Solve for x. (2x+3) (x-6)

Answer:

a2 is a3 B is 2 and a4 is -2

Step-by-step explanation:

just math and more math

Answer:

We would use the explicit formula since the explicit formula is used for finding the nth term in a sequence. The reason why it's not the recursive is because the recursive formula helps you find the next terms using a formula of the preceding term or term before the next term.

The probability that exactly two out of the next twelve passengers buying a ticket with this airline will prefer a window seat is approximately 0.283, or 28.3%.

To calculate the probability that exactly two out of the next twelve passengers buying a ticket with this airline will prefer a window seat, we can use the binomial probability formula.

The formula for calculating the binomial probability is:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of exactly k successes,

n is the total number of trials,

k is the number of successful outcomes,

p is the probability of success in a single trial, and

(1-p) is the probability of failure in a single trial.

In this case, we have:

n = 12 (total number of trials)

k = 2 (number of successful outcomes)

p = 0.40 (probability of success, which is 40%)

Substituting these values into the formula, we get:

P(X = 2) = (12C2) * (0.40^2) * (1-0.40)^(12-2)

Calculating this expression, we find:

P(X = 2) ≈ 0.283

So, the probability that exactly two out of the next twelve passengers buying a ticket with this airline will prefer a window seat is approximately 0.283, or 28.3%.

Learn more about probability here:

https://brainly.com/question/32117953

#SPJ11

Answer:

108 slices

Step-by-step explanation:

One pie is 6 slices so 6*18 is equal to 108

The probability that the student will fail, given that he guesses the answers, is 0.227.

Since there are only two possible outcomes for each question (true or false),

the probability of guessing a correct answer is 1/2 = 0.5.

Likewise, the probability of guessing a wrong answer is also 1/2 = 0.5.

To find the probability of failing the exam,

we need to find the probability of answering less than 11 questions correctly.

Using the binomial probability formula,

the probability of getting k successes (correct answers) in n trials (questions) is given by:

P(k) = (n C k) * p^k * q^(n-k)

where p is the probability of success (getting a correct answer),

q is the probability of failure (getting a wrong answer), and (n C k) is the number of combinations of n things taken k at a time.

In this case,

n = 17, p = 0.5, and

q = 0.5.

The number of ways to get less than 11 correct answers is:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)P(X = k) = (n C k) * p^k * q^(n-k)

Substituting the values:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

P(X = 0) = (17 C 0) * (0.5)^0 * (0.5)^17 = 0.0015

P(X = 1) = (17 C 1) * (0.5)^1 * (0.5)^16 = 0.0146

P(X = 2) = (17 C 2) * (0.5)^2 * (0.5)^15 = 0.0586

P(X = 3) = (17 C 3) * (0.5)^3 * (0.5)^14 = 0.1558

P(X = 4) = (17 C 4) * (0.5)^4 * (0.5)^13 = 0.268

P(X = 5) = (17 C 5) * (0.5)^5 * (0.5)^12 = 0.327

P(X = 6) = (17 C 6) * (0.5)^6 * (0.5)^11 = 0.2732

P(X = 7) = (17 C 7) * (0.5)^7 * (0.5)^10 = 0.1537

P(X = 8) = (17 C 8) * (0.5)^8 * (0.5)^9 = 0.0573

P(X = 9) = (17 C 9) * (0.5)^9 * (0.5)^8 = 0.013

P(X = 10) = (17 C 10) * (0.5)^10 * (0.5)^7 = 0.0015

Therefore, P(X < 11) = 0.0015 + 0.0146 + 0.0586 + 0.1558 + 0.268 + 0.327 + 0.2732 + 0.1537 + 0.0573 + 0.013 + 0.0015P(X < 11) = 0.8857

Thus, the probability of failing is: P(fail) = P(X < 11) = 0.8857

The probability that the student will fail, given that he guesses the answers, is 0.227 (rounded to three decimal places).

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ11

Answer:

Area=105

Step-by-step explanation:

If we were to close the rectangle it would be 15ft x 8ft which equals 120ft

but then we'd have to find the area of the small rectangle inside being

3ft x 5ft = 15 ft

So, we'd have to subtract 15 ft from 120 ft giving us the answer of 105 ft

The side length of the cube is 4 feet. Then the surface area of the cube will be 96 square feet.

Suppose that: The side length of the considered cube is L units. Then, we get:

The volume of that cube = L³ cubic units.

The surface area of that cube = 6L² square units.

In February 2003, the Battlefords Chamber of Commerce in Saskatchewan placed a cage containing a 64-cubic foot ice cube along Yellowhead Highway. Then the side length of a cube will be

64 = L³

L = ∛64

L = 4 feet

Then the surface area of the cube will be

SA = 6 x 4²

SA = 6 x 16

SA = 96 square feet

More about the volume and surface area of the cube link is given below.

https://brainly.com/question/13789496

#SPJ1

Answer:

Assuming an ideal pulley system, the force required to lift a 10 Newton box with one pulley would be 10 Newtons. This is because the force required to lift an object using a pulley system is equal to the weight of the object being lifted. In an ideal pulley system, there is no friction or energy loss, so the force required is equal to the weight of the object. Therefore, if the weight of the box is 10 Newtons, a force of 10 Newtons would be required to lift it with one pulley.

P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

1) The statement is true. Suppose (x^,y^) is an extreme point of P. To show that x^ is an extreme point of Q, we need to prove that for any two distinct points x_1, x_2 in Q, the line segment connecting x_1 and x_2 lies entirely in Q. Since Q is the projection of P onto x-space, it means that for any x in Q, there exists y in R^k such that Ax + By ≥ b.

Now, let's assume x_1 and x_2 are two distinct points in Q. Since they belong to Q, there exist corresponding y_1 and y_2 in R^k such that Ax_1 + By_1 ≥ b and Ax_2 + By_2 ≥ b. Since P is a polyhedron, the set of points that satisfy Ax + By ≥ b is a convex set. Therefore, the line segment connecting x_1 and x_2, denoted by [x_1, x_2], lies entirely in P. Since the projection of a convex set onto a subspace is also a convex set, [x_1, x_2] lies entirely in Q. Thus, x^ is an extreme point of Q.

2) The statement is false. Suppose x^ is an extreme point of Q. It does not necessarily imply the existence of a corresponding y^ such that (x^, y^) is an extreme point of P. This is because the projection Q onto x-space may not capture all the extreme points of P. It is possible for multiple points in P to project to the same point in Q, making it impossible to uniquely determine y^.

3) The statement is true. If x^ is an extreme point of Q and P does not contain a line, then there exists a corresponding y^ such that (x^, y^) is an extreme point of P. Since P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

Learn more about convex set

brainly.com/question/32604567

#SPJ11

Answer:

y= \(\frac{3w}{4x}\)+ \(\frac{18}{x}\)

Step-by-step explanation:

Hope this helps. Plz give brainliest.

Answer:

70

Step-by-step explanation:

If y=30 when x=6, 5x=y (because they are in direct proportion).

So, when x=14 replace x.

5*14=y

y=70

you can prove this because 70/14=30/6=5

so, the proportions are equal

The difference in volume between the cereal box and pastry box is 167.991 cubic inches.

What are Dimensions?

Dimensions refer to the measurement of the size or extent of an object or space in a particular direction, such as length, width, and height. In the context of boxes, dimensions are used to describe the length, width, and height of a box, usually given in inches or centimeters.

To find the volume of a rectangular box, we use the formula:

Volume = length x width x height

Let's first find the volume of the cereal box:

Volume of cereal box = 7 inches x 12 inches x 2 inches = 168 cubic inches

Now let's find the volume of the pastry box:

Volume of pastry box = 3% inches x 3% inches x 2% inches = 0.009 cubic inches

Now, to find the difference in volume between the two boxes, we subtract the volume of the pastry box from the volume of the cereal box:

168 cubic inches - 0.009 cubic inches = 167.991 cubic inches

Hence, the difference in volume between the cereal box and pastry box is 167.991 cubic inches.

To learn more about Dimensions, Visit

https://brainly.com/question/27404871

#SPJ1

Using the given information, the radius of the sphere to the nearest meter is 13m

From the question, we are to determine the radius of the sphere

Using the formula for calculating the volume of a sphere,

\(V = \frac{4}{3} \pi r^{3}\)

Where V is the volume

and r is the radius

From the given information,

V = 9198 m³

Then,

\(9198 = \frac{4}{3} \times \pi r^{3}\)

\(9198 = \frac{4}{3} \times 3.14 \times r^{3}\)

\(4 \times 3.14 \times r^{3} = 9198 \times 3\)

\(4 \times 3.14 \times r^{3} = 27594\)

\(r^{3} = \frac{27594}{4 \times 3.14}\)

\(r = \sqrt[3]{\frac{27594}{4\times 3.14} }\)

r = 12.99995 m

r ≅ 13 m

Hence, the radius of the sphere to the nearest meter is 13m.

Learn more on Calculating volume of a sphere here: https://brainly.com/question/21209558

#SPJ1

Answer:

A.-6

Step-by-step explanation:

on edg

Answer:

A) -6

Step-by-step explanation:

Answer:

x=41

Step-by-step explanation:

0.25(x-13)=7

We move all terms to the left:

0.25(x-13)-(7)=0

We multiply parentheses

0.25x-3.25-7=0

We add all the numbers together, and all the variables

0.25x-10.25=0

We move all terms containing x to the left, all other terms to the right

0.25x=10.25

x=10.25/0.25

x=41

The solution to the equation; 0.25(x - 13) = 7 as given is; x = 41

According to the question;

The solution to the given equation can be evaluated as follows;

x = 41.

Read more on one variable equation;

https://brainly.com/question/21528555

The 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

To find the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers, we can use the formula for the confidence interval for a proportion.

The formula for the confidence interval is:

CI = p1 ± Z * √((p1 * (1 - p1)) / n)

Where:

CI is the confidence interval,

p1 is the sample proportion (proportion of accidents involving teenage drivers),

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z ≈ 1.96),

n is the sample size (number of accidents checked).

Given:

Number of accidents checked (sample size), n = 582

Number of accidents involving teenage drivers, x = 91

First, we calculate the sample proportion:

p1 = x / n = 91 / 582 ≈ 0.1566

Now we can calculate the confidence interval:

CI = 0.1566 ± 1.96 * √((0.1566 * (1 - 0.1566)) / 582)

Calculating the standard error of the proportion:

SE = √((p1 * (1 - p1)) / n) = √((0.1566 * (1 - 0.1566)) / 582) ≈ 0.0184

Substituting the values into the formula:

CI = 0.1566 ± 1.96 * 0.0184

Calculating the values:

CI = 0.1566 ± 0.0361

Finally, we can simplify the confidence interval:

CI = (0.1205, 0.1927)

Therefore, the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

To know more about confidence interval refer here:

https://brainly.com/question/32278466#

#SPJ11

According to question,  the probability that x > 0.5 is 1/4.

To find the probability P(x > 0.5), we need to integrate the given PDF over the range where x > 0.5:

P(x > 0.5) = ∫∫(x > 0.5) fx,y (x, y) dxdy

= ∫∫(x > 0.5) 2xy dxdy, where the limits of integration are 0 to 1 for y and 0.5 to 1 for x.

= ∫0^1 ∫0.5^1 2xy dxdy

= 1/4

what is probability?

The probability of an event is the measure of the likelihood of that event occurring. It is a number between 0 and 1, inclusive, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. If the probability of an event is p, then the probability of the complement of that event (i.e., the event not occurring) is 1-p.

To learn more about probability visit:

brainly.com/question/30034780

#SPJ11

Answer: I don't know

Step-by-step explanation:

We have the following response after answering the given question: As a equation result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

Which nation experienced the hottest summer?

We may examine the average temperature for each nation throughout the observed weekends to determine which nation experienced the hottest summer.

Country A: (21.4°C) (18+20+22+23+24)/5

(24+26+28+29+27)/5 = 26.8°C for Country B.

The summer was therefore hotter in Country B, with an average temperature of 26.8°C.

b) Over the summer, which nation saw more erratic weather?

We may examine the temperature ranges recorded for each nation to determine which experienced more erratic weather during the summer.

24°C - 18°C equals 6°C in Country A.

29°C - 24°C equals 5°C in country B.

As a result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x

(b) The domain of V in interval notation is 0<x<5,

(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773

(d) The maximum volume of the box is 192.421 cm^2.

In the given question,

A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) We have to express the volume V of the box as a function of x.

If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.

So V = x(10-2x) (20-2x)

V = x(10(20-2x)-2x(20-2x))

V = x(200-20x-40x+4x^2)

V = x ( 200 - 60 x + 4x^2)

V = 4x^3-60x^2+200x

(b) Now we have to give the domain of V in interval notation.

Since the lengths must all be positive,

10-2x > 0 ≥ x < 5 and x> 0

So 0 < x < 5

(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.

We take the derivative of V:

V'(x) = 12x^2-120x+200

Taking V'(x)=0

0 = 4 (3x^2-30x+50)

3x^2-30x+50=0

Now using the quadratic formula:

x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

From the equationl a=3, b=-30, c=50

Putting the value

x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)

x= \(\frac{30\pm\sqrt{900-600}}{6}\)

x= \(\frac{30\pm\sqrt{300}}{6}\)

x= \(\frac{30\pm17.321}{6}\)

Since x<5,

So x= \(\frac{30-17.321}{6}\)

x= 2.113

So H = 2.113, W = 5.773, L= 15.773.

d) Now we have to find the maximum volume of the box.

V = HWL

V= 2.113*5.773*15.773

V = 192.421 cm^3

To learn more about volume of rectangle link is here

brainly.com/question/13798973

#SPJ4

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

Learn more about function here:

https://brainly.com/question/2253924

#SPJ1

Answer:

(-8,5)

Step-by-step explanation:

The answer explained step by step on the picture.

Yes, the solution of the dual offer computational advantages over solving the primal directly

Let us consider the given primal problem:

Minimize z = 50x₁ + 60x₂ + 30x₃

subject to

5x₁ + 5x₂ + 3x₃ ≥ 50

x₂- x₃ ≥ 20

7x₁ + 6x₂ - 9x₃ ≥ 30

5x₁ + 5x₂ + 5x₃ ≥ 35

2x₁ + 4x₂ + 15x₃ ≥ 10

12x₁ +10x₂ ≥ 90

x₂ - 10x₃ ≥ 20

x₁, x₂, x₃ ≥ 0

We will now form the dual problem by introducing the dual variables y₁, y₂, y₃, y₄, y₅, y₆, y₇, and the objective function of the dual problem is to maximize the sum of the right-hand side coefficients of the primal constraints multiplied by the dual variables.

The constraints of the dual problem are formed by the coefficients of the primal objective function.

Maximize w = 50y₁ + 20y₂ + 30y₃ + 35y₄ + 10y₅ + 90y₆ + 20y₇

subject to

5y₁ + y₂ + 7y₃ + 5y₄ + 2y₅ + 12y₆ ≥ 50

5y₁ + 5y₂ + 6y₃ + 5y₄ + 4y₅ + 10y₆ - 10y₇ ≥ 60

3y₁ - y₂ - 9y₃ + 5y₄ + 15y₅ ≥ 30

Now, we can solve this dual problem using the simplex method or any other optimization technique.

To know more about objective function here

https://brainly.com/question/29185392

#SPJ4

Complete Question:

Solve the dual of the following problem, and then find its optimal solution from the solution of the dual. Does the solution of the dual offer computational advantages over solving the primal directly?

Minimize z = 50x₁ + 60x₂ + 30x₃

subject to

5x₁ + 5x₂ + 3x₃ ≥ 50

x₂- x₃ ≥ 20

7x₁ + 6x₂ - 9x₃ ≥ 30

5x₁ + 5x₂ + 5x₃ ≥ 35

2x₁ + 4x₂ + 15x₃ ≥ 10

12x₁ +10x₂ ≥ 90

x₂ - 10x₃ ≥ 20

x₁, x₂, x₃  ≥ 0

The value of s is 8

First, we need to know that perpendicular bisectors are lines that divides into equal parts

From the diagram shown, we have that;

Line NO is equal to Line MO

This is represented as;

NO = 3s + 12

MO = 36

Equate the expressions, we get;

3s + 12 = 36

collect the like terms, we have;

3s = 36 - 12

subtract the value, we have;

3s = 24

Divide both sides by the coefficient of s in the equation;

s = 24/3

Divide the values

s = 8

Learn about bisectors at: https://brainly.com/question/11006922

#SPJ1

Answer: where is the diagram ?

Step-by-step explanation:

Answer:

x=2.3

Step-by-step explanation:

Isosceles triangle means both sides are the same length, triangle is also right meaning you can plug values into Pythagorean theorem (\(a^2+b^2=c^2\))

\(x^2+x^2=\sqrt{11}^2 \\2x^2=11\\x=\sqrt{\frac{11}{2} } \\x=2.345...\\x=2.3\)

Assuming all my math is right, this is your answer

According to the question the position function with the given initial velocity and position is \(\[s(t) = -19t^2 + 24t.\]\)

To find the position function, we need to integrate the acceleration function twice.

First, integrate the acceleration function to find the velocity function:

\(\[v(t) = \int a(t) dt = \int -38 dt = -38t + C_1.\]\)

Next, integrate the velocity function to find the position function:

\(\[s(t) = \int v(t) dt = \int (-38t + C_1) dt = -19t^2 + C_1t + C_2.\]\)

Using the given initial conditions v(0) = 24 and s(0) = 0, we can find the constants:

\(\[v(0) = -38(0) + C_1 = 24 \implies C_1 = 24,\]\)

\(\[s(0) = -19(0)^2 + 24(0) + C_2 = 0 \implies C_2 = 0.\]\)

Therefore, the position function is:

\(\[s(t) = -19t^2 + 24t.\]\)

To know more about visit-

brainly.com/question/26046991

#SPJ11

Answer:

22 m/s

Step-by-step explanation:

Take the distance and divide by the time

1210 m/55s

22 m/s

Answer:

Step-by-step explanation:

\(speed = \frac{distantce}{time} \\ = \frac{1210m}{55s} \\ = 22m {s}^{ - 1} \)

Answer:

X=23

Step-by-step explanation: