Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the derivative exists.

f(x) = -x^2 +4x-5

f’(x) = _____
(Type an expression using x as the variable.)

Answer:

Step-by-step explanation:

Look at the last term, - 28.

It means, the product of roots is a positive number (28).

The polynomial is a degree three so it has 3 possible roots.

Positive product can be obtained if all 3 numbers are positive or 2 negative and 1 positive.

Therefore number of positive roots is one or three.

Further, double check using the graphical solution (see attached), it shows one root only. It means the other roots are complex.

Correct option is A

The exact growth rate (r) for the exponential model or the slope (m) and y-intercept (b) for the linear model. More data points or additional information about the population growth pattern would be needed to construct a precise model for P(t).

To find a model for P(t), representing the U.S. population in 1960, we need to determine the growth or decay rate over time. Without additional information or assumptions about the population growth, we cannot provide an exact model. However, we can explore two common models: exponential growth and linear growth.

1. Exponential Growth Model:

If we assume that the U.S. population experienced exponential growth, we can use the formula P(t) = P₀ * e^(rt), where P₀ represents the initial population, r is the growth rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.71828).

Using the given information that the U.S. population in 1960 was 181 million, we can write the equation as follows:

181,000,000 = P₀ * e^(r * 1960)

2. Linear Growth Model:

Alternatively, if we assume that the U.S. population grew linearly, we can use the formula P(t) = mt + b, where m is the slope (rate of change) and b is the y-intercept.

Using the given information, we can form an equation as follows:

181,000,000 = m * 1960 + b

Without further information or data points, we cannot determine the exact growth rate (r) for the exponential model or the slope (m) and y-intercept (b) for the linear model. More data points or additional information about the population growth pattern would be needed to construct a precise model for P(t).

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Answer:

71 pages / day

Step-by-step explanation:

You are looking for pages per day so:

   497 pages / 7 days = 71 pages/day

For burning less calories from Routine 1 Abdul's inequality has a solution which is expressed as t < (5, ∞).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The total number of calories burned in Routine 1 after t minutes of running can be expressed as -

22 + 18.5t

Similarly, the total number of calories burned in Routine 2 after t minutes of running can be expressed as -

50 + 12.9t

To find when Routine 1 burns fewer calories than Routine 2, we need to set up an inequality where the total calories burned in Routine 1 is less than the total calories burned in Routine 2 -

22 + 18.5t < 50 + 12.9t

Simplifying this inequality, we get -

5.6t < 28

Dividing both sides by 5.6, we get -

t < 5

Therefore, for any value of t less than 5 minutes, Routine 1 will burn fewer calories than Routine 2.

In interval notation, we can express this as -

t < (5, ∞)

Therefore, the solution is obtained as t < (5, ∞).

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Answer:

(0.5, -3)

Step-by-step explanation:

I'll use substitution and elimination to show two different ways of solving the equation.

Substitution:

   So we can either substitute x or y and it really doesn't matter. It may be more simple to substitute a certain variable in some equations.

   4x - 3y = 11

   4x = 3y + 11

   2x = (3y + 11) / 2

   In this case I didn't completely solve for x since I only need the value of 2x to substitute into the second equation

   \(\frac{3y+11}{2}-7y=22\\\\2(\frac{3y+11}{2}-7y)=2(22)\\3y+11-14y=44\\11-11y=44\\-11y=33\\y=-3\)

  Now that we have the value y we can substitute it back into either equation to solve for x.

   \(4x-3(-3) = 11\\4x+9=11\\4x=2\\x=0.5\)

 So the solution is (0.5, -3)

Elimination:

   In this method we manipulate one of the equations to get the absolute value of one of the coefficients equal to the coefficient in the other equation with the only difference being the sign, so one is positive and one is negative. It doesn't matter which variable you chose to cancel out nor does it matter which equation you manipulate but it can sometimes be more simple to try to cancel out a certain variable if the value is smaller.

   \(4x-3y = 11\\-0.5(4x-3y) = -0.5(11)\\-2x+1.5y=-5.5\\\)

   Now that we have an equation where the -2x can be canceled out by adding the other equation 2x-7y = 22 we add the two equations to get

   \(\ \ \ -2x + 1.5y = -5.5\\+2x - 7y = 22\\ 0 -5.5y = 16.5\\\)

   Now that you canceled out the x you can solve for y and then use substitution to solve for x

   \(-5.5y = 16.5\\y=-3\\\)

   Now substitute this into any of the original equations to solve for x

   \(2x - 7(-3) = 22\\\2x+21=22\\2x=1\\x=1/2\)

   So the solution is (0.5, -3)

For a pure resistive circuit, the RMS value of the current is used to determine the power dissipated by the resistor. P = I2R, where P is the power, I is the RMS value of the current, and R is the resistance of the circuit.

The given function is I(t) = 10 sin t, where I represent the time-dependent current in amperes. Mean and RMS values of the current over time 0 to π and 0 to 2π can be calculated as follows:

Mean value:

The mean value of the current waveform is given as Zero mean value implies the current waveform has equal positive and negative areas over the period.

RMS value:

The RMS (root mean square) value of a periodic waveform is defined as the square root of the mean value of the squares of the instantaneous values over one period.

Mathematically,

RMS current overtime period 0 to π is I

RMS = I 1

= 10/√2

=7.07A

RMS current overtime period 0 to 2π is I RMS = 7.07A

The RMS value of the current gives a better indication of the heating effect of the current in the circuit. The larger the RMS value of the current, the greater the amount of heat produced in the circuit.

For a pure resistive circuit, the RMS value of the current is used to determine the power dissipated by the resistor. P = I2R, where P is the power, I is the RMS value of the current, and R is the resistance of the circuit.

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Hey there! I'm happy to help!

3 hours is 180 minutes as there are 60 minutes in 1 hour. How many times does 30 minutes go into 180 minutes?

180/30=6

So, we have six of these 30 minute time slots that fit into 3 hours. So, we multiply our 37.5 miles by six to find the total mileage!

37.5×6=225

Caroline drove 225 miles.

Have a wonderful day! :D

For the given data, in a triathlon 6 men and 19 women are participating then the ratio of number of men participants to the total number of participants  is equal to 6 /25.

As given in the question,

In a triathlon,

Number of men participants is equal to 6

Number of women participants is equal to 19

Total number of participants = (6 + 19)

                                            = 25

Ratio of number of men participants to the total number of participants is

= ( Number of men participants) / Total number of participants

= ( 6 / 25 )

Therefore, for the given  data in a triathlon 6 men and 19 women are participating then the ratio of number of men participants to the total number of participants  is equal to 6 /25.

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Answer:

85

Step-by-step explanation:

2x+192=180

2x= -12

x= -6

-6+91= 85

Dilation and Stretch are non-rigid transformations.

Non - Rigid transformation:

Non-rigid transformations can change the size or shape of the archetype, or both size and shape. The two transformations Strain and Shear are not rigid. The resulting image of the transform is changed in size, shape, or both.

A non-rigid transformation is a transformation that changes the length or angle of a shape's sides. Nonrigid transformations are dilation and stretching.

All types of transformations except dilation are rigid transformations.

Dilation transformations are divided into two types

Therefore non-rigid transformations are Dilation and Stretching

Dilation:

Dilation (usually denoted by ⊕) is one of the fundamental operations in mathematical morphology. Originally developed for binary images, it was expanded first to grayscale images and then to full meshes. Stretch operations typically use a structuring element to examine and expand the shapes contained in the input image.

Strechting:

A non-rigid transformation changes the size or shape of an object. Resizing (stretching horizontally, vertically, or both) is a non-rigid transformation.

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Answer:

The number line that represents the solutions to –2|x| = –6 is:

```

-----------o----o-------------

-3 0 3

```

The solution is |x| = 3, which means x can be either -3 or 3. The absolute value bars indicate that the value inside must be positive or zero, so the negative solution is flipped to positive.

a) The parameter of interest is the difference in proportions of shrubs that sprout between the treatment and control groups.

b) We can perform a significance test to determine if there is evidence to support the alternative hypothesis that the proportion of shrubs that sprout in the treatment group is greater than the proportion of shrubs that sprout in the control group.

a. The appropriate hypotheses for performing a significance test are:

Null hypothesis (H0): The proportion of shrubs that sprout in the treatment group is equal to the proportion of shrubs that sprout in the control group.

Alternative hypothesis (Ha): The proportion of shrubs that sprout in the treatment group is greater than the proportion of shrubs that sprout in the control group.

The parameter of interest is the difference in proportions of shrubs that sprout between the treatment and control groups.

b. To check if the conditions for performing the test are met, we need to ensure that the following assumptions are satisfied:

Random sampling: The shrubs were randomly assigned to the treatment and control groups, so this assumption is met.

Independent samples: The shrubs in the treatment and control groups are independent of each other, so this assumption is met.

Large sample size: Both the treatment and control groups have at least 10 shrubs, which satisfies this assumption.

Success-failure condition: At least 10 shrubs must sprout and at least 10 shrubs must not sprout in both the treatment and control groups. In this case, all 12 shrubs in the treatment group sprouted and 8 out of 12 shrubs in the control group sprouted. Therefore, this assumption is satisfied.

Since all the assumptions are satisfied, we can perform a significance test to determine if there is evidence to support the alternative hypothesis that the proportion of shrubs that sprout in the treatment group is greater than the proportion of shrubs that sprout in the control group.

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Answer:

7 m is the answer

.... hope it's right and hlp u !

Answer:

area of circle = πR²

area if shaded region = π × 49 × 49 - π × 42 × 42

= 7539.14 - 5538.96

= 2000. 18m²

(π=3.14)

Answer:

2

Step-by-step explanation:

Answer:

he needs to mix 18 pineapple cups

Step-by-step explanation:

48÷8=6

3×6=18

8-3

48-18

Answer:

The box contains 20 milk chocolates.

Step-by-step explanation:

Given that the chocolate box has milk chocolates and dark chocolates in a ratio of 2 milk chocolates for every 3 dark, and the total number of chocolates in the box is 50 units, to determine how many milk chocolates are in the box. it is necessary to perform the following calculation:

50 / (2 + 3)

50/5

10

Milk chocolates: 2 x 10 = 20

Dark chocolates: 3 x 10 = 30

Therefore, the box contains 20 milk chocolates.

Answer:

10 units

Step-by-step explanation:

Formula to find the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is,

d = \(\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\)

Distance between two points (0, -7) and (-6, 1) will be,

d = \(\sqrt{(0+6)^2+(-7-1)^2}\)

  = \(\sqrt{36+64}\)

  = \(\sqrt{100}\)

  = 10

Therefore, distance between the given points is 10 units.

Answer:

B, C, F

Step-by-step explanation:

The choices B, C, and F are right because if you do the Vertical line test, the vertical line only intersects one point in the graph. The function only has one output value for each input value.

Answer:

The right option is option e.T-shaped.

Step-by-step explanation:

The molecular geometry or shape of clf3 is T-shaped. It acquires such shape because of presence of two lone pairs which take equatorial position and there are greater repulsions. The hybridisation is sp3d and it has 2 lone pairs

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Option e) T-shaped

The shape or molecular geometry  of ClF₃ is T-shaped. It acquires such a shape due to the presence of two lone pairs in the equatorial position and has greater repulsion. The hybrid is sp³d and it has 2 lone pairs.

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Strength and direction with a negative correlation so we cannot use a correlation close to 0 in predictions.

Given,

When using correlation for prediction.

Here,

When using correlation for prediction strength and direction with a negative correlation so we cannot use a correlation close to 0 in predictions.

Thus option F is correct.

Hence none of the above options are correct.

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Answer:

D.

Step-by-step explanation:

Answer: D is the correct answer

Step-by-step explanation:

I learned this last year and got a 100 on the subject

Answer:

The number needed is 180

Step-by-step explanation:

Have a nice day! I hope this helps!

Answer:

(4,3)

You didn't list if it was clockwise or counterclockwise, so I will just assume that you were asking for clockwise.

Step-by-step explanation:

If it is a 270 degree rotation cw, then it changes from (x,y) to (y,-x).

(-3,4) ---> (4,3)

Therefore, the height of the tree is approximately 3.67 meters making triangle.

Let h be the height of the tree. Then, using the properties of similar triangles, we can set up the following proportion:

h / 1.25 = (h + x) / 15.45

where x is the length of Gabriella's shadow. To find x, we can use a similar proportion:

h / 10.2 = 1.25 / x

Solving the second proportion for x, we get:

x = 10.2 * 1.25 / h

Substituting this expression for x into the first proportion, we get:

h / 1.25 = (h + 10.2 * 1.25 / h) / 15.45

Multiplying both sides by 15.45 * h * 1.25, we get:

15.45 * h - 15.45 * 1.25 = h * 10.2

Expanding and rearranging, we get a quadratic equation in h:

15.45h - 19.3125 = 10.2h

5.25h = 19.3125

h = 3.67 meters (rounded to two decimal places)

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The constant of proportionality (r) in the equation y = r * x is approximately equal to 963.702.

To find the constant of proportionality (r) in the equation y = r * x, we can use the given data points where xxx and yyy are proportional. Let's analyze the data:

Data Point 1: xxx = 333, yyy = 303030

Data Point 2: xxx = 101010, yyy = 100100100

Data Point 3: xxx = 161616, yyy = 160160160

To determine the constant of proportionality (r), we need to find the ratio between yyy and xxx for each data point. Let's calculate these ratios:

Ratio 1: yyy/xxx = 303030/333 ≈ 909.909

Ratio 2: yyy/xxx = 100100100/101010 ≈ 990.099

Ratio 3: yyy/xxx = 160160160/161616 ≈ 990.099

From these ratios, we can observe that they are approximately equal to each other. Therefore, we can conclude that the constant of proportionality (r) is approximately equal to the average of these ratios:

r ≈ (909.909 + 990.099 + 990.099) / 3 ≈ 963.702

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Answer:

570 miles

Step-by-step explanation:

If Damian rides 38 each week and we want to know how much it was for 15 weeks, then we just multiply the two to get 570 miles in a 15 week period.

Answer:570

Step-by-step explanation:

38 times 15= 570

It's crucial to take a collaborative approach and involve employees in the change process as much as possible.

In the unfreezing stage, it is important to gather information and input from various stakeholders in order to influence change effectively. Therefore, asking the VP and analyst questions such as "What do you think are the areas that need improvement in our current system?" or "How do you think changing the system would benefit our organization?" can provide valuable insight into the motivation for change.

Surveying a sample set of employees at each location to ask their opinions on the current system and whether they think changes are necessary is also a good approach. This can help to identify common pain points and gauge the level of employee buy-in for potential changes. It's important to also consider other factors such as the cost and feasibility of implementing changes, as well as potential risks and benefits.

Mandating change without proper analysis and buy-in from employees may lead to resistance and resentment. Ultimately, the decision to change or not should be based on a thorough assessment of the situation, including feedback from stakeholders and the potential impact on the organization.

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