let k(x)=3h(x)+4x^4/g(x). given the following table of values, find k'(-1)

The mean absolute deviation is 2.5.

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

How to calculate the mean deviation from the mean:

Given data:1, 1, 3, 5, 5, 6, 8, 11

So, mean of the data is

= 1+ 1 +3 +5 +5+ 6+ 8 +11 / 8

= 40 /8=

5

Now, Mean absolute deviation is

= | 1-5| + |1-5| + |3-5 | + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|/ 8

= 4 + 4 + 2+ 0 + 0+ 1 + 3 +6 /8

= 20/8

=2.5

Hence, the mean absolute deviation is is 2.5.

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1 trillion to the tenth power is (10¹⁴)¹⁰ or  (10¹³)¹⁰.

So, 1 trillion to the tenth power:

Therefore, 1 trillion to the tenth power is (10¹⁴)¹⁰ or  (10¹³)¹⁰.

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Answer: We have to find the volume of the pool and the number of pit balls that can fill it.

(1) We can find the volume of the pool with the following formula:

Using the equation (1) the volume of the pool is determined as follows:

(2) The number of ball pits that can fill the pool is as follows:

Therefore the answer is:

ANSWERS

(a) 0.420

(b) 0.400

(c) With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small

EXPLANATION

(a) The experimental probability is given by,

In this case, Donna spun the dial 1000 times and 420 times it landed on yellow,

Hence, the experimental probability of landing on yellow is 0.420.

(b) The theoretical probability is given by the geometry of the spinner and, if it is fair, the number of yellow sections,

In this case, the spinner is divided into 10 equally sized slices, and 4 of them are yellow,

Hence, the theoretical probability of landing on yellow is 0.400.

(c) As we can see in parts a and b, for 1000 trials, the experimental and theoretical probabilities are almost the same - i.e. there is a small difference. This is known as the law of large numbers which states that if the number of trials of an experiment is large, the experimental probability of each event should be close to the theoretical probability.

Hence, the true statement is the first one: with a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.

PROBLEM:

To find the point-slope form of the equation of the line passing through points (0, 0) and (-4, 7)

METHOD:

The point-slope form of the equation of a line is given to be:

Step 1: Find the slope of the line.

The formula to calculate the slope of a line is given to be:

We can use the two points provided to find the slope of the line such that:

Therefore, the slope is given to be:

Step 2: Pick a point on the line to use for the equation.

Step 3: Use the values gotten from Steps 1 and 2 to write out the equation of the line in the point-slope form:

ANSWER:

The slope-intercept form of the line is given to be:

Answer:

Explanation:

Step 1. The function we have is:

And we are asked to find the derivative of the function. The rule to find the derivative for this type of function is:

Step 2. Before we apply the derivative rule, remember the following:

This means that we need to derivate each part or term of the function and combine them for the total derivative.

Step 3. Apply the derivative rule from step 1 to the given function.

First we rewrite the function as follows:

Apply the derivative rule:

Step 4. The last step is to simplify the expression:

Answer:

we can make a relation

where x is the missing value

if she bikes 2/3km in 4 minutes how much kilometers she bike on 1 minute?

we solv using cross multiplication

we multiply 1 and 2/3 and the divide by 4

she will bike 1/6km in one minute

The predicted temperature of the substance after 3.5 minutes implies that x =3.5, and we are to find y.

Therefore,

Therefore, the predicted temperature of the substance, 3.5 minutes after the start of the experiment is 40.5 degrees Celsius

Given

The function,

To find the type of function, domain, range, x-intercept, y-intercept, one minimum or maximum, intervals where the function is positive, intervals where the function is negative.

Explanation:

It is given that,

Since the function is related to modulus value.

Then, the type of the function is Absolute value function.

Also, Since

Then, the domain of the function is,

Set h(x)=z,

The range of the absolute function c | a x + b | + k is f(x) is greater than equal to k.

Then,

Therefore, the range is,

From, the graph

From the figure there is no x-intercept.

Also, the y-intercept is 6.

Now, to find the critical points

The polygon EFGH is a polygon.

What is polygon?

A polygon is a form of planar figure in geometry and is defined as a closed polygonal chain made up of a finite number of straight line segments. A region that is enclosed by a bounding plane, a bounding circuit, or both is referred to as a polygon. The portions of a polygonal circuit are referred to as its edges or sides.

To check the polygon EFGH is a square or not, first to find the length of each side of polygon.

If the length of each side is equal then the polygon EFGH is a square.

(Since length of each side of square is equal).

We know,

[tex]d \sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}[/tex]

where,

d = distance

[tex](x_1, x_2)[/tex] = Coordinates of the first point.

[tex](x_2, y_2)[/tex] = Coordinates of the second point.

So,

[tex]EF = \sqrt{(3-(-2))^2 + (3.5-3.5)^2} = \sqrt{25 + 0} = 5[/tex]

[tex]FG = \sqrt{(3-3)^2 + (-1.5-3.5)^2 } = \sqrt{0 + 25} = 5[/tex]

[tex]GH = \sqrt{(-2-3)^2 + (-1.5-(-1.5))^2} = \sqrt{25 + 0} = 5[/tex]

[tex]EH = \sqrt{(-2-(-2))^2 + (-1.5-3.5)^2} = \sqrt{0 + 25} = 5[/tex]

From above the length of each side is equal.

Therefore, given polygon EFGH is a square.

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It takes 400 years for $600 to earn $72 at the rate of 0.03 percent annual

"Simple" interest refers to the straightforward crediting of cash flows associated with some investment or deposit.

The formula for calculating Simple interest

I=PRT

Where I is the Interest

P=Principle amount

I is interest Amount

R is rate of interest per year as a percent

T is time period involved

P=600

I=72

r=0.03%

t=?

I=PRT

Plug in the values P, R and I

72=600×(0.03%)×T

72=600×0.0003×T

72=0.18×T

400=T

Hence it takes 400 years, for amount  $600 to earn $72 at the rate of 0.03 percent annual.

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Answer:   -11

Step-by-step explanation:

Answer:

• $250

• y=200+50x

• Graph A

• Yes

Explanation:

(a)Han cellphone's plan costs a fixed fee of $200 and an extra $50 per month.

Therefore:

(b)If Han uses the phone for x months

Extra Cost = 50x

Therefore:

(c)Since the number of months = x; and

Total cost for x months = y

When x=24

The graph that shows the cost of the cell phone plan over a period of two years using months as the units of time is Graph A.

(d)We see that the equation y=50x+200 has a proportional constant (50).

Another approach is to say that it is a linear equation.

Therefore, there is a proportional relationship between time and the cost of the cell phone plan.

The costs of repairing iPads in UAE are normally distributed with a standard deviation of 73 Dhs. If 8% of the costs exceed 279 Dhs, then the mean of the costs is 1.405072

The mean of the Costs stands for the typical sum of money spent on a product's production. Depending on how many units are made, this amount may change.

Let X be the price of fixing iPads in the UAE (in Dhs)

X ~ N (μ, σ = 73)

if 8% of the costs are greater than 297 Dhs.

P (X > 297) = 8%

P(X > 297) = 0.08

We must determine the mean value (μ)

P (X > 297) = 0.08

P [(X - μ) / σ > (297 - μ) / 73] = 0.08

P [Z < (297 - μ) / 73] = 0.08

P [Z < (297 - μ) / 73] = 1 - 0.08

P [Z < (297 - μ) / 73] = 0.92

(297 - μ) / 73 = Z⁻¹(0.92)

(297 - μ) / 73 = 1.405072    (Using R software)

297 - μ = 73 * 1.405072

μ = 297 - (73 * 1.405072)

μ = 297 - 102.5702

μ = 194.4298

μ ≅ 194

Therefore, the mean of the cost (μ) = 194 dhs.

Using R Software, we can compute;

Z⁻¹ (0.92) is,

=qnorm(0.92) ` → (Command)

'1.405072 → (Output)

⇒ Z⁻¹ (0.92) = 1.405072

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The actual distance is 90 miles between the town and the state capital based on the scale of the map

1/2 inch on the map = 10 miles

So, 1 inch = 20 miles

Distance between the town and state capital = 4 1/2 inches

The mathematical relationship between a small unit of measurement on a map, such as an inch or centimetre, and the corresponding real-world unit of distance, such as a kilometre or a mile, is known as a map scale.

The actual distance in miles between the town and the state capital is given by:

Distance between town and state capital* Scale of the map

= 4.5*20

= 90 miles

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A non-zero matrix A with A² = 0 is A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex].

We need to find a 2 x 2 non- zero matrix with A² = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

A² = A x A

If A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex], then A x A =  [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex] x  [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

                                          = [tex]\left[\begin{array}{cc}a^2+bc&ab+bd\\ac+dc&bc+d^2\end{array}\right][/tex]

This is called matrix multiplication.

Now consider the matrixes of the form A = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]

Then A² =   [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]  x  [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]

              =  [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

Also Consider a matrix A = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]

Then A² =    [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] x  [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]

              =  [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

So any matrix of the form  [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] and   [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] with x any number, will give A² = 0

In particular, A =  [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex] is a non-zero matrix with A² = 0.

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the inverse function = f^-1(x) is option C

First let's state what we are given:

f(x) = x^3 - 5

We are to find the inverse of f(x).

To do this, first let's represent f(x) with y

y = = x^3 - 5

Then, we would interchange x and y

From the answer we got, the inverse function = f^-1(x) is option C

Equation is -(x+4)² +4.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. The vertex form of a quadratic equation is y = a (x h) 2 + k as opposed to the regular quadratic form, which is an x 2 + b x + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.

Given Data

Solutions (-6, 0) and (-2,0)

y = a(x - (-6)) (x-(-2))

y  = a(x+6) (x+2)

Vertex (-4,4)

at x = -4 and y = 4

4 = a(-4+6)(-4+2)

4 = a (2)(-2)

a = -1

y = -1(x+6)(x+2)

y = -(x²+8x+12)

y = =(x² + 3x +4x+4²-4²+12)

y = -(x+4)² +4

Equation is -(x+4)² +4.

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The line is given by 3x + 6y = 8

To find the slope and the y-intercept, we must rewrite the equation in the form y = ax + b, where a is the slope and b is the y-intercept.

The first step is subtract 3x from both sides of the equation:

3x + 6y - 3x = -3x + 8

6y = -3x + 8

Then, we divide both sides by 6:

6y/6 = (-3x + 8)/6

y = -x/2 + 4/3

Therefore, the slope is -1/2 and the y-intercept is 4/3

Probability of drawing 3 green marbles in a row with replacement is 0.059

The probability that you draw 7 blue marbles in a row without replacement is 0

Probability is used to determine the odds in favor or against a random event happening. The probability that the random event happens lie between 0 and 1. The more likely it is that an event would happen the closer the probability value would be to 1.

Probability of drawing 3 green marbles in a row with replacement = (7/18) x (7/18) x (7/18) = 0.059

The probability that you draw 7 blue marbles in a row without replacement = (6/18) x (5/17) x (4/16) x (3/15) x (2/14) x (1/13) x 0 = 0

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Answer:  0.77

Step-by-step explanation:

The end behavior of the given function will be given by Down on the left down on the right.

A function may be defined as the expression in which for one value of input variable there is only one value of output variable. The input variable or the independent variable is x, and the output variable or the dependent variable is y. In the given function f(x) = -3x⁴ + 7x² - x + 13 we will use the Power and Polynomial Functions features. For final behavior of power functions of the form f(x) = axⁿ where n is represented as a non-negative integer depends on the power and the constant. Here, the leading coefficient is -3x⁴. So, when x → ∞ the value of f(x) → -∞ and when x → -∞ then the value of f(x) → -∞. So, the final answer for the behavior will be given by "Down on the left, down on the right".

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a) Perimeter =  17.4 cm

b) Perimeter   =210.6 cm

How are the perimeters calculated?

a) The perimeter of an irregular polygon = Sum of all the sides of the polygon.

Converting value of all sides to centimetres.

Perimeter = 3.4 +3.2 +4.3 +3.7+2.8

                 = 17.4 cm

b) The perimeter of an irregular polygon = Sum of all the sides of the polygon.

Converting value of all sides to centimetres.

Perimeter = 29.1+25.3+30+28.6+32.6+36.5+28.5

                 =210.6 cm

What is the perimeter of a polygon?

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5⁶ is the simplified form of the expression ( 5⁶/5³ )².

Given the expression in the question;

( 5⁶/5³ )²

To simplify the expression; us the law of indices.

xᵃ ÷ xᵇ = xᵃ⁻ᵇ

Hence, perform the operation inside the parenthesis

( 5⁶/5³ )²

( 5⁶ ÷  5³ )²

( 5⁶⁻³ )²

( 5³ )²

To remove the parenthesis, apply the law of indices.

( xᵃ )ᵇ = xᵃ ˣ ᵇ

( 5³ )²

5³ ˣ ²

5⁶

Therefore, the simplified form of the expression is 5⁶.

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The function of the total money raised from both donors after walking d kilometers is T(d) = 12d + d^2

From the question, the given parameters are:

Also, from the question, T is the total money raised from both donors at d kilometers

This means that the equation of the total money can be represented a

T(d) = A(d) + B(d)

Substitute the known values in the above equation

So, we have the following equation

So, we have

T(d) = 10d + 2d + d^2

Evaluate the like terms in the above equation

T(d) = 12d + d^2

The equation cannot be further simplified

Hence, the composite function is T(d) = 12d + d^2

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Complete question

Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money, A, in dollars, that he receives from the first donor given that he walks d kilometers is given by the formula A(d)=10d

The money, B, in dollars, that he receives from the second donor given that he walks d kilometers is given by the formula B(d)=2d+d^2

Let T be the total money that Onur raises from those donors by walking d kilometers in the walkathon.

Write a formula for T(d) in terms of A(d) and B(d)

Answer:

x=12

Step-by-step explanation:

(4x + 7) + 35 = 90

(4x+7)=90-35
4x+7=55
4x=55-7
4x=48

x=12

Answer:

x=12

Step-by-step explanation:

it just is.,...........

The formula for exponential growth is expressed as

y = a(1 + r)^t

where

y is the population after t years

ais the initial population

r is the growth rate

t is the number of years

From the information given,

a = 350

r = 14% = 14/100 = 0.14

By substituting these values into the equation, the function to model th growth rate is

y = 350(1 + 0.14)^t

y = 350(1.14)^t

We would substitute values of t into the equation to determine corresponding values of y. We have

For t = 2, y = 350(1.14)^2 = 454.86

For t = 6, y = 350(1.14)^6 = 768.24

For t = 10, y = 350(1.14)^10 = 1297.52

We would plot these values of y on the y axis and the corresponding values of t on the x axis. The graph is shown below

The time when the population will reach 20000 would be the value of x at the point where y = 20000 on the graph. It is around y = 30.87

Thus, the population will reach 20000 in approximately 31 years

We can confirm this by solving the equation. We have

20000 = 350(1.14)^t

20000/350 = 1.14^t

57.14 = 1.14^t

Taking natural log of both sides, we have

ln 57.14 = ln1.14^t = tln1.14

t = ln 57.14/ln1.14

t = 30.87505

see the figure below to better understand the problem

we have that

Answer:

4x>13

Step-by-step explanation:

4 × X=4x

>=more than symbol

The solution is option C.