Ask question

Ask question

All categories

3 years ago

5

Kayla used 4/14 of her allowance to buy yogurt and 8/14 of her allowance to go skating. What fraction of her allowance does she

have left? Explain your thinking.

1 answer:

Monica [59]3 years ago

7 0

4/14+8/14=12/14, so she has 2/14 left

You might be interested in

PLEASE HELP !!!!!<br>Solve.<br>y +30 < 15<br><br>

Troyanec [42]

Hello there! y < -15

To solve, isolate y. To do this, subtract 30 from both sides of the equation.

y + 30-30 < 15-30

y < -15

This is your final answer. The statement is saying that y must be less than -15 when you add 30 to it for your final answer to be less than 15.

I hope this was helpful and have a great rest of your day! :)

5 0

3 years ago

Read 2 more answers

Consider the three points ( 1 , 3 ) , ( 2 , 3 ) and ( 3 , 6 ) . Let ¯ x be the average x-coordinate of these points, and let ¯ y

loris [4]

Answer:

$m=\dfrac{3}{2}$

Step-by-step explanation:

Given points are: ( 1 , 3 ) , ( 2 , 3 ) and ( 3 , 6 )

The average of x-coordinate will be:

$\overline{x} = \dfrac{x_1+x_2+x_3}{\text{number of points}}$

<u>1) Finding $(\overline{x},\overline{y})$ </u>

Average of the x coordinates:

$\overline{x} = \dfrac{1+2+3}{3}$

$\overline{x} = 2$

Average of the y coordinates:

similarly for y

$\overline{y} = \dfrac{3+3+6}{3}$

$\overline{y} = 4$

<u>2) Finding the line through $(\overline{x},\overline{y})$ with slope m.</u>

Given a point and a slope, the equation of a line can be found using:

$(y-y_1)=m(x-x_1)$

in our case this will be

$(y-\overline{y})=m(x-\overline{x})$

$(y-4)=m(x-2)$

$y=mx-2m+4$

this is our equation of the line!

<u>3) Find the squared vertical distances between this line and the three points.</u>

So what we up till now is a line, and three points. We need to find how much further away (only in the y direction) each point is from the line.

Distance from point (1,3)

We know that when x=1, y=3 for the point. But we need to find what does y equal when x=1 for the line?

we'll go back to our equation of the line and use x=1.

$y=m(1)-2m+4$

$y=-m+4$

now we know the two points at x=1: (1,3) and (1,-m+4)

to find the vertical distance we'll subtract the y-coordinates of each point.

$d_1=3-(-m+4)$

$d_1=m-1$

finally, as asked, we'll square the distance

$(d_1)^2=(m-1)^2$

Distance from point (2,3)

we'll do the same as above here:

$y=m(2)-2m+4$

$y=4$

vertical distance between the two points: (2,3) and (2,4)

$d_2=3-4$

$d_2=-1$

squaring:

$(d_2)^2=1$

Distance from point (3,6)

$y=m(3)-2m+4$

$y=m+4$

vertical distance between the two points: (3,6) and (3,m+4)

$d_3=6-(m+4)$

$d_3=2-m$

squaring:

$(d_3)^2=(2-m)^2$

3) Add up all the squared distances, we'll call this value R.

$R=(d_1)^2+(d_2)^2+(d_3)^2$

$R=(m-1)^2+4+(2-m)^2$

<u>4) Find the value of m that makes R minimum.</u>

Looking at the equation above, we can tell that R is a function of m:

$R(m)=(m-1)^2+4+(2-m)^2$

you can simplify this if you want to. What we're most concerned with is to find the minimum value of R at some value of m. To do that we'll need to derivate R with respect to m. (this is similar to finding the stationary point of a curve)

$\dfrac{d}{dm}\left(R(m)\right)=\dfrac{d}{dm}\left((m-1)^2+4+(2-m)^2\right)$

$\dfrac{dR}{dm}=2(m-1)+0+2(2-m)(-1)$

now to find the minimum value we'll just use a condition that $\dfrac{dR}{dm}=0$

$0=2(m-1)+2(2-m)(-1)$

now solve for m:

$0=2m-2-4+2m$

$m=\dfrac{3}{2}$

This is the value of m for which the sum of the squared vertical distances from the points and the line is small as possible!

5 0

3 years ago

Eduardwww [97]

Answer:

personal loan acquire generally more risk since it is unknown on what the money may be used on and so banks have limited knowledge on whether they can get played back. However mortgages are used to buy assets, and banks go through credit scores and personal income which is why they can loan a much bigger amount.

3 0

3 years ago

Read 2 more answers

For Carolina's birthday, her mom took her and 4 friends to a water park. Carolina's mom paid $40 for 5 student tickets. What was

Law Incorporation [45]

Answer:

The price for one student ticket is $8

5 0

3 years ago

Make a down payment of $1500 and finance the rest of $20000 at 1.9% interest rate, making equal monthly payments for 5 years.

Rudik [331]

We know that we have to m<span>ake a down payment of $1500 and finance the rest of $20000 at a 1.9% interest rate, making equal monthly payments for 5 years. Our first step to solve this problem would be to convert 5 years into months.

1 year = 12 months

12 * 5 = 60 months

Therefore, in 5 years there are 60 months.

Now lets solve this problem step by step.

Subtract the down payment from $20,000

</span>$20000-$1500=$18500

Multiply the remaining number by the interest rate.

$18500 *1.9 = $35150

Divide 35150 by number of months in 5 years (60)

$35150 / 60 = $585

<span>Therefore, you have to pay $585 per month. </span>

7 0

3 years ago