Write the cubic function represented by the graph,
(2,0)
(-3,0)
(0,0)
(-1,-36)
F(x)=

Answer: 16

Step-by-step explanation: 16%x1=.16 meters, then multiply by 100 to get 16 centimeters.

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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The area of the triangle is 59.6\(m^2\)

Now, According to the question:

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

In the question, Area unit is not mentioned.

But i take the unit in meter.

Now, We have the given data is:

In triangle HPK:

K = 8 m

P = 14.9 m

To find the area of triangle.

We know that :

Area of Triangle is  = 1/2 × b × h.

A  = 1/2 × 8 × 14.9

A = 59.6 \(m^2\)

Hence, The area of the triangle is 59.6

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The answers to the questions are:

This defined as the total number of points that a person has been able to cover at a given period. It is calculated by taking the time and the speed of takeoff into consideration. The speed that a person used and the time it took them to get to their destination is what is used to calculate distance

The time it takes for sunlight to reach is given as

distance/speed

778000000000/300000000

=2593.33 * 60

= 43.22 minutes

The formula for distance is given as speed * time

speed = 15km/hr

time = 1 hour

The distance = 15 * 1

= 15 km/hr

If the time is 2*1/2

the distance = 15 / 2.5

= 6 km

Expressed as a fraction we have the following

0.37 = 37/100

0.086 = 86/1000

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The percent increase in the flight increase is \(18.35\)%

Definition of percentages.

A percentage is a ratio of some value out of a hundred.

With this definition in mind, if \(20\)% of \(200\) students have a test tomorrow, then a total of \(40\) students have a test tomorrow.

Percentage Increase Calculation Example #1

For the first example, we find the percentage increase for the following scenario:

If your total savings of $\(60\) at the beginning of the week grew to $\(90\) by the end of the week, what is the percentage increase?

This is where our three-step process comes in:

Step 1: Find the difference in values ​​by subtracting the initial value from the final value.

In this case, the final value minus the initial value can be calculated as follows:

\(90 -60 = 30\)

So in this example, the difference between the two values ​​would be \(30\). Remember that when calculating the percentage increase, you will always subtract the smaller value from the larger value.

Step 2:Divide the difference by the initial number

The next step is to take the difference (\(30\) in this example) and divide it by the starting number (\(60\) in this example) like this:

\(30/60 = 0.50\)

Always express your answer as a decimal (this will make your life a lot easier when you get to step three).

Step 3: Multiply by \(100\)

The last step is to multiply the decimal result from step two by one hundred and express the final result as a percentage.

\(0.50 * 100 = 50\)

Final answer: 50% increase

That is all! Using three steps, you can conclude that there was a \(50\)% increase in the money you had from the beginning of the week to the end of the week.

Hence percent increase can be found as follows:

=$\((432-365)/365*100\)

=\(18.35\)%

Therefore, a percent increase in the flight increase is \(18.35\)%

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21

\( \frac{1}{2} height \: of \: trapezium(a + b) = area \: of \: trapezium\)

half the height is 3

a=7

b=x

3(7+x)=84

21+3x=84

place the like terms on one side

84-21=3x

63=3x

x=21

Answer:

12 pencils

Step-by-step explanation:

let no. of pencils bought be x.

54 - 0.75x - 2.50 = 42.50

9 = 0.75x

x = 12

Topic: algebraic equations

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:

 =  − 2

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

Answer:

Nope

Step-by-step explanation:

3 + 9 + 2 + 7 = 21

21 is not divisible by 9, Therefore, 3927 is not divisible by 9.

Answer:

No. not by a full number

Step-by-step explanation:

Because if we whip out our calculators we get 436.333333333

Answer:

E

Step-by-step explanation:

=√9pr / (pr)^-3/2

=3√(pr) × (pr)^3/2

= 3p²r²

Answer:

E. 3p²r²

Step-by-step explanation:

√9pr / (pr)^-3/2=

3(pr)^1/2*(pr)^3/2=

3(pr)^(1/2+3/2)=

3(pr)^2=3p^2r^2

Without the individual probability of a passenger showing up, we cannot calculate the exact probability of the number of people who show up exceeding the capacity of the plane

To solve this problem, we need to determine the probability that more than 65 people (the capacity of the plane) will show up from the 70 booked passengers.

Step 1: Identify the relevant information
- Maximum capacity of the plane: 65
- Number of people booked: 70

Step 2: Calculate the probability of each possible outcome
To exceed the capacity, at least 66 passengers must show up. We need to calculate the probability of 66, 67, 68, 69, and 70 passengers showing up. However, we don't have information on the individual probability of a passenger showing up. If we had this information, we could use the binomial probability formula.

Step 3: Express the final answer
Unfortunately, without the individual probability of a passenger showing up, we cannot calculate the exact probability of the number of people who show up exceeding the capacity of the plane. Please provide the probability of a passenger showing up so we can give you an accurate answer.

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Answer:  2(x+3)^2 - 1

To shift the f(x) function 3 units to the left, the xy axis must move 3 units to the right. This effectively means each x input is 3 units larger than before. That's why we replace every x with x+3.

The Glasgow Coma Scale (GCS) is a neurological assessment tool used to measure a patient's level of consciousness after an injury or illness.

It consists of three components: eye opening, verbal response, and motor response. Each component is assigned a score ranging from 1 to 6, with a higher score indicating a better neurological status. The maximum score a patient can achieve is 15, with 5 being the minimum score for a patient to be considered conscious.

Regarding the highest numerical value assigned to eye opening, the answer is A. 6 points. Eye opening is one of the three components of the GCS, and it measures the patient's ability to open their eyes spontaneously, in response to verbal stimuli, or in response to painful stimuli.

A score of 6 is given when the patient opens their eyes spontaneously, which is the highest score for this component. A score of 5 is given when the patient opens their eyes in response to verbal stimuli, and a score of 4 is given when the patient opens their eyes in response to painful stimuli. Scores lower than 4 indicate a severe neurological impairment.

In summary, the highest numerical value assigned to eye opening when computing the GCS is 6 points, which is given when the patient opens their eyes spontaneously.

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Answer:

Undercoverage

Step-by-step explanation:

Using a local telephone book to select a simple random sample could introduce UNDERCOVERAGE bias.

I hope it helps! Have a great day!

Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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x1 = -2, x2 = 1, and x3 = 5.5

This system of equations can be solved by first combining the equations and then isolating one of the variables. To combine the equations, subtract the first equation from the second equation:

4x1 + 5x2 + 5x3 = 9

- (x1 + x2 + 3x3 = -4)

3x1 + 4x2 + 2x3 = 13

Next, isolate one of the variables. In this case, let's isolate x3:

3x1 + 4x2 + 2x3 = 13

- (2x3) - (-2x3) = 0

3x1 + 4x2 = 13

x3 = \frac{13 - (3x1 + 4x2)}{2}

Now that x3 has been isolated, substitute it into one of the original equations and solve for the remaining two variables:

x3 = \frac{13 - (3x1 + 4x2)}{2}

x1 + x2 + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x2:

x2 = \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4}

Substitute this expression for x2 into one of the original equations and solve for x1:

x1 + \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4} + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x1 and then plug this value back into the expression for x2 to find x2:

x1 = -2

x2 = 1

x3 = \frac{13 - (-2 + 4x2)}{2}

x3 = \frac{13 - (-2 + 4 \cdot 1)}{2}

x3 = \frac{13 - 2}{2}

x3 = 5.5

Therefore, the solution to the system of equations is x1 = -2, x2 = 1, and x3 = 5.5.

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The dimensions of the painting are 24 feet by 32 feet. Given the perimeter of the painting is 112 feet. Let the width be x feet. The length is 8 feet more than its width, therefore, the length = x + 8 feet. Perimeter of a rectangle = 2 (l + w).

Substitute x + 8 for l and x for w in the above equation : 2 (l + w)

= 2 (x + 8 + x)

= 4x + 16 feet

But given the perimeter of the painting is 112 feet4x + 16

= 112 feet

Subtract 16 from both sides of the above equation

4x = 112 - 16

= 96

Divide both sides by 4x = 24

The width of the painting is 24 feet

The length of the painting = x + 8

= 24 + 8

= 32 feet

Therefore, the dimensions of the painting are 24 feet by 32 feet.

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Answer:

Step-by-step explana8tion:

80$ with that 6%

This theorem states that:

\(a^2+b^2=c^2\)

In this diagram, notice how there are two smaller triangles that create the large triangle.

To find a and b, we can look at the two small triangles instead of seeing everything as a whole.

Let the top triangle be Triangle A and the bottom triangle be Triangle B.

Solve for a using the Pythagorean theorem:

\(a^2+b^2=c^2\\12^2+6^2=a^2\\a=\sqrt{12^2+6^2}\\a=13.42\)

Solve for b using the Pythagorean theorem:

\(a^2+b^2=c^2\\6^2+3^2=b^2\\b=\sqrt{6^2+3^2}\\b=6.71\)

a = 13.42

b = 6.71

The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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Answer:

negative because the answer would be -42

Step-by-step explanation:

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

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Step-by-step explanation:

1. ∠EBC = x (Theorem One: The angle at the centre of the circle is twice the angle at the circumference subtended on the same arc. You already have this one labelled)

2. ∠FCD = x (F rule / corresponding angles are equal)

3. ∠CAE = x (Theorem Two: Angles at the circumference subtended by the same arc are congruent)

4. ∠BED = ∠DCF = ∠FCD = x (Theorem Fifteen: The exterior angle of a cyclic quadrilateral is congruent to the interior opposite angle)

5. ∠CDF = ∠BED = x (F rule / corresponding angles are equal)

6. ∠CAE = ∠OAE = ∠OEA = x  (CAE and OAE are the same angles, OF and OA are radii, thus they must both be equivalent in magnitude, therefore making the triangle ΔAOE isosceles. Base angles of an isosceles triangle are always equal, since we knew ∠OAE from '3.' was x, we found that ∠OEA was also x)

The age of Layla who youngest of four siblings is 18 years old

The age of 4 sibling are in consecutive even integers

Age of 1st sibling = x

Age of 2nd sibling = x + 2

Age of 3rd sibling = x + 4

Age of 4th sibling = x + 6

Sum of the sibling age = 84

x + x + 2 + x + 4 + x + 6 =84

4x + 12 = 84

4x = 84 -12

4x = 72

x = 18

Layla is youngest  sibling hence her age will be 18 years

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The question is incorrect the correct question is :

Layla is the youngest of four siblings whose ages are consecutive even integers. If the sum of their ages is 84, find Layla's age

Answer:

it goes 5.5.4.7.9.10.10.10.11

Step-by-step explanation:

Answer:

8 and 9

Step-by-step explanation:

78 is in between 64 and 81 which are the squares of 8 and 9

We have that for the Question "Consider the square root of 79. Between which two whole numbers will square root of 79 lie on a number line.​" it can be said that the two whole numbers square root of 79 will be.

\(x=\pm 8.89\)

x=-8.89

x=+8.89

From the question we are told

Consider the square root of 79. Between which two whole numbers will square root of 79 lie on a number line.​

Generally the equation for the square root of 79 is mathematically given as

\(x=\sqrt{79}\\\\Therefore\\\\x=\pm 8.89\)

Therefore

The two whole numbers square root of 79 will be.

\(x=\pm 8.89\)

x=-8.89

x=+8.89

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Answer: 23.945 (945 repeated)

Step-by-step explanation:

886/37 is exactly 23.945945995

23 and 35/37 in decimal form

Answer:

A. less than three batteries were used in five hours.

Answer:

a

Step-by-step explanation: