find the probability of rolling a 2 with a pair of dice. (round your answer to three decimal places.)

Answer:

A

Step-by-step explanation:

-2 5/6, -2/3, 1 1/6, 1 5/6

Are all ordered from least to greatest

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

There are 7 ways for 345 to be written as the sum of an increasing sequence of two or more consecutive positive integers.

We need to find consecutive numbers (an arithmetic sequence that increases by 1) that sum to 345. This calls for the sum of an arithmetic sequence given that the first term is k, the last term is g, and with n elements, which is:

                                           n(k+g)/2.

There are 7 ways can 345 be written as the sum of an increasing sequence of two or more consecutive positive integers.

We look for sequences of n consecutive numbers starting at k and ending at k + n − 1. We can now substitute g with k+n- 1. Now we substitute our new value of g into n(k + g)/2 to get the sum i.e.

                                n(k+k+n-1)/2 = 345

This simplifies to n(2k+n-1)/2 = 345.

This gives a nice equation. We multiply out the 2 to get that n. (2k+n-1): =690. This leaves us with 2 integers that multiply to 690 which leads us to think of factors of 690.

We know the factors of 690 are:

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

So, through inspection (checking), we see that only 2, 3, 5, 6, 10, 15, and 23 work. This gives us the answer to 7 ways.

To know more about Consecutive Numbers:

brainly.com/question/26352026

#SPJ4

Answer:

55 days

Step-by-step explanation:

1 day = 45 minutes

=> x days = 2475 ÷ 45

=> x days = 55 days

Therefore, he had rode 55 days in the whole summer.

Answer:

5x + 15

Step-by-step explanation:

Given

9x + 6 - 4x + 9 ← collect like terms

= (9x - 4x) + (6 + 9)

= 5x + 15

Answer:

-3 sqrt 2 or -4.242640687

Step-by-step explanation:

The average time it takes to rent a video tape is 0.141 minutes.

Given data:Customers arrive at a video rental desk at the rate of 12 per minute(Poisson).
Each server can handle 8.15 customers per minute(Poisson). If there are 3 servers, we need to determine the average time it takes to rent a video tape.
Let us assume λ = 12 and μ = 3 × 8.15 = 24.45
Average time it takes to rent a video tape = 1 / (μ - λ/n)
Where, n = number of servers⇒ Average time it takes to rent a video tape = 1 / (24.45 - 12/3)⇒ Average time it takes to rent a video tape = 1 / 8.45⇒ Average time it takes to rent a video tape = 0.1185 minutes = 0.141 rounded to three decimal places.

Thus, the average time it takes to rent a video tape is 0.141 minutes.

To know more about average time, click here

https://brainly.com/question/14521655

#SPJ11

The solution of the given system of equations by substitution is (-2, -3).

Given a system of equations,

9y - 7x = -13 [Equation 1]

-9x + y = 15 [Equation 2]

We have to find the solution of the given system of equations.

From [Equation 2],

y = 15 + 9x [Equation 3]

Substitute [Equation 3] in [Equation 1].

9 (15 + 9x) - 7x = -13

135 + 81x - 7x = -13

74x = -148

x = -2

y = 15 + (-18) = -3

Hence the solution of the given system of equations is (-2, -3).

Learn more about System of equations here :

https://brainly.com/question/24065247

#SPJ1

The total number different groups of four subjects are possible are 4845 ways.

The formula for the combination is-

ⁿCr = n!/r!(n - r)!

We are wondering in how many distinct options there are to choose 4 subjects out of 20;

n = 20

r = 4.

Sequence is not important because the topics can be arranged in any order and still form the same group, hence we must use a combination:

Review the combination's definition:

²⁰C₄ = 20!/4!(20 - 4)!

²⁰C₄ = 20!/4!16!

²⁰C₄ = 4845

Thus, the total number of different groups four subject groupings is 4845.

To know more about the combination, here

https://brainly.com/question/28065038

#SPJ4

5 is the value of the convergent integral.

To determine whether the integral is convergent or divergent, we will evaluate the integral from 0 to 1 of 7 - 9x dx, which is given by the expression:
∫(7 - 9x) dx from 0 to 1
First, we find the antiderivative of 7 - 9x:
Antiderivative(7 - 9x) = 7x - (9x^2)/2
Now, we evaluate this antiderivative at the limits of integration:
(7(1) - (9(1)^2)/2) - (7(0) - (9(0)^2)/2) = (7 - 9/2) - (0) = 5
Since the result is a finite number, the integral is convergent, and its value is 5.

Learn more about integral convergence or divergence: https://brainly.com/question/15314665

#SPJ11

Answer:

Each bag of chip costs 0.99 (99 cents)

Step-by-step explanation:

Soda = 1.75

Bag of chips = x

1.75 + 3x = 4.72

Subtract 1.75 from both sides;

3x = 2.97

Divide both sides by 3;

x = 0.99

Answer: 72 is the answer

Step-by-step explanation: Hope i helped!

****Isra****

The probability mass function of the discrete random variable x is:

p(x = -2) = 1/3

p(x = -1) = 1/6

p(x = 0) = 1/6

p(x = 1) = 1/6

p(x = 2) = 1/3

To determine the value of a, we first need to confirm that the probability mass function satisfies the two conditions of a valid probability mass function:

For this probability mass function, the possible values of x are -2, -1, 0, 1, and 2. Therefore, we can calculate the sum of probabilities as:

p ( x = -2 ) + p ( x = -1 ) + p ( x = 0) + p (x = 1) + p (x = 2)

= \(|(-2)| \times a + |(-1)| \times a + |0| \times a + |1| \times a + |2| \times a\)

= 2a + a + 0 + a + 2a

= 6a

To satisfy the first condition of a valid probability mass function, the sum of probabilities must be equal to 1. Therefore, we can set up the equation:

6a = 1

a = 1/6

Thus, the value of a that satisfies the conditions of a valid probability mass function is a = 1/6. Therefore, the probability mass function of the discrete random variable x is:

p(x = -2) = 1/3

p(x = -1) = 1/6

p(x = 0) = 1/6

p(x = 1) = 1/6

p(x = 2) = 1/3

for such more question on probability

https://brainly.com/question/24756209

#SPJ4

Proof:

Multiply both of the sides by 3. You would get 12d = c - d. Add d on both sides, and you would get c = 12d

Here, we are required to proof c = 13d from 4d=1/3(c-d)

Ultimately, c = 13d (proof)

We have;

Cross product

4d × 3 = c - d

therefore, By collecting like terms;

C = 12d +d

and Ultimately, c = 13d ......

Read more:

https://brainly.com/question/21406377

Answer:

2 angles are acute and right angles

Step-by-step explanation:

acute is less then 90 degrees and a right angles is 90

An outlier is a mathematical value in a set of data which is quite distinguishing from the other values.

Its more like outliers are values uncommonly far from the middle. Mostly, outliers have a significant impact on mean, but not on the median, or mode.

Hence making the outliers are crucial in their influence on the mean.

we can say that the outlier is a data point that lies outside the entire pattern in a distribution.

They are mostly shown as dots and its known that the whiskers are required to change. Whiskers stretch out to the farthest point in the data set that isn't an outlier.

To know more about outliers mean, click here:

brainly.com/question/30014356

#SPJ4

The probability that the time until an accident occurs exceeds the mean time by more than 2 standard deviations is 0.0228 or 2.28%.

Using the standard normal distribution (Z) table.
Step 1: Convert the problem into a Z-score. In this case, the Z-score is 2 because we are looking for the probability of exceeding the mean by more than 2 standard deviations.
Step 2: Look up the Z-score of 2 in the standard normal distribution table. You will find a probability value of 0.9772. This value represents the probability that the time until an accident occurs is within 2 standard deviations from the mean.
Step 3: Since we are looking for the probability that the time exceeds the mean by more than 2 standard deviations, we need to find the probability of the complement. Subtract the probability found in Step 2 from 1.
1 - 0.9772 = 0.0228
So, the probability that the time until an accident occurs exceeds the mean time by more than 2 standard deviations is 0.0228 or 2.28%.

for such more question on  probability

https://brainly.com/question/24756209

#SPJ11

Solution

For this case we have a non regular polygon

so then we can conclude that the answer is:

False

Since some polygons can have symmetry lines

The equation that represents the relationship between the x values and the y values in Isabel's table is y = 5/4 x - 11.5

Linear functions are functions that have a leading degree of 1. The linear equation is expressed as:

y = mx + b

where:

m is the slope

b is the y-intercept

Using the coordinate points (2, 14) and (6, 19)

Determine the slope

Slope = 19-14/6-2
Slope = 5/4

For the y-intercept

14 = 5/4(2) + b
14 = 2.5 + b
b = 11.5

Determinethe required linear equations

y = 5/4 x + 11.5

Learn more on linear equation here https://brainly.com/question/1884491

The given system represents the interaction between two species with populations x and y. To analyze the system's behavior, we need to find the critical points, construct the corresponding linear systems, and determine the eigenvalues and eigenvectors. The stability of each critical point can be classified based on the eigenvalues.

Explanation: To find the critical points, we set both derivatives equal to zero:

x(1.5 - x - 0.5y) = 0

y(2 - 0.5y - 1.5x) = 0

Solving these equations, we can identify the critical points. Let's denote them as (x_c, y_c):

Critical Point 1: (0, 0)

Critical Point 2: (1, 2)

Critical Point 3: (2, 0)

Next, we construct the corresponding linear systems by taking the linearization around each critical point. We compute the partial derivatives of the system with respect to x and y and evaluate them at each critical point:

Linear System around Critical Point 1 (0, 0):

dx/dt = 1.5x

dy/dt = 2y

Linear System around Critical Point 2 (1, 2):

dx/dt = -x - 0.5y

dy/dt = -1.5x - 0.5y

Linear System around Critical Point 3 (2, 0):

dx/dt = -0.5x

dy/dt = 2y - 3x

To determine the stability of each critical point, we find the eigenvalues and eigenvectors of the coefficient matrices in the linear systems.

For Critical Point 1:

Eigenvalues: λ1 = 1.5, λ2 = 2

Eigenvectors: v1 = (1, 0), v2 = (0, 1)

For Critical Point 2:

Eigenvalues: λ1 = -1, λ2 = -0.5

Eigenvectors: v1 = (-1, 1), v2 = (-2, 1)

For Critical Point 3:

Eigenvalues: λ1 = -0.5, λ2 = 2

Eigenvectors: v1 = (1, -2), v2 = (0, 1)

Based on the eigenvalues, we can classify the stability of each critical point:

- Critical Point 1 is unstable.

- Critical Point 2 is a stable node.

- Critical Point 3 is a saddle point.

Therefore, the stability and type of each critical point have been determined based on the eigenvalues and eigenvectors of the corresponding linear systems.

Learn more about critical points here:
brainly.com/question/33412909

#SPJ11

Answer:

19

Step-by-step explanation:

A' represents everything out A

B' represents everything out B

C' represents everything out C

So only the outside is left hope this helps

Answer:

the answer is on the top right  with 10-19 one dot on 10 and 1 on 19

Step-by-step explanation:

just did the test and got it right let me know if you  need more help

a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

Learn more about initial principal here:

https://brainly.com/question/26100282

#SPJ11

Answer:

x^2 + 11x + 18.

Step-by-step explanation:

The length = x + 9 and the width = x + 2.

So the area

= length * width

= (x + 9)(x + 2)

= x(x + 2) + 9(x + 2)

= x^2 + 2x + 9x + 18

= x^2 + 11x + 18.

We can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

We have been given an expression  2x² + 12x + 8

We need to write given expression in the form a(a + b)² + c, where a, b and c are numbers.

2x² + 12x + 8

=  2x² + 12x + 18 - 18 + 8

= (√2x + 3√2)² - 10

= (√2)² (x + 3)² - 10

= 2(x + 3)² - 10

Comparing with a(a + b)² + c, where a, b and c are numbers.

a = 2, b = 3 and c = -10

Therefore, we can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

Learn more about an expression here:

https://brainly.com/question/1859113

#SPJ9

Answer:

x= 2, y= 1

Step-by-step explanation:

3x -y= 5 -----(1)

-x +y= -1 -----(2)

(1) +(2):

3x -y -x +y= 5 -1

2x= 4

Divide both sides by 2:

x= 4 ÷2

x= 2

Substitute x= 2 into (2):

-2 +y= -1

y= -1 +2

y= 1

Ava's age is 26 years when Ava and Olivia's ages are consecutive even integers and the sum of Ava's age and 2 times Olivia's age is 74.

According to the question,

Ava and Olivia's ages are consecutive even integers.

Now, let's take Olivia's age to be x years.

So, Ava's age would be (x+2) years because their ages are consecutive even integers. (Even numbers are the number which are divisible by 2.)

We have the sum of Ava's age and 2 times Olivia's age is 74.

So, we have the following expression:

(x+2+2x) = 74

3x+2 = 74

3x = 74-2

3x = 72

x = 72/3 (3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)

x = 24 years

So, Olivia's age is 24 years.

Now, we have:

Ava's age = (x+2) years

Ava's age = (24+2) years

Ava's age = 26 years

Hence, Ava's age is 26 years.

To know more about consecutive even integers here

https://brainly.com/question/26438608

#SPJ1