Find the largest open interval where the function is changing as requested decreasing; f(x)=x^3-4x

(a) The number of choices with no restriction is 10,000.

(b) The number of choices with no repeated digits is 5,040.

(c) The number of choices with no repeated digits and the third digit as 0 is 648.

(a) With no restriction, there are 10 choices for each digit, ranging from 0 to 9. Since a 4-digit pin code consists of four digits, the total number of choices is 10^4 = 10,000.

(b) When no digit is repeated, the number of choices for the first digit is 10. For the second digit, there are 9 choices remaining (as one digit has been used). Similarly, for the third digit, there are 8 choices remaining, and for the fourth digit, there are 7 choices remaining. Therefore, the total number of choices is 10 × 9 × 8 × 7 = 5,040.

(c) When no digit is repeated and the third digit is fixed as 0, the number of choices for the first digit is 9 (excluding 0). For the second digit, there are 9 choices remaining (as one digit has been used, but 0 is available).

For the fourth digit, there are 8 choices remaining (excluding 0 and the digit used in the second position). Therefore, the total number of choices is 9 × 9 × 8 = 648.

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Answer:

here is your answer

Answer:hey guys just saying its 1/52

Step-by-step explanation:

Given the equation:

Answer:

4 payments

Step-by-step explanation:

170-50 = 120 left to pay

120/30 = 4

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer:

30,324

Step-by-step explanation:

30,000 x 4.5 = 135.00

135.00 x 4 + 540.00 four quarters in a year

6 years  x 540 = 3,240

30,000 + 3,240 = 33. 240

Answer:

x=23

Step-by-step explanation:

The two angles are equal so you can set 8x-77 and 3x+38 equal to each other and write it as:

8x-77=3x+38

Then you get like terms on the same sides by subtracting 3x from both sides and getting:

5x-77=38

Then you add 77 to both sides and get:

5x=115

Then you divide both sides by 5 and get x=23

Answer:

∠K = 123°

∠L = 97°

∠O = 83°

∠N = 40°

Step-by-step explanation:

∠K and ∡57° are Supplementary, so their sum is equal to 180°

180 - 57 = 123

∠K = 123°

∠N and ∡140° are also Supplementary

180 - 140 = 40

∠N = 40°

The area of a triangle is equal to 180 when all angles are added together

40 + 57 = 97

180 - 97 = 83

∠O = 83°

∠L is an outside angle, which is equal to the sum of the 2 further angles (in this case ∡57° and ∠N) which we found was 97° when solving for ∠O

∠L = 97°

Now to check ∠K we add ∠O and ∠N

83 + 40 = 123

Now we also check ∠O with ∡140°

140 - 57 = 83

So all of the angles check out correctly

The number of scores above 18 in a sample of 1000 cases with a mean of 14 and a standard deviation of 2.5 is 2 or higher. This can be found using standard normal distribution and z-scores.

To find the number of scores above 18, we need to calculate the z-score that corresponds to 18 and then use a standard normal distribution table to find the proportion of scores that are above that z-score. The z-score can be calculated as (18-14)/2.5 = 2.

Next, we can look up the proportion of scores that correspond to a z-score of 2 or higher in a standard normal distribution table. This proportion represents the number of scores in the sample that are above 18, assuming a normal distribution.

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Answer:

1 Meter equals 100 Centimeters, therefore 1 Square meter is equal to 100 centimeters squared. Thus, \(1 M^{2}\) is equal to \(100^{2}\) when counting in Centimeters square. Now that we have gotten the basics down, Lets convert the other necessary units.

\(1 m^{2} = 10,000 cm^{2}\)

\(1 mm^{2} = 0.01cm^{2}\)

\(1 km^{2} = 1,000,000 m^{2}\)

Now, using that knowledge, we can find the answers to all questions.

1) 0.15 \(m^{2}\)

2) 0.086 \(m^{2}\)

3) 0.1 \(cm^{2}\)

4) 600,000 \(cm^{2}\)

5) 0.0001 \(km^{2}\)

6) 400 \(cm^{2}\)

7) 52,100 \(mm^{2}\)

8) 500,000 \(m^{2}\)

9) 0.087 \(mm^{2}\)

10) 50 \(cm^{2}\)

That's all folks!

Answer:

Answer on Edmentum! :)

Step-by-step explanation:

Hope this helps!

The number of children were 172 and number of  adults were 278.

An equation that makes a straight line when it is graphed.

Given that, A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests

According to question,

12x+25y = 9014

x+y = 450

Solving using elimination method, we get,

x = 172 and y = 278

Hence, The number of children were 172 and number of  adults were 278.

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The counterexample for the conjecture If the perimeter of a rectangle is 40 units, the area must be at least 1 square unit is: A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.

What is counterexample?

The term counterexample refers to an instance or example that makes the statement false. This is used in logic to check if a statement is true or not. Counter example tend to counter the statement being discussed with valid points.

The question wants to show the relationship that may exist between perimeter and area of a rectangle.

The counterexample provided the dimensions that gave the perimeter which is 40 but failed to give area of 1 square unit

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There are several strategies for resolving systems of linear equations, including:

(1) Graphing Techniques

(2) The Substitution Method

(3) Using a linear combination

(4) The Matrix Approach

(1) Graphing Techniques: This is helpful if you only require a general answer or are confident that the intersection occurs at integer locations. Simply plot the two lines to determine their intersection.

(2) The Substitution Method: One linear equation for y must first be solved in terms of x. Then, in the other linear equation, replace y with that expression. You'll receive a formula in x. If you can solve this, you'll know the intersection's x-coordinate. Then, to determine the equivalent y-coordinate, insert x into either equation.

(3) Using a linear combination: In order for the x-terms or the y-terms to cancel out, add (or subtract) a multiple of one equation to (or from) the other equation. To obtain the other coordinate, first solve for x (or y, depending on which is remaining) and then substitute.

(4) The Matrix Approach: Actually, this is only a simplified notation of the Linear Combination method.

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Answer:

Up

Step-by-step explanation:

Answer:

~ 1.9 gal

Step-by-step explanation:

80 miles  /  42 miles/gal = 1.9 gal

Answer:

3/4p²+5p+3

Step-by-step explanation:

\(\dfrac{3}{4}p^2+5p+3\) is the correct answer on simplifying \(\left(\dfrac{3}{2}p+1\right)\left(\dfrac{1}{2}p+3\right)\).

Simplification of expression is to get an expression in the rearranged form.

Simplify the given expression as-

\(\left(\dfrac{3}{2}p+1\right)\left(\dfrac{1}{2}p+3\right)=\dfrac{3}{4}p^2+3\times \dfrac{3p}{2}+\dfrac{p}{2}+3\\=\dfrac{3}{4}p^2+5p+3\)

Thus, option C is the correct answer.

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To find the values of x and sv, we can use the properties of circles and their chords. Given that qr = 15, sr = 15, uz = 22, and vz = 5x - 3, we need to determine the values of x and sv.

The first step is to recognize that qr and sr are chords of the circle, and uz and vz are the perpendicular bisectors of qr and sr, respectively. Since the perpendicular bisectors of chords pass through the center of the circle, we can conclude that z is the center of the circle.

To find x, we can set the lengths of the perpendicular bisectors uz and vz equal to each other: uz = vz. Substituting the given values, we have 22 = 5x - 3. Solving this equation, we find x = 5.

To find sv, we need to determine the length of the chord sv. Since z is the center of the circle, the chord sv is equal to twice the length of vz. Substituting the value of x = 5 into vz = 5x - 3, we have vz = 5(5) - 3 = 22. Therefore, sv = 2vz = 2(22) = 44.

In summary, the value of x is 5 and the length of sv is 44.

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This is the probability that the equipment is not rented for y-1 consecutive days (i.e., (\((4/5)^{(y-1)}\))), followed by a rental on the yth day (i.e., (1/5)).

The normal, also known as the mean, is a measure of central tendency that's calculated by adding up a set of figures and also dividing the sum by the total number of values. In other words, the normal is the sum of all values divided by the number of values. It's a useful statistic for recapitulating a dataset and giving an idea of what a typical value might be

Given by the question.

Since the equipment is leased on average only one day in five, the probability of renting the equipment on any given day is 1/5. We can model the number of days between rentals as a geometric distribution with parameter p = 1/5. Specifically, let Y be the number of days between two consecutive rentals. Then,

P (Y = y) = \((4/5) ^{(y-1)}\)* (1/5)

for y = 1, 2, 3, ...

Note that this assumes that the rentals are independent and identically distributed, so the probability of rental on any given day is the same, regardless of when the last rental occurred.

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Rhonda has approximately 0.77 seconds to react before the volleyball hits the ground.

To calculate the time Rhonda has to react, we need to determine how long it takes for the volleyball to reach the ground after Marsha serves it. We can use the equation of motion, which relates the initial velocity (u), time (t), and height (h) of an object in free fall.

The initial velocity of the volleyball is 15 ft/s in the upward direction. Since the ball is 3.5 feet above the ground when struck, we consider the total distance traveled by the ball as the sum of the initial height and the height of the fall.

Using the equation h = ut + (1/2)gt^2, where g is the acceleration due to gravity (approximately 32.2 ft/s^2), we can rearrange the equation to solve for time (t):

3.5 = 15t - (1/2)(32.2)t^2

Simplifying this quadratic equation, we get:

16.1t^2 - 15t + 3.5 = 0

Solving this equation, we find two roots: t ≈ 0.23 s and t ≈ 1.08 s. Since we are interested in the time it takes for the ball to hit the ground, we discard the smaller root (0.23 s) because it corresponds to the time it takes for the ball to reach its maximum height.

Therefore, Rhonda has approximately 1.08 seconds - 0.31 seconds (the time it takes for the ball to reach its initial height) = 0.77 seconds to react before the volleyball hits the ground.

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The third term in the recursive sequence is 9

A recursive sequence is a sequence of numbers where each term is defined by a formula that uses one or more of the previous terms in the sequence. In other words, each term depends on the term(s) that come before it.

Since a₁ = 3 and  \(a_{k+1}\)= 2a\(_{k}\) - 1

a₂  = 2a₁ - 1  

a₂  = 2(3) - 1 = 6 - 1 = 5

a₃ = 2a₂ - 1  

a₃ = 2(5) - 1 = 10 - 1 = 9  

Thus, the third term in the recursive sequence will be 9

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The solution to the given ODE dy/dt = 2y with the initial condition y(5) = 3 over the domain [0, 5] is y(t) = (3 / exp(10)) × exp(2t).

The ODE dy/dt = 2y represents a simple exponential growth equation. The general solution to this ODE is given by y(t) = y0 × exp(2t), where y0 is the constant determined by the initial condition. In this case, the initial condition is y(5) = 3.

To find the specific solution, we substitute the initial condition into the general solution and solve for y0. Substituting y(5) = 3 into y(t) = y0 × exp(2t), we get 3 = y0 × exp(2 × 5), which simplifies to y0 = 3 / exp(10).

Thus, the solution to the ODE with the given initial condition is y(t) = (3 / exp(10)) × exp(2t).

This solution describes the behavior of the function y(t) over the interval [0, 5], showing exponential growth with a rate determined by the coefficient 2 in the ODE.

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The equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

The equation of the tangent to the curve y = f(x), passing through the point (a, b) can be written as -

(y - b) = (dy/dx) (x - a)

Given is the curve y = f(x) = x⁴ + 6x² − x.

The given curve is -

y = x⁴ + 6x² − x

f'(x) = dy/dx = d(x⁴ + 6x² − x)/dx

f'(x) = dy/dx = 4x³ + 12x + 1

Now -

f'(x){1, 6} = (dy/dx){1, 6} = 4 x 1 x 1 x 1 + 12 x 1 + 1

f'(x){1, 6} = 17

We can write the equation as -

(y - 6) = 17(x - 1)

Therefore, the equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

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The shape that has a bigger area is the regular hexagon.

The shape that has a bigger area is the regular hexagon. A hexagon is a polygon with six sides while a pentagon is a polygon with five sides. The area of a polygon measures the surface of the shape.

The polygon with six sides has a greater surface so it is expected that its area will be bigger than that of the pentagon with fewer sides.

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Answer: If two forecasters have unbiased forecasts, then they should have the same average error over many forecasts. In that sense, they would be equally good at forecasting.

Step-by-step explanation:

The statement that is true regarding evaluating the quality of a forecast is:

If both forecasters have an unbiased forecast, then they are equally good at forecasting.

Explanation:

A biased forecast can have a zero forecast error if the bias happens to offset the error in the forecast. However, a zero forecast error does not necessarily indicate that the forecast is unbiased.

In the mean squared error (MSE) evaluation, one single observation can make a very large difference because the errors are squared before they are averaged. Therefore, outliers can have a large impact on the MSE.

If we are evaluating the same forecaster, then the mean squared error is not always lower than the mean absolute error. It depends on the specific forecast and the distribution of errors.

However, if two forecasters have unbiased forecasts, then they should have the same average error over many forecasts. In that sense, they would be equally good at forecasting.

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Answer:

$1.40

Step-by-step explanation:

If It's $7.00 for 5 pounds of oranges you would have to take the $7.00 and divide it by the number of pounds purchased which is 5.

$7.00 / 5 = $1.40

The linear programming model for this problem is Max 1000F + 1000T

Given that,

If the quantity of flip top pens to be produced is f and the quantity of tiptop pens to be produced is t, then

Number of lots of Flip top pens to produce = F

Number of lots of Tip top pens to produce = T

Therefore, The linear programming formulation is given by:

Max 1000F + 1000T

s.t.

Plastic: 3F + 4T <= 39

Ink Assembly:  5F + 4T <= 45

Molding time: 5F + 2T <= 37

F, P >= 0

Hence, the linear programming model for this problem is Max 1000F + 1000P

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Answer:

y=4x+2

Step-by-step explanation:

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Approximately 21.5 out of 50 randomly selected U.S. smartphone owners will have attempted to limit their cell phone use in the past.

In the Deloitte survey conducted in 2017, it was found that 0.43 of U.S. smartphone owners had made an effort to limit their phone use. This percentage serves as an estimate for the entire population of U.S. smartphone owners.

To determine the approximate number of smartphone owners who have attempted to limit their cell phone use in a sample of 50, we multiply the sample size (50) by the estimated percentage (0.43). This calculation gives us 21.5, indicating that around 21.5 out of the 50 randomly selected U.S. smartphone owners will have tried to limit their phone use in the past.

The calculation is based on the assumption that each pick from the sample is independent, meaning that the behavior of one smartphone owner does not influence the behavior of another. This assumption allows us to use the estimated percentage from the survey to estimate the number of smartphone owners in the sample who have attempted to limit their phone use.

It's important to note that this calculation provides an approximation and not an exact number. The actual number of smartphone owners in the sample who have attempted to limit their phone use may vary. However, this estimation gives us a reasonable expectation based on the data available.

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The set of numbers {6, 8, 14} and the set {11, 14, 22} could represent the three sides of a triangle.

To determine whether a set of numbers could represent the sides of a triangle, we need to check if it satisfies the triangle inequality theorem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let's evaluate each set of numbers:

1. {6, 8, 14}

  The sum of the two smaller sides is 6 + 8 = 14, which is greater than the third side 14. Therefore, this set could represent the sides of a triangle.

2. {13, 20, 34}

  The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 34. Hence, this set cannot represent the sides of a triangle.

3. {11, 14, 22}

  The sum of the two smaller sides is 11 + 14 = 25, which is greater than the third side 22. Therefore, this set could represent the sides of a triangle.

4. {13, 20, 35}

  The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 35. Hence, this set cannot represent the sides of a triangle.

In summary, the sets {6, 8, 14} and {11, 14, 22} could represent the three sides of a triangle.

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