In the diagram below DA bisects

The solution to the system of equations is:x = -3 and y = 2.

To solve the following system of equations using matrix inverse:4x + 5y = 143x - 2y = -1

Using the matrix inverse, we can rewrite the system of equations into a matrix equation:

AX = B

where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

The variable matrix X can be found by multiplying the inverse of A to the constant matrix B, which is:X = A⁻¹B

To use matrix inverse, let us first obtain the coefficient matrix A, constant matrix B, and inverse of matrix A.

Then we will use these matrices to obtain the variable matrix X.

A = [4 5; 3 -2]

B = [14; -1]

A⁻¹ = (1/22) [-2 -5; -3 4]

X = A⁻¹BX = (1/22)[-2 -5; -3 4][14; -1]= [-3; 2]

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the randomly generated integer between 0 and 100 (inclusive). If there is a tie, the winner will be randomly selected from the tied submissions. What is the probability that a person who buys a ticket with a single submission will win the lottery

The probability that a person will win depends on the number of people who buy tickets and submit their integers. Assuming there are n participants, each person's submission has a 1/n chance of being selected as the winner.

Since there are 101 possible integers that can be generated, the probability that any given person's submission is exactly correct is 1/101. Therefore, the probability that a person who buys a ticket with a single submission will win the lottery is 1/n * 1/101.

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Answer:

x > 14

Step-by-step explanation:

Let the number of hours nathans volleyball team trains in a week be x

If the number 14 is less than the number of hours nathans volleyball team trains in a week, this is expressed as;

14 < x

Rearranging the inequality expression will reverse the inequality sign as shown;

x > 14

Hence the inequalities that represents the number of hours that the volleyball team trains in a week is x > 14

Answer:

P = 3/11

Step-by-step explanation:

There are:

6 red marbles

4 blue marbles

2 yellow marbles.

So there are a total of 12 marbles in the bag, such that each one has the same probability of being randomly picked.

We want to find the probability that the first pick is not yellow (so it can be either blue or red), and the second pick is a blue marble.

Now there are two cases.

The first marble is red and the second blue

the first marble is blue and the second blue

We need to find the probability in each case.

The probability that the first marble is red is equal to the quotient between the number of red marbles (6) and the total number of marbles (12)

p = 6/12

Now, for the second draw, we need a blue marble, the probability in this case is the quotient between the number of blue marbles (4) and the total number of marbles in the bag (now there are 11, because one is already taken)

q = 4/11

The joint probability is equal to the product of the individual probabilities, then:

P₁ = p*q = (6/12)*(4/11) = 2/11

And for the other case, we draw two blue marbles:

For the first draw, the probability is:

p = 4/12

And for the second draw, now there are 3 blue marbles and 11 total marbles, then the probability is:

q = 3/11

The joint probability is:

P₂ = (4/12)*(3/11) = 1/11

The total probability is then:

P = P₁ + P₂ = 2/11 + 1/11 = 3/11

Answer:

A

Step-by-step explanation:

First u need to do the square 7 times 7 is 49 and one triangle is 70 and divide that by 2 it will equal 35 so there is 4 triangles so times that by 4 is will equal 140 and plus 49 is will equal 189

Answer:

hey

Step-by-step explanation:

option A) i.e. 189 cms

The width of the tank, which has a length 4 feet longer than its width, the height is 2 feet more than the width which is three feet.

The Hit and Trial Method is a very useful to solve the roots in a equation. In this , substituting different values of the variable and checking the equality of LHS and RHS is the trial and error method.

We have a tank ( cuboid shape) with

length, width and height and volume of tank is 105 cubic feet. Let length , width and height of tank be "l" feet , "w " feet and "h" feet.

lenght, l = w + 4

height, h = w + 2

Volume of tank , V = l× h × w

=> (w + 4 )×w × (w + 2) = 105

=> w ( w² + 6w + 8) = 105

=> w³ + 6 w²+ 8 w = 105

Using the hit and trial method to solve the above cubic equation in one variable, w.

We get, w = 3

So, the required width is 3 feet .

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The simplified form of the expression is \(7x^5 - 3x^4 - x^3 - x^2 + 4x.\)

The given expression is a polynomial expression, which can be simplified by combining the like terms. The like terms have the same variable and the same exponent. The given expression can be rearranged and combined as follows:

To simplify the given expression, we need to combine the like terms.

Starting with the x^5 term, we see that there is only one term with \(x^5\)which is \(7x^5.\)

Moving on to the\(x^4\)terms, we have two terms with\(x^4,\) namely \(3x^4\)and \(-3x^4\), which add up to 0. Therefore, we can eliminate the\(x^4 t\)erms from the expression.

\(7x^5 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 - 3x^3\)

\(= 7x^5 - 3x^4 + 2x^3 - 3x^3 - 5x^2 + 4x^2 + 6x - 2x\) (rearranging the terms)

\(= 7x^5 - 3x^4 - x^3 - x^2 + 4x\) (combining the like terms)

Therefore, the simplified form of the expression is \(7x^5 - 3x^4 - x^3 - x^2 + 4x.\)

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The radius of the cone with the given volume and height is given by :

Option C. The radius of the cone is same as a cylinder with a volume 500(3) and with the same height.

As given in the question,

Volume of the cone = 500cm³

Height of the cone is equal to 5cm

Let 'r' be the radius of the cone

Volume of the cone = ( 1/3)πr²h

⇒500 = ( 1/3)πr²(5)

⇒500(3) = πr²(5)

Volume of the cylinder with same height = πr²(5)

As volume of cylinder = πr²h

Therefore, the radius of the cone with given volume and height is equal to option C. the radius of the cone is same as a cylinder which has volume (500)(3) and same height as of cone.

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The probability of selecting the 2 of hearts or the 4 of clubs from a 52-card deck is 51/2652.

The probability of selecting the 2 of hearts is 1/52 since there is only one 2 of hearts in the deck, and the probability of selecting the 4 of clubs is also 1/52 since there is only one 4 of clubs in the deck.

To calculate the probability of selecting either card, we add the probabilities: 1/52 + 1/52 = 2/52.

However, since we have counted the probability of selecting both cards (2 of hearts and 4 of clubs) twice, we need to subtract the probability of selecting both cards, which is 1/52 x 1/51 (probability of selecting the 2 of hearts and then the 4 of clubs without replacement).

Therefore, the final probability is (2/52) - (1/52 x 1/51) = 1/26 - 1/2652 = 51/2652.

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9514 1404 393

Answer:

  ∠Y = 55°

Step-by-step explanation:

Complementary angles have a sum of 90°.

  ∠S + ∠Y = 90°

  (5∠Y -240°) +∠Y = 90°

  6∠Y = 330° . . . . . . . . . . . . add 240°, collect terms

  ∠Y = 55° . . . . . . . . . divide by 6

Cost of Goods Manufactured is an accounting term used to describe the total cost of producing and manufacturing goods. It includes all direct and indirect costs of production, including labor, materials, overhead, and other expenses. Below are the five components of the cost of goods manufactured.

Direct Materials: It includes the cost of raw materials used in manufacturing a product.

Direct Labor: It includes the wages paid to workers who directly worked on the production line or in manufacturing a product.

Factory Overhead: It includes all indirect costs of manufacturing a product such as depreciation on equipment, rent, insurance, utilities, etc. Work-in-Process

Inventory: It includes the cost of materials, labor, and overhead that has been incurred but has not yet been completed. Finished Goods Inventory: It includes the cost of goods that have been fully manufactured but have not yet been sold.

To calculate the cost of goods manufactured, the sum of all these five components is calculated. It helps manufacturers to determine the total cost of goods manufactured and the cost per unit of production. Cost of goods manufactured is essential in determining the pricing strategy for a product as it helps to ensure that the product is profitable.

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I am very unsure what your question is, but the simple tip is to divide it by two each year as it is decreasing by a half..

To find the number of copies sold in subsequent years, you can use the formula:

N = N0 * (1/2)^t

where N is the number of copies sold in a given year, N0 is the initial number of copies sold (in this case, 600,000), t is the number of years since the book was released.

For example, to find the number of copies sold in the second year after the book was released:

N = 600,000 * (1/2)^1

N = 300,000

So, 300,000 copies were sold in the second year. To find the number of copies sold in subsequent years, you can continue to plug in values of t and solve for N.

The amount of wrapping paper, in square centimeters, needed to completely cover the cylinder is SA = 2π(1.2)² + 1.2π(3.8).

The lateral surface area of a cylinder is also called the curved surface area of the cylinder.

Suppose that Radius of the considered cylinder = 'r' units

Height of the considered cylinder = 'h' units

Then, the lateral surface area of that cylinder is:

\(S_L = 2\pi r h \: \rm unit^2\)

We are given that a cylinder with the diameter labeled 2.4 centimeters and the height labeled 3.8 centimeters.

Therefore, we have;

Diameter = 2.4 cm

Height = 3.8 cm

Radius = 1.2 cm

So, The total area is;

SA = 2π(1.2)² + 1.2π(3.8).

The amount of wrapping paper,needed to completely cover the cylinder

SA = 2π(1.2)² + 1.2π(3.8).

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Answer: The answer you're looking for is A.

Step-by-step explanation: 7th-grade math exam used the answer from the person above and they were right!

Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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Explanation:

distance = rate*time

Train A travels a distance of 100x kilometers after x hours elapse

Train B travels 150x kilometers

The two trains pass each other when their distances add up to the 200 kilometers mentioned. Assume the two trains are on separate parallel tracks.

trainA+trainB = 200

100x+150x = 200

250x = 200

x = 200/250

x = 4/5

They will pass each other at the 4/5  hour marker

This converts to (4/5)*60 = 0.8*60 = 48 minutes

It will take her less than 10 minutes to get to school if she goes at a speed of 40 miles per hour.

To find the time it will take Heidi to get to school at a speed of 40 miles per hour, we can use the formula:

Time = Distance / Speed

Let's assume the distance to school remains the same. We'll calculate the time using both speeds:

Speed = 27 miles per hour:

Time = Distance / Speed = Distance / 27 miles per hour = 10 minutes

Speed = 40 miles per hour:

Time = Distance / Speed = Distance / 40 miles per hour

Since we don't have the actual distance, we can't calculate the exact time. However, we know that the time will be less than 10 minutes because Heidi is traveling at a faster speed. So, it will take her less than 10 minutes to get to school if she goes at a speed of 40 miles per hour.

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Answer:

answer: 1/36 or 2.8%

Step-by-step explanation:

Green is the answer because probability for this will be found by doing the chances for both multiplied by each other there is a 1/6 chance of getting 5 so 1/6 x 1/6 = 1/36 so thats why green is the answer. Hope that helps!

The equation y = |x - 5| + |x + 5| can be rewritten as:

y = { -2x - 10, for x < -5,

 { 10, for -5 ≤ x ≤ 5,

 { 2x + 10, for x > 5.

When -5 < x < 5, both |x - 5| and |x + 5| are non-negative. So we can rewrite y = |x - 5| + |x + 5| as follows:

If x < -5, then x - 5 < -5 and x + 5 < 0, so we have:

y = -(x - 5) - (x + 5) = -2x - 10

If -5 ≤ x ≤ 5, then x - 5 < 0 and x + 5 ≥ 0, so we have:

y = -(x - 5) + (x + 5) = 10

If x > 5, then x - 5 ≥ 0 and x + 5 > 5, so we have:

y = (x - 5) + (x + 5) = 2x + 10

Therefore, the equation y = |x - 5| + |x + 5| can be rewritten as:

y = { -2x - 10, for x < -5,

 { 10, for -5 ≤ x ≤ 5,

 { 2x + 10, for x > 5.

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Given question is incomplete, the complete question is below

Rewrite each equation without absolute value for the given conditions. y = |x-5| + |x+5| if -5 < x < 5

Answer:

q²-10q+16

Step-by-step explanation:

FOIL stands for:

First -> (q-2)(q-8)

Outer -> (q-2)(q-8)

Inner -> (q-2)(q-8)

Last -> (q-2)(x-8)

Following FOIL, we get:

(q-2)(q-8)

(q)(q)+(q)(-8)+(-2)(q)+(-2)(-8)

q²-8q-2q+16

q²-10q+16

Therefore, the expanded form is q²-10q+16

To determine the revealed preference between bundles A, B, and C, we need to compare the choices made by Betty under different price conditions.  1. When prices are ($2, $4, $1), Betty chooses bundle C over bundle A. This implies that C is directly revealed preferred to A at these prices.

2. When prices are ($5, $3, $3), Betty chooses bundle A over bundle B. This implies that A is directly revealed preferred to B at these prices.

3. When prices are ($3, $1, $4), Betty chooses bundle B over bundle C. This implies that B is directly revealed preferred to C at these prices. Based on these comparisons, we can conclude the following: - Bundle C is directly revealed preferred to bundle A. - Bundle A is directly revealed preferred to bundle B. - Bundle B is directly revealed preferred to bundle C. There are no cases of indirect revealed preference, where one bundle is preferred to another through a series of choices. Therefore, each pair of bundles has a clear ordering of direct revealed preference. Bundle C is directly preferred to A, A is directly preferred to B, and B is directly preferred to C.

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9514 1404 393

Answer:

  6.302×10^7 kg

Step-by-step explanation:

Since we want to find the difference in mass, we need to have the same exponent on both numbers. For that purpose, it is convenient to change the representation of the train's mass to 0.998×10^7 kg.

The carrier has more mass by the amount of ...

  7.3×10^7 -0.998×10^7 = (7.300 -0.998)×10^7 = 6.302×10^7 . . . kg

_____

Your (scientific or graphing) calculator or a spreadsheet can figure this for you and give you the scientific notation display.

Answer:

Explanation:

First we evalaute g(x) at x = 3

Now we evaluate F(g(3)) by putting in g(3) = 9.

Hence,

which is our answer!

Answer:

Angle CAB= 28°

Angle ABC= 45°

Angle DCA= 73°

Angle DCE=107°

Step-by-step explanation:

The solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

(a - b) / (a + b) = 3/5

To solve for a in terms of b, we cross multiply:

5(a - b) = 3(a + b)

Expanding the brackets, we get:

5a - 5b = 3a + 3b

Simplifying the equation by combining like terms, we get:

5a - 3a = 8b

2a = 8b

Dividing both sides of the equation by 2, we get:

a = 4b

Therefore, the solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

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The complete question is:

The equation given is A = 4b. Please write an appropriate question related to this equation.

I hope this helps you

(3+19)+(4i-5i)

22-i

a) The relation is reflexive, symmetric, and transitive.

b) The relation is not reflexive, symmetric, or transitive.

a) For each watermelon x, x is related to x because the measured weight of x is at least the measured weight of x. Therefore, the relation is reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is also related to x (meaning the measured weight of y is at least the measured weight of x). Therefore, the relation is symmetric.

For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is related to z (meaning the measured weight of x is at least the measured weight of z). Therefore, the relation is transitive.

b) For each watermelon x, x is not related to x because no two watermelons have the same measured weight. Therefore, the relation is not reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is not related to x (meaning the measured weight of y is not at least the measured weight of x).

Therefore, the relation is not symmetric. For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is not related to z (meaning the measured weight of x is not at least the measured weight of z).

Therefore, the relation is not transitive.

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Answer:s

Step-by-step explanation:

If a number k, is selected at random from a set of 11 consecutive even integers, the  probability that k = 10 is 1/11

One number, k , is selected at random from a set of 11 consecutive even integers.

So, the sample space is 11

We need to find the  probability that k = 10

The desirable outcome is 1

Probability = desirable outcomes/sample space

P(k = 10) = 1/11

Therefore, if a number k , is selected at random from a set of 11 consecutive even integers, the  probability that k = 10 is 1/11.

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