V=Vw-ce^-kt is the velocity V as a function of time t when wind is blowing 20 knots and after 1 half hour the boat moves at 10 knots
What is acceleration?Acceleration is a vector quantity that is defined as the rate at which an object's velocity varies. When an object's velocity changes, it is said to be accelerating.
On occasion, sports broadcasters will suggest that a person is accelerating if they are traveling quickly. But speed has nothing to do with acceleration. Even while traveling very quickly, a person may not be accelerating. Changing the speed at which an item is travelling is what acceleration is all about. A substance is not accelerating if its velocity is not changing. The information on the right depicts an object that is speeding as it moves northward. Throughout time, the velocity is shifting. Every second, the velocity is changing by a fixed amount of 10 m/s.
How to solve?
Based on the information from the exercise, we have the equation:
dt/dv=k(Vw−V)
where V is velocity of the boat in knots/hour, tt is time in hours, Vw is velocity of wind.
This equation can be written:
dv/dt = k(Vw -V)
dv/Vw-V =kdt
Now, the variables are separated, tt appears only on the right side, and v only on the left. Integrate the left side in relation to v, and the right side in relation to t:
dv/Vw-V =kdt
∫dv/Vw-V =∫kdt
let Vw -V = u
-dv=du
dv= -du
∫-du/u =k∫dt
-ln|u| =kt +C
-ln|Vw-V| = kt + C
V=Vw-ce^-kt
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a farmer plans to enclose a rectangular pasture adjacent to a river. (see figure). the pasture must contain 80,000 square meters in order to provide enough grass for the herd. what dimensions will require the least amount of fencing if no fencing is needed along the river?
Therefore, L has a relative and absolute minimum when x = 400 m
What is Perimeter and Area ?The area is as defined as the amount of space occupied by any shape in two dimensions. Whereas, Perimeter is the boundary or the outline of a flat shape.
Let x = length of the side parallel to the river
y = length of each of the other two sides
Then xy = 80,000, so y = 80,000/x
Minimize: L = length of the fence
L = x + 2y
= x + 160,000/x, where x > 0
L' = 1 - 160,000/x2 = (x2 - 160,000)/x2
L' = 0 when x = 400 or -400
Since x can't be negative, x must be 400.
When 0 < x < 400, L' < 0. So, L is decreasing.
When x > 400, L' > 0. So L is increasing.
Therefore, L has a relative and absolute minimum when x = 400 m
y = 80,000/x = 200 m
The fence is shortest if the side parallel to the river has length 400 m and the other 2 sides each have length 200 m.
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Pls Help me, It's Urgent.
The relationship between RS and RT is RT is the base of this isosceles triangle.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
We know the sum of all the interior angles in a triangle is 180°.
Given, A triangle RST,
So, ∠S + ∠T + ∠R = 180°.
50° + 65° + ∠R = 180°.
∠R = 65°.
This is an isosceles triangle with two similar sides RS and ST.
The relation between RS and RT is RT is the base of this isosceles triangle.
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alent to 5(2x-1)+2(x+4)
Answer:
12x+3
Step-by-step explanation:
distribute the 5 to both the 2x and -1
10x-5
do the same with the the 2. Distribute the 2 to the x and to the 4.
2x+8
10x-5+2x+8
add like terms: the 10x and the 2x are like terms and the -5 and 8 are like terms
12x+3 : the answer
The freshmen competed with the sophomores to see who could raise the most money by recycling. The appropriate design for testing the significance of the difference between the means is a. related-samples t-test. b. independent-samples t-test. c. one-sample i-test. d. z-test
The appropriate design for testing the significance of the difference between the means is called an independent-samples t-test.
The Independent Samples t- test analyzes the means of two separate groups to observe if there is statistical support that the population mean values are statistically substantially different.
A parametric test is said to be the Independent Samples t Test and the Independent t Test is another name for this test. Both examine the significance of a discrepancy between two means.
Independent-sample t tests compare scores on the same variable for the two different groups of cases, whereas paired-sample t tests compare scores on two different variables for the same group of instances.
When doing a t-test, it is usual to make the following assumptions: like the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and an equality of variance in standard deviation.
The appropriate design for testing the significance of the difference between the means is - b. independent-samples t-test.
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Suppose you have two bank accounts. In Account A you deposit $200 In Account B you deposit $400. Account A has a simple interest rate of 3.9%. Account B has a simple interest rate of 2.7%. One year later, you get a bank statement from each bank and one of the statements shows an incorrect amount of interest. The interest for Account A is $7.80. The interest for Account B is $1,080. Which account statement is incorrect? Find the bank's likely error.
The account in which there was a mistake in the calculation of the simple interest is account B.
What is the account statement that is incorrect?We know that the interest is an amount of money that is obtained on top of the initial money that was deposited. The initial money that you deposit in the account is called the principal. The rate is the percentage at which the interest is calculated and the time is the period that has elapsed since the deposit was made.
Given that;
I = PRT/100
I = interest
P = principal
R = rate
T = time
For account A
I = 200 * 3.9 * 1/100
I = $7.8
For account B;
I = 400 * 2.7 * 1/100
I = $10.8
We can see that there must have been a calculation error as the interest in account B was being calculated.
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What is the length of the diameter of the base of the cone?
a
56 cm
b
112 cm
c
139 cm
d
278 cm
The length of diameter of the base of the cone will be 112 cm. Hence, option b is correct.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given information in the question,
Use the equation of Pythagoras's theorem,
106² = 90² + r²
r² = 106² - 90²
r = √3136
r = 56 cm.
Then, the diameter will be,
D = 2r
D = 2(56)
D = 112 cm.
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Use technology to find points and then graph the line y=2x-1, following the instructions below.
Answer: 1st point : 0,-1 second point : 1,0
Step-by-step explanation: the y intercept is -1. The slope is 2/1 rise over run. Two rise 1 over
What does -3+x-1/3x+4 equal
[tex]\frac{2x+3}{3}[/tex]
Step-by-step explanation:1. Combine multiplied terms into a single fraction-3 + x - [tex]\frac{1}{3}[/tex]x + 4
-3 + x + [tex]\frac{-x}{3}[/tex] + 4
2. Add the numbers-3 + x + [tex]\frac{-x}{3}[/tex] + 4
1 + x + [tex]\frac{-x}{3}[/tex]
3. Find common denominator1 + x + [tex]\frac{-x}{3}[/tex]
[tex]\frac{3}{3}[/tex] + [tex]\frac{3x}{3}[/tex] + [tex]\frac{-x}{3}[/tex]
4. Combine fractions with common denominator[tex]\frac{3}{3}[/tex] + [tex]\frac{3x}{3}[/tex] +[tex]\frac{-x}{3}[/tex]
[tex]\frac{3 + 3x - x}{3}[/tex]
5. Combine like terms[tex]\frac{3 + 3x - x}{3}[/tex]
[tex]\frac{3 + 2x}{3}[/tex]
6. Rearrange Terms[tex]\frac{3 + 2x}{3}[/tex]
[tex]\frac{2x+3}{3}[/tex]
Solution:[tex]\frac{2x+3}{3}[/tex]
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Suppose that R(x) is a polynomial of degree 13 whose coefficients are real numbers.
Also, suppose that R(x) has the following zeros.
2, -4, 3i, -4+i
Answer the following.
(a) Find another zero of R(x).
(b) What is the maximum number of real zeros that R(x) can have?
(c) What is the maximum number of nonreal zeros that R(x) can have?
Answer:
(a) Other zeros: 3i and -4-i
(b) 9
(c) 10
Step-by-step explanation:
Given information:
Polynomial function with real coefficients.Degree: 13Zeros: 2, -4, 3i, -4+iPart (a)For any complex number [tex]z=a+bi[/tex], the complex conjugate of the number is defined as [tex]z^*=a-bi[/tex] .
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if R(x) is a polynomial with real coefficients, and 3i is a root of R(x)=0, then its complex conjugate -3i is also a root of R(x)=0.
Similarly, if -4+i is a root of R(x)=0, then its complex conjugate -4-i is also a root of R(x)=0.
Part (b)The degree of the polynomial is the greatest of the exponents of its various terms.
The degree of R(x) with just the given roots (including the complex conjugates) is 6, which includes 2 real zeros.
As the actual degree of R(x) is 13, the maximum number of real zeros would be 7 more than the given real zeros.
Therefore, the maximum number of real zeros that R(x) can have is 9.
Part (c)For each complex root there is also a complex conjugate root.
We have been given 2 complex zeros and 2 real roots, so when we include the complex conjugates, the degree of R(x) is 6.
The actual degree of R(x) is 13, so the maximum number of non-real zeros is 6 more (as they come in pairs) than the already given 4 non-real zeros. Therefore, the maximum number of non-real zeros that R(x) can have is 10.
In triangle def, m∠d = (2x 19)°, m∠e = (3x 24)°, and m∠f = 87°. determine the degree measure of the exterior angle to ∠d. 54° 39° 141° 126°
The exterior angle with angle d is equivalent to 141 degrees, and the value of x is equal to 10.
Explain the term exterior angle?Whenever a side of a triangle is extended, an external angle of the triangle is created.We must keep in mind that the total of all the angles in a triangle equals 180 degrees in order to solve this puzzle.
The given angles are-
m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°.Using that formula in this case;
Thus, sum of all angles is 180°.
m < d + m < e + m < f = 180°
(2x + 19)° + (3x + 24)° + 87° = 180°
x = 10°
But if angle D is on a straight line, it is possible to find its exterior angle because angle D plus its exterior angle add up to 180 degrees.
Suppose y = external angle.
m < d + y = 180°
2x + 19 + y = 180°
And x = 10°
2(10) + 19 + y = 180°
y = 141°
Thus, the measure of the degree measure of the exterior angle is found as 141°.
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The correct question is-
In triangle DEF, m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°. Determine the degree measure of the exterior angle to ∠D.
54°
39°
141°
126°
A bus leaves Deltaville at 11:32 it’s a travels at an average speed of 42 km/h if it arrives in eastwich at12:42 what is the distance between the two towns ?
Help pls I have a test after tomorrow
The distance between the two towns is 49 km
What is average speed?
Average speed is calculated by dividing distance by time (eg miles/hour).
The entire distance traveled by the object in a specific amount of time is its average speed. A scalar quantity, average speed, exists. The magnitude serves as its representation, and it lacks direction.
A body's average speed is its mean value over a given amount of time. Since a moving body's speed fluctuates over time and is not constant, an average speed formula is required. The total time and total distance numbers can be used, even with fluctuating speed, and with the aid of the average speed formula, we can get a single value to represent the entire motion.
Difference in times = 12:42 - 11:32 = 1.17 hours
Formula:
Distance = speed * time
= 42 * 1.17
= 49 km
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determine the value(s) of the local extrema you identified in the previous step. write dne for all extrema that do not exist. separate multiple answers with a comma, if necessary.
Local minimum at: (1, -7) , (3, -7).
Local maximum at : DNE
What to find: Local extrema.
To solve the given problem, we will use the steps below:
Local extrema:
A local extremum of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.
OR
Local extrema on a function are points on the graph where the -coordinate is larger (or smaller) than all other -coordinates on the graph at points ''close to'' . A function has a local maximum at , if for every near .
Locate the local extremum from the graph.
From the graph given, we have two local minimum.
At x = 1, f(1) =-7
Hence, the local minimum is (1, -7)
At x=3, f(3) =-7
Hence, the local minimum is ( 3, - 7)
Therefore, the local minimum are (1, -7) , (3, -7).
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Alejandro has a computer support business. He estimates that the cost to run his business can be represented by X = 48 x + 500, where x is the number of customers. He also estimates that his income can be represented by R = 65 x - 145. How many customers he will need in order to break even?
The number of customers Alejandro will need in order to break even is 38 customers.
How to find the number of customers to break even?Given data:
Cost of business = 48 x + 500
Income = R = 65 x - 145
Let x is the number of customers.
Income equation
R= 65x- 145
Substitute 48x + 500 for y
48x + 500 = 65x -145
Substract 48x from both side
500 = 17x - 145
Add 145 to each side
645 = 17x
Divide both side by 17x
x =645 /17
x = 37.9
x = 38 customers (Approximately)
Therefore the number of customers is 38 customers.
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Write and solve an equation for the following situation: mia was getting ready to go back to school. She purchased 7 pens and a binder that cost $1. 25. She spent a total of $7. 90. How much did each pen cost?.
Answer: $0.95
Step-by-step explanation:
7.90 - 1.25 = 6.65
6.65 divided by 7 = 0.95
An ant travels at a constant rate of 30 cm every 2 minutes. at what pace does the ant travel per centimeter?
The ant travels at a pace of 1/15 mins per centimeters.
What is Pace?
Meaning of pace is rate of movement.
Pace is the inverse of speed.
If speed is measured in units of distance per unit of time then pace is measured in units of time per unit of distance.
We know speed is total distance travelled in the total time taken
speed = distance/time
According to the given question:
Ant travels 30cm in every 2 minutes
Distance travelled by ant = 30 cm
Time taken to travel this distance = 2 minutes
Therefore, speed of the ant is
30/2 = 15 cm per min
Now pace = inverse of speed
pace = 1/15 min per cm
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3/4 - 1/8 how much is it? help me please
Answer:5/8
Step-by-step explanation:
[tex]\begin{gathered} \boxed{ \sf \frac{3}{4} - \frac{1}{8}} = \\ \\ \sf \frac{8 \div 4 \times 3 - 8 \div 8 \times 1}{8} = \\ \\ \sf\frac{6 - 1}{8} = \\ \\ \sf \boxed{ \sf\frac{5}{8}} \end{gathered}[/tex]
Therefore, the result of this subtraction of fractions is five eighths.
How to subtract unlike fractions:
Heterogeneous fractions are fractions that have different denominators.
To subtract heterogeneous fractions we follow these steps:
We find the common denominator, which is the least common multiple of the denominators. We divide the common denominator by the other denominator and multiply by the numerator.We will write the above results as numerators with the subtraction sign between them.We subtract the numerators.We simplify the result if possible.The Alpha.a family is traveling due west on a road that passes a famous landmark. at a given time the bearing to the landmark is n 62° w, and after the family travels 9 miles farther the bearing is n 38° w. what is the closest the family will come to the landmark while on the road? (round your answer to two decimal places.) mi
The closest distance the family will come to the landmark while on the road is 12.03 miles.
Here, the situation represented in the question can be depicted as shown in the image below.
The family moves from F1 to F2 as the angle changes from 62 to 38.
Now, using trigonometric ratios in the smaller triangle we have-
Cot 62 = X/Y
X = Y Cot 62
Similarly, Cot 38 = (X + 9)/ Y
Substituting the value of X in the above equation we get-
Y Cot 38 = (Y Cot 62 + 9)
Y Cot 38 - Y Cot 62 = 9
Y(Cot 38 - Cot 62) = 9
Y = 9/ (Cot 38 - Cot 62)
Y = 9/ (1.2799 - 0.5317)
Y = 9/ 0.7482
Y = 12.028
Thus, the closest distance the family will come to the landmark while on the road is 12.03 miles.
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Where is the hole for the following function located? f (x) = startfraction x + 3 over (x minus 4) (x + 3) endfraction.
A hole can be found at x = -3.
What is unitary method?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
When the denominator is zero, the function will have a hole at the x-values and become undefined. In a language of mathematics:
There are two answers to this equation:
The function will have a gap at those x-values.
Hence, A hole can be found at x = -3.
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if θ measures 0 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car?
The measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car is 0 or origin.
Terminal ray:
In geometry, terminal ray refers the ray in the terminal position, after the rotation, is called the terminal side of the angle.
Given,
Here we need to find if θ measures 0 radians, then the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car.
While we looking into the given question,
the value of θ = 0 radians
And the Slope of terminal ray is calculated by using the formula,
=> tan θ
Then Slope = tan 0
Now, by using radians calculator,
=> tan 0 = 0
Therefore, the slope of the terminal ray is 0 which means the origin of the line.
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Which answers are equivalent to the ratio 13 to 25?
Select all that apply.
13:25
25/13
25:13
13/25
Please help I'm majorly confused!!
The ratio of 13 to 25 is 13/25 because 13 is a prime number
RatioThe ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related. For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole. For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.
In this question, we have to find the ratio between 13 to 25
To do this, we simply divide 13 by 25
13÷25 = 13/25
This is so because the two numbers are not divisible as 13 is a prime number.
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7. Gabriela goes to dinner with some
friends and pays the bill. Each person
orders a meal that cost $14.95. Gabriela
gave the server a $11.96 tip. The total bill,
including the tip, was $71.76. How many
friends did Gabriela pay for?
F(x)=3x
3
kx−5, and
x
1
x1 i a factor of
f
(
x
)
f(x), then what i the value of
k
k?
The function will have a value of 0 at x = 1. In that case, the variable "k" will have a value of 2.
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Given f(x) = 3x³ + kx – 5, and the factor of the given function is (x – 1).
If the factor (x – 1) is zero. Then the value of the function will be zero.
x – 1 = 0
x = 1
At x = 1, the value of the function will be zero. Then the value of the variable 'k' will be calculated as,
f(1) = 3(1)³ + k(1) – 5
0 = 3 + k – 5
k = 5 – 3
k = 2
The function's value will be 0 at x = 1. The variable "k" will then have a value of 2.
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write the equation of the parabola in vertex form
vertex (4,4), point (3,-2)
f(x)=?
Hence, the equation of parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] is
[tex]y=-6(x-4)^2+4[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
The parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] .
Here [tex](x,y)=(3,-2)[/tex] and [tex](x_1,y_1)=(4,4)[/tex]
The general formula is
[tex]y=a(x-x_1)^2+y_1[/tex] ....[tex](1)[/tex]
Substitue the given values in the equation [tex](1)[/tex], we get
When [tex](x_1,y_1)=(4,4)[/tex]
[tex]y=a(x-4)^2+4[/tex]
When [tex](x,y)=(3,-2)[/tex]
[tex]-2=a(3-4)^2+4\\\\-2=a(-1)^2+4\\\\-2=a+4\\\\a+4+2=0\\\\a+6=0\\\\a=-6[/tex]
So, the equation is of thr form
[tex]y=-6(x-4)^2+4[/tex]
Hence, the equation of parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] is
[tex]y=-6(x-4)^2+4[/tex].
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if the racetrack publishes that the odds in favor of a horse winning a race are 2 to 6, what is probability that the horse will not win the race? a) 0.1667 b) 0.2500 c) 0.7500 d) 0.0833 e) 0.5000 f) none of the above.
The probability that the horse will not win the race is 0.7500.
The mathematical branch known as probability deals with determining the possibility of an event occurring. The conversions between probability and odds are feasible. This is because the odds are determined by dividing the likelihood that an event will occur by the likelihood that it won't.
Here, the odds of a horse winning a race are given as 2 to 6. Then, the probability of winning the horse race is calculated as,
[tex]\begin{aligned}\text{Odds}&=\frac{p}{1-p}\\\frac{2}{6}&=\frac{p}{1-p}\\2(1-p)&=6p\\2-2p&=6p\\2&=6p+2p\\8p&=2\\p&=\frac{2}{8}\\&=\frac{1}{4}\end{aligned}[/tex]
Then, the probability of not winning the horse race is,
[tex]\begin{aligned}q&=1-p\\&=1-\frac{1}{4}\\&=\frac{3}{4}\\&=0.75\end{aligned}[/tex]
The answer is 0.75. Therefore, the correct option is option c.
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if it is known that the lifetime of a light bulb has an exponential distribution with parameter 1/250, what is the probability the bulb works
The probabilities for the given hours are,
[tex](a) Pr(100 < x < 250) = 0.302440605\\(b) Pr(\frac{x > 300}{x > 200})=0.670320046\\ (c) Pr(x > 100) = 0.670320046[/tex]
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
P.D.F , [tex]f(x) = \frac{1}{250}e^\frac{-x}{250} ; x \geq 0\\[/tex]
C.D.F , [tex]F(X) = 1-e^\frac{-x}{250} ;x \geq 0[/tex]
(a)
[tex]Pr(100 < x < 250) = F(250) - F(100)\\Pr(100 < x < 250) = (1-e^\frac{-250}{250})-(1-e^\frac{100}{250} )\\ Pr(100 < x < 250) = (e^\frac{-2}{5}-e^-^1) \\ Pr(100 < x < 250) = 0.670320046 - 0.367079441\\ Pr(100 < x < 250) = 0.302440605[/tex]
(b)
[tex]Pr(\frac{x > 300}{x > 200}) = \frac{Pr[(x > 300) intersection(x > 200)]}{Pr(x > 200)} \\ Pr(\frac{x > 300}{x > 200}) = \frac{Pr(x > 300)}{Pr(x > 200)} \\Pr(\frac{x > 300}{x > 200}) = \frac{1 - F(300)}{1-F(200)} \\Pr(\frac{x > 300}{x > 200}) = \frac{e^\frac{-300}{250} }{e^\frac{-200}{250} } \\Pr(\frac{x > 300}{x > 200}) = e^\frac{-2}{5} \\Pr(\frac{x > 300}{x > 200})= 0.670320046[/tex]
(c)
[tex]Pr(x > 100) = 1-Pr(x < 100) = 1- F(100) = e^\frac{-100}{250} = e^\frac{-2}{5} = 0.670320046[/tex]
Hence, the probabilities for the given hours are,
[tex](a) Pr(100 < x < 250) = 0.302440605\\(b) Pr(\frac{x > 300}{x > 200})=0.670320046\\ (c) Pr(x > 100) = 0.670320046[/tex]
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Complete question:
Complete question is attached below,
please help i cant solve this problem
Which best describes the meaning of the statement "If A, then B'?
Answer: If A is true, then B must be true.
#2 Which equation is the correct slope intercept form equation for the
table below?
X
Y
3
5
y=2x-11
y= 2x + 11
y= 11x-2
y=-2x +11
6
-1
q
-7
12
- 13
9 points
what is the largest area of a rectangle that can be inscribed in a semicircle of radius 6? round to the nearest whole numb
The largest area of a rectangle that can be inscribed in a semicircle of radius 6 is 36.
What is the semicircle?
A semicircle is a one-dimensional locus of points that makes up one-half of a circle in mathematics. A semicircle's whole arc is always 180 degrees long. It just has one symmetry line.
The equation of the semicircle is
x² + y² = r² .............(1)
The area of the rectangle is
A = 2xy ..................(2)
From equation (1), we get
y² = r² - x²
y = √r² - x²
Plugging this value in equation (2)
A = 2x√r² - x²
Differentiating wrt. x using the product rule,
[tex]\frac{dA}{dx} = 2\sqrt{r^2 - x^2} - 2\frac{x^2}{\sqrt{r^2 - x^2} }[/tex]
[tex]\frac{2r^2 - 4x^2 }{\sqrt{r^2 - x^2} }[/tex]
The critical points are when
[tex]\frac{dA}{dx} = 0[/tex]
that is
[tex]\frac{2r^2 - 4x^2 }{\sqrt{r^2 - x^2} } = 0[/tex]
r² = 2x²
x = r/√2
Then,
y = √r² - x²
= √r² - (r/√2)²
= r/√2
The maximum area is
A = 2 . r/√2 . r/√2 = r²
A = r² = (6)² = 36
Hence, the largest area of a rectangle that can be inscribed in a semicircle of radius 6 is 36.
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f(1) = 12 +10 |1| me pueden ayudar porfavor
Answer:
Your answer is 22.
Tu respuesta es 22. Además, no hablo español, usé Translate