Identify which factoring pattern each of the following polynomials fit:
[] y^2 + 12y - 36
[] x^2 + 121
[] x^2 - 6x + 9
[] y^2 - 64
[] 9x^2 - 121
[] 4y^2 + 20y + 25

1. Perfect Square Trinomial
2. Difference of Squares
3. Neither

To calculate the probability of getting exactly one pair and one three-of-a-kind in Yahtzee, we need to consider the number of ways we can achieve this outcome divided by the total number of possible outcomes when tossing five dice.

1. Calculate the number of ways to obtain one pair:

  There are 6 possible values for the pair (1, 2, 3, 4, 5, 6), and for each value, we have 6 choose 2 ways to select the two dice for the pair. Therefore, there are 6 * (6 choose 2) = 6 * 15 = 90 ways to obtain one pair.

2. Calculate the number of ways to obtain a three-of-a-kind:

  Again, there are 6 possible values for the three-of-a-kind (1, 2, 3, 4, 5, 6), and for each value, we have 6 choose 3 ways to select the three dice for the three-of-a-kind. Therefore, there are 6 * (6 choose 3) = 6 * 20 = 120 ways to obtain a three-of-a-kind.

3. Calculate the total number of possible outcomes when tossing five dice:

  Each of the five dice can take on 6 possible values, so there are 6^5 = 7776 possible outcomes when tossing five dice.

4. Calculate the probability:

  The probability of getting exactly one pair and one three-of-a-kind is given by the number of favorable outcomes divided by the total number of possible outcomes:

  Probability = (Number of ways to obtain one pair) * (Number of ways to obtain a three-of-a-kind) / (Total number of possible outcomes)

             = 90 * 120 / 7776

             = 1,080 / 7776

             = 0.1389 (rounded to four decimal places)

Therefore, the probability of seeing exactly one pair and one three-of-a-kind in Yahtzee is approximately 0.1389 or 13.89%.

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Answer:

y=-1/6x-2

Step-by-step explanation:

Lets find the slope of the given line

6x-7=y,m=6

The slope of the perpendicular line would be=-1/6

Using the point-slope form y-y1=m(x-x1)

y--1=-1/6(x--6)

y+1=-1/6(x+6)

6y+6=-x-6

6y=-x-6-6

6y=-x-12

y=-1/6x-2

The five dealers included in the sample are: Dealer 02: 05, Dealer 06: 28, Dealer 09: 38, Dealer 03: 08, Dealer 11: 66

To select a random sample of five dealers from the given random numbers, we need to use a method known as random sampling without replacement, which ensures that no dealer is selected more than once.

Here are the steps to select a random sample of five dealers from the given random numbers:

Step 1: List all the dealers using the given random numbers in ascending order.02, 05, 08, 20, 21, 28, 29, 31, 38, 49, 59, 66

Step 2: Assign each dealer a number between 01 and 12. Dealer 01 corresponds to 02, dealer 02 corresponds to 05, dealer 03 corresponds to 08, and so on.

Step 3: Generate five random numbers between 01 and 12 using a random number generator or by drawing numbers from a hat. For instance, let's assume that the five random numbers we get are 02, 06, 09, 03, and 11.02 corresponds to dealer 05, 06 corresponds to dealer 28, 09 corresponds to dealer 38, 03 corresponds to dealer 08, and 11 corresponds to dealer 66.

Therefore, the five dealers included in the sample are: Dealer 02: 05, Dealer 06: 28, Dealer 09: 38, Dealer 03: 08, Dealer 11: 66

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Answer:

c 52

Step-by-step explanation:

x=10

4 ×10=40

40+12=52

Based on the given information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own graphing TI calculators so it can be estimated that the proportion of students who do not own a TI graphing calculator is 50%.

To estimate the proportion of students who do not own a TI graphing calculator, we can use the information provided that out of the 4 students who owned a TI calculator, 2 had graphing calculators. Since we know that all graphing calculators are TI calculators, we can assume that the 2 students with graphing calculators are included in the total count of students who own TI calculators. Therefore, the remaining 2 students who own TI calculators must have non-graphing calculators.

Based on this information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own non-graphing TI calculators. Therefore, we can estimate that the proportion of students who do not own a TI graphing calculator is 50%.

It's important to note that this is an estimation based on the limited information provided. To obtain a more accurate estimate, a larger sample size or more comprehensive data would be needed. Additionally, this estimation assumes that the sample of 4 students is representative of the entire student population in terms of calculator ownership. If there are any biases or limitations in the sampling method or if the sample is not representative, the estimate may not accurately reflect the true proportion of students who do not own a TI graphing calculator.

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Answer:

First, get it into slope-intercept:

y = -3/5x + 4/5

The slope is -3/5

Step-by-step explanation:

Answer:

\(\displaystyle x \approx 9.2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:  

Step 1: Define

Angle θ = 35°

Opposite leg = x

Hypotenuse = 16

Step 2: Solve for x

The line a is an illustration of a proportional linear equation, and the equation of line a is y = 1.4x

The line a passes through the following points:

(x,y) = (0,0) and (1.3, 1.82(

The above means that line a is a proportional linear equation

The constant of proportionality (k) is calculated using:

k = y/x

Using the values on the table, we have:

k = 1.82/1.3

Divide

k = 1.4

Substitute k = 1.4 in k = y/x

y/x = 1.4

Multiply both sides by 1.4

y = 1.4x

Hence, the equation of the line a is y = 1.4x

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a. The inverse of the function f(x) is obtained as option A - \(f^{-1}(x) = \frac{(x - 4)}{3}\) for all x.

b. The equation is verified as \(f(f^{-1}(x)) = x\) and \(f^{-1}(f(x)) = x\) is proved.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

a. To find the inverse function of f(x) = 3x + 4, we can follow these steps -

Step 1: Replace f(x) with y: y = 3x + 4.

Step 2: Solve for x in terms of y: x = (y - 4) / 3.

Step 3: Replace x with \(f^{-1}(x): f^{-1}(x) = \frac{(x - 4)}{3}\).

Therefore, the equation for \(f^{-1}(x)\) is \(f^{-1}(x) = \frac{(x - 4)}{3}\) for all x.

b. To verify that the expression for \(f^{-1}(x)\) is correct, we need to show that \(f(f^{-1}(x)) = x\) and \(f^{-1}(f(x)) = x\) for all values of x.

\(f(f^{-1}(x))\) = f[(x - 4) / 3]

= 3[(x - 4) / 3] + 4

= x - 4 + 4

= x.

Therefore, \(f(f^{-1}(x)) = x\).

\(f^{-1}(f(x))\) = [(3x + 4) - 4] / 3

= x / 3.

Therefore, \(f^{-1}(f(x)) = x\).

Since we have shown that \(f(f^{-1}(x)) = x\) and \(f^{-1}(f(x)) = x\) for all values of x, we can conclude that the equation for \(f^{-1}(x)\) is correct.

Therefore, the equation \(f^{-1}(x)\) is the correct solution.

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Answer:

Below

Step-by-step explanation:

You didn't include the picture......

each cube has a volume of  1/4 * 1/4 * 1/4 = 1/64 cm^3

     count the total number of cubes and multiply by  1/64

                                         to get volume in cm^3

The set of parametric equations for the line is:

x = -13 - t

y = 1 - √(3)t

z = 3 + 2t

To find the set of parametric equations for the line tangent to the space curve r(t) = (-2 sin t, 2 cos t, 4 sin t) at the point P(-13, 1, 3), we need to find the derivative of r(t) and evaluate it at t = t₀, where t₀ is the value of t that corresponds to the point P.

The derivative of r(t) is:

r'(t) = (-2 cos t, -2 sin t, 4 cos t)

To find t₀, we need to solve the equation r(t₀) = P:

(-2 sin t₀, 2 cos t₀, 4 sin t₀) = (-13, 1, 3)

From the second component, we can see that cos t₀ = 1/2, which means t₀ = π/3 or t₀ = -π/3.

Substituting t₀ = π/3 into r'(t), we get:

r'(π/3) = (-2 cos(π/3), -2 sin(π/3), 4 cos(π/3)) = (-1, -sqrt(3), 2)

So the line tangent to the space curve at P has direction vector (-1, -√(3), 2), which means the set of parametric equations for the line is:

x = -13 - t

y = 1 - √(3)t

z = 3 + 2t

where t is a parameter that varies along the line.

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Answer:

135

Step-by-step explanation:

the triangle is 90-45-45

the square is 90-90-90-90

where the two meet just add 45 + 90

135

The opposite of being short $4.28 would be having $4.28 or more. That is a surplus or extra of $4.28.

Surplus refers to an amount or quantity that is left over or in excess of what is needed or used. It can refer to various things, such as:

In finance, a surplus refers to an excess of revenue over expenses, or an excess of assets over liabilities. It means having more of something than is necessary or expected.

Therefore, the opposite of being short $4.28 would be having $4.28 or more. This is often referred to as having a surplus or extra of $4.28.

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The value of the sum of squares due to regression (SSR) is 17.43.

Certainly! In statistics, the sum of squares is a measure that quantifies the variability or dispersion of data points around a certain value. It is commonly used in regression analysis to assess how well a regression line or model fits the observed data.

The total sum of squares (SST) represents the total variability in the dependent variable, which is the sum of the squared differences between each data point and the overall mean of the dependent variable. It is a measure of the total deviation of the data points from the mean.

The sum of squares due to error (SSE), also known as the residual sum of squares, represents the unexplained variability in the dependent variable after accounting for the regression model. It is calculated by summing the squared differences between the observed values and the predicted values from the regression model.

The sum of squares due to regression (SSR), also known as the explained sum of squares, represents the variability in the dependent variable that can be attributed to the regression model. It is calculated by subtracting the SSE from the SST.

In the given scenario, the SST is 23.32 and the SSE is 5.89. By subtracting the SSE from the SST, we obtain the SSR. Substituting the values:

SSR = SST - SSE

   = 23.32 - 5.89

   = 17.43

Therefore, the value of the sum of squares due to regression (SSR) is 17.43.

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Answer:

13

Step-by-step explanation:

2(x – 3) + 3y

Let x=5 and y = 3

2(5 – 3) + 3*3

Parentheses first

2(2) +3*3

Multiply

4+9

Add

13

Answer:

y = - 2x + 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{1}{2} \) x - 1 ← is in slope- intercept form

with slope m = \(\frac{1}{2} \)

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular} \) = - \(\frac{1}{m} \) = - \(\frac{1}{\frac{1}{2} } \) = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute (5, - 1 ) into the partial equation

- 1 = - 10 + c ⇒ c = - 1 + 10 = 9

y = - 2x + 9 ← equation of perpendicular line

In order to write 4/6 as 2/3 we would break apart pieces and to write 4/6 as 8/12 we would combine pieces.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below.

In order to write 4/6 as 2/3 we have to express in its simplest form. This means that you have to divide 4/6 by 2. In order to write 4/6 as 8/23, multiply 4/6 by 2.

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Answer:

False

Step-by-step explanation:

I believe it's false because both triangle have the exact same measurements, they would have to be congruent

Answer:

B. False

Step-by-step explanation:

Did the quiz.

Step-by-step explanation:

expand and multiply the terms

Answer:

The correct answer option is 192

Step-by-step explanation:

We are given the results of a random survey about the preferred service for streaming movies.

We are to find the number of people we would expect to prefer Company B.

Number of people using service B = 32

Total number of people = 125

Number of people expected to prefer Company B =32/125 x 750  = 192

Answer:

d percent=d÷mp×100%

Step-by-step explanation:

72000÷36

write Ans your self please

Answer:

selling price after the discount is = Rs (3200 -480)

= Rs 2720

Answer:

Finding slope: y2-y1/x2-x1

3-9/1+2

=-6/2

Divide 2 from both

=-3/1 or -3

Slope= -3

Finding y-intercept= y=mx+b

Choose any point on the line to plug in the x and the y then plug in the slope.

I choose (1,3)

3=-3×1+b

3=-3+b

Add 3 to both sides

6=b

Y-intercept=6

Equation: y=-3x+6

Step-by-step explanation:

Answer:

A scalar quantity is defined as the physical quantity with only magnitude and no direction.

a) The first 4 terms of the sequence n + 5 are 6, 7, 8, and 9. The 10th term is 15.

b) The first 4 terms of the sequence 2n - 1 are 1, 3, 5, and 7. The 10th term is 19.

a) n + 5

The given sequence is n + 5. We can find the first 4 terms by substituting the values of n from 1 to 4.

Then we can find the 10th term by substituting n = 10.

1st term = n + 5 = 1 + 5 = 6

2nd term = n + 5 = 2 + 5 = 7

3rd term = n + 5 = 3 + 5 = 8

4th term = n + 5 = 4 + 5 = 9

10th term = n + 5 = 10 + 5 = 15.

So, the first 4 terms of the sequence n + 5 are 6, 7, 8, and 9. The 10th term is 15.

b) 2n - 1.

The given sequence is 2n - 1. We can find the first 4 terms by substituting the values of n from 1 to 4. T

hen we can find the 10th term by substituting n = 10.

1st term = 2n - 1 = 2(1) - 1 = 1

2nd term = 2n - 1 = 2(2) - 1 = 3

3rd term = 2n - 1 = 2(3) - 1 = 5

4th term = 2n - 1 = 2(4) - 1 = 7

10th term = 2n - 1 = 2(10) - 1 = 19.

So, the first 4 terms of the sequence 2n - 1 are 1, 3, 5, and 7. The 10th term is 19.

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Answer:

=>A. -6x - 4

Step-by-step explanation:

=>-4(x + 2) - 2x + 4

=> -4x-8-2x+4

=> -6x-4

Answer:

38.6 sq ft

Step-by-step explanation:

This composite figure consists of a trapezoid and a triangle on top

A(trapezoid) = 1/2h(sum of bases)

= 1/2(3.6)(7+9)

= 8(3.6)

= 28.8

A(triangle) = 1/2bh

base = 7

height = 6.4-3.6 which is 2.8

A = 1/2(7)(2.8)

= 3.5(2.8)

= 9.8

28.8 + 9.8 = 38.6

The correct option b. 0.004629 for  the probability of observing a 1 three times in a row.

Probability of an event = (Number of favorable events) /   (total number of event).

P(B) = (Event B) / (total number of event).

The number of times the dice are rolled has no bearing on the outcome of the roll.

The likelihood of receiving 1 is 1/6.

The likelihood of obtaining 1 three times in a row is equal to the likelihood of getting 1 the first time, the second time, and the third time.

Receiving 1 three times in succession has a probability;

= 1/6 x 1/6 x 1/6

= 1/216.

As a result, there is a 0.463% chance that you'll get 1 three times in a row.

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Answer:

0.04 mol/ Liter

Step-by-step explanation:

If you have 8.1 grams of NaOH in 5 L of solution, what is the molarity? (Round answers to the nearest hundredth)

The formula for molarity = Number of moles/ Volume in Liters

Step 1

Find the Number of moles of NaOH

We find the Molar mass of NaOH

Na = 23, O = 16, H = 1

Molar mass = 23 + 16 + 1 = 40 g/mol

Grams of NaOH in the solution = 8.1 grams

Number of moles = Mass/Molar mass

= 8.1 g/40 g/mol

= 0.2025 moles

Step 2

Molarity = 0.2025moles/ 5 L

= 0.0405 mol/ Liter

Approximately = 0.04 mol/L