A continuous random variable X that can assume values between x=4 and x=8 has a densty function given by f(x)= 4
1
​ , (a) Show that the area under the curve is equal to 1. (b) Find P(7 3
​ ( 4
1
​ )dx=∣ 8
=1 B. ∫ −[infinity]
[infinity]
​ ( 4
1
​ )dx=[infinity] [infinity]
[infinity]
​ =1 C. ∫ 4
4
​ ( 4
1
​ )dx=4 4
4
​ =1 D. ∫ 7
8
​ ( 4
1
​ )dx= 7
8
​ =1

(a) Since f is exponential, we can write f(t) = \(Ce^{kt}\) for some constants C and k. We can use the information f(6) = 13 and f(14) = 23 to solve for C and k:

f(6) = \(Ce^{6K}\) = 13

f(14) = \(Ce^{14k}\) = 23

Now that we have divided both equations, we have:

f(14)/f(6) = \(Ce^{14K} / Ce^{6K}\)

                 = \(e^{8k}\)  = 23/13

When we take the natural logarithm of both sides, we obtain:

8k = ㏑ 23/13

k = 1/8 ln (23/13)

Substituting this value of k into the first equation, we get:

\(13 = Ce^{6k} = Ce^{6*1/8 ln (23/13)} = C(23/13)^{3/4}\)

Solving for C, we get:

\(C = 13/(23/13)^{3/4} = 13 (13/23)^{3/4}\)

Therefore, the formula for f(t) assuming f is exponential is:

\(13 (13/23)^{3/4} e^{t/8ln(23/13)}\)

(b) To find \(f^{-1}(P)\), we solve for t in the equation P = f(t):

\(P = 13(13/23)^{3/4} e^{t/8ln(23/13)} = t = 8 ln (P/13(13/23)^{3/4} ) ln(23/13)\)

Therefore, the formula for \(f^{-1} (P)\) is:

\(f^{-1} (P) = 8ln (P/ 13(13/23)^{3/4} ) ln (23/13)\)

(c) To find f(50), we simply plug in t = 50 into the formula for f(t):

\(f(50) = 13 (13/23)^{3/4} e^{50/8ln(23/13)} = 39\)

(rounded to the nearest whole number)

(d) To find \(f^{-1}(50)\) , we plug in P = 50 into the formula for \(f^{-1} (P)\):

\(f^{-1}(50) = 8 ln (50/13(13/23)^{3/4} ) ln (23/13) = 35.7\)

(rounded to at least one decimal)

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In order to calculate the slope of a line that passes through the points (-2, 6) and (8, 4), we can use the formula:

Where (x1, y1) and (x2, y2) are the points coordinates. So we have:

So the slope of the line is -1/5.

Answer:

9.3%

Step-by-step explanation:

Answer:

Let's denote the total cost as C and the number of hours as h. The equation to model this relationship can be written as:

C = 5 + 0.25(h - 2)

The first part, 5, represents the flat rate for 2 hours or less. The second part, 0.25(h - 2), represents the additional hours beyond 2 hours, where each hour costs $0.25.

To calculate the cost of parking for 10 hours, we can substitute h = 10 into the equation:

C = 5 + 0.25(10 - 2)

C = 5 + 0.25(8)

C = 5 + 2

C = $7.00

Therefore, you would have to pay $7.00 to park for 10 hours.

To find out how many hours $10 will buy, we can set the equation equal to $10 and solve for h:

10 = 5 + 0.25(h - 2)

0.25(h - 2) = 10 - 5

0.25(h - 2) = 5

h - 2 = 5 / 0.25

h - 2 = 20

h = 20 + 2

h = 22

Therefore, $10 will buy you 22 hours of parking

Given:

Jennifer writes the letters M-O-N-T-A-N-A on cards.

To find:

The probability of picking an N.

Solution:

We have,

Total number of cards = 7

Total number of cards with letter N = 2

Now, the probability of picking an N is:

\(\text{Probability}=\dfrac{\text{Number of cards with letter N}}{\text{Total number of cards}}\)

\(\text{Probability}=\dfrac{2}{7}\)

Therefore, the probability of picking an N is \(\dfrac{2}{7}\).

Option C, y = 15sin(π/8x), models the tide height after 12am with a sinusoidal wave, an amplitude of 15, and a period of 16 hours.

The function y = 15sin(π/8x) represents a sinusoidal wave with an amplitude of 15. The coefficient of x, π/8, determines the period of the wave. Since low tide occurs at 4am and high tide at 12pm, the time span is 8 hours (12pm - 4am = 8 hours).

The period of the wave is calculated by 2π divided by the coefficient of x, which gives 2π/π/8 = 16. Therefore, the function completes one cycle every 16 hours, representing the tide pattern.

The additional term "+ 7.5" shifts the wave upwards by 7.5 feet, accounting for the average water level.


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Given that 235 out of 1100 people said that they had heard of the new beverage, we can say that the population proportion of people who know of the beverage is not 0.18 using the z test.

A z test of proportion will assess whether or not a sample from a population represents the true proportion of the entire population.

Here we want to test

H0: population proportion of people who knew the new drink was 0.18.

(p = 0.18)

H1: population proportion of people who knew the new drink wasn't 0.18.

(p ≠ 0.18)

The appropriate test statistic is:

z =  \(\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }\)

where \(p_0\) is the population proportion under null hypothesis i.e., 0.18 here.

p is the sample proportion given.

In the given question, 235 out of 1100 people said they had heard of the new beverage.

So, p = 235/1100 = 0.2136

n = sample size = 1100 for the given question.

Thus, z = \(\frac{0.213-0.18}{\sqrt{\frac{0.18(1-0.18)}{1100} } }\) = 2.9

Using the standard normal table, we should reject the null hypothesis at 10% level of significance if z calculated value is greater that 1.28

Since, 2.9 > 1.28, we shall reject the null hypothesis at 10% level of significance.

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Answer:

12x+16-4y

Step-by-step explanation:

Answer:

lets start with x = 5x+7x=12x

now y = 2y-6y= -4y

now reg numbers = 8+8=16

now add all of them not litteraly add by add as in make them into a expression

so

12x-4y+16

Answer: A, y=1/2x+2

Step-by-step explanation:

The line meets the y-intercept at (0,2), and the slope is 1/2.

The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05  and the number of miles is 13.

Here we will use the linear equation concept to solve the problem. Since we don't know the number of miles represent it with a variable 'x' and form a Linear equation according to the given condition in the problem. Now solve the resultant equation for the value of variable 'x'  

Here we have  

The taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. the total fare was $33.05, not including the tip.    

Let 'x' be the number of miles in the taxi ride

Total cost to travel 'x' mile = 3.80 + 2.25(x)  

From the given data, the total fare was $33.05

=> 3.80 + 2.25(x) = 33.05

=> 2.25x = 33.05 - 3.80

=> 2.25x = 29.25

=> x = 29.25/2.25

=> x = 13

Therefore,

The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05  and the number of miles is 13.

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9514 1404 393

Answer:

  x = 22

Step-by-step explanation:

When lines l and m are parallel, the marked angles are supplementary.

  (2x -3)° +(6x +7)° = 180°

  8x +4 = 180 . . . . . . . . . . . divide by °, collect terms

  8x = 176 . . . . . . . . . . subtract 4

  x = 22 . . . . . . . . divide by 8

d) Rolling an even number that is less than 2 is not a valid outcome when rolling a die.therefore, option d) is correct.

The outcome that is not possible is (d) rolling an even number that is less than 2 on a die.

A standard die has six sides numbered from 1 to 6, and all the even numbers on a standard die are 2, 4, and 6.

The statement "rolling an even number that is less than 2" contradicts the fact that the lowest even number on a die is 2.

Thus, it is not possible to roll an even number that is less than 2 on a standard die, making it an invalid outcome.

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Answer:

a=42°

Step-by-step explanation:

90-48=42

C+b=180

I'm going to have to think about c and b. It has been too long since I have done this. Sorry! Hope this helps get you started though!  

Jeff had to borrow money over an extended period of time to pay for a car. Therefore, he needed to set up a loan agreement with a lender.

A loan agreement is a formal document that specifies the terms and conditions of a loan. This document lays out the loan's payment schedule, interest rate, fees, and other details. When someone like Jeff needs to borrow money to buy a car, they may choose to use a personal loan. A personal loan is a type of unsecured loan that doesn't require collateral. When taking out a personal loan, you agree to pay back the borrowed amount plus interest over a set period. In order to secure a loan, Jeff needs to provide proof of income and creditworthiness. He needs to show that he is able to pay back the loan and is not a risky borrower. The lender will review his application and decide whether or not to grant him the loan.

In summary, Jeff had to set up a loan agreement with a lender to borrow money over an extended period of time to pay for his car. A loan agreement outlines the details of the loan, including the payment schedule, interest rate, fees, and other terms and conditions. By securing a personal loan, Jeff was able to buy the car he needed and make payments over time.

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Answer:

46

Step-by-step explanation:

length x width x height

7 x 5 x 3

Answer: surface area = 142

Volume = 105

* make sure to add labels (units^2, etc.)

Step-by-step explanation:

Area = length x height

Volume = length x width x height

Answer: it’s A..

Step-by-step explanation:

No, because it fails the vertical line test.

This region is bounded by the lines and the non-negativity constraints (x₁ ≥ 0, x₂ ≥ 0).

Let's start by graphing the constraint inequalities:

4x₁ + x₂ ≤ 100

x₁ + x₂ ≤ 80

x₁ ≤ 40

x₁ ≥ 0, x₂ ≥ 0

First, plot the lines corresponding to the equations:

4x₁ + x₂ = 100 (let's call it line A)

x₁ + x₂ = 80 (line B)

x₁ = 40 (line C)

Now, let's shade the feasible region determined by the constraints. This region is bounded by the lines and the non-negativity constraints (x₁ ≥ 0, x₂ ≥ 0).

The feasible region will be the area of the graph that satisfies all the constraints and lies within the boundaries.

Once we have the feasible region, we can identify the optimal solution point by evaluating the objective function at each corner point of the feasible region.

Finally, we select the corner point that gives the maximum value of the objective function.

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When the time needed to complete a final examination is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes, a) The probability of completing the exam in one hour or less is 0.0087.  b. The probability that a student will complete the exam in more than minutes 60 but less than minutes 75 is 0.3009. c. The number of students expected to be unable to complete the exam in the allotted time is 6 students.

Normal distribution refers to a probability distribution that is symmetric about the mean, illustrating that that data that is near the mean appear are more frequent than data that is far from the mean. In graphical form, the normal distribution forms a bell curve.

In the given normally distributed data with the mean µ = 79 minutes and standard deviation σ = 8 minutes:

a) The probability of completing the exam in an hour or less is given by P(x≤60).

Standardizing the 60 minutes to determine z:

z = (x - µ)/ σ = (60 – 79)/8 = - 2.375

Hence, P(x≤60) = P(z≤-2.375)

From the normal probability table, the probability is:

P(x≤60) = P(z≤-2.375) = 0.0087

b) The probability of completing the exam in more than 60 minutes but less than 75 minutes is given by P(60 < x <75)

Standardizing the 60 and 75 minutes to determine z:

z = (x - µ)/ σ = (60 – 79)/8 = - 2.375

z = (x - µ)/ σ = (75 – 79)/8 = - 0.5

Hence, P (60 < x <75) = P(-2.375 < x < -0.5)

From the normal probability table, the probability is:

P (60 < x <75) = P (-2.375 < x < -0.5) = P(z< -0.5) – P(z <-2.375)

= 0.30954 - 0.00866 =  0.30088 = 0.3009

c) The probability of completing the exam in more than 90 minutes or less is given by P( x ≤ 90)

Standardizing the 90 minutes to determine z:

z = (x - µ)/ σ = (90 – 79)/8 = 1.375

Hence. P( x ≤ 90) =  P(z  ≤  1.375)

From the normal probability table, the probability is:

P (x ≤ 90) = P(z  ≤  1.375) = 0.91621

It means that 91.62% of the class will finish just in time.

Hence, in a class of 60 students, the number of students who will finish in the allotted time is 91.62%* 60 ≈ 54.

The number of students expected to not finish in time = 60 - 54 = 6 students.

Note: The question is incomplete. The complete question is: The time needed to complete a final examination in a particular college course is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes. Answer the following questions. a. What is the probability of completing the exam in one hour or less (to 4 decimals)? b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)? c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to nearest whole number)?

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∫_A^B ∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr dθ.

This represents the full iterated integral for F_sav over the given solid cylinder.

(a) The iterated integral for F_sav with the given limits of integration is as follows:

∫∫∫_W (10%)(x^2 + y^2 + z^12) dz dr dθ,

where the limits of integration are A = 0, B = C = 0, D = 6, and E = -1.

(b) To evaluate the integral, we begin with the innermost integration with respect to z. Since z ranges from -1 to 6, the integral becomes:

∫∫_D^E (10%)(x^2 + y^2 + z^12) dz.

Next, we integrate with respect to r, where r represents the radial distance from the z-axis. As the solid cylinder is centered about the z-axis and has a base radius of 6, r ranges from 0 to 6. Thus, the integral becomes:

∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr.

Finally, we integrate with respect to θ, where θ represents the angle around the z-axis. As the cylinder is symmetric about the z-axis, we integrate over a full circle, so θ ranges from 0 to 2π. Hence, the integral becomes:

∫_A^B ∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr dθ.

This represents the full iterated integral for F_sav over the given solid cylinder.

The problem asks for the iterated integral of F_sav over the solid cylinder W. To evaluate this integral, we use the cylindrical coordinate system (r, θ, z) since the cylinder is centered about the z-axis. The function inside the integral is 10% times the sum of squares of x, y, and z^12. By integrating successively with respect to z, r, and θ, and setting appropriate limits of integration, we obtain the final iterated integral. The integration limits are determined based on the given dimensions of the cylinder.

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Answer: The value of x is 20

Step-by-step explanation:

The angles are vertical angles so they have to equal each other in other to solve for x.

(x + 40) = 3x          

x + 40 = 3x     subtract x from both sides

-x            -x

40 = 2x     Divide both side by 2

x= 20

Step-by-step explanation:

f(2) = -3 means when x is 2, the f(x) is equal to -3. To solve b, we plugin in 2 into x, and plugin -3 for f(x), we get

f(x) = 3x + b

- 3 = 3(2) + b

- 3 = 6 + b

  b = -9

The mean (μ) of a hypergeometric distribution is given by: 8.181

The standard deviation (σ) of a hypergeometric distribution is given by:

1.644

Here, we have,

To find the mean value and standard deviation of the number of projects not among the first 15 that are from the second section, we need to calculate the probabilities for different numbers of projects from the second section.

Let's denote:

N1: Number of students in the first section (25)

N2: Number of students in the second section (30)

N: Total number of projects graded (15)

To calculate the probability of exactly 10 projects being from the second section, we can use the hypergeometric distribution.

The formula for the hypergeometric distribution is:

P(X = k) = (C(N2, k) * C(N1, N - k)) / C(N1 + N2, N)

Where:

X is the random variable representing the number of projects from the second section among the first 15 graded projects.

C(a, b) is the binomial coefficient, also known as "a choose b."

Using this formula, we can calculate the probability for X = 10:

P(X = 10) = (C(30, 10) * C(25, 15 - 10)) / C(55, 15)

Next, we can calculate the mean and standard deviation.

The mean (μ) of a hypergeometric distribution is given by:

μ = N * (N2 / (N1 + N2))

  = 15 * (30 / (25 + 30) )

  = 8.181

The standard deviation (σ) of a hypergeometric distribution is given by:

σ = √(N * (N1 / (N1 + N2)) * (N2 / (N1 + N2)) * ((N1 + N2 - N) / (N1 + N2)) )

  = √(15 * (25 / (25 + 30)) * (30 / (25 + 30)) * (25+30 - 15 )/(25+30)) )

  = 1.644

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complete question:

An Instructor Who Taught Two Sections Of Engineering Statistics Last Term, The First With 25 Students And The Second With 30, Decided To Assign A Term Project. After All Projects Had Been Turned In, The Instructor Randomly Ordered Them Before Grading. Consider The First 15 Graded Projects. (A) What Is The Probability That Exactly 10 Of These Are From The

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 30, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects.

what are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section?

On solving the provided question, we can say that in this circle the radius is \(7\pi /6\) area = \(\pi r^2\) =3.14*7/6*2/6*3.14*3.4 = 13.0365822222 = 12 units sq.

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

in this circle the radius is \(7\pi /6\)

area = \(\pi r^2\) =3.14*7/6*2/6*3.14*3.4 = 13.0365822222 = 12 units sq.

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the dog

Step-by-step explanation:

lkjnijbn

Answer:

Step-by-step explanation:

from the sign it's a right angle, so 90°

90 = x - 8 + 6x

90 + 8 = 7x

98 = 7x

x = 98 : 7

x = 14

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

check

90 = 14 - 8 + 6 * 14       (remember pemdas)

90 = 14 - 8 + 84

90 = 90

the answer is good

Find angle 1

x - 8

14 - 8 =

6°

Find angle 2

6x

6 * 14 = 84°

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

check

84 + 6 = 90°

the answer is good

Answer:

\(\textsf{a)} \quad \textsf{Equation}: \quad \boxed{x-8+6x=90}\)

\(\begin{aligned}\textsf{b)} \quad m \angle 1 & =\boxed{6^{\circ}}\\ m \angle 2 & =\boxed{84^{\circ}}\end{aligned}\)

Step-by-step explanation:

From inspection of the given diagram, the sum of the two angles is 90° (indicated by the right angle sign):

\(\implies m \angle 1+m \angle 2=90^{\circ}\)

\(\implies (x - 8)^{\circ} + (6x)^{\circ} = 90^{\circ}\)

\(\implies x-8+6x=90\)

\(\textsf{Equation}: \quad \boxed{x-8+6x=90}\)

To find the measure of each angle, solve the equation for x:

\(\implies x-8+6x=90\)

\(\implies x+6x-8=90\)

\(\implies 7x-8=90\)

\(\implies 7x-8+8=90+8\)

\(\implies 7x=98\)

\(\implies \dfrac{7x}{7}=\dfrac{98}{7}\)

\(\implies x=14\)

Substitute the found value of x into the expression for each angle:

\(\implies m \angle 1=(x-8)^{\circ}\)

\(\implies m \angle 1=(14-8)^{\circ}\)

\(\implies m \angle 1=\boxed{6^{\circ}}\)

\(\implies m \angle 2=(6x)^{\circ}\)

\(\implies m \angle 2=(6 \cdot 14)^{\circ}\)

\(\implies m \angle 2=\boxed{84^{\circ}}\)

Answer:

D

Step-by-step explanation:

It is exponential decay if it was growth then it would say 1+0.12 not 1-0.12

In a Linear Programming problem, the objective function line is moved in the direction that reduces cost.

Linear Programming (LP) is an operation research approach used to determine the best outcomes, such as optimum profit, minimum cost, or maximum yield, given a set of constraints represented as linear relationships. Linear programming's fundamental idea is to find the best value of a linear objective function that takes into account a variety of constraints that are linear inequalities or equations. The goal of the constraints is to restrict the values of the decision variables. A linear programming problem consists of a linear objective function and linear inequality constraints, as well as decision variables. In a Linear Programming problem, we try to maximize or minimize a linear objective function, which represents our target. This objective function is expressed as a linear equation consisting of decision variables, each of which has a coefficient. Linear programming's ultimate goal is to find values of the decision variables that maximize or minimize the objective function while still satisfying the system of constraints we're working with. In this case, the objective function line is moved in the direction that reduces cost, which means we are minimizing the cost. We do this by moving the objective function line down towards the minimum point. This is the point where the objective function has the smallest possible value that meets all of the constraints.

Thus, in a Linear Programming problem, the objective function line is moved in the direction that reduces cost.

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Answer:

97/4 = 24.25 hours

Step-by-step explanation:

68 = 17x

x = 68/17 = 4

The Lewis dot structure for BF2 is:

 F     B     F

  \   /    

   B    

  /   \

 F     B     F

In this molecule, there are three atoms (one boron and two fluorine) and a total of 12 valence electrons. Boron is in group 3, so it has 3 valence electrons, while each fluorine atom has 7 valence electrons.

To form the Lewis dot structure, we first place the atoms in a linear arrangement. Each fluorine atom shares one electron with the boron atom, giving a total of two shared electrons (or one bond) between the boron and each fluorine atom. This gives us a total of four electrons (or two bonds) between the boron and the two fluorine atoms.

The remaining four electrons are placed as nonbonding electron pairs around each fluorine atom to satisfy the octet rule. Therefore, there are a total of two bonding domains and two nonbonding electron domains around the boron atom. The electron domain geometry is tetrahedral, and the molecular geometry is linear.

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