Suppose a bus arrives at a bus stop every 26 minutes. If you arrive at the bus stop at a random time, what is the probability that you will have to wait at least 4 minutes for the bus?

The function f(x) = –2x^3 + 39x^2 -216x + 6 has one local minimum at x = 4 and one local maximum at x = 9.

To determine if the function f(x) = –2x^3 + 39x^2 -216x + 6 has a local minimum or maximum, we need to find the critical points of the function and then determine the nature of those critical points.

First, we take the derivative of the function to find the critical points:

f(x) = –2x^3 + 39x^2 -216x + 6

f'(x) = –6x^2 + 78x - 216

f'(x) = –6(x^2 - 13x + 36)

f'(x) = –6(x - 4)(x - 9)

Setting f'(x) = 0, we get:

–6(x - 4)(x - 9) = 0

This gives us two critical points at x = 4 and x = 9.

To determine the nature of these critical points, we need to look at the sign of the derivative on either side of each critical point.

When x < 4, we have:

f'(x) = –6(x^2 - 13x + 36) < 0

When 4 < x < 9, we have:

f'(x) = –6(x^2 - 13x + 36) > 0

When x > 9, we have:

f'(x) = –6(x^2 - 13x + 36) < 0

This means that f(x) is decreasing on the interval (–∞, 4), increasing on the interval (4, 9), and decreasing on the interval (9, ∞). Therefore, we have a local minimum at x = 4 and a local maximum at x = 9.

To confirm this, we can evaluate the function at these critical points:

f(4) = –2(4)^3 + 39(4)^2 -216(4) + 6 = –26

f(9) = –2(9)^3 + 39(9)^2 -216(9) + 6 = 603

Therefore, the function f(x) = –2x^3 + 39x^2 -216x + 6 has one local minimum at x = 4 and one local maximum at x = 9.

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The upper and lower bound of the cross-sectional area of the insulation, would be A = [ 3129, 3137 ] cm².

The upper and lower bound of A would be found by the formula :

A = π x ( R ² - r ² )

The upper bound is therefore:

= π x  (( 48. 75 / 2) ² - ( 19.2 45 / 2) ²)

= π x ( 1183. 0625 - 184. 857025 )

= π x 998. 205475

= 3, 137 cm²

The lower bound will then be:

= π x ( ( 48. 65 / 2 ) ²- (19. 255 / 2) ²)

= π x ( 1180. 9225 - 184. 963025)

= π x 995. 959475

= 3, 129 cm²

The interval form is therefore A = [ 3129, 3137 ] cm²

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Answer:

$264,000

Step-by-step explanation:

PV = $110,000

i = 6%

n = 15 years

Compound formula:

FV = PV (1 + i)^n

FV = 110,000 (1 + 0.06)^15

FV = 110,000 · 2.40(rounded) = $264,000

Comets could be visible from Earth when they are most likely to fall down into earth

The mode of transportation that I will choose is motorized scooter this is because it is relatively cheap when compared to the other forms of transportation.

A motorized scooter  could be a moderately cheap mode of transportation compared to other alternatives such as cars, cruisers, or indeed bikes.

The starting price of obtaining a motorized bike is for the most part lower than that of a car or cruiser, and the continuous costs such as fuel, support, and protections are too ordinarily lower.

From the question, you can see that the price of the scooter at 5 miles is $10 and it is relatively cheap when compared to the rest.

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The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.

We can use trigonometry to find the x and y components.

x3 = 12 * cos(15°) ≈ 11.59 km (east)

y3 = -12 * sin(15°) ≈ -3.10 km (south, hence the negative sign)

Leg #4: 14 km [South]

x4 = 0 km (no east/west movement)

y4 = -14 km (south, hence the negative sign)

Now, let's find the total x and y displacements:

x_total = x1 + x2 + x3 + x4 ≈ 0 + 10 + 11.59 + 0 ≈ 21.59 km

y_total = y1 + y2 + y3 + y4 ≈ 8 + 0 - 3.10 - 14 ≈ -9.10 km

Now, we can find the distance and direction he needs to ride to get back to the starting point:

Distance=  

[tex]\sqrt{21.59^2 + (-9.10)^2}[/tex])

23.21 km

Direction:

angle =

arctan(9.10 / 21.59)

= 23.13°

The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.

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The rotation used in this problem is given as follows:

90º clockwise rotation.

The five more known rotation rules are given as follows:

A vertex and it's equivalent is given as follows:

A(1,3) and A'(3, -1).

Hence the rule is:

(x,y) -> (y, -x).

Which is the rule for a 90° clockwise rotation = 270º counterclockwise rotation.

The image is presented at the end of the answer.

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Answer:

90° clockwise rotation

Step-by-step explanation:

I did the exam and got it correct

Ethan's monthly salary is $1450.

Ethan's monthly salary, we can use the debt to income ratio formula, which is calculated by dividing monthly debt expenses by monthly income.

Given:

Monthly expenses = $1160

Debt to income ratio = 0.8

Let's assume Ethan's monthly salary as S.

We can set up the equation using the debt to income ratio formula:

Debt to income ratio = Monthly expenses / Monthly income

0.8 = $1160 / S

To solve for S (monthly salary), we can rearrange the equation:

S = $1160 / 0.8

Dividing $1160 by 0.8 gives us:

S ≈ $1450

Therefore, Ethan's monthly salary is approximately $1450.

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Answer:

Step-by-step explanation:

To find the solution set to the inequality w - 10 < 16, we can solve for w by adding 10 to both sides of the inequality:

w - 10 + 10 < 16 + 10 w < 26

This means that any number less than 26 is part of the solution set to the inequality. So, out of the given options, the number that is not part of the solution set is D. 27 because it is greater than 26.

Answer:

Vertical Compression by factor of 1/4

Step-by-step explanation:

Two methods:

Method 1. Transformations

Method 2. Algebraic input-output tables

Method 1. Transformations

The Main concept of this question is about Transformations of functions -- specifically, multiplying on the outside by a positive number less than 1.

The transformation that occurs when multiplying a function by a positive number on the outside of the function is a vertical stretch or compression.

Positive numbers larger than 1 will stretch it vertically, whereas positive numbers smaller than 1 will compress it vertically.

Therefore, multiplying by 1/4 on the outside, a positive number less than 1, will vertically compress the function down to one-fourth the size.

This means that for g(x), all points on the original function f will have their heights reduced to 1/4 their original height (or depth) -- making all points on g(x) 1/4 their previous distance from the x-axis on the "f" function.

Method 2. Algebraic input-output tables

Observe on the graph three points on the function f:

Using the equation relating f and g, [tex]g(x)=\frac{1}{4}f(x)[/tex], we can find how those points would look like on the new function g(x).

For [tex]f(0)=0[/tex]

[tex]g(0)=\frac{1}{4}[f(0)]\\g(0)=\frac{1}{4}[0]\\g(0)=0[/tex]

For [tex]f(1)=4[/tex]

[tex]g(1)=\frac{1}{4}[f(1)]\\g(1)=\frac{1}{4}[4]\\g(1)=1[/tex]

For [tex]f(3)=0[/tex]

[tex]g(3)=\frac{1}{4}[f(3)]\\g(3)=\frac{1}{4}[0]\\g(3)=0[/tex]

These known points should correctly identify the graph from the possible choices.

148.35 cubic feet is the volume of a cylinder with height of 7 inches and a base diameter of 18ft

We have to find the volume of a cylinder

V=πr²h

h is the height of cylinder and r is radius of the base.

Given height is 7 inches which is 0.583333 feet

Diameter is 18 ft

Radius is 9 ft

Now plug in value of height and radius

Volume=π(9)²×0.5833

=3.14×81×0.5833

=148.35 cubic feet

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The volume of cement in cubic feet that will be needed is 45 cubic feet.

Volume is the space occuppied by an object.

To calculate the volume of cement in cubic feet that will be needed, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The grocery store's earning income is $30,030 if they sell 200 tomatoes in one day.

We need to find how much the grocery store earns when it sells 200 tomatoes in one day. When The grocery store’s earnings in dollars can be modeled by the equation,

y = 0.75x² + 0.15x

where,

x = number of tomatoes they sell = 200

To find the earnings we need to substitute x in the equation it can be given as,

y = 0.75x² + 0.15x

y = 0.75(200)² + 0.15(200)

y = $30,030

Therefore, the grocery store's earning income is $30,030 if they sell 200 tomatoes in one day.

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The volume of the cylinder is 4004 cubic metres.

The diameter of the cylinder is 28 metres and the height of the cylinder is 6.5 metres.

Therefore, the volume of the cylinder can be found as follows:

Hence,

volume of a cylinder = πr²h

where

Therefore,

volume of the cylinder =  22 / 7 × 14² × 6.5

volume of the cylinder = 22 / 7 × 196 × 6.5

volume of the cylinder = 28028 / 7

volume of the cylinder = 4004 cubic metres

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The circumference of the circle is 6.28 kilometers if the diameter of the circle is 2 kilometers and assuming the value of π is 3.14 kilometers.

The diameter of the circle = 2 kilometers

The circumference of a circle is calculated by using the formula,

C = π *d

where,

C = circumference of a circle

d = diameter of the circle

π = Constant value = 3. 14 Km

Substituting the above-given values into the equation, we get:

C = π*d

C = 3.14 x 2 km

C = 6.28 km

Therefore, we can conclude that the circumference of the circle is 6.28 kilometers.

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The decay of the radioactive substance can be modeled by the exponential decay function:

y = a(1 - r)^t

where:

- y is the amount of substance present after t hours

- a is the initial amount of substance (in grams), which is 120 grams in this case

- r is the decay rate per hour, which is 18% or 0.18 in decimal form

- t is the time elapsed in hours

Plugging in the values we get:

y = 120(1 - 0.18)^t

Simplifying:

y = 120(0.82)^t

So this is the equation that represents the number of grams, y, present after t hours, given the initial amount of 120 grams and a decay rate of 18% per hour.

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To minimize your losses while gambling at a casino and playing slot machines, you need to minimize your regret R in the experts problem. R is defined as the difference between your total cost and the best expert's cost.

To minimize R, follow these steps:

1. Begin by assigning equal weight to each expert (slot machine).
2. After each day t, observe the cost c_ti for each expert i.
3. Update the weights by multiplying them by (1 - c_ti), making sure they remain non-negative.
4. Normalize the weights so they sum up to 1.
5. On day t+1, choose the expert with the highest weight to take advice from.

By following this adaptive strategy, you will minimize your regret R, allowing you to reduce your losses while gambling at the slot machines.

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If she continues to increase the length of her runs the same way, it will not be enough to reach the half-marathon distance of 13.1 miles within the remaining time of the training program.

Sariah has just begun training for a half-marathon, which is 13.1 miles. There are 6 weeks of training runs remaining before the race. In her first week of training, Sariah ran 3 miles. She ran 4.5 miles the second week and 6 miles the third week.

To determine if there is enough time left in the training program for her to get up to half-marathon distance, let's analyze the pattern of her weekly increases in distance:

Week 2 - Week 1 = 4.5 miles - 3 miles = 1.5 miles increase
Week 3 - Week 2 = 6 miles - 4.5 miles = 1.5 miles increase

Sariah is consistently increasing her weekly mileage by 1.5 miles. With 3 weeks of training already completed, she has 3 more weeks to go. Let's see if she can reach the half-marathon distance of 13.1 miles:

Week 4: 6 miles + 1.5 miles = 7.5 miles
Week 5: 7.5 miles + 1.5 miles = 9 miles
Week 6: 9 miles + 1.5 miles = 10.5 miles

After 6 weeks of training, Sariah will have increased her longest run to 10.5 miles. Unfortunately, this is not enough to reach the half-marathon distance of 13.1 miles within the remaining time of the training program.

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The solution to the equation is m = 0.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

To solve the equation:

(-3m^ {5}) (-2m^ {4}) = (-6m^ {9})

We can simplify the left side of the equation by multiplying the terms:

(-3m^ {5}) (-2m^ {4}) = (6m^ {9})

Now we have:

6m^ {9} = (-6m^ {9})

To solve for m, we can divide both sides by 6m^ {9}:

m^ {9} = -m^ {9}

Since the powers of m on both sides are equal, we can simplify to:

2m^ {9} =0

Dividing both sides by 2, we get:

m^ {9} =0

Taking the ninth root of both sides, we get:

m = 0

Therefore, the solution to the equation is m = 0.

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Complete Question:

Simplify the expression: $(-3m^ {5}) (-2m^ {4}) $.

Step-by-step explanation:

To determine the appropriate fraction for the line plot, we need to find the greatest common factor (GCF) of all the pencil lengths, and then express each length as an equivalent fraction with the GCF as the denominator.

The GCF of the pencil lengths is 1. Therefore, we can simply express each pencil length as an equivalent fraction with 1 as the denominator:

3/1, 7/1, 8/1, 5/1, 1/1, 4/1, 6/1, 8/1, 4/1, 2/1, 5/1

Now, we can see that the smallest unit increment we can use on the line plot is 1/8. This is because 1/8 is the smallest fraction that can represent all of the pencil lengths above the label (5/8, which is equivalent to 10/16).

Therefore, the students should use 1/8 as the fraction for the line plot.

We can say with 95% confidence that the true mean cholesterol content of all such eggs is between 223.99 milligrams and 232.01 milligrams.

To construct a 95% confidence interval for the true mean cholesterol content of all such eggs, we can use the following formula:

CI = X ± Zα/2 * σ/√n

where:

X = sample mean = 228 milligrams

Zα/2 = the critical value from the standard normal distribution corresponding to a 95% confidence level, which is 1.96

σ = population standard deviation = 19.0 milligrams

n = sample size = 82

Substituting the values into the formula, we get:

CI = 228 ± 1.96 * 19.0/√82

= 228 ± 4.01

= (223.99, 232.01)

Therefore, we can say with 95% confidence that the true mean cholesterol content of all such eggs is between 223.99 milligrams and 232.01 milligrams.

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The point (–2, 5) is located above the point (–2, –1).

The point (1, 212) is located to the left of the point (4, 212).

The point (3, –6) is located below the point (3, –3).

The point (−212, 1) is located to the left of the point (–3, 1).

The point (312, 12) is located to the right of the point (12, 12).

The point (2, 5) is located above the point (2, –5).

a. (–2, 5) is above (–2, –1). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (–2, 5) is located above the point (–2, –1).

b. (1, 212) is to the left of (4, 212). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (1, 212) is located to the left of the point (4, 212).

c. (3, –6) is below (3, –3). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate decreases as you move down on the coordinate plane, the point (3, –6) is located below the point (3, –3).

d. (−212, 1) is to the left of (–3, 1). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate decreases as you move to the left on the coordinate plane, the point (−212, 1) is located to the left of the point (–3, 1).

e. (312, 12) is to the right of (12, 12). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (312, 12) is located to the right of the point (12, 12).

f. (2, 5) is above (2, –5). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (2, 5) is located above the point (2, –5).

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Answer: That made no sense

Step-by-step explanation:

Answer:

Step-by-step explanation:

If there are 180 degrees in a triangle total and in this problem we know that one angle is 49 and the other is 39, we can assume that subtracting 39 and 49 from 180 will find x. In this case, x will be 92.

S = lim[n → ∞] sn
 = lim[n → ∞] (306n^2 + 35n + 306)
 = ∞
So unfortunately, the series (n + 16)(n + 18) diverges to infinity and does not have a finite sum.To find the sum S of the series (n + 16)(n + 18), we need to take the limit of the sequence of partial sums as n approaches infinity. So let's first find the formula for the nth partial sum sn:

sn = (1 + 16)(1 + 18) + (2 + 16)(2 + 18) + ... + (n + 16)(n + 18)
  = ∑[(k + 16)(k + 18)] (from k = 1 to n)

Using the formula for the sum of squares, we can expand each term in the sum:

(k + 16)(k + 18) = k^2 + 34k + 288

So now we have:

sn = ∑(k^2 + 34k + 288) (from k = 1 to n)
  = ∑k^2 + 34∑k + 288n (from k = 1 to n)
  = n(n + 1)(2n + 1)/6 + 34n(n + 1)/2 + 288n
  = 306n^2 + 35n + 306

Now we can take the limit of sn as n approaches infinity to find S:

S = lim[n → ∞] sn
 = lim[n → ∞] (306n^2 + 35n + 306)
 = ∞

So unfortunately, the series (n + 16)(n + 18) diverges to infinity and does not have a finite sum.

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The probability of the mouse finding its way out before reaching a dead end or going out in the opening can be estimated by dividing the number of successful outcomes by the total number of trials in the sample.

To create a simulation to determine the probability that the mouse will find its way out before coming to a dead end or going out in the opening, we can follow these steps:

The probability of the mouse finding its way out before reaching a dead end or going out in the opening can be estimated by dividing the number of successful outcomes by the total number of trials in the sample. This simulation approach can help us understand the probability of success in a random maze environment, and also explore the impact of various factors such as maze complexity, size and starting position of the mouse on the outcome.

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The value of the given expression is 44. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four basic operations, also referred to as "arithmetic operations," are thought to explain all real numbers. Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.

We are given an expression as [tex]\frac{1}{2}[/tex] (7) (4) + 6 (5).

We know that when there is no sign in between two numbers, it denotes multiplication.

So, we get

⇒  [tex]\frac{1}{2}[/tex] * (7)  * (4) + 6 * (5)

⇒ 14 + 30

⇒ 44                                            (Using addition operation)

Hence, the value of the given expression is 44.

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Answer:

(3-x)^2=y

Step-by-step explanation:

There are infinitely many possible solutions for the lengths of the three sides of the triangle.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

If we call x the length of the smallest side, then the other two sides are x+1 and x+2 (since they are three consecutive integers). According to the triangle inequality, the sum of any pair of sides must be greater than the length of the third side.

Therefore, we have:

x + (x+1) > (x+2) (and also x + (x+2) > (x+1) and (x+1) + (x+2) > x)

Simplifying each inequality, we get:

2x + 1 > x + 2 (and also 2x + 2 > x + 1 and 2x + 3 > x)

Which gives:

x > 1

So the smallest side must be greater than 1 cm.

Now, to find the length of the three sides, we can choose any value greater than 1 for x. For example, if we take x=2, then the three sides are:

2 cm, 3 cm, and 4 cm

If we take x=3, then the three sides are:

3 cm, 4 cm, and 5 cm

And so on. Therefore, there are infinitely many possible solutions for the lengths of the three sides of the triangle.

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The probability that the smallest bell rings the first three days in a row is 1/27. when Each day three church bells are rung in a random order

In the given data there are 3 bells in the church in which there is a small bell and the three bells are rung in a random order. we need to find the probability that the smallest bell rings the first three days in a row.

The probability that the smallest bell rings on any given first day can be given as  = 1/3

Because there are three bells and each bell has an equal chance of being rung first. The probability that this happens three days in a row is given as

= (1/3) × (1/3) × (1/3)

= 1/27

Therefore, the probability that the smallest bell rings the first three days in a row is 1/27

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