Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:

\(a\sqrt{x+b} +c=d\)

The computer will cost £ 33512.32

Given,

the cost of the computer = 2500

Depreciation = 12%

Cost after 3 years =?

compound interest is calculated as,

A = P(1 + r/n)nt

r = 12/100 = 0.12

So, A= P(1 + r/n)nt

A = 2500 (1+.12/1)1*3

A= 2500 (1.12)³

A= 2500 * 1.404928

A = 3512.32

So, The computer will cost £ 33512.32

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The production phase could have a larger contribution to acidification potential than the use and end-of-life phases for both conventional vehicles and EVs. The distance traveled in one year of normal commuting could be more suitable in this case.

A. The functional unit, which is defined as the quantified performance of a product system or service that will be used as a reference for conducting the life cycle assessment, is important for evaluating the impacts of products or systems on the environment.

The following are the different functional units that are acceptable or not acceptable to assess the environmental impacts of the product or system.

The first functional unit, one vehicle, is not appropriate as it doesn't represent the amount of driving a person could expect to do if they bought a new car and drove it until the end of its life.

The second functional unit, distance traveled in one full gas tank or battery charge, would not be appropriate for our purpose as it is not clear what type of vehicle it will be used for.

The third functional unit, one year of normal commuting, would not be appropriate as it does not consider all the environmental impacts over the lifetime of the vehicle.

The fourth functional unit, 1 kg of vehicle, would not be appropriate as it is too small of a functional unit to evaluate the environmental impacts of the vehicle.

B. If we also wanted to consider riding the public bus as a personal transportation option, 200,000 miles driven would not be an appropriate choice of functional unit. This is because buses are used for transportation purposes, and they will have different environmental impacts than cars.

Therefore, the distance traveled in one year of normal commuting could be more suitable in this case.

C. One other impact category we could consider is the acidification potential. The production phase could have a larger contribution to acidification potential than the use and end-of-life phases for both conventional vehicles and EVs.

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There are 1089 in² in a square 11 yards on a side.

A square which is 11 yards on a side is 11 x 11 = 121 square yards. To convert square yards to square inches, multiply by the conversion factor of 9 square inches per square yard: 121 square yards x 9 square inches/square yard = 1089 square inches.

The area of a square is given by: A = l

Where,

Multiplication refers to binary operations in which different numerical sets are established. In mathematics the process of multiplication is elementary in several operations, it is also accompanied by addition, subtraction and division. Multiplication is the opposite of division.

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2/3 ×12

= 2/1 × 4

= 2× 4

=8

........

Step-by-step explanation:

f(x) = -3x²

f(4) = -3(4²)

= -48

Answer:

a. The company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

b. The number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

Step-by-step explanation:

Note: This question is not complete and it has some errors in the figures used. The correct complete question is therefore provided before answering the question as follows:

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 27 − 0.2x  (for 0 ≤ x ≤ 135), the price function for cars sold in Europe is q = 15 − 0.1y  (for 0 ≤ y ≤ 150), and the price function for cars sold in Asia is r = 19 − 0.1z (for 0 ≤ z ≤ 190), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 26 + 3(x + y + z) thousand dollars.

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

P(x, y, z) =

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

The explanation to the answers is now given as follows:

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

p = price function for cars sold in America = p = 27 − 0.2x (for 0 ≤ x ≤ 135)

q = price function for cars sold in Europe = 15 − 0.1y (for 0 ≤ y ≤ 150)

r = price function for cars sold in Asia = 19 − 0.1z (for 0 ≤ z ≤ 190)

C = company's cost function = 26 + 3(x + y + z) = 26 + 3x + 3y + 3z

P(x, y, z) = profit function

x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively

Therefore, we have:

TR = Total revenue = px + qy + rz …………………………….. (1)

Substituting the relevant values into equation (1), we have:

TR = (27 − 0.2x)x + (15 − 0.1y)y + (19 − 0.1z)z

TR = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2

Also,

P(x, y, z) = TR – C ……………………………………… (2)

Substituting the relevant values into equation (2), we have:

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – (26 + 3x + 3y + 3z)

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – 26 – 3x – 3y – 3z

P(x, y, z) = 27x – 3x +15y – 3y +19z – 3z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26 ……………….. (3)

Therefore, the company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26.

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

As indicated in the question, the number cars that should be sold in each market to maximize profit can be calculated by deriving the three partials Px, Py, and Pz from the profit function P(x, y, z), i.e. equation (3) in part a above, and set equal to zero and then solve as follows:

In America

From equation (3), we have:

Px = 24 – 0.4x = 0

Therefore, we have:

24 – 0.4x = 0

24 = 0.4x

x = 24 / 0.4

x = 60

In Europe

From equation (3), we have:

Py = 12 – 0.2y = 0

Therefore, we have:

12 – 0.2y = 0

12 = 0.2y

y = 12 / 0.2

y = 60

In Asia

From equation (3), we have:

Pz = 16 - 0.2z = 0

Therefore, we have:

16 - 0.2z = 0

16 = 0.2z

z = 16 / 0.2

z = 80

Based on the above calculations, the number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

If an interval estimate is said to be constructed at the 90 confidence level, the confidence coefficient would be 0.9.

Confidence level:

Confidence level means the proportion or frequency of acceptable confidence intervals that contain the true value of the unknown parameter.

For example,

A 0% confidence level means you have no faith at all that if you repeated the survey that you would get the same results.

Confidence Coefficient:

Confidence coefficient states the confidence level stated as a proportion, rather than as a percentage.

For example, if you had a confidence level of 99%, the confidence coefficient would be .99.

Given,

Here we know that the confidence level is 90%, now we have to find the confidence coefficient of it.

Based on the definition,

The confidence coefficient for 90% confidence level is 0.9.

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Answer:

liter

Step-by-step explanation:

The basic unit of volume in the metric system is a liter.

because we measure volume (v) in liters.

Therefore, the answer is liter

Info related to the question : −

The complete inequality is -2 < x < 35

The figure attached to the question is the given parameter

From the figure, we understand that:

Side length BA and side length BD are equal.

This is represented as:

BA = BD

Because the side length AC is less than the side length CD, then it means that:

The measure of the angle ABC is less than the measure of the angle CBD

This is represented as:

∠ABC < ∠CBD

Where

ABC = x + 2

and

CBD = 37

Substitute ABC = x + 2 and CBD = 37 in the inequality expression ∠ABC < ∠CBD

So, we have:

x + 2 < 37

Subtract 2 from both sides of the inequality

x + 2 - 2 < 37 - 2

Evaluate the differences

x < 35

From the question, we have the following incomplete inequality

-2 < x < [ ]

Complete the inequality as follows:

-2 < x < 35

Hence, the complete inequality is -2 < x < 35

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Answer:

70° , 70°

Step-by-step explanation:

The 2 angles are corresponding and are congruent, then

23x + 1 = 4 + 22x ( subtract 22x from both sides )

x + 1 = 4 ( subtract 1 from both sides )

x = 3

Then the angles are

23x + 1 = 23(3) + 1 = 69 + 1 = 70°

4 + 22x = 4 + 22(3) = 4 + 66 = 70°

Answer:

70° & 70°

Step-by-step explanation:

These angles are known as corresponding angles. This means they are congruent.

23x + 1 = 4 + 22x

23x + 1 - 22x = 4 + 22x - 22x

x + 1 = 4

x + 1 - 1 = 4 - 1

x = 3

Substitute the value for the variable.

23(3) + 1 = 70

4 + 22(3) = 70

The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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Answer:

C. 11

Step-by-step explanation:

Calculating range is subtracting the highest data value(11) from the lowest data value(0)

11 - 0 = 11

144. Use the formula for the volume of a cone, since the answer is in terms of pi disregard the pi in the formula and solve using (r^2)(h/3) which will give you the answer in terms of pi.

The object hits the ground after 17.5 seconds.

f(x) = ax2 + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they always have the same fundamental "U" form.

The height of an object modeled by the function:

h(t) = −16t^2 + 4900

The object hits the ground when h(t) = 0

The equation becomes:

0 = −16t^2 + 4900

-16t² = -4900

t² = 4900/16

t² = 306.25

t = √306.25

t = 17.5 secs

Thus, the object hits the ground after 17.5 seconds.

Complete question: An object is 4900 ft above the ground. The object falls, and its height is given by the quadratic function: h(t) = −16t 2 + 4900. The height of the object above the ground is in feet and the time, t, is in seconds. Determine when the object hits the ground.

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Answer:

multiply by 49.8 or add 10975 cm.

Large cat's meal tastes more like tuna fish

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Zane's cat loves tuna fish

so he adds 2 ounces of tuna fish to 10 ounces of cat food for small cat

and he adds 3 ounces of tuna fish to 12 ounces of cat food for large cat

to know whose meal tastes as tuna fish calculate their percentages

for small cat 2% is added to 10%

that means (2/12)*100=16.6

for large cat 3% is added to 12%

that means (3/15)*100=20

by this we can conclude that, large cat's meal tastes more like tuna fish

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The probability of a read error is roughly 0.00285.

We must take into account the likelihood of read errors for each of the three types of alignments in order to determine the likelihood of a read mistake (skewed, off-center, and properly aligned).

The likelihood of a read error for skewed alignments is 0.01 while the likelihood of a skewed alignment is 10%. Consequently, the likelihood that a read error will occur as a result of a skewed alignment is (0.01)(0.10) = 0.001.

The likelihood of a read mistake for an off-center alignment is 0.02 and the likelihood of an off-center alignment is 5%. Therefore, (0.02)(0.05) = 0.001 represents the likelihood that a read error will result from an off-center alignment.

The likelihood of a read mistake is 0.001 for correctly aligned read operations, while the probability of a perfectly aligned read operation is 100% - 10% - 5% = 85%. Therefore, the likelihood that a read mistake will result from a read operation that is correctly aligned is (0.001)(0.85) = 0.00085.

The likelihood of a read error for each type of alignment can be added to determine the overall likelihood of a read mistake:

0.001 + 0.001 + 0.00085 = 0.00285

So,the probability of a read error is roughly 0.00285.

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The standard deviation of the total weight of the boxes that are shipped from this source is 3.02 pounds. Therefore, the correct answer is option B.

What is the standard deviation of the total weight of the boxes that are shipped from this source?

To find the standard deviation of the total weight of the boxes that are shipped from this source, we need to add the weight of the books and the weight of the packing material to the mean weight of the boxes and take the standard deviation of the sum of the weights.

According to the given information,

Mean weight of boxes shipped, μ1 = 1.5 pounds

Standard deviation of boxes shipped, σ1 = 0.3 pounds

Mean weight of the packing material, μ2 = 0.5 pounds

Standard deviation of the packing material, σ2 = 0.1 pounds

Mean weight of books shipped, μ3 = 12 pounds

Standard deviation of books shipped, σ3 = 3 pounds

We know that if X1, X2, X3 are three independent random variables, then the standard deviation of their sum Y is given by:

σY = √σ₁²+ σ₂² + σ₃²σY = √(0.3)² + (0.1)² + (3)²σY = √0.09 + 0.01 + 9σY = √9.1σY = 3.02

Thus, the standard deviation of the total weight of the boxes that are shipped from this source is 3.02 pounds. Therefore, the correct answer is option B.

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Answer:

Step-by-step explanation:

2 + 4x/9 ≥ 4 + x

4x/9  ≥ 2 + x                 - 2 from both sides

4x ≥ 18+ 9x                   x 9 both sides

-18 ≥ 5x                         subtracted 18 and 4x from both sides

-18/5 ≥ x                        divided both sides by 5

    -18/5 is greater than x     thus x is less than -18/5

x  ≤ -18/5   <--------------  Answer is 1    

(i) Assumptions of classical linear regression: linearity, independence, homoscedasticity, no perfect multicollinearity, zero conditional mean, and normality. Violation: perfect multicollinearity between X2, X3, and X4.

(ii) Omitted variable bias occurs when X4 is omitted from the model, leading to a biased estimate of β2 compared to α2 if X2 and X4 are correlated.

In the given model, the assumption of no perfect multicollinearity is violated when the regressors X2, X3, and X4 are defined as the log of per capita GDP, the log of the square of per capita GDP, and the proportion of population with graduation, respectively. X3 is a function of X2, and X4 may be correlated with both X2 and X3. This violates the assumption that the independent variables are not perfectly correlated with each other.

Omitted variable bias in β2 compared to α2 occurs when X4 is omitted from the model. This bias arises because X4 is a relevant explanatory variable that affects the dependent variable (Y), and its omission leads to an incomplete model. The bias in β2 arises from the correlation between X2 and X4. If X2 and X4 are not correlated, β2 will equal α2, and there will be no omitted variable bias. However, if X2 and X4 are correlated, omitting X4 from the model will result in a biased estimate of β2 because the omitted variable (X4) affects both Y and X2, leading to a bias in the estimation of the relationship between Y and X2.

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Answer: $62

Step-by-step explanation:

From the question, we are informed that someone earned $204 from a job last week and has two relatives with birthdays coming up and wants to

spend the same amount on each of them but still wants to have $80 left.

To calculate the amount of gift spent on each, we have to deduct $80 from $204 firstly. This will be:

= $204 - $80

= $124

This means that the person will spend $124 on both of them, then we divide $124 by 2. This will be:

= $124/2

= $62

The amount spent on each gift will be $62.

Answer:

\(1205.8 \: {in}^{3} \)

Step-by-step explanation:

For given cylinder:

Radius (r) = 4 in

Height (h) = 24 in

\(V_{cylinder} =\pi {r}^{2} h \\ \\ = 3.14(4)^{2} (24) \\ \\ = 1,205.76 \\ \\ \approx 1205.8 \: {in}^{3} \)

Answer:

Sam will finish 42 pages in 126 minutes.

Step-by-step explanation:

Number of pages read by Sam = 6

Time taken to read these pages = 18 minutes

Rate at which Sam is reading the pages of the book = \(\frac{\text{Number of pages read}}{\text{Time taken to read these pages}}\)

= \(\frac{6}{18}\)

= \(\frac{1}{3}\) pages per minute

Number of pages read in 126 minutes = Rate of reading × Time

                                                            = \(\frac{1}{3}\times 126\)

                                                            = 42 pages

Therefore, Sam will finish 42 pages in 126 minutes.

The graphs of triangle XYZ and its image after a dilation by a scale factor of 3 centered at the origin are shown below.

In Mathematics and Geometry, a dilation refers to a type of transformation that is typically used for altering the side lengths (dimension) of a geometric figure, but not its shape.

In this scenario and exercise, we would have to dilate the coordinates of the pre-image (triangle XYZ) by using a scale factor of 3 centered at the origin in order to produce triangle X'Y'Z' as follows:

Coordinate X (6, -1)        →       (6 × 3, -1 × 3) = X' (18, -3).

Coordinate Y (-2, -4)        →      (-2 × 3, -4 × 3) = Y' (-6, -12).

Coordinate Z (1, 2)        →       (1 × 3, 2 × 3) = Z' (3, 6).

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Complete Question:

Use the given vertices to graph △XYZ and its image after a dilation centered at the origin with scale factor k=3.

X(6, -1), Y(-2,-4), Z(1, 2)

Answer:

58.1cm

Step-by-step explanation:

perimeter of a semi-circle = πd/2

d is the diameter

Given

diameter = 37cm

Perimeter of the semi circle =  π(37)/2

Perimeter of the semi circle = 18.5(3.14)

Perimeter of the semi circle = 58.09 cm

Hence the perimeter of the semi-circle is 58.1cm

The length of Stan's movie is 2 hours 25 minutes

The length of Talia's movie is 2 hours 55 minutes.

In order to determine the length of the movies, subtract the end time of the movie from the time the movie started.

Subtraction is the mathematical operation that is used to calculate the difference between two or more numbers. The sign that is used to represent subtraction is -.

Length of the movie = time the movie ended - time the movie started

Length of Stan's movie = 9:40 - 7:15 = 2 : 25 hours

Length of the Talia's movie = 10 : 10 - 7 : 15 = 2 : 55 hours

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Answer:

2 times a number more than 4

Answer:B

Step-by-step explanation:

Part A

Given

Solution

We ask to double the time i.e

Part B

Given

Solution

The half-life would be 5

Step-by-step explanation:

We can prove the statement by mathematical induction.

Base Case: For n = 0, we have 9n - 3n = 1, which is divisible by 6, since 1 = 6*0 + 1.

Inductive Step: Assume that 6 divides 9k - 3k for some non-negative integer k. We need to show that 6 also divides 9(k+1) - 3(k+1).

Starting with 9(k+1) - 3(k+1), we can simplify it as follows:

9(k+1) - 3(k+1) = 9k + 9 - 3k - 3

= (9k - 3k) + (9 - 3)

= 6k + 6

Since 6 divides both 6k and 6, it also divides their sum, 6k + 6. Therefore, we have shown that 6 divides 9(k+1) - 3(k+1).

By the principle of mathematical induction, we can conclude that 6 divides 9n - 3n for all non-negative integers n.