explosive devices used in mining operations produce nearly circular craters when detonated. the radii of these craters are exponentially distributed with mean 10 feet. find the mean and variance of the areas produced by these explosive devices.

Step-by-step explanation:

vertex form :

y = a(x - h)² + k

(h, k) are the coordinates of the vertex.

"a" is the orientation (up-down) and widening factor.

we use the given h, k and x, y (the given point) to calculate "a".

-5 = a(2 - 3)² + 1 = a(-1)² + 1 = a + 1

a = -6

and the full vertex form is then

y = -6(x - 3)² + 1

just a quick addition to the superb reply by "reinhard10158" above

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=3\\ k=1 \end{cases}\implies y=a(x-3)^2 + 1\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=-5 \end{cases} \\\\\\ -5=a(2-3)^2 + 1\implies -6=a(-1)^2\implies -6=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=-6(x-3)^2 + 1 \end{array}} ~\hfill[/tex]

Initial value that take the LaPlace transform of both sides of the given differential equation to create the corresponding algebraic equation is [tex]y(t) = 3t + sin4t + 3cos4t[/tex]

In terms of its usefulness in resolving physical issues, the Laplace transform is an important transform that is probably second only to the Fourier transform. The Laplace transform is especially helpful in solving linear ordinary differential equations, such as those that arise in the analysis of electronic circuits.

The initial value-

[tex]y" + 16y = 48t\\y(0)=3,y'(0)=7\\L( f^{n}(t) ) = s^{n}L(f(t)) - s^{n - 1}(f(0)) - s^{n - 2}(f(0)).........................................f^{n - 1} (0)\\[/tex]

By the formula,

[tex]s^{2}Y(s) - sy(0) - y'(0) + 16Y(s) = 48L(t)\\L(t^{n}) = \frac{n!}{s^{n+1} } \\\\On substitutinf the values,\\Y(s)(s^{2} + 16) - 3s - 7 = \frac{48}{s^{2} }\\Y(s)(s^{2} + 16) = \frac{48}{s^{2} } +3s + 7\\Y(s) = \frac{48 + s^{3} -7s^{2} }{s^{2}((s^{2} + 16) }\\Y(s) = \frac{3}{s^{2} } + \frac{4}{(s^{2} + 16} + \frac{3s}{(s^{2} + 16}[/tex]

On taking LaPlae inverse both side,

[tex]Y(t) = L( \frac{3}{s^{2} } ) + L( \frac{4}{(s^{2} + 16)} ) + L( \frac{3s}{(s^{2} + 16)} )\\Y(t) = 3t + sin4t + 3cos4t\\[/tex]

To know more about Laplace transform visit:

https://brainly.com/question/14487937

#SPJ4

The value of f(2)-g(-7) is -34

A function is defined as a relation between a set of inputs having one output each.

Given are two functions, f(x) = -|3-8x| and g(x) = x²+4x

f(2) = -|3-8x2|

= -|3-16|

= -13

g(x) = (-7)²+4(-7)

= 49-28

= 21

f(2)-g(-7) = -13-21 = -34

Hence, The value of f(2)-g(-7) is -34

For more references on functions, click;

https://brainly.com/question/21145944

#SPJ1

Answer:

C no solution.

Step-by-step explanation:

The lines are parallel, they will never intersect.

The variable expression are

cost at each agency to rent a car for 280 miles

The company that has a lower cost for 400 miles

The required expression is a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

Definition of variable to suit the problem

y = output variable (total cost/)

m = slope (cost  per mile driven)

x = input variable (number of miles)

c = y intercept (Car Rental charges)

The equation as described in the problem is represented using linear function as as follows

y = $0.18x + $27.60 - Blue Car Rental

y = $0.14x + $40.40 - Red Car Rental

the total cost at each agency to rent a car for one day and drive it 280 miles

y = $0.18x + $27.60 - Blue Car Rental

y = 0.18 * 280 + 27.60

y = $78

y = $0.14x + $40.40 - Red Car Rental

y = 0.14 * 280 + 40.40

y = $79.60

Write and solve an inequality

$0.18x + $27.60 < $0.14x + $40.40

0.18x + 27.60 < 0.14x + 40.40

0.18x - 0.14x < 40.40 - 27.60

0.04x < 12.80

x < 320 miles

Mr. Kao rents a car for one day

y = $0.18x + $27.60 - Blue Car Rental

y = 0.18 * 400 + 27.60

y = $99.60

y = $0.14x + $40.40 - Red Car Rental

y = 0.14 * 400 + 40.40

y = $96.40

comparing the both shows that Red Car Rental has a lower cost

Learn more about linear functions for costing at:

https://brainly.com/question/29213643

#SPJ1

These rules of five letters (a, b, c, d, and e) and five numbers allow for 28,800 different passwords. Additionally, she makes sure that no two letters or two numbers are ever placed back-to-back.

The basic counting concept is a method for keeping track of all the potential outcomes in a scenario. According to this statement, there are n*m methods to carry out both of these acts if there are n ways to execute one activity and m ways to conduct another action after that.

Here,

Eloise has 10 alternatives since the password's initial character can be any letter or number. She has five alternatives, and her second selection must be from the set (letter or number) that has not previously been utilized. She has four choices remaining, and Choice 3 is from the same group as Choice 1. She gets four possibilities since Choice 4 is the second item in the same set as Choice 2. The choices 5 and 6 come from separate sets, each of which has three possibilities; the choices 7 and 8 come from separate sets, each of which has two options; and the choices 9 and 10 come from separate sets, each of which has only one option left.

10 5 4 4 3 3 2 2 1 1

10 ×5 ×4 ×4 ×3 ×3 ×2 ×2 ×1 ×1 = 28,800

28,800 different passwords conform to these rules of five letters (a, b, c, d, and e) and five numbers (2, 3, 4, 5, and 6). additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive.

To know more about counting principle,

https://brainly.com/question/28384306

#SPJ4

Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus.

According to given data  determined parking meter rates throughout the campus area.

What is the hypothesis for regression?

For simple linear regression, the chief null hypothesis is H0 : β1 = 0, and the corresponding alternative hypothesis is H1 : β1 = 0. If this null hypothesis is true, then, from E(Y ) = β0 + β1x we can see that the population mean of Y is β0 for every x value, which tells us that x has no effect on Y .

Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus.

#SPJ4

know more about this topic visit this link

https://brainly.com/question/17642661

Answer:

Step-by-step explanation:

kwik trip

Answer:

Let x be the number of pennies, and y  be the number of nickels.

1 penny = 0.01 dollar

1 nickel = 0.05 dollar.

The equations that will describe the given problem will be,

0.01 x + 0.05 y = 0.81

y = x + 9

Plugging the second equation into the first gives us,

0.01 x + 0.05(x+ 9) = 0.81

0.06 x + 0.45 = 0.81

0.06 x = 0.36

y = 15

So, Kennedy has 6 pennies, and 15 nickels.

Step-by-step explanation:

To maintain the same child-to-adult ratio, the number of adult needed for 108 children are 18.

As the stated question-

At the preschool, there's many 36 children and 6 adults.

Thus, this is solved by using unitary method.

36 children -----> 6 adults.

1 children -----> 6/36 adults.

For 108 children, multiply both sides by 108.

108 children -----> 6 x 108/36 adults.

108 children -----> 18 adults.

Thus, to maintain the same child-to-adult ratio, the number of adult needed for 108 children are 18.

To know more about the ratio of the number, here

https://brainly.com/question/12024093

#SPJ4

The probability that an Endure All battery selected at random will last more than 610 hours is 0.1056.

A probability distribution that is symmetric around the mean is the normal distribution, sometimes referred . Eventsare approximately normal happen more often than information that are far the mean.

The normal distribution appears as a "bell curve" on a graph.

A probability bell curve is more properly described as the normal distribution.

In a normal distribution, the mean is 0 and the standard deviation is 1. The kurtosis is 3, and there is no skew.All  normal distributions are symmetrical.

Natural occurrences frequently resemble the usual distribution.

However, in finance, most price distributions are not fully normal.

How to solve?

Given that μ = 500, σ = 40, for x > 550

z = 550-500/40

z = 1.25

From the normal distribution table, P(z > 1.25) = 1 - P(z < 1.25) = 1 - 0.8944 = 0.1056

To learn more about the normal distribution, visit:

brainly.com/question/4079902

#SPJ4

The number of chocolate bars which Mr Banda bought is equal to 50 chocolate bars.

In order to determine the number of chocolate bars and the number of hot chips that Carter bought, we would have to write a system of linear equation and assign variables to the number of chocolate bars and number of candies respectively, and then translate the word problem into algebraic equation as follows:

Since chocolate bars cost $1.1 each and hot chips 0.40 each and Mr Banda spent $87 on buying 130 chocolate bars and hot chips, we would have the following system of linear equation:

1.1x + 0.40y = 87    ......equation 1

x + y = 130              ......equation 2

From equation 2, we have:

y = 130 - x        ......equation 3

Substituting equation 3 into equation 1, we have:

1.1x + 0.40(130 - x) = 87

1.1x + 52 - 0.4x = 87

0.7x + 52 = 87

0.7x = 87 - 52

0.7x = 35

x = 35/0.7

x = 50 chocolate bars.

Read more on equation here: https://brainly.com/question/14776651

#SPJ1

The different ways in which 6 candles be chosen 84 ways.

What is a combination?

The combination is a method of choosing things from a collection where the order of the choices is irrelevant.

Given, When we have 'n' types of elements and choose 'r' elements from them, then we have C(n+r-1, r) combinations.

n=4(4 types of candles), r=6(no of candles to pick)

Choose 6 different candles, then

=C(4+6-1,6)

=C(9,6)

= 9! / (9-6)! (6!)

= 9!/ 6! 3!

=84

The different ways in which 6 candles can be chosen are 84 ways.

To learn more about a combination

https://brainly.com/question/28065038

#SPJ4

Answer:

64

Step-by-step explanation:

do multiplication :)

1. The expected number of cars is given as follows: 2.87.

2. The standard deviation of the number of cars is given as follows: 0.94.

The discrete distribution is given from the table in this problem, as follows:

The expected value is given by the sum of each outcome multiplied by it's probability, as follows:

E(X) = 0 x 0.005 + 1 x 0.12 + 2 x 0.125 + 3 x 0.5 + 4 x 0.25 = 2.87.

The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, as follows:

S(X) = sqrt((0-2.87)² x 0.005 + (1-2.87)² x 0.12 + (2-2.87)² x 0.125 + (3-2.87)² x 0.5 + (4-2.87)² x 0.25) = 0.94.

More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440

#SPJ1

The HAACP principle addressed by cooking the duck breast to 165 degrees F is a 'critical limit'.

What is the critical limit?

A critical limit is a value to which a biological, chemical or physical factor must be controlled to prevent food safety hazards. These are the conditions under which potential hazards can be controlled, reduced, or eliminated. They are monitored by observation or measurement, such as measuring the temperature of food storage to avoid spoilage.

Critical limits are based on factors such as:

Temperature, Humidity, Moisture level, pH, Water activity (Aw), Time, Salt concentration, and Preservatives.

Production processes that fail to stay within the bounds of the critical limits must be stopped or the products must be discarded.

Hence the answer is critical limit.

Read more about critical limit at

https://brainly.com/question/27982871

#SPJ4

The 1.5 standard deviations below the mean implies that the Z-score value will be equal to -1.5.

The test score 70 is 1.5 standard deviations below the mean .

We have given that,

The Score standardized test are Normally distributed,

Mean ,μ = 100

Standard deviations, s.d = 20

we have to calculate test score is 1.5 standard deviations below mean.

so, Z- score = -1.5

This is the z-score formula or z-score equation.

Z = (x − μ )/σ

Where, Z--> z-score

x---> the value in question

μ--> mean of the distribution

σ --> standard deviation of the distribution

plugging all known the value in formula

-1.5 = (x- 100)/20

=> -1.5 × 20 = x - 100

=> x = -30 + 100 = 70

So, 70 is the test score that is 1.5 standard deviations from the mean.

To learn more about Z-score , refer :

https://brainly.com/question/24213960

#SPJ4

1. Radius is changing at the rate of 0.00042cm/sec when the radius is 75cm.

2.The implicit differentiation to determine dy/dx of relation sin(2x^2y^3)-3x^3=1 is 9x² - 4xy³ cos(2x² y³) / 6x²y² cos(2x² y³)

1. a) check the image attached

r= radius

h=height

b) Volume of conical tank ,V = (1/3)πr²h

= (1/3)πr²(2r)

V = 2/3πr³

c) Rate of change of volume with respect to time is denoted as dV/dt

Rate of change of radius is denoted as dr/dt

d) V = 2/3πr³

dV/dt =  2/3π (3r²) dr/dt

dV/dt = 2πr²  dr/dt

e) Rate of change in volume, dV/dt = 15cm³ / sec  ,  r =75cm

∴ 15 = 2π(75)² .  dr/dt

dr/dt = 15 / (2π(75)²)

dr/dt = 15/35342.92

dr/dt = 0.00042 cm/sec

∴Radius is changing at the rate of 0.00042cm/sec when the radius is 75cm.

2. sin(2x² y³) - 3x³ = 1

Differentiating :

cos(2x² y³) [2x² y³dy/dt + 2y³ 2x] - 9x² = 0

6x²y² dy/dx . cos(2x² y³) + 4xy³ cos(2x² y³) - 9x² = 0

dy/dx = 9x² - 4xy³ cos(2x² y³) / 6x²y² cos(2x² y³)

Hence, the implicit differentiation to determine dy/dx of relation sin(2x^2y^3)-3x^3=1 is 9x² - 4xy³ cos(2x² y³) / 6x²y² cos(2x² y³)

To know more about volume check the below link:

https://brainly.com/question/1972490

#SPJ4

On solving the given question, by the Help of LaPlace Inverse form we got - [tex]y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]

In terms of its usefulness in resolving physical issues, the Laplace transform is an important transform that is probably second only to the Fourier transform. The Laplace transform is especially helpful in solving linear ordinary differential equations, such as those that arise in the analysis of electronic circuits.

Take Laplace for DE we get -

[tex]L(y)" + 8L(y)' =0\\s^2Y (s) - sy(0) - y'(0) 8(sY(s) - y(0))=0\\Y(s)(s^2 + 8s) + 3s 4 + 24 =0\\Y(s)(s^2 + 8s) = -3s - 28\\Y(s) = \frac{-3s - 28}{(s^2 + 8s) } \\Right Side = \\\frac{-7}{2s} + \frac{1}{2(s+8)} \\ Now taking inverse LaPlace - \\y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]

To know more about LaPlace Transform visit:

https://brainly.com/question/1675085

#SPJ4

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x-6y=24\implies -6y=-x+24\implies y=\cfrac{-x+24}{-6} \\\\\\ y=\cfrac{-x}{-6}+\cfrac{24}{-6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{6}} x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{6}} ~\hfill \stackrel{reciprocal}{\cfrac{6}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{6}{1}\implies {\Large \begin{array}{llll} -6 \end{array}}}}[/tex]

Answer:

-6

Step-by-step explanation:

i just got this question and it wasn’t 1/6 it was -6

Answer:

12

Step-by-step explanation:

(5x-8)/6x

Answer:

one solution

Step-by-step explanation:

the solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is (1, 2 )

Since there is only 1 point of intersection then there is only one solution.

The perimeter of the triangle ABC is 12 units. Hence, option (B) is correct.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given right angle triangle,

The vertices are A(-3, 2), B(-3, -1) and C(1, -1)

The distance between AB = 3,

And the distance between BC = 4

To find the distance of AC, use Pythagoreans theorem,

AC² = AB² + BC²

       = 3² + 4²

       = 9 + 16

AC² = 25

AC = 5

The perimeter of triangle ABC = AB + BC + AC

= 3 + 4 + 5

= 12

The perimeter of the triangle ABC is 12 unit.

To know more about Triangle on:

https://brainly.com/question/2773823

#SPJ1

The two methods are identical because by both using algebra tiles and factoring symbolically, one need to think of the factors.

Factoring simply has to do with the process of writing a number or another mathematical object as a product of different factors, and this is usually smaller or simpler objects that are of the same kind.

Factoring is a common mathematical process that's used for separating the factors, or numbers, which multiply to form another number. Some numbers are affected by multiple factors.

For example, in a situation when you multiply the factors 6 and 4, 8 and 3, 12 and 2, and 24 and 1, you get the number 24.

Algebra tiles are rectangular and square tiles that represent numbers and variables. Using algebra tiles allows us to solve our problems in a more visual manner. It allows us to see exactly what quantities we're dealing with. It's as if we're using building blocks to assist us.

Learn more about factor on:

https://brainly.com/question/24734894

#SPJ1

The critical value for right tailed test is 2.998, the critical value for left tailed test is - 1.717.

First, we must know the following data,

df = degree of freedom = n - 1

α = significance level

Next, t test have three type of test which is

Then, to find critical value using the t distribution table search df value in left column of table and search the α in the top row of the table (depending on the type of test, use one tail row for this case). For example, see attached image.

Thus, the right tailed test critical value is 2.998, and the left tailed test critical value is - 1.717.

Learn more about t distribution table here:

brainly.com/question/22817055

#SPJ4

Answer: Yes, it will overload the truck.

Step-by-step explanation:

To begin, form an algebraic equation.

200(r) + 425(f)

Second, substitute your numbers for the variables.

200(18) + 425(11) = ?

Third, multiply your numbers of fridges by the weight of each.

3600 + 4675 = 8275 is the total

Finally, determine whether or not if it is greater than the weight limit the truck has.

7200 < 8275

Therefore, the total weight is greater than the weight limit.

The correct answer is:

Reject null hypothesis H0, we cannot conclude the proportion of customer complaints is more for the old dough.

As given in the question,

Let us consider proportion of customer complaints with old dough is p₁

And proportion of complaints with new dough is p₂

Difference in proportion of complaints in old and new dough

= p₁ - p₂

Null hypothesis : H0 : p1 ≥ p2

p₁ - p₂  ≥ 0

Alternative hypothesis : Ha : p1 < p2

p1 - p2 < 0

Let 'x' represents the number of complaints

Sample size = n

Sample proportion = x/n

Old dough:

Number of complains with old dough 'x₁' = 6

Number of pizzas with old dough 'n₁' = 385

p₁ = 6/385

   = 0.01558

   = 0.016

New dough:

Number of complains with new dough 'x₂' = 16

Number of pizzas with new dough 'n₂' = 340

p₂ = 16/340

   = 0.04705

   = 0.047

Pooled proportion test:

[tex]\bar{p}[/tex] = (x₁+ x₂)/(n₁ + n₂)

  = (6 + 16)/(385 + 340)

  = 0.0303

  = 0.03

1 -  [tex]\bar{p}[/tex] = 1 - 0.03

      = 0.97

z = (p₁ - p₂)/√[tex]\bar{p}[/tex](1 - [tex]\bar{p}[/tex])(1/n₁ + 1/n₂)

 = (0.016 - 0.047)/√(0.03)(0.97)(1/385 + 1/340)

 = (-0.031)/ √(0.03)(0.97)(0.0026 + 0.0029)

 = - 0.031/√0.00016005

 = -0.031 / .01265

 = -2.45

It is left tailed test.

p value for the area to the left of the z score using normal distribution table:

p value = 0.007143

Significant level 'α' for  95% confidence level:

= 1 - 0.95

= 0.05

Since 0.05 > 0.0.007143

Reject null hypothesis.

Therefore, reject H0, we cannot conclude the proportion of customer complaints is more for the old dough.

The complete question is :

Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p1 be the proportion of customer complaints with the old dough and p2 be the proportion of customer complains with the new dough. Based on a 95% confidence for the difference of the proportions, what can be concluded?

Multiple Choice

A. Reject H0, we can conclude the proportion of customer complaints is more for the old dough

B. Do not reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

C. Do not reject H0, we can conclude the proportion of customer complaints is more for the old dough

D. Reject H0, we cannot conclude the proportion of customer complaints is more for the old dough

Learn more proportion here

brainly.com/question/7096655

#SPJ4

Answer:

cos x = - 0.809, find the values of x. ( - 180≤ x ≥ 180 )

x = - 135° and x = 45°

The dimensions of the can are radius of can = 4cm and

height of can = 78.6cm

What is the volume of cylinder?

A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up.

Thus, the volume of the cylinder can be given by the product of the area of base and height.

Volume of cylinder = πr²h

According to the given question:

We have V cylinder = V = 400cc

We will first find the areas involved

Let x = radius of base then area of the base =  π*x² and this is the area of the top too

For lateral area we need to get h the height of the cylinder as function of x

V = πx²h   ⇒  h= v/πx²    ⇒   h = 400/πx²

Now the total area of the cylinder is:

A(x) = Area of the base + area of the top + lateral area

A(x) = 2*π*x² + 2πx h ⇒  A(x) =  2*π*x² + 2πx (V/πx² )

A(x) =  2*π*x² + 800/x

Taking derivatives:

A´(x)  =  4πx  - 800/x²

A´(x) = 0                4πx  - 800/x² =0     ⇒ πx - 200/x² = 0

( πx³  -  200 )/ x²  = 0      

πx³  -  200 = 0      

x = 4 cm

and h = 400/πx²    ⇒  h = 78.6 cm

To know more about volume of cylinder visit

https://brainly.com/question/24337953

#SPJ4

A regression model can only predict values that are lower or higher than the actual value. As a result, the only way to determine the model's accuracy is through residuals.

What is regression ?

Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aims to establish the nature and strength of the relationship between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).

The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS).

Based on a line of best fit, linear regression determines the linear relationship between two variables.

The slope of a straight line used to represent linear regression thus indicates how changing one variable affects changing another..

In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept. Regression without linearity.

Hence, A regression model can only predict values that are lower or higher than the actual value.

learn more about regression click here:

https://brainly.com/question/28178214

#SPJ4