Let X1,X2,...,Xn be a random sample from a normal distribution N(μ,36). It can be shown that RR={(x1,…,xn):∑ni=1x2i≥c is the best critical region for testing H0:σ2=4 against Ha:σ2=16. Find the probability of type II error β when n=15 and α=0.05.

One variable, from either of the equations, the subject of that equation and substitute it in the other equation.

We have,

To describe the process of solving a system of equations using substitution.

Now,

For any given system of linear equations, we use a method called substitution method for solving the equations.

We can make one variable, from either of the equations, the subject of equation and substitute it in the other equation.

This way, we get to find the value of the remaining variable and next we substitute this value in one of the equations to get the value of the variable left.

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System of linear equations represented by the augmented matrix . It means that we can take any real value for x1 and x2, while x3 will always be -t/6. Here, the system of linear equations has an infinite number of solutions.

The augmented matrix | 1 0 0 || 0 1 6 | is representing the following system of linear equations;`x1 = 0``x2 + 6x3 = 0`Using x2 = t and

solving for x1 in terms of t;x2 = tx1 = 0 (when x2 = t)Then, the solution set of the system of linear equations represented by the augmented matrix | 1 0 0 || 0 1 6 | is {x1=0, x2=t, x3=-t/6}

where t is an arbitrary constant.

We can see that x1 and x2 are arbitrary constants, but x3 = -t/6. It means that we can take any real value for x1 and x2, while x3 will always be -t/6.

Here, the system of linear equations has an infinite number of solutions.

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The hour hand will stop at the 9 o'clock position.A clock typically has 12 hours marked on its face, and a complete revolution of the hour hand corresponds to 12 hours or 360 degrees.

To determine where the hour hand will stop after making 3/4 of a revolution clockwise, we need to calculate the angle it will cover in a equation.

A full revolution is 360 degrees, so 3/4 of a revolution is (3/4) * 360 = 270 degrees.

Starting at the 12 o'clock position, the hour hand will move clockwise, and after covering 270 degrees, it will stop at a new position.

To find the location on the clock where the hour hand stops, we divide 270 degrees by the angle covered by each hour mark on the clock face. Since the hour hand moves 30 degrees for each hour (360 degrees divided by 12 hours), we divide 270 by 30:

270 degrees / 30 degrees per hour = 9 hours.

Therefore, the hour hand will stop at the 9 o'clock position.

To summarize, if the hour hand starts at 12 and makes 3/4 of a revolution clockwise, it will stop at the 9 o'clock position.

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The capacitance of a parallel plate capacitor can be calculated using the formula:

C = (ε₀ * A) / d

Therefore, the correct option is:

d. 2.3 x 10^-10 F

Where:

C is the capacitance

ε₀ is the permittivity of free space (approximately 8.854 x 10^-12 F/m)

A is the area of one of the plates

d is the separation distance between the plates

Given that the radius of each plate is 2.5 mm, the area (A) can be calculated as follows:

A = π * r^2

A = π * (2.5 mm)^2

The separation distance between the plates is 0.75 mm.

Now we can substitute the values into the capacitance formula:

C = (ε₀ * A) / d

C = (8.854 x 10^-12 F/m) * (π * (2.5 mm)^2) / (0.75 mm)

Let's calculate the value:

C ≈ 2.3228 x 10^-10 F

Rounding to the nearest significant figure, the capacitance is approximately 2.3 x 10^-10 F.

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De acuerdo con lo anterior podemos inferir que para los amigos Pedro y John, el incremento de masa muscular se representa por un número decimal periódico mixto.

El número decimal periódico mixto se refiere a un número decimal que tiene una parte entera, una parte decimal y una parte periódica, que se repite de forma continua.

Al observar los incrementos de masa muscular de los amigos, encontramos que Pedro tiene un incremento de masa muscular de 5/6 kg, lo cual se representa como 0.8(3) kg, donde el "3" se repite de forma continua.

Por otro lado, John tiene un incremento de masa muscular de 16/45 kg, que se representa como 0.3(5) kg, donde el "5" se repite de forma continua.

Entonces, la respuesta correcta es la opción D: Pedro y John.

Nota: Esta pregunta está incompleta. Aquí esta la información completa:
Imagen anexada.

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The equation of the new line, after dilation by a scale factor of 3 and centering at the origin, is y' = 9x - 18.

To dilate a line by a scale factor of k and center it at the origin, you multiply the coordinates of each point on the original line by the scale factor. Since the given line is y = 3x - 6, we can perform the dilation as follows:

The original line: y = 3x - 6

To dilate it by a scale factor of 3, we multiply both the x-coordinate and the y-coordinate of each point by 3:

New line: y' = 3 * y and x' = 3 * x

Substituting these values into the original equation, we have:

y' = 3(3x - 6)

Simplifying, we get:

y' = 9x - 18

Therefore, the equation of the new line, after dilation by a scale factor of 3 and centering at the origin, is y' = 9x - 18.

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In the given scenario where x > y > 2, the expressions from least to greatest value are: (x^3y^26)^(-2), (x^2y^5)^(-2), (9xy)^2, and (5x^4y^3)^3.



To determine the order of the expressions from least to greatest value when x > y > 2, we can simplify each expression and compare their values.

1. (x^3y^26)^(-2):

  Simplifying the expression, we have (x^(-6)y^(-52)).

  Since x > y > 2, x^(-6) > 1 and y^(-52) > 1, which means the expression is less than 1.

2. (x^2y^5)^(-2):

  Simplifying, we get (x^(-4)y^(-10)).

  Similar to the previous expression, x^(-4) > 1 and y^(-10) > 1, making this expression also less than 1.

3. (5x^4y^3)^3:

  Simplifying gives (125x^12y^9).

  Since x > y > 2, x^12 > y^12 and y^9 > 2^9, we can conclude that this expression is the greatest.

4. (9xy)^2:

  Simplifying, we have (81x^2y^2).

  Since x > y > 2, 81x^2 > 4x^2 and 81y^2 > 4y^2, this expression is greater than (x^3y^26)^(-2) and (x^2y^5)^(-2), but smaller than (5x^4y^3)^3.

Therefore, the order of the expressions from least to greatest value is:

(x^3y^26)^(-2) < (x^2y^5)^(-2) < (9xy)^2 < (5x^4y^3)^3.

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The answer is 25. 3. Hence, option B is the correct answer.

Given that the two vertical posts stand side by side. One post is 8 feet tall and the other is 17 feet tall, and a 24-foot post is stretched between the tops of the posts, we need to find how far apart are the posts?We have to use the Pythagorean Theorem to find the distance. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of the triangle.The figure can be drawn as below:

Here, AB is the 24 foot post, and A and B are the tops of the shorter and the taller post, respectively.

From the figure, we can observe that:

In triangle ABC,

AB² = AC² + BC² (According to Pythagoras theorem)

AC = 8 feet

BC = 17 feet

AB = 24 feet

Substituting the values in the above formula we get,

24² = 8² + 17²

576 = 64 + 289

576 = 353 + BC²

BC² = 576 - 353

BC² = 223

BC = sqrt(223)

The distance between the two posts is the length of the line segment CD, which is BC minus the length of the line segment AD.

Therefore,

Distance between the posts = BC - AD= sqrt(223) - 24= 3.17 ft (approx)

Therefore, the answer is 25. 3. Hence, option B is the correct answer.

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This equation allows you to calculate the number of years (t) based on the principal (P), interest earned (I), and interest rate (r) for simple interest calculations.

To solve the formula I = Prt for t in terms of P, I, and r, we can rearrange the equation to isolate t.

Starting with the original formula:

I = Prt

Dividing both sides by Pr:

I/Pr = (Prt)/Pr

Simplifying:

I/Pr = t

Therefore, t = I/Pr.

In terms of P, I, and r, the expression for t would be:

t = I / (P * r)

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The option that saves Marcus the most money is "Buy 3, get 1 free" as it provides a free tire, resulting in the lowest total cost.

Let's calculate the total cost for each option to find the cheapest price.

Option 1: $50 rebate - Since Marcus needs to replace four tires, the total cost without any discount would be 4 * $170 = $680. With a $50 rebate, the total cost would be $680 - $50 = $630.

Option 2: Buy 3, get 1 free - In this option, Marcus would need to buy three tires at the regular price of $170 each, totaling 3 * $170 = $510. However, he would receive one tire for free, so the total cost would remain $510.

Option 3: 30% off when you buy a full set of 4 tires - The regular price for four tires is 4 * $170 = $680. With a 30% discount, the total cost would be $680 - (30/100 * $680) = $476.

Option 4: Tires on sale for $150 each - If Marcus chooses this option, the total cost for four tires would be 4 * $150 = $600.

Comparing the total costs, we can see that the "Buy 3, get 1 free" option has the lowest total cost of $510, making it the most cost-effective choice for Marcus.

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In Trapezoid QRST, with midpoints M and P on the legs, if PM is equal to 2x, QR is equal to 3x, and TS is equal to 10, we need to find the value of PM.

In a trapezoid, the midpoints of the legs divide the bases into two equal segments. Let's consider the given information:

PM = 2x (length of segment PM)

QR = 3x (length of segment QR)

TS = 10 (length of segment TS)

Since M and P are midpoints, we can conclude that PM is equal to half of QR:

PM = 1/2 * QR

Substituting the given value of QR:

2x = 1/2 * 3x

To solve for x, we can multiply both sides of the equation by 2:

4x = 3x

Subtracting 3x from both sides:

4x - 3x = 3x - 3x

x = 0

Since x is equal to 0, we can substitute it back into the expression for PM:

PM = 2x

PM = 2(0)

PM = 0

Therefore, PM is equal to 0.

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To find the value of k, we need to determine the value of k for which x = 2 is a zero of the polynomial p(x).

Given the polynomial p(x) = x^2 - 2k + 2, we know that x = 2 is a zero of the polynomial. This means that when x = 2, the polynomial evaluates to zero.

Substituting x = 2 into the polynomial, we have:

p(2) = (2)^2 - 2k + 2 = 0

Simplifying the equation, we get:

4 - 2k + 2 = 0

Combining like terms:

6 - 2k = 0

To find the value of k, we isolate the term with k by subtracting 6 from both sides:

-2k = -6

Dividing both sides by -2:

k = 3

Therefore, the value of k that makes x = 2 a zero of the polynomial is k = 3.

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The height is less than 5√2 feet and the base is less than 20√2 feet.

A parallelogram is a two-dimensional shape with two pairs of parallel sides. It has four sides and four angles. It is similar to a rectangle, except that its opposite sides are parallel and not necessarily of equal length.

A parallelogram with a base four times the height has the formula A=bh, where b is the length of the base and h is the height. Therefore, if the base is four times the height, then we can write b=4h. We can substitute this value of b into the formula A=bh to obtain A=4h×h=4h². Thus, the area of the parallelogram is 4h².

Therefore, the height is less than 5√2 feet. We can find the corresponding value of the base by using the equation b=4h. Thus, the base is less than 4(5√2)=20√2 feet.Since we know the height and the base of the parallelogram, we can calculate its area. The formula for the area of a parallelogram is A=bh, so we can write:A=(20√2)(5√2)=200 square feet.Since the area of the parallelogram is less than 200 square feet, it must be less than this value.

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216 . Therefore, we can cut out 64 cubes with a side of 6cm from a cube with a side of 24cm, hence the total number of 6cm cubical boxes that can be cut out from a cube of side 24cm is:64 x 3 = 192.

To find out how many 6cm cubical boxes can be cut out from a cube of side 24cm, we need to divide the volume of the large cube by the volume of the small cube (6cm x 6cm x 6cm).

Given that the side of the large cube is 24cm.To calculate the number of 6 cm cubes that can be made from this, we need to find out how many 6 cm cubes are there in one side of the large cube.Dividing the side of the large cube by the side of the small cube gives:24/6 = 4Since the cube is a 3D figure, we need to multiply this by itself two more times, since there are three dimensions:4 x 4 x 4 = 64Therefore, we can cut out 64 cubes with a side of 6cm from a cube with a side of 24cm, hence the total number of 6cm cubical boxes that can be cut out from a cube of side 24cm is:64 x 3 = 192.

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To convert the rate of water flow from meters per minute to kilometers per hour, we need to multiply by a conversion factor. Since there are 60 minutes in an hour and 1000 meters in a kilometer, the conversion factor is (60/1000).

So, the rate of flow in km/h is (300 * 60/1000) = 18 km/h.

Therefore, the correct answer is option b) 18.

To find the ratio of 1 liter to 350 ml, we need to convert both measurements to the same unit. Since 1 liter is equal to 1000 ml, the ratio becomes:

1 liter : 1000 ml

To simplify the ratio, we divide both sides by 50:

(1 liter / 50) : (1000 ml / 50)

Therefore, the correct ratio is option a) 20:7.

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As x approaches infinity, the value of the function f(x) = log4x approaches infinity as well. The logarithm function with a base greater than 1 increases without bound as its input increases, so the value of log4x becomes arbitrarily large as x becomes larger.

The logarithm function log4x represents the exponent to which the base 4 must be raised to obtain x. As x approaches infinity, the function evaluates the behavior of the logarithm for extremely large values.

In this case, as x becomes larger and larger, log4x increases without bound. This means that there is no finite limit or specific value that f(x) approaches as x approaches infinity. Instead, f(x) grows infinitely, indicating that the function's value becomes arbitrarily large as x becomes larger. Therefore, the value of f(x) = log4x approaches infinity as x approaches infinity.

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The factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).

The equivalent factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).

To find the factored form, we need to factor out the greatest common factor (GCF) from the given expression. The GCF of the coefficients 12, 42, and 90 is 6, and the GCF of the variables x^4, x^3, and x^2 is x^2.

Factoring out the GCF, we have:

6x^2(2x^2 - 7x - 15)

Next, we need to factor the quadratic expression within the parentheses. We are looking for two binomials that, when multiplied together, result in 2x^2 - 7x - 15.

The factors can be found by considering two numbers whose product is -30 (the product of the coefficient of x^2, 2, and the constant term, -15) and whose sum is -7 (the coefficient of x, -7).

By trial and error, we can determine that the factors are (2x + 3) and (x - 5).

Thus, the factored form of the expression 12x^4 - 42x^3 - 90x^2 is 6x^2(x - 5)(2x + 3).

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During the late 19th and early 20th centuries, many artists were seeking a different world due to several reasons.

1. Social and Political Changes During the late 19th and early 20th centuries, social and political changes were occurring at a rapid pace. The industrial revolution led to the growth of cities, which, in turn, caused a breakdown in traditional society. As a result, many artists were seeking a different world that was more in line with their ideals.2. Technological Advancements Inventions such as the telegraph and the telephone enabled artists to communicate with one another and share their ideas. Artists were inspired by new technologies and used them to create new forms of art.3. World War I World War I was a traumatic event that had a significant impact on the artistic community. Many artists were disillusioned by the horrors of war and sought to create a new world that was free from conflict and violence.4. Industrialization and Urbanization .The growth of industry and the shift from rural to urban life had a profound effect on the artistic communit.5. Romanticism .Romanticism was a cultural movement that emphasized emotion, imagination, and individualism. Many artists were inspired by the romantic ideal and sought to create works that expressed their innermost feelings and thoughts. The movement emphasized the importance of nature, beauty, and the sublime, which were seen as antidotes to the dehumanizing effects of industrialization and urbanization.

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Three minutes ago, Sergio's water tank had approximately 12 gallons of water before the crack started leaking at a rate of 2 gallons per minute.

Based on the given information, we know that the current water level in the tank is 6 gallons. The leak in the tank is causing a loss of 2 gallons per minute. To determine the water level three minutes ago, we need to calculate the amount of water that was lost during that time.

Since the leak is causing a loss of 2 gallons per minute, we can multiply the rate of leakage by the number of minutes, which in this case is 3. So, 2 gallons per minute multiplied by 3 minutes gives us a loss of 6 gallons during this period.

To find the water level three minutes ago, we need to subtract the amount lost from the current water level. Starting with the current water level of 6 gallons and subtracting the 6 gallons lost, we find that three minutes ago, the tank had approximately 12 gallons of water. Therefore, the initial water level in Sergio's tank three minutes ago was approximately 12 gallons before the crack started leaking.

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1352.53 Pa of pressure is exerted on the ground by a 535N student if the soles of her shoes have an area of 0. 396m/2.

To calculate the pressure exerted on the ground by the student, we can use the formula:

Pressure = Force / Area

Given:

Force (F) = 535 N

Area (A) = 0.396 m²

Using these values, we can calculate the pressure:

Pressure = 535 N / 0.396 m²

Pressure ≈ 1352.53 Pascal (Pa)

Therefore, the pressure exerted on the ground by the student is approximately 1352.53 Pa.

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y = 5x

This equation implies that each box of cookies costs $5.

To write an equation that models the relationship between the cost, y, of buying boxes of cookies, x, we need the values from the table. Since you haven't provided the specific values in the table, I'll give you an example equation based on a general scenario.

Let's assume that the cost of buying boxes of cookies follows a linear relationship with the number of boxes purchased. In this case, the equation can be written in the form:

y = mx + b

Where:

y represents the cost of buying boxes of cookies.

x represents the number of boxes purchased.

m represents the slope of the line, which indicates the rate of change in the cost per box.

b represents the y-intercept, which is the initial cost when no boxes are purchased.

You would need to substitute the actual values from your table into this equation to create a specific model for your situation. For instance, if the table shows the following data:

Boxes (x) Cost (y)

1            5

2            10

3            15

4            20

We can use these values to find the slope (m) and y-intercept (b) using linear regression techniques. Then, the equation that models this situation would be:

y = 5x

This equation implies that each box of cookies costs $5.

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the inequality 4.25x ≤ 12 represents the amount of fabric Chase needs to buy, ensuring that he stays within his limit of 12 bookmarks.

To determine the amount of fabric Chase needs to buy, we multiply the number of bookmarks (x) by the fabric required per bookmark (4.25 inches). This gives us the total amount of fabric needed for x bookmarks.

Since Chase wants to make no more than 12 bookmarks, we set up the inequality 4.25x ≤ 12. This means that the product of 4.25 and x should be less than or equal to 12. By doing so, we ensure that the total amount of fabric required does not exceed the limit of 12 bookmarks.

Solving this inequality, we can find the maximum value for x, which represents the number of bookmarks Chase can make within the given fabric constraint. Dividing both sides of the inequality by 4.25, we have x ≤ 12/4.25.

Therefore, the inequality 4.25x ≤ 12 represents the amount of fabric Chase needs to buy, ensuring that he stays within his limit of 12 bookmarks.

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The division calculation of 733 divided by 4 can be solved by finding the greatest multiple of 100 that can be multiplied by 4 without exceeding 733. The quotient is obtained by dividing this multiple by 4.

To solve 733 ÷ 4, we begin by finding the greatest multiple of 100 that can be multiplied by 4 without exceeding 733. In this case, the multiple is 700 (100 multiplied by 7). Next, we divide this multiple by 4 to obtain the quotient. The division can be performed as follows:

175

4 | 733

We start by dividing 7 (the tens digit of 700) by 4, which equals 1. We place this quotient of 1 on top. Then, we multiply 1 by 4, which equals 4, and subtract it from 7 to get the remainder of 3. We bring down the ones digit of 33, and the process is repeated. We divide 33 by 4, which gives us 8 with no remainder. Therefore, the quotient of 733 ÷ 4 is 183, with no remainder.

In summary, when dividing 733 by 4, we find the greatest multiple of 100 that can be multiplied by 4 without exceeding 733, which is 700. Dividing 700 by 4 gives us a quotient of 175. Therefore, the answer to 733 ÷ 4 is 183.

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The measurement that is more accurate but less precise than 5.3 pounds is 5 pounds.

Accuracy refers to how close a measurement is to the true value, while precision refers to the level of consistency or reproducibility of a measurement.

In this scenario, the scale measured a 4.5-pound brick as weighing 5.3 pounds. Comparing this measurement to the true value, we can say that it is not accurate because it overestimates the weight of the brick. However, it is relatively precise because it provides a specific value (5.3 pounds) rather than a range of values.

To find a measurement that is more accurate but less precise than 5.3 pounds, we look for a value that is closer to the true weight of the brick (4.5 pounds) but still lacks precision. Among the given options, 5 pounds is the closest value to the true weight of the brick, making it more accurate. However, it is less precise because it represents a rounded value without indicating any decimals.

Therefore, among the options provided, 5 pounds is the measurement that is more accurate but less precise than 5.3 pounds.

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To find the length of the diagonal of a rectangular pool whose dimensions are given, you can use the Pythagorean Theorem.

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, if we consider the length and width of Catherine's pool as the two shorter sides of a right-angled triangle, we can use the Pythagorean Theorem to find the length of the diagonal (the hypotenuse).

The formula to find the length of the diagonal is given by: diagonal=\sqrt{length^2+width^2} where length and width are the dimensions of the rectangle. So, for Catherine's pool, we have:length = 95 feet width = 55 feet Using the formula, we get: diagonal=\sqrt{length^2+width^2}= \sqrt{(95)^2 + (55)^2}= \sqrt{9025 + 3025}= \sqrt{12050}= 109.59\ \text{feet} Therefore, the length of the diagonal of Catherine's pool is approximately 109.59 feet.

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Maggie can make anywhere from 5 to 4 sales to earn at least $225 and go to the lake with her friends.

Maggie gets paid $15 per hour plus $25 for every sale she makes. The number of sales she makes can be represented by x.

In order to calculate Maggie's earnings in terms of commission, we can use the equation 25x.

To calculate Maggie's earnings in terms of hourly pay, we can use the equation 15(8), since she works from 8am until 4pm, which is 8 hours. This simplifies to 120.The total amount Maggie earns can be represented by the equation:

Total earnings = 25x + 120

To find the minimum number of sales Maggie needs to make to earn at least $225, lets set up the inequality:

25x + 120 ≥ 225

Subtracting 120 from both sides, we get:

25x ≥ 105

Dividing both sides by 25, we get:

x ≥ 4.2

Maggie cannot make a fraction of a sale, so we can round up to find the minimum number of sales she needs to make, which is 5 sales.

To find the maximum number of sales Maggie can make, lets consider the fact that she is scheduled to work from 8am until 4pm, which is 8 hours. If she makes 0 sales, she will earn $120 (her hourly pay for 8 hours of work).

To find the maximum number of sales, we can set up the equation:25x + 120 ≤ 225

Subtracting 120 from both sides, we get:

25x ≤ 105

Dividing both sides by 25, we get:

x ≤ 4.2

Maggie cannot make a negative number of sales, so we can round down to find the maximum number of sales she can make, which is 4 sales.

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The possible values of the number of sales that Maggie can make to go to the lake are 5 and 4.

Given:

Maggie gets paid $15 per hour plus $25 for every sale she makes.

She needs to make at least $225 today.

She is scheduled to work from 8 am until 4 pm.

To find:

All the possible values of the number of sales that Maggie can make to go to the lake.

Solution:

Let's consider x to be the number of sales that Maggie makes.

To determine the minimum amount she needs to earn:

Her hourly wage for 8 hours of work = $15 × 8 = $120

Total earnings that she needs = $225 - $120 = $105

If y is the number of sales she needs to make to earn $105, then:

$25y = $105

Dividing both sides by $25, we get:

y = 4.2

This means she needs to make at least 5 sales.

Let's calculate the maximum number of sales that she can make. If she has to earn $240 for 8 hours of work:

Total earnings required = $240 - $120 = $120

$25y = $120

Dividing both sides by $25, we get:

y = 4.8

This means the maximum number of sales she can make is 4.

As such, the possible values of the number of sales that Maggie can make to go to the lake are 5 and 4.

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The cost of the printer was £468.75. Sean made a 32% profit on its cost price. He sold both the laptop and the printer for a total of £1,300, with the laptop alone fetching £1,150.

To find out the cost of the printer, you need to first calculate the cost of the laptop. Then, you can use that information along with the total selling price to determine the cost of the printer.

Let the cost of the laptop be L and the cost of the printer be P. Total selling price of both items = £1,300Amount Sean got just for the laptop = £1,150.Cost of printer = Total - Amount Sean got just for laptop= £1,300 - £1,150 = £150Sean made a 32% profit on the cost of the printer.

Profit percentage is calculated using the following formula:

Profit percentage = (Profit / Cost price) x 10032% = (Profit / Cost price) x 10032 / 100 = Profit / Cost price0.32 = Profit / P Profit = 0.32PNow, we know that the total selling price of both items is £1,300 and that the cost of the laptop is L. So, we can write:L + P = £1,300We also know that Sean made a profit of 32% on the cost of the printer. So, the selling price of the printer is 132% of its cost price. We can write this as:  .Selling price of printer = 1.32PAdding the selling prices of bot h items, we get:L + 1.32P = £1,300Now we can substitute L + P = £1,300 into this equation:L + 1.32P = £1,300L + 1.32P = L + P + 0.32PL + 0.32P = £1,3000.32P = £150P = £150 / 0.32P = £468.75.Therefore, the cost of the printer was £468.75.

The cost of the printer was £468.75. Sean made a 32% profit on its cost price. He sold both the laptop and the printer for a total of £1,300, with the laptop alone fetching £1,150.

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Answer:

Step-by-step explanation:

D)

[tex]\frac{4\sqrt{b} }{\sqrt{3}-b }[/tex]                         > in order to get rid of root on bottom like this, you

                                  need to multiply top and bottom by conjugate

                                  √3 +b

[tex]=\frac{4\sqrt{b} }{\sqrt{3}-b }\frac{\sqrt{3}+b}{\sqrt{3}+b}[/tex]              > Distribute on top and FOIL bottom

[tex]=\frac{4\sqrt{3b}+4b\sqrt{b} }{3 -b^{2} }[/tex]               >This is simplified, you cannot combine anything else

E)

[tex]\frac{3\sqrt{a^{2} } } {\sqrt{3} } / 2a^{\frac{3}{2} }[/tex]                    >√a² = a

[tex]=\frac{3a } {\sqrt{3} } / 2a^{\frac{3}{2} }[/tex]                    >Division of fraction keep change flip

[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2a^{\frac{3}{2}} }[/tex]                  >Because 2a is not in parenthesis 3/2 exp.

                                     is only for a

[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2\sqrt{a^{3} } }[/tex]              > You can make 1 set of a² so 1 comes out but 1 stays

[tex]=\frac{3a } {\sqrt{3} } * \frac{1}{2a\sqrt{a } }[/tex]              >put like items under root

[tex]=\frac{3a } {2a\sqrt{3a} }[/tex]                     >multiply top and bottom by root

[tex]=\frac{3a } {2a\sqrt{3a} }*\frac{\sqrt{3a}}{\sqrt{3a}}[/tex]             >multiply

[tex]=\frac{3a\sqrt{3a} } {2a(3a)} }[/tex]                       >3a cancels

[tex]=\frac{\sqrt{3a} } {2a} }[/tex]                           >This is simplified

Among the 45 footballers, stretching regularly is associated with a lower injury rate. Out of the 36 footballers who stretch, 6 got injured, while among the 9 footballers who do not stretch, 4 got injured.

The frequency tree represents the data from the report on the impact of stretching on preventing injury in a football team. The tree shows that out of the 45 footballers in the squad, 36 of them stretch regularly. Among the footballers who stretch, 6 got injured last year. The total number of injured players last year was 10.

From the given information, we can analyze the relationships between the different categories. Out of the 45 footballers, 36 stretch regularly, which means that 9 footballers do not stretch. Since the total number of injured players is 10 and 6 of them are from the stretching group, the remaining 4 injured players must come from the non-stretching group.

To summarize, the report suggests that among the 45 footballers, stretching regularly is associated with a lower injury rate. Out of the 36 footballers who stretch, 6 got injured, while among the 9 footballers who do not stretch, 4 got injured. These findings highlight the potential benefits of incorporating stretching exercises into the team's routine to help prevent injuries. However, it is important to consider other factors and conduct further analysis to establish a more comprehensive understanding of injury prevention in the football team.

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