13 POINTS! EVALUATE AND SHOW ALL WORK

Ah bg de cf

Step-by-step explanation:

i think thats how you do it becuse i did that

Answer:

Yes because there are still only two possible outcomes

Step-by-step explanation:

I think it’s this one cause I’m on it too

The size of angle x is 54 degrees.

Let O be the complete angle,

<O = 360

Angle between diagonals = 360/5 = 72 degrees.

All diagonals of regular pentagon are equal and their opposite angles are equal .

With angle center O it forms a triangle:

sum of angles = 180

x + x + 72 = 180

2x + 72 = 180

2x = 180 - 72

2x = 108

divide by 2 on both sides

2x/2 = 108/2

x = 108/2

x = 54 degrees.

Therefore the size of angle x is 54 degrees.

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Answer:

Leslie did not find the common denominator of the fractions before adding them.

Step-by-step explanation:

Correct way:

\(\frac{2}{11} + \frac{3}{4} = \frac{8}{44} + \frac{33}{44} = \frac{41}{44}\)

Answer:

P=14x+18

Step-by-step explanation:

perimeter:

P=2(2x+4)+2(5x+5)=4x+8+10x+10=14x+18

I hope this help you

Answer:

third

Step-by-step explanation:

Answer:

3(x-2)=x-6 would be correct

Answer:

Here is your answer

((4 * 10) ^ 10) ^ 10 =

(40 ^ 10) ^ 10 =

10485760000000000 ^ 10 = 16069380442589902755419620923411626025222029937827928353013760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Step-by-step explanation:

Answer:

The answer I got was 56.6%.

The ratio of the trigonometric function of the right triangle, cos A is 3/5.

Given that,

In △ABC , ∠C is a right angle.

Then the opposite side to the right angle will be the hypotenuse.

So AB is the hypotenuse.

Sin A = BC / AB [ Since sine of an angle is opposite side / hypotenuse]

BC / AB = 4/5

BC = 4 and AB = 5

Using the Pythagoras theorem,

Third side, AC = √(5² - 4²) = 3

Cos of an angle is the ratio of adjacent side to the hypotenuse.

Cos A = 3/5

Alternatively, we can use the identity,

sin²A + cos²A = 1

to find the value of cos A.

Hence the value of cos A is 3/5.

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Probability that from 3 to 6 have blowouts is 0.4477 Probability that fewer than 4 have blowouts is 0.3615Probability that more than 5 have blowouts is 0.3973.

Given: It is found that 25% of the trucks fail to complete the test run without a blowout.Probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.In order to find the probability of the given events, we will use Binomial Distribution.

Let’s find the probability of given events one by one:a) From 3 to 6 trucks have blowouts Number of trials = 15 (n)Number of success = trucks with blowouts (x)Number of failures = trucks without blowouts = 15 - xProbability of a truck with blowout = p = 0.25Probability of a truck without blowout = q = 1 - 0.25 = 0.75We need to find

P(3 ≤ x ≤ 6) = P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6)P(x = r) = nCr * pr * q(n-r)

where nCr = n! / r!(n-r)!P(x = 3)

= 15C3 * (0.25)3 * (0.75)12

= 0.1859P(x = 4) = 15C4 * (0.25)4 * (0.75)11

= 0.1670P(x = 5)

= 15C5 * (0.25)5 * (0.75)10 = 0.0742P(x = 6)

= 15C6 * (0.25)6 * (0.75)9 = 0.0206P(3 ≤ x ≤ 6)

= 0.1859 + 0.1670 + 0.0742 + 0.0206

= 0.4477

Therefore, the probability that from 3 to 6 trucks have blowouts is 0.4477.b) Fewer than 4 trucks have blowoutsNumber of trials = 15 (n)Number of success = trucks with blowouts (x)Number of failures = trucks without blowouts = 15 - xProbability of a truck with blowout = p = 0.25Probability of a truck without blowout = q = 1 - 0.25 = 0.75We need to find P(x < 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)P(x = r) = nCr * pr * q(n-r)where nCr = n! / r!(n-r)!P(x = 0) = 15C0 * (0.25)0 * (0.75)15 = 0.0059P(x = 1) = 15C1 * (0.25)1 * (0.75)14 = 0.0407P(x = 2) = 15C2 * (0.25)2 * (0.75)13 = 0.1290P(x = 3) = 15C3 * (0.25)3 * (0.75)12 = 0.1859P(x < 4) = 0.0059 + 0.0407 + 0.1290 + 0.1859= 0.3615Therefore, the probability that fewer than 4 trucks have blowouts is 0.3615.c) More than 5 trucks have blowoutsNumber of trials = 15 (n)Number of success = trucks with blowouts (x)Number of failures = trucks without blowouts = 15 - xProbability of a truck with blowout = p = 0.25Probability of a truck without blowout = q = 1 - 0.25 = 0.75

We need to find P(x > 5)P(x > 5) = P(x = 6) + P(x = 7) + ... + P(x = 15)P(x = r) = nCr * pr * q(n-r)

where nCr = n! / r!(n-r)!

P(x > 5) = 1 - [P(x ≤ 5)]P(x ≤ 5) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)P(x = 0) = 15C0 * (0.25)0 * (0.75)15

= 0.0059P(x = 1) = 15C1 * (0.25)1 * (0.75)14 = 0.0407P(x = 2)

= 15C2 * (0.25)2 * (0.75)13 = 0.1290P(x = 3)

= 15C3 * (0.25)3 * (0.75)12 = 0.1859P(x = 4)

= 15C4 * (0.25)4 * (0.75)11 = 0.1670P(x = 5)

= 15C5 * (0.25)5 * (0.75)10

= 0.0742P(x ≤ 5)

= 0.0059 + 0.0407 + 0.1290 + 0.1859 + 0.1670 + 0.0742

= 0.6027P(x > 5) = 1 - 0.6027= 0.3973

Therefore, the probability that more than 5 trucks have blowouts is 0.3973.Answer:Probability that from 3 to 6 have blowouts is 0.4477Probability that fewer than 4 have blowouts is 0.3615Probability that more than 5 have blowouts is 0.3973.

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Answer:

The answer is D.

Answer:

i did this in Algebra 1

it's D.

Step-by-step explanation:

:)))

Answer:

Step-by-step explanation:

Because we have 3 unknowns, we need to come up with 3 equations. If the total number of animals is 440 and that number is made up of a combination of goats (g), ducks (d), and chickens (c) the first equation is

g + d + c = 440

The next equation is found in the fact that the number of ducks is one-quarter the number of chickens:

\(d=\frac{1}{4}c\) and solving for c gives us that

c = 4d

The last equation says that of the total number of animals, 440, half the goats and half the ducks got away, leaving only 320 animals behind. The last equation, the tricky one, is:

\(440-\frac{1}{2}g-\frac{1}{2}d=320\) and simplifying that:

\(-\frac{1}{2}g-\frac{1}{2}d=-120\) and because nobody hates fractions more than I do, I'm going to get rid of them by multiplying everything by 2 to get:

-g - d = -240

We've got these equations now, but what I'm going to do is to sub in what c equals (c = 4d) for c in the first equation:

 g + d + 4d = 440 and

 g + 5d = 440 and pair that with the one right above:

-g -  1d = -240 and use elimination to solve. The g's cancel each other out, leaving us with 4d = 200 and d = 50. So there were 50 ducks originally. Now we will sub that in to solve for c:

c = 4d so

c = 4(50) and

c = 200. Now we will sub both those values into the very first equation we put together to solve for g:

g + 200 + 50 = 440 and

g + 250 = 440 so

g = 190.

Add them all together just to be sure we have the 440 that we were told we had in the beginning (and we do, so we're all done!)

Answer:

Step-by-step explanation:

You want to know the intercepts and slope of the line whose equation is ...

  14x +y = 140

Each intercept is the solution to the equation when the other variable is set to zero.

To find the y-intercept, use x=0: y = 140.

To find the x-intercept, use y=0: 14x = 140   ⇒   x = 10

The slope is the coefficient of x when the equation is solved for y:

  14x +y = 140

  y = -14x +140 . . . . . the x-coefficient is -14

The y-intercept is 140; the slope is -14; the x-intercept is 10.

__

Additional comment

As you can see, when the equation is in standard form:

  ax +by = c

The intercepts are ...

  x-intercept = c/a

  y-intercept = c/b

and the slope is ...

  slope = -a/b

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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If a road was made directly from his home to his place of work, its distance will be 16.6 mi.

If a man drives east from his home, makes a left turn at an intersection, and then travels north to his place of work, then the path he travels resembles the sides of a right triangle (see attached photo).

if a road was made directly from his home to his place of work, then this path will be the hypotenuse of the triangular path.

Using Pythagorean theorem, we can solve for the distance of the road.

c^2 = a^2 + b^2

where c is the distance of the road

a is the distance he travels to the east

b is the distance he travels up north

c^2 = a^2 + b^2

c^2 = (14 mi)^2 + (9 mi)^2

c^2 = (196 + 81) mi^2

c^2 = 277 mi^2

c = 16.64331698 mi

distance of the road = c = 16.64331698 mi

Rounding off to the nearest tenth of a mile:

distance of the road = 16.6 mi

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To find and simplify f(p), where f(x) = -5x + 6, we substitute the variable p into the function and evaluate it. The simplified expression for f(p) is -5p + 6.

In this case, the function f(x) is given as -5x + 6. To find f(p), we substitute p in place of x in the function. Substituting p into the expression, we get -5p + 6. Thus, the simplified form of f(p) is -5p + 6.

The function f(x) represents a linear equation with a slope of -5 and a y-intercept of 6. When we substitute p for x, we essentially evaluate the function at the value p. The result, -5p + 6, gives us the value of f(p) for the given value of p. The expression -5p + 6 represents the linear equation with the same slope and y-intercept as the original function, but evaluated at the specific value of p. This means that if we substitute any value of p into f(p), the result will be -5 times that value plus 6.

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Answer: x^-4

Step-by-step explanation:

x^-10 · x^6

When you're multiplying exponents, use the first rule: add powers together when multiplying like bases.

-10 + 6 = -4

x^-4

324 is the maximum value of the product of these three numbers

What is maxima and minima?

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, and minima will be its lowest.

The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.

Let the three nonnegative numbers are x,y,z

According to the question

x+y+z=36

and y=2x

therefore, 3x+z=36--------------------------------------------------(1)

z=36-3x

Let 3xz= u--------------------------------------------------------------(2)

differentiating equation 2

du/dx=3z + 3xdz/dx

or

du/dx= z + xdz/dx

differentiating equation 1

3 + dz/dx = 0

dz/dx = -3

du/dz = 36-3x + x(-3)

du/dx = 12 - 2x--------------------------------------------------------------(3)

for maxima put du/dx = 0

x=6-------------------------------------------------------------------------------(4)

again differentiating du/dx = 12 - 2x

d2u/dx2=-2

which means 3xz= u is maximum at x=6

from equation 1 and 4

we get 18+z=36

z=18

Therefore 3xz= 3(6)(18)=324

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The updated solution is x1 = 5/2, x2 = 9/4, and x3 = 0.

To apply the Simple Active-Set Method to the given problem, we first write the Lagrangian function as:

L(x, λ) = x1^2 + 2x2^2 + 3x3^2 - λ(x1 + x2 + x3 - 1)

where λ is the Lagrange multiplier.

At each iteration, we need to identify the active set of constraints and solve a subproblem to find the search direction. We start with the initial guess x0 = (5, 9, 2)^T and assume that all constraints are inactive.

Step 1: Check Optimality

We calculate the gradient of the Lagrangian as:

∇L(x, λ) = [2x1 - λ, 4x2 - λ, 6x3 - λ, -(x1 + x2 + x3 - 1)]

Setting this gradient to zero, we get:

x1 = λ/2

x2 = λ/4

x3 = λ/6

x1 + x2 + x3 = 1

Substituting these values into the constraint inequalities, we get:

λ/2 ≥ 0

λ/4 ≥ 0

λ/6 ≥ 0

These conditions imply that λ ≥ 0. Since the objective function is strictly convex, the point x0 = (5, 9, 2)^T is not optimal.

Step 2: Identify Active Constraints

Since λ ≥ 0, the first two inequality constraints are inactive. The third inequality constraint is active, i.e., x3 = 0.

Substituting x3 = 0 into the objective function and the remaining constraints, we get:

minimize f(x) = x1^2 + 2x2^2

subject to x1 + x2 ≥ 1

x1 ≥ 0

x2 ≥ 0

The active-set subproblem is to minimize the above objective function subject to the given constraints.

Step 3: Solve Active-Set Subproblem

We use a reduced Newton method to solve the active-set subproblem. The reduced Hessian is given by:

H = [2  0]

[0  4]

At the current point x0 = (5, 9, 0)^T, we have:

∇f(x0) = [10, 36]^T

Solving the equation HΔx = -∇f(x0), we get:

Δx = [-5/2, -9/4]^T

Step 4: Update Solution

The search direction Δx is in the direction of decreasing f(x). However, we need to ensure that the constraints are satisfied after taking the step Δx. In particular, we need to check if any previously inactive constraints have become active or any previously active constraints have become inactive.

In this case, the only active constraint is x1 + x2 ≥ 1. We can take the full step Δx = [-5/2, -9/4]^T since it satisfies the constraint x1 + x2 ≥ 1.

Therefore, the updated solution is x1 = 5/2, x2 = 9/4, and x3 = 0.

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Answer:

The water level decreased by 1/18 inches each hour.

Step-by-step explanation:

A rate of change is a rate that describes how one quantity changes in relation to another quantity. Between 11 P.M. and 8:54 A.M.​, the water level in a swimming pool decreased by 11/20, for each hour it decreases by 33/554

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

Given that,  Between 11 P.M. and 8:54 A.M.​, the water level in a swimming pool decreased by 11/20. Assuming that the water level decreased at a constant​ rate, we need to find the amount of water level drop each​ hour.

In an hour we will have sixty minutes.

We need to calculate the number of minutes between 11 pm and 8: 54 am.

The minutes between 11 P.M. and 8:54 A.M. is 594 minutes.

So in 554 min water level drop is 11/20.

So in 1 min=11/20×1/554

So in 60 min

We need to multiply with sixty

= 60(11/20×1/554)

We need to solve 60(11/20×1/554), we get

=3(11/554)

3 times of eleven  by five hundred fifty four.

=33/554

Hence 33/554  water level drop each​ hour when water level decreased at a constant​ rate.

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Answer:

-72x^4 + 34x^3 + 145x^2 - 65x - 14

Step-by-step explanation:

(-9x² + 11x +2) x (8x² + 6x -7)

= -72x^4 - 54x^3 + 63x^2 + 88x^3 + 66x^2 - 77x + 16x^2 + 12x - 14

= -72x^4 + 34x^3 + 145x^2 - 65x - 14

So, the answer is  -72x^4 + 34x^3 + 145x^2 - 65x - 14

Answer:

Step-by-step explanation:

diameter = 2r  

where r = 9.8

plugin value of r = 9.8 into the formula:

diameter = 2(9.8)

               = 19.6 units

The length of the diameter of the circle is option D 19.6 units.

Diameter is defined as the line from one point in the circle to the other point through the center of the circle.

WE know that the diameter = 2r  

where r = 9.8

Substitute value of r = 9.8 into the formula:

The diameter = 2(9.8)

The diameter = 19.6 units

Hence, the length of the diameter of the circle is option D 19.6 units.

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The correct distance for placing the brake anchor is 6 feet away from the base of the tree.

Let's break down the information given:

Vince measured 24 feet away from the base of the tree because the bungee cord is 24 feet long.

He added 18 extra feet to allow the bungee cord to stretch to capacity.

Vince placed the brake anchor 42 feet from the base of the ending tree.

The flaw in Vince's process lies in his failure to account for the additional stretch of the bungee cord. By placing the brake anchor at 42 feet, he did not consider the extended length the bungee cord would reach.

To find the correct distance, we need to subtract the total length of the bungee cord, including the additional stretch, from the distance Vince measured. Let's calculate this step by step:

Total length of the bungee cord, including extra stretch:

24 feet (length of the bungee cord) + 18 feet (extra stretch) = 42 feet

Distance the brake anchor should be placed away from the base of the tree:

24 feet (Vince's measurement) - 42 feet (total length of the bungee cord) = -18 feet

The negative result indicates that Vince's anchor should be placed 18 feet closer to the base of the tree than his initial measurement. This means

=> (24 feet - 18 feet) = 6 feet.

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We establish the given binomial expression (x + y)^4 in the following way

The nth power of the sum of two integers a and b may be represented as the sum of n + 1 terms of the form, according to the binomial theorem, which states that for every positive integer n.

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

(x+y) 4=

((x+y)2) 2=

(x2+2xy+y2) 2=

(x2+2xy) 2+2(x2+2xy) (y2)+(y2) 2=

(x4+4x3y+4x2y2)+(2x2y2+4xy3)+(y4)=

x4+4x3y+6x2y2+4xy3+y4

The binomal theorem is a more comprehensive strategy:

(x+y)

n=∑k=0n(nk)

⋅xn−k⋅yk=∑k=0n(nk)

⋅xk⋅yn−k\sWhere\s(nk)=n!((n−k)!)⋅(k!)

n!={1n⋅((n−1)!)

n=0n>0

∑k=0nf(k)=f(0)+f(1)+f(2)+…+f(n)

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Answer:

4

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

It can't be 6 or 5 because 20 isn't divisible by 6 and 36 isn't divisible by 5

The area of the rooftop garden as required in the task content is; 272 ft².

It follows from the task content that the area of the rooftop garden is to be determined.

As evident in the attached image; the rooftop garden was modelled as a composite figure of a rectangle and a triangle.

Therefore, the area of the rooftop garden is the sum of areas of the rectangle and the triangle.

Where the heights of the triangle is; 20 - 12 = 8 ft.

Therefore, we have;

Area = { (1/2) × 8 × 8 } + { 12 × 20}

Area = 32 + 240

Area = 272 ft².

Ultimately, the required area of the rooftop garden is; 272 ft².

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The area of the equilateral triangle is approximately 58.78 square inches.

An equilateral triangle has all sides equal, so we can divide the perimeter by 3 :

45 inches ÷ 3 = 15 inches

Therefore, each side of the equilateral triangle measures 15 inches.

Area = (√3 / 4) x (side length)²

After putting the values,

Area = (√3 / 4) x 15 x 15 square inches

Area = (√3 / 4) x 225 square inches

Area = 58.78 square inches

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To sketch the region enclosed by the curves y = cos(x) and y = sin(2x) for the interval 0 ≤ x ≤ 2, we can follow these steps:

1. Plot the graphs of the two functions separately on the given interval.

For y = cos(x):

- Start by marking key points on the graph: (0, 1), (π/2, 0), (π, -1), (3π/2, 0), (2π, 1).

- Connect the points smoothly to create a curve that oscillates between 1 and -1.

For y = sin(2x):

- Start by marking key points on the graph: (0, 0), (π/4, 1), (π/2, 0), (3π/4, -1), (π, 0), (5π/4, 1), (3π/2, 0), (7π/4, -1), (2π, 0).

- Connect the points smoothly to create a curve that oscillates between 1 and -1, but with twice the frequency of the cosine curve.

2. Identify the region enclosed by the curves.

- The region enclosed by the curves is the area between the two curves from x = 0 to x = 2.

3. Shade the region enclosed by the curves.

- Shade the area between the two curves on the interval 0 ≤ x ≤ 2.

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9 kilograms of cashews were mixed with 3 kilograms of nuts to make 12 kg of the mixture.

What are the arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

Let's assume that x kilograms of cashews were mixed with (12 - x) kilograms of nuts costing $10 per kilogram to make 12 kg of the mixture.

The total cost of the cashews used in the mixture is 8x dollars, and the total cost of the nuts used is 10(12 - x) dollars. The total cost of the mixture is (12)(8.50) = 102 dollars.

Since the mixture contains 12 kg of nuts and cashews, we can set up the following equation to solve for x:

8x + 10(12 - x) = 102

Expanding the equation gives:

8x + 120 - 10x = 102

Simplifying and solving for x gives:

-2x + 120 = 102

-2x = -18

x = 9

Hence, 9 kilograms of cashews were mixed with 3 kilograms of nuts to make 12 kg of the mixture.

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Answer:

Im mad that you didnt helped me >:(