Mathematics College

A presidential candidate plans to begin her campaign by visiting the capitals in 44 of 4343 states. what is the probability that she selects the route of fourfour specific capitals? is it practical to list all of the different possible routes in order to select the one that is best?

Answers

Answer 1

If the 4 states have to be in a specific order say ABCD, then the total number of different possible routes is:

43P4 = 2,961,840

So the probability is:

1 / 2,961,840 = 3.38 x 10^-7

But if the 4 states can be in any order such as DBAC, ACBD etc, then the total number of different possible routes is:

43C4 = 123,410

So the probability is:

1 / 123,410 = 8.1 x 10^-6

No I don’t think it is practical to list all the different possible routes to select the one that is best. We can simply use mathematical models to solve for that one.

Related Questions

Margo borrows $1900, agreeing to pay it back with 6% annual interest after 13 months. How much interest will she pay?

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$127.68 interest. $2027.68 total amount.

Find the percent of tip: Cost of meal: $28.00 Tip: $3.36 The percent of the tip was ___%.

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12% because 28.00 divided by 3.36

Answer:

12.00%

Step-by-step explanation:

[tex]$3.36\\[/tex] ÷ [tex]$28.00\\[/tex] = [tex]0.12\\[/tex]

[tex]100 *0.12=12%\\[/tex] %

If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. the cost to play the game is $5. what is the expectation of this game?
a. $3.06
b. -$2.78
c. -$3.06
d. $2.78

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Chance to win $10 is 3/36 Chance to win $20 is 2/36 Chance to lose is 31/36 So if cost of play is $5: ((3*5) + (2*15) - (5*31))/36 = -3.06 C. $-3.06

Final answer:

The expected value of the gambling game with a cost of $5, and potential winnings of $10 for a sum of 10 or $20 for a sum 3, is −$2.78. The calculation shows the player will lose $2.78 on average per game, indicating it is not a profitable game to play long term. So, option (b) is correct.

Explanation:

The student is interested in determining the expected value of a gambling game where rolling two dice can result in either winning money or losing the cost to play. To find the expected value, we must consider the probability of each outcome and its associated payoff.

First, we calculate the chances of rolling a sum of 10 with two dice. There are three combinations that give a sum of 10: (4,6), (5,5), and (6,4). Since there are 36 possible outcomes when rolling two dice, the probability of obtaining a sum of 10 is 3/36 or 1/12.

Similarly, the only combinations that result in a sum of 3 are (1,2) and (2,1). Thus, the probability of rolling a sum of 3 is 2/36 or 1/18.

The expected value (EV) can be calculated using the formula:

EV = (−cost to play) + [P(sum of 10) × winnings for 10] + [P(sum of 3) × winnings for 3]

Substituting the given values yields:

EV = (−5) + [(1/12) × 10] + [(1/18) × 20]

After calculating, we find tha-

EV = −$2.78.

Since the expected value is negative, this implies that, on average, the player will lose $2.78 per game. Therefore, playing this game would result in an average loss over time.

Which number is 100 times greater than 6 thousandths

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6 thousandths = .006 so times that by 100
.006 * 100 = .6

248mph equals how many meters per second

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keeping in mind there are 1.609 kilometers in 1 mile, and 1000 meters in 1 kilometer, and 60 minutes in an hour and 60 seconds in a minute, therefore 60*60 seconds in an hour, or 3600 seconds, then

[tex]\bf \cfrac{248~\underline{mile}}{\underline{hr}}\cdot \cfrac{1.609~\underline{km}}{\underline{mile}}\cdot \cfrac{1000~m}{\underline{km}}\cdot \cfrac{\underline{hr}}{3600~sec}\implies \cfrac{248\cdot 1.609\cdot 1000~m}{3600~sec} \\\\\\ \cfrac{399032~m}{3600~sec}\approx 110.84\frac{m}{sec}[/tex]

What is the effect of decreasing the alpha level (for example, from a = .05 to a = .01)? it decreases the probability of a type i error. it decreases the size of the critical region. it decreases the probability that the sample will fall into the critical region. all of the other options are results of decreasing alpha?

Answers

The effect of decreasing the alpha level from 0.05 to 0.01. it decreases the probability that the sample will fall into the critical region, it decreases the probability of a Type I error, and it decreases the size of the critical region.
Therefore, the answer is that all of other options are results of decreasing alpha.

There are three highways in the county. the number of daily accidents that occur on these highways are poisson random variables with respective parameters .3, .5, and .7. find the expected number of accidents that will happen on any of these highways today.

Answers

There is a theorem that we can use to find the expected value of a random variable that is a sum of other random variables as follows.

If [tex]X=X_1 + X_2 + ...+X_k[/tex], then [tex]E(X)=E(X_1)+E(X_2)+...+E(X_k)[/tex].

In this case, let X = the number of accidents that will happen on any of those highways today,
[tex]X_1,X_2,X_3[/tex] are the numbers of accidents on each highway, respectively.

Then [tex]X = X_1+X_2+X_3[/tex].

Since [tex]X_1,X_2,X_3[/tex] are Poisson variates, their expected values are the parameters given, .3, .5 and .7.

So [tex]E(X_1)=.3, E(X_2) = .5, E(X_3) = .7[/tex]
Thus, [tex]E(X)=E(X_1)+E(X_2)+E(X_3) = .3 + .5 + .7 = 1.5[/tex]

The answer is 1.5.

Final answer:

To find the expected number of accidents on three highways with Poisson distributions, sum the individual expectations: 0.3, 0.5, and 0.7, resulting in an expected 1.5 accidents per day.

Explanation:

The student asked how to find the expected number of accidents that will happen on any of the three highways in a day, given that the number of daily accidents on these highways are Poisson random variables with parameters 0.3, 0.5, and 0.7 respectively. To solve this, we shall sum the parameters of the Poisson distributions because the expectation of the sum of independent random variables is the sum of their expectations.

Therefore, we calculate the expected number of accidents as follows:

For the first highway with parameter 0.3, the expected number of accidents is 0.3.

For the second highway with parameter 0.5, the expected number of accidents is 0.5.

For the third highway with parameter 0.7, the expected number of accidents is 0.7.

Adding these together, we get:

Expected number = 0.3 + 0.5 + 0.7 = 1.5 accidents per day.

You deposit $5000 each year into an account earning 8% interest compounded annually. How much will you have in the account in 20 years?

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is this using A=P(1+r)^t or A=Pe^rt

What is the end behavior of f(x)=5x^3-2x+5

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f ( x) = 5x^3 - 2x + 5

y = 5x ^3 - 2x + 5

LEFT END = RISING & RIGHT END = RISING

f(x) = 5x³-2x+5

The end behavior of a polynomial is the behavior of the graph when:
x→ + ∞ and x → - ∞

when x → + ∞, f(x) → +∞

and when x → - ∞ , f(x) → - ∞

You follow the sign of the greatest exponent , that is 3 (on 5x³)

identify the type of of function represented by the equation y=2x^2

Answers

I think it is a parabola

I believe this is a quadratic function.

which of the following was a result of prison reform during the 1800s
A. a decrease in prisons
B. a decrease in crime
C. the formation of mental hospitals
D. the formation of public schools in rural areas

Answers

Which of the following was a result of prison reform during the 1800s
A. a decrease in prisons

Answer:

C. the formation of mental hospitals

Step-by-step explanation:

During that time the jail and asylum conditions were worse.

The inmates especially the mentally ill, were bound in chains and locked in cages.

Hence, with the reform movement, came the formation of mental hospitals. Public asylums were made for the mentally ill incarcerated people.

You swim the 50-meter freestyle in 28.12 seconds.This is 0.14 second less than your previous fastest time. What was your previous fastest time?

Answers

if your fastest time was 0.14 seconds more before today then you previous fastest time would be 28.26

If a person swim the 50-meter freestyle in 28.12 seconds. This is 0.14 second less than persons previous fastest time is 28.26.

What is Equation?

Two or more expressions with an equal sign is called as equation.

Given that,

One swim the 50-meter freestyle in 28.12 seconds..

The previous fastest time be x.

The new fastest time is 28.12 seconds.

New fastest time is 0.14 second less than your previous fastest time.

So, 28.12+0.14=x

28.26=x

Hence the previous fastest time is 28.26 seconds.

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Alyssa is building a brick mailbox. She is going to stack bricks that are each \dfrac23 \text{ft}
3

2
ftstart fraction, 2, divided by, 3, end fraction, f, t tall, and the finished stack of bricks needs to be 4\dfrac23 \text{ft}4
3

2
ft4, start fraction, 2, divided by, 3, end fraction, f, t tall.
How many bricks will go in the stack?

Answers

Given that each of the brick is [tex]\frac{2}{3}[/tex] ft tall and the finished stack of bricks is [tex]4\frac{2}{3}[/tex] ft tall.

Let the number of bricks in the stack be x, then

[tex] \frac{2}{3} x=4 \frac{2}{3} = \frac{14}{3} \\ \\ \Rightarrow x= \frac{ \frac{14}{3} }{ \frac{2}{3} } = \frac{14}{3} \times \frac{3}{2} \\ \\ = \frac{14}{2} =7[/tex]

Therefore, 7 bricks will go in the stack.

Can someone please help?

Answers

3(b-4)+5b=44
distribute
3b-12+5b=44
combine number with numbers and variables with variables
8b=56
decide by 8 on both sides
b=7

We need to solve the equation:
3(b-4)+5b=44
There is only one unknown in the equation. The unknown is b.
We must isolate the unknown b on one side of the equation.
According the law of multiplication we can write the following:
3b-3*4+5b=44
3b-12+5b=44
(3b+5b)-12=44
8b-12=44

We shift a number from one side of an equation
to the other by writing it on the other side with the inverse operation,so we obtain:
8b=44+12
8b=56
b=56/8
b=7

A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?

Answers

4 $10
1 $5
4 $1
3 $.25
1 $.10
1 $.01
4 tens 1 five 4 ones 3 quarters 1 dime and one penny

ANSWER FAST
Marshall bought some pet supplies for $15. The sales tax was 6%. He wrote the expression 1.06(15) to find his total cost.

Which equivalent expression could he also use to find the total cost?

A. 15+0.6(15)
B. (1+0.06)15
C. 1+0.06(15)
D.15 + 0.06

Answers

A. 15+0.6(15)
You posted this question twice, hah.
Do you need work to show it?

At what projection angle will the range of a projectile equal to 6 times its maximum height?

Answers

i not sure but it might be 60 kilogrames

The formula for maximum height is:

H = v²sin²θ/2g

The formula for range is:

R = v²sin(2θ)/g

The relationship between the two is written as:
R = 6H
v²sin(2θ)/g = 6(v²sin²θ/2g)
v²sin(2θ)/g = 3v²sin²θ/g)
Cancelling out like terms,
sin(2θ) = 3sin²θ
Solving for θ using a scientific calculator,
θ = 33.7°

order 40/97,3/41,1/6 from least to greatest

Answers

Ordered from Lease to Greatest:

3/41, 1/6, 40/97

Find the mean median mode and range of this date 49,49,54,55,52,49,55, if necessary round to the nearest tenth

Answers

The numbers from least to greatest is (49, 49, 49, 52, 54, 55, 55) The mean is 51.8 (52 rounded), 52 is median, mode is 49, and the range is 6. :)

The Lombardo family went out to dinner and their full mean costed $62. If they left a 20% tip, how much did they tip?

Answers

their total would be $74.40 :)

Samantha parents bought her a new bed they paid 136 each month for 9 months how much did the bed cost

Answers

The cost of the bed was $1236.

Find the height of a door on a scale drawing if the door is 2 meters tall and the scale is 1 centimeter = 4 meters. Round to the nearest tenth.

Answers

1 cm in the drawing = 4 meters real measure
Since you want the drawing measure for a real 2 m, and 2 m is half of 4 m, then the drawing measure is 0.5 cm

If 1 cm = 4 m, then
0.5 cm = 2 m

Answer: 0.5 cm

The height of the door in the drawing will be 1/2 centimeters.

What is scale factor?

Scale factor is used to compare the size of two objects. Mathematically, we can write -

{K} = S{O1}/S{O2}

13 mg

Given is that the height of a door on a scale drawing if the door is 2 meters tall and the scale is 1 centimeter = 4 meters.

Height of the door = 2 meters

Scale : 1 centimeter = 4 meters.

So, in one meters, there will be - 1/4 centimeters.

In 2 meters, there will be -

(1/4) x 2 = 1/2 centimeters

Therefore, the height of the door in the drawing will be 1/2 centimeters.

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find the equation to the line that is perpendicular to y=2x-3 and goes through the point (-1,2)

Answers

first off, let's see this equation [tex]\bf y=\stackrel{slope}{2}x-3[/tex]

so, notice, since it's already in slope-intercept form, we know the slope is just 2.

a line that is perpendicular to it, will have a negative reciprocal slope to it, let's check.

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad 2\implies \cfrac{2}{1}\\\\ slope=\cfrac{2}{{{ 1}}}\qquad negative\implies -\cfrac{2}{{{ 1}}}\qquad reciprocal\implies - \cfrac{{{ 1}}}{2}[/tex]

so, what is the equation of a line whose slope is -1/2 and goes through -1,2?

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -1}}\quad ,&{{ 2}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{1}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=-\cfrac{1}{2}[x-(-1)] \\\\\\ y-2=-\cfrac{1}{2}(x+1)\implies y-2=-\cfrac{1}{2}x-\cfrac{1}{2}\implies y=-\cfrac{1}{2}x-\cfrac{1}{2}+2 \\\\\\ y=-\cfrac{1}{2}x+\cfrac{3}{2}[/tex]

License plates in a particular state display 2 letters followed by 3 numbers. How many different license plates can be manufactured for this state?

Answers

Final answer:

In Mathematics, to calculate the number of different license plates with 2 letters followed by 3 numbers, multiply the possibilities for each position: 26 × 26 for letters and 10 × 10 × 10 for numbers to get 676,000 different license plates.

Explanation:

The question pertains to the concept of permutations and combinations in Mathematics, specifically calculating the number of different license plates that can be manufactured when the format is two letters followed by three numbers. The number of possible license plates is found by multiplying the number of options for each component. For the letters, there are 26 possible choices for each of the two letter positions (assuming the English alphabet is used and letters can be repeated). For the numbers, there are 10 possible choices for each of the three number positions (using digits 0-9).

To calculate the total number of different license plates, we multiply the possibilities for each part: 26 × 26 × 10 × 10 × 10 = 676,000 different license plates. This calculation is known as the Rule of Product in combinatorics, which states that if one event can occur in 'm' ways and a subsequent event can occur in 'n' ways, then the total number of ways the two events can occur is m × n.

Final answer:

To determine the number of different license plates, multiply the number of alphabetic combinations (26 for each of the 2 letters) by the numeric combinations (10 for each of the 3 numbers), resulting in 676,000 possible plates.

Explanation:

The question is asking us to calculate the number of different license plates that can be manufactured with a specific format, which is 2 letters followed by 3 numbers. To solve this, we will assume there are 26 possibilities for each letter (A through Z) and 10 possibilities for each number (0 through 9).

For the two letters at the start, since both positions can hold any of the 26 letters in the alphabet, the total number of combinations for the two letters is 26 × 26.

For the three numbers following, each position can hold any digit from 0 to 9, giving us 10 × 10 × 10 combinations for the numbers.

To find the total number of different license plates, we multiply the number of possibilities for the letters by the number of possibilities for the numbers:

Total license plates = 26 × 26 × 10 × 10 × 10 = 676,000.

Therefore, there can be 676,000 different license plates manufactured for this state with the given format.

Write in the standard form a+bi (-4+8i)-(7-4i)

Answers

(-4+8i) - (7-4i)

Start by distributing...

(-4+8i) - (7-4i)

-4 + 8i - 7 + 4i

Combine like terms....

- 4 - 7 + 8i + 4i

- 11 + 12i

solve for first two positive solutions sin(3x)cos (4x)+cos(3x)sin(4x)=-0.9

Answers

sin(3x)cos (4x)+cos(3x)sin(4x)=-0.9
Then sin(3x+4x) = 0.9
sin(7x) = 0,9
Arcsin(,9) = 64.158 degrees or 115.842
x = 9.165 and 16.549

Every night, Mary spends 3 hours doing homework, 30 minutes practicing the piano, and 35 minutes talking on the phone. What is the total number of minutes Mary spends doing these activities?

Answers

four hours and five minutes

Tasha earns $400 per week plus a commission of 10% on her weekly sales. Each week she saves of her earnings. In the expression , what does the expression 400 + 0.1s represent in this situation?

Answers

Final answer:

In this situation, the expression 400 + 0.1s represents Tasha's total earnings for the week, including her base salary and commission.

Explanation:

In this situation, the expression 400 + 0.1s represents Tasha's total earnings for the week. The $400 represents her base salary, and the 0.1s represents the commission she earns on her sales. The value of s represents Tasha's total sales for the week.

For example, if Tasha's total sales for the week are $2000, then her commission would be 0.1($2000) = $200. Adding this to her base salary of $400, her total earnings for the week would be $400 + $200 = $600.

Therefore, the expression 400 + 0.1s represents Tasha's total earnings for the week, including her base salary and commission.

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Raj eats 1/11 of a pound of grapes in 1/25 of a minute. How many minutes will it take him to eat a full pound of grapes?

Answers

[tex]\bf \begin{array}{ccll} \stackrel{lbs}{grapes}&minutes\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{11}&\frac{1}{25}\\\\ 1&m \end{array}\implies \cfrac{\frac{1}{11}}{1}=\cfrac{\frac{1}{25}}{m}\implies \cfrac{\frac{1}{11}}{\frac{1}{1}}=\cfrac{\frac{1}{25}}{\frac{m}{1}} \\\\\\ \cfrac{1}{11}\cdot \cfrac{1}{1}=\cfrac{1}{25}\cdot \cfrac{1}{m}\implies \cfrac{1}{11}=\cfrac{1}{25m}\implies 25m=11\implies m=\cfrac{11}{25}[/tex]

A card is randomly selected from a deck of 52 cards. Find the probability that the card is between four and eight (inclusive) or is a club.

Answers

Answer:

20/52+13/52-5/52=.538

Step-by-step explanation:

The probability that the card is between four and eight (inclusive) or is a club is 4/13.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The number of cards can be written as,

The number of cards between 4 and 8 is 3 {4,5,6,7,8}.Number of club cards = 13Number of cards between 4 and 8 from heart, spades, and diamonds = 15

Now, the probability that the card is between four and eight (inclusive) or is a club is,

Probability

= (Number of club cards+ Number of cards between 4 and 8)/(Total number of cards)

= (13+15)/(52)

= 28/52

= 4/13

Hence, the probability that the card is between four and eight (inclusive) or is a club is 4/13.

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A presidential candidate plans to begin her campaign by visiting the capitals in 44 of 4343 states. what is the probability that she selects the route of fourfour specific​ capitals? is it practical to list all of the different possible routes in order to select the one that is​ best?

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A presidential candidate plans to begin her campaign by visiting the capitals in 44 of 4343 states. what is the probability that she selects the route of fourfour specific capitals? is it practical to list all of the different possible routes in order to select the one that is best?