What is the probability of rolling a number less than or equal to 8 with two dice, given that at least one of the dice must show a 6?

Answers

Answer 1

Final answer:

The probability of rolling a number less than or equal to 8 with two dice, given at least one die shows a 6, is 5/36, considering all the valid dice combinations that meet the criteria.

Explanation:

The probability of rolling a number less than or equal to 8 with two dice, given at least one must be a 6, is calculated by considering the possible combinations of dice that adhere to these conditions. First, we determine how many outcomes include at least one 6:

If the first die is a 6, the other die can be 1, 2, or a 3 (since 6+4 is already 10, which is greater than 8).

If the second die is a 6, the first die can again be 1, 2, or 3.

Both dice can be 6, which adds one more outcome.

These are mutually exclusive events, therefore we add their probabilities. There are 5 outs of 36 possible rolls (3+3) when the numbers can sum up to less than or equal to 8 with at least one die showing a 6 (1+6, 2+6, 3+6, 6+1, 6+2, 6+3).

The probability of rolling a number less than or equal to 8, given that at least one die shows a 6, is 5/36.

Answer 2

The probability of rolling a number less than or equal to 8 with two dice, given that at least one die shows a 6, is [tex]$ \frac{10}{11} $.[/tex]

To find the probability of rolling a number less than or equal to 8 with two dice, given that at least one of the dice must show a 6, we can use conditional probability.

Let's consider the outcomes where at least one die shows a 6:

- (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

- (1, 6), (2, 6), (3, 6), (4, 6), (5, 6)

Out of these 11 outcomes, the ones where the sum of the two dice is less than or equal to 8 are:

- (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)

- (1, 6), (2, 6), (3, 6), (4, 6), (5, 6)

So, there are 10 favorable outcomes out of 11 possible outcomes when at least one die shows a 6.

Therefore, the probability of rolling a number less than or equal to 8 with two dice, given that at least one of the dice must show a 6, is [tex]$ \frac{10}{11} $.[/tex]

Related Questions

What times what equals 80.73

Answers

80.98498747 is your answer

Kurt johnson delivers packages for a delivery company. he receives $7.50 for every package delivered. what does kurt earn in a week if he delivers 48 packages? 360.00 405.00 555.00 640.00

Answers

y = 7.50x.....y = earnings per week , x = number of packages delivered

48 packages.....so x = 48
y = 7.50(48)
y = 360.....so if he delivers 48 packages, he earns $ 360

Answer:

He earned $ 360.00.

Step-by-step explanation:

Given,

The amount he gets for a package of delivery = $ 7.50

The number of packages he delivered in a week = 48,

Hence, the amount he earned in the week = The amount he gets for a package of delivery × The number of packages he delivered

= 7.50 × 48

= $ 360.00

In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B′. What is the scale factor of the dilation?

1

2

0.5

-0.5

Answers

Answer:

The diameter of B is from -2 to 2, which = 4 units.

The diameter of B' is from -1 to 1, which equals 2 units.

2/4 = 1/2 = 0.5 scale factor.

The answer is C. 0.5

Step-by-step explanation:

A surveyor, standing 100 ft. from the base of a building, measures the angle of elevation to the top of the building to be 75 degrees. How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?

Answers

right well height = 100tan75
= 373.205 Ft

dH/da = 100sec^2(a)

Fractional change in height = dH/H = 0.04

0.04 = 100 sec^2 a da/H
da = 0.04 H / 100 sec^2a
da = 0.01

Hope this helps

A vehicle travels on a highway at a rate of 65 mi/h how long does it take the vehical to travel 25 mi?

Answers

use the velocity formula and solve for time.v=d/t
t=d/v

Substitute your variables and solve.
65 mi/hr = 65 / 3600 mi/second
25 mi / ( 65/3600) = 1384.6 seconds

Answer:

Step-by-step explanation:

A vehicle travels at a rate of 65 m/h, How long does it take the vehicle to travel at 25 miles?

Apply the "distance formula":

d = rt

25 = 65t

25/65 = t

5/13 hour = t

0.385 hour = t

23.08 minutes = t

What is another way to write 250,000 ml?

Answers

250 Liters; or, 250 L, is another way to write "250,000 mL"
_______________________
(Note that "mL" is another way to write "ml"; or "milliliters".
____________________________
Lengthy explanation:
_________________________________
One other way to write 250,000 mL is to convert that value to "L" (Liters).
_________________________________
Note the exact version: 1000 mL = 1 L
_________________________________
So:
_______________
250,000 mL * ([tex] \frac{1 L}{1000 mL} [/tex] ) = ? L ;
___________________________________________
Note: The "mL" notations "cancel out") ; and we are left with:
_________________________________________________
250,000 mL =
___________________________________
([tex] \frac{250,000}{1000} [/tex] L ;
__________________________________
250,000 ÷ 1000 = ? L
______________________
Take: "250,000" and move back the last 3(three) decimal places:
_____________________________
250,000 ÷ 1000 = 250 L
_____________________________

another way to write it would be 250 liters.

hope this helps you

What is the best approximation of the sine of 50°?

A. 0.2624

B. 0.6428

C. 0.7660

D. 1.1918

Answers

The best and most correct answer among the choices provided by your question is the first choice or letter A.

As I calculated it, sine 50 is equivalent to 0.2623748537.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

How are mc091-2.jpg and mc091-3.jpg related?

Answers

check what u wrote cause its not numbers fix it so i can help you

its 1 image and doesnt show anything

What is the solution to the equation?

5(8 + 7) = 5 • x + 5 • 7

A.
x = 1

B.
x = 5

C.
x = 7

D.
x = 8

Answers

D. X=8 distribute the 5 to the 8 and 7 which is 40 + 35 = 5 times x + 5 times 7 Multiply 5 times x and 5 and 7. Add left side to equal 75. Subtract 35 from both sides. Divide by 5 on both sides. Get x = 8 5(8+7) =5x+35 40+ 35 = 5x + 35 75= 5x +35 40= 5x X=8

Find the missing length. The triangle in each pair are similar.

Answers

The answer is 39.
B/c 27/45=.6
.6*65=39

Answer:

39 UNIT

Step-by-step explanation:

According to similar triangle.

Let's call NG "X"

45/27 = 65/x

X=( 65*27)/45

X= 1755/45

X = 39

Simplify (8j3 + 5j2 – 3) – (5j3 + 7j2 – 12j + 7) ...?

Answers

The answer to the problem is:

8j^3 + 5j^2 - 3 - 5j^3 - 7j^2 + 12j - 7

3j^3 - 2j^2 + 12j - 10

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Answer:

3j^3 - 2j^2 + 12j - 10

Step-by-step explanation:

I took the test and got a 100%

An Antique vase is projected to be worth $1000 in 2 years and $1,300 after 5 years. If the value continues to appreciate at the same rate, what will it be worth in 8 years?

Answers

The value of the antique vase after 8 years with a consistent appreciation rate, it would amount to $1,600.

An antique vase:

Value after 2 years: $1,000

Value after 5 years: $1,300

To find the value after 8 years, we can assume a constant rate of appreciation:

In 8 years, the value will be: $1,000 + ($1,300 - $1,000) = $1,300 + ($1,300 - $1,000) = $1,600

Miss fernandez built two rectangular gardens the length of garden a is 2 feet longer than twice its width the list of garden b is 1 foot less than the width of garden a the length of garden b is 2.5 times its width the two gardens have the same perimeter what are the dimensions of the gardens

Answers

For garden A, let width = w, length = L
For garden B, let width = x, length = y

So we are given the following:
L = 2+2w
x = w - 1
y = 2.5x
2w+2L = 2x+2y ------> w+L = x+y

Ok lets do some substituting into the perimeter equation
[tex]w + (2+2w) = (w-1) + 2.5(w-1)[/tex]
adding like terms...
0.5w = 5.5
w = 11

This means that:
L = 2+2(11) = 24

x = 11-1 = 10
y = 2.5x = 2.5(10) = 25

Final solution:
Garden A is 11 by 24
Garden B is 10 by 25

Wendy wants $15,000 saved in 6 years to make a down payment on a house. How much money should she invest now at 4.65% compounded annually in order to meet her goal?

Answers

A=P(1+R/100)^n
A=$15000, n=6 years, R=4.65
Therefore,
15000=P(1+4.65/100)^6
15000=P(1.3135)
P=15000/1.3135
=$11420 (to the nearest dollars)

Six times the sum of a number and twelve is forty.

Which equation represents this?

6N + 12N = 40
6N + 12 = 40
6(N + 12) = 40

Answers

The last one
6(N+12)= 40

Depends if number twelve is multiplied by six as well. In other words, it depends if the text means:
six times the sum of (a number and twelve) or six times the sum of a number and than plus 12 equal 40.

In first case answer is:
6(N + 12) = 40 and in second
in second:
6N + 12 = 40

solve for X. y=1/4 (x)+3

Answers

The answer is:
____________________
x = 4y - 12 ; (Assuming the problem meant to solve for "x"; "in terms of "y").
_______________________
{Otherwise, the question might be "incomplete".}.
______________________________________________
The question seems incomplete; how can we solve for "x" when we do not know what "y" equals?
__________________________
However, it could be possible to "solve for x" in terms of "y". To so this, we need to isolate ""x" on one side of the equation:
_______________________________
Given: y=1/4 (x) + 3 ; Let us multiply the ENTIRE EQUATION (both sides) by "4", to get rid of the "1/4" (fraction coefficent) of "x", and to "cancel out" the "1/4" fraction cofficient of "x" to the implied "1"; to help solve for "x" :
________________________________________
4 *{ y= 1/4 (x) + 3} ;
______________________
4y = x + 12 ; Now we can subtract "12" from EACH SIDE of the equation; to isolate "x" on one side of the equation; and to solve for "x":
_______________________
4y - 12 = x + 12 - 12 ;
________________________
4y - 12 = x ; This is our answer:
___________________________
x = 4y - 12 ; (Assuming the problem meant to solve for "x"; "in terms of "y").

If a satellite launch has a 97% chance of success, what is the probability of three consecutive successful
launches? ...?

Answers

91%

0.97 ^ 3 = 0.91

= 91%

Answer: The required probability of three consecutive successful launches is 91.27%.

Step-by-step explanation: Given that a satellite launch has a 97% chance of success.

We are to find the probability of three consecutive successful launches.

Let P(A) denotes the probability of the event of the success of the satellite launch.

Then, according to the given information, we have

[tex]P(A)=97\%=\dfrac{97}{100}=0.97.[/tex]

Therefore, the probability of three consecutive successful launches will be

[tex]p\\\\=P(A)\times P(A)\times P(A)\\\\=0.97\times0.97\times0.97\\\\=0.912673\\\\=0.912673\times100\%\\\\=91.2673\%\\\\=91.27\%.[/tex]

Thus, the required probability of three consecutive successful launches is 91.27%.

A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal parts of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?

Answers

Final answer:

To maximize profit, the candy manufacturer should use mathematical linear programming. The decision variables are the amounts of Candy A (x) and Candy B (y). The profit function P = 285x + 260y is to be maximized subject to constraints arising from available stock of dark chocolate, caramel, and walnuts, leading to a typical linear programming problem.

Explanation:

To solve this problem, we need to use Linear Programming, a mathematical model that helps in making optimal decisions. The candies are what we call decision variables. Our decision variables here are Candy A and Candy B.

Candy A: x kilograms (dark chocolate and caramel in equal parts).

Candy B: y kilograms (two parts of dark chocolate and one part of walnut).

We want to maximize the profit function P = 285x + 260y subject to constraints arising from the available stock of dark chocolate (DC), caramel (C), and walnuts (W).

DC constraint: A uses DC in equal parts, and B uses two parts DC. Therefore, x + 2y ≤ 360.C constraint: A uses equal parts C, x ≤ 430 (as B doesn't use C).W constraint: B uses one part W, y ≤ 210 (as A doesn't use W).

The next step is to solve these inequalities graphically or using mathematical methods to get values of x and y that maximize P while respecting constraints. This case, where we want to optimize a certain function with respect to constraints, is a typical linear programming problem in mathematics.

Learn more about Linear Programming here:

https://brainly.com/question/34674455

#SPJ12

A furniture company misprinted a sales ad for a living room set but honors the advertised price. For each customer who purchases the living room set, the company suffers a loss of $125. Write a function to represent the company's total loss. What is the value of the function for an input of 50, and what does it represent? ...?

Answers

We can say that there are x customers.
So,
f (x) = 125x
To get how much money the company loses, we can make x equal to 50.
f (50) = 125(50) = 6250
The company loses $6,250 when 50 customers purchase the furniture.

If arc CE= 40°, and m∠CDE = 30°, what is arc AB ?

A) 70°
B) 100°
C) 140°
D) 20°

Answers

Based on the given figure above, the correct answer would be option B. The measure of arc AB is 100°. If you try to analyze the image, you can say that it is 100 degrees given that arc CE is 40 degrees. By definition, one measure of an arc is the angle formed by the arc at the center of the circle that it is a part of. Hope this answer helps.

Answer:

B is the right answer [tex]100^{o}[/tex]

Step-by-step explanation: Hope This Helps ;)

Oscar Montez’s savings account has a principal of $7,201. It earns 6% interest compounded quarterly. What is the amount of interest he earned by the end of the second quarter?

Answers

compounded quarterly means that one quarter of the interest is added to the account each quarter one quarter of 6% is 1.5% x = 7201 (1 + .06/4)^2 ___ .06/4 is the interest per compounding , and 2 is the number of compoundings

the function f is defined by f(x)=x2+3x-10
if f(x+5)=x2+kx+30, k=____________(<<

Answers

I hope this helps you

What is d if p equals 15 in d=-3p^2+168p-315

Answers

so first you will substitute p for 15
so your equation will look like d=3(15)^2+168(15)-315
then you will simplify
to get d= 2025+2520-315
simplify again
to get d=4230

sub
-3(15^2)+168(15)-315=
-3(225)+2520-315=
-675+2205=
1530

d=1530 when p=15

PLEASE HELP!!
Oscar entered y=−0.4^x+3y=−0.4^x+3 into an online graphing tool.

What function did he graph?

y=(−0.4)x+3y=(−0.4)x+3

y=(−0.4)x+3y=(−0.4)x+3

y=−(0.4)x+3y=−(0.4)x+3

y=−(0.4)x+3

Answers

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
Among the choices provided above the function the Oscar graph is
y=(−0.4)x+3y=(−0.4)x+3

Help With Number 8 Please?

Answers

The answer is about 8.14 years :)

Because, ↓

Unit Rate = [tex] \frac{I}{1300 * 0.0425 } [/tex] which is equal to → [tex] \frac{450}{1300 * . 0425} [/tex]

and that's how I found out that my answer is 8.14 years

I = p r t First subtract 1750-1300 to find out how much interest was earned. 450=1300(.0425)t ; solve by multiplying 1300*.0425 then divide 450 by that number. You get approx 8.14 years.

Mr. Shaw graphs the function f(x) = –5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?

a.) y – 12 = –5(x + 2)
b.) y – 12 = 2(x + 2)
c.) y + 12 = 2(x – 2)
d.) y + 12 = –5(x – 2)

Answers

I hope this helps you

Point slope formula has fallowing shape:
y-y1=m(x-x1)

where x1 and y1 are coordinates of the given point.

in f(x) = -5x + 2 we can see that slope is -5
m = -5

if we exchange all of this in point slope formula we get:

y - 12 = -5(x - (-2)) = -5(x+2

Answer is a)

Which of the following statements is true?

A.A radius is always a chord.
B.A tangent is always a secant.
C.A diameter is always a chord.
D.A chord is always a diameter.
Please help

Answers

A isnt correct because radius goes from center of circle to any point on circle. Chord on the other hand connects 2 points on circle...

B is also false. Secant goes through circle while tangent only touches it in one point.

C is correct. Chord connects as said before 2 points on circle and in some cases it can connect 2 points in such way that it goes through center which is diameter.

D is not correct because chord doesnt have to pass trought center of circle in order to connect any 2 points on circle.

find all the zeros of the function y=x^3+6x^2+x+6

Answers

Final answer:

The zeros of a function are the values of x for which the function equals zero. The function given here is a cubic function, and finding its zeros can be complex, often requiring numerical methods or advanced mathematical approaches like the cubic formula.

Explanation:

This problem deals with finding the zeros of the cubic function y=x^3+6x^2+x+6. A zero of a function is a value of x for which the function equals zero. You can find the zeros of this function by setting the equation equal to zero and solving for x.

Unfortunately, this particular cubic equation does not have an easy solution using basic algebraic methods. We can't factor it in an easy and straightforward manner. However, you can use numerical methods, or online calculator tools, to get an approximate value for the zeros. Alternatively, you can use the cubic formula (somewhat similar to the quadratic formula), but this requires knowledge of more advanced mathematics.

Please consult your teacher or textbook for more detailed instructions on how to use higher level methods to solve cubic equations. Remember that each method has its own level of accuracy and complexity, so choose the method that best suits your abilities and the requirements of your task.

Learn more about Zeros of Function here:

https://brainly.com/question/31654173

#SPJ12

The mean number of hours that Raphael worked over the past four weeks is 37.75. If he works 40 hours this week, what will the mean number of hours be that he will have worked over the five-week period?
What is the five-week mean?

Answers

Multiply 37.75 x 4 to get the total number of hours Raphael worked the past 4 weeks. (The mean is just the total number divided by the number of parts).

37.75 x 4 = 151

Then, add 40 to that total to get the new total.

151 + 40 = 191

Now, divide that number by 5 (as in 5 weeks, the new number of parts).

191/5 = 38.2 hours

The mean for the first four weeks:
Total hours in 4 weeks / 4 = average of four weeks.
Total hours in 4 weeks = 37.75 x 4
= 151
Total hours in 5 weeks = 151 + 40
= 191
5-week mean = 191 / 5
= 38.2

Which of the following is not a way to prove a quadrilateral is a parallelogram?

Answers

I think it's the second answer choice.

The way to not prove a quadrilateral is a parallelogram is; Show one set of opposite sides of the quadrilateral is congruent.

Parallelogram and Congruence

A parallelogram is a quadrilateral which has opposite sides to be congruent and parallel as the name implies and hence, opposite angles of the parallelogram are congruent.

However, showing one set of opposite sides of the quadrilateral is congruent is not a confirmatory test for a parallelogram, as it evades the parallel law of opposite sides of the Parallelogram.