Inayah claims that the pool is draining at a rate of 1. 36% per hour

The value of the function f(x) at x = 2 is 48.

The question asks us to find the value of the function f(x) = 4[tex]x^3[/tex] at x = 2 and its derivative f'(x) at x = 2.

The value of the function f(x) at x = 2, we simply plug in x = 2 into the function and evaluate:

f(2) = 4[tex](2)^3[/tex] = 4(8) = 32

Therefore,

The value of the function f(x) at x = 2 is 32, which we can write as f(2) = 32.

To find the derivative of the function f(x) at x = 2, we first need to find the general formula for the derivative of f(x), which we can do using the power rule for derivatives.

The power rule states that

To find the derivative of f(x) at x = 2, we simply plug in x = 2 into the formula for f'(x) that we just found:

f'(2) = [tex]12(2)^2[/tex] = 48

Therefore,

The derivative of the function f(x) at x = 2 is 48, which we can write as f'(2) = 48To find the derivative of the function

f'(x) = 12[tex]x^2[/tex]

To find the value of f(2), we can simply plug in x = 2 into the original function:

f(2) = 4[tex](2)^3[/tex] = 32

To find the value of f'(2), we can plug in x = 2 into the derivative we just found:

f'(2) = 12[tex](2)^2[/tex] = 48

Therefore,

f(2) = 32 and f'(2) = 48.

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Jen can fill 4 bags completely with the 5 1/2 cups of M&Ms she has, given that each bag requires 1 1/4 cups of M&Ms.

First, we need to find the total number of cups of M&Ms Jen has

5 1/2 cups = 11/2 cups

Then, we divide the total number of cups by the number of cups needed to fill each bag

(11/2 cups) ÷ (1 1/4 cups/bag)

To divide by a fraction, we can multiply by its reciprocal

(11/2 cups) x (4/5 cups/bag)

= 44/10 cups

Simplifying, we get

= 4 2/10 cups

= 4 1/5 cups

So, Jen can fill 4 bags completely.

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The term which is important in terms of making meaning of those scores is measures of central tendency (mean, median, mode), option A.

A single number that seeks to characterise a set of data by pinpointing the centre location within that set of data is referred to as a measure of central tendency. As a result, measurements of central location are occasionally used to refer to measures of central tendency.

These also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.

The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, certain indicators are more useful than others.

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Answer:

approximately 42.85 of whatever unit

Total string used = Number of bracelets × String used per bracelet

Total string used = 77 × 17.8 = 1370.6 cm

Let's denote the total amount of string used as "T". We know that the girl used xx centimeters of string to make 77 bracelets, and each bracelet required 17.8 centimeters of string.

To find the total string used, we can set up the following equation:

T = 77 * 17.8

Simplifying the equation, we have:

T = 1369.6

Therefore, the girl used a total of 1369.6 centimeters of string to make all the bracelets.

In conclusion, the equation T = 77 * 17.8 can be used to determine the total amount of string used, and the solution to the equation is T = 1369.6 centimeters.

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The following are correct about the triangle;

1. angle C is 60°

2. angle B is 60°

3. The length of segment DB is 3

4. The length of side x is 3√3

An equilateral triangle is a type of triangle in which all it's sides and angles are equal.

Since all the angles of an equilateral triangle are equal, then,

x+x+x = 180

3x = 180

x = 180/3 = 60°

therefore each angle is 60°

angle C and angle B are 60°

Using Pythagorean theorem

x² = 6²- 3²

x² = 36-9

x² = 27

x = √27

x = √9×3

x = 3√3

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The solution of the system of equations is given by the ordered pair (-2, 2).

Based on the table, a x-value that is a solution to the equation is -2.

The solution to the equations are (-6, 3) and (-4, -5).

An ordered pair which is the best estimate for the solution of the system is: A. (-0.5, -1.75).

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

8x - 4y = -24    ......equation 1.

4x - 12y = -32  ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-2, 2).

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The value of the fraction is 3/-2

A fraction can simply be described as the part of a whole variable, a whole number or a whole element.

The different types of fractions in mathematics are;

From the information given, we have that;

4/-2 - 3/-6

find the lowest common factor

12 - 3/-6

subtract the value, we get;

9/-6

Divide the values into simpler forms

3/-2

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If x > 2.5, both expressions within absolute value symbols are positive.

The equation becomes: y = (2x + 5) - (2x - 5) = 10.

For the given intervals of x:

If x < -2.5, both expressions within absolute value symbols are negative. Thus, the equation is: y = -(2x + 5) - (-(2x - 5)) = -10.

If x > 2.5, both expressions within absolute value symbols are positive.

The equation becomes: y = (2x + 5) - (2x - 5) = 10.

If -2.5 ≤ x ≤ 2.5, the first expression is positive and the second is negative.

The equation is: y = (2x + 5) - (-(2x - 5)) = 4x.

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The quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7) have a minimum point. The minimum value of the function is -11.

To find the maximum or minimum of the quadratic equation in factored form f(x) = 0.5(x+3)(x-7), we need to convert it to standard form by expanding the terms:

f(x) = 0.5(x² - 4x - 21)

f(x) = 0.5x² - 2x - 10.5

The coefficient of x² is positive, so the parabola opens upwards and we have a minimum point.

To find the x-coordinate of the minimum point, we can use the formula x = -b/2a, where a = 0.5 and b = -2:

x = -(-2)/2(0.5) = 2

So the minimum point is at x = 2. To find the y-coordinate, we can substitute x = 2 into the equation:

f(2) = 0.5(2)^2 - 2(2) - 10.5 = -11

Therefore, the minimum value of the function is -11.

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The value of 'a' is 2/3.

The problem presents a ratio, 4:15, that is equal to a ratio involving 'a' and 2 1/2. To solve for 'a', we need to isolate it on one side of the equation by cross-multiplying.

In the first step, we convert 2 1/2 to an improper fraction, 5/2, so that we can use it in the equation. We then cross-multiply by multiplying both sides of the equation by 5/2.

This eliminates the denominator on the right-hand side and simplifies the left-hand side.

Solve for 'a'

To solve for 'a', we can use cross-multiplication.

First, we need to convert 2 1/2 to an improper fraction:

2 1/2 = 5/2

Now we can write the equation as:

4/15 = a/(5/2)

To solve for 'a', we cross-multiply:

4/15 * 5/2 = a

a = 2/3

Finally, we solve for 'a' by multiplying 4/15 by 5/2 and simplifying the result. The answer is 2/3, which represents the value of 'a'.

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Answer:

Step-by-step explanation:

To answer question a, we use the formula:

time taken = (number of tyres to fit x time taken to fit one tyre) / number of tyres fitted at once

In this case, Liam takes 124 minutes to fit 4 tyres to a lorry. To find out how long it would take him to fit 6 tyres, we plug in the values:

time taken = (6 x 124) / 4
time taken = 186 minutes

So it would take Liam 186 minutes to fit 6 tyres to a lorry.

For question b, we know that Liam takes 124 minutes to fit 4 tyres, so he takes 31 minutes to fit 1 tyre. If he works for 93 minutes, we can find out how many tyres he can fit:

number of tyres = time taken / time taken to fit one tyre
number of tyres = 93 / 31
number of tyres = 3

So Liam can fit 3 tyres in 93 minutes.

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The MAD for Doctor A's data set is 0.67 and the MAD for Doctor B's data set is 0.83. Doctor A's data set has less variation than Doctor B's data set, as indicated by their respective MADs.

To calculate the mean absolute deviation (MAD) for a data set, we first find the mean of the data set, and then find the absolute deviation of each value from the mean. We then find the mean of these absolute deviations.

a) For Doctor A's data set on corrective lenses, the mean is:

Mean = (15+18+17+16+14)/5 = 16

The absolute deviations from the mean are:

|15-16| = 1

|18-16| = 2

|17-16| = 1

|16-16| = 0

|14-16| = 2

The mean of these absolute deviations is:

MAD = (1+2+1+0+2)/5 = 1.2

Therefore, the MAD for Doctor A's data set is 1.2.

b) For Doctor B's data set on corrective lenses, the mean is:

Mean = (17+19+20+16+18)/5 = 18

The absolute deviations from the mean are:

|17-18| = 1

|19-18| = 1

|20-18| = 2

|16-18| = 2

|18-18| = 0

The mean of these absolute deviations is:

MAD = (1+1+2+2+0)/5 = 1.2

Therefore, the MAD for Doctor B's data set is also 1.2.

Comparing the two data sets using their MAD, we can see that they have the same amount of variation or dispersion from the mean. Both sets have a MAD of 1.2, indicating that the average absolute deviation of each value from the mean is the same for both sets.

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Answer:

Doctor A MAD: 11.8

Doctor B MAD: 9.32

Step-by-step explanation:

This is what I got on the assignment.

The probability of drawing a star-shaped chip is 5/8.

The theoretical probability of drawing a star-shaped circular chip from the bag is 5/8 or 0.625 or 62.5%. Out of the total of eight circular chips, five are stars, and three are squares.

Therefore, the probability of drawing a star-shaped chip is the ratio of the number of star-shaped chips to the total number of chips in the bag, which is 5/8.

To understand this conceptually, we can think of probability as a fraction where the numerator is the number of favorable outcomes (in this case, drawing a star-shaped chip) and the denominator is the total number of possible outcomes (all the circular chips in the bag).

Thus, the theoretical probability of drawing a star-shaped chip is 5/8 because there are five star-shaped chips out of the total eight circular chips in the bag.

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The number of cakes that can be made with a large bag of sugar, we first need to determine the amount of sugar in a small bag and then calculate the amount of sugar needed for one cake.

1. Find the amount of sugar in a small bag:
Since the large bag contains 30 cups of sugar and is 2.5 times larger than the small bag, we can write the equation:
Small bag = Large bag / 2.5
Small bag = 30 cups / 2.5
Small bag = 12 cups of sugar

2. Determine the amount of sugar needed for one cake:
The small bag contains enough sugar to make 9 cakes and have 0.75 cups of sugar remaining. So, we can subtract the remaining sugar from the total amount in the small bag:
Sugar used for 9 cakes = 12 cups - 0.75 cups
Sugar used for 9 cakes = 11.25 cups

Now, we can find the amount of sugar needed for one cake:
Sugar per cake = Sugar used for 9 cakes / 9
Sugar per cake = 11.25 cups / 9
Sugar per cake = 1.25 cups

3. Calculate the number of cakes that can be made with a large bag of sugar:
Cakes from large bag = Large bag sugar / Sugar per cake
Cakes from large bag = 30 cups / 1.25 cups
Cakes from large bag = 24

Therefore, a baker can make 24 cakes with a large bag of sugar.

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1. All square, upper triangular matrices are diagonalizable. (TRUE)

2. If a matrix is diagonalizable, then it is invertible. (FALSE)

1. True: All square, upper triangular matrices are diagonalizable.

A square matrix is diagonalizable if it can be transformed into a diagonal matrix by a similarity transformation, which means there exists an invertible matrix P such that P^-1 * A * P is a diagonal matrix. Upper triangular matrices have all their elements below the main diagonal equal to zero.

Since the eigenvalues of an upper triangular matrix are equal to its diagonal elements, we can form a diagonal matrix with these eigenvalues. Since there exists such a diagonal matrix, all square, upper triangular matrices are diagonalizable.

2. False: If a matrix is diagonalizable, it is not necessarily invertible

Diagonalizable matrices can be transformed into a diagonal matrix with the eigenvalues along the main diagonal.

However, invertibility requires that the matrix have a nonzero determinant, which means that all of its eigenvalues must be nonzero.

If a diagonalizable matrix has a zero eigenvalue, its determinant will be zero, and it will not be invertible. Therefore, diagonalizability does not guarantee invertibility.

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(a) The critical numbers happen when x = 3 or x = -1/2

(b) f is decreasing on (-∞, -1/2), increasing on (-1/2, 3), and increasing on (3, ∞).

(c) f has a local minimum value of -22 at x = 3, and a local maximum value of 25.5 at x = -1/2.

(d) f is concave downward on (-∞, 1/4) and concave upward on (1/4, ∞).

(e) The inflection point of f is at x = 1/4.

(a) To find the critical numbers of f, we need to find the values of x where the derivative of f equals zero or does not exist.

f'(x) = 12x² - 6x - 18 = 6(2x² - x - 3) = 6(x - 3)(2x + 1)

Setting f'(x) equal to zero, we get:

6(x - 3)(2x + 1) = 0

x = 3 or x = -1/2

These are the critical numbers of f.

(b) To find the intervals where f is increasing and decreasing, we need to examine the sign of the derivative f'(x) in the intervals determined by the critical numbers.

When x < -1/2, f'(x) < 0, so f is decreasing on the interval (-∞, -1/2).

When -1/2 < x < 3, f'(x) > 0, so f is increasing on the interval (-1/2, 3).

When x > 3, f'(x) > 0, so f is increasing on the interval (3, ∞).

(c) To find the local minimum and maximum values of f, we need to examine the critical numbers and the end points of the intervals.

f(3) = 4(3)³ - 3(3)² - 18(3) + 5 = -22

f(-1/2) = 4(-1/2)³ - 3(-1/2)² - 18(-1/2) + 5 = 25.5

Thus, f has a local minimum value of -22 at x = 3, and a local maximum value of 25.5 at x = -1/2.

(d) To find the intervals where f is concave upward and concave downward, we need to examine the sign of the second derivative f''(x).

f''(x) = 24x - 6 = 6(4x - 1)

When x < 1/4, f''(x) < 0, so f is concave downward on the interval (-∞, 1/4).

1/4 < x, f''(x) > 0, so f is concave upward on the interval (1/4, ∞).

(e) To find the inflection points of f, we need to examine the points where the concavity changes.

The concavity changes at x = 1/4, which is the only inflection point o

Step-by-step explanation:

sqrt (5/3)  = sqrt 5 / sqrt 3    

  multiply by ONE in the form   sqrt (3) / sqrt 3

      sqrt 5 / sqrt 3    *    sqrt 3 / sqrt 3

             = sqrt 15 / 3    

Or maybe you meant  

  sqrt (5) / 3  =  .745

The probability that the next customer will pay with a credit card is 9/40.

To find the probability that the next customer will pay with a credit card, we need to determine the total number of customers and then calculate the fraction of those who used a credit card.

Step 1: Find the total number of customers.
56 customers paid cash, 6 customers used a debit card, and 18 customers used a credit card.
Total customers = 56 + 6 + 18 = 80 customers

Step 2: Calculate the probability of a customer using a credit card.
Number of customers who used a credit card = 18
Total number of customers = 80

Probability = (Number of customers who used a credit card) / (Total number of customers)
Probability = 18 / 80

Step 3: Simplify the fraction.

Divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 18 and 80 is 2.
18 ÷ 2 = 9
80 ÷ 2 = 40

Simplified fraction: 9/40

So, the probability that the next customer will pay with a credit card is 9/40.

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Answer:

c=4

Step-by-step explanation:

as there is only one solution for this quadratic equation which is supposedly have 2 or more answers, c can only be 4 in order to be the same equation as the the first one x-4=0

The scale factor of figure KLMN to figure PQRS is 6 cm / 3 cm = 2.

To find the scale factor of figure KLMN to figure PQRS, given KN = 3 cm, MN = 7 cm, RS = 14 cm, and PS = 6 cm, follow these steps:

1. First, find the length of a side in figure KLMN. We can use KN since it's given: KN = 3 cm.
2. Next, find the corresponding side length in figure PQRS. Since KN corresponds to PS, we have: PS = 6 cm.
3. Now, find the scale factor by dividing the length of the side in figure PQRS by the length of the corresponding side in figure KLMN: scale factor = PS/KN = 6 cm / 3 cm.

The scale factor of figure KLMN to figure PQRS is 6 cm / 3 cm = 2.

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A frequency table was created using data points representing the number of holes in each of Grandma Marion's dresses. The table shows the number of dresses with 5, 7, and 8 holes, respectively.

To create a frequency table for the given data, first, the unique values in the data set are identified, which are 5, 7, and 8. Then, the number of occurrences of each unique value is counted, resulting in the frequencies 1 for 5, 2 for 7, and 3 for 8.

Count the frequency of each data point

5: 1 dress

7: 2 dresses

8: 3 dresses

Finally, these values are organized into a table with two columns, one for the unique values and another for their corresponding frequencies. The resulting frequency table shows the number of dresses with each number of holes eaten by moths.

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To find the area enclosed by the figure, we first need to find the area of  the square and the  area of each semicircle.

The area of the square is simply the length of one of its sides squared, which is:

54 m x 54 m = 2,916 m²

The area of each semicircle is half the area of a full circle with the same radius as the side of the square. The radius of each semicircle is 54 m/2 = 27 m.

The area of each semicircle is:

1/2 x π x 27 m² = 1/2 x 3.14 x 27 m x 27 m ≈ 1,442.31 m²

Since there are four semicircles, the total area of the semicircles is:

4 x 1,442.31 m² = 5,769.24 m²

Therefore, the total area enclosed by the figure is:

2,916 m² + 5,769.24 m² ≈ 8,685.24 m²

Frank's answer of 1,662.12 m² is significantly less than the actual area. He may have made the mistake of only calculating the area of one of the semicircles instead of all four, or he may have forgotten to include the area of the square.

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The profit per pig is $4 and the profit per goose is $8.

Let's start by defining the variables:

a = number of pigs Farmer Jones raises

y = number of geese Farmer Jones raises

The problem tells us that he wants to raise at most 16 animals, so we can write:

a + y ≤ 16

It also tells us that he wants no more than 12 geese, so we can write:

y ≤ 12

We know that it costs $5 to raise a pig and $2 to raise a goose, and he has $550 available to spend. So the cost of raising the animals can be expressed as:

5a + 2y ≤ 550

Finally, we want to maximize his profits. The profit per pig is $4 and the profit per goose is $8. So the objective function for Farmer Jones' profits is:

Profit = 4a + 8y

To summarize, the linear programming model for this problem is:

Maximize: Profit = 4a + 8y

Subject to:

a + y ≤ 16

y ≤ 12

5a + 2y ≤ 550

where a and y are non-negative integers.

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Answer:

x = 4, y = 1, z = 5

Step-by-step explanation:

z + x =9....(3) we can say it's x + z = 9

x - z = - 1

x + z = 9

______ -

- 2z= - 10

z = 10/2

z = 5

if z + x = 9

5 + x = 9

x = 9 - 5

x = 4

if x + y = 5

4 + y = 5

y = 5 - 4

y = 1

The rank of the coefficient matrix A is 5.

Since the system AX = B is consistent and has 12 equations and 8 variables, the rank of the coefficient matrix A must be less than or equal to 8 (the number of variables).

If the solution of the system contains 3 free variables, it means that the dimension of the null-space of A is 3. By the rank-nullity theorem,

we know that the dimension of the null-space of A plus the rank of A is equal to the number of columns of A (which is 8 in this case).

Therefore, we have:

rank(A) + dim(null(A)) = 8

rank(A) + 3 = 8

rank(A) = 5

So, the rank of the coefficient matrix A is 5.

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