Evaluate the derivative of the following functions
f(x) = (x cos x + 1)³

To find the mean of the distribution, we simply multiply the probability of getting a son (0.52) by the number of people surveyed (57):

Mean = 0.52 x 57 = 29.64

Rounding to the nearest person, the mean is 30. To find the standard deviation, we can use the formula:
Standard deviation = square root of (p x q x n), Where p is the probability of success (0.52), q is the probability of failure (1 - 0.52 = 0.48), and n is the sample size (57). Standard deviation = square root of (0.52 x 0.48 x 57) = 4.75

Standard deviation (σ) = √(n × p × (1 - p))
σ = √(57 × 0.52 × 0.48)
σ ≈ 3.71 ≈ 4 (rounded to the nearest person)
So, the mean of the distribution is approximately 30 sons, and the standard deviation is approximately 4 sons.

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The speed of skaters was 10 km per hr.

Mathematically, the speed of an object is directly proportional to the distance traveled and inversely proportional to the time taken. In simple words, the more the speed, the distance traveled is more in a short period and vice-versa.

Let the speed of the skater be x

We know, speed = \(\frac{Distance}{Time}\)

According to the question:

\(\frac{20}{x} = \frac{40}{x + 10}\)

Cross multiplying both sides,

20(x+10) = 40x

20x + 200 = 40x

20x = 200

x = 10

Thus, the speed of skaters was 10 km per hr.

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Step-by-step explanation:

y = 4x + 3.

Therefore y = 7 + 3x

=> (4x + 3) = 7 + 3x

=> x = 4.

y = 4(4) + 3 = 19.

The solution pair is (4,19).

Answer:

Step-by-step explanation:

Find 5% of $79:

Answer:

Abdul must pay $ 3.95.

Step-by-step explanation:

Now we have to,

→ find the amount of tax he must pay.

Then the amount will be,

→ (79/100) × 5

→ 0.79 × 5 = $ 3.95

Hence, he must pay $ 3.95.

The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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a. The distribution of X is normal with mean 9.7 ppm and standard deviation 1.5 ppm: X ~ N(9.7, 1.5)

b. The distribution of the sample mean is also normal with mean μ = 9.7 ppm and standard deviation σ/√n = 1.5/√36 = 0.25 ppm: ~ N(9.7, 0.25)

c. We need to find P(X > 9.4).Looking up the standard normal distribution table, we find P(Z > -0.2) = 0.5793. Therefore, the probability that one randomly selected city's waterway will have more than 9.4 ppm pollutants is 0.5793.

d.  Therefore, the probability that the average amount of pollutants is more than 9.4 ppm is 0.8849.

e. Yes, the assumption that the distribution is normal is necessary because we are using the central limit theorem to approximate the distribution of the sample mean. The central limit theorem applies only when the sample size is sufficiently large (n ≥ 30) and the population distribution is approximately normal.

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Converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters. By definition conversion of units means the conversion between different units and measurements of the same quantity done by the process of multiplication or division. In maths, conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons. Units are used for measuring length, measuring weight, measuring capacity, measuring temperature, and measuring speed.

If we want to calculate how many Grams are 1000 Milligrams we have to multiply 1000 by 1 and divide the product by 1000. So for 1000, we have (1000 × 1) ÷ 1000 = 1000 ÷ 1000 = 1 Gram.

So finally 1000 mg = 1 g

Thus, converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

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Answer:

The answer is ( -1/2 , 1/2) , (-1,2)

Step-by-step explanation:

hope this helps

The new price after a 35% markup on a cost of $20 is $27.

The amount of money saved with a 15% discount on a cost of $36 is $5.4.

1. New Price = Cost + Markup

New Price = $20 + 0.35*$20

New Price = $20 + $7

New Price = $27

Therefore, the new price after a 35% markup on a cost of $20 is $27.

In order to calculate the amount of money saved with a 15% discount on a cost of $36, we need to find 15% of the cost and then subtract it from the original cost:

Discount = 15% * Cost

Discount = 0.15 * $36

Discount = $5.4

Amount saved = Discount = $5.4

Therefore, the amount of money saved with a 15% discount on a cost of $36 is $5.4.

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1. Cost: $20

Markup: 35%

What is the new price ?

2. Cost: $36

Discount: 15%

How much money would you

save ?

Answer:

5. 1=112º

5. 2=68º

5. 3=112º

6. 1=45º

6. 2=45º

6. 3=135º

Step-by-step explanation:

5. 1 is a vertical angle to 112º, so they are equal (1 is obtuse)

5. 2 and 112º form to create a straight angle (line/180º) (supplementary angles) so subtracting the known number (112) from the total (180) gives you the number of the missing angle (2 is acute)

5. 3 is the same as 1 (3 is obtuse)

6. 1 and 45º are equal to each other (1 is acute)

6. 2 and 1 and 45º are equal and vertical angles (2 is acute)

6. 3 and 45º form to create a straight angle (line/180º) (supplementary angles) so subtracting the known number (45) from the total (180) gives you the number of the missing angle (3 is obtuse)

When the radius is 2 feet, the rate of change of the radius is approximately 0.089 ft/min (rounded to three decimal places).

To find the rate of change of the radius when the radius is 2 feet, and air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute, we can use the following steps:
Determine the volume formula for a sphere: V = (4/3)πr³.

Differentiate the volume formula with respect to time (t) to find dV/dt: dV/dt = d((4/3)πr³)/dt.
Apply the chain rule: dV/dt = (4/3)π(3r²)(dr/dt).
Simplify the equation: dV/dt = 4πr²(dr/dt).
Solve for the rate of change of the radius (dr/dt): dr/dt = dV/dt / (4πr²).
Plug in the given values: dV/dt = 4.5 cubic feet per minute and r = 2 feet.
Calculate the rate of change of the radius (dr/dt): dr/dt = 4.5 / (4π(2²)).
Simplify and compute the answer: dr/dt = 4.5 / (16π).
When the radius is 2 feet, the rate of change of the radius is approximately 0.089 ft/min (rounded to three decimal places).

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The difference in the total number of hours practiced in March and April is  \(24\frac{1}{2}\) hours

To find the difference in the total number of hours practiced in March and April

we need to calculate the total number of hours practiced in each month and then find the difference between the two totals.

In March:

Ballet: \(2\frac{1}{2}\) hours per week × 2 weeks = 5 hours

Jazz: \(4\frac{3}{4}\) hours per week × 2 weeks = 9 1/2 hours

Total hours practiced in March = 5 hours (ballet) + \(9\frac{1}{2}\) hours (jazz)

= \(14\frac{1}{2}\) hours

In April:

Ballet: \(3\frac{1}{4}\) hours per week × 4 weeks = 13 hours

Jazz: \(6\frac{1}{2}\) hours per week × 4 weeks = 26 hours

Total hours practiced in April = 13 hours (ballet) + 26 hours (jazz) = 39 hours

To find the difference, we subtract the total hours in March from the total hours in April:

39 hours (April) - \(14\frac{1}{2}\) hours (March) = \(24\frac{1}{2}\) hours

Therefore, the difference in the total number of hours practiced in March and April is  \(24\frac{1}{2}\) hours

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The sum of vectors a and b in unit-vector notation is (-4.4 m)i + (1.2 m)j + (6.5 m)h.

The magnitude of the vector a + b can be determined using the Pythagorean theorem. The magnitude, denoted as |a + b|, is calculated as the square root of the sum of the squares of the components. In this case, |a + b| = √[(-4.4 m)^2 + (1.2 m)^2 + (6.5 m)^2]. Solving this equation yields |a + b| ≈ 7.35 m.

To determine the direction of a + b relative to the unit vector h^, we can express the vector a + b as a linear combination of unit vectors. In this case, we have (-4.4 m)i + (1.2 m)j + (6.5 m)h = (-4.4 m)i + (1.2 m)j + (6.5 m)(0)i + (6.5 m)(0)j + (6.5 m)(1)h. Therefore, the direction of a + b relative to the unit vector h^ is parallel to the h-axis, with a magnitude of 6.5 m.

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Answer:

c. 6

d. 3

Step-by-step explanation:

:-)

Answer:

Option B is correct ...

\(solution \\ 3 - 2x = 9 \\ or \: - 2x = 9 - 3 \\ or \: - 2x = 6 \\ or \: x = \frac{6}{ - 2} \\ x = - 3\)

hope this helps..

Good luck on your assignment...

Answer:

\( \boxed{\sf (b) \ x = -3} \)

Step-by-step explanation:

\( \sf Solve \: for \: x: \\ \sf \implies 3 - 2x = 9 \\ \\ \sf Subtract \: 3 \: from \: both \: sides: \\ \sf \implies (3 - \boxed{3}) - 2x = 9 - \boxed{3} \\ \\ \sf 3 - 3 = 0 : \\ \sf \implies - 2x = 9 - 3 \\ \\ \sf 9 - 3 = 6 : \\ \sf \implies - 2x = \boxed{6} \\ \\ \sf Divide \: both \: sides \: of \: - 2 x = 6 \: by \: - 2: \\ \sf \implies \frac{ - 2 x}{ - 2} = \frac{6}{ - 2} \\ \\ \sf \frac{ - 2}{ - 2} = 1 : \\ \sf \implies x = - \frac{6}{2} \\ \\ \sf \implies x = - \frac{3 \times \cancel{2}}{ \cancel{2}} \\ \\ \sf \implies x = - 3\)

The area of the parallelogram whose vertices are listed (0,0), (2,8), (7,4), (9,12). The area of the parallelogram is 20 square units.

To find the area of a parallelogram, we need to know the base and height of the parallelogram. One of the sides of the parallelogram will serve as the base, and the height will be the distance between the base and the opposite side.

We can start by drawing the parallelogram using the given vertices:

(0,0)         (7,4)
     *---------*
     |         |
     |         |
     |         |
     *---------*
(2,8)         (9,12)

We can see that the sides connecting (0,0) to (2,8) and (7,4) to (9,12) are parallel, so they are opposite sides of the parallelogram. We can use the distance formula to find the length of one of these sides:

d = √[(9 - 7)^2 + (12 - 4)^2]
 = √[(2)^2 + (8)^2]
 = √68

So the length of one side is √68.

Next, we need to find the height of the parallelogram. We can do this by finding the distance between the line connecting (0,0) and (2,8) and the point (7,4). We can use the formula for the distance between a point and a line to do this:

h = |(7 - 0)(8 - 4) - (2 - 0)(4 - 0)| / √[(2 - 0)^2 + (8 - 0)^2]
 = |28 - 8| / √68
 = 20 / √68

Now we have the base (√68) and the height (20 / √68) of the parallelogram, so we can find the area using the formula:

A = base x height
 = (√68) x (20 / √68)
 = 20

Therefore, the area of the parallelogram is 20 square units.

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The equation that represents the total area of the blueberry field will be y = 84x.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Six workers are hired to harvest blueberries from a field.

Each is given a plot with an area of 84 square ft.

Then the equation that represents the total area of the blueberry field will be

Let x be the number of workers and y be the total area field. Then we have

y = 84x

Then the area of the total field will be

y = 84 (6)

y = 504 square ft

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Answer:

Your answer should be x = 2

Step-by-step explanation:

149 + 13(2) + 5 = 180.

Hope this helps.

Answer:

x=2

Step-by-step explanation:

You add 149 and 5, which is 154. Then you take the total which is 180, and subtract it by 154. So 180-154=26 Then you take and do 26/13 which is 2.

149+13(2)+5=180

149+26+5=180

Definitely 2.

Hope this helps!!!

Answer

The point of their intersection best estimate for the solution of the system of equations

The final answer

Answer:

The answer is D, did the test.

Step-by-step explanation:

Answer:

13,728 in.²

Step-by-step explanation:

volume = length × width × height

V = 30 in. × 22 in. × 20.8 in.

V = 13,728 in.²

Answer:

It is the value of the coin when it was originally purchased. t=0  y=3

Step-by-step explanation:

The y intercept is the value when t=0

It is the value of the coin when it was originally purchased.  y=3

Answer:

1. (any number less than 10) < 10

2. 520 (division)

   520

➗     2

   260

3. (any number less than 3 *1 or 2*) < 3

4. (any number greater than 1) > 1

5. (Subtraction - A number subtracting two and the result is less than 10) < 10  

Step-by-step explanation:

1. The symbol "<" shows greater than. It is facing the number "10",

So, we need to get any number below 10. As example: 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9. The numbers I mentioned there are what you can use for question 1.

-----------------------------------------------------------------------------------------------------------------

2. The number 520' is what I find to be multi-result but I would do division. Number 520 is part of the addition, subtraction, multiplication, and division but I am doing division.

Divison:

   520

➗     2

   260

Multiplication:

    260

  x     2

    520

Addition:

  500

+  20

  520

Subtraction:

 550

-   30

 520

These are the examples that you can try for number 2.

-----------------------------------------------------------------------------------------------------------------

3. First, you can see that there is the greater symbol here again, "<".

But this time, it's pointing to 3. Which means the number is less than 3.

The only numbers that are less than 3 is 1 and 2 so those are the 2 options you can choose.

-----------------------------------------------------------------------------------------------------------------

4. This time, the symbol is less. It's now pointing at 1, so you can pick any number that is greater than 1.

Example:

5 > 1

Like that! You can pick any number that is greater than 1 for this question!

-----------------------------------------------------------------------------------------------------------------

5. the equation "-2 < 10" is about a number subtracting 2 but than the results come in being less than 10. Since we have spotted the greater symbol as "<", and the subtraction symbol as "-".

Now, first we find a number that can subtract 2 but less than 10 in the result.

The options we have are:

1. 2 (2-2=0 ; 0 < 10)

2. 3 (3-2=1 ; 1 < 10 )

3. 4 (4-2=2 ; 2 < 10 )

4. 5 (5-2=3 ; 3 < 10 )

And so on until you reach number 9 as the result!

-----------------------------------------------------------------------------------------------------------------

Hope this helped you! I tried my best to help you. But have a good day!

Answer: A: 7.75

Step-by-step explanation:

20.50 + 3.75 - 5.25 + 750 - 18.75 = 7.75

To calculate the probability of two separate events using the ratio method, we must first understand the odds associated with each event. The odds are expressed as a ratio, with the first number representing the chances of success and the second number representing the chances of failure. For example, the odds of an event happening might be 3:2, which indicates that there is a 3/5 chance of success.

Once the odds for each event are known, we can calculate the probability of both events occurring by multiplying the odds of each event together. So, for example, if the odds of Event A are 3:2 and the odds of Event B are 4:5, the probability of both events occurring is 3/2 * 4/5 = 6/10. This means that there is a 6 in 10 chance of both events occurring.

To sum up, calculating the probability of two separate events using the ratio method is fairly simple. Just look at the odds associated with each event and multiply them together to get the probability of both events occurring.

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The statements that only apply to C3, C4, and CAM photosynthesis are:

1. C3, C4, and CAM plants all have cells that have chloroplasts which attach CO2 directly to ribulose bisphosphate to produce sugars.

2. CAM plants have one set of cells that harvests CO2 and passes the carbon to another set of cells that builds sugars.

3. Stomata open at night to allow gas exchange and sugars are produced during the day.

The statement that applies to all three types of photosynthesis is: Light energy, CO2, and H20 are needed to make sugars.

C4 and CAM plants have adaptations that prevent the Calvin cycle from shutting down in periods of dryness. These adaptations include C4 plants using a carbon concentrating mechanism that separates the fixation of CO2 from the Calvin cycle and CAM plants using a process called crassulacean acid metabolism (CAM), where CO2 is taken up at night and stored as an acid until the following morning when it is converted into sugars in the Calvin cycle.

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The truth set of each predicate with the domain being the set of integers is

The truth set of a predicate is the set of all elements in the domain that make the predicate true.

For the given predicates, with the domain being the set of integers,

P(x): x^3 ≥ 1

The inequality x^3 ≥ 1 is satisfied for all x such that x ≥ 1 or x ≤ -1. This is because any integer raised to an odd power will always have the same sign as the integer itself, and the only integers whose cubes are less than 1 in absolute value are 0 and 1. Therefore, the truth set of P(x) is {x | x ≤ -1 or x ≥ 1}.

Q(x): x^2 = 2

There are no integers x such that x^2 = 2. Therefore, the truth set of Q(x) is the empty set, ∅.

R(x): x < x^2

The inequality x < x^2 is satisfied for all x such that x < 0 or x > 1. If 0 ≤ x ≤ 1, then x^2 ≤ x, and the inequality does not hold. Therefore, the truth set of R(x) is {x | x < 0 or x > 1}.

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Answer: 1: -8x+6

Step-by-step explanation:

Check the picture below.

Answer:

7-isoceles, 8- equilateral 9-scalene

Step-by-step explanation:

isoceles have 2 identical sides unlike scalene, where all sides have different lengths.

is obtuse and acute I think

Answer:

48 children went to the big picnic

Step-by-step explanation:

hope that helps>3

Answer:

48 children

Step-by-step explanation: