Madison, John, and Michael had a challenge to see who could bike the farthest in one day. Madison biked 12 miles, John biked 4 times as many miles as Michael and Michael biked 2 times as many miles as Madison. How many miles did John bike?

The estimation error for a total of m tries would be approximately |(3000P / m) - p| / (1 + 0.002m / (3000|P - p|))

To estimate the chance of winning a $10 credit per draw, we can use the Monte Carlo method by simulating the lucky draw process and calculating the proportion of times we win the prize.

Let p be the pre-defined winning probability in the website's setting, and n be the total number of times we try the drawing. After trying for 3000 times, the estimated winning probability is the proportion of times we win, which is denoted by P. The error between the estimated winning probability and the pre-defined winning probability is given by

error = |P - p|

We are given that the error after trying for 3000 times is , which means

0.002 = |P - p|

Since the winning probability is identical each time, we have P = number of wins / n. Therefore, the number of wins after trying for 3000 times is

number of wins = P x n = 3000P

Substituting this into the expression for the error, we get

0.002 = |P - p| = |(number of wins / n) - p| = |(3000P / n) - p|

Solving for n, we have

n = 3000P / (0.002 + |P - p|)

Now, we want to find the estimation error when we try the drawing for a total of times. Let m be the new total number of tries. Using the same formula, we have

estimation error = |P - p| = |(number of wins / m) - p| = |((3000P / n) x (n / m)) - p|

Substituting n and simplifying, we get

estimation error = |(3000P / m) - p| / (1 + 0.002m / (3000|P - p|))

Therefore, the estimation error for a total of m tries would be approximately

|(3000P / m) - p| / (1 + 0.002m / (3000|P - p|))

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The cost per mile obtained from the cost per gallon and the  fuel efficiency of the vehicle is $0.08 per mile.

The cost per mile of fuel required to drive the vehicle is obtained as follows:

Cost of fuel per gallon = $2.25 per gallon.

Fuel efficiency of the vehicle =  28 miles per gallon

Cost per mile = $2.25/28 miles per gallon

Cost per mile = $0.08 per mile

In conclusion, the cost per mile is obtained from the cost per gallon and the  fuel efficiency of the vehicle.

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Answer:

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A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.

Easy

Solution

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Radius of the wheel =r=

2

60

=30 cm

Circumference of the wheel =2πr=2×

7

22

×30=

7

1320

cm

Distance covered in 1 revolution =

7

1320

cm

Distance covered in 140 revolutions =

7

1320

×140=26400 cm=264 m=

1000

264

km

Distance covered in one minute = Distance covered in 140 revolutions =

1000

264

km

Distance covered in 1 hour =

1000

264

×60=15.84 km

Hence, the speed with which the boy is cycling is 15.84km/hr.

The probability that these two spins added together would equal 7 is 1/25.

The probability that each spin will land on a specific number is 1/5. Since the spins are independent, we can multiply the probability of each spin landing on the desired number to find the probability of both spins landing on the desired numbers.

To get the sum 7, Charlie's spinner needs to land on 4, which is (1/5) and Libby's spinner needs to land on 3 which is also (1/5).

The probability of both spins landing on the desired numbers is (1/5) * (1/5) = 1/25.

It is important to note that the probability is low because the spins are independent events, meaning that the outcome of one spin does not affect the outcome of the other spin.

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Using the vertical line test, the graph that represents a function is: Graph C.

A simple test we can carry out quickly to determine if a graph represents a function is the vertical line test.

Using the vertical line test, a vertical line is drawn across the curve in the given plane. If the vertical line intersect the curve more than once, it is not a function, but if it intersects the curve at just exactly one point, then the graph represents a function.

If we draw a vertical line across each of the given graphs, only the graph in option C will be intersected at exactly only one point.

Therefore, graph C represents a function.

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Answer:

Let h = the number of hamburgers

Let d = the number of drinks

System of Equations:

5.50h + 2.25d = 42

h + d = 10

Step-by-step explanation:

For our system of equations, we can allow h to represent the number of hamburgers purchased and d to represent the number of drinks purchased.

First equation:  We know that (cost of one hamburger * quantity of one hamburger) + (cost of one drink * quantity of one drink) = total cost

Since it costs $5.50 per hamburger, $2.25 per drink, and the total cost is $42.00, our first equation is:  

5.50h + 2.25d = 42

Second equation:  We further know that total quantity of hamburgers + total quantity of drinks = 10 amount of food and drinks purchase

Thus, our second equation is:

h + d = 10

The system of equations for the number of hamburgers (H) and drinks (D) is: 5.50H + 2.25D = 42 and H + D = 10.

Let's denote the number of hamburgers as H and the drinks as D. Hence, the system of equation can be written as follows:

1. 5.50H + 2.25D = 42, which represents the total cost of hamburgers and drinks.

2. H + D = 10, which represents the total number of items bought.

You can solve this system of equations by either substitution, elimination, or graphing methods to get the exact number of hamburgers and drinks.

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the approximations for the given values are:
(a) f(1) ≈ 30
(b) f(2) ≈ 45
(c) f(3) ≈ 45
(d) f(5) ≈ 30
(e) f(3) - f(2) ≈ 0
(f) f(3 - 2) ≈ f(1) ≈ 30.



(a) From the given information, we can determine that f(1) is approximately equal to 30.
(b) Similarly, using the information provided, we can approximate f(2) to be 45.
(c) Using the given data, we can approximate f(3) to be 45.
(d) By analyzing the information given, we can approximate f(5) to be 30.

  (e) To find f(3) - f(2), we subtract the approximated values of f(2) and f(3). From the given information, f(2) is approximately 45 and f(3) is also approximately 45. Therefore, f(3) - f(2) is approximately 45 - 45, which equals 0.
(f) The expression f(3 - 2) represents the value of the function f evaluated at the difference between 3 and 2. Since the difference between 3 and 2 is 1, we can say that f(3 - 2) is equal to f(1). From the given information, f(1) is approximately 30.

These approximations are based on the given information about the behavior of the curve as it passes through specific points on the graph. It is important to note that these are approximations and may not be exact values of the function at those points.



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Answer:

0, 5x

Step-by-step explanation:

0 in the first box

5x in the second box

Answer:

75 & 21

Check:

75 + 21 = 96

21 * 4 - 9 = 75

Correct!

Answer:

the smaller number is 21 and the larger number is 75

Step-by-step explanation:

First make a simple equation where x = the smaller number and y = the larger number

ie: 96=x+y

Now make an equation to find the larger number.

ie: y=4x-9

Now substitute the y value in the first equation for the y value in the second equation

ie: 96=x+(4x-9)

Then solve for x

ie: x=21

Then plug in your new x value into the first or second equation to solve for y.

ie: 96=21+y

ie: y=75

Answer:

0

Step-by-step explanation:

First of all, simplify the equation on both sides. You will get 5x - 2 = 2x - 2. Add two to both sides, and you get 5x=2x. Subtract 2x from both sides to get 3x=0, so x will equal 0.

Answer:

5x = 2x

Step-by-step explanation:

5x- 2 = 2 + 2x

5x - 2+ 2 = -2 + 2x +2

Step-by-step explanation:

multiple 2× 4

then your answer. would be 8

Answer:

(5²)⁴ =5²×5⁴  =5⁸

Step-by-step explanation:

Under ideal conditions, the frequency of the dominant allele increases in each generation. Option A.

The frequency of the dominant allele increases in each generation because it is expressed in the phenotype of organisms and is therefore more likely to be passed on to the next generation.

Alternately, under ideal conditions, the frequency of the recessive allele decreases in each generation. In other words, the alleles do not necessarily reach a 50/50 balance.

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Answer:

Steve was correct in his statement.

Step-by-step explanation:

According to standard notation, opening bracket ( \([\) ) represents the lower bound of a set so that elements of the set are equal or greater than lower bound. In addition, closure parenthesis ( \()\) ) represents the upper bound of a set so that element of the set are less than upper bound.

In consequence, Steve was correct in his statement.

Answer: The answer is A bc you have to multiply .57 and 18. Hope this helps

The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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From the histogram of the distribution, it is found that Zoe is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.

An histogram is a graph that shows the number of times each element of x was observed in the distribution. When the input is an interval of values, as is the case in this problem, it shows the number of observations that is in each interval.

Hence, from the histogram in this distribution, it is found that:

75 is a greater amount than 50, hence Zoe's statement is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.

The complete problem is given by the image at the end of the answer.

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Answer:

Tip Total: $ 154,500.00

Total (Bill + Tip): $ 1,184,500.00

Answer:

It would be C

Step-by-step explanation:

since the whole area of the circle is 18 and the sector takes up one-fourth of the circle you would just divide 18 by 4 to get 4.5

Answer:

C.4.5 ft^2

Step-by-step explanation:

If the area of the whole circle is 18 ft^2, and a whole circle is 360 degrees, and you are looking for the area of 90 degrees of that circle (which is one fourth of the circle) you would divide the area by 4, to get the area for that sector.

360/90= 4: meaning that 90 degrees is 1/4 of a circle.

So, you would divide 18 by 4.

18/4=4.5

Hope this helps!

Answer:

720 m²

Step-by-step explanation:

The surface area of the prism is the sum of the areas of its 5 surfaces.

Area of triangle= ½ ×base ×height

Area of front face

= ½(6)(8)

= 24 m²

Area of back face= 24 m²

Area of rectangle= length ×breadth

Area of base

= 8(28)

= 224 m²

Area of right surface

= 10(28)

= 280 m²

Area of left surface

= 6(28)

= 168 m²

Total surface area

= 24 +24 +224 +280 +168

= 720 m²

Answer:

57.57% (round probably) for allergies and 42.42% for non allergies

Step-by-step explanation:

To find the percentage,

take the amount of people who have allergies and put it over the total number of people who speak two languages (33) and divide

19/33 x 100 = 57.57% (repeating so id round up to tenths)

same with no allergies

14/33 x 100 = 42.42% (also repeating)

Answer:

step 3

Step-by-step explanation:

4*7=28

Not 26

Answer:

No, is the answer. :)

Step-by-step explanation:

The correct answer is: c. The n-th error term (e_n) can be predicted with e_n = 0.91 * e_n - 1.

This statement indicates that there is a correlation or relationship between consecutive error terms, where the n-th error term can be predicted based on the previous error term. In a simple linear regression model, the error terms are assumed to be independent and have no correlation with each other.

However, if there is a correlation between the error terms, it violates the assumption of independence, which can lead to biased and unreliable regression results. Therefore, this condition suggests that the result from the simple linear regression model could be potentially misleading.

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Answer:

S.D = 236.5

~~~~~~~~~~~~~~~~~~

300,

785,

670,

187,

760,

724

Answer:

300, 790, 670, 190, 760, 720

Taking the limit as n approaches infinity, we get: ∬0≤x≤10≤y≤1xy da = (1/4) ∞^2 (∞+1)^2 = ∞ Therefore, the integral diverges to infinity.

To compute the integral ∬0≤x≤10≤y≤1xy da using the Riemann sum approach, we first split the domain of integration into squares using straight lines x = in and y = jn, where (i,j = 1,2,...,n). Each square has area (1/n)^2. We then approximate the value of the integral by computing the Riemann sum:

Σ f(xi, yj) ΔA

where xi and yj are sample points in the ith and jth subintervals, respectively, and ΔA is the area of the corresponding square.

In this case, f(x,y) = xy and we have n^2 squares, so we have:

∬0≤x≤10≤y≤1xy da = limn→∞ Σ f(xi, yj) ΔA
= limn→∞ Σ xy (1/n)^2
= limn→∞ (1/n^2) Σ xi Σ yj

Now, we can compute Σ xi and Σ yj using the formula for the sum of consecutive integers:

Σ xi = (1 + 2 + ... + n) = n(n+1)/2
Σ yj = (1 + 2 + ... + n) = n(n+1)/2

Substituting these values, we get:

∬0≤x≤10≤y≤1xy da = limn→∞ (1/n^2) (n(n+1)/2)^2

Simplifying this expression, we get:

∬0≤x≤10≤y≤1xy da = limn→∞ (1/4) n^2 (n+1)^2

Taking the limit as n approaches infinity, we get:

∬0≤x≤10≤y≤1xy da = (1/4) ∞^2 (∞+1)^2 = ∞

Therefore, the integral diverges to infinity.

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Answer: 24.9 hours

Step-by-step explanation:

They are travelling a total distance of 1,740 miles at a speed of 70 miles per hour. Assuming they do not rest, they will take:

Time = Distance/ Speed

= 1,740/70

= 24.9 hours