will provide image of problem

Answer:

I think 1st option is ✔️ correct

Answer:

ACE

Step-by-step explanation:

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Answer: B

Step-by-step explanation:

2/3 means 1.5

Answer:

Undefined

Step-by-step explanation:

Answer:

4.9 in

Step-by-step explanation:

6/11 = x/9

6/11 times 9 = x

x = 4.9

The vertex form of the quadratic equations in standard form are, respectively:

Case 9: y = 2 · (x + 2)² - 12

Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11: y = 3 · (x - 4 / 3)² - 16 / 3

Case 12: y = - 3 · (x - 3)²

Case 13: y = (x - 4)² + 3

Case 14: y = (x - 1)² - 7

Case 15: y = (x + 3 / 2)² - 9 / 4

Case 16: 2 · (x + 1 / 4)² - 1 / 8

Case 17: y = 2 · (x - 3)² - 7

Case 18: y = - 2 · (x + 1)² + 10

In this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.

The two forms are introduced below:

Standard form

y = a · x² + b · x + c

Where a, b, c are real coefficients.

Vertex form

y - k = C · (x - h)²

Where:

Now we proceed to determine the vertex form of each quadratic equation:

Case 9

y = 2 · x² + 4 · x - 4

y = 2 · (x² + 2 · x - 2)

y = 2 · (x² + 2 · x + 4) - 12

y = 2 · (x + 2)² - 12

Case 10

y = - (1 / 2) · x² - 3 · x + 3

y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]

y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)

y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11

y = 3 · x² - 8 · x

y = 3 · [x² - (8 / 3) · x]

y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)

y = 3 · (x - 4 / 3)² - 16 / 3

Case 12

y = - 3 · x² + 18 · x - 27

y = - 3 · (x² - 6 · x + 9)

y = - 3 · (x - 3)²

Case 13

y = x² - 8 · x + 19

y = (x² - 8 · x + 16) + 3

y = (x - 4)² + 3

Case 14

y = x² - 2 · x - 6

y = (x² - 2 · x + 1) - 7

y = (x - 1)² - 7

Case 15

y = x² + 3 · x

y = (x² + 3 · x + 9 / 4) - 9 / 4

y = (x + 3 / 2)² - 9 / 4

Case 16

y = 2 · x² + x

y = 2 · [x² + (1 / 2) · x]

y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)

y = 2 · (x + 1 / 4)² - 1 / 8

Case 17

y = 2 · x² - 12 · x + 11

y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)

y = 2 · (x - 3)² - 7

Case 18

y = - 2 · x² - 4 · x + 8

y = - 2 · (x² + 2 · x - 4)

y = - 2 · (x² + 2 · x + 1) + 2 · 5

y = - 2 · (x + 1)² + 10

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Answer:

The value is  \(P(X > 3.30) = 0.12405\)

Step-by-step explanation:

From the question we are told that

   The mean GPA is  \(\mu = 3.25\)

   The standard deviation is \(\sigma = 0.75\)

    The sample size is  n  =  300

Generally the standard error of mean is mathematically represented as

     \(\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }\)

=>   \(\sigma_{\= x} = \frac{0.75}{\sqrt{300} }\)

=>   \(\sigma_{\= x} = 0.0433\)

Generally the  probability that a random sample of 300 students will have a mean GPA greater than 3.30 is mathematically represented as

     \(P(X > 3.30) = P(\frac{X - \mu}{\sigma_{\= x}} > \frac{3.30 -3.25}{ 0.0433} )\)

\(\frac{\= X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ \= X )\)

    \(P(X > 3.30) = P(Z> 1.155 )\)

From the z table the probability of  (Z >  1.155 ) is

     \(P(Z> 1.155 ) = 0.12405\)

   \(P(X > 3.30) = 0.12405\)

Answer:

4.3362962963

Step-by-step explanation:

A=1/2bh

29.7cm^2=1/2 13.5h

You're gonna multiply each side by 2 to cancel out the fraction equaling,

58.54= 13.5h

You're then gonna divide w=each side by 13.5 to get h left alone on one side and a number on the other equaling your answer. 4.3362962963. Round to whatever decimal place you need.

The rate of change of the simple index over one day is approximately 12.78%.

To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.

On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:

Total value of Stock A on Monday = 5000 * $2.75 = $13,750

Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:

Total value of Stock B on Monday = 3000 * $4.30 = $12,900

The total value of the index on Monday is the sum of the values of Stock A and Stock B:

Total value of the index on Monday = $13,750 + $12,900 = $26,650

On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.

The total value of Stock A on Tuesday is:

Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500

The total value of Stock B on Tuesday is:

Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550

The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:

Total value of the index on Tuesday = $15,500 + $14,550 = $30,050

To calculate the percent change in the index, we use the formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%

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The value of \(b_{1}\) is 69/4h and value of \(b_{2}\) is 43/4h if the area of trapezoid is 14 square units.

Given that area is equal to 1-2(\(b_{1} -b_{2}\))h and area is 14 square units.

We know that area of trapezoid is equal to (a+b)h/2.

We have to put the given equation equal to 14 to get our first equation.

14=1-2(\(b_{1} -b_{2}\))h

14=1-2\(b_{1}\)h+2\(b_{2}\)h

2\(b_{1}\)h-2\(b_{2}\)h=-13------------1

Now put the value of area in the formula of area of trapezoid.

14=\((b_{1} +b_{2})h/2\)

\(b_{1}\)h+\(b_{2}h\)=28-----------------2

Multiply equation 2 by 2 and then subtract 2 from 1

\(2b_{1}h -2b_{2}h -2b_{1}h-2b_{2}h\)=-13-56

-4\(b_{2}h\)=-43

\(b_{2}\)=43/4h

Put the value of \(b_{2}\) in 2 to get the value of \(b_{1}\).

\(b_{1} h+43/4h*h=28\)

\(b_{1}\)=69/4h

Hence The value of \(b_{1}\) is 69/4h and value of \(b_{2}\) is 51/4h if the area of trapezoid is 14 square units.

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Answer:

There are six possible committees if only men are chosen

Step-by-step explanation:

Here, we want to find the number of possible committees if only men are chosen

In this case, what will happen is that we shall be selecting the 5 people from the available 6 men

Mathematically, we can have this in 6C5 ways

which is read as 6 combination 5 ways

And that will be 6 ways

So there are six possible committees if only men are selected

Answer:

\(y = 25x +1950\)

Step-by-step explanation:

Given

\((x_1,y_1) = (30,2700)\)

\((x_2,y_2) = (50,3200)\)

Required

Determine the linear function

We start by calculating the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

So, we have:

\(m = \frac{3200 - 2700}{50 - 30}\)

\(m = \frac{500}{20}\)

\(m = 25\)

The equation is then calculated as:

\(y - y_1 = m(x - x_1)\)

This gives:

\(y - 2700 = 25(x - 30)\)

\(y - 2700 = 25x - 750\)

Make y the subject

\(y = 25x - 750 + 2700\)

\(y = 25x +1950\)

The coordinates of point Q in the rectangle named QRST is (5, 5).

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given:

We have the Graph having coordinate T(5, 2).

and, length of QT = 3 unit

As, the vertical distance shows the y coordinate then the y coordinate of Q is 3.

and, the x coordinate is same as T.

Then, the Coordinate of Q is (5, 2+3) or (5, 5).

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Answer:

B, A, C

Step-by-step explanation:

add the like terms together (ending in x2 with x2, ending in x with x etc )

Answer:

B A C

Step-by-step explanation:

combining like terms

The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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Haleema would have approximately £3947.46 in her account after 2 years and 11 months, considering the monthly compounding interest of 5%.

To calculate the amount of money in Haleema's account after 2 years and 11 months, we need to consider the monthly compounding interest on the account.

The interest rate is given as 5% per year, which means the monthly interest rate is (5%/12) = 0.4167%.

Let's calculate the final amount using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = £3700, r = 0.004167, n = 12 (monthly compounding), and t = 2.917 (2 years and 11 months).

Plugging these values into the formula, we get:

A = £3700(1 + 0.004167/12)^(12*2.917)

A ≈ £3947.46

The amount of money in Haleema's account after 2 years and 11 months would be approximately £3947.46.

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Polynomial M is 2(x - \((\frac{1}{12}a)^{2}\) - (1/72)\(a^{2}\) + by

To find the polynomial M, we need to rearrange the equation given to us. We can start by adding M to both sides of the equation to isolate the constant term. This gives us:

2\(x^{2}\) - (1/3)ax + by = M

Now, we have the polynomial M in terms of x, a, b, and y. However, this is not in its simplest form yet. We can simplify this further by factoring out the coefficient of x. This gives us:

2(\(x^{2}\) - (1/6)ax) + by = M

Now, we can complete the square inside the brackets to get a perfect square trinomial. This means taking half of the coefficient of x, squaring it, and adding it and subtracting it inside the brackets. This gives us:

2((x - \((\frac{1}{12}a)^{2}\)  - (1/144)\(a^{2}\)) + by = M

Simplifying this further, we get:

2(x - \((\frac{1}{12}a)^{2}\)  - (1/72\(a^{2}\) + by = M

Therefore, the polynomial M is given by:

M = 2(x - \((\frac{1}{12}a)^{2}\)  - (1/72)\(a^{2}\) + by

This is the final answer for the polynomial M.

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Polynomials are algebraic expressions whose standard form is defined below:

\(p(x) = \sum \limit_{i=0}^{n} c_{i}\cdot x^{i}\)

The expression p(x) = - 13 represents a zeroeth polynomial.

Herein we must present what the form of polynomials are. Polynomials are algebraic expressions whose standard form is defined below:

\(p(x) = \sum \limit_{i=0}^{n} c_{i}\cdot x^{i}\)     (1)

Where:

An example is the expression p(x) = - 13, real numbers can be define as zeroeth polynomials. In this regard, the example can be seen as:

p(x) = 0 · xⁿ + 0 · xⁿ⁻¹ + ... + 0 · x² + 0 · x - 13

The statement is incomplete. We decided to re-define the statement to what polynomials are.

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Answer:

4/5

Step-by-step explanation:

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(2,\:-5\right),\:\left(x_2,\:y_2\right)=\left(12,\:3\right)\\\\m=\frac{3-\left(-5\right)}{12-2}\\\\m =(\frac{3+5}{12-2})\\\\ m=(\frac{8}{10})\\ \\Simplify\\m=\frac{4}{5}\)

For the linear function built from the scatter plot, it is found that:

The slope-intercept representation of a linear function is the rule presented as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:

b = 500.

When the input increases by 200, the output increases by 1000, hence the slope is:

m = 1000/2 = 5.

Thus the equation is:

y = 5x + 500.

The graph is given by the image at the end of the answer.

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Part (a)

The equilibrium price occurs at the intersection of the supply and demand curves. See the diagram below to see how this looks. Ignore the red line and green lines for now. Those will apply for part (b).

If the price was below equilibrium, then we would have a shortage and it would lead to a pressure to push prices upward. If the price was below equilibrium, then there would be a surplus or oversupply, leading to a downward pressure in prices. So inevitably the price lands on the equilibrium if given enough time and there are no external forces acting on the market.

==============================================================

Part (b)

Let's say we have two people labeled person A and person B. If person A gets a higher education, while person B does not, then person A is likely to earn more money. Person B will see this and want to may want to earn more money as well, so that makes their demand for higher education go up.  While of course this rule doesn't work for everyone, in general we'll have enough people to effectively push the demand curve to the right while the supply curve remains where it is. Check out the diagram below to see what I mean.

==============================================================

Part (c)

Refer to the diagram in part (b). We have a new demand curve which intersects the supply curve to produce a new equilibrium point with price P1 and quantity Q1. So effectively the tuition has gone up due to higher demand.

==============================================================

Part (d)

If a government provides a subsidy, then this would lower the cost of education to provide people with more opportunities to improve their earning potential. The subsidy would provide a portion of the tuition which gives the illusion of the tuition price being lowered. In a way it's like getting a grant from the government to then pay that money toward your tuition.

29 years from now, the father will be 49 years old.

Let's start by setting up the given information:

Currently, the father is 20 years old, and the son is 5 years old.

In 10 years, the father will be twice as old as the son.

The father is currently four times as old as the son.

Determine the age of the father and son in 10 years:

In 10 years, the father's age will be 20 + 10 = 30 years.

In 10 years, the son's age will be 5 + 10 = 15 years.

Write equations based on the given information:

The father's age in 10 years will be twice the son's age in 10 years: 30 = 2 × 15.

The father's current age is four times the son's current age: 20 = 4 × 5.

Solve the equations:

From the second equation, we find that the son's current age is 5 years.

Plugging this value into the first equation, we get: 30 = 2 × (5 + 10).

Simplifying further, we have: 30 = 2 × 15, which is true.

Determine the current age of the son in 29 years:

The son's current age is 5 years.

Adding 29 years to the son's current age, we find that the son will be 5 + 29 = 34 years old.

Determine the current age of the father in 29 years:

The father's current age is 20 years.

Adding 29 years to the father's current age, we find that the father will be 20 + 29 = 49 years old.

Therefore, 29 years from now, the father will be 49 years old.

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The domain of the function above is [-2, 3].

The range of the function above is [-2.5, 2].

The intervals over which the function is increasing is [-2, 1.5] U [-2.5, 2].

The intervals over which the function is decreasing is [1.5, -2.5].

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this rational expression (function)   shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-2, 3] or -2 ≤ x ≤ 3.

Range = [-2.5, 2] or -2.5 ≤ y ≤ 2.

Additionally, the intervals over which the function is increases over the interval [-2, 1.5] and [-2.5, 2], while it decreases over the interval [1.5, -2.5].

In conclusion, the given function is not constant over any interval.

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Certain types of songs tend to have a call-and-response structure because A. It can have many different sections

A call and response in music is a series of two independent phrases that are typically composed in separate portions of the piece, with the second phrase being heard as a direct remark or answer to the first.

Direct imitation between instruments, a questioning phrase and subsequent response, a statement of affirmation from one instrument to another, or variations on a direct call by a group of instruments are examples of call and response.

Therefore, certain types of songs tend to have a call-and-response structure because it can have many different sections

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Answer:

did not list

Step-by-step explanation:

Answer:

Step-by-step explanation:

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

V = (3.14)(16)(12)

V = 50.24 cm³