What is the strongest relationship you can infer between two variables from this statement?

Point T is the centroid. Find TE if XE =21

KIM [24]

Answer:

7

Step-by-step explanation:

Thing about centroids is they create segments that are spilt with one piece $\frac{1}{3}$ and the larger piece $\frac{2}{3}$ .

So, if the whole segment is 21, then the large piece is $\frac{2}{3}$ of 21. The small piece is $\frac{1}{3}$ of 21.

TE = 21 · $\frac{1}{3}$ = $\frac{21}{3}$ = 7

8 0

3 years ago

Read 2 more answers

James believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request.

ivolga24 [154]

If the system is fair, one would expect that the same proportion of students received their requested math class, independent of whether they are on the honor roll or not. We have that from the 356 students on the honor roll, 315 received their requested class. This percentage is around 88.5%, hence 88,5% of honor students get the class they requested. Of the 144 students not on the honor roll, 64 get their requested class. The ratio is 64/144=44.4%. We see that the percentage is a lot smaller, almost half of the percentage for the honor students. Hence, we have that there is actually injustice since if you are an honor student you have almost double the chance to get your preferred class.

7 0

4 years ago

Mari has 3 friends who are available to go with her to the movies, but she only has 2 extra tickets. How many different choices

aliina [53]

Answer:

3 different choices

Step-by-step explanation:

This problem is a combination problem: She has 3 friends, and we want to know how many groups of 2 friends there are. We can solve this using the combination of 3 choose 2:

C(3,2) = 3!(1! * 2!) = 3*2/2 = 3 possibilities

If we call her three friends A, B and C, the groups that can be formed are:

A and B

A and C

B and C

6 0

3 years ago

Which of the following statements have the same result? Explain each step in solving each one.

STALIN [3.7K]

$f(x) = 5x + 1\\\\subtitute\ x = 1\ to\ the\ equation\\\\f(1) = 5\cdot1 + 1 = 5 + 1 = 6\\----------------------\\f(x)=\dfrac{2x+3}{5}\to y=\dfrac{2x+3}{5}\ \ \ \ |multiply\ both\ sides\ by\ 5\\\\5y=2x+3\ \ \ \ |subtract\ 3\ from\ both\ sides\\\\2x=5y-3\ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\x=\dfrac{5y-3}{2}\\\\f^{-1}(x)=\dfrac{5\cdot(-1)-3}{2}=\dfrac{-5-3}{2}=\dfrac{-8}{2}=-4\\---------------------\\3y-7=y+5\ \ \ |add\ 7\ to\ both\ sides\\3y=y+12\ \ \ \ |subtract\ y\ from\ both\ sides\\2y=12\ \ \ \ |divide\ both\ sides\ by\ 2\\y=6$

Answer: f(1) when f(x) = 5x + 1 and 3y - 7 = y + 5

6 0

3 years ago

100 POIntsSarah has been running a dog-walking business since 2010. She walks dogs twice a day, takes them to the park, and retu

Svetach [21]

----------------------------------------------------------------------------------------------------------

Problem (a): $\textsf{Rate of change = \$100 per year, Initial value = \$350}$

Problem (b): $\textsf{y = 100x + 350}$

----------------------------------------------------------------------------------------------------------

The first step that we must take before attempting to solve the problem is to understand what the problem is asking us to do and what is given to us to help do so. So in the first part we are asked what the rate of change and initial value for Sarah's business. Using that information we would be able to complete the second part which asks us to write an equation in slope-intercept form. In this problem we are given two points which resemble how much Sarah charged each customer for the given years.

Now that we know what we must accomplish, we can move onto actually solving the problem. So first we must determine what the rate of change is and this is basically like finding the slope. This can be done by subtraction the y-values in the numerator and the x-values in the denominator.

<u>Determine the rate of change</u>

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{750 - 350}{2014 - 2010}$

$m = \frac{400}{4}$

$m = 100$

Now we can see that the rate of change would be an increase of $100 per year after calculating the slope. The next part was to determine the initial value for Sarah's business and this can be easily done because we know that she has had this business since 2010 and we are given that the price in 2010 was $350.

----------------------------------------------------------------------------------------------------------

We now have completed part (a) and we can move onto the next part which is to create an equation in slope-intercept form to represent the fees that Sarah charges each year.

So we know that the slope is an increase of $100 per year which means that we will have a positive slope. We also know the initial price that Sarah charged in her first year which will represent the y-intercept or the first point on the graph.

m ⇒ This represents the slope of the line that is being written.

b ⇒ This represents the y-intercept of the line that is being written.

<u>Plug in the values</u>

$y = mx + b$

$y = 100x + 350$

After plugging in the values we have a finished expression in slope-intercept form which represents the scenario that is going on with Sarah's business. We see that that initial price was 350 and we increase that by 100 each year. Therefore, the final equation in slope-intercept form is y = 100x + 350.

----------------------------------------------------------------------------------------------------------

7 0

2 years ago