What is the probability of rolling 2 sixes in a row with a single die?

9514 1404 393

Answer:

  3(x)(4x -3)(2x -5)

Step-by-step explanation:

First of all, recognize that all coefficients are multiples of 3, and all terms have x as a common factor. This means your first factorization is ...

  (3x)(8x^2 -26x +15)

Now, you can use the "X-method" or similar to factor the quadratic. Start by looking for factors of (8)(15) = 120 that have a total of -26. Both will be negative. Here is a list of the positive factor pairs.

  120 = 1·120 = 2·60 = 3·40 = 4·30 = 5·24 = 6·20 = 8·15 = 10·12

The sums of these factor pairs are ...

  121, 62, 43, 34, 29, 26, 23, 22

The pair with a sum of 26 is highlighted.

Using this information, you can complete the X-method diagram, or you can use these numbers to rewrite the quadratic x-term to have 2 parts:

  8x^2 -20x -6x +15

Now, the quadratic can be factored by grouping:

  =  (8x^2 -20x) +(-6x +15)

  = 4x(2x -5) +3(-2x +5)

Recognizing the sign difference between the parentheses contents, we can factor the quadratic to be ...

  = (4x -3)(2x -5) . . . . . note the sign gets attached to the 3

So, the complete factorization of the original expression is ...

  24x^3-78x^2+45x = 3(x)(4x -3)(2x -5)

Answer:

8

Step-by-step explanation:

5 pounds = 40$

1 pound = x$

x$= 1 ×40 /5

x$=8

Answer:

Step-by-step explanation:

you got 5 pounds for 40 dollars

so you'll divide 40 dollars by 5 pounds. it will give you dollars per pound price

40/5

=$8

The model e(y) is used to relate the expected value of the dependent variable, e(y), to a single qualitative variable with four levels. In this case, the qualitative variable represents different categories, and the model aims to examine how these categories affect the dependent variable. The model can be represented as:

e(y) = β0 + β1X1 + β2X2 + β3X3

Here, X1, X2, and X3 are dummy variables representing three of the four levels of the qualitative variable. The fourth level is considered the reference category, and its effect is captured by the constant term, β0.

The coefficients β1, β2, and β3 measure the difference in e(y) between the respective level and the reference category. By analyzing these coefficients, we can better understand the impact of different categories on the dependent variable e(y).

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Answer:

Step-by-step explanation:

y = mx +b

Here, m is slope and b is y-intercept

1) y = -5x - 6

Slope = -5

y-intercept = -6

2) y = 2x

Slope = 2

y-intercept = 0

Answer:

Step-by-step explanation:

First of all, I have a strong feeling that that is supposed to be

\(log_2(32)=y\) so I'm going to go with that. We can solve for y by rewriting that in exponential form. Exponential form and log form are inverses of each other. If the log form of an equation is

\(log_b(x)=y\), the exponential form of it is

\(b^y=x\). We will apply that here to solve for y:

\(2^y=32\)

which is asking us, "2 to the power of what equals 32?". We can use our calculator to raise 2 to consecutive powers til we reach the one that gives us a 32, or we could solve it by writing the 32 in terms of a 2:

\(2^y=2^5\)

Since both bases are the same, 2, then the exponents are equal to one another. y = 5. This is an important rule to remember while solving either log or exponential equations.

Answer:

35 x^4  - 5x^3

Step-by-step explanation:

5x^3 (7x−1)

Distribute

5x^3 (7x) +5x^3 *(−1)

35 x^3 *x - 5x^3

35 x^4  - 5x^3

Answer:

Answer:

35 x^4  - 5x^3

Step-by-step explanation:

5x^3 (7x−1)

Distribute

5x^3 (7x) +5x^3 *(−1)

35 x^3 *x - 5x^3

35 x^4  - 5x^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think is 75 persons 14 persons/ year

Answer:

c negative one , negative 2

Answer:

c negative one , negative 2

Step-by-step explanation:

Check the picture below.

\(\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(5)(3)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(4)(3)}~~ + ~~\stackrel{semi-circle}{\cfrac{1}{2}\pi (2)^2}}\implies 15~~ + ~~6~~ + ~~2\pi \stackrel{using~\pi =3.14}{\implies 27.28}\)

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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The required probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The total number of ways to choose any 2 students from a group of 12 is given by the combination formula:

C(12,2) = 12! / (2! * 10!) = 66

This means there are 66 total ways for Mr. Mackinson to choose any 2 students from the class.

To calculate the probability of choosing 2 girls, we need to count the number of ways to choose 2 girls from the group of 6 girls. We can use the combination formula again:

C(6,2) = 6! / (2! * 4!) = 15

This means there are 15 ways for Mr. Mackinson to choose any 2 girls from the class.

So the probability of Mr. Mackinson choosing 2 girls is:

P(2 girls) = number of ways to choose 2 girls / total number of ways to choose 2 students

= C(6,2) / C(12,2)

= 15 / 66

= 0.2273

Therefore, the probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.

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The function f(x) = 0.45x + 12.50 models the situation where a bank charges $.45 for each check written plus a service charge of $12.50. The "x" represents the number of checks written during the month.

The function that models this situation can be written as:

f(x) = 0.45x + 12.50

In this function, "x" represents the number of checks written during the month. The term "0.45x" represents the monthly charge for maintaining the account based on the number of checks written (0.45 for each check). The term "12.50" represents the service charge.

To calculate the total monthly charge, you would substitute the value of "x" into the function. For example, if you wrote 10 checks during the month, the total monthly charge would be:

f(10) = 0.45(10) + 12.50
      = 4.50 + 12.50
      = $17.00

In conclusion, the function f(x) = 0.45x + 12.50 models the situation where a bank charges $.45 for each check written plus a service charge of $12.50. The "x" represents the number of checks written during the month.

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Answer:if you are looking for the hypotenuse use Pythagoras theorem 17.2047

Step-by-step explanation:square both the base and height .Add their total then find the square root

Let x = 8.132132132...

Then 1000x = 8132.132132132...

Subtract x from 1000x to eliminate the fractional part:

1000x - x = 8132.132132132... - 8.132132132...

999x = 8132 - 8 = 8124

x = 8124/999 = 2708/333

Answer:

−2y3+4y2+18x+8

Step-by-step explanation:

Let's simplify step-by-step.

4(y2+2)+6x−2y3+12x

Distribute:

=(4)(y2)+(4)(2)+6x+−2y3+12x

=4y2+8+6x+−2y3+12x

Combine Like Terms:

=4y2+8+6x+−2y3+12x

=(−2y3)+(4y2)+(6x+12x)+(8)

=−2y3+4y2+18x+8

Answer:

ok i think it might be +278

Step-by-step explanation:

so try +278

Answer:

wanna zoom

Step-by-step explanation:

The measure of x, <DEG and <GEF are 8, 135 and 45 degrees respectively

The sum of angles on a straight line is 180 degrees. From the given diagram;

<DEG + <GEF = 180 degrees

Given the following parameters

Substitute

18x - 9 + 4x + 13 =180

22x + 4 = 180

22x = 176

x = 176/22

x = 8

Determine the measure of m<DEG

m<DEG =. 18x - 9

m<DEG = 18(8) - 9

m<DEG = 135 degrees

For the other angle

<GEF = 180 - 135

<GEF = 45degrees

Hence the measure of x, <DEG and <GEF are 8, 135 and 45 degrees respectively

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\(\displaystyle \boxed{\text{First Attachment, 14}}\)

Answer:

x = 30

y = 60

Step-by-step explanation:

      First, vertical angles are congruent. This helps us fill in more of the angles so we can find x and y.

      Next, supplementary angles add up to 180°, aka a line. We can use this to fill out even more of the diagram given.

      Lastly, corresponding angles on parallel lines are congruent.

      By using the information above, we can decide that x = 30 and y = 60. See the first attachment for all the angle values filled out.

\(\displaystyle \boxed{\text{Second Attachment, 12}}\)

Answer:

x = 65

Step-by-step explanation:

      From the above explanation, we will be using vertical angles and supplementary angles to solve this question. See the second attachment.

      We also know there are 180 degrees in a triangle.

      Lastly, we know that alternate interior angles are congruent.

      Using this knowledge, we can decide that x = 65.

\(\displaystyle \boxed{\text{Third Attachment, 13}}\)

Answer:

x = 30

Step-by-step explanation:

      Again, we will be using vertical angles, supplementary angles, and corresponding angles to solve this question. See the third attachment.

      After placing vertical angles down from the given information, we can fill in more using corresponding angles.

      Lastly, we know there are 360 degrees in a circle. We can create an equation from this and solve.

      Using this information, we can decide that x = 30.

The solution to the equation 2n + 5 = 6( n² - 5 ) is n = ( 1 - √(211 )) / 6 and n = ( 1 + √(211 )) / 6

Given the quadratic equation in the question;

2n + 5 = 6( n² - 5 )

First we simplify the given equation;

2n + 5 = 6( n² - 5 )

2n + 5 = 6n² - 30

6n² - 2n - 5 - 30 = 0

6n² - 2n - 35 = 0

To solve for n, we use the quadratic formula.

n = (-b±√(b² - 4ac)) / (2a)

Compare 6n² - 2n - 35 = 0 to the quadratic equation in its standard form an² + bn + c = 0.

Plug the values into the quadratic formula

n = (-b±√(b² - 4ac)) / (2a)

n = ( -(-2) ±√( (-2)² - 4 × 6 × -35 )) / (2 × 6 ))

n = ( 2 ±√( 4 + 840 )) / ( 12 )

n = ( 2 ±√( 844 )) / ( 12 )

n = ( 2 ±2√(211 )) / ( 12 )

n = ( 1 ± √(211 )) / 6

n = ( 1 - √(211 )) / 6 or n = ( 1 + √(211 )) / 6

Therefore, the values of n are ( 1 - √(211 )) / 6 and ( 1 + √(211 )) / 6.

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Answer:

36

Step-by-step explanation:

Given

x² + 12x = 11

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(6)x + 36 = 11 + 36

(x + 6)² = 47

Answer: 36

Step-by-step explanation:

given:

x² + 12x = 11

perfect square:

a² + 2ab + b²

a² = x² ⇒ x * x

2ab = 12x ⇒ 2(6)x

b² = 6² ⇒ 36

x² + 12x + 36 = 11 + 36

(x+6)(x+6) = 47

Both sides must be added with 36. I took the test : ) Hope it helps.

Answer:it is the 2 one

Step-by-step explanation: trust me

\(Answer:\large\boxed{y=\frac{2}{3} x+6}\)

Step-by-step explanation:

First let's convert 2x - 3y = 12 into \(y = mx + b\)  form.

In order to do this, solve for y.

\(2x-3y=12\)

\(-3y=-2x+12\)

\(y=\frac{2}{3} x-4\)

This shows us that the slope is   \(\boxed{\frac{2}{3}}\)

Now we use the point-slope formula:

\((y-y1)=m(x-x1)\)

where m is the slope and y1 and x1 are the point the line passes through

Using the point (-6,2) and slope, 2/3, we can find the equation:

\((y-2)=\frac{2}{3} (x-(-6))\)

\((y-2)=\frac{2}{3} (x+6)\)

\((y-2)=\frac{2}{3} x+4\)

\(\large\boxed{y=\frac{2}{3} x+6}\)

Answer:

➩ 2,250 envelopes.

Step-by-step explanation:

Given that, Nicole buys 125 envelopes per box for her home office.

Therefore, She will have 18*125 envelopes in all

So, 18*125 is 2,250 envelopes

The value of a $1000 investment at the end of 3 years, with 10% interest compounded annually, is approximately $1331.

Compound interest is a method of calculating interest on an initial amount of money, where the interest earned in each period is added to the principal, and subsequent interest is calculated based on the new total.

The formula for compound interest is given by:

\(A = P(1 + r/n)^{nt}\)

Where:

A is the future value or total amount including interest.

P is the principal or initial amount of money.

r is the annual interest rate (expressed as a decimal).

n is the number of times interest is compounded per year.

t is the number of years.

To find the value of a $1000 investment at the end of 3 years, we can substitute t = 3 into the given expression:

\(Value = 1000(1.1)^t\\Value = 1000(1.1)^3\\Value = 1000(1.331)\\Value \approx $1331\)

Therefore, the value of a $1000 investment at the end of 3 years, with 10% interest compounded annually, is approximately $1331.

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To solve the given first-order linear differential equation du/dt = Pu with initial condition u(0)=[53​], we can apply the matrix exponential method. The solution to this equation is given by u(t) = e^(Pt)u(0), where e^(Pt) is the matrix exponential.

Given the projection matrix P = [21​21​​21​21​​], we can compute e^(Pt) and then multiply it by the initial condition u(0) = [53​].

Since part of u(0) increases exponentially while the nullspace part stays fixed, this indicates that one eigenvalue of P is positive, causing exponential growth, while the other eigenvalue is zero, keeping the nullspace part constant.

To solve the equation du/dt=Pu, where P is a projection, we can use the fact that P is idempotent (P^2=P) and hence diagonalizable. Let's denote the eigenvalues of P by λ_1 and λ_2, and the corresponding eigenvectors by v_1 and v_2, respectively. Since P is a projection, we have λ_1=1 and λ_2=0, and v_1 is the direction of the part of u that increases exponentially, while v_2 is the direction of the nullspace part of u that stays fixed.

Using the eigendecomposition of P, we can write u(t)=c_1e^λ_1tv_1+c_2e^λ_2tv_2=c_1e^t v_1+c_2v_2, where c_1 and c_2 are constants determined by the initial conditions. Specifically, we have u(0)=c_1v_1+c_2v_2=[5/3 1/3]^T, which implies c_1=(5/3)v_1^T[5/3 1/3]=(5/3), and c_2=[5/3 1/3]^Tv_2=(1/3).

Therefore, the solution of the differential equation is u(t)=(5/3)e^t v_1+(1/3)v_2, which means that the part of u in the direction of v_1 increases exponentially with a rate of e^t, while the part of u in the direction of v_2 stays fixed. This is consistent with the given initial condition that part of u increases exponentially while the nullspace part stays fixed.

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Using proportions, it is found that the equivalent ratio to six-seconds would be of 3 to 1.

A proportion is a fraction of total amount, and the measures are related using a rule of three.

In this problem, six quarters are equivalent to two pennies. Dividing into two groups, there would be a penny in each group, and we want to find the amount of quarters.

The rule of three is:

2 pennies - 6 quarters

1 penny - x quarters

Applying cross multiplication:

\(2x = 6\)

\(x = \frac{6}{2}\)

\(x = 3\)

The equivalent ratio to six-seconds would be of 3 to 1.

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You can find the coefficient of variation for your data set using a TI-84 calculator by following the below steps.

To find the coefficient of variation (CV) using a TI-84 calculator, follow these steps:

1. Enter the data set values into a list on your calculator. For example, if your data is stored in the list L1, enter the values into L1.

2. Calculate the mean of the data set using the calculator's statistical functions. Press the [STAT] button and navigate to the "Calc" menu. Choose the appropriate mean function (e.g., "1-Var Stats" or "mean") and select the list that contains your data (e.g., L1).

3. Calculate the standard deviation of the data set using the calculator's statistical functions. Press the [STAT] button, navigate to the "Calc" menu, and choose the appropriate standard deviation function (e.g., "1-Var Stats" or "stdDev"). Select the list containing your data (e.g., L1).

4. Divide the standard deviation by the mean and multiply by 100 to calculate the coefficient of variation. Store the standard deviation and mean values in variables if necessary. Use the formula CV = (stdDev / mean) * 100 to calculate the coefficient of variation.

By following these steps, you can find the coefficient of variation for your data set using a TI-84 calculator.

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To find the coefficient of variation on a TI-84 Plus calculator, enter the dataset into a list, calculate the mean and standard deviation, and then divide the standard deviation by the mean and multiply by 100.

To find the coefficient of variation on a TI-84 Plus calculator, follow these steps:

By following these steps, you can find the coefficient of variation for a dataset using a TI-84 Plus calculator.

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A sample size of 20 people is often enough to get a good estimate of the population mean and standard deviation, provided that the sample is random and unbiased. Hence, measuring the pace of every 20th person who walks by is a good method to get a representative sample.

The method used to measure the walking pace of the people who walk by is: Selecting high pedestrian traffic places and then measuring the pace (in steps per minute) of every 20th person who walks by.

What is a high pedestrian traffic place?

A high pedestrian traffic place is a place where there is a large number of people who are walking at a certain time. For example, a busy sidewalk, a crowded market, or a train station. The researcher is interested in how fast people walk in different parts of the country. He wants to measure the pace of people in various parts of the United States. To do so, he randomly selects 50 cities and towns from all over the country and then finds a place with high pedestrian traffic in each city. Then he measures the pace of every 20th person who walks by. This method is used to get a representative sample of the people who walk in different parts of the country. Measuring the pace of every 20th person is done to make sure the random sample and not biased

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