Given that line k bisects BD at point C and that BC=9x−13 and BD=118, find CD.

Answer:

Subtracting the number 5 every time.

Answer:

x y

1 2

2 2

3 2

4 2

5 2

To write the equation y = -2x + 6 as a table, we need to substitute different values of x into the equation and solve for y. Here is an example of a table with some values of x and the corresponding values of y:

x y

1 4

2 2

3 0

4 -2

5 -4

Step-by-step explanation:

The probability of drawing two balls of the same color from the bag, where there are 6 green balls and 4 red balls, is 21%.

To determine the probability, we need to consider the possible combinations of drawing two balls from the bag. Since each ball is replaced after being drawn, the total number of possible outcomes is the product of the number of balls for each draw:

10 balls (6 green + 4 red) for the first draw multiplied by 10 balls for the second draw, resulting in 100 possible outcomes.

Next, we calculate the number of favorable outcomes, which means drawing two balls of the same color. We have two cases: drawing two green balls or drawing two red balls.

The number of ways to choose two green balls from the six available is C(6, 2) = 15, and the number of ways to choose two red balls from the four available is C(4, 2) = 6. Therefore, the total number of favorable outcomes is 15 + 6 = 21.

Finally, we divide the number of favorable outcomes (21) by the total number of possible outcomes (100) to obtain the probability: 21/100 = 0.21 or 21%.

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Answer: 490.63

Step-by-step explanation:

The two negatives cancel out when we divide or multiply. Think of negative as opposite. Having two opposites cancel.

The slash means fraction and it also means division

6/7 = 6 divided by 7

6/7 = six sevenths

So that allows us to go from fraction to decimal form 6/7 = 0.857 approximately after using your calculator or long division.

Answer: 8

\(m^{2} = 9+55\\m^{2} = 64\\m=8\)

Answer: m = 8

9 + 55 = 64

\(\sqrt{64}\) = 8

\(8^{2}\) = 64

Answer:if that is 68 get should be 68 degrees too

Step-by-step explanation:

Step-by-step explanation:

68+68+y=180

136+y=180

y=180-136

y=44°

T°=90-44

T°=46°

x+x+46=180

2x=180-46

2x=136

x=136÷2

x=38°

To find a particular solution for the differential equation x^2y''-3xy'+13y=2x^4, we can use the method of undetermined coefficients. We assume a particular solution of the form y_p = Ax^4 + Bx^3 + Cx^2 + Dx + E, where A, B, C, D, and E are constants to be determined. Substituting this into the differential equation and equating coefficients, we can solve for the constants and obtain the particular solution.

The given differential equation is a second-order linear homogeneous equation with constant coefficients. To find a particular solution, we need to add a function y_p that satisfies the equation, but is not a solution of the homogeneous equation. The method of undetermined coefficients assumes that the particular solution has the same form as the nonhomogeneous term, which is 2x^4 in this case. Since the degree of the polynomial is 4, we assume a particular solution of the form y_p = Ax^4 + Bx^3 + Cx^2 + Dx + E.

We differentiate this function twice to obtain y_p'' = 24Ax^2 + 12Bx + 2C and y_p' = 4Ax^3 + 3Bx^2 + 2Cx + D. Substituting these into the differential equation, we get:

x^2(24Ax^2 + 12Bx + 2C) - 3x(4Ax^3 + 3Bx^2 + 2Cx + D) + 13(Ax^4 + Bx^3 + Cx^2 + Dx + E) = 2x^4

Simplifying and equating coefficients, we get the following system of equations:

24A - 12B + 13A = 2 => A = 1/3
12A - 6B + 26B - 13D = 0 => B = -2/39
2C - 6C + 13C = 0 => C = 0
-3D + 13D = 0 => D = 0
13E = 0 => E = 0

Therefore, the particular solution is y_p = (1/3)x^4 - (2/39)x^3. The general solution is the sum of the homogeneous solution and the particular solution.

To find a particular solution for a differential equation, we can use the method of undetermined coefficients, which assumes that the particular solution has the same form as the nonhomogeneous term. We can solve for the constants by equating coefficients and obtain the particular solution. In this case, we assumed a particular solution of the form y_p = Ax^4 + Bx^3 + Cx^2 + Dx + E and found that the particular solution is y_p = (1/3)x^4 - (2/39)x^3. The general solution is the sum of the homogeneous solution and the particular solution.

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The probability that the family will have three children of the same gender is 1/4 or 25%.

To calculate the probability of having three children of the same gender, we can consider the possible outcomes for each child's gender.

Since the probability of having a boy or a girl is equal (assuming a 50% chance for each), we have two possible outcomes for each child: boy (B) or girl (G).

The total number of possible outcomes for the three children is 2 * 2 * 2 = 8, as each child has two possible genders.

Now, let's calculate the number of favorable outcomes where all three children have the same gender.

If they have all boys (BBB), there is only one favorable outcome.

If they have all girls (GGG), there is also only one favorable outcome.

Therefore, the total number of favorable outcomes is 1 + 1 = 2.

The probability of having three children of the same gender is then 2 favorable outcomes out of 8 possible outcomes, which can be expressed as 2/8 or simplified to 1/4.

So, the probability that the family will have three children of the same gender is 1/4 or 25%.

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Answer: good luck

Step-by-step explanation:

;)

Answer: x = 5

Step-by-step explanation:

Vertical angles are congruent. Hence, 30 = 6x. Diving both sides by 6 gives x=5

The solution to the given problem is `f(x + h) - f(x) / h = 10x + 5h + 3` and the slope of the given function `f(x) = 5x² + 3x` is `10x + 5h + 3`.

To evaluate and simplify the function `f(x) = 5x² + 3x`, we need to substitute the given equation in the formula for `f(x + h)` and `f(x)` and then simplify. Thus, the given expression can be expressed as

`f(x + h) = 5(x + h)² + 3(x + h)` and

`f(x) = 5x² + 3x`

To solve this expression, we need to substitute the above values in the above mentioned formula.

i.e., `

= f(x + h) - f(x) / h

= [5(x + h)² + 3(x + h)] - [5x² + 3x] / h`.

After substituting the above values in the formula, we get:

`f(x + h) - f(x) / h = [5x² + 10xh + 5h² + 3x + 3h] - [5x² + 3x] / h`

Therefore, by simplifying the above expression, we get:

`= f(x + h) - f(x) / h

= (10xh + 5h² + 3h) / h

= 10x + 5h + 3`.

Thus, the final value of the given expression is `10x + 5h + 3` and the slope of the function `f(x) = 5x² + 3x`.

Therefore, the solution to the given problem is `f(x + h) - f(x) / h = 10x + 5h + 3` and the slope of the given function `f(x) = 5x² + 3x` is `10x + 5h + 3`.

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The total milliliters of punch is 2x + y.

To find the total amount of milliliters of punch, we need to add together the amount of water, apple juice, and grape juice used to make it. Since the punch is made up of "water by volume" and "the rest is grape juice," we know that the ratio of water to grape juice is 1 : 1. If we know the amount of grape juice used in milliliters, we can use that to find the amount of water and apple juice used, and then add all three amounts together to find the total amount of milliliters of punch.

Let's say that "x" milliliters of grape juice were used to make the punch. Since the ratio of water to grape juice is 1 : 1, we know that the same amount of water, "x" milliliters, were used. To find the total amount of milliliters of water and grape juice, we add x + x = 2x milliliters.

However, the prompt also mention "apple juice" is also included in the punch, so we need to add the amount of apple juice used in the punch to find the total milliliters of punch. If the amount of apple juice used is "y" milliliters, then the total milliliters of punch is 2x + y.

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Answer:

h ≈ 259.81

Step-by-step explanation:

i used the hexagon calculator

Answer:

150 sqrt 3        = 259.8076  units^2

Step-by-step explanation:

Interior angles of hexagon = 120 degrees ....now look at the Right  1/2 of the hexagon...  see illustration....this is a trapezoid...

One base is 10 units

the other labelled 'base' is

 10 cos 60    +   10 cos 60   + 10    = 20 units

the height of this trapezoid is  10 sin 60 = 10 * sqrt(3)/2 = 5 sqrt(3)

   the area of this trapezoid is then   1/2 ( 10+ 20) * 5 sqrt (3)  = 75 sqrt 3

there are TWO of these trapezoids in the hexagon so total area is then

   2 * 75 sqrt 3

        150 sqrt 3

The probability P(A and B) has a value of (d) 0.2

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

These mean that

P(A) = 0.4

P(B) = 0.5

From the question, we have

The events are independent events

This means that

P(A and B) = P(A) * P(B)

So, we have

P(A and B) = 0.4 * 0.5

Evaluate

P(A and B) = 0.2

Hence, value is 0.2

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Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

Answer:

A) Plumber B charges 55 dollars per hour (105=50+55(1)) because for 1 hour the total is 105, meaning that 105 is y and 1 is x. 50+55=105

B) Plumber A charges more because he charges 100 dollars vs Plumber B's 50 dollars.

C) Plumber A:  250=100+30(5)       Plumber B:  325=50+55(5)

Plumber A charges less money for working 5 hours.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that,

Two plumbers charge an initial fee and an hourly rate.

The equation y=100+30x -----(I) models plumber A's fee, where y is the total charge, in dollars, and x is the number of hours worked.

Part A:

From the table, we have (1, 105) and (2, 160)

Now, m=(160-105)/(2-1)

= 55

Substitute m=55 and (x, y)=(1, 105) in y=mx+c, we get

105=55(1)+c

c=60

Substitute m=55 and c=60 in y=mx+c, we get

y=55x+60 -----(II)

By comparing (I) and (II), we can conclude that plumber B charges more hourly fee.

Part B: By comparing (I) and (II), we can conclude that plumber A charges more initial fee.

Part C: Substitute x=5 in y=100+30x, we get

y=$250

Substitute x=5 in y=55(5)+60, we get

y=$335

Plumber A charges less money for working 5 hours.

Therefore, plumber A charges more initial fee.

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If triangles 1 and 2 are similar then ratio of two sides is 25:52

A triangle is a polygon with edges and three terminals. It belongs to the basic geometric shapes. A triangle containing the angles A, B, and C is referred to by the term ABC.

Any three Euclidean points that are not collinear result in a triangle and a rectangle. In other words, any triangle is exclusively covered by that plane and is contained within that plane.

We know that any two triangles are similar by three axioms:

SSS , AAS , SAS or AAA axiom of similarity.

In the Euclidean plane, every triangle is contained within a single plane, but in higher-dimensional Euclidean spaces, this is no longer the case. This article addresses triangles in terms of geometry, more specifically the Euclidean plane, unless otherwise stated.

ratio of the sides of two triangle are in same ration when the triangles are similar

Now given ratio is 25:52, hence the ratio of the sides will be same.

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Answer:

3472

Step-by-step explanation:

pls mark brainiest I solved it.

Answer:

3.572

Step-by-step explanation:

I don't know what to explain or how

Answer:

1296

Step-by-step explanation:

Answer:

what i dont understand the word

Answer:

x>22

Step-by-step explanation:

Solve the inequality:

-3x<-14-52

-3x<-66

x>22

( You have to switch the sign because you are dividing by a minus)

Answer: 14

Step-by-step explanation:

Given

Excavation cone measures

height \(h=6\ ft\)

Diameter \(d=30\ ft\)

Truck can dump \(125\ ft^3\) at a time

The volume of a cone is

\(V=\dfrac{1}{3}\pi r^2h\)

Putting values

\(\Rightarrow V=\dfrac{1}{3}\times \pi\times 15^2\times 6\\\Rightarrow V=1413.9\approx 1414\ ft^3\)

No of trips(N) required to accumulate this much volume is given by

\(\Rightarrow N=\dfrac{1414}{125}=13.3\approx 14\)

Therefore, 14 trips are necessary to accumulate a cone of volume \(1414\ ft^3\)

Answer:

Step-by-step explanation:

Answer:

(a) To find the probability that at most 8 accidents involve a single vehicle, we need to calculate the probability of 0, 1, 2, ..., 8 accidents involving a single vehicle and then add them up. Using the binomial distribution formula with n=20 and p=0.6 (the probability of an accident involving a single vehicle), we get:

P(X ≤ 8) = Σi=0^8 (20 choose i) * 0.6^i * (1-0.6)^(20-i) = 0.000 + 0.002 + 0.014 + 0.062 + 0.178 + 0.345 + 0.409 + 0.262 + 0.068 = 0.999

Therefore, the probability that at most 8 accidents involve a single vehicle is 0.999.

(b) To find the probability that exactly 8 accidents involve a single vehicle, we simply plug in i=8 in the binomial distribution formula:

P(X = 8) = (20 choose 8) * 0.6^8 * (1-0.6)^(20-8) ≈ 0.167

Therefore, the probability that exactly 8 accidents involve a single vehicle is approximately 0.167.

(c) To find the probability that exactly 10 accidents involve multiple vehicles, we need to calculate the probability of exactly 10 accidents involving multiple vehicles and 10 accidents involving a single vehicle. Using the binomial distribution formula with n=20 and p=0.6, we get:

P(X = 10) = (20 choose 10) * 0.4^10 * 0.6^10 ≈ 0.117

Therefore, the probability that exactly 10 accidents involve multiple vehicles is approximately 0.117.

(d) To find the probability that between 5 and 8, inclusive, involve a single vehicle, we need to calculate the probability of 5, 6, 7, and 8 accidents involving a single vehicle and then add them up. Using the binomial distribution formula with n=20 and p=0.6, we get:

P(5 ≤ X ≤ 8) = Σi=5^8 (20 choose i) * 0.6^i * (1-0.6)^(20-i) ≈ 0.854

Therefore, the probability that between 5 and 8, inclusive, involve a single vehicle is approximately 0.854.

(e) To find the probability that at least 5 accidents involve a single vehicle, we need to calculate the probability of 5, 6, ..., 20 accidents involving a single vehicle and then add them up. Using the binomial distribution formula with n=20 and p=0.6, we get:

P(X ≥ 5) = Σi=5^20 (20 choose i) * 0.6^i * (1-0.6)^(20-i) ≈ 0.999

Therefore, the probability that at least 5 accidents involve a single vehicle is approximately 0.999.

(f) To find the probability that exactly 8 accidents involve a single vehicle and the other 12 involve multiple vehicles, we need to multiply the probability of 8 accidents involving a single vehicle by the probability of 12 accidents involving multiple vehicles. Using the binomial distribution formula with n=20 and p=0.6, we get:

P(X = 8) * P(X = 12) = (20 choose 8) * 0.6^8 * (1-0.6)^(20

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

(a) The given quadratic function is f(x1,x2) = 2x1^2 + x2^2 −2x1x2 + 2x1 − 2x2.

To find the global minimum (z) of f, we need to find the critical points of the function.

We can calculate the partial derivatives of f with respect to x1 and x2 as follows:

f1(x1,x2) = ∂f/∂x1 = 4x1 - 2x2 + 2f2(x1,x2) = ∂f/∂x2 = 2x2 - 2x1 - 2

Setting these partial derivatives to zero, we get4x1 - 2x2 + 2 = 0           (1)

2x2 - 2x1 - 2 = 0             (2))

Solving equations (1) and (2), we getx1 = 1 and x2 = 1

Substituting x1 = 1 and x2 = 1 in the given quadratic function, we get f(1,1) = -1

Therefore, the global minimum of f is z = -1 and its optimal value is f(x) = 2x1^2 + x2^2 −2x1x2 + 2x1 − 2x2.

(b) Suppose that we apply the steepest descent algorithm to f with setting α = minα f(x+αd)-f(x). If we start with ro- (0,0), then ind x1 and x2.

Initial point: r0 = (0, 0)

The gradient of f at point r0 is given by

∇f(r0) = (f1(r0), f2(r0))= (4r1 - 2r2 + 2, 2r2 - 2r1 - 2)

We need to find the direction d in which f decreases fastest. For this, we need to take the negative of the gradient, i.e., d = -∇f(r0) = (-4r1 + 2r2 - 2, -2r2 + 2r1 + 2)

We need to find the optimal value of α that minimizes f(x+αd)-f(x)

We haveα = minα f(r0+αd)-f(r0)= minα [2(r1 + αd1)^2 + (r2 + αd2)^2 - 2(r1 + αd1)(r2 + αd2) + 2(r1 + αd1) - 2(r2 + αd2)] - [2r1^2 + r2^2 - 2r1r2 + 2r1 - 2r2]= minα [2(4α^2 - 4α + 1) + 4α^2 - 4α + 1 - 4α^2 + 4α + 2α + 2] - [2(0)^2 + 0^2 - 2(0)(0) + 2(0) - 2(0)]= minα [4α^2 + 2α + 4] - 2= minα [4α^2 + 2α + 2]

Thus,α = -b/2a = -2/8 = -1/4

Substituting α = -1/4 in d, we get d = (-1/2, -1)Therefore,x1 = r1 + αd1 = 0 + (-1/2) = -1/2x2 = r2 + αd2 = 0 + (-1) = -1

Thus, (x1, x2) = (-1/2, -1)

(c) The optimality gap is given by f(x)-fa) = f(-1/2, -1) - f(1, 1)= 2(-1/2)^2 + (-1)^2 −2(-1/2)(-1) + 2(-1/2) − 2(-1) - [2(1)^2 + (1)^2 −2(1)(1) + 2(1) − 2(1)]= 5/2 - 3 = 1/2

For any nonnegative integer n, the explicit form of optimality gap f(x)-fa) is given by(1/2)2^(-n)

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Answer:-2x^2+16x-8

Step-by-step explanation:

the other person subtracted backwards ‍♀️

Answer:

6.32 cm

Step-by-step explanation:

Area of a circle = \(\pi r^2\)   (where r is the radius)

Given area = \(10\pi\) cm²

⇒ \(10\pi=\pi r^2\)

\(\implies 10=r^2\)

\(\implies r=\sqrt{10}\)

Diameter = 2r    (where r is the radius)

\(\implies d=2r=2\sqrt{10}=6.32\) cm (nearest hundredth)

Area of a circle = \(πr²\)

Given area = \(10π cm²\)

\(\bold\red{ ⇒} 10π = πr²\)

\(\bold\red{⇒ } 10 = r²\)

\(\bold\red{⇒ } r = \sqrt{10}\)

Diameter = [tex]2r\)

\(\bold\red{⇒}2\sqrt{10} =\bold\pink{6.32 cm} \) \(\bold\green{ [nearest \: hundredth]}\)