What are the solutions to the equation 7x² + 3x – 4 = 0?

The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission if each boat has a failure rate of 1 failure per 100 hoursis 99.5%. Hence, the correct option is (A).

To determine the probability of mission success, we'll need to calculate the probability of failure for each boat and then use the binomial probability formula.

Here are the steps:

1. Calculate the probability of failure for each boat during the 20-hour mission: Since each boat has a failure rate of 1 failure per 100 hours, the probability of failure for each boat in 20 hours is 20/100 = 1/5 or 0.2.

2. Calculate the probability of success for each boat: The probability of success for each boat is 1 - probability of failure = 1 - 0.2 = 0.8.

3. Use the binomial probability formula to find the probability of at least 11 boats operating successfully:
P(X ≥ 11) = 1 - P(X ≤ 10), where X is the number of successful boats.

4. Calculate P(X ≤ 10) using the binomial probability formula:

P(X ≤ 10) = ∑[C(16, k) × (0.8)^k × (0.2)^(16-k)], where k ranges from 0 to 10, and C(16, k) is the binomial coefficient or the number of ways to choose k successes from 16 boats.

5. Calculate 1 - P(X ≤ 10) to get the probability of mission success.

After performing the calculations, the probability of mission success is found to be approximately 99.5%, which corresponds to option A.

So, the probability of mission success, given that at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission and each boat has a failure rate of 1 failure per 100 hours, is approximately 99.5%.

Hence, option (A) is correct.

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60 is the answer of multiplication .

What does math multiplication mean?

Multiplication in mathematics is a technique for determining the sum of two or more numbers. It is one of the fundamental operations in mathematics that we employ on a daily basis. One of the fundamental operations in mathematics is multiplication.

                        The result of multiplying two or more numbers together is known as the product. The first number that the other is multiplied by in a two-number operation is referred to as the multiplicand.

        15 x 4  =  60

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The amount of money that will be in the savings account on week 100 is $250.

To find the amount of money that will be in the savings account on week 100, we can use the formula for linear interpolation which is given by:

`(y2 - y1) / (x2 - x1) = (y - y1) / (x - x1)`,

where `y1`, `y2` are the amounts of money in the savings account at week `x1`, `x2` respectively, and we need to find `y` at week `x = 100`.

Given that on week 8, she had $20.00 and on week 12, she had $30.00, we can let

`x1 = 8`,

`y1 = 20`,

`x2 = 12`,

`y2 = 30` and `x = 100`.

Plugging these values into the formula for linear interpolation, we get:(30 - 20) / (12 - 8) = (y - 20) / (100 - 8)

Simplifying, we get:

2.5 = (y - 20) / 92

Multiplying both sides by 92, we get:

230 = y - 20

Adding 20 to both sides, we get:

y = 250

Therefore, the amount of money that will be in the savings account on week 100 is $250.

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The inequality to find the scores she must make on the final exam to pass the course with an average of 77 or higher is (310 + x) / 5 >= 77.

The meaning is that she should have a score of 75 or higher to pass.

From the information, Shureka washburn has scores of 69,80,71, and 90 on her algebra tests and she must make on the final exam to pass the course with an average of 77 or higher.

Therefore, the inequality to express the information will be:

(69 + 80 + 71 + 90 + x)/5 >= 77

(310 + x) / 5 >= 77

Crops multiply

310 + x >= 77 × 5

310 + x >= 385

x >= 385 - 310

x >= 75

She needs 77 or more in order to pass the course.

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Answer:

9528.75

Step-by-step explanation:

1089x8.75, or 1089x8 and 3/4 which is 9528.75

The general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

Given a recurrence relation tn = 120,-2 - 166n-3 + 2 we have to derive the general solution form for the recurrence sequence.

We have the recurrence relation tn = 120,-2 - 166n-3 + 2

We need to find the solution for the recurrence relation.

Associated Homogeneous Equation: First, we need to find the associated homogeneous equation.

                                     tn = -166n-3 …..(i)

The characteristic equation is given by the following:tn = arn. Where ‘a’ is a constant.

We have tn = -166n-3..... (from equation i)ar^n = -166n-3

                                Let's assume r³ = t.

Then equation i becomes ar^3 = -166(r³) - 3ar^3 + 166 = 0ar³ = 166

Hence r = ±31.10.3587Complex roots: α + iβ, α - iβ

Characteristics Polynomial:

                   So, the characteristic polynomial becomes(r - 31)(r + 31)(r - 10.3587 - 1.7503i)(r - 10.3587 + 1.7503i) = 0

The general solution of the Homogeneous equation:

Now we have to find the general solution of the homogeneous equation.

                  tn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)

                        nWhere C1, C2, C3, C4 are constants.

Computing a Particular Solution:

                Now we have to compute the particular solution.

                                  tn = 120-2 - 166n-3 + 2

Here the constant term is (120-2) + 2 = 122.

The solution of the recurrence relation is:tn = A122Where A is the constant.

The General Solution of Non-Homogeneous Equation:

        The general solution of the non-homogeneous equation is given bytn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)n + A122

Hence, we have derived the general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

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The amount more in interest over the life of the loan which Nellie have to pay is $14814.

Bankruptcy is the procedure by which the people who are unable to pay the debts to creditors, may get relief from some or all the debts.

Nellie has a bankruptcy on her credit report and therefore pays higher interest rates on her current loans.

Nellie took out a car loan for $45,000 payable for 6 years at an interest rate of 15%. Thus, the interest is,

\(I=\dfrac{45000\times6\times15}{100}\\I=40500\)

If she had not applied for bankruptcy, she would have been able to take out the loan at a rate of 6%. In this case, the interest paid would be,

\(I=\dfrac{45000\times6\times6}{100}\\I=16200\)

The difference between the interest paid would be,

\(I=40500-16200\\I=24300\)

Hence, the amount more in interest over the life of the loan which Nellie have to pay is $14814.

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Suzette's average dance time per week relative to her goal as calculated from the information given is - 0.07 hours

To obtain the average dance time per week, we need to find the mean value of information given in the table :

Dance time = (2.4, - 3, 2 1/4, 0 - 2)

Number of weeks = 5

The average dance time per week :

The average dance time per week = (-0.35 ÷ 5) = - 0.07

Therefore, Suzette's average dance time per week relative to her goal is - 0.07 hours

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Answer:

-0.07

Step-by-step explanation:

I got it correct in the test

I got a 100% so yw if this helps and correct me if im wrong pls

Answer:

the slope is 3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

First calculate the total number of students in all the schools:

= 618 + 378 + 204  

= 1,200 students

Use this number to calculate the proportion of the total population that a school so that this can then be used to determine the proportion of the 20 delegates they should sent.

North Middle school:  

= 618/1,200 * 20  

= 10 students

Central Middle School:  

= 378 / 1,200 * 20  

= 6 students

South Middle School:  

= 204/1,200 * 20  

= 4 students  

The number of discount tickets was sold is 139.

The linear equation of two variables is the equation where the highest degree of two variables is 1.

Here given that the organizer receives 2884 by selling tickets.

The number of tickets sold is 430

The full price of one ticket is 8.

The discount price of ticket is 4.

Let the number of full price ticket sold is x and the number of discount ticket sold is y.

Then the total price will be = (the price of full price ticket* number of tickets) + (number of discount ticket sold*discount price of one ticket)

= 8x+4y

From the above it is clear that 8x+4y=2884 ------equation 1

total number tickets are = x+y

⇒ x+y =430 -------equation 2

multiplying 8 in equation 2 will be

8x+8y=3440

then subtracting equation 1 from the above equation

8x+8y -(8x+4y)=3440-2884

⇒4y=556

⇒y=556/4

⇒y=139

Therefore the number of discount tickets sold is 139.

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Answer:

A.) DGF

Step-by-step explanation:

The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10

A quadratic polynomial is a polynomial of the form ax² + bx + c

For any given quadratic polynomial we have

x² - (sum of zeros)x + (products of zeros) = 0

Given that the sum and product of its zeroes respectively 3/2 and 5,

We have that

Substituting the values of the variables into the equation, we have

x² - (sum of zeros)x + (products of zeros) = 0

x² - (3/2)x + (5) = 0

x² - (3/2)x + (5) = 0

Multiplying through by 2, we have

2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2

2x² - 3x + 10 = 0

So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10

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The dollar gains depreciated relative to the pound when the price of pounds in dollars increases, for instance, from $1 = 1 pound to $2 = 1 pound.

Devaluation of a currency can take place in both absolute and relative terms. When the value of one currency declines in relation to the values of other currencies, this is referred to as a relative devaluation. For instance, the British pound sterling may be worth more today than it did yesterday in terms of US dollars.

A currency's value declines when compared to other currencies, which is known as currency depreciation. Political unrest, interest rate differences, weak economic fundamentals, and investor risk aversion are a few examples of the causes of currency devaluation.

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The statement "there are 250 degrees in the sum of the interior angles of a polygon" is sometimes true.

In a polygon, the sum of the interior angles depends on the number of sides or vertices it has. The formula to calculate the sum of the interior angles of a polygon is (n-2) * 180 degrees, where 'n' represents the number of sides or vertices.

Let's consider a few examples:

1. Triangle: A triangle has 3 sides or vertices. Using the formula, (3-2) * 180 = 180 degrees. Therefore, the sum of the interior angles of a triangle is always 180 degrees.

2. Quadrilateral: A quadrilateral has 4 sides or vertices. Applying the formula, (4-2) * 180 = 360 degrees. Hence, the sum of the interior angles of a quadrilateral is always 360 degrees.

3. Pentagon: A pentagon has 5 sides or vertices. Using the formula, (5-2) * 180 = 540 degrees. Therefore, the sum of the interior angles of a pentagon is always 540 degrees.

As we can see from these examples, the sum of the interior angles of a polygon can vary depending on the number of sides or vertices it has. So, the statement "there are 250 degrees in the sum of the interior angles of a polygon" is sometimes true, but not always.

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Answer:

true

Step-by-step explanation:

Let us calculate the determinant of this quadratic equation:

Δ = b^2 - 4ac = 16-4*(-1)*(-4) = 0

The equation has one solution

x = -b/2a = 2

If 'A" denotes the event that student takes statistics and B denotes event that the student is senior, the P(A' or B') is 0.85.

To find P(A' or B'), we want to find the probability that a student is not a senior or does not take statistics (or both).

We know that the total number of students surveyed is 100, and out of those students:

15 seniors take statistics

35 seniors take calculus

18 juniors take statistics

32 juniors take calculus;

The probability P(A' or B') is written as P(A') + P(B') - P(A' and B');

To find the probability of a student not taking statistics, we add the number of students who take calculus (seniors and juniors) and divide by the total number of students:

⇒ P(A') = (35 + 32) / 100 = 0.67;

To find the probability of a student not being a senior, we subtract the number of seniors who take statistics and calculus from the total number of students who take statistics and calculus;

⇒ P(B') = (18 + 32) / 100 = 0.50

= 1 - 0.50 = 0.50;

Next, to find probability of student who is neither senior nor does not take statistics, which is 32 students,

So, P(A' and B') = 32/100 = 0.32;

Substituting the values,

We get,

P(A' or B') = 0.67 + 0.50 - 0.32 = 0.85;

Therefore, the required probability is 0.85.

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The given question is incomplete, the complete question is

A student surveyed 100 students and determined the number of students who take statistics or calculus among seniors and juniors. Here are the results.

               Statistics   Calculus

Senior           15              35

Junior           18               32

Let A be the event that the student takes statistics and B be the event that the student is a senior.

What is P(A' or B')?

Answer:

ok, here is your answer

Step-by-step explanation:

As the question and information provided do not have a specific part (a), (b), and (c) to be answered, I will provide a general approach to solving this problem.

Let's define the objective function and constraints of the given problem.

Objective function: To minimize the cost of producing Super and Regular gasoline

Cost = (price of High-Quality Fuel * amount purchased from High-Quality Fuel) + (price of Junk Petroleum * amount purchased from Junk Petroleum) + (cost of blending Super gasoline) + (cost of blending Regular gasoline)

Constraints:

- The total amount of Super gasoline produced should be less than or equal to the total amount of gasoline purchased

- The total amount of Regular gasoline produced should be less than or equal to the total amount of gasoline purchased

- The amount of High-Quality Fuel used to produce Super gasoline should be less than or equal to the total amount of High-Quality Fuel purchased

- The amount of Junk Petroleum used to produce Super gasoline should be less than or equal to the total amount of Junk Petroleum purchased

- The amount of High-Quality Fuel used to produce Regular gasoline should be less than or equal to the total amount of High-Quality Fuel purchased

- The amount of Junk Petroleum used to produce Regular gasoline should be less than or equal to the total amount of Junk Petroleum purchased

- The octane rating of Super gasoline should be greater than or equal to 96

- The octane rating of Regular gasoline should be greater than or equal to 87

- The lead content of Super gasoline should be less than or equal to 0.5 grams per litre

- The lead content of Regular gasoline should be less than or equal to 0.15 grams per litre

Now, we can set up the linear programming model for this problem and use software like Excel Solver or MATLAB to solve it and find the optimal values of the decision variables (H, J, S, R, HS, HR, JS, JR). The optimal solution will give us the minimum cost of producing Super and Regular gasoline while satisfying all the constraints.

Answer:

About 5 foot 1 inch

Step-by-step explanation:

(CM!) The equation is leagnth of the femur times 2.47 +54.1= Heightx

16 in= 40.64cm

40.64 x 2.47=100.38

100.38+54.1=154.48-convert to inches

60.82 inches

Answer:

e i hope that is correct answer

Answer:

a. x=21/8

b.x=5/6

c.x=5/8

d.x=4

e.x=112.5

Step-by-step explanation:

The statement "Two planes orthogonal to a third plane are parallel" is false. The statement "Two lines parallel to a plane are parallel" is true. The statement "Two planes parallel to a third plane are parallel" is true. The statement "Two planes parallel to a line are parallel" is true.

Two planes orthogonal to a third plane are not necessarily parallel. Orthogonal planes are those that intersect at a right angle, forming a 90-degree angle between their normal vectors. However, they can still have different orientations and positions in 3-dimensional space. Imagine a cube where two adjacent faces are orthogonal to the top face. These two faces are not parallel to each other. Therefore, orthogonality does not imply parallelism in the case of planes.

If two lines are parallel to the same plane, they are indeed parallel to each other. This is because lines parallel to a plane have their direction vectors lying within the plane. As a result, both lines maintain a constant direction and never intersect, making them parallel.

If two planes are parallel to a third plane, they are indeed parallel to each other. This can be understood by considering the definition of parallel planes, which states that parallel planes never intersect and have the same normal vector. If two planes are parallel to a third plane, they share the same normal vector as the third plane, meaning they must also have the same orientation and never intersect.

If two planes are parallel to a line, they are indeed parallel to each other. This is due to the fact that a line lies within an infinite number of planes. If two planes are parallel to a line, they are both parallel to the infinite number of planes containing that line. Thus, they are parallel to each other as well.

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Answer:

12y-10y=2z-2D

2y=2z-3D

Divide both sides by 2

Y=z-3D

Absolutely

The derivative of f in the direction of u = <4, 4, 4> is 48√3.

The derivative of a function represents the rate at which the function changes with respect to its independent variable(s). It measures the slope or steepness of the function at a specific point.

To find the directions in which the function increases and decreases most rapidly at point P0(1, 1, 1), we need to calculate the gradient vector (∇f) at that point and identify its components. The gradient vector will point in the direction of the steepest increase in the function.

Given the function f(x, y, z) = 2ln(xy) + 2ln(yz) + 2ln(xz), we can calculate the partial derivatives with respect to each variable:
∂f/∂x = 2/y + 2/z
∂f/∂y = 2/x + 2/z
∂f/∂z = 2/x + 2/y

Now, we evaluate the partial derivatives at point P₀(1, 1, 1):
∂f/∂x = 2/1 + 2/1 = 4
∂f/∂y = 2/1 + 2/1 = 4
∂f/∂z = 2/1 + 2/1 = 4

So, the gradient vector at P0(1, 1, 1) is (∇f) = <4, 4, 4>. The components of this vector indicate that the function increases most rapidly in all directions at that point.

To find the derivatives of the function in those directions, we can take the dot product of the gradient vector (∇f) with a unit vector in each direction at that point.
u = <4, 4, 4> / √(1² + 1² + 1²) = <4/√3, 4/√3, 4/√3>

To find the derivative of f in the direction of u, we take the dot product:
∇f · u = <4, 4, 4> · <4/√3, 4/√3, 4/√3> = 16/√3 + 16/√3 + 16/√3 = 48√3

So, the derivative of f in the direction of u = <4, 4, 4> is 48√3.

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Answer: 7= 1(5)+b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

y = mx + b

Given that the coordinate is (5, -7), you know that x = 5 and y = -7

Variable m represents the slope, so m = -1

Now simply plug in all the numbers:

y = mx + b

-7 = (-1)(5) + b

Answer:

Since both terms are perfect squares, factor using the difference of squares formula.

(x+9y)(x−9y)

Answer:

Step-by-step explanation:

x^2-81y^2

=(x)^2-(9y)^2

=(x-9y)(x+9y)

The number of years for the value of $900 to reach $1,800 if the rate of interest is 4%, is 25 years.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

The amount after some years, A = $1800,

The rate of interest, r = 4% per annum,

The principal amount, p = $900,

Calculate the number of years as shown below,

A = P + SI

1800 = 900 + p × r × t / 100

Here, t is the time in years,

1800 - 900 = 900 × 4 × t / 100

900 = 3600t / 100

900 = 36t

t = 900 / 36

t = 25

Thus, the number of years will be 25.

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Answer:

where's the data

Step-by-step explanation: