hectictar

Using the equation  1 GB  =  1000 MB ,  we get.....

1 GB  =  1000 MB

                                     Multiply both sides of the equation by  6.8

6.8 GB  =  6800 MB

How many  1.43  MB  fit into  6800 MB  ?

6800 MB / 1.43 MB  ≈  4755.245

He won't be able to fit  4756  books on the tablet.

He can fit  4755  books on the tablet at most.

"Joost still has 6.8 memory on his tablet"

6.8 what? 6.8 GB? 6.8 MB?

Is  00001  a  "5-digit number" ?

Is  1  a  "5-digit number" ?

If we're meant to include the numbers 0-9999 in the list of "5-digit numbers" then the question may have said

"How many nonnegative numbers less than 100000 are there which are multiples of 5 and. . ."

3)

2)
\(f(x) = \left\{ \begin{array}{cl} -2x & \text{if } x < 0, \\ \frac{x}{2} & \text{if } x \ge 0. \end{array} \right.\)

Let  y  =  f(x)  so we can say that...

The range includes the smallest possible y value to the biggest possible y value.
 

A graph might help:

The smallest possible y value is  0

There isn't a biggest possible y value because we can always find a bigger one, so we say it's  ∞

So the range is  [0, ∞)

1)

\(f(x) = \left\{ \begin{array}{cl} 3x & \text{if } x < 3, \\ 3^x & \text{if } x \ge 3. \end{array} \right.\)

Let's find  f(2)

2  <  3     so  we use   f(x)  =  3x

f(2)  =  3(2)

f(2)  =  6

Let's find  f(3)

3  ≥  3     so we use   f(x)  =  3^x

f(3)  =  3³

f(3)  =  27

Let's find  f(4)

4  ≥  3  so we use   f(x)  =  3^x

f(4)  =  . . .?  Can you figure this one out?

\(\frac{x}{3}+\frac{4}{5} < \frac{5}{3}\)

                                      Subtract  \(\frac45\)  from both sides of the inequality.

\(\frac{x}{3}+\frac{4}{5}{\color{blue}-\frac45} < \frac{5}{3}{\color{blue}-\frac45}\)

\(\frac{x}{3} < \frac{5}{3}-\frac45\)

                                      Get a common denominator on the right side.

\(\frac{x}{3} < \frac{5}{3}\cdot\frac55-\frac45\cdot\frac33\)

\(\frac{x}{3} < \frac{25}{15}-\frac{12}{15}\)

                                      Combine the fractions on the right side.

\(\frac{x}{3} < \frac{13}{15}\)

                                      Multiply both sides by  3 , a positive number.

\(\frac{x}{3}{\color{blue}\cdot3} < \frac{13}{15}{\color{blue}\cdot3}\)

\(x < \frac{39}{15}\)

                                      And  \(\frac{39}{15}\)  =  2.6

\(x <2.6\)

What is the largest integer  x  such that  x < 2.6   ?

What is the largest integer less than  2.6 ?

The largest integer less than  2.6  is  2 , so

x  =  2

I think you’re pretty much on the right track

Assuming:   \(x^2 + y^2 - 6x + py + q = 0\)

\(x^2 + y^2 - 6x + py + q = 0\)
                                                    Subtract  q  from both sides of the equation
\(x^2 + y^2 - 6x + py = -q\)
                                                    Rearrange the terms on the left side of the equation.
\(x^2 - 6x + y^2 + py = -q\)
                                                                                          Add  9  and add  \((\frac{p}{2})^2\)  to both sides of the equation.

\(x^2 - 6x + 9 + y^2 + py + (\frac{p}{2})^2 = -q + 9 + (\frac{p}{2})^2\)
                                                                                           Factor both perfect square trinomials on the left side.
\((x - 3)^2 + (y + \frac{p}{2})^2 = -q + 9 + (\frac{p}{2})^2\)

Now we can see that the center of the circle is the point  (3, -\(\frac{p}{2}\))

Because the circle is tangent to the y-axis,

radius  =  distance between center and y-axis

radius  =  distance between  (3, -\(\frac{p}{2}\))  and  (0, -\(\frac{p}{2}\))

radius  =  3

area  =  π · radius²

area  =  π · 3²

area  =  9π     sq. units

You can play around with the sliders on this graph to check:

Here's the list of possible outcomes from CPhill's answer:

1,1      2,1      3,1      4,1      5,1

1,2      2,2      3,2      4,2      5,2

1,3      2,3      3,3      4,3      5,3

1,4      2,4      3,4      4,4      5,4

1,5      2,5      3,5      4,5      5,5

num of outcomes where no 3 is spun  =  16      so      probability that num spins showing 3 is 0  =  16 / 25  =  0.64

num of outcomes where one 3 is spun  =  8      so      probability that num spins showing 3 is 1  =  8 / 25  =  0.32

num of outcomes where two 3's are spun  =  1      so      probability that num spins showing 3 is 2  =  1 / 25  =  0.04

Do you see where the 16, 8, and 1 come from?

3)

A spinner is divided into four equal sections that are numbered 2, 4, 7, and 9. The spinner is spun twice.

How many outcomes have a product less than 30 and contain at least one odd number?

Here's the "dumb" way to do it, haha

List of all possible outcomes:

2, 2

2, 4

2, 7

2, 9

4, 2

4, 4

4, 7

4, 9

7, 2

7, 4

7, 7

7, 9

9, 2

9, 4

9, 7

9, 9

The ones that have a product less than 30 and contain at least 1 odd number are colored blue.

You got it right