Need help with the picture attached, involving derivatives.

The expanded form of 8! is 8×7×6×5×4×3×2×1.

A whole number's factorial is the result of multiplying the integer by each natural number below it.

The sign '!' can be used to indicate a factorial symbolically.

Therefore, 'n factorial' is denoted by the number n and is the product of n up to whole numbers below n except zero.

Given, A factorial number 8!.

Therefore, 8! = 8×7×6×5×4×3×2×1.

The product of all whole numbers below 8 and except zero.

We use factorials in permutation and combination also.

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The midpoint of the  1/3 and 6/11 as a fraction is, 29/33

The midpoint of two numbers can be found by taking the average of the two numbers. To find the average of two fractions, you need to find a common denominator, add the numerators, and divide the sum by the denominator.

Given that,

Two fractions,

1/3 and 6/11

To find the common denominator for 1/3 and 6/11, you can find the least common multiple (LCM) of the denominators:

LCM(3, 11) = 33

Next, convert each fraction to an equivalent fraction with a denominator of 33:

1/3 = 11/33

6/11 = 18/33

Finally, add the numerators and divide the sum by the denominator to find the average:

(11 + 18) / 33 = 29/33

The midpoint of 1/3 and 6/11 as a fraction is 29/33.

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Profit function is P(x) = 3.1x - 0.05x² - 181

The profit a business makes is equal to the revenue it takes in minus what it spends as costs. To obtain the profit function, subtract costs from revenue.

P(x) = R(x) - C(x)

Given,

Cost C(x) = 181 +2.9x

Revenue R(x) = 6x -0.05x²

Profit P(x) = R(x) - C(x)

                = 6x - 0.05x² - (181 +2.9x)

                = 6x - 0.05x² - 181 - 2.9x

         P(x) = 3.1x - 0.05x² - 181

Hence,  P(x) = 3.1x - 0.05x² - 181 is the profit function.

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The scalar projection of vector b onto vector a is 57/289 and the vector projection of vector b onto vector a is (0.38, 0.92).

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

The scalar projection of vector b onto vector a is given by:

(b . a) / ||a||^2

= (3 * -8 + 5 * 15) / ( -8^2 + 15^2)

= 165 / 289

= (57/289)

The vector projection of vector b onto vector a is given by:

proj(b onto a) = (b . a) / ||a||^2 * (a / ||a||)

= (57/289) * (-8/√(-8^2 + 15^2), 15/√(-8^2 + 15^2))

= (0.38, 0.92)

Note: sqrt(-8^2 + 15^2) = sqrt(289) = 17

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The X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.

The lowest 2.5% boundary for a normal distribution with a mean of 50 and standard deviation of 4 can be calculated using the Z-score formula.

Z = (X - mean) / standard deviation

We want to find the X value for which Z = -1.96 since -1.96 represents the boundary for the lowest 2.5% of a standard normal distribution.

Plugging in the mean and standard deviation:

-1.96 = (X - 50) / 4

Solving for X:

X = 50 - 1.96 × 4

X = 43.04

So, the X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.

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The area of the surface generated when the given curve is revolved about the x-axis with y=8√x on [9,20] is approximately 764.26 square units.

The area of the surface generated when the given curve is revolved about the x-axis is calculated using the formula:

A = 2 * π * ∫[a,b] y * √(1 + (dy/dx)²) dx,

where y = 8√x, and a and b are the limits of integration, i.e., a = 9, and b = 20.

First, we'll find the derivative of y with respect to x:

dy/dx = 8 / (2 * √x)

Now, we can substitute the values into the formula:

A = 2 * π * ∫[9,20] 8√x * √(1 + (8 / (2 * √x))²) dx

Using the change of variable u = √x, the above equation becomes:

A = 16π * ∫[3,4.472] u² * √(1 + (8 / u)²) du

Evaluating the definite integral, we get:

A = 16π * (u³ / 3) * √(1 + (8 / u)²) |[3,4.472]

A = 16π * [(4.472³ / 3) * √(1 + (8 / 4.472)²) - (3³ / 3) * √(1 + (8 / 3)²)]

A = 16π * [(4.472³ / 3) * √(1 + (8 / 4.472)²) - (27 / 3) * √(1 + (8 / 3)²)]

A ≈ 764.26

So, the area of the surface generated when the given curve is revolved about the x-axis is approximately 764.26 square units.

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In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.

There are 3 centers to choose from, and for each center there are 4 choices for each of the two guard positions and 4 choices for each of the two forward positions. So, there are:

3 * 4 * 4 * 4 = 192

different starting lineups without x.

Lineups with x as guard: There are 3 centers, 3 choices for the first guard (since x can play either guard or forward), 4 choices for the second guard, and 4 choices for each forward. So, there are

3 * 3 * 4 * 4 = 144

different lineups with x as guard.

Lineups with x as forward: There are 3 centers, 4 choices for each guard, 3 choices for the first forward (since x can play either guard or forward), and 4 choices for the second forward. So, there are 3 * 4 * 3 * 4 = 144 different lineups with x as forward.

In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.

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The equation y = e^-4 can be evaluated using a graphing calculator by plugging in -4 for x and finding the corresponding y-value.

On a graphing calculator, this is usually done by setting the calculator to the "y=" mode and entering the equation y = e^x. Then, by entering -4 as the value of x, the corresponding y-value can be found.

The result would be y = e^-4 = 0.0183. To four decimal places, this value is 0.0183.

Scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.

The evidence that allowed scientists to conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus comes from the application of the quantum mechanical model. The quantum mechanical model states that the energy of an electron is quantized, meaning it can only occupy discrete energy levels rather than any random energy level in between. This is expressed mathematically through the equation E n = nhf, which states that the energy of an electron is equal to the product of Plank's constant (h) and the frequency (f) of the electron's orbit multiplied by the quantum number (n). This equation demonstrates that electrons can only occupy certain energy levels and not any random energy level. Therefore, scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.

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x=-10, 2

you would have to factor it.

refer to picture

The quadratic regression equation for the data-set in this problem is given as follows:

y = 0.96x² - 5.77x + 1.38.

Regression equations are obtained inserting the points of a data-set into a calculator.

In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.

The points are given as follows:

(-1,8), (5,-4), (7,8), (2,-6).

Inserting these points into a calculator, the regression equation is given as follows:

y = 0.96x² - 5.77x + 1.38.

Meaning that the second option is the correct option.

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The speed of the slower boat is 15 mph and the speed of the faster boat is 35 mph.

The problem involves using the formula for distance, speed, and time, which is:

distance = speed × time

In this case, we are given the distance between two boats (400 miles) and the time it takes for them to meet (8 hours), and we need to find the speed of each boat. This involves solving a linear equation to find the unknown speed. The problem also involves the concept of finding the rate of change of distance, which is the sum of the speeds of the two boats.

Let's call the speed of the slower boat = x mph.

The speed of the faster boat would be = x + 20 mph.

The distance between the two boats decreases at a rate = x + x + 20 = 2x + 20 mph.

The time it takes for the two boats to meet is 8 hours, so the distance between the two boats when they meet is:

400 = (2x + 20) × 8

Solving for x:

400 = 16x + 160

16x = 240

x = 15

So, the speed of the slower boat is 15 mph and the speed of the faster boat is x + 20 = 35 mph.

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Answer:

19) x=10⁰ 20) x=17⁰

Step-by-step explanation:

19) angles in a straight line add upto 180⁰

 6x-10⁰+4x⁰+6+7x+14⁰=180⁰

collect like terms

 17x+10⁰=180⁰

 17x=1170⁰

x=10⁰

20)58⁰ alternates with 4x-10 therefore;

4x-10⁰=58⁰

4x=58⁰+10⁰

4x=68⁰

x= 17⁰

The lateral surface area of the rectangular prism given in the picture is 36 cm ²

The lateral surface area of a rectangular prism can be found by the formula :

= 2 x height x ( Length + Breadth )

Height = 2 cm

Length = 3 cm

Breadth = 6 cm

The lateral surface area is therefore:

= 2 x 2  x ( 3 + 6 )

= 4 x 9

= 36 cm ²

In conclusion, the lateral surface area is 36 cm ².

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The larger the p-value, the more likely it is that the null hypothesis that the population coefficient is equal to 0 is true regarding p-value.

In a linear regression model, p-values are associated with the estimated coefficients and provide information about the statistical significance of each predictor variable. The null hypothesis for each predictor is that the population coefficient for that predictor is equal to 0, meaning that it has no effect on the response variable.

The p-value is the probability of observing the estimated coefficient given the null hypothesis is true. If the p-value is small, it means that the observed coefficient is unlikely to be due to chance, If the p-value is large, it means that the observed coefficient could easily be due to chance and we cannot reject the null hypothesis.

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The new coordinate of the points after the dilation will be (3, 5).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The point is (6, 10). And the scale factor is 1/2. Then the new coordinate of the points after the dilation is given as,

⇒ (1/2)(6, 10)

⇒ (1/2 x 6, 1/2 x 10)

⇒ (3, 5)

The new coordinate of the points after the dilation will be (3, 5).

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Answer:

-1/3

Step-by-step explanation:

multiply across

1/2 * -2/3

-2/6

-1/3

There is 700 number of $5 bills and 200 number of $10 bills

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

Let x represent the number of $5 bills and y represent the number of $10 bills.

There is a total of 900 $5, $10 dollar bills, hence:

x + y = 900        (1)

The value of all the bills is $5500, hence:

5x + 10y = 5500     (2)

From both equation, solving simultaneously:

x = 700, y = 200

There are 700 $5 bills and 200 $10 bills

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This indicates that the cutoff value for the amount of minutes before contacting the consumer is 674 minutes, rounded to the closest minute.

Quartiles are three numbers that divide sorted data into four equal portions with an equal amount of observations each. A quantile is a sort of quantile. The first quartile is sometimes known as the lower quartile or Q1. Second quartile: Also known as the median or Q2. Third quartile: Also known as the higher quartile or Q3.

Here,

To find the upper fence, we need to calculate the following statistics:

Q1 (first quartile), Q2 (median), and Q3 (third quartile) of the data

Interquartile range (IQR), which is the difference between Q3 and Q1

Upper fence, which is Q3 + 1.5 * IQR

First, we need to order the data in ascending order:

339, 350, 358, 388, 430, 458, 458, 463, 480, 489, 501, 536

Next, we can find the quartiles:

Q1 = 388

Q2 = 458

Q3 = 501

IQR = Q3 - Q1 = 501 - 388 = 113

Finally, we can calculate the upper fence:

Upper fence = Q3 + 1.5 * IQR = 501 + 1.5 * 113 = 674

This means that the cutoff point for the number of minutes at which the customer should be contacted is 674 minutes, rounded to the nearest minute.

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The solution is Option B.

The angle ∠AEC is a right angle by definition of perpendicular bisector

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as AB

Let the second line be represented as CD

Now , AB is perpendicular to the line CD

where , the measure of ∠CEB = 90°

And , angles on a straight line has a sum of 180°

So , the measure of ∠AEC is a right angle by perpendicular bisector theorem

Hence , the measure of the perpendicular angle ∠AEC is 90°

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Answer: Definition of Perpendicular Bisector

Step-by-step explanation:

Took the test!

An equation for Windy Kite's total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.

An equation for Kites-R-Fun's total cost, y, in terms of the number of kites purchased, x, is y = 4x + 8.

Based on the table, if the Alaskan customer wants to buy 4 kites, Kites-R-Fun charges the least.

If the Alaskan customer wants to buy 10 kites, Windy kites charges the least.

The solution to the system of equations is (6, 32).

The meaning of the solution is that 6 kites would cost a total of $32 at both Windy kites and Kites-R-Fun.

In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:

Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:

y = 2x + 20

When x = 4, the total cost for Windy kites is given by:

y = 2(4) + 20

y = $28.

When x = 7, the total cost for Windy kites is given by:

y = 2(7) + 20

y = $34.

When x = 10, the total cost for Windy kites is given by:

y = 2(10) + 20

y = $40.

For Kites-R-Fun, a linear equation that models the total cost is given by:

y = 4x + 8

When x = 4, the total cost for Kites-R-Fun is given by:

y = 4(4) + 8

y = $24.

When x = 7, the total cost for Kites-R-Fun is given by:

y = 4(7) + 8

y = $36.

When x = 10, the total cost for Kites-R-Fun is given by:

y = 4(10) + 8

y = $48.

Lastly, we would use an online graphing calculator to plot the system of linear equations as shown in the graph attached below.

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The rate of change of the volume of the cone at the given instant is 1 238 768 66.67 cm^3/s.

The volume of a cone can be calculated using the formula V = (πr^2h)/3, where r is the radius and h is the height of the cone.

At the given instant, radius = 8 88 cm and height = 10 1010 cm.

Substituting these values in the formula we get,

[tex]V = (π(8 88 cm)^2(10 1010 cm))/3 = 2 477 537 33.33 cm^3[/tex]

The rate of change of the volume of the cone at that instant can be calculated as follows:

Let dV/dt be the rate of change of the volume at that instant.

[tex]dV/dt = (dV/dr)*(dr/dt) + (dV/dh)*(dh/dt) \\dr/dt = 3 33 cm/s \\dh/dt = -4 44 cm/s[/tex]

Differentiating the volume of a cone formula with respect to r and h, we get

[tex]dV/dr = (πr^2h) dV/dh = (πr^2h)/3[/tex]

Substituting these values in the equation for dV/dt, we get

[tex]dV/dt = (π(8 88 cm)^2(10 1010 cm)) + (π(8 88 cm)^2(10 1010 cm))/3 * (-4 44 cm/s) = 1 238 768 66.67 cm^3/s[/tex]

Therefore, the rate of change of the volume of the cone at the given instant is [tex]1 238 768 66.67 cm^3/s[/tex].

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The number of times both services left the interchange together from 9am to 12 noon is 0.

Let's call the number of 15-minute intervals that have passed since 9 am "t".

So, the time that bus number 801 leaves the interchange after t intervals is 9am + 15t minutes.

Similarly, the time that bus number 802 leaves the interchange after t intervals is 9 am + 20t minutes.

For both services to leave the interchange at the same time, the number of 15-minute intervals that have passed since 9 am must be the same for both buses.

In other words, 15t must equal 20t.

Dividing both sides of this equation by 5, we get 3t = 4t.

This equation has no solution, which means that bus number 801 and bus number 802 never leave the interchange at the same time from 9am to 12 noon.

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The total number of ways are 225, 225.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given:

There are 11 kittens and 15 puppies.

so, we have to select 3 kittens from 11 kittens and 4 puppies from 15 puppies.

Then, the number of ways can be

= C(11, 3) x C(15, 4)

= 990 / 6 x 32,760/ 24

= 165 x 1365

= 225, 225.

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Answer:

Below

Step-by-step explanation:

You cannot 'solve' this equation..... you have only one equation and TWO unknowns p and x      you will need another equation relating p and x to solve this

The range of the function shown in the graph below is [-6, ∞].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph,

The y-coordinate value is the range of the function.

We see that,

The y-coordinate value is from -6 to ∞.

So,

Range = [-6, ∞].

Thus,

The range of the function is [-6, ∞].

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The equation represents the relationship between the independent variable, x, and the dependent variable is y= 2x

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

The table of values

On the yable of values, we can see that

y is twice of x

When represented as an equation, we have

y = 2x

Hence, the equation is y = 2x

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(C) $563,700 in cash was received from customers during the year.

Accounting lingo for partial payment of an amount outstanding is "on the account."

The phrase "on account" can also refer to buying or selling anything on credit.

On credit is another way to say "on the account."

Simply changing a sales representative's job title won't make them an account manager.

The needed abilities are varied.

Account managers require abilities in project management, financial control, consultative/value selling, and planning, some of which may require training.

So, gross sales of $560,000.

Accounts receivable decreased ($22,500 - $18,800). $3,700.

Money obtained from clients. $563,700.

Note that the further details provided in the question are not necessary to determine the total amount of money received from customers for the year.

Therefore, (C) $563,700 in cash was received from customers during the year.

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Equation used to represent the amount of interest that was paid​ is S.I = 900 × 0.11 × 0.5 and the amount is $49.5.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Simple interest amount can be calculated using the formula,

S.I = Prt

Here P is the principal amount, r is the rate of interest and t is the time in years.

Given a loan of $900 at a rate of 11% with paid off in 6 months.

P = $900,

r = 11% = 0.11 and

t = 6 months = 0.5 year

S.I = 900 × 0.11 × 0.5

    = 49.5

Hence the amount of simple interest is $49.5.

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If we select three balls, the probability of selecting exactly one white one is 16.

There are 6 balls in a box.

2 white and 4 black.

If we select three balls, then we have to determine the probability of selecting exactly one white.

First we determine the number of ways of selecting three balls in total of 6 balls. So

[tex]^{6}C_{3} = \frac{6!}{3!(6-3)!}[/tex]

[tex]^{6}C_{3} = \frac{6!}{3!3!}[/tex]

[tex]^{6}C_{3} = \frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]

Simplify

[tex]^{6}C_{3}[/tex] = 5 × 4

[tex]^{6}C_{3}[/tex] = 20

Now determining the probability of selecting the 3 balls out of non white balls.

[tex]^{4}C_{3}=\frac{4!}{3!(4-3)!}[/tex]

[tex]^{4}C_{3}=\frac{4!}{3!1!}[/tex]

Simplify

[tex]^{4}C_{3}=\frac{4\times3!}{3!\times1}[/tex]

[tex]^{4}C_{3}[/tex] = 4

Now, the probability of selecting exactly one white one = The number of ways of selecting three balls in total of 6 balls - The probability of selecting the 3 balls out of non white balls

The probability of selecting exactly one white one = 20 - 4

The probability of selecting exactly one white one = 16

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