1.- If f(x)= x^8, then f'(x) =
2.- If g(x)= -4x^4 then g'(x) =
3.- If h(x)= 1/x^5 then h'(x) =

a) The distance value is the leverage value from the output which is 0.004

b) The 99% prediction interval is [7.676, 9.146]

a) We are interested in finding and reporting the prediction interval on the output.

Thus, the prediction interval on the output is [7.9188, 8.9025]

Let us consider the estimated value for y as yₓ

We have

x₁ = 3.7, x₂ =3.9, x₃ = 6.5, β₀= 7.5891, β₁ = -2.3577, β₂= 1.6122, β₃= 0.5012

We know that yₓ = β₀ +β₁x₁ + β₂x₂ + β₃x₃

By substituting the value

x₁ = 3.7, x₂ =3.9, x₃ = 6.5, β₀= 7.5891, β₁ = -2.3577, β₂= 1.6122, β₃= 0.5012 into the above equation we get

yₓ =7.5891-(2.3577*3.7)+(1.6122*3,9)+(0.5012*6.5) = 8.411

Let us calculate the value for the prediction interval

The 100 (1 - a) \% prediction interval is

yₓ ±(tₐ/₂ * x * s* √ 1+distance value )

The distance value is the leverage value from the output which is 0.004

We have yₓ =8.411, t₀.₀₀₅.₂₆ =3.067 and s = 0.235. By substituting these values we find that the 95% prediction interval is

8, 411 + (2.3788 * 0.235sqrt(1 + 0.04)) = [7.841, 8, 981]

b) If Enterprise Industry's plan to have in inventory of the number of bottles implied by the upper limit of the prediction interval, which is approximately 9, it can be very confident that it will have enough bottles to meet demand for detergent in the future sales period.

Thus, the bottles are approximately 9

By multiplying the number of bottles implied by the lower limit of the prediction interval, that is approximately 8, by the price of the detergent that is $3.7. we get the minimal revenue from detergent in the future sales period that is $29.6

We are interested in calculating a 99% prediction interval for the demand of detergent in the future sales period

We have yₓ =8.411, t₀.₀₀₅.₂₆ =3.067 and s = 0.235 By substituting these values, we find that the 95% prediction interval is as follows

8, 411 ± (3.067 * 0.235sqrt(1 + 0.04)) = [7.676, 9.146]

Therefore the 99% prediction interval is [7.676, 9.146]

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[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi[/tex]

The limits on the vertical asymptotes of the function are given as follows:

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

On a graph, at the vertical asymptotes, the graph just approaches the point, it does not cross the point.

Hence the vertical asymptotes are given as follows:

x = -6, x = -2 and x = 2.

We must observe the limits to the left(denoted by the - sign) and to the right (denoted by the + sign) of each asymptote.

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The calculated value of the area of the rhombus is 35 sq units

From the question, we have the following parameters that can be used in our computation:

The rhombus

Also, we have

x = 3, y = 5 and h = 4

Using shape decomposition, we have the following

Shapes = Rectangle and 2 triangles

So, the area is

Area = Rectangle + 2 triangles

Using the area formulas, we have

Area = 1/2 * xy + 1/2 * xy + hy

substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 3 * 5 + 1/2 * 3 * 5 + 4 * 5

Evaluate

Area = 35

Hence, the area is 35 sq units

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The limits of the end-behavior of this graph are listed below

The limits that describe the end behavior of a graph are the values that the function approaches as x goes to positive or negative infinity.

The graph has a hole at (-4, 2), then the function is not defined at x = -4, but the limit as x approaches -4 exists and is equal to the value of the function at that point (since the function is continuous except at the hole).

The graph touches the x-axis at x = 2 to x = 6, this means that the function has roots or zeros at x = 2 and x = 6.

The horizontal asymptote is y = 1, this means that the function approaches 1 as x goes to positive or negative infinity.

To summarize, the end behavior of the graph can be described as follows:

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We find the equation that represents the temperature (t) at hour (t) using the slope-intercept form and it is:

[tex]t = -2 h + 32[/tex]

The temperature, t, in Burrtown starts at 32°F at midnight, when [tex]h = 0[/tex]. This represents the y-interception of the right line, when [tex]h=0[/tex] hours, [tex]t=32^\circ\text{F}[/tex]:

[tex]\text{Point}=(h,t)\longrightarrow Point=(0,32)=(0,b)\longrightarrow b=32[/tex]

For the next few hours, the temperature drops 2 degrees every hour. This represents the slope of the line (m): [tex]m=-2[/tex], negative because the temperature drops.

Slope-Intercept form:

[tex]y=mx+b: y=t, m=-2, x=h, b=32[/tex]

Replacing the values:

[tex]\boxed{\bold{t=-2h+32}}[/tex]

Complete Question-

The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the next few hours, the temperature drops 2 degrees every hour. Which equation represents the temperature, t, at hour h?

The number line where we plotting -2 1/6 and 11/6 is attached

From the question, we have the following parameters that can be used in our computation:

-2 1/6 and 11/6

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-13/6 and 11/6

This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6

Using the above as a guide, we have the following:

The number line is attached

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To find the ordered pair solutions for the system of equations y = -x² + 2 and y = x, we can set the two equations equal to each other:

-x² + 2 = x

Now we can rearrange this equation into standard quadratic form by moving everything to one side:

-x² + x + 2 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = -1, b = 1, and c = 2

Plugging these values into the formula, we get:

x = (-1 ± √(1 - 4(-1)(2))) / 2(-1)

x = (-1 ± √9) / (-2)

x = (-1 ± 3) / (-2)

So the solutions for x are x = -1 and x = -2.

To find the corresponding values of y, we can plug these values of x into either of the original equations. Let's use y = x:

When x = -1, y = -1

When x = -2, y = -2

Therefore, the ordered pair solutions for this system of equations are (-1, -1) and (-2, -2).

Answer:

We did this by substituting the slope and point values into the equation

y

=

m

x

+

b

and then solving the equation for b.

We will now show you how you can use either use the slope and a point or just two points to define the equation of the line using point-slope form:

y

−

y

1

=

m

(

x

−

x

1

)

This is an important formula, as it will be used in other algebra courses and often in calculus to find the equation of a tangent line. We need only one point and the slope of the line to use the formula. After substituting the slope and the coordinates of one point into the formula, we can simplify it and then write the equation in slope-intercept form.

POINT-SLOPE FORM

Given a point

(

x

1

,

y

1

)

and slope m, point-slope form will give the following equation of a line:

y

−

y

1

=

m

(

x

−

x

1

)

Now that we know both the slope-intercept form and the point-slope for linear equations, when we are asked to find an equation for a linear function, we can choose which method to use based on the information we are given and our personal preferences. The information provided may be in the form of a graph, a point and a slope, two points, and so on. Let’s look at the graph of the function f below and determine its equation.

Answer:

? = 7.5

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact is 90°

thus the triangle is right

using Pythagoras' identity in the right triangle

?² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )

? = [tex]\sqrt{56.25 }[/tex] = 7.5

1. The probabilities of Poison distribution are: [tex]P(0) = (e^{(-0.689)} * 0.689^0) / 0! = 0.5012[/tex]. [tex]P(1) = (e^{(-0.689)} * 0.689^1) / 1! = 0.3447[/tex]. [tex]P(2) = (e^{(-0.689)} * 0.689^2) / 2! = 0.1189[/tex].

The Poisson distribution is a discrete probability distribution that defines the number of events that take place during a specific period of time or space, provided that they do so independently of one another and at a certain average rate. Siméon Denis Poisson, a French mathematician, invented it in the early 19th century to simulate the occurrence of uncommon events, such as horse kick fatalities in the Prussian army. He gave it his name.

The mean or expected value of the number of occurrences in the interval is represented by the Poisson distribution's single parameter, indicated by the Greek letter lambda.

The Poisson distribution is given as:

[tex]P(X = x) = (e^{(-\lambda)} * \lambda ^x) / x![/tex]

Now,

a. For P(0) we have:

λ = (total number of homicides) / (total number of city-years)

= 193 / 280 = 0.689

Substituting the values of  λ = 0.689 and x = 0 we have:

[tex]P(0) = (e^{(-0.689)} * 0.689^0) / 0! = 0.5012[/tex]

b. For P(1), we can plug in λ = 0.689 and x = 1 :

[tex]P(1) = (e^{(-0.689)} * 0.689^1) / 1! = 0.3447[/tex]

c. For P(2), we can plug in λ = 0.689 and x = 2:

[tex]P(2) = (e^{(-0.689)} * 0.689^2) / 2! = 0.1189[/tex]

d. For P(3), we can plug in λ = 0.689 and x = 3:

[tex]P(3) = (e^{(-0.689)} * 0.689^3) / 3! = 0.0272[/tex]

e. P(4), we can plug in λ = 0.689 and x = 4:

[tex]P(4) = (e^{(-0.689)} * 0.689^4) / 4! = 0.0047[/tex]

2 ) The comparison for the actual and distributed values is:

Expected 0 homicides: 0.5012 * 280 ≈ 140.35

Expected 1 homicide: 0.3447 * 280 ≈ 96.72

Expected 2 homicides: 0.1189 * 280 ≈ 33.32

Expected 3 homicides: 0.0272 * 280 ≈ 7.62

Expected 4 homicides: 0.0047 * 280 ≈ 1.31

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Answer:

S - S - P

Step-by-step explanation:

(S) Statistic - The opinion of just those employees who were there on time one morning about a new training program would be a statistic as it represents a sample of the entire population of employees in the company.

(S) Statistic - The range of employees' salaries in a study about a small company with 25 employees would be a statistic as it represents a characteristic of a sample of employees from the company.

(P) Parameter - The average decrease of all the homes sold in Gwinnett in a study about the value of American homes in 2012 would be a parameter as it represents a characteristic of the entire population of American homes in Gwinnett.

Answer:

Z = 60

Step-by-step explanation:

60+60+z=180

120+z=180

z=180-120

Z = 60

Answer:

**NEED ANSWER ASAP DUE TOMORROW**

What are two observations of quasars that prove they cannot be a part of the milky way galaxy?

Step-by-step explanation:

The line segment XY is tangent to circle Z by using the Pythagorean theorem to find the radius of the circle, and the formula for the distance between a point and a line to find the distance between the center of the circle and the line.

Now let's look at the information given in the problem. We are given the length of line segment XY, which is 3.6 units. We are also given the lengths of two line segments that connect the endpoints of XY to the center of the circle Z: YZ, which is 1.8 units, and ZX, which is 2.7 units.

To determine if XY is tangent to circle Z, we need to check if it is possible for a circle with center Z and radius r to pass through points X and Y. If it is not possible, then XY must be tangent to the circle.

In this case, we can use the lengths of YZ and ZX as the legs of the right triangle, and r as the hypotenuse. We can set up the following equation:

r² = YZ² + ZX²

Substituting the given values, we get:

r² = 1.8² + 2.7²

r² = 7.29

r = √7.29

r ≈ 2.7

Now that we know the radius of circle Z, we can check if it is possible for it to pass through points X and Y. To do this, we need to find the distance between the center of the circle and the line XY. If this distance is equal to the radius of the circle, then XY is tangent to the circle.

To find the distance between the center of the circle and the line XY, we can use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / √(A² + B²)

where A, B, and C are constants that depend on the equation of the line, and x and y are the coordinates of any point on the line.

In this case, we can use the equation of line XY, which is:

y = 0

Substituting this into the formula, we get:

distance = |A(0) + B(1) + C| / √(A² + B²)

distance = |B| / √(B²)

distance = 1 / √1

distance = 1

Since the distance between the center of circle Z and line XY is 1 unit, and the radius of circle Z is also 1 unit, we can conclude that XY is tangent to circle Z.

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Answer:

Step-by-step explanation:

To find the total cost of interest, we first need to find the total payment over the life of the loan:

Total payment = Monthly payment x Number of payments

Total payment = $370.41 x (30 x 12)

Total payment = $133,347.60

Next, we need to subtract the principal (loan) amount to find the total interest paid:

Total interest = Total payment - Principal

Total interest = $133,347.60 - $69,000

Total interest = $64,347.60

Rounding to the nearest whole dollar, the total cost of interest is $64,348.

The proportion is solved and the height of the tower is H = 117 m

Given data ,

A pole that is 3m tall casts a shadow that is 1.17 m long

And , a nearby tower casts a shadow that is 45.5m long

So , the proportion is given by

Let the height of the tower be H

And , 3 / 1.17 = H / 45.5

On simplifying the equation , we get

Multiply by 45.5 on both sides , we get

H = 116.6667 m

H = 117 m

Hence , the height of the tower is H = 117 m

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The equation of the line that is parallel to the given line and passes through the point (7,-4) is y = -2x + 10.

The equation of the line that is perpendicular to the given line and passes through the point (7,-4) is y = 1/2x - 15/2.

The equation of a line that is parallel to a given line is calculated as follows;

y = -2x + 6

slope of this line = - 2

Any line that is parallel to this line will also have a slope of -2.

The equation of the line that is parallel to the given line and passes through the point (7,-4):

y - y1 = m(x - x1)

y - (-4) = -2(x - 7)

y + 4 = -2x + 14

y = -2x + 10

The slope of the line perpendicular to the line = 1/2

y - y1 = m(x - x1)

y - (-4) = (1/2)(x - 7)

y + 4 = (1/2)x - (7/2)

y = 1/2x - 7/2 - 4

y = 1/2x - 15/2

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Volume of solid generated when the trapezoid is rotated about side DE=549.8.

A trapezoid is a quadrilateral with only one pair of parallel sides. It is also known as a trapezium in some countries.

The volume of a solid is the amount of space it occupies in three-dimensional space.There are different formulas to calculate the volume of different types of solids, such as cubes, spheres, cylinders, and cones.

Given trapezoid DEFG formed when right angle HGD is cut by line FE.

Volume of solid generated about side DE:

[tex]V_{GDH}[/tex]=1/3×πr²h

=1/3×π(5+5)²(6)

=200π

[tex]V_{FEG}[/tex]=1/3×π×r²h=1/3×π×(5)²×3

=25π

Volume of Solid=[tex]V_{GDH}[/tex]-[tex]V_{FEH}[/tex]

=200π-25π=175π

=549.78 ≈549.8

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(a)The probability is approximately 0.4441 or 44.41%.

(d) The probability of getting exactly 1 adult who says they were too young is approximately 0.3513 or 35.13%.

Probability is defined as the ratio of favourable outcome to the total number of outcome.

A number is a mathematical concept that represents a quantity or a value. It is an abstract idea used to count, measure, or compare quantities of objects, events, or abstract entities. Numbers can be classified into various types, such as natural numbers (e.g., 1, 2, 3), whole numbers (e.g., 0, 1, 2, 3), integers (e.g., -3, -2, -1, 0, 1, 2, 3), rational numbers (e.g., fractions like 1/2, 3/4, etc.), irrational numbers (e.g., π or square root of 2), and real numbers (which include both rational and irrational numbers). Numbers are fundamental to mathematics and play a crucial role in many areas of science, engineering, economics, and everyday life.

The probability that at least one of the selected adults says they were too young is equal to 1 minus the probability that none of them say they were too young.

Let p = probability that an adult says they were too young to get tattoos

p = 13% = 0.13

The probability that none of the selected adults say they were too young is given by:

P(none say they were too young) = (1 - p)^10

Putting the values of p, we get:

P(none say they were too young) = (1 - 0.13)^10 ≈ 0.4441

Let p = probability that an adult says they were too young to get tattoos

p = 13% = 0.13

Let X = number of adults out of 10 who say they were too young

Using the binomial probability formula, we have:

P(X = 1) = (10 choose 1)×(0.13)¹ ×(1 - 0.13)⁹

where "10 choose 1" is the binomial coefficient, representing the number of ways to choose 1 out of 10.

Plugging in the value for p, we get:

P(X = 1) = (10 choose 1) × (0.13)¹× (1 - 0.13)⁹≈ 0.3513

So, the probability of getting exactly 1 adult who says they were too young is approximately 0.3513 or 35.13%.

Since 1 is not significantly low compared to the probability of getting exactly 1 adult who says they were too young (which is 0.3513), we cannot conclude that 1 is a significantly low number of adults who say they were too young to get tattoos based on the given information. Additional statistical analysis and comparison with appropriate thresholds would be necessary to make a conclusive determination.

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Answer:4.9987

Step-by-step explanation:

Formula for the volume of a cylinder: (π)(r^2)(h)  which is pi x radius squared x height

The final product is 314 therefore you make that number equal to the formula and plug in the known variables to the formula which becomes

314 = (π)(r^2)(4)

Since you know both the value for pi and the height, by following the reverse order of PEMDAS (because we are trying to solve for an unknown variable), you can divide the values of height and pi from both sides since they are being multiplied to radius squared. We are doing this in order to isolate the radius on one side which will give us the value for the radius.

This leaves you with 24.9873 = r^2

The final step is to squareroot both sides as squareroot eliminates a square.

This leaves us with  

r = 4.9987

Thus, the given system of equation has one unique solution (-3, 6).

Two or even more equations with the same variables are referred to be a system of equations. The intersection of the lines is the location where an equation system has a solution. Systems of equations can be solved using one of four techniques: graphing, substitution, elimination, or matrices.

Given:  system of equations:

y = 3x + 15  ...eq 1

3x + 3y = 9 (divide by 3)

x + y = 3

y = 3 - x  ..eq 2

equation eq 1 and eq 2

3x + 15  = 3- x

3x + x = 3 - 15

4x = -12

x = -3

y = 3 - (-3) = 3 + 3 = 6

Solution - (-3, 6)

Thus, the given system of equation has one unique solution (-3, 6).

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Step-by-step explanation:

this is because if the acute angle is equal to or less than 45° it will be less than or equal to 90° but it the angle is more than 45° then it will be a obtuse angle if it is doubled .

eg.

acute angle is 44°

then if it is doubled it will be 44 ˣ 2

= 88°

But if the angle is 46 °

then if it is doubled it will be 46  ˣ 2

= 92°

hope this helps you.

The ordered pair that is potted in quadrant II is (-4, 6)

The domain of the second quadrant in a Cartesian coordinate system, also identified as a Cartesian plane, is located above the x-axis and to the left of the y-axis.

This area forms one of four quadrants that comprise the entirety of said system, frequently leveraged for graphing functions or equations and illustrating various data points.

Examining the graph, the point plotted in the second quadrant is (-4, 6)

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The statements true of function f given by f(Θ) = tan(Θ):

A: Since the tangent function has a repeating pattern, it is a periodic function.

B: The domain of the tangent function is restricted because it has vertical asymptotes at certain values of Θ (specifically, odd multiples of π/2).

C: The range of the tangent function is not all real numbers, but rather all values except for its vertical asymptotes.

D: The period of the tangent function is 2π, because the pattern repeats every 2π radians.

E: The period of the tangent function is not π.

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Answer:

If Kiran's cat eats 1/2 cup of food each day, then in a week (7 days), the cat can eat:

1/2 cup/day x 7 days = 3.5 cups

So Kiran's cat can eat 3.5 cups of food in a week.

We need to multiply the equation x = 3 by a factor of 5 to find the equilibrium of the scale.

According to the statement, we find the following mathematical equation that describes the initial situation of the scale:

x = 3

Then, if we multipliy the equation by a factor of 5 on both sides (by property of compatibility with multiplication), then we find the following expression:

5 · x = 15

A factor of 5 must be added to the mathematic equation.

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Answer:

3 7/8 - 1/4 = 3 5/8 times mile = 3.625 miles

Thats how its done

Step-by-step explanation:

In linear equation, Balanced diet is of utmost importance for proper functinality and growth of our body.

What is a linear equation in mathematics?

An algebraic equation of the form y=mx b, where m is the slope and b is the y-intercept, and only a constant and first-order (linear) term is referred to as a linear equation.

                               The aforementioned is occasionally referred to as a "linear equation in two variables" where y and x are the variables. There might be more than one variable in a linear equation. It is known as a bivariate linear equation, for example, if a linear equation has two variables.

he recommended daily requirement of Calories is Men: 2400 , Women: 1900 , Children: 1800 Also daily requirement for protein is Men: 55 gm , Women:45 gm and Children:33 gm Calculate the total requirement of calories and proteins for each of the two families.

Given the details of two families A and B.

A : 4 men, 6 women and 2 children  

B : 2 men, 2 women and 4 children

Hence, the number of people in both the families A and B can be represented in matrix form with rows denoting the family and columns denoting the number of people of each type as

X = [ 4 6 2 2 2 4 ]

The calorie and protein requirements for different types of people are also given.

Men: 2400 calories, 45gm proteins

Women: 1900 calories, 55gm proteins

Children: 1800 calories, 33gm proteins

Hence, the required calories and proteins can be represented in matrix form with each row corresponding to different type of people as

Y = ⎡ ⎢ ⎢ ⎣ 2400 45 1900 55 1800 33 ⎤ ⎥ ⎥ ⎦ [240045190055180033]

Now,  

The required number of calories and proteins for each of the two families can be obtained by taking the product of the matrices X and Y.

Thus,

The requirement of calories and protein is as follows

Family A : 24600 calories and 576 grams protein

Family B : 15800 calories and 332 grams protein

It can be said that a balanced diet with proper amounts of calories and protein must be consumed by the people of all ages in order to lead a healthy life.

So 24600 calories and 576 grams of proteins are needed for Family A and 15800 calories and 332 grams of proteins are needed for Family B.

Balanced diet is of utmost importance for proper functinality and growth of our body. So people must be aware to take food which provides all the necessary nutrients.

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