m]
b)What happens to the distance when the child completes one circuit? The distance will increase beause he is now completing the circuit so he is covering more ground in his movement:
- distance circuit = 2*(PI)*radius = 2(PI)(5.25) = 32.99 [m]
32.99 is more than 16.49 so we are certain that the distance increases.