Evaluate each expression when x = 4
1. 5x + 10
2. 18+ x -8
3. *x + 50

Answer: 2200 yards

Step-by-step explanation:

First find the unit rate, 660/3 = 220

So, Owen can jog 220 yards in one minute.

220 times 10 to find how much Owen can jog in 10 minutes.

220*10 = 2200.

Answer:

2200

Step-by-step explanation:

The probability of the arrow landing on section a is 1/5 since there are 5 equal sections. The probability of the coin landing on heads is 1/2 since there are only 2 possible outcomes (heads or tails) for the coin.

To find the probability of both events happening, we need to multiply the probability of the arrow landing on section a by the probability of the coin landing on heads. This gives us (1/5) * (1/2) = 1/10. So the probability that the arrow will land on the section labeled a and the coin will land on heads is 1/10. In other words, there is a 1 in 10 chance of both events happening. It is important to note that each event is independent of each other, meaning the outcome of one does not affect the other. This is because the spinner and the coin are not connected or related in any way.

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The radius of the base after rotating the rectangle will be 5

Since it has a perimeter of 32 units and it is to be rotated about the line, the solid to be created is a cylinder.

Let's calculate its radius from the perimeter;

\(2p=32\)

\(2(b+h)=32\)

\(b+h=16\)

\(b=16-h\)

Also, \(bh=60\)

Thus;

\(h(16-h)=60\)

\(h^2-16h+60=0\)

Using the online quadratic formula, we have h = 6

Thus; b = 16 - 6 = 10

Since the line of rotation is the center, and the radius is half the line segment of the basis, then the radius is 10/2 = 5.

Thus the radius of the base after rotating the rectangle will be 5

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Answer:

cylinder and 6 units

Step-by-step explanation:

on e2020

The numerical length of line segment \(\(\overline{JL}\)\) is approximately -11.67 units.

To determine the numerical length of line segment \(\(\overline{JL}\)\), we need to determine the value of JL provided the equations; KL = 2x - 2, JL = 4X-9, and JK = 5X+2.

Since point K is on line segment \(\(\overline{JL}\)\), we can equate the lengths KL and JK and solve for x:

KL = JK

2x - 2 = 5x + 2

By rearranging the equation, we get:

2 - 2 = 5x - 2x + 2

0 = 3x + 2

3x = -2

\(x = -\frac{2}{3}\)\)

Now that we have the value of x, we can substitute it into the equation for JL to calculate its numerical length:

JL = 4x - 9

\(\(JL = 4\left(-\frac{2}{3}\right) - 9\)\\\\\)

\(\\\(JL = -\frac{8}{3} - 9\)\\\\\)

\(\(JL = -\frac{8}{3} - \frac{27}{3}\)\\\\)

\(\(JL = -\frac{35}{3}\)\)

Therefore, the numerical length of line segment \(\(\overline{JL}\)\) is \(\(-\frac{35}{3}\)\) or approximately -11.67 units.

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This function compare to the logistic mean response function in part is as following:

The equation is, E{Yi} = πi = Fl = (β0 + β1xi)

E{Yi} = Exp(βo + β1Xi) / 1 + Exp(βo + β1Xi)

A) plot the logistic mean response function. When βo = 20 and β1 = -0.2

Let,

E{Yi} = Exp(βo + β1Xi) / 1 + Exp(βo + β1Xi)

where,

βo = 20

β1 = -0.2

E{Yi} = 1/2

Xi = 100

B) = For what value of X is the mean response equal to 0.5

Mean response  = 1/2

= E{Yi} = Exp(βo + β1Xi) / 1 + Exp(βo + β1Xi)

= 1/2

= Exp(βo + β1Xi)

Xi = -βo/β1

c) The odds when x = 125, when x = 126 and the ratio of the odds, when x = 126 to odds when x = 125

Odd = \(e^{\beta o + \beta 1 Xi}\)

Odd(125) = \(e^{\beta o + \beta 1 125}\)

odd(126) = \(e^{\beta o + \beta 1 +126}\)

Rate of odd = Odd126/odd125

Rate of Odd = \(e^{\beta 1}\)

One of the most popular techniques in data mining in general and binary data categorization in particular continues to be logistic regression (LR). The primary goal of this study is to provide an overview of the key LR features when applied to data analysis, specifically from an algorithmic and machine learning standpoint.

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Complete question:

a. Plot the logistic mean response function (14.16) when = 20 and β,--.2

b. For what value of X is the mean response equal to.5:?

c. Find the odds when X 125, when X-126, and the ratio of the odds when X-126 to the odds when X-125. Is the odds ratio equal to exp(B,) as it should be?

The conclusion is:

y(t) = (500e^(0.09t+ln(99))) / (1 + e^(0.09t+ln(99)))

We have the differential equation:

dy/dt = 0.09y(1 - y/500)

To solve this, we can separate variables and integrate both sides:

dy / (y(1 - y/500)) = 0.09 dt

We can use partial fractions to break up the left-hand side:

dy / (y(1 - y/500)) = (1/500) (1/y + 1/(500 - y)) dy

Now we can integrate both sides:

∫ (dy / (y(1 - y/500))) = ∫ (1/500) (1/y + 1/(500 - y)) dy

ln |y| - ln |500 - y| = 0.09t + C

where C is the constant of integration.

Simplifying:

ln |y / (500 - y)| = 0.09t + C

Taking the exponential of both sides:

|y / (500 - y)| = e^(0.09t+C)

Since y(0) = 5, we can use this initial condition to find the value of C:

|5 / (500 - 5)| = e^C

C = ln(495/5)

C = ln(99)

So the equation becomes:

|y / (500 - y)| = e^(0.09t + ln(99))

Simplifying further:

y / (500 - y) = ± e^(0.09t + ln(99))

y = (500e^(0.09t+ln(99))) / (1 ± e^(0.09t+ln(99)))

Using the initial condition y(0) = 5, we can determine that the positive sign is appropriate:

y = (500e^(0.09t+ln(99))) / (1 + e^(0.09t+ln(99)))

Therefore, the solution to the differential equation is:

y(t) = (500e^(0.09t+ln(99))) / (1 + e^(0.09t+ln(99)))

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Answer:

Step-by-step explanation:

An=3*n

Answer:

n=3m

Step-by-step explanation:

n represent the number of movies he will watch

m shows the amoutn of month

The probability that a pupil uses neither pool nor gym is 11/70

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.

Number of pupil that can use pool and gym = 28

Number of people that can use pool = 48

Number of people that can use gym = 39

Number of people that can use pool only = 48 - 28 which is 20

Number of people that can use gym only = 39 - 28 = 11

Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59

Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.

Probability = required outcome / possible outcome

Required outcome = 11

possible outcome = 70

Probability = 11/70

In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70

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Answer:

e = 25/3

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)

The correct answer is b. frequency.

Data collection in a functional analysis typically involves recording the frequency of a target behavior. In functional analysis, the focus is on understanding the function or purpose of a behavior, and frequency data helps to identify patterns and determine the relationship between the behavior and environmental events.

During a functional analysis, various conditions are manipulated to assess how they impact the occurrence of the behavior. The frequency of the behavior is typically recorded within each condition to determine if there are differences in its occurrence based on the specific environmental variables being manipulated.

While duration and momentary time sampling are also data collection methods used in behavioral analysis, they are not specifically associated with functional analysis. Duration refers to measuring the length of time a behavior occurs, while momentary time sampling involves recording whether a behavior is occurring or not at specific intervals of time.

In functional analysis, frequency data is typically the primary method for collecting and analyzing data to understand the relationship between behavior and environmental variables.

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Data collection in a functional analysis is usually based on three components: duration, frequency, and momentary time sampling. Duration observes the amount of time a behavior occurs. Frequency measures how often a behavior occurs. Momentary time sampling observes the existence of behavior at specified time intervals.

In the context of a functional analysis, typically the data collection methods revolve around three primary types: duration, frequency, and momentary time sampling.

Duration refers to the total amount of time that a behavior happens. It generally is measured from the moment the behavior begins until it ends. It's important when the length of time that the behavior occurs can impact its functionality.

Frequency records how often a behavior occurs within a set observational period. It’s used when the number of times the behavior occurs is the important aspect to measure.

Momentary time sampling is a method of measuring behavior in which the existence or nonexistence of behaviors are recorded at precisely specified time intervals. This process involves observing whether the behavior occurs or does not occur at the moment the interval ends. This method is beneficial as it does not need continuous observation.

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Answer:

It would be $465 marked up.

Step-by-step explanation:

55% of 300 is 165.

So marked up its 465 and marked down its 135.

Answer:

the answer is yes vfmkvfmfmkrkfm

Step-by-step explanation:

Answer:

D - 18,900 mowers

Step-by-step explanation:

To determine the number of lawn mowers sold 3 years after a model is introduced, we can substitute t = 3 into the given function.

y = 5500 ln (9t + 4)

Let's calculate it step by step:

y = 5500 ln (9(3) + 4)

y = 5500 ln (27 + 4)

y = 5500 ln (31)

y ≈ 5500 * 3.4339872

y ≈ 18,886.43

Therefore, approximately 18,886 mowers will be sold 3 years after the model is introduced.

The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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Step-by-step explanation:

-4

4

and those are the only ones i know

The answer is c) 50%. A random sample means that each member has an equal chance of being selected. This means that out of a sample size of any number, the percentage of members selected will always be 50%.

For example, if we have a random sample of 100 members, 50 of them will be selected. This principle applies to any population size, regardless of whether it's 10 or 10,000. It's important to note that this applies only to random samples, as non-random samples can have a biased selection process which affects the percentage of members selected. In summary, the percent of members in a random sample that have an equal chance of being selected is always 50%.

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Answer:

1) 63x²+68x+12=0

2) x⁴-8x²+15=0

3) -5x²-(5/x²)+26=0

Step-by-step explanation:

1)

x=-6/7 and x=-2/9

7x=-6 and 9x=-2

7x+6=0 and 9x+2=0

(7x+6)(9x+2)

63x²+14x+54x+12

63x²+68x+12=0

2)

x=√3 and x=√5

x²=3 and x²=5

x²-3=0 and x²-5=0

(x²-3)(x²-5)

x⁴-5x²-3x²+15

x⁴-8x²+15=0

3)

x=\(\sqrt[2]{5}\) and x=\(\sqrt[-2]{5}\)

x²=5 and x⁻²=5

x²=5 and (1/x²)=5

x²-5=0 and (1/x²)-5=0

(x²-5)((1/x²)-5)

1-5x²-(5/x²)+25

-5x²-(5/x²)+26=0

The exact solution and its approximation rounded to two decimal places are 2. 6213 and 2. 62 respectively.

An algebraic expression can be described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.

These expressions are also made up of arithmetic operations which includes;

From the information given, we have that;

(2x − 1)^2 = 18

Find the square root of both sides, we have;

√(2x − 1)^2 = √18

Note that square root rules out the square, we have;

2x - 1 = 4. 24264

collect like terms

2x = 4. 24264 + 1

2x = 5. 24264

Make 'x' the subject

x = 5. 24264/2

x = 2. 6213

Hence, the value is 2. 6213

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Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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Answer:

the answer is A 1390

Answer:

 1331π cm³

Explanation:

\(\sf V_{cylinder} = \pi (radius)^2 (height)\)

Here given:

Hence find volume:

\(\sf \rightarrow\pi (11)^2 (11)\)

\(\sf \rightarrow 121\pi ( (11)\)

\(\sf \rightarrow 1331\pi \quad \approx \:\:\ 4181.46 \ cm^3\)

Answer:

(3×6)÷5

Step-by-step explanation:

We are given the following expression:

(3/5)*6

The 6 can also be written as a fraction(6/1).

So we have a multiplication of fractions, is which we multiply the numerators and denominators.

So

(3*6)/5

The fraction sign means division

So the answer is:

(3×6)÷5

To prove that a cycle graph Cn has exactly n labeled spanning trees, we can use the principle of inclusion-exclusion. First, consider a tree T that is composed of the n edges of Cn. This tree has n edges and is therefore an n-edge tree. In order for it to be a labeled spanning tree, every vertex must be labeled with a distinct label. Since Cn has n vertices, there are n! ways to label the vertices, giving us n! labeled spanning trees.

Now, we can use inclusion-exclusion to determine the number of labeled spanning trees that are a subset of T. For each vertex vi in T, we can choose any label from the set of n labels. For each of these labels, we can choose any edge from the n edges in T. The total number of labeled spanning trees that are a subset of T is therefore: n2 × n!

Now, we can subtract the number of labeled spanning trees that are a subset of T from the total number of labeled spanning trees to get the number of labeled spanning trees that are not a subset of T. The number of labeled spanning trees that are not a subset of T is: n! - n2 × n! = n! - n2! Therefore, the total number of labeled spanning trees of Cn is n!.

This proves that a cycle graph Cn has exactly n labeled spanning trees.

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The subtended arc is 2.8 times as long as the circle's radius [r].

The area of a circle is given as follows -

A = πr² = π(d/2)²

where -

r - radius

d - diameter

Given is that a circle with a radius 5cm long is centered at an angle's vertex. The angle's rays subtend an arc length of 14cm along the circle.

Assume that the subtended arc is [x] times as long as the circle's radius [r]. So, we can write -

x = (Arc length)/(radius)

x = 14/5

x = 2.8

Therefore, the arc subtended by the rays is 2.8 times as long as the circle's radius [r].

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Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.

The expression actually is: ∛(16)/e

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The word "apalachicola" has 12 characters, including repeated characters. There are 12!/(4!2!2!2!) = 27,720 distinct permutations of the characters in the word.

To calculate the number of distinct permutations, we need to consider the repeated characters in the word "apalachicola." The word has 12 characters, with the following repetitions: 4 'a's, 2 'c's, 2 'i's, and 2 'l's.

The formula to calculate the number of distinct permutations when there are repeated characters is given by n!/ (r1! * r2! * ... * rk!), where n is the total number of characters, and r1, r2, ..., rk are the frequencies of each repeated character.

Applying the formula, we get 12!/(4!2!2!2!) = 27,720 distinct permutations of the characters in the word "apalachicola." This means that by rearranging the letters in different ways, we can form 27,720 unique combinations of the characters in the word.

In summary, there are 27,720 distinct permutations of the characters in the word "apalachicola," considering the repeated characters.

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Answer:

As a fraction 0.13 (13 repeating) is 1399

Step-by-step explanation:

0.13 = 13/99

The solution of the given linear equation is y = 80.

According to the given question.

We have an equation.

-y + 13 = -67

Since, we have to solve the above linear equation in variable.

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable -y + 13 = -67 is given by

-y + 13 = -67

⇒ - y = -67 -13 (subtractting 13 from both the sides)

⇒ -y = -80

⇒ y = 80

Hence, the solution of the given linear equation is y = 80.

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Answer:

100 cm²

Step-by-step explanation:

Given that :

Length of prism = 20 cm

Height, h = 5cm

Width, w = 4 cm

The surface are of the side with clear material can be obtained by calculating the area of rectangule (front)

Area of rectangle = Length * height

Area = 20 * 5 = 100 cm²

Answer:

RESPOSTA:B) 440.000

Step-by-step explanation:

UMA BASICA EXPLICAÇÃO: BASTA PEGAR OS 5 500HAB/KM

E MULTIPLICAR ELE PELO TERRITORIO QUE É:80KM

5 500HAB × 80KM = 440.000

A breadth-first search (BFS) is a traversal algorithm that visits a starting vertex and then visits every vertex along each path starting from that vertex to the path's end before backtracking.

In a BFS, a queue is typically used to keep track of the vertices that need to be visited. The starting vertex is added to the queue, and then its adjacent vertices are added to the queue. The process continues until all vertices have been visited. This approach ensures that the traversal visits vertices in a breadth-first manner, exploring the vertices closest to the starting vertex first before moving on to the ones further away.

So, A breadth-first search (BFS) is a traversal algorithm that visits a starting vertex, then visits every vertex along each path starting from that vertex to the path's end before backtracking. This approach explores all vertices at the same level before moving on to the next level, ensuring a breadth-first exploration. Therefore, the statement is true.

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Answer:

The original length is 9 cm and the original width 5 cm

Step-by-step explanation:

The area of  a rectangle A is given as the product of its' length L and width W.

Given that the width of a rectangle is 4cm less than the length then

W = L - 4

If each dimension were increased by 3cm, then the new

Length

= L + 3

Width

= W + 3

the width of the new rectangle formed would be 2/3 the length of the new rectangle

W + 3 = 2/3(L + 3)

3W + 9 = 2L + 6

3W = 2L +6 - 9

3W = 2L - 3

Recall that W = L - 4

3(L - 4) = 2L - 3

3L - 12 = 2L - 3

3L - 2L = 12 - 3

L = 9 cm

W = 9 - 4

= 5 cm