Solve the area of a trapezoid formula for the variable h: A = 1/2h(b1 + b2)

If i have three rolls of a dice and for the first and second you choose to either keep your roll or keep going, what is the best

AleksAgata [21]

Answer:

On the first roll, we keep a result of 5 or 6, and roll again if it is 4 or lower
On the second roll, we keep any result equal or greater that 4 and we roll again for 1,2 or 3
We keep anything we obtained from the third row

The expected value is 14/3 = 4.666

Step-by-step explanation:

When you throw a roll the expected value is 3.5 (the average of 1,2,3,4,5 and 6). This means that any roll with value 3 or below is worth changing, because the expected value will transform into 3.5 from the 3 or less you had before.

This means that in your second roll you will keep the result as long as it is 4 or more and you will roll once more if it is 3 or less, hence, you can

get a 4, 5 and 6 on your second roll and keep it, so that your value is that number
get 1, 2 or 3 on your second roll and roll again, with an expected value of 3.5.

Rolling a third time has a probability of 3/6 = 0.5, obtaining a 4 has a probability of 1/6, same for 5 and 6. Thus, the expected value from the second roll onwards is

1/2 * 3.5 + 1/6 * 4 + 1/6 * 5 + 1/6 * 6 = 4.25

This means that, after the first roll, we can keep that value or throw again with an expected value of 4.25 (using the strategy depicted above). We can roll again if we got a result of 4 or below expecting a higher value or keep a result of 5 or 6.

The strategy can be ssummarized as follows

On the first roll, we keep a result of 5 or 6, and roll again if it is 4 or lower
On the second roll, we keep any result equal or greater that 4 and we roll again for 1,2 or 3
We keep anything we obtained from the third row

The probability of getting 4 or below is 4/6 = 2/3, and the expected value for the second roll onwards is 4.25, hence the expected value of the strategy we pick is

1/6 * 5 + 1/6*6 + 2/3* 4.25 = 4.666 = 14/3

8 0

3 years ago

What is the greatest common factor of 4k, 18k4, and 12? 2 4 2k 4k

photoshop1234 [79]

Answer:

Greatest Common Factor is $2$

Step-by-step explanation:

Greatest Common Factor is the highest factor that will divide all the numbers. To find the Greatest common factor, first we need to find out the numbers that all the values have in common.

Factors of 4k=1, 2, 4 and k

Factors of 18k=1, 2 , 3, 6, 9, 18 and k

Factors of 12=1, 2, 3, 4, 6 and 12

Common factors are = 1 and 2.

Therefore,

Greatest Common Factor = $1\times2$

= $2$

8 0

3 years ago

Read 2 more answers

5x – (13 – x) >_9x – 7

ad-work [718]

Answer:

x<_2

Step-by-step explanation:

first off solve this like a regular equation the >_ dosent matter till later

so basically first multiply - by 13 and -x so you get -13 and x (multiplying two negatives = a positive)

so its 5x-13+x>_9x-7

add 5x and x to get 6x-13 on one side

then you get 6x-13>_9x-7 then subtract -9x from both sides

so its now -3x-13>_-7 add 13 so you get -3x>_6

then divide both sides by -3 (when you divide an equation with a >< or <_ >_ by a negative number that sign switches) so it will now be x<_2

that your final answer hope this helps :)

6 0

3 years ago

-x+ 2y = 10<br> -3x+By = 11

adoni [48]

Answer:

change the equation into one variable.

2 y equals 10 + x

y equals 5 + x by 2

now put that into the second equation

-3x + b parentheses 5 + x / 2 equals 11

-3x+b(5+ x/2)

-3x + b5 + bx/2 = 11

8 0

3 years ago

Read 2 more answers

Rectangle ABCD is similar to rectangle RSTU .

Alenkasestr [34]

Answer:

The scale factor of a dilation from ABCD to RSTU is $\frac{1}{2}$

Step-by-step explanation:

We know that the rectangle ABCD is similar to rectangle RSTU.

Given that in rectangle ABCD the longest sides are DC and AB and in the rectangle RSTU the longest sides are UT and RS ⇒ The scale factor of a dilation will transform the sides DC and AB into UT and RS

Working with the lengths of the sides :

DC.(Scale factor) = UT

AB.(Scale factor) = RS

Replacing with the values of the lengths (Scale factor : SF) :

$DC.SF=UT\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}$