A tram travels at 10 km/hr for 2 hours and then at 13 km/hr for 1 hour. Find its average speed

The last time Sierra played softball, she hit the ball 45% of the times she was at bat. Based on this information, how many time

Ymorist [56]

Answer:

Number of times she will hit the ball the next time she plays softball if she is at bat 20 times = 9 times

Step-by-step explanation:

Percentage of times Sierra hit the ball when she was at bat playing softball= 45%

So, we can find:

Number of times she will hit the ball the next time she plays softball if she is at bat 20 times = $\textrm{45\% of 20 times} =0.45\times 20=9\ times$

3 0

3 years ago

The value of

marusya05 [52]

$\large\underline{\sf{Solution-}}$

We have to find out the value of the fraction.

Let us assume that:

$\sf \longmapsto x =2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ... \infty} } }$

We can also write it as:

$\sf \longmapsto x =2 + \dfrac{1}{x}$

$\sf \longmapsto x =\dfrac{2x + 1}{x}$

$\sf \longmapsto {x}^{2} =2x + 1$

$\sf \longmapsto {x}^{2} - 2x - 1 = 0$

Comparing the given equation with ax² + bx + c = 0, we get:

$\sf \longmapsto\begin{cases} \sf a =1 \\ \sf b = - 2 \\ \sf c = - 1 \end{cases}$

By quadratic formula:

$\sf \longmapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1}$

$\sf \longmapsto x = \dfrac{2 \pm \sqrt{8} }{2}$

$\sf \longmapsto x = \dfrac{2 \pm2 \sqrt{2} }{2}$

$\sf \longmapsto x = 1 \pm\sqrt{2}$

$\sf \longmapsto x = \begin{cases} \sf 1 + \sqrt{2} \\ \sf 1 - \sqrt{2} \end{cases}$

But "x" cannot be negative. Therefore:

$\sf :\implies x = 1 + \sqrt{2}$

So, the value of the fraction is 1 + √2.

4 0

2 years ago

If x is a positive integer then the solution set of 4x+2<14 is

taurus [48]

4x + 2 < 14
4x < 14 - 2
4x < 12
x < 12/4
x < 3 S = { x <3 }

3 0

3 years ago

The set of the consecutive odd numbers 1, 3, 5, 7, ... , N has a sum of 400. How many numbers are in the set?

Amanda [17]

Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.

First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.

Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:

 1, 3, 5, 7, 9, 11, 13, 15 .

Number of items in the set . . . 8
Sum of all the items in the set . . . 64

Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?

Let's check it out:

Even-numbered lists of odd numbers:

1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .

Amazing ! The sum is always the square of the number of items in the set !

For a sum of 400 ... which just happens to be the square of 20,
we just need the first 20 consecutive odd numbers.

I slogged through it on my calculator, and it's true.

I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).

3 0

3 years ago

Express the number 20000 as a single digit integer times a power of 10

PolarNik [594]

The answer is 2 x 10^4 or 2 to the power of 4 (4th power) where;
2 x 10 x 10 x 10 x 10
2 x 10 =20
20 x 10= 200
200 x 10 = 2000
2000 x 10 = 20 000

Expressing a number to a single digit integer times a power of 10 is also writing a number in scientific form,where the number is multiplied by 10 to nth "power". Scientific notation is also called standard index form whereby, too large or too big numbers.
In writing the scientific notation of a number it follows this form: m x 10^n ( m is multiplied to 10 to the power of n) where, m, the coefficient, is the real number and n is the exponent integer.

3 0

3 years ago