a) Factorise x²-2x-3

The sale's person commission from the sale of $37,000 worth of furnaces is $2,220. If this is doubled, he would have $4,440.

If the salesperson's commission from the sale of $37,000 is at the rate of 6%, then we will do the following:

6/100 × $37,000 = $2,220

If sales, double, we will now record the amount, 74,000. Now 6% of 74,000 will be $4,440. So, the resultant amount, if the salesperson was to increase his sales to double the original, will be $4,440.

This follows a simple logic. When you have a number and are told to double it, you simply multiply by 2. In the same manner, we multiply the salesperson's commission by 2.

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Answer: 1 1/4 yards

Step-by-step explanation: To convert from feet to yards, divide the value in feet by 3. So, 3 3/4 ft = (3 3/4)/3 = 1.25 yd (exactly).

Answer:

5/4 yards

Step-by-step explanation:

Convert feet to fraction.

[tex]3+\frac{3}{4} =\frac{(3)(4)+3}{4} =\frac{15}{4}[/tex] ft.

If we know that each yard equals 3 feet, divide by 3:

[tex]\frac{\frac{15}{4} }{3} =\frac{15}{(4)(3)} =\frac{15}{12}[/tex]

Simplified:

[tex]\frac{5}{4}[/tex]  yards

Hope this helps.

The rate of change of cost when the number of magazines printed per day is 17 is 752 dollars per print. The correct option is C.

The function C(x) = 25x² - 98x represents the cost of printing magazines per day at a printing press. To find the rate of change of cost when 17 magazines are printed per day, we need to calculate the derivative of the function with respect to x (the number of magazines printed), which represents the rate of change at a given point.

The derivative of C(x) with respect to x can be found using the power rule for differentiation. For a function of the form f(x) = [tex]ax^n[/tex], its derivative is f'(x) = [tex]n*ax^{(n-1)[/tex].

Applying the power rule to our function, we get:
C'(x) = 2(25x) - 98 = 50x - 98.

Now, we need to evaluate C'(x) when x = 17 (the number of magazines printed per day):
C'(17) = 50(17) - 98 = 850 - 98 = 752.

Therefore, the rate of change of cost when the number of magazines printed per day is 17 is 752 dollars per print. So, the correct answer is: C. 752$/print.

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The measurements from greatest to least would be ordered as follows:

First, we need to convert all the units to the same unit. Let's convert everything to inches, since that is the smallest unit.

6 yards = 6 x 3 = 18 feet

18 feet = 18 x 12 = 216 inches

2 1/2 feet = 2 x 12 + 6 = 30 inches

So now we have:

6 yards = 216 inches

2 1/2 feet = 30 inches

45 inches = 45 inches

Putting these in order from greatest to least, we have:

216 inches, 45 inches, 30 inches

Therefore, the measurements from greatest to least would be ordered as follows:

6 yards, 45 inches, 2 1/2 feet

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The full question is:
Put the measurements from greatest to least. 45 inches, 6 yards, and 2 1/2 feet

Neave should mark 12 sections as "win" on the prize wheel to achieve the expected number of winners of 60 out of 200 students.

To determine how many sections should be marked "win" on Neave's prize wheel, we need to consider the expected number of winners and the total number of sections on the wheel.

Neave wants the expected number of winners to be 60 out of 200 students. This means that the probability of winning should be 60/200 = 0.3 or 30%.

If the wheel is split into 40 equally sized sections, we can assume that each section has an equal probability of being selected by a student. Therefore, to have a 30% chance of winning, we need to mark a proportionate number of sections as "win".

To calculate the number of sections to mark as "win", we multiply the total number of sections by the desired probability of winning:

40 sections * 0.3 = 12 sections.

It's important to note that the concept of expected value assumes an idealized scenario with perfect randomness. In reality, the actual number of winners may vary due to random chance and individual spin outcomes.

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The z-score for the 90th percentile is approximately 1.28, for the 62nd percentile is approximately 0.31, and for the first quartile (25th percentile) is approximately -0.67.

To calculate the percentiles for this dataset, we need to use the z-score formula. Unfortunately, I cannot directly provide you the responses for the 90th, 62nd, and first quartile percentiles without more information.

However, I can help you understand the process of finding these percentiles:

1. Determine the z-score corresponding to the desired percentile using a z-score table or calculator. For example, the z-score for the 90th percentile is approximately 1.28, for the 62nd percentile is approximately 0.31, and for the first quartile (25th percentile) is approximately -0.67.

2. Use the following formula to find the response corresponding to the z-score:

  Response = Mean + (Z-score × Standard Deviation)

For example, to find the 90th percentile:

  Response = 5.7 + (1.28 × 2.3)

Calculate this for each percentile using their respective z-scores, and you will find the responses you are looking for.

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Answer:

Step-by-step explanation:

to solve this question, we need to use the graph on the left to find the proportions of students who prefer each pasta dish, and then multiply those proportions by 400 to get the estimated number of students in the whole school who prefer each pasta dish. Then we need to plot those numbers on a bar graph with the pasta dishes on the horizontal axis and the number of students on the vertical axis. The graph below shows one possible way to create the bar graph:

We can see that the vertical axis is numbered from 0 to 120 in increments of 20. The bars show the estimated number of students who prefer each pasta dish, based on the sample of 16 students. For example, since 4 out of 16 students prefer spaghetti, we can estimate that 4/16 x 400 = 100 students in the whole school prefer spaghetti. Similarly, since 3 out of 16 students prefer lasagna, we can estimate that 3/16 x 400 = 75 students in the whole school prefer lasagna. We can repeat this process for the other pasta dishes and plot them on the graph.

✧☆*: .｡. Hope this helps, happy learning! (*✧×✧*) .｡.:*☆

Amelia's rate of reading was approximately 1.67 books per month (calculated by dividing the total number of books, 5, by the number of months, 3).

To calculate Amelia's rate of reading in books per month, we divide the total number of books she read (5) by the number of months (3). Therefore, her rate of reading is 5/3 books per month.

To resize the right columns to represent the unit rate, you would need to scale them down. If the left column represents the number of months and the right column represents the number of books read, you could adjust the scale so that each unit on the right column represents 1 book per month.

For example, if each square unit on the left column represents 1 month and each square unit on the right column represents 0.5 books, you could resize the right column so that each square unit represents 1 book. This would ensure that the visual representation accurately reflects the unit rate of books per month.

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Guadalupe drove at an average speed of 33.75 miles per hour.

To find the average speed, we need to divide the total distance by the total time:

Average speed = t d/t t

Guadalupe drove 45 miles in 1 1/3 hours, which is the same as 4/3 hours.

So, average speed = 45 miles / (4/3) hours

= 45 x 3/4

= 33.75 miles per hour (rounded to two decimal places)

Therefore, Guadalupe drove at an average speed of 33.75 miles per hour.

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Answer:

$4139.93

Step-by-step explanation:

Formula for amount accrued at compound interest annually is given by

A = P( 1+ r)ⁿ

where
P = principal
r = interest rate expressed as a decimal
n = number of years

Given P = 3900, r = 1/100 = 0.01, n = 6 we get

A = 3900(1 + 0.01)⁶ = 3900(1.01)⁶ = 4139.93

So the amount accrued after 6 years = $4139.93

None of the provided answer choices are correct, as the correct answer should be 41 lb.

To find the total weight of the box and the presents, you simply add the weights together:

Box weight: 14 lb
Present 1 weight: 15 lb
Present 2 weight: 12 lb

Total weight = 14 lb + 15 lb + 12 lb = 41 lb

None of the provided answer choices are correct, as the correct answer should be 41 lb.

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There are 20 different ways the students can be chosen for the positions of editor-in-chief and assistant editor-in-chief.

There are 5 students in the newspaper staff, and two positions to fill i.e. editor-in-chief and assistant editor-in-chief. We need to find the number of different ways the students can be chosen for these positions.

To solve this problem, we can use the formula for permutation

We know the formula for Permutation is

[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]

Here, n=5 and r=2

So, P(5,2) = 5!/(5-2)!

= 5!/3!

= 120/6

= 20

Therefore, there are 20 different ways the students can be chosen for the positions of editor-in-chief and assistant editor-in-chief.

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The student's use of the t procedure for a confidence interval was appropriate because the sample size was greater than 30 and the population standard deviation was unknown. A 95% confidence interval was calculated using the t-distribution.

It was an appropriate use of the t procedure for a confidence interval. The student wanted to assess the average time spent studying for his most recent exam taken in class, and he used a sample of 45 students to estimate the population mean with a 95% confidence interval.

Since the population standard deviation is not known, the student used the t-distribution to calculate the confidence interval. The t-distribution is used when the sample size is small, and the population standard deviation is unknown.

The student assumed that the sample was randomly selected, and the data was approximately normally distributed. By using the t procedure, the student was able to estimate the population mean with a margin of error and a level of confidence of 95%.

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The equation for the company's profit, P(x), is P(x) = 6.6x - 2,300, where x is the number of items sold.

To find the equation P(x) for the company's profit, we can first determine the slope (m) and the y-intercept (b) of the linear equation P(x) = mx + b.

1. Calculate the slope (m) using the given information:

m = (P2 - P1) / (x2 - x1)
m = ($30,700 - $24,100) / (5000 - 4000)
m = $6,600 / 1000
m = $6.6

2. Use one of the points to find the y-intercept (b):

P(x) = mx + b
$24,100 = $6.6(4000) + b
$24,100 = $26,400 + b
b = -$2,300

3. Write the equation for P(x):

P(x) = 6.6x - 2,300

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The estimated quantity of the substance at t = 1.9 is approximately 35.3 units.

To estimate the quantity of the substance at t = 1.9 using linear approximation, we can use the formula:

ΔR ≈ dR/dt * Δt

Given the point R(2) = 35 and the differential equation dR/dt = -1/5(R – 20), we can first find the value of dR/dt at t = 2.

dR/dt(2) = -1/5(R(2) – 20) = -1/5(35 – 20) = -1/5(15) = -3

Now, we can calculate Δt, which is the difference between the given t-value (2) and the desired t-value (1.9):

Δt = 1.9 - 2 = -0.1

Next, we can calculate ΔR using the linear approximation formula:

ΔR ≈ dR/dt * Δt ≈ -3 * (-0.1) = 0.3

Finally, we can estimate the quantity of the substance at t = 1.9 by adding ΔR to the given value of R(2):

R(1.9) ≈ R(2) + ΔR ≈ 35 + 0.3 = 35.3

Therefore, the estimated quantity of the substance at t = 1.9 is approximately 35.3 units.

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Answer:

C) 1,050

Step-by-step explanation:

We can see that to get from 8.4 to 42 and to get from 42 to 210, we have to multiply by 5.

To complete the sequence, multiply 210 by 5

210·5

=1,050

Hope this helps!

The height of the pile of books in terms of a and b is 4a cm + 2b cm.

To find the height of the pile of books in terms of a and b, we need to multiply the number of books by the thickness of each book. Since there are (2a+b) books in the pile and the thickness of each book is 2cm, the height of the pile can be expressed as:

(2a+b) x 2cm

Expanding this expression, we get:

4a cm + 2b cm

Therefore, the height of the pile of books in terms of a and b is 4a cm + 2b cm. This means that for every additional 'a' book, the height of the pile will increase by 4cm and for every additional 'b' book, the height of the pile will increase by 2cm.

It's important to note that this formula assumes that all the books are the same size and have the same thickness. If there are any variations in size or thickness, the formula may not accurately represent the height of the pile. Additionally, it's important to ensure that all units of measurement are consistent (in this case, cm for both the thickness of the book and the height of the pile).

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The expression 148 + 19x³ represents the sum of 148 and the product of a number raised to the third power and 19.

To write the phrase "the sum of 148 and the product of a number raised to the third power and 19" in symbols using the variable x, we can write it as:

148 + 19x³

Here, we are adding 148 to the product of 19 and x raised to the third power. This expression represents the sum of 148 and the product of a number raised to the third power and 19. We can substitute any value for x to get the result of the expression. For example, if x is 2, then the expression becomes:

148 + 19(2³) = 148 + 19(8) = 300

Therefore, the sum of 148 and the product of a number raised to the third power and 19 is represented by the expression 148 + 19x³.

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The slope of UF is 1/6

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

The slope is given = change in point on y axis/ change in point on x axis

slope = y2-y1/x2-x1

The cordinate of F = (-2,-3) and U ( 4, -2)

y1 = -3 and y2 = -2

x1 = -2 and x2 = 4

slope = -2-(-3)/4-(-2)

= -2+3/(4+2)

= 1/6

therefore the slope of UF is 1/6

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The length of the platform is given by the expression -2 + sqrt(3x^2 + 10x) meters.

Let's start by using the formula for the area of a rectangle, which is:

Area = length x width

We are given that the width of the platform is (x+4) meters, so we can write:

Area = length x (x+4)

We are also given that the area of the platform is 3x^2+10x−8, so we can set these two expressions equal to each other and solve for the length:

3x^2+10x−8 = length x (x+4)

Expanding the right side, we get:

3x^2+10x−8 = length x^2 + 4length

Subtracting 4length from both sides, we get:

3x^2+10x−8−4length = length x^2

Rearranging, we get a quadratic equation:

length x^2 + 4length − 3x^2 − 10x + 8 = 0

To solve for length, we can use the quadratic formula:

length = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 4, and c = -3x^2 - 10x + 8. Plugging in these values, we get:

length = (-4 ± sqrt(4^2 - 4(1)(-3x^2 - 10x + 8))) / 2(1)

Simplifying under the square root:

length = (-4 ± sqrt(16 + 12x^2 + 40x - 32)) / 2

length = (-4 ± sqrt(12x^2 + 40x)) / 2

length = (-4 ± 2sqrt(3x^2 + 10x)) / 2

length = -2 ± sqrt(3x^2 + 10x)

Since the length must be positive, we take the positive square root:

length = -2 + sqrt(3x^2 + 10x)

Therefore, the length of the platform is given by the expression -2 + sqrt(3x^2 + 10x) meters.

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We can use the distance formula to find the distance between two points in a coordinate plane:

d = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

Using the given coordinates of the two points, we have:

x1 = -2, y1 = 7

x2 = -5, y2 = 9

Substituting these values into the distance formula, we get:

d = √[(-5 - (-2))² + (9 - 7)²]

d = √[(-3)² + 2²]

d = √(9 + 4)

d = √13

Therefore, the distance between the points (-2, 7) and (-5, 9) is approximately √13 units. We can also approximate this value as 3.61 units (rounded to two decimal places).

The Fourier series Using the complex form of f(x) is

f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25

where k is an integer.

To find the Fourier series of the function f(x) over the interval [-1, 1], we first note that f(x) is periodic with period T = 0.5. We can then write f(x) as a Fourier series of the form

f(x) = a0/2 + ∑[n=1, ∞] (ancos(nπx) + bnsin(nπx))

where

a0 = (1/T) ∫[0,T] f(x) dx

an = (2/T) ∫[0,T] f(x)*cos(nπx) dx

bn = (2/T) ∫[0,T] f(x)*sin(nπx) dx

Since f(x) = 0 for x < -0.25 and x > 0.25, we only need to consider the interval [-0.25, 0.25]. We can break this interval into subintervals of length 0.5 centered at integer values k

[-0.25, 0.25] = [-0.25, 0.25] ∩ [1.5, 2.5] ∪ [-0.25, 0.25] ∩ [0.5, 1.5] ∪ ... ∪ [-0.25, 0.25] ∩ [-1.5, -0.5]

For each subinterval, the Fourier coefficients can be calculated as follows

a0 = (1/0.5) ∫[-0.25, 0.25] f(x) dx = 1/2

an = (2/0.5) ∫[-0.25, 0.25] f(x)*cos(nπx) dx = 0

bn = (2/0.5) ∫[-0.25, 0.25] f(x)sin(nπx) dx = 2(-1)^k/(nπ)

Therefore, the Fourier series of f(x) is

f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25

where k is an integer.

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The volume of the prism is 78 cubic feet.The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism.

In this case, the base of the prism is a right triangle with legs measuring 3 feet and 4 feet, so its area is (1/2)(3)(4) = 6 square feet. The height of the prism is 13 feet. Therefore, the volume of the prism is V = Bh = (6)(13) = 78 cubic feet.To understand this calculation, think of the prism as a stack of identical, parallel cross sections. Each cross section is a copy of the base, with an area of 6 square feet.

The height of each cross section is the same, and equal to the height of the prism, which is 13 feet. To find the total volume of the prism, we add up the volumes of all these cross sections, which is equal to the area of the base times the height of the prism.

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To find the surface area of a prism, you need to add up the area of all of its faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Make sure that all of these measurements are in the same units, such as inches or centimeters.

Once you have calculated each of the areas, add them together to get the total surface area of the prism. Make sure to include the units in your answer, which will be in square inches or in2.

You will need to know its dimensions and follow these steps:

1. Determine the shape and dimensions of the base and top faces.
2. Calculate the area of the base and top faces.
3. Determine the shape and dimensions of the lateral faces.
4. Calculate the area of the lateral faces.
5. Add the areas of all the faces to find the total surface area.

Without specific dimensions, I cannot provide a numerical answer. However, once you have the dimensions, follow the steps above to find the surface area of the prism in square inches (in²).

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The approximate probability that someone might answer the next call E.J. makes is 0.25 or 25%. The correct answer is C. 0.25.

To find the approximate probability that someone might answer E.J.'s next call, we'll use the information provided and follow these steps:

1. Calculate the total number of calls made: answered calls (40) + unanswered calls (120).
2. Find the proportion of answered calls to the total calls.
3. Express the proportion as a probability (as a percentage or fraction).

Let's do the calculations:

1. Total calls = 40 (answered) + 120 (unanswered) = 160 calls
2. Proportion of answered calls = 40 answered calls / 160 total calls = 1/4
3. Probability = 1/4 = 0.25 (as a decimal) or 25% (as a percentage)

So, the approximate probability that someone might answer the next call E.J. makes is 0.25 or 25%. The correct answer is C. 0.25.

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Answer:

The answer is A. 135 cm2.

Area of a parallelogram is base * height. In this case, the base is 24 cm and the height is 9 cm. Therefore, the area is 24 * 9 = 135 cm2.

Answer: the answer would be 360

Step-by-step explanation:

the equation for area of a parallelogram is base x height.

The base is 24 as it is at the top of the shape.

The height is 15 as well since a parallelogram is congruent.

multiply the two and it gives you 360

The number of times of rolling a 5 or a 6 in the fair die is 24

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

Fair 6-sided die = 72 times

In a 6-sided die, we have

P(5 or 6) = 2/6

When evaluated, we have

P(5 or 6) = 1/3

So, when the die is rolled 72 times, we have

Expected value = 1/3 * 72

Evaluate

Expected value = 24

Hence, the number of times is 24

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Step-by-step explanation:

I have provided answer in attachment... this is solution of brainly tutor..

Answer: To have infinitely many solutions, the equation must be true for all values of x. In other words, the left side and right side of the equation must be equivalent, meaning that the coefficients of x on both sides of the equation must be equal, and the constant terms on both sides must be equal.

We can simplify the given equation as follows:

5(x + 3) = a(x + 4) + 3x + b

5x + 15 = ax + 4a + 3x + b

Simplifying further, we get:

8x + 4a + b = 5x + 15

Rearranging terms, we get:

3x + 4a + b - 15 = 0

For this equation to have infinitely many solutions, the coefficients of x on both sides must be equal to zero, meaning that:

3 = 0

This is not possible, so the equation cannot have infinitely many solutions for any values of a and b.

Therefore, there are no values of a and b for which the given equation will have infinitely many solutions.

The height of the cylindrical ornament is approximately 5.7 centimetres (option b).

To find the height of the cylindrical ornament given that 450 cubic centimetres of wood is used and the radius of the base is 5 centimetres, you can use the formula for the volume of a cylinder: V = π × radius² × height.

Step 1: Write down the given values.
Volume (V) = 450 cubic centimetres
Radius (r) = 5 centimetres

Step 2: Plug the given values into the formula.
450 = π × (5)² × height

Step 3: Solve for the height.
450 = π × 25 × height
450 = 78.54 × height

Step 4: Divide both sides by 78.54 to find the height.
height = 450 / 78.54
height ≈ 5.7 centimetres

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