Find the Equation of the Perpendicular Line
Instructions: Find the equation of the line through point (-1, 2) and perpendicular to x + 3y = 3.

y =

Answers

Answer 1

Answer:

  y = 3x +5

Step-by-step explanation:

The equation of a perpendicular line can be formed by swapping the x- and y-coefficients, and negating one of them. The constant in the equation will be chosen to make the equation true at the given point.

Coefficients swapped

The desired equation in the given standard form will be ...

  3x -y = c . . . . . . for some new constant c

Note that we have kept the x-coefficient positive, and have negated the y-coefficient.

Constant value

The new constant will make the equation true at the point (-1, 2):

  3(-1) -(2) = c = -5

So, the standard-form equation is ...

  3x -y = -5

Slope-intercept form

The answer form suggests you want to solve this for y. Adding y+5 to both sides will give the form you want:

  3x -y +(y+5) = -5 +(y+5)

  3x +5 = y

  y = 3x +5

Find The Equation Of The Perpendicular LineInstructions: Find The Equation Of The Line Through Point

Related Questions

what is the equation of the line that is paralle to y=3x-8 and passes thur the point (4,-5)

Answers

⊰_________________________________________________________⊱

Answer:

The equation is-: y=3x

Step-by-step explanation:

[tex]\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}[/tex]

[tex]\pmb{\tt{done \ !!}}[/tex]

⊱_________________________________________________________⊰

A well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece. What is the probability of getting a cookie with no more than 3 chips? Round your answer to four decimal places.

Answers

The probability of getting a cookie with no more than 3 chips is 0.714.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece.

Using poison ratio:

[tex]\rm P (X = k) = \dfrac{\lambda^k e^{-\lambda}}{k!}[/tex]

λ is the mean number of chocolate chips in a piece

[tex]\rm P (X = 6) = \dfrac{6^k e^{-6}}{k!}[/tex]

P(X ≥ 5) = 1 - P(X < 5)

P(X ≥ 5) = 1 - P(X = 0) + P(X = 1)  + P(X = 2)  + P(X = 3) + P(X = 4)  

[tex]\rm P(X \geq 5) = 1-[\dfrac{6^0 e^{-6}}{0!}+\dfrac{6^1 e^{-6}}{1!}+\dfrac{6^2 e^{-6}}{2!}+\dfrac{6^3 e^{-6}}{3!}+\dfrac{6^4 e^{-6}}{4!}][/tex]

After solving;

P(X ≥ 5) = 0.714

Thus, the probability of getting a cookie with no more than 3 chips is 0.714.

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Which of the following has a slope of –2 and a y-intercept of 4?


y = 2x – 4


y = –2x – 4


y = –2x + 4


y = 2x + 4

Answers

SOLVING

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Which equation has a slope of -2 and a y-intercept of 4?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

All of these equations are in [tex]\bf{y=Mx+b}[/tex] form.

The y-int. is b. The slope is M.

[tex]\bf{y\!=\!\!-2x+\!4}[/tex] | put in the values

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                [tex]\bf{=\!\!y=-2x+4}[/tex]

[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]

                 

Set up an algebraic equation and then solve.
The width of a rectangle is 14 units less than the length. If the area is 120 square
units, then find the dimensions of the rectangle.
Length:
Width:

Answers

Answer:

Width: 6

Length: 20

Step-by-step explanation:

So the area of a rectangle can be defined as: [tex]A=wl[/tex] where w=width and l=length.

In this case we don't know what the length is, so let's just say the length is the variable l, and since the width is 14 units less than the length, we can express it as (l-14). this gives us the equation: [tex]A=l(l-14)=l^2-14l[/tex]. We can solve for l, since we're given the area which is 120. So let's set the equation equal to that:

Original Equation:

[tex]A=l^2-14l[/tex]

Substitute 120 as A (given)

[tex]120=l^2-14l[/tex]

There is many ways to solve this equation: factoring, quadratic equation, completing the square etc... but in this case I'll just complete the square

Add (b/2)^2 to both sides to complete the square

[tex]120+(\frac{-14}{2})^2=l^2-14l+(\frac{-14}{2})^2[/tex]

Simplify

[tex]169=l^2-14l+49[/tex]

Rewrite right side a square binomial

[tex]169=(l-7)^2[/tex]

Take the square root of both sides

[tex]13=l-7\\[/tex]

Add 7 to both sides

[tex]20=l[/tex]

to solve for width simply subtract 14 from the length which is 20, so the width is 6

Width: 6

L: 20

Find the 8th term of the sequence with formula tn= 7+2 (n-1)

Answers

Answer:

Your answer is 71

Step-by-step explanation:

7+2(n-1)

we have our n as 8

so,7+2(8-1)

9(7)=63

Complete the sentence.
The amount of time it takes to eat an apple is most likely to be a function of
the
OA. size of the apple
B. orchard where the apple was harvested
O C. store where the apple was purchased
OD. color of the apple

Answers

The answer is A because the bigger/ larger the Apple the longer time it takes to eat it

A random variable is not normally distributed, but it is mound shaped. It has a mean of 11 and a standard deviation of 4.

If you take a sample of size 14, can you say what the shape of the sampling distribution for the sample mean is? Why?

Answers

Using the Central Limit Theorem, nothing can be stated about the shape of the sampling distribution for the sample mean, as the sample size is less than 30.

What does the Central Limit Theorem state?

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, we have a skewed variable and n < 30, hence nothing can be stated about the shape of the sampling distribution for the sample mean.

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graph F(x) = |x - 1|

Answers

Modulus function is a function gives absolute value of a number or variable. It gives magnitude of the number or variables. It is also known as an absolute value the function. The result of this modulus function is always positive.

Draw the graph:

f(x) = |x-1|

f(x) = -(x-1) when x-1 is negative

f(x) = (x-1) when x-1 is positive

when x = -2, f(x) = 3

when x = -1, f(x) = 2

when x = 0, f(x) = 1

when x = 1, f(x) = 0

when x = 2, f(x) = 1

Using this values, draw the graph of f(x) = |x-1|

Hence, the required modulus of x-1 graph.

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Divide: StartFraction 5 Over 8 EndFraction divided by three-fourths

Answers

The value gotten when 5/8 is divided by 3/4 is 5/6.

What is the value gotten from the division?

A fraction is a non-integer that is made up of numerator and a denominator. An example is 5/8. Division is the process of grouping a number into equal parts using another number.

5/8 ÷ 3/4

5/8 × 4/3 = 5/6

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Find the equation of the plane passing through the points A=(1,1,1), B=(1,4,5), C=(−3,-2,0).

Find the area of the triangle the 3 points from the first equation.

Find the angle between the 2 vectors; (1) from A to B and (2) from C to B.

Answers

Equation of the plane

Take any two pairs of the given points and make vectors out of them. For example, the vector from A to B is

[tex]\vec v_1 = \langle 1,4,5\rangle - \langle 1,1,1\rangle = \langle0,3,4\rangle[/tex]

and the vector from A to C is

[tex]\vec v_2 = \langle -3,-2,0\rangle - \langle1,1,1\rangle = \langle-4,-3,-1\rangle[/tex]

These vectors lie in the same plane (the one we want). We can get a third vector that is normal to the plane by taking their cross product (details omitted).

[tex]\vec n = \vec v_1 \times \vec v_2 = \langle 9,-16,12 \rangle[/tex]

If [tex]\vec u = \langle x,y,z\rangle[/tex] is an arbitrary vector, then the vector from any of the points A, B, or C to [tex]\vec u[/tex] will lie in our plane. That is, if we start from A,

[tex](\vec u - \langle1,1,1\rangle) \cdot \vec n = 0[/tex]

and this reduces to the equation of the plane,

[tex]\langle x - 1, y - 1, z - 1 \rangle \cdot \langle 9, -16, 12 \rangle = 0[/tex]

[tex]9 (x - 1) - 16 (y - 1) + 12 (z - 1) = 0[/tex]

[tex]\boxed{9x - 16y + 12z = 5}[/tex]

Area of triangle ABC

This follows immediately from the cross product identity

[tex]\|\vec x \times \vec y\| = \|\vec x\| \|\vec y\| \sin(\theta)[/tex]

where [tex]\theta[/tex] is the angle between [tex]\vec x[/tex] and [tex]\vec y[/tex]. The left side corresponds to the area of the parallelogram spanned by [tex]\vec x[/tex] and [tex]\vec y[/tex]; half of this area would be that of a triangle. (see attached)

In our case, we have

[tex]\|\vec n\| = \|\vec v_1 \times \vec v_2\| = \sqrt{481}[/tex]

so the area of ABC is [tex]\boxed{\dfrac{\sqrt{481}}2}[/tex].

Angle between A to B and between C to B

We already know the first vector, [tex]v_1[/tex].

The vector from C to B is

[tex]\vec v_3 = \langle 1,4,5 \rangle - \langle -3,-2,0 \rangle = \langle 4, 6, 5 \rangle[/tex]

Recall the dot product identity,

[tex]\vec x \cdot \vec y = \|\vec x\| \|\vec y\| \cos(\theta)[/tex]

Then

[tex]\vec v_1 \cdot \vec v_3 = \|\vec v_1\| \|\vec v_3\| \cos(\theta) \implies \cos(\theta) = \dfrac{38}{5\sqrt{77}} \implies \theta \approx \boxed{29.9914^\circ}[/tex]

Given f(x)-3x-1 and g(x)-2x-3, for which value of x does g(x)=f(2)?

Answers

Answer:

x = 4

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=3x-1\\g(x)=2x-3\end{cases}[/tex]

f(2) means substitute x = 2 into function f(x):

[tex]\begin{aligned}g(x) & = f(2)\\ \implies 2x-3 & = 3(2)-1\\2x-3 & = 6-1\\2x - 3 & = 5\\2x - 3 + 3 & = 5 + 3\\2x & = 8\\\dfrac{2x}{2} & = \dfrac{8}{2}\\x & = 4\end{aligned}[/tex]

Therefore,  g(4) = f(2).

f(2)

3(2)-16-15

so

g(x)=52x-3=52x=8x=4

Translate the following from words to an algebraic expression or equation,
denoting the unknown by n.
52a. The express train travels 5 mph faster than the local train.
52b. The length of a rectangle is 7 inches more than its width.
52c. The area of a triangle, if the altitude is twice the base
52d. The sum of 3 consecutive even numbers
52e. 15% of the amount by which a number exceeds 10,000

Answers

Answer:

a. n+5

b. n+ 7

c. 1\2(n×2n)

d. n +n+1 n+2

witch hazel is listed at 12 per galon, less 34.5%. what is the net cost of the amount needed in filling the prescription

Answers

The net cost of the amount needed in filling the prescription is 7.86 per gallon

Net cost

Cost of witch hazel = 12 per gallonDiscount = 34.5%

Net cost = 12 - (34.5% of 12)

= 12 - (0.345 × 12)

= 12 - 4.14

= 7.86 per gallon

Therefore the net cost of the amount needed in filling the prescription is 7.86 per gallon

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A suitcase measures 18 inches long and 12 inches high. What is the diagonal length of the suitcase?

Answers

Answer:

21.6 in

Step-by-step explanation:

Imagine the suitcase as a rectangle, with length of 18 in and width of 12 in. In order to find the diagonal length, simply use the Pythagorean Formula, a^2 + b^2 = c^2, and solve for c!

In this case, a = 18 and b = 12.

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The length of a rectangle is five times the width. If the area of the rectangle is 45
square inches, then find the length and width.

Answers

Step-by-step explanation:

sol;

l=5w

area=l*w

or,45=5w*w

or,45=5w2

or,45\5=w2

0r[tex]\sqrt{9}[/tex]=w

or,3=w

again,

l=5w

l=5*3

l=15

Therefore, length is 15 inch and width is 3 inch.

Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n = Tom's weight in pounds.

(n - 30) + n = 210
(n + 30) + n = 180
(n + 30) + n = 210
(n - 30) + n = 180

Answers

The equation that represents the given problem would be (n-30) + n = 210. The correct option is the option A; (n-30) + n = 210

What is a linear equation?

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

From the given information,

n = Tom's weight in pounds

If Jim weighs 30 pounds less than Tom

Jim weighs will be (n - 30)

Thus,

The sum of their weight

(n-30) + n

∴ (n-30) + n = 210

Hence, the equation that represents the given problem would be (n-30) + n = 210. The correct option is the option A; (n-30) + n = 210

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Please help me....trying to get my HS diploma, i did not graduate :(

A ball is thrown in air and it's height, h(t) in feet, at any time, t in seconds, is represented by the equation h(t)=−t2+7t. When is the ball higher than 10 feet off the ground?

A. 2 B. −5≤t≤−2
C. 2≤t≤5
D. −5

Answers

When t is between 2 and 5, the ball will be above 10 feet.so answer is:

C. 2 ≤ t ≤ 5

Given, height h(t) = ₋t² ₊ 7t

At what values of time t is the ball 10 feet above the ground = ?

To find out the time we need to set up an inequality.

Inequality expression is given as = ₋t² ₊ 7t ≥ 10

                                                       = ₋t² ₊ 7t ₋ 10 ≥ 0

                                                       = ₋(t² ₋ 7t ₊ 10) ≥ 0

                                                       = t² ₋ 7t ₊10 ≥ 0

Now, factorize the expression and get the factors.

= t² ₋ 2t ₋ 5t ₊ 10 ≥ 0

=t(t ₋ 2) ₋ 5(t ₋ 2) ≥ 0

=(t ₋ 2) (t ₋ 5) ≥ 0

Hence t value ranges from t = 2 and 5.

As a result, when t is between 2 and 5 seconds, the ball will be farther than 10 feet, 2 ≤ t ≤ 5

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1. How many variables are involved in the chi-square test?
2. Which type of chi-square test is this?
A.goodness of fit B.test of independence
3. How many degrees of freedom are involved?
4. Using the chi-square critical values table is the result of this rest statistically significant?
A. Yes B.No

Answers

The result of the respective questions are:

This chi-square test only takes into consideration one variable.The  type of chi-square test this is is a Goodness of Fitdf= 3NO

How many variables are involved in the chi-square test?

a)

This chi-square test only takes into consideration one variable.

b)

The  type of chi-square test this is, is a Goodness of Fit

To test the hypothesis, we must determine whether the actual data conform to the assumed distribution.

The "Goodness-of-Fit" test is a statistical hypothesis test that determines how well the data that was seen resembles the data that was predicted.

c)

Parameter

n = 4

Therefore

Degrees of freedom

df= n - 1

df= 4 - 1

df= 3

d)

In conclusion

Parameters

[tex]\alpha = 0.05[/tex]

df = 3

Hence

Critical value = 7.814728

Test statistic = 6.6

Test statistic < Critical value, .

NO, the result of this test is not statistically significant.

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Find an equation of the line passing through the given points. Use function notation to write the equation,
(-4,9) and (2,-3)

Answers

y= -2x*1 is the answer

MATH: EXPONENTIAL WORK PROBLEM 1. HELP PLEASE! 13 pts

Answers

The amount of the radioactive substance is 374.6 g

How to determine the amount of radioactive substance?

The given parameters are:

Initial, a = 424 mgRate, r = 6%Time, t = 2 hours

The amount of the radioactive substance is calculated as:

A(t) = a(1 - r)^t

This gives

A(t) = 424 * (1 - 6%)^t

At 2 hours, we have:

A(2) = 424 * (1 - 6%)^2

Evaluate

A(2) = 374.6

Hence, the amount of the radioactive substance is 374.6 g

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A trader sold an article for N150 and
made a profit of 20%. What was the
cost price of the article?

Answers

Answer:

125

Step-by-step explanation:

N150=120%

? =100

150×100/120

=125

The cost price of the good is $125.

What is cost price?

Cost price is the total amount of money that it costs a manufacturer to produce a given product or provide a given service.

Given that a good has been sold for $150 which made a profit of 20% we need to find the cost price of the good,

Let the cost price be x,

So,

x × 120% = 150

x = 150 × 100 / 120

x = 125

Hence the cost price of the good is $125.

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ram takes 20 minutes to inspect a car, while robert takes only 18 minutes.if both start inspecting car at 8.00 hours what is the first time at which both will have finished inspecting a car at the same point time

Answers

Answer:

11:00

Step-by-step explanation:

here we have to calculate the LCM of 20 and 18

20 = 2² × 5

18 = 2 × 3²

Then

LCM(20 , 18) = 2² × 5 × 3² = 20 × 9 = 180

The

After 180 minutes (3 hours) they will have finished inspecting a car at the same point time.

Then

At 8:00 + 3 = 11:00 Ram and Robert will have finished inspecting a car at the same point time.

What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months? a. $25.47 b. $202.55 c. $611.20 d. $4,861.20 please select the best answer from the choices provided a b c d

Answers

The total finance charge is $611.20 (Option c) for this compound interest.

Data Given

Principal, P = $4250

Rate of Compound Interest, R = 13.25%

Time, t = 24 months, i.e., 2 years

Since it is compounded monthly, n = 12

Calculating the Total Finance Charge

We know that the formula for total amount of finance charge in a Compound Interest is,

[tex]A=P\frac{r(1+r)^{n} }{(1+r)^{n} - 1}[/tex]

Substituting the values of P, R and n, we get,

[tex]A=4250\frac{13.25(1+13.25)^{24} }{(1+13.25)^{24} - 1}[/tex]

[tex]A = 611.20[/tex]

Thus, the total finance charge is $611.20

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Find the sum of s = 1 - (1)/(4) + (1)/(6)-(1)/(9)+ (1)/(11)- (1)/(14)...

Answers

The sum of the equation is

[tex] \frac{859}{2772} [/tex]

How to find the sum

Given the expression

s = 1 - (1)/(4) + (1)/(6)-(1)/(9)+ (1)/(11)- (1)/(14)

Let's find the LCM, which is 2772

s =

[tex] \frac{2772 - 693 + 462 - 308 +252 - 198}{2772} [/tex]

Add the numerators, do the addition before the substraction

s =

[tex] \frac{859}{2772} [/tex]

Thus, the sum of the equation is

[tex] \frac{859}{2772} [/tex]

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Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression shows the depreciated sales value of the gadget: 2,020 − 22m
What does the coefficient of the expression represent? The number of months Megan will wait to sell the gadget The monthly depreciation value of the gadget The amount of money Megan will get when she sells the gadget The original value of the gadget

Answers

The coefficient (m) of the expression represents: C. the monthly depreciation value of the gadget.

What is depreciation?

Depreciation can be defined as a process in which the monetary value of a physical asset decreases or falls over a period of time, especially due to wear and tear.

In this scenario, we can infer and logically deduce that the coefficient (m) of the given expression represents the monthly depreciation value of Megan's gadget.

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Answer:

it is C

Step-by-step explanation:

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100POINTS WHY NOT
sally took money from her bank account to go out of town for an audition.she spot 54$ for a round trip ticket and 1/2 of the remaining money on her hotel bill.she spent $7.90 for food and arrived home with $15.10.How much money did Sally take from her bank account??

Answers

Answer:

$100

Step-by-step explanation:

Given information:

$54 = cost of ticketCost of hotel = 1/2 remaining money after purchase of ticket$7.90 = cost of food$15.10 = remaining money

Let x = money taken from bank account

If Sally paid $54 for her ticket, then the money remaining at that point can be defined as:  [tex]x-54[/tex]

If the cost of the hotel was half of the remaining money, then:

[tex]\textsf{Cost of hotel}=\dfrac{1}{2}(x-54)}[/tex]

To find how much money Sally took from her bank account, create an equation with the given information and solve for x.

[tex]\implies \textsf{Money in bank} - \textsf{ticket} - \textsf{hotel} - \textsf{ food} =\textsf{remaining money}[/tex]

[tex]\implies x - 54 - \dfrac{1}{2}(x - 54)-7.90=15.10[/tex]

[tex]\implies x - 54 - \dfrac{1}{2}x+27-7.90=15.10[/tex]

[tex]\implies \dfrac{1}{2}x-34.90=15.10[/tex]

[tex]\implies \dfrac{1}{2}x=50[/tex]

[tex]\implies x=100[/tex]

Therefore, Sally took $100 from her bank account.

Which point is a solution to the system?

Answers

Answer:

what solution bc i could answer this pls let me know the equation but......

Step-by-step explanation:

to find a solution you can add divide or subtract to find the solution like x=2

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1 z=-0.92 z=1.23

Answers

The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.

What is Normal Distribution?

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

1.) The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.

2.) The area of the shaded region for a z-score of 1.23 is 0.8907, which means the area that will be shadeded in the normal distribution graph is 89.07% of the total.

Now, the area of the shaded region will be,

Area = 0.8907 - 0.1788

        = 0.7119

        = 71.19%

Hence, the area of the shaded region is 71.19%.

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solve the equation cos (x/2) = cos x + 1. what are the solutions on the interval 0° ≤ x < 360°?

Answers

Answer:

Step-by-step explanation:

cos (x/2)=cos x+1

cos (x/2)=2cos ²(x/2)

2 cos²(x/2)-cos (x/2)=0

cos (x/2)[2 cos (x/2)-1]=0

cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)

x/2=2nπ+π/2,2nπ+3π/2

x=4nπ+π,4nπ+3π

n=0,1,2,...

x=π,3π

or x=180°,540°,...

180°∈[0,360]

so x=180°

or

2cos(x/2)-1=0

cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)

x/2=360n+60,360n+300

x=720n+120,720n+300

n=0,1,2,...

x=120,300,840,1020,...

only 120° and 300° ∈[0,360°]

Hence x=120°,180°,300°

Find the probability of rolling a sum of 7 or 11. (sum of 7 or 11) = _______________




b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) = ______________




c. Find the odds against rolling a sum of 7 or 11.








d. In gambling the “odds against” (or “odds on”) usually expresses how much you can gain with a win for each
dollar you bet. If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11,
how much money will you win? Include your winnings plus your initial bet.

Answers

a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11) is 2/9. b. the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) is 7/9.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The probability of getting a total of 7 = 6/36

The probability of getting total of 11 = 2/36

a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11)

= 6/36 + 2/36

= 2/9

b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11)

= 1- 2/ 9

= 7/9

c. Find the odds against rolling a sum of 7 or 11.

= 2/9

d. The money you will win, If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11.

10 x  2/9 = 20/9

10 x 7/9 = 70/9

Thus, The money you will win $10.

Learn more about probability here;

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