What is the following quotient? 2- sqrt 8 / 4 + sqrt 12

Answers

Answer 1
C is the answer.

We multiply the top and bottom of this by the conjugate (switch the sign of the square root):

(2-sqrt8)(4-sqrt12)/(4+sqrt12)(4-sqrt12)

Multiying the top we have
8-2sqrt12-4sqrt8+sqrt(8×12)

Multiplying the bottom we have:
16-4sqrt12+4sqrt12-12

On top, we simplify the radicals and get
8-4sqrt3-8sqrt2+4sqrt6

On bottom, we have
16-12=4

Now we divide everything on top by 4 and get
2-sqrt3-2sqrt2+sqrt6
Answer 2

we have

[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}[/tex]

Multiply the numerator and denominator by the conjugate of the denominator

so

[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}*\frac{4-\sqrt{12}}{4-\sqrt{12}}=\frac{(2-\sqrt{8})(4-\sqrt{12)}}{4^{2}-(\sqrt{12})^{2}}\\ \\= \frac{2*4-2*\sqrt{12}-4*\sqrt{8}+\sqrt{12}*\sqrt{8}}{16-12}\\ \\=\frac{8-4\sqrt{3}-8\sqrt{2}+4\sqrt{6}}{4} \\ \\=2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]

therefore

the answer is

[tex]2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]


Related Questions

What is the relative minimum of the function?

Answers

minimum is the bottom of the U shape
(1,-5)

relative min = -5 

Answer:

The required relative minimum is -5

Step-by-step explanation:

Relative minimum is the point where the graph shows its minimum point or the lowest point of the graph.

Like here, we have been given a parabolic shape so, the minimum of this parabola is the coordinate of y in its vertex point.

So, its relative minimum is -5.

Derive the equation of the parabola with a focus at (0, –4) and a directrix of y = 4. (2 points)

A f(x) = –16x2
B f(x) = – x2
C f(x) = x2
D f(x) = 16x2

Answers

Equation of parabola with focus at (0,-4) and directrix is y=4 .

As we know parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.

The parabola is opening downwards.

Let any point on parabola is (x,y).

Distance from focus(0,-4) to (x,y) = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]

Distance from (x,y) to directrix, y=4 is =[tex]\left | y-4 \right |[/tex]

As these distances are equal.

[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |\\{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]

→x²+y²+8 y +16 = y² - 8 y+16

→ x² = -8 y - 8 y= -16 y   [ Cancelling y² and 16 from L.H.S and R.H.S ]

So , equation of parabola is , x²= - 16 y or f(x)= -x²/16


The Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]

Equation of parabola with focus at [tex](0,-4)[/tex] and directrix is [tex]y=4[/tex] .

Parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.

The parabola is opening downwards.

Let any point on parabola is [tex](x,y)[/tex].

Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^2+(y+4)^2[/tex]

[tex]d=\sqrt{x^2+(y+4)^2[/tex]

Distance from [tex](x,y)[/tex] to directrix, [tex]y=4[/tex] is =[tex]\left | y-4 \right |[/tex]

As these distances are equal.

[tex]\sqrt{x^2+(y+4)^2}=\left | y-4 \right |[/tex]

[tex]d={x^2+(y+4)^2=(y-4)^2[/tex]

[tex]x^2+y^2+8y+16=y^2-8y+16[/tex]

[tex]x^2=-8y-8y[/tex]

[tex]x^2=-16y[/tex]

[tex]y=\dfrac{-x^2}{16}[/tex]

So, the Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]

Learn more about parabola here:

https://brainly.com/question/21685473?referrer=searchResults

Two f-18s are catapulted off an aircraft carrier and fly on courses that diverge at a 60° angle. if each flies at a constant rate of 500 mph, after how many hrs will the fighters be 1200 mi apart?

Answers

Answer: The will be 1200 miles apart after 2.4 hours.

First draw a picture of an angle of 60 degrees. The vertex is the starting point of the plane and they are flying away from it.

If you drew points for the new positions of the plane and connected them, you would have triangle. The planes are flying at the same speed, so they would be isosceles triangles. And since the vertex angle is 60 degrees, the other angles have to be 60 as well. This makes it an equilateral triangles, meaning all the sides are the same.

So the distance between the planes is equal to the distance that they have flow.

Simply divide 1200 by 500 to get 2.4 hours.



If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation. 3x + 2y = −21 x − 3y = 4

Answers

Hello,

[tex] \left \{ {{3x+2y=-21} \atop {x-3y=4}} \right. \\\\ \left \{ {{3x+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{3(4+3y)+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{12+9y+2y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{12+11y=-21} \atop {x=4+3y}} \right. \\\\ \left \{ {{11y=-21-12} \atop {x=4+3y}} \right. \\\\ \left \{ {{11y=-33} \atop {x=4+3y}} \right. \\\\ \left \{ {{y=-3} \atop {x=4+3(-3)}} \right. \\\\ \left \{ {{y=-3} \atop {x=5}} \right. \\\\ Sol=\{(5,-3)\}\\\\ [/tex]

Consider the two functions shown here. What is the rate of change of each function?


Function 2: y = ½ x + 7

Answers

The rate of change is the same as the slope.

Let's find the slope of function 1 using the Rise Over Run rule.
The rise is 2 and run is 1. So your rate of change is 2/1 or 2 for function 1

Function 2 is a y = mx + b equation, the slope is usually "m" or before the x
y = 1/2x + 7
1/2 is your rate of change for function 2

What is the value represented by the letter A on the box plot of data?

{5, 20, 40, 50, 50, 85}


Enter your answer in the box.

Answers

the answer would be 5
The value of A is 5

The lowest number is always the farthest to the left.



I hope this helps!

A bicycle shop rents bicycles for $3.50 per hour and helmets for $6 per day. Ashley has $20 to spend to rent a helmet and a bicycle for some number of hours. For how many hours can she rent the bicycle?

Answers

Because the helmet is rented per day, subtract I️t from the $20

20-6=14

And then divide the new total amount by 3.50

14 / 3.50 = 4

Ashley can rent the bike for 4 hours

will give brainlist

what is the approximate area of the figure

Answers

The radius of this circle is 4 centimeters, so the area of half of the circle will be 25.135, I'll call it 25.

The rectangle is 8 cm by 14 cm, so that has an area of 112.

Now, add 25 and 112. This will give you about 137.

Answer:

the answer is 137.1

Step-by-step explanation:

Divide the figure into recognizable shapes. Find the area of each shape and add them together.

10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE. DO BOTH PARTS OF 1 AND ALL OF 2.

Answers

One A
y = e^x
dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals.
One B
y = x*e^x
y' = e^x + xe^x Using the multiplication rule.
You want the slope and the value of the of y to be the same. The slope is y' of the tangent line
xe^x = e^x + xe^x
e^x = 0
This happens only when x is very "small" like x = - 4444444

y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y'
y1 = e^x
y1' = e^x
y2 = ln(x)
y2' = 1/x
y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line = 
y' = e^1*ln(1) + e^1/1
y' = e*0+e  = e
y = mx + b
y = ex + b
to find b we use y= e^x ln(x)

e^x ln(x) = e*x + b
e^1 ln(1) = e*1 + b
ln(1) = 0
0 = e + b
b = - e

line equation and answer.
y = e*x - e

Which answer describes the transformation of f (x) = x^2 −1 to g(x)=(x+2)^2−1 ?

a horizontal compression by a factor 2

a vertical stretch by a factor of 2

a horizontal translation 2 units to the left

a vertical translation 2 units down

Answers

Answer: A horizontal translation 2 units to the left

In this case, we are changing the variable x before it is being squared. This will have the effect of changing the input of the function. Imagine input 2 into the equation. Your first step would be to add 2. Therefore, you would need to start with a negative 2 to get us back to 0, or the beginning.

Since -2 is to the left of 0, the graph is moving 2 units to the left.

5. The two trapezoids are similar. Which is a correct proportion for corresponding sides?

A. BA FG
— = —
FE BC

B. BA CD
— = —
FE GD

C. BA AD
— = —
FE GD

D. BA AD
— = —
FE FG

Answers

I think it should be A
[tex] \frac{BA}{FE} [/tex]  = [tex] \frac{AD}{ED} [/tex] =  [tex] \frac{CD}{FD} [/tex] = [tex] \frac{BC}{FG} [/tex]  

Answer B

Help please! Math Nation Section 6 Test Yourself Practice Tool.

Answers

Answer: D)  [tex]y=-5(x-5)^2+1125[/tex]

Step-by-step explanation:

Let x be the number of $2 increases in price and y be the revenue.

By using the given table , lets check all the options

A) [tex]y=(x+5)^2-1125[/tex]

For x=1, y=1045

[tex]y=(1+5)^2-1125=36-1125=-1089\\\\But\ 1045\neq-1089[/tex]

B)  [tex]y=(x-5)^2+1125[/tex]

For x=1, y=1045

[tex]y=(1-5)^2+1125=14+1125=1139\\\But\ 1045\neq1139[/tex]

C)   [tex]y=-5(x+5)^2-1125[/tex]

[tex]y=-5(1+5)^2-1125=-5(36)-1125=-1305\\\\But\ 1045\neq-1305[/tex]

D) [tex]y=-5(x-5)^2+1125[/tex]

[tex]y=-5(1-5)^2+1125=-5(16)+1125=1045[/tex]

Hence, this is the quadratic equation that models the data.

Based on the table of values, an equation of the quadratic that models the data is: D. [tex]y = -5(x-5 ) ^2+ 1125[/tex]

In Mathematics and Euclidean Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:

[tex]y = a(x - h)^2 + k[/tex]

Where:

h and k represents the vertex of the graph.a represents the leading coefficient.

In order to determine an equation for the line of best fit or quadratic regression line that models the data points contained in the table of values, we would have to use a graphing calculator (Microsoft Excel).

Based on the scatter plot (see attachment) which models the relationship between the number of $2 increase in price (in dollars), x and revenue, y, the quadratic regression is given by:

[tex]y =-5x^2 + 50x + 1000\\\\y = -5(x^2 - 10x) + 1000\\\\y = -5(x^2 - 10x + (\frac{10}{2})^2 ) + 1000+ (\frac{10}{2})^2\\\\y = -5(x^2 - 10x + 25 ) + 1000+25\\\\y = -5(x-5 ) ^2+ 1125[/tex]

What is the value of X?
Sin64 degree= cos x
Enter your answer in the box.

Answers

sin 64° = cos x
cos x = sin 64°
x = cos⁻¹ (sin 64°)
x = 26°

Answer:

x = 26° is the answer.

Step-by-step explanation:

We have to find the value of x from the given equation.

sin 64° = cos x

since sin 64° = 0.8987

Therefore cos x = 0.8987

[tex]x = cos^{-1}(0.8987) = 26[/tex]

x = 26°

What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .? PLEASE HELP ME, ALSO CAN YOU EXPLAIN HOW YOU GOT THE ANSWER SO I CAN FIGURE IT OUT ON MY OWN THE NEXT TIME.

Answers

a. 25/40 , 36/40, 49/ 40.
you are adding by odd numbers example 1+3=4. 4+5=9 .9+7=16. 16+9=25 and so on.
b. 47/101, 76/101, 123/101
you are adding by the answers
example. 3+1=4. 4+3=7. 7+4=11. 11+7= 18. 18+11= 29. 29+18=47. 47+29=76. 76+47=124.

A cup of coffee contains 130 mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how much caffeine will remain in the body after 3 hours?

Write the exponential function and solve.
a.
4072-06-01-04-00_files/i0260000.jpg; 184 mg
b.
4072-06-01-04-00_files/i0260001.jpg; about 346 mg
c.
4072-06-01-04-00_files/i0260002.jpg; less than 1 mg
d.
4072-06-01-04-00_files/i0260003.jpg; about 92 mg

Answers

---
y(t) = a*e^(kt)
---
now:
130 mg
---
one hour from intake:
130 * (1 - 0.11) = 115.7 mg
---
y(1) = 115.7 = 130*e^(k(1))
115.7 = 130*e^k
115.7/130 = e^k
ln( 115.7/130 ) = ln( e^k )
ln( 115.7/130 ) = k
k = -0.1165338

---
three hours from intake:
y(3) = 130*e^(3k)
y(3) = 91.64597
---
answer:
three hours after drinking a cup of coffee, 91.6 mg of caffeine will remain in the body


What are the x and y intercepts of the line? 2x - 3y = 12

Answers

Just plug in a 0 to fine the x and y intercepts just like 
2x0-3y=12 Now that would be 3y=12
y=4
So the y intercept is 4
then do the same to find x
Like 2x-3x0=12 That would be 2x=12 
x=6
That is how you find x and y intercepts. Hope this helped

A segment has endpoints at (3,−4) and (3,−17). How many units long is the segment?

Answers

[tex]\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points}\ (3,\ -4)\ \text{and}\ (3,\ -17).\ \text{Substitute:}\\\\d=\sqrt{(3-3)^2+(-17-(-4))^2}=\sqrt{0^2+(-13)^2}=\sqrt{(-13)^2}=13\\\\Answer:\ \boxed{13\ units}[/tex]

Find the measure of the complement and the supplement of the angle.

Answers

Two angles are complementary if their measures add up to 90 deg.
Two angles are supplementary if their measures add up to 180 deg.

Complement: 90 - 12 = 78
Supplement: 180 - 12 = 168

Answer: B. complement 78 deg, supplement 168 deg
Hello there!

[tex]*[/tex] (Complementary angles): These angles are not greater than or less than 90°.

Therefore, we then do [tex] \left[\begin{array}{ccc}12-90=78\end{array}\right] [/tex].

[tex]*[/tex] (Supplementary angles): These kind of angles would be angles that are no greater than to 180°.

We then do [tex] \left[\begin{array}{ccc}180-12=168\end{array}\right] [/tex].

Your correct answer: (Option B).

The cake store is having a 25\%25%25, percent off sale on all of its cakes. If the cake you want regularly costs \$9$9dollar sign, 9, how much would you save with the discount?

Answers

25% = 25/100 = 0.25

9*0.25 = 2.25.

You save $2.25 with the discount. 

Answer:

$2.25.

Step by step explanation:

We have been given that the cake store is having a 25% off sale on all of its cakes.

To find our savings with the discount we will find 25% of $9 (regular cost of cake).

[tex]\text{Savings with the discount}=9\times\frac{25}{100}[/tex]

[tex]\text{Savings with the discount}=9\times\frac{1}{4}[/tex]

[tex]\text{Savings with the discount}=\frac{9}{4}=2.25[/tex]

Therefore, we will save $2.25 with the given discount.

Solve the single variable equation for n.
4(-n + 4) + 2n = 2n

a. n = 4
b. no solution
c. infinitely many solutions

Answers

plug in 4 for the n in both side and see do they equal then try one more number like 3 for n then if that one also lead to each side being equal then your ANSWER would be C if not then your ANSWER would be A and if it didnt equalled on both side by either number than it would be B
4(-n + 4) + 2n = 2n
-4n + 16 + 2n = 2n
-4n + 16 = 0
-4n = -16
   n = 4

answer
a. n = 4 

Find the area of the circle if the square has an area of 900 in2. Give your answer in terms of pi

Answers

There is no attached picture, but I guess it is like the one I attached.
If so, the first thing is finding the side measure:
[tex]A_{square}=l^2 \\ l= \sqrt{A} = \sqrt{900} \;\;\Rightarrow l=30\;in[/tex]
Now, radius is half this measure: 15 in.
And circle area is:
[tex]A_{circle}=\pi r^2=\pi\cdot(15)^2\:\;\Rightarrow A_{circle}=225\pi\;in^2[/tex]

Final answer:

The area of the inscribed circle within a square with an area of 900 in² is 225π in².

Explanation:

The subject here is circle geometry, which is a part of Mathematics. Given that the area of the square is 900 in², we want to find the area of the inscribed circle. The side length a of the square can be found by taking the square root of the area, so a = √{900} = 30 inches. The diameter of the circle is the same as the side of the square, which means the radius r is half of that, so r = 30 / 2 = 15 inches. The formula for the area of a circle is A = πr², and substituting in our value of r, we get:

A = π * (15 in)² = 225π in²

6. Angle ABC is congruent to which angle?
1. Angle CAB
2. Angle XYZ
3. Angle XZY
4. Angle YZX
~
7.
Side CA is congruent to which side?
1. ZX
2.YX
3.XY
4.YZ

Answers

6. Angle ABC is congruent to XYZ
7. ZX

Answer:

[tex]\angle ABC \cong \angle XYZ[/tex]

[tex]CA \cong ZX[/tex]

Step-by-step explanation:

According to the given figures:

[tex]\angle ABC \cong \angle XYZ[/tex]

Also,

[tex]CA \cong ZX[/tex]

Therefore, the answer to the first question is Angle XYZ, and the answer to the second question is ZX.

You can deduct these answers by observing the number of line that match each pair of congruent elements.

Suppose the number of dropped footballs for a wide receiver, over the course of a season, are normally distributed with a mean of 16 and a standard deviation of 2.

What is the z-score for a wide receiver who dropped 13 footballs over the course of a season?




−3

−1.5

1.5

3












Answers

The z-score is the number of standard deviations away from the mean. We first subtract the actual score from the mean, then divide the difference by the standard deviation. In this case, our actual score is 13, so we subtract from the mean of 16, then divide by the SD of 2
(13 - 16) / 2 = -1.5

In right triangle PQR, P and Q are complementary angles. The value of sin Q is 9/
41
. What is the value of cos P?

Will be given brainley

Answers

All that given means is they add up to 90o. They must since the triangle is a right triangle.
That's my LOL for the night. It's very late where I am. Probably where you are too. 
Draw the diagram. This is a very important question. I don't want to just tell you because in many disguises, this problem shows up more than once. So draw the diagram.

Put the Sin of Q in. Sin(Q) is PR/QP Label PR as 9 and QP is 41. Make sure you agree with me before reading the rest.

Do you agree? Good you can go on. 
Now go down to <RPQ. A cosine is the adjacent side over the hypotenuse. What I was giggling about when I saw it was that the Cos of P is the Same as the Sin(Q). This fact is going to turn up many times in many different forms. Of all the questions you've asked tonight, this is the one you must pay the closes attention to.

9/41 = Cos P <<<<==== Answer.
Answer:

Option: A is the correct answer.

The value of cos P is:

             A)   [tex]\dfrac{9}{41}[/tex]

Step-by-step explanation:

We know that if two angles A and B are complementary then,

[tex]A+B=90[/tex]

i.e.

[tex]B=90-A[/tex]

Here we have angle P and angle Q are complementary i.e.

[tex]P=90-Q[/tex]

Also, we are given,

[tex]\sin Q=\dfrac{9}{41}[/tex]

We are asked to find:

[tex]\cos P[/tex]

It could also be written as:

[tex]\cos P=\cos (90-Q)\\\\i.e.\\\\\cos P=\sin Q\\\\i.e.\\\\\cos P=\dfrac{9}{41}[/tex]

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

[tex]\frac{5x^{5}-3x^{3}+2x^{2}-x}{x+2}=5x^{4}-10x^{3}+17x^{2}-32x+63- \frac{126}{x+2}[/tex]

The coefficient of the x term is -32.

Which quadrilateral will always have 4-fold reflections symmetry

Answers

The answer is a square

Answer:

square

Step-by-step explanation:

i got it right in edge

Marisha plots her flower garden on a computer. She determines that the circle that defines the part of the garden that gets watered by the sprinkler is (x−8)2+(y+10)2=25.

What is the diameter, in meters, of the circular area that gets watered by the sprinkler?

2.5 m

5 m

10 m

20 m

Answers

If the radius of the circle will be 5, then the diameter of the circle is 10 m. Then the correct option is C.

What is an equation of a circle?

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

Marisha plots her flower garden on a computer.

She determines that the circle that defines the part of the garden that gets watered by the sprinkler is (x − 8)² + (y + 10)² = 25.

Then the equation can be written as

(x − 8)² + (y + 10)² = 5²

The radius of the circle will be 5

Then the diameter of the circle is given as

d = 2r

d = 2 x 5

d = 10 m

Learn more about the equation of a circle here:

https://brainly.com/question/10165274

#SPJ2

Determine the 10th term 0.1,0.5,2.5

Answers

Find the pattern first which is multiply by 5. This problem is geometric sequence so you have to use this formula to find the 10th term:
An=AR^n-1
A(10)=0.1(5)^(10-1)
A(10)=195312.5

Which is the best estimate for (6.3x10^-2)(9.9x10^-3) written in scientific notation?

Answers

it should be 6.237*10^-4

Answer:

[tex]6 \times 10^{-4}.[/tex]

Step-by-step explanation:

We are given expression [tex](6.3 \times 10^{-2})(9.9\times 10^{-3})[/tex].

In order to multiply above given expression, we need to multiply 6.3 by 9.9 first.

On multiplying 6.3 by 9.9 , we get 62.37.

Now we would multiply  [tex]10^{-2} \ by \ 10^{-3}.[/tex]

Therefore,

[tex]10^{-2} \times 10^{-3}= 10^{-2-3}= 10^{-2-3} = 10^{-5}.[/tex]  

Therefore,

[tex](6.3 \times 10^{-2})(9.9\times 10^{-3}) =62.37 \times 10^{-5}[/tex]

Again [tex]62.37 \times 10^{-5}[/tex] could be written as [tex]6.237 \times 10^{-4}[/tex].

Now, [tex]6.237 \times 10^{-4}[/tex] could be round to [tex]6 \times 10^{-4}.[/tex]

Therefore, correct answer is  [tex]6 \times 10^{-4}.[/tex]

If two 6-sided number cubes are rolled, what is the probability that you will roll a 1 first and then roll a 5 with the second cube?

Answers

The answer is 1/36. This is because there are 36 possible outcomes and this is only one of them. 

If you were to ask what the odds of getting a 1 and a 5, it would be higher, but the fact that they need to come in that order give you the above answer. 

Final answer:

The probability of rolling a 1 first and then rolling a 5 with two 6-sided number cubes is 1/36.

Explanation:

To find the probability of rolling a 1 first and then rolling a 5 with the second cube, we need to consider the probabilities of each event separately. The probability of rolling a 1 on the first cube is 1/6, since there is only one face with a 1 out of six possible outcomes.

The probability of rolling a 5 on the second cube is also 1/6. Since these events are independent, we can multiply their probabilities to find the overall probability:

Probability of rolling a 1 first and then rolling a 5 = (1/6) * (1/6) = 1/36

Other Questions
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