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Answer:

  385.7 ft

Step-by-step explanation:

The relation between speed, distance, and time is ...

  distance = speed × time

The speed is given in miles per hour, but the time is given in seconds and the distance is wanted in feet. This suggests a conversion of speed to feet per second is appropriate.

  \(\dfrac{52.7\text{ mi}}{\text{h}}\times\dfrac{1\text{ h}}{3600\text{ s}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}=\dfrac{52.7\cdot22\text{ ft}}{15\text{ s}}=77.29\overline{3}\text{ ft/s}\)

The distance traveled is the product of this speed and the time period.

  \(\dfrac{77.29\overline{3}\text{ ft}}{1\text{ s}}\times4.99\text{ s}=385.6937\overline{3}\text{ ft}\approx\boxed{385.7\text{ ft}}\)

Answer:

Step-by-step explanation:

5. y=40x

6. y=2.2x

Answer:

C) No solution

Step-by-step explanation:

This has no solution, as it simplyfies to 0 = 0:

-8x + 6 = 1 - 8x + 5

8x - 8x  = 1 + 5 - 6

8x - 8x = 6 - 6

0 = 0

The organizer  demanded to collect 74 pieces of artwork per day for the remaining time to meet the  needed aggregate of 1,230 pieces.    

To find out how  numerous pieces of artwork the organizer  demanded to collect per day for the remaining time, we need to calculate the total number of pieces of artwork  needed and abate the number of pieces  formerly collected.  

The organizer  demanded a aggregate of 1,230 pieces of artwork. During the first 10 days, they collected 86 pieces per day, performing in a aggregate of 86 * 10 =  860 pieces collected.  thus, the number of pieces of artwork remaining to be collected is 1,230- 860 =  370.  

Since there were only 5 days left before the exhibition, the organizer  demanded to collect 370 pieces of artwork within those 5 days.  

To calculate the number of pieces of artwork  demanded per day for the remaining time, we divide the total number of pieces  demanded by the number of days / 5 =  7

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the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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Answer:

Don't understand 12am like how

Answer:

in slope it is - 3/2

in y intercept (0,1)

hope it helps

The measure of each interior angle of a decagon is 144 degrees.

1. A decagon is a 10 sided polygon.

2. The sum of the interior angles of any polygon with n sides is (n - 2) * 180 degrees.

3. For a decagon, n = 10, therefore the sum of the interior angles is (10 - 2) * 180 degrees = 8 * 180 degrees = 1440 degrees.

4. Therefore, the measure of each interior angle of a decagon is 1440 degrees / 10 = 144 degrees.

The measure of each interior angle of a decagon is 144 degrees.

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The r function that the data analyst can use to do this automatically is the clean names function.

When it comes to data manipulation, R is an excellent tool. It enables the use of several preprocessed packages, making data manipulation much easier.

Janitor's clean names() function will make all of your variable names consistent in a single line of code.

In R, a data analyst is cleaning up their data. To avoid errors in their analysis, they want to ensure that their column names are unique and consistent. What R function can they use to automate this? The clean names() function will ensure that column names are both unique and consistent.

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Answer:

32.1

Step-by-step explanation:

You add the code chunk arrange(bill_length_mm) to sort the column bill_length_mm in ascending order. The correct code is penguins %>% arrange(bill_length_mm). Inside the parentheses of the arrange() function is the name of the variable you want to sort. The code returns a tibble that displays the data for bill_length_mm from shortest to longest. The shortest bill length is 32.1mm.

The expression of the decimal 0.139 in fraction form of p/q gives; 139/1000

We are given the decimal 0.139.

Now, when we want to convert to fraction, it means we want the decimal expression to have a numerator and a denominator.

Thus;

0.139 can also be expressed as; 139/1000

Therefore, the expression of the decimal 0.139 in fraction form of p/q gives; 139/1000

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Answer:

84

Step-by-step explanation:

Lauren has read 4 books per month. So the answer would be 84.

Answer:

D. (1, 5)

Step-by-step explanation:

the solution to the system of equations is the point of lines intersect => (1, 5)

Answer:436

Step-by-step explanation:

Since Colin scored 141 and Brian scored 154 more than Colin that would be (154+141). So Brian scored 295, so you add Brian's score and Colin's so 295+141, the total score is 436

Answer:

A. $21.59

Step-by-step explanation:

$151.13 ÷ 7 tons= $21.59 each per ton

The statements that accurately compare the domain and range of the functions are: The domain of all three functions is all real numbers, The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The domain of a function refers to all the possible input values that make the function defined. For the quadratic function f(x) = 3x², there are no values of x that make the function undefined, so the domain of f(x) is all real numbers. To find the range of f(x), we can calculate the vertex of the parabola, which is (0,0). The range of f(x) is all real numbers greater than or equal to zero.

For the quadratic function f(x) = 3x², we can determine the vertex using the formula:

h = -b/2a

In this case, a = 3 and b = 0, so:

h = -0/2(3) = 0/6 = 0

The x-coordinate of the vertex is 0.

To find the y-coordinate, we evaluate the function at the vertex:

f(0) = 3(0)² = 0

So the vertex of the parabola is (0,0).

Since the coefficient of x² is positive, the parabola opens upwards, and the minimum value of the function occurs at the vertex. Therefore, the range of f(x) is all real numbers greater than or equal to zero.

For the rational function g(x) = 1/3x, the function is undefined when the denominator is equal to zero. Thus, we solve for the value(s) of x that make the denominator zero:

3x = 0

Dividing both sides by 3, we get:

x = 0

Therefore, the domain of g(x) is all real numbers except zero. The range of g(x) is all real numbers except zero, since the function cannot equal zero.

For the linear function h(x) = 3x, there are no values of x that make the function undefined. Thus, the domain of h(x) is all real numbers. The range of h(x) is also all real numbers, since the function is a straight line that passes through the origin and extend infinitely in both directions.

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Answer:

86 degrees

Step-by-step explanation:

Alrighty, a simple 180-degree triangle, we can see that the two angles add up to 86, so what would make our angle G1 94 since 180-86 = 94, but we are tasked with finding the other side of that angle, let's call it G2, what should we do?

Since this is a flat 180-degree line, we do it again!

180-94 = 86 degrees

And there ya have it

Though, if you need the technical side, it's because a whole of a triangle is 180 degrees

Given that angles F is 58 and E is 28, we add those two up to find angle EGF. How to find EGF you ask? Simple- 180 degrees (Because it's a triangle) minus 86 (Added angles of E and F), that would equal 94.

Now, we are tasked with finding TGF. We do not have TGF but we have EGF. Learning that, we see the line ET, indicating that we have found ourselves a 180-degree line. What do we do with this line? We use it to calculate TGF with EGF

Since EGF is 94, we take the 180 - 94 to equal 86, and that is how you find TGF

Answer:

6,3,-3, and -6

Step-by-step explanation:

You just replace y with the given numbers, then solve for x

The slope of the tangent line to the given polar curve at the specified point is √3.

What is polar equation?

Cartesian coordinates, which may be found by moving across an x-axis and up and down the y-axis in a rectangular pattern, are complemented by polar coordinates. Polar coordinates are written as (r,) as opposed to the (x, y) used for Cartesian coordinates.

A point's location in polar coordinates is determined by its r from the origin and the angle θ (measured in radians) between the line leading to the point and the x-axis.

As given,

For the polar equation r = 4 sin θ, we have

x = r cosθ

x = 4 sinθ cosθ

x = 2sin2θ

y = r sinθ

y = 4 sin²θ

Differentiate obtained values of x and y with respect to θ respectively,

dx/dθ = d(2sin2θ)/dθ

dx/dθ = 2cos2θ (2)

dx/dθ = 4cos2θ

Similarly,

dy/dθ = d(4sin²θ)/dθ

dy/dθ = 4sin2θ

Evaluate the slope (dy/dx) as follows:

dy/dx = (dy/dθ) / (dx/dθ )

dy/dx = (4 sin2θ) / (4 cos2θ)

dy/dx = (sin2θ) / (cos2θ)

dy/dx = (tan2θ)

At θ = π/6

slope = dy/dx

Substitute values,

slope = tan2( π/6)

slope = tan( π/3)

slope = √3.

Hence, the slope of the tangent line to the given polar curve at the specified point is √3.

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Answer:

87 million

Step-by-step explanation:

Every 2 months the money increases by 18million.

45 - 27 = 18

18 + 18 + 6 = 42

45 + 42 = 87

The function rule for f⁻¹ is f⁻¹(y)=(x/4)+4. And, the function rule for g⁻¹ is g⁻¹(v)=(4u-65)/2.

The inverse function is defined as the function that is considered "undo" or reverse of another function. For example, let us consider a function to be f. Then, the inverse function is written as f⁻¹.

a) Given f(x)=4x-16. Let's consider y=f(x)=4x-16. Then,

y=4x-16

4x=y+16

x=(y+16)/4

=(y/4)+4

To find the inverse function, then put x=y, we get,

f⁻¹(y)=(x/4)+4

b) Given g(u)=(2u+9)/4+14. Let g(u)=v=(2u+9)/4+14. Then,

v-14=(2u+9)/4

2u+9=4v-56

2u=4v-65

u=(4v-65)/2

To find the inverse function, then put u=v, we get,

g⁻¹(v)=(4u-65)/2

The required answers are f⁻¹(y)=(x/4)+4 and g⁻¹(v)=(4u-65)/2.

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The complete question is -

a. Given that f(a) = 4x-16 where f(x) = y, define a function rule for f⁻¹.

f⁻¹(y) =

b. Given that g(u) = (2u + 9)/4 +14 where g(u) = v, define a function rule for g⁻¹.

g⁻¹(v) =

Answer:

875

Step-by-step explanation:

If there are 100 tagged rabbits and which there are 40 tagged out of 350 we get

The amount tagged/ The amount of rabbits = Tagged come back/Caught

If we replace the equations we get the equation

100/x = 40/350

Step 1. Cross Multiply

40x = 35000

x = 875

There are 875 rabbits

Answer:

169

Step-by-step explanation:

I had to memorize this for a competition :)

Answer: 169

Step-by-step explanation: All we need to do is 13x13 which equals 169.

13x10=130, 13x3=39, 130+39=169.

Hope this helps! :)

In the given scenarios, the situation with an equal chance or 50-50 probability is winning a raffle that sold a total of 100 tickets if you bought 50 tickets.

So, the correct answer is C.

In this case, you have a 50% chance of winning the raffle, as you possess half of the total tickets sold.

The other scenarios do not present equal probabilities:

Rolling a number between 1 and 6 on a standard six-sided die has a 1/6 chance for each number, while spinning a spinner with four equal-sized sections (red/green/yellow/blue) has a 1/4 chance of landing on any specific color.

Lastly, reaching into a bag with 17 strawberry chews and 3 cherry chews presents a 3/20 chance of pulling out a cherry chew.

Hence the answer of the question is C.

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The values of the angles m∠1 and m∠3 is equal to 73°.

A transversal may be defined as a line which cuts a pair of parallel lines and forms several angles. When transversal cuts parallel lines the alternate interior angles are equal as well as the corresponding angles are equal. Also, the pair of vertically opposite angles are equal. From the figure attached. ∠4 = ∠8 as they are corresponding angles. So, m∠8 = m∠4 = 107°. Now, we know that ∠1 and ∠4 formed a pair of linear angles and the sum of the measures of the linear angles is 180°. So,

m∠1 + m∠4 = 180°

We know, m∠4 = 107°

m∠1 = 180° - 107°

m∠1 = 73°

Now, ∠1 and ∠3 are vertically opposite angles, so they are equal as the parallel lines are cut by transversal. Therefore, m∠1 = m∠3

=> m∠1 = 73°

=> m∠3 = 73°

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Answer:

4

Step-by-step explanation:

Answer:

\(SA = 2.94 \, \textrm{units}^2\)

Step-by-step explanation:

The surface area of a regular 3D figure can be represented as:

\(SA = A_{\textrm{\,1 side}} \cdot (\# \textrm{ of sides})\).

Therefore, the surface area of a cube is:

\(SA = s^2 \cdot 6\)

where \(s\) is the length of a side.

To solve this problem, simply input the given side length into the above formula:

\(SA = 0.7^2 \cdot 6\)

and simplify.

\(SA = 0.49 \cdot 6\)

\(SA = 2.94 \, \textrm{units}^2\)

the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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Given:

The expression is:

\(f^3+11g-4h\)

The given values are \(f=3,\ g=2,\ h=7\).

To find:

The value of the given expression for the given values.

Solution:

We have,

\(f^3+11g-4h\)

After substituting \(f=3,\ g=2,\ h=7\), we get

\(f^3+11g-4h=(3)^3+11(2)-4(7)\)

\(f^3+11g-4h=27+22-28\)

\(f^3+11g-4h=49-28\)

\(f^3+11g-4h=21\)

Therefore, the value of the given expression is 21.

The inverses of the functions f(x) = x + 3 and f(x) = 2x + 4 are

y = x - 3 and x = (y + 4)/2.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

The first graph y = x + 3.

To find the inverse we'll solve for 'x'.

y = x + 3.

x = y - 3.

y = x - 3.

f⁻¹(x) = x - 3.

And,

y = 2x - 4.

2x = y + 4.

x = (y + 4)/2.

f⁻¹(x) = (x + 4)/2.

The graph of the function y = x + 3 is shifted 3 units up to y = x.

And the graph y = 2x - 4 is shifted 4 units down and is steeper than y = x.

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