The box plot shows the number of new vocabulary wores students learned last week. What

If the ratio of the length of segment AC to the length of segment CB is 3:1, what is the y-coordinate of point C?

Yuki888 [10]

Answer:

The coordinates of point C are (8,8.5)

Step-by-step explanation:

The picture of the question in the attached figure

Let

$(C_x,C_y)$ ----> coordinates of point C

we have that

The horizontal distance AB is equal to

$AB_x=10-2=8\ units$

The vertical distance AB is equal to

$AB_y=10-4=6\ units$

Find the horizontal coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

so

$\frac{AC_x}{CB_x}=\frac{3}{1}$

$AC_x=3CB_x$ ----> equation A

$AC_x+CB_x=8$ ----> equation B

substitute equation A in equation B

$3CB_x+CB_x=8$

$4CB_x=8\\CB_x=2$

$AC_x=3(2)=6$

so

The x-coordinate of point C is equal to the x-coordinate of point A plus the horizontal distance between the point A and point C

$C_x=A_x+AC_x=2+6=8$

Find the vertical coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

so

$\frac{AC_y}{CB_y}=\frac{3}{1}$

$AC_y=3CB_y$ ----> equation A

$AC_y+CB_y=6$ ----> equation B

substitute equation A in equation B

$3CB_y+CB_y=6$

$4CB_y=6\\CB_y=1.5$

$AC_y=3(1.5)=4.5$

so

The y-coordinate of point C is equal to the y-coordinate of point A plus the vertical distance between the point A and point C

$C_y=A_y+AC_y=4+4.5=8.5$

therefore

The coordinates of point C are (8,8.5)

5 0

3 years ago

A recipe calls for 2 cups of milk every 6 1/4 Of flour. If you increase the flour to 43 3/4, how many cups of milk will you use?

Elza [17]

Answer:

14 Cups

Step-by-step explanation:

43 3/4 = 43.75

6 1/4 = 6.25

43.75 % 6.25 = 7 x 2 = 14

6 0

3 years ago

Read 2 more answers

Deshawn has two bags of marbles. The first bag has 2 blue, 3 orange, and 5 red. The second bag has 4 pink, 10 blue, and 6 brown.

madreJ [45]

Answer: 0.1

Step-by-step explanation:

Given

Bag-I has 2 blue,3 orange, 5 red

Bag-II has 4 Pink,10 blue, 6 brown

No of ways of choosing a blue marble from bag-I

$\Rightarrow ^2C_1$

Total no of ways of choosing a marble from bag-I

$\Rightarrow ^{10}C_1$

No of ways of choosing a blue marble from bag-II

$\Rightarrow ^{10}C_1$

Total no of ways of choosing a marble from bag-II

$\Rightarrow ^{20}C_1$

The probability that he will pull out a blue marble from each bag is

$\Rightarrow P=\text{Probability of pulling a blue marble from bag-I}\times \text{Probability of pulling a blue out bag-II}$

$\Rightarrow P=\dfrac{^2C_1}{^{10}C_1}\times \dfrac{^{10}C_1}{^{20}C_1}\\\\\Rightarrow P=\dfrac{2}{10}\times \dfrac{10}{20}=\dfrac{1}{10}$

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Csqrt%7B111%7D%5C%3A%5Ctimes%20%5Csqrt%7B111" id="TexFormula1" title="\sqrt{111}\:\times \sq

Natali5045456 [20]

Answer:

742.5625

Step-by-step explanation:

Square root of 111 is 27.75 so mulitply both and get 742.5625

8 0

3 years ago

Read 2 more answers

A researcher measures daily driving distance from college and weekly cost of gas for a group of commuting college students. What

juin [17]

Answer:

There is a positive correlation between these two variables.

Step-by-step explanation:

Positive correlation is an association amid two variables in which both variables change in the same direction.

A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

As the distance covered by the vehicle increases the amount of gas consumed also increases. Thus, the weekly cost of gas will also increase.

Thus, there is a positive correlation between these two variables.

6 0

4 years ago