Solve the equation.
x² - x - 6 = 0

Probability that exactly 20 will be in the interval 0.5 to 0.75 Is about 7.8%

To find the probability that exactly 20 random numbers will be in the interval 0.5 to 0.75, we need to use the binomial distribution formula. Let p be the probability of a number falling in the interval (0.5 to 0.75), which is 0.25. Let n be the total number of random numbers generated, which is 100.

We want exactly 20 of these numbers to fall within the interval (0.5 to 0.75). Therefore, using the binomial distribution formula, we get: P(X = 20) = (100 choose 20) * (0.25)^20 * (0.75)^80

Using a binomial calculator, we find that P(X = 20) is approximately 0.078, or 7.8%. This means that if we generate 100 random numbers over the interval 0 to 1 many times, we can expect to see exactly 20 of them fall within the interval (0.5 to 0.75) about 7.8% of the time.

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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\(y=x+3\) for x

Flip the equation:

\(x+3=y\)

Add -3 to both sides:

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

\(\fbox{x = y - 3}\)

__________________________________________________________

\(x-2y=-1\) for y

Add -x to both sides:

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

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

Divide both sides by -2:

\(\dfrac{-2y}{-2} =\dfrac{-x-1}{-2}\)

\(\fbox{y = $\dfrac{1}{2}x+ \dfrac{1}{2} $}\)

The number of inches of wire that can be bought for 45 cents is 0.15 inches.

Given that 18 inches of wire costs 54 cents. We are to find how many inches of wire can be bought for 45 cents, at the same rate.

Let's consider the cost of one inch of wire = $54/18

= $3/1

Now, we need to find the number of inches of wire can be bought for 45 cents.

$3/1

$0.45/x = 3/1  

(cross-multiplication)

⇒ $x = (0.45 × 1)/3

= 0.15 inches

Therefore, the number of inches of wire that can be bought for 45 cents is 0.15 inches.

Note: We have converted the price of 18 inches of wire into 1 inch of wire so that we can compare the rate of both.

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The probability that more than 72% of the sampled UCF students will vote in the presidential election is approximately 0.0475 or 4.75%.

To calculate the probability that more than 72% of the sampled UCF students will vote in the presidential election, we need to use the normal distribution approximation since the sample size is large.

First, we find the mean (μ) and standard deviation (σ) of the sampling distribution using the given population proportion (p) of 0.70 and the sample size (n) of 1250:

μ = p = 0.70

σ = √(p(1-p)/n) = √(0.70 * 0.30 / 1250) ≈ 0.012

Next, we need to standardize the desired proportion of more than 72% (0.72) using the z-score formula:

z = (x - μ) / σ

z = (0.72 - 0.70) / 0.012 ≈ 1.67

Now, we can find the probability using the standard normal distribution table or calculator. The probability that more than 72% of the sampled students will vote in the presidential election is the area under the curve to the right of the z-score of 1.67.

Using the standard normal distribution table or calculator, we find that the probability is approximately 0.0475.

Therefore, the probability that more than 72% of the sampled UCF students will vote in the presidential election is approximately 0.0475 or 4.75%.

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The reduced gradient is analogous to the residual for linear models.

In linear regression, the residual represents the difference between the observed values and the predicted values of the dependent variable. Similarly, in optimization, the reduced gradient represents the difference between the current solution and the optimal solution. It is a measure of how far the current solution is from the optimal solution in the direction of the search. By minimizing the reduced gradient, we can move closer to the optimal solution.

The reduced gradient is a widely used optimization technique in non-linear programming that allows for efficient computation of the descent direction at each iteration while accounting for constraints. It involves calculating a partial derivative of the objective function with respect to the variables that are not restricted by the constraints, and then projecting the resulting gradient onto the space defined by the constraints. The resulting vector is called the reduced gradient, and it points in the direction of the steepest descent that is feasible.

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Answer:

she can buy 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Therefore,

NOTE: n can't be equal to a negative number

hence n=20

Answer:

2, -7, 3 are your answers! :).

Step-by-step explanation:

The opposite of a positive would be it's negative form, and the opposite of a negative would be it's positive form.

The answer obtained from multiplying the measurements 64.49 and 6.57 is 423.70.

According to the rules governing significant figures, the result of a multiplication or division should have the same number of significant figures as the measurement with the fewest significant figures.

In this case, both measurements, 64.49 and 6.57, have four significant figures each. When multiplied together, the result is 423.6993. However, since the measurement 6.57 has the fewest significant figures, the final answer should be rounded to match that.

Therefore, the answer is rounded to three decimal places, resulting in 423.700. The zero at the end is included to indicate that the measurement is known to that level of precision.

Hence, considering the rules of significant figures, the answer obtained from multiplying the measurements 64.49 and 6.57 is 423.700.

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Answer:

Four (4) terms.

Step-by-step explanation:

36x³ + 27x² - \(18x^{1}\) - \(9x^{0}\)

The gives four terms.

Answer:

Hopefully this can help

Step-by-step explanation:

Answer:

\(3x^{2} (x+5)(x-5)\)

Step-by-step explanation:

Answer:

Barbados won the Bronze.

Step-by-step explanation:

The information indicates that Jamaica finished before Barbados, but behind Trinidad which means that Trinidad was the first one, then Jamaica and the third one was Barbados:

1. Trinidad

2. Jamaica

3. Barbados

Then, it indicates that Haiti finished before Guyana, but behind Barbados which indicates that Haiti was in 4th place after Barbados and  the last one was Guyana:

1. Trinidad

2. Jamaica

3. Barbados

4. Haiti

5.Guyana

According to this, the answer is that Barbados won the Bronze.

Answer:

4²+b² = 5²

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to find the length of the missing side.

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.  Algebraically, this is represented as

a²+b² = c²

We have the measure of one leg, 4 in.  We also have the measure of the hypotenuse, 5 in.  This gives us

4²+b² = 5²

I hope this helps <3

Answer:

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

Step-by-step explanation:

y - 3 = (1/2)(x - 1)

Distribute the 1/2

y - 3 = (1/2)x - 1/2

Add 3 to both sides

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

Answer:

10- It is linear and the constant of proportionality is $6

11- x-intercept(s): (5,0)

y-intercept(s): (0,−2)

12- y-intercept(s): (0,3)

Slope: -2

13- B) 2/3

14- C) 2

Answer: Since −3x does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3x to both sides.

y=5x−7

−2y=3x−12

Divide each term in the equation by −2.

y=5x−7

y=−3x/2+6

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

(2,3)

Answer:

582 dance songs

194 rock songs

301 country songs

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation: its just the answer lol

a. The congruent angles to angle 1 are given as follows: <7, <3 and <5.

b. The supplementary angles to angle 1 are given as follows: <2, <8, <4 and <6.

Two angles are classified as congruent when they have the same angle measure.

Hence the congruent angles to angle 1 are given as follows:

Two angles are called supplementary when the sum of their measures is of 180º, hence the supplementary angles to angle 1 are given as follows:

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The given differential equation does not have a unique solution with the initial condition y(0) = 1. The lack of uniqueness is due to the presence of a non-zero term (4y²) involving the dependent variable y, which introduces multiple possible solutions.

The given differential equation is a first-order ordinary differential equation of the form v/(x) = 2² + 4x + 4y² - 1. To determine whether a unique solution exists, we need to analyze the coefficients and terms involved.

Since the term 4y² is present in the equation, it introduces a non-linearity. When solving a differential equation with non-linear terms, multiple solutions can arise. In this case, due to the presence of the non-linear term 4y², there will be more than one possible solution satisfying the given differential equation.

Hence, the differential equation v/(x) = 2² + 4x + 4y² - 1 does not possess a unique solution with the initial condition y(0) = 1, as there will be multiple solutions that satisfy the equation. The non-linear term 4y² allows for different trajectories that satisfy the equation, resulting in a lack of uniqueness.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer: Exactly 26 of them are are home owners

Step-by-step explanation:

Answer:

\(A = 54\)

Step-by-step explanation:

Given

\(\sin A = \cos B\)

\(A=1.5B\)

Required

Find A

If \(\sin A = \cos B\)

Then:

\(A +B = 90\)

Substitute \(A=1.5B\) in \(A +B = 90\)

\(1.5B + B = 90\)

\(2.5B = 90\)

Solve for B

\(B = \frac{90}{2.5}\)

\(B = 36\)

Substitute \(B = 36\) in \(A=1.5B\)

\(A = 1.5 * 36\)

\(A = 54\)

The difference between the predicted regression value and the actual value is called the residual.

Let's assume a simpler model: Y= β₀+ β₁X + E. For linear regression, let ε∼N(0,σ2). The most important thing here is that ϵ is a normal random variable. This makes Y a normal random variable with mean β0+β1X and variance σ₂.

Regression Analysis:

Regression analysis is a set of statistical techniques used to estimate the relationship between a dependent variable and one or more independent variables. It can be used to assess the strength of relationships between variables and model future relationships between variables.

Assumptions:

One of the main assumptions of regression analysis is that residuals with mean equal to 0 are normally distributed. Residuals must be both positive and negative. If this condition is not met (residuals are only positive or negative, i.e. the model is either consistently Regardless, it means that it has not been properly selected for prediction.

Poor predictions are due to (i) the regression model should contain non-linear terms rather than only linear terms, (ii) multicollinearity of the independent variables, and (iii) missing important predictor variables (features). Poor understanding of the problem and data, (iv) non-constant data variance, or (v) extrapolation (prediction) far beyond the range of the independent variables used to estimate the parameters of the model.

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Answer:

0

Step-by-step explanation:

m=y2-y1 / x2-x1

m= -1-1/-1-2

m=0/-3

m=0

Answer:

2,875

Step-by-step explanation:

$5000 • 5.75% ( or 0.0575 ) = $2,875

Answer:

5555+2929

= 8484

its an irrational no.

thanks

Answer:

\(B) : \: ( 2,4)\)