4. Expand these brackets:

a. 9(2q + 3)

Answer:

v = 5

Step-by-step explanation:

Collect like-terms:

[tex]8v = 3v + 25[/tex]

[tex]8v - 3v = 25[/tex]

[tex]5v = 25[/tex]

Divide both sides by 5 to make v the subject:

[tex]v = 5[/tex]

Based on these expected future dividends and the rate of return required by investors, the price of the stock should be $414 in year 1, $476 in year 2, $547 in year 3, $93.24 in year 4, $114.53 in year 5, and $138.49 in year 6.

To calculate the price of the stock, we need to first determine the expected future dividends. We know that the current dividend is $3.60, and we can use the dividend growth rate to calculate the expected future dividends.

For the first three years, we can use the 15% dividend growth rate to calculate the expected dividends as follows:

Year 1: $3.60 x 1.15 = $4.14

Year 2: $4.14 x 1.15 = $4.76

Year 3: $4.76 x 1.15 = $5.47

The Gordon growth model is as follows:

P = D / (r - g)

where:

P = price of the stock

D = expected dividend payment

r = rate of return required by investors

g = expected dividend growth rate

Using the formula, we can calculate the price of the stock as follows:

Year 1: P = $4.14 / (0.16 - 0.15) = $414

Year 2: P = $4.76 / (0.16 - 0.15) = $476

Year 3: P = $5.47 / (0.16 - 0.15) = $547

After year 3, the expected dividend growth rate is 8%, so we can use this rate to calculate the price of the stock beyond year 3.

Year 4: P = $5.47 x 1.08 / (0.16 - 0.08) = $93.24

Year 5: P = $5.96 x 1.08² / (0.16 - 0.08) = $114.53

Year 6: P = $6.47 x 1.08³ / (0.16 - 0.08) = $138.49

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After filling up the gravy dish, Bernice will have 410 ml of gravy left in the pot.

We have,

Determine the amount of gravy needed to cover the turkey:

We know that Bernice made 950 ml of gravy to go with a 5 kg turkey.

There are different ways to estimate how much gravy is needed to cover a turkey, but a common rule of thumb is to allow for about 1/2 cup (or 120 ml) of gravy per serving.

Assuming that the turkey will be served to about 8 people, we can estimate that Bernice will need:

We can write it as an expression:

= 120 ml/serving x 8 servings

= 960 ml of gravy

This means that Bernice made just enough gravy to cover the turkey and have a little bit left over.

Calculate how much gravy will be left in the pot:

We know that the capacity of the gravy dish is 540 ml.

If Bernice fills up the gravy dish with gravy, she will have.

= 950 ml - 540 ml

= 410 ml of gravy left in the pot.

Therefore,

After filling up the gravy dish, Bernice will have 410 ml of gravy left in the pot.

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Answer:

2 and 4

Step-by-step explanation:

Answer: 4,2

Step-by-step explanation:

Mode: Number that repeats itself more

If there are 2 or more numbers that repeat themself the same amount you put both.

4,2,4,2,3,0,1,2,4,1,3,4,2

4: 4 times

2: 4 times

3: 2 times

0: 1 time

1: 2 times

Answer:

c

Step-by-step explanation:

That's all because it makes more sense and uses a explanation

The surface area of the prism including rectangles and triangles is equal to 13920 square units.

Prism has,

Two rectangles with side length 20 and 120.

Area of rectangle = length × width

                             = 20 × 120

                             = 2400

2400 × 2 = 4800

Two rectangles with side length 20 and 30.

Area of rectangle = length × width

                             = 20 × 30

                             = 600

600 × 2 = 1200

Two rectangles with side length 17 and 120.

Area of rectangle = length × width

                             = 17 × 120

                             = 2040

2040 × 2 = 4080

One rectangle with side length 120 and 30

Area of rectangle = length × width

                             = 30 × 120

                             = 3600

Two triangles with base 30 and height 8.

area of triangle = ( 1/2) × 30 × 8

                          = 120

120 × 2 = 240

Surface area of the prism

= Area of all rectangles + Area of two triangles.

= 4800 + 1200 + 4080 + 3600 + 240

= 13920

Therefore, the surface area of the prism is equal to 13920 square units.

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Answer:

a= b/2

Step-by-step explanation:

it is in internet

​

Answer:y=4/3x-14/3

Step-by-step explanation:

1. Find the slope of the original line

3/4x-y=7/2

-y=-3/4+7/2

y=3/4x-7/2

2. Using this find the negative reciprocal

3/4 -------- -4/3

3. Now insert -2,-2 in the equation y=-4/3x

-2=-4/3(-2)

-2=8/3

4. Find the needed intercept to make true.

-2=8/3-14/3

Therefore, y=-4/3x-14/3

The volume of the rectangular prism is 97.5 cubic yards. (option b).

In this case, the rectangular prism has dimensions of 3 yards by 5 yards by 6 and one-half yard. To find its volume, we need to multiply these three dimensions together.

First, we need to convert the height of the prism to yards, as the other two dimensions are already given in yards. We know that 1 yard is equal to 3 feet, so 6 and one-half yards is equal to (6 x 3) + (1/2 x 3) = 18 + 1.5 = 19.5 feet. We then convert this to yards by dividing by 3, which gives us 6.5 yards.

Now, we can find the volume of the rectangular prism by multiplying the three dimensions together:

Volume = length x width x height

Volume = 3 yards x 5 yards x 6.5 yards

Volume = 97.5 cubic yards

Hence the correct option is (b).

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Pour développer il faut appliquer la distributivité de la multiplication :

7m + 5.5(2+m) = 7m + 5.5 x 2 + 5.5m

= 7m + 11 + 5.5m

Il faut combiner les termes contenant m :

= 7m + 5.5m + 11

= (7 + 5.5)m + 11

= 12.5m + 11

Answer:

Shandin should use the median to describe the prices since it is a more robust measure of center that is not affected by extreme values. In this case, the median is $80, which represents the middle value when the prices are arranged in ascending order: $65, $79, $80, $95, and $175. The mean and range can be affected by the extreme value of $175, and the MAD is a measure of dispersion rather than center.

Answer:

D

Step-by-step explanation:

The domain and the range of the given function is x ≥ 1 and y ≥ -4 respectively.

Given is a function, y ≤ √(x-1) -4, we need to find the domain and the range,

Domain = all the input values.

Range = all the output values.

So, the function is =

y ≤ √(x-1) -4

The related function can be written as =

y = √(x-1) -4

The function is defined if =

√(x-1) ≥ 0

∴ (x-1) ≥ 0

x ≥ 1,

In the given inequality, the sign of inequality is ≥, it means the points on the boundary line are included in the solution set. Thus, 1 is included in the domain.

So, the domain of the given inequality is x ≥ 1.

Now,

√(x-1) ≥ 0

√(x-1) -4 ≥ 0 - 4

y ≥ -4

The points on the boundary line are included in the solution set. Thus, -4 is included in the range.

So, the range of the given inequality is y ≥ -4.

Hence, the domain and the range of the given function is x ≥ 1 and y ≥ -4 respectively.

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The solution to the simultaneous equation is x = 6 and y = 3.

To solve this system of equations, we can use the method of elimination. First, we want to eliminate one of the variables, either x or y. In this case, it is easiest to eliminate y. To do so, we can multiply the second equation by 3, which gives us:

6x + 3y = 45

6x - 6y = 18

Now, we can subtract the second equation from the first:

6x + 3y - (6x - 6y) = 45 - 18

Simplifying this expression, we get:

9y = 27

Dividing both sides by 9, we get:

y = 3

Now that we know the value of y, we can substitute it into either equation to find the value of x. Let's use the first equation:

6x + 3y = 45

6x + 3(3) = 45

6x + 9 = 45

Subtracting 9 from both sides, we get:

6x = 36

Dividing both sides by 6, we get:

x = 6

Correct Question :

Solve the following simultaneous equation using algebra

6x+3y=45

2x-2y=6

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The probability of the high school baseball player getting at least 2 hits in a game with 8 at bats, given his 0.197 batting average, is approximately 0.378.

To calculate the probability of the player getting exactly 2 hits in the game, we can use the binomial probability formula:

P(X = x) = (n choose x) x pˣ x (1-p)ⁿ⁻ˣ

Where:

P(X = x) is the probability of getting exactly k hits

n is the number of trials (in this case, 8 at bats)

k is the number of successful trials (in this case, 2 hits)

p is the probability of a successful trial (in this case, 0.197)

Using this formula, we can calculate the probability of the player getting exactly 2 hits in the game:

P(X = 2) = (8 choose 2) x 0.197² x (1-0.197)⁸⁻² = 0.214

So the probability of the player getting exactly 2 hits in the game is 0.214.

To calculate the probability of the player getting at least 2 hits in the game, we need to add up the probabilities of getting exactly 2 hits, exactly 3 hits, exactly 4 hits, and so on, up to 8 hits. This can be a bit cumbersome to do by hand, but fortunately, there are tools available to help us with this.

Using a binomial probability calculator or a statistical software program, we can find that the probability of the player getting at least 2 hits in the game is approximately 0.378.

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The area of each wing to founds the total area as; 26000 square inches

We need to find the area of each wing to founds the total area In square inches

The dimensions are;

Length = 100 + 100 = 200 unit

Width = 70 + 70  = 130

Now the area of the wing

= Length x width

= 200 x 130

= 26000

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The 10th term of the sequence is 1024/729

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

a2 = 36

a7 = 128/27

The nth term of a geometric sequence is

an = a1 * r^(n -1)

So, we have

a2 = a1 * r = 36

a7 = a1 * r^6 = 128/27

Divide the equations

r^5 = (128)/(27 * 36)

This gives

r = [(128)/(972)]^1/5

So, we have

r = [(32)/(243)]^1/5

r = 2/5

Also, we have

a1 = 128/(27r^6)

The 10th term of the sequence is

a10 = a1 * r^9

So, we have

a10 = 128/(27r^6) * r^9

This gives

a10 = 128/(27) * r^3

This gives

a10 = 128/(27) * [2/3]^3

Evaluate

a10 = 128/27 * 8/27

This gives

a10 = 1024/729

Hence, the 10th term is 1024/729

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The probability of winning on the first roll is 0.22

Solution-

As in the game of casino, two dice are rolled simultaneously.

So the sample space would be,

|S| = 36

Let E be the event such that the sum of two numbers are 7, so

E = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

|E| = 6

P(E) = 6/36

Let F be the event such that the sum of two numbers are 11, so

F = {(6,5), (5,6)}

|F| = 2

P(F) = 2/36

Now,

P(E∪F)= 0.22

The probability of winning on the first roll is 0.22

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For Matthew, the height is given as [tex]52 + 8 sin (\pi/6t)[/tex]

To express the characteristic repetition of certain actions or events, a sine function is often employed.

This mathematical function links a position on the edge of a unit circle with the height of its corresponding y-coordinates. Conveyed generally as sin(x), it represents angle measurement in radians.

This repeatable pattern attains values between -1 to 1 and reappears once per every 2π radians. There are numerous applications of this type of sinusoidal oscillation pattern, including signal processing, engineering, and physics among others.

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The new coordinates of the vertices of the translated triangle are A′(−3, 6), B′(0, 10), and C′(−3, 3). (option 2)

A triangle is a three-sided polygon with three vertices. In this problem, we are given a triangle ABC with vertices A(−3, 3), B(0, 7), and C(−3, 0). The coordinates of the vertices represent the location of each vertex in the coordinate plane.

Using this method, we can determine the new coordinates of the vertices of the translated triangle. The options given for the new coordinates of the vertices are:

A′(−3, 0), B′(0, 4), C′(−3, −3)

A′(−3, 6), B′(0, 10), C′(−3, 3)

A′(−6, 3), B′(−3, 7), C′(0, 0)

A′(0, 3), B′(3, 5), C′(0, 0)

We can check each option by adding 3 to the y-coordinate of each vertex in the original triangle.

In the first option, the new coordinates of vertex A are (−3, 3+3) = (−3, 6), which matches the coordinates given in option 2.

Therefore, the correct answer is option 2.

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The graph of the equation above include the following: D. graph D.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first graph of a quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function y= 1/2x² + 2x -6 is positive 1/2, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -8.

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This week, Michelle works 33 hours. She is paid $10 per hour. Her take-home pay is $277.11 after taxes. She pays $ 52.89 in payroll tax.

We know that Michelle works for 33 hours this week and her pay for one hour is $10. So, firstly we will calculate her total pay for this week.

Total pay for week = pay for one hour × hours worked

= 10 × 33

= $ 330

Now, after taxes her pay is $277.11. So,

Tax = Pay before tax - pay after tax

= 330 - 277.11

= $ 52.89

A payroll tax is a tax paid by both employees and employers on wages, tips, and salaries. Employers withhold taxes from employees' paychecks and pay them to the government.

Federal, state, and municipal income taxes, as well as the employee's contribution of Social Security and Medicare taxes (FICA), are all included.

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The inverse of the given function include the following: A. G⁻¹(x) = (x + 2)/5

In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

g(x) = y = 5x - 2

x = 5y - 2

5y = x + 2

By dividing all through by 5, we have;

G⁻¹(x) = y⁻¹ = (x + 2)/5

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The resistance in the circuit is 9.6 Ohms.

Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.

Given that:

V = √(PR)

Where P is the power and R is the resistance in ohms.

Make the resistance R, the subject of the formula.

V = √(PR)

V² = (√(PR) )²

V² = PR

PR = V²

R = V²/P

Plug in Voltage V = 120V and Power P = 1500 watts

R = V²/P

R = (120)² / 1500

R = 14400 / 1500

R = 9.6 Ω

Therefore, the resistance is 9.6 Ω.

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The area of the enclosed region is  16√2 - 8 squared units

We have,

The region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π consists of two parts, one above the x-axis and one below the x-axis. We can find the area of each part separately and then add them to get the total area.

First, let's find the x-coordinates of the points where the curves intersect. These are the points where 4 sin(x) = 4 cos(x), or sin(x) = cos(x), which occurs when x = π/4 + kπ/2 for any integer k. Since we are only interested in the intersection points between x = 0 and x = 0.9π, we only need to consider the case k = 0. So the intersection point is x = π/4.

Now, let's consider the part of the region above the x-axis. We need to find the area between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = π/4. This is given by the integral:

A1 = ∫[0, π/4] (4 sin(x) - 4 cos(x)) dx

Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:

A1 = ∫[0, π/4] (4 sin(x) - 4 sin(x + π/2)) dx

 = ∫[0, π/4] (4 sin(x) + 4 sin(x)) dx   (since sin(x + π/2) = sin(x))

 = 8 ∫[0, π/4] sin(x) dx

 = 8 [-cos(x)] [0, π/4]

 = 8 (1 - 1/√2)

 = 8√2 - 8

Next, let's consider the part of the region below the x-axis. We need to find the area between the curves y = 4 cos(x) and y = 4 sin(x) from x = π/4 to x = 0.9π. This is given by the integral:

A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 sin(x)) dx

Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:

A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 cos(x - π/2)) dx

 = ∫[π/4, 0.9π] (4 cos(x) + 4 sin(x)) dx   (since cos(x - π/2) = sin(x))

 = 4 ∫[π/4, 0.9π] (2 cos(x) + 2 sin(x)) dx

 = 4 [2 sin(x) - 2 cos(x)] [π/4, 0.9π]

 = 4 (2/√2 + 2) - 4 (1 - 1/√2)

 = 8√2

So the total area of the region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π is:

A = A1 + A2

A = 8√2 - 8 + 8√2

A = 16√2 - 8 squared units

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We can add 13 and 15, or 49 and 28, or 20 and 47, or 45 and 35 to make 10 in the equations

To add choose 2 numbers to make 10, we can use the fact that 10 is the sum of 6 and 4.

Therefore, we can add a number that is 6 more than 10 and another number that is 4 less than 10.

This gives us the following equations:

13 + 15 = 28, since 13 + 15 = 28 and 10 = 6 + 4

49 + 28 = 77, since 49 + 28 = 77 and 10 = 6 + 4

20 + 47 = 67, since 20 + 47 = 67 and 10 = 6 + 4

45 + 35 = 80, since 45 + 35 = 80 and 10 = 6 + 4

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Answer: 6.996

Step-by-step explanation:

As given in the problem, V = πr²h

We are given V and r, so all we must do is plug them in and solve for h

[tex]351.68=\pi (4)^2h\\351.68=\pi 16h\\h=6.996[/tex]

Answer:

B 2

Step-by-step explanation:because a quart is 0.25 of a gallon

The correct statement about the product of 5/12 and 7 is given as follows:

C. The product is greater than 5/12 but less than 7.

The multiplication operation for this problem is given as follows:

5/12 x 7.

The factors of the operation are given as follows:

5/12 and 7.

When two fractions multiply each other, the product is given by the multiplication of the numerators divided by the multiplication of the denominators, hence:

5/12 x 7 = (5 x 7)/(12 x 1) = 35/12.

35/12 is a number close to 3, which is:

Hence option C is the correct statement.

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