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Xelga [282]
4 years ago
5

Two dice are rolled, and the sum of the face values is six. What is the probability that at least one of the dice came up a thre

e
Mathematics
1 answer:
gizmo_the_mogwai [7]4 years ago
8 0

Answer : P(\text{ atleast one of the dice come up 3})= \frac{1}{5}

Explanation :

We know that ,

Sample space of " sum of faces is 6"= \{(3,3),(4,2),(2,4),(5,1),(1,5)\}

Atleast one of the dice come up 3 = \{(3,3)\}

So,

Probability = \frac{\text{No. of favourable outcomes}}{\text{Total no. of outcomes}}

P(\text{ atleast one of the dice come up 3})= \frac{1}{5}

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Luke is 5 years younger than 3 times Sydney’s age, s. In this situation, what does 3s represent?
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Answer:

3 multiplied by sydneys age

Step-by-step explanation:

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3 years ago
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find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu
topjm [15]

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}

Now, differentiate P with respect to x, and we get,

\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}

Solving the above equation to zero, we get,

\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

\begin{aligned}y&=108-36\\y&=72\end{aligned}

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

brainly.com/question/1635103

#SPJ4

4 0
1 year ago
0.31 repeating as a fraction
sukhopar [10]
I believe its 31/100! <span>To write 0.3111 as a fraction you have to write 0.3111 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.</span>

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3 years ago
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Six and forty-two ten-thousandths as a decimal
sergey [27]

Answer:

6.0042

Step-by-step explanation:

6 and forty-two ten-thousandths as a decimal.

mixed number : 6\frac{42}{10,000}

decimal : 6.0042

7 0
3 years ago
“Determine whether 3x+12+x is equivalent to 4(3+x). Use properties of operations to justify your answer” PLEASE HELP
Firdavs [7]

Answer:

It’s equivalent.

Step-by-step explanation:

Collect like terms: 4x+12 = 4(3+x)

Expand brackets: 4x+12 = 12+4x

Rearrange: 4x+12 = 4x+12

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3 years ago
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