Three polynomials are factored below but some coefficients and constants are missing. all of the missing values of a, b, c and d are integers. 1. x^2 +2x-8=(ax+b)(cx+d) 2. 2x^3+2x^2-24x=2x(ax+b)(cx+d) 3. 6x^2-15x-9=(ax+b)(cx+d) Fill in the table with the missing values of a,b,c and d.

Answer:The answer to the first question is b = 3.

The answer to the second question is t = 8.

The answer to the third question is m = 2 and n = 7.

The answer to the fourth question is y = 84.

The answer to the fifth question is b = 5 and c = 3.

Step-by-step explanation:

The Poisson distribution is a probability distribution that describes the number of independent occurrences of an event in a fixed interval of time or space.

In this case, the random variable is the number of occurrences during an interval. Therefore, the statement "the random variable is the number of occurrences during an interval" applies to the Poisson distribution. Another statement that applies to the Poisson distribution is "the probability of the event is proportional to the interval size". This means that the probability of observing k events in a fixed interval is proportional to the length of the interval. However, the statement "the probability of an individual event occurring is quite large" does not describe the Poisson distribution. In fact, the Poisson distribution assumes that the probability of an individual event occurring is small, but the number of events is large. Finally, the statement "the intervals do not overlap and are independent" is not a defining characteristic of the Poisson distribution, although it is often assumed in practical applications. In summary, the Poisson distribution is a probability distribution that models the number of independent occurrences of an event in a fixed interval. The probability of the event is proportional to the interval size, and the random variable is the number of occurrences during an interval.

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As you can see above the given polynomial simplified is equal to:

The leading coefficient is the coefficient of the term of highest degree.

The term with highest degree in the given polynomial is:

Explanation:  effective interest rate equivalent to a nominal rate of 10% compounded monthly 10.47%

Answer: 10.47%

A complex fraction is a fraction that contains fractions in its numerator, denominator, or both. The simplified complex fraction is 2/5.

To simplify the given complex fraction 2/(x+y) divided by 5/(x+y), you can multiply the numerator of the first fraction by the reciprocal of the denominator of the second fraction.

Recall that dividing by a fraction is equivalent to multiplying by its reciprocal.

So, we have:

(2/(x + y)) / (5/(x + y)) = (2/(x + y)) * ((x + y)/5)

So, the simplified expression is (2/(x+y)) * ((x+y)/5).

Now, we can simplify further by canceling out the common factor of (x + y) in the numerator and denominator:

resulting in 2/5.

Therefore, the simplified complex fraction is 2/5.

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c) 0.01

To Write percentage in decimal or fraction we divide it by 100

therefore,

\(\begin{gathered}\\\implies\quad \sf 2\% = \frac{2}{100} \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf 2\% = 0.02 \\\end{gathered} \)

Half of 0.02 = \(\sf\frac{1}{\cancel2} \times\cancel{0.02}\)

\(\implies\boxed {0.01}\)

Half of 2 percent written as a decimal is 0.01

Paul jumps  63 inches further than the other person.

To find this, we need to find the difference between the two lengths,

We know that someone jumps 2 yards and 9 inches.

And Paul jumps 4 yards.

Let's convert the two lengths to inches, we know that:

1 yard = 36 inches

Then:

2 yards=  2*36 in = 72 inches.

4 yards = 4*36 in = 144 inches.

So we can rerwrite:

Someone jumps 72 in + 9 in = 81 inches.

Paul jumps 144 inches.

The difference is:

144 in - 81in = 63 in

That is the answer.

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Answer:

JK = 39

Step-by-step explanation:

HJ and JK are segments of line segment HK, so they must add up to the length of KH.

HJ + JK = HK

By substituting in the values of each line segment, we can solve for t.

(4t - 15) + (5t - 6) = 15

9t - 21 = 15

9t = 36

t = 9

Now that we have t, we can plug it in in order to find the value of JK.

JK = 5t - 6

5(9) - 6

45 - 6

39

JK = 39

The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.

From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"

Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.

In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.

Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.

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To find the equation of the tangent line to the curve y = tan²(2x) at x = π/4, we need to determine the slope of the tangent line at that point and then use the point-slope form of a line to write the equation.

First, let's find the derivative of y with respect to x. Using the chain rule, we have:

dy/dx = 2tan(2x) sec²(2x).

Now, let's substitute x = π/4 into the derivative:

dy/dx = 2tan(2(π/4)) * sec²(2(π/4))

      = 2tan(π/2) * sec²(π/2)

      = 2(∞) * 1

      = ∞.

The derivative at x = π/4 is undefined, indicating that the tangent line at that point is vertical. Therefore, the equation of the tangent line is x = π/4. Note that the equation y = 2/tan(2x) (sec²(2x) + 1/2) is not the equation of the tangent line, but rather the equation of the curve itself. The tangent line, in this case, is vertical.

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Answer:

x = 3

Step-by-step explanation:

1) Divide both sides by -2.

\(6^x=\frac{-432}{-2}\)

2) Two negatives make a positive.

\(6^x=\frac{432}{2}\)

3) Simplify \(\frac{432}{2}\) to 216.

\(6^x=216\)

4) Convert both sides to the same base.

\(6^x=6^3\)

5)  Cancel the base of 6 on both sides.

x = 3

\(\huge\text{Hey there!}\)

\(\huge\textbf{Equation:}\)

\(\mathbf{-2(6)^x = -432}\)

\(\huge\textbf{DIVIDE -2 to BOTH SIDES:}\)

\(\mathbf{\dfrac{-2(6^x)}{-2} = \dfrac{-432}{-2}}\)

\(\huge\textbf{SIMPLIFY IT!}\)

\(\mathbf{6^x = 216}\)

\(\huge\textbf{Solve for the current exponent:}\)

\(\mathbf{6^x = 216}\)

\(\huge\textbf{Log them:}\)

\(\mathbf{Log \ 6^x = log = 216}\)

\(\huge\textbf{Take the log to both of the sides:}\)

\(\mathbf{x \times log (6) = log(216)}\)

\(\huge\textbf{Convert it:}\)

\(\mathbf{x = \dfrac{log(216)}{log(6)}}\)

\(\huge\textbf{SIMPLIFY IT!}\)

\(\mathbf{x = 3}\)

\(\huge\textbf{Answer:}\)

\(\huge\boxed{\mathsf{x = 3}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer: it equals A

Step-by-step explanation:

The Moellers had 1,500 miles remaining to reach their destination. On the first day, the Moellers drove 1/2 (or 0.5) of the 3,000 miles, which is 1,500 miles. This means they had 1,500 miles remaining to reach their destination.

On the second day, they drove 1/4 (or 0.25) of the remaining 1,500 miles, which is 375 miles. Therefore, they had 1,125 miles remaining to reach their destination after driving 1/2 on the first day and 1/4 on the second day.

Based on the given information, the Moellers drove 1/3 of the distance on the first day and 1/4 of the remaining distance on the second day. Let's calculate the remaining distance to reach their destination:

Total distance: 3,000 miles

First day: 1/3 of 3,000 miles = 1,000 miles

Remaining distance after the first day: 3,000 - 1,000 = 2,000 miles

Second day: 1/4 of 2,000 miles = 500 miles

Remaining distance after the second day: 2,000 - 500 = 1,500 miles

So, the Moellers had 1,500 miles remaining to reach their destination.

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Answer:

7 and 1

Step-by-step explanation:

x+y=8

x-y=6

solve this

Answer:

The answer to your question is 18

Step-by-step explanation:

Process

1.- Write the fraction given

              \(\frac{-108}{-6}\)

2.- Divide the numbers as usual

               18

         6  108

               48

                 0

3.- Divide the signs

      negative / negative = positive

4.- Write the answer

        \(\frac{-108}{-6}= 18\)

5.- Check the result

Multiply 18 by -6 and the result must be -108

       -6 x 18 = 108

We know a negative times a negative is equal to a positive.

- 108 / - 6      is the same as 108 / 6     because the larger number is on top.

Therefore she can drop the negative signs and solve 108/6 to verify her answer.

Answer:

1155.0

Step-by-step explanation:

The accumulated value of the investment of $15,000 for 4 years at an interest rate of 5% is approximately $18,319.41 when compounded semiannually, $18,404.43 when compounded quarterly, $18,483.23 when compounded monthly, and $18,500.56 when compounded continuously.

What is compound interest?

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

We can use the formula for the accumulated value of an investment, which is:

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

where:

A is the accumulated value (or future value) of the investment

P is the principal (or present value) of the investment, which is $15,000 in this case

r is the annual interest rate as a decimal, which is 0.05 (since the interest rate is 5%)

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

t is the number of years

(a) Compounded semiannually:

If the investment is compounded semiannually, then n = 2 (twice a year) and t = 4 years. Substituting these values into the formula, we get:

\(A = $15,000(1 + 0.05/2)^{(2*4)}\)

A  ≈ $18,319.41

So the accumulated value of the investment, compounded semiannually, is approximately $18,319.41.

(b) Compounded quarterly:

If the investment is compounded quarterly, then n = 4 (four times a year) and t = 4 years. Substituting these values into the formula, we get:

\(A = $15,000(1 + 0.05/4)^{(4*4)}\)

≈ $18,404.43

So the accumulated value of the investment compounded quarterly, is approximately $18,404.43.

(c) Compounded monthly:

If the investment is compounded monthly, then n = 12 (twelve times a year) and t = 4 years. Substituting these values into the formula, we get:

\(A = $15,000(1 + 0.05/12)^{(12*4)}\) ≈ $18,483.23

So the accumulated value of the investment, compounded monthly, is approximately $18,483.23.

(d) Compounded continuously:

If the investment is compounded continuously, then n approaches infinity and the formula becomes:

\(A = Pe^{(rt)}\)

Substituting the given values into the formula, we get:

\(A = $15,000e^{(0.05*4)}\)

≈ $18,500.56

So the accumulated value of the investment, compounded continuously, is approximately $18,500.56.

Therefore, the accumulated value of the investment of $15,000 for 4 years at an interest rate of 5% is approximately $18,319.41 when compounded semiannually, $18,404.43 when compounded quarterly, $18,483.23 when compounded monthly, and $18,500.56 when compounded continuously.

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The answer is 406 apples.

2436 apples divided by 6 boxes gives you the number of apples in each box.

Answer:

assuming that the problem was actually

-1/12 x ^ 2 + 2x + 4

height = 16

(12,16)

forty feet (40) feet

vertex = -b/2a = -2/(-1/6) = 12

f(12) = - 144/ 12 + 24 + 4 = -12+ 24 + 4   = 16

Step-by-step explanation:

An expression for the change she will receive is 8b - 100 = 100

You should be aware that an expression in math is a sentence with a minimum of two numbers or variables and at least one math operation

The given parameters are

Nathan buys 9 items

She gives the cashier $100

The expression 8(b) -100 = 100%

Where 100 is the full amount payable

Therefore, the expression becomes 8b -100=100

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The transformation from the parent function is a translation by 1 unit right and 3 units up

From the question, we have the following function that can be used in our computation:

f(x) = x²

f(x) = (x − 1)² + 3

First, we have the transformation to be:

From f(x) = x² to f(x) = (x − 1)²

This means the function is translated right by 1 unit

Next, we have:

From f(x) = (x − 1)² to f(x) = (x − 1)² + 3

This means the function is translated up by 3 units

Hence, the transformation is 1 unit right and 3 units up

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Range of function is {5, 4, 3, 2, 1, 0,1} and the function is monotonous.

A function is a mathematical expression that state the relationship between an independent variable and a dependent variable. The value of independent variable is called domain and the value of dependent variable is called range.

given, a function f(x) = √ (x² - 4x +4)

now for every input value of x we will get an output value for f(x).

we select the domain of function as x = {-3, -2, -1, 0, 1, 2, 3}

when we put the x value in the function, we get f(-3) = √[(-3²) - 4×(-3)+4]

                                                                            f(-3) = √25 =5

     similarly, f( -2) = 4

                            f(-1) = 3

                             f(0) = 2

                               f(1) = 1

                            f(2) =0

                           f(3) = 1

the range of function is {5, 4, 3, 2, 1, 0,1}

The range of function indicates that it is neither increasing nor decreasing.

hence the function is a monotonous function.

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Answer:

Y= 1/2x-5

Step-by-step explanation:

Answer:

Approximately \(58.2\; \text{nautical miles}\) (assuming that the bearing is \({\rm S$29^{\circ}$W}\).)

Step-by-step explanation:

Let \(v\) denote the speed of the ship, and let \(t\) denote the duration of the trip. The magnitude of the displacement of this ship would be \(v\, t\).

Refer to the diagram attached. The direction \({\rm S$29^{\circ}$W}\) means \(29^{\circ}\) west of south. Thus, start with the south direction and turn towards west (clockwise) by \(29^{\circ}\) to find the direction of the displacement of the ship.

The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of \(v\, t\). The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly \(29^{\circ}\).

Since the hypotenuse is of length \(v\, t\), the dashed line segment opposite to the \(\theta = 29^{\circ}\) vertex would have a length of:

\(\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}\).

Substitute in \(\begin{aligned} v &= 20\; \frac{\text{nautical mile}}{\text{hour}}\end{aligned}\) and \(t = 6\; \text{hour}\):

\(\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}\).

The simple exponential smoothing model can be best described as (B) "an expression combining the most recent forecast and actual data value". B is the correct answer.

Simple exponential smoothing is a time series forecasting technique that creates predictions using a weighted average of previous observations. As the observations get older, the weights decrease exponentially. The forecast for the next period is created by fusing the most recent forecast with the most recent actual data value using the smoothing parameter alpha. This can be mathematically stated as:

F_t+1 = αY_t + (1-α)F_t

where F_t is the forecast for period t, Y_t is the actual value for period t, α is the smoothing parameter, and F_t+1 is the forecast for period t+1.

Option B is the correct answer.

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Answer:

Step-by-step explanation:

<5=75

<11=75

<16=65

Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

One product/service that is currently in the decline stage is DVD rentals. The decline can be attributed to the rapid rise of digital streaming platforms and the decreasing popularity of physical media. Companies competing in a declining market have strategic options such as harvesting and divesting. Harvesting involves maximizing profits from the declining product/service by reducing costs and maintaining a loyal customer base, while divesting involves exiting the market and reallocating resources to more profitable ventures.

DVD rentals are in the decline stage of the product lifecycle due to several factors. The advent of digital streaming platforms like Netflix, Hulu, and Amazon Prime Video has revolutionized the way people consume media. The convenience and vast content libraries offered by these platforms have led to a significant decline in DVD rentals. Moreover, the proliferation of high-speed internet connections and the increasing availability of streaming devices have made it easier for consumers to access digital content.

In a declining market, companies have strategic options to consider. One option is harvesting, which involves maximizing profits from the declining product/service. Companies can achieve this by reducing costs associated with production, distribution, and marketing, as the demand for the product/service diminishes. They may also focus on retaining their loyal customer base by providing incentives, discounts, or exclusive offers. For example, DVD rental companies may lower rental fees, offer bundle deals, or introduce loyalty programs to retain their remaining customers.

Another strategic option is divesting, which involves exiting the declining market altogether. Companies may choose to reallocate their resources to more profitable ventures or invest in emerging technologies or industries. In the case of DVD rentals, companies could divest by shutting down physical rental stores and selling off their DVD inventory. They could then shift their focus to digital streaming services or invest in other areas with growth potential, such as content production or streaming device manufacturing.

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The root of the equation \(\(f(x) = x^3 - 3x - 1\)\) between -1 and 1, after the second iteration of the False Position method, is approximately -1.

The False Position method involves finding the x-value that corresponds to the x-intercept of the line passing through \(\((a, f(a))\)\) and \(\((b, f(b))\),\)where (a) and (b) are the endpoints of the interval.

Let's begin the iterations:

Iteration 1:

\(\(a = -1\), \(f(a) = (-1)^3 - 3(-1) - 1 = -3\)\)

\(\(b = 1\), \(f(b) = (1)^3 - 3(1) - 1 = -3\)\)

The line passing through (-1, -3) and (1, -3) is (y = -3). The x-intercept of this line is at (x = 0).

Therefore, the new interval becomes [0, 1] since the sign of f(x) changes between\(\(x = -1\) and \(x = 0\).\)

Iteration 2:

\(\(a = 0\), \(f(a) = (0)^3 - 3(0) - 1 = -1\)\)

\(\(b = 1\), \(f(b) = (1)^3 - 3(1) - 1 = -2\)\)

The line passing through\(\((0, -1)\) and \((1, -2)\) is \(y = -x - 1\)\). The x-intercept of this line is at (x = -1).

After the second iteration, the new interval becomes [-1, 1] since the sign of f(x) changes between (x = 0) and (x = -1).

Therefore, the root of the equation \(\(f(x) = x^3 - 3x - 1\)\) between -1 and 1, after the second iteration of the False Position method, is approximately -1.

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