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2 years ago

10

Assign a probability to the following event, and give the method used to assign it: What is the probability that a randomly sele

cted day of the week will be a Friday

1 answer:

ycow [4]2 years ago

7 0

Answer:

$\frac{1}{7}$

Step-by-step explanation:

We know, that probability of an event E, is $\textrm{P}(\textrm{E})=\frac{\textrm{Number of favorable outcomes}}{\textrm{Total number of outcomes}}$ .

Here, there are $7$ days in a week.

So, total number of outcomes $=7$ .

And only one day, that is, Friday is selected.

So, number of favorable outcomes $=1$ .

Therefore, probability $=\frac{1}{7}$ .

Hence, the probability that a randomly selected day of the week will be a Friday $=\frac{1}{7}$ .

You might be interested in

Some of the children at a school arrive by car.

scZoUnD [109]

Answer:

<u>74%</u>

Explanation:

You can build a two-way relative frequency table to represent the data:

These are the columns and rows:

Car No car Total

Boys

Girl

Total

Fill the table

<em>30% of the children at the school are boys</em>

Car No car Total

Boys 30%

Girl

Total

<em>60% of the boys at the school arrive by car</em>

That is 60% of 30% = 0.6 × 30% = 18%

Car No car Total

Boys 18% 30%

Girls

Total

By difference you can fill the cell of Boy and No car: 30% - 18% = 12%

Car No car Total

Boy 18% 12% 30%

Girl

Total

Also, you know that the grand total is 100%

Car No car Total

Boy 18% 12% 30%

Girl

Total 100%

By difference you fill the total of Girls: 100% - 30% = 70%

Car No car Total

Boy 18% 12% 30%

Girl 70%

Total 100%

<em>80% of the girls at the school arrive by car</em>

That is 80% of 70% = 0.8 × 70% = 56%

Car No car Total

Boy 18% 12% 30%

Girl 56% 70%

Total 100%

Now you can finish filling in the whole table calculating the differences:

Car No car Total

Boy 18% 12% 30%

Girl 56% 14% 70%

Total 74% 26% 100%

Having the table completed you can find any relevant probability.

The probability that a child chosen at random from the school arrives by car is the total of the column Car: 74%.

That is because that column represents the percent of boys and girls that that arrive by car: 18% of the boys, 56% of the girls, and 74% of all the the children.

8 0

3 years ago

2x^3-x^2-3x=210<br> the answer is 5 but I want to know why.

mel-nik [20]

Answer:

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

Step-by-step explanation:

1) Move all terms to one side.

$2x^{3} -x^{2} -3x-210=0$

2) Factor $2{x}^{3}-{x}^{2}-3x-210$ using Polynomial Division.

1 - Factor the following.

$2x^{3} -x^{2} -3x-210$

2 - First, find all factors of the constant term 210.

$1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210$

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

$2*1^{3} -1^{2} -3*1-210=-212$

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

$2(-1)^{3} -(-1)^{2} -3*-1-210=-210$

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

$2*2^{3} -2^{2} -3*2-210=-204$

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

$2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224$

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

$2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174$

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

$2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264$

Substitute 5 into x. Since the result is 0, x-5 is a factor..

$2\times {5}^{3}-{5}^{2}-3\times 5-210 =0$

------------------------------------------------------------------------------------------

⇒ $x-5$

4) Polynomial Division: Divide $2{x}^{3}-{x}^{2}-3x-210$ by $x-5$ .

$2x^{2}$ $9x$ $42$

-------------------------------------------------------------------------

$x-5$ | $2x^{3}$ $-x^{2}$ $-3x$ $-210$

$2x^{3}$ $-10x^{2}$

-----------------------------------------------------------------------

$9x^{2}$ $-3x$ $-210$

--------------------------------------------------------------------------

$42x$ $-210$

$42x$ $-210$

-------------------------------------------------------------------------

5) Rewrite the expression using the above.

$2x^2+9x+42$

$(2x^2+9x+42)(x-5)=0$

3) Solve for $x.$

$x=5$

4) Use the Quadratic Formula.

1 - In general, given $a{x}^{2}+bx+c=0$ , there exists two solutions where:

$x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}$

2 - In this case, $a=2,b=9$ and $c = 42.$

$x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}$

3 - Simplify.

$x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

5) Collect all solutions from the previous steps.

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

4 0

2 years ago

Read 2 more answers

Help anyone ??? Please

lana [24]

Angle F is equal to angle G so 5x + 18 = 7x-12 so you would solve for x which would equal 15

7 0

3 years ago

Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the g

kati45 [8]

Answer:

Option: D is correct.

Step-by-step explanation:

since we are given a inequality as:

$y$

Clearly from the graph of the following inequality we could see that the origin is included in the shaded region and the shaded area is below the line.

Also it could be seen that if we put the origin points i.e. (0,0) in the inequality than 0<2 and the condition is true and hence origin is included in the shaded area.

Hence, option D is true.

6 0

3 years ago

1/4d=1/5g(g+e)-h <br> solve for d<br> Please show your work.

loris [4]

Answer:

See below

Step-by-step explanation:

To solve for d, multiply both sides of the equal sign by 4.

4(1/4d) = 4 (1/5g(g+e)-h)

4/4d = 4(1/5 $g^{2}$ + 1/5ge - h)

d = 4/5 $g^{2}$ + 4/5ge - 4h

5 0

3 years ago