Ian is trying to minimize the time he needs to spend on the bus going from Toronto (origin) to Windsor (destination). Since there is no direct bus from Toronto to Windsor, he needs to choose from different buses available between Toronto, Waterloo, Hamilton, London, and Windsor.The travel times between these cities are summarized in table below (only consider westbound routes). A dash indicates that there is no westbound bus connecting those two cities. If we model our problem as a shortest path problem by defining Xij=1 if we travel from city i to city j, what is the constraint corresponding to node London?WaterlooHamiltonLondonWindsorToronto75 min60 min--Waterloo--65 min180 minHamilton--80 min-London---115 minQuestion 4 options:X(Waterloo-London) + X(Hamilton-London) >= 1X(Waterloo-London) + X(Hamilton-London) – X(London-Windsor) = 065*X(Waterloo-Windsor) + 80*X(Hamilton-London) – 115*X(London-Windsor) = 065*X(Waterloo-Windsor) + 80*X(Hamilton-London) + 115*X(London-Windsor) = 0X(Waterloo-London) + X(Hamilton-London) + X(London-Windsor) <= 2

Answer:

9

Step-by-step explanation:

The number is 9. To find it, you can use the following steps:

Let x be the number. Then the equation is 3x - 2 = 25.

Add 2 to both sides: 3x = 27.

Divide both sides by 3: x = 9.

Hope this helps :)

Answer:

Step-by-step explanation:

3x - 2 = 25

3x = 25 + 2

3x = 27

x = 27 : 3

x = 9

------------------------------

check

3 x 9 - 2 = 25

27 - 2 = 25

25 = 25

the answer is good

An exponential function with a vertical stretch by a factor of 2 and a translation left 1 unit and up 2 units is given as follows:

y = 2(2)^(x + 1) + 2.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

A vertical stretch by a factor of k means that the definition of the function is multiplied by k.

The parent function in the context of this problem is given as follows:

y = 2^x.

Hence the exponential function with a vertical stretch by a factor of 2 and a translation left 1 unit and up 2 units is given as follows:

y = 2(2)^(x + 1) + 2.

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-4y-1

Step-by-step explanation:

If you subtract \({ \green{ \tt{8y + 7}}} \)from \({ \red{ \tt{4y - 8}}}\) then the resultant answer will be as follows

\( \: \: \: \: \: { \red{ \tt{4y - 8}}} \\ - \ \: { \green{ \tt{8y + 7}}} \\ = -{ \blue{ \tt{ 4y - 1}}}\)

Answer:

18/8= 9/4

Step-by-step explanation:

3x6=18 the denominator is 8 so 8x1 is 8 simplified by 2

hope this helped!

Answer:2 1/4

Step-by-step explanation:

Because I know what it is

Answer:

Step-by-step explanation:

Step-by-step explanation:

(5√2 - 4√3) (5√2 - 4√3)

= (5√2)² - 20√6 - 20√6 + (4√3)²

= 50 - 40√6 + 48

= 98 - 40√6

Answer:

the second one!

Step-by-step explanation:

Answer:

34°

Step-by-step explanation:

So both angles marked are equal, I think according to some rule in math, but yea, so if one is 34° then the other one is also 34°

3

Step-by-step explanation:

3520 = 12.5h + 1000

-1000 -1000

2520 = 12.5h

---------------------

12.5 12.5

180 = h

The function f(x) is given by f(x) = (x^5) - (x^4) + (5x^2) - (5x) + 2.

The function f(x) is given as f ''(x) = 20x^3 - 12x^2 + 10, with initial conditions f(0) = 2 and f(1) = 7. We need to find the function f(x).

Integrating f ''(x) with respect to x, we get f'(x) = 5x^4 - 4x^3 + 10x + C1, where C1 is the constant of integration. Integrating f'(x) with respect to x, we get f(x) = (x^5) - (x^4) + (5x^2) + (C1*x) + C2, where C2 is another constant of integration.

Using the initial condition f(0) = 2, we get C2 = 2. Using the initial condition f(1) = 7, we get C1 + C2 = 2, which gives us C1 = -5. Therefore, the function f(x) is given by f(x) = (x^5) - (x^4) + (5x^2) - (5x) + 2.

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Assuming that for all rational number a and irrational number b, ab is irrational, we can prove by contradiction by choosing a rational number a and an irrational number b such that ab is rational.

To show that there exist a rational number a and an irrational number b such that ab is rational, we can use the following proof by contradiction:

Assume that for all rational numbers a and irrational numbers b, ab is irrational.

Let's choose any rational number a and let b be the square root of 2 which is known to be an irrational number. Then ab = a√2 is the product of a rational number and an irrational number, and by our assumption, this product should be irrational.

However, we can see that ab can actually be rational if we choose a carefully. For example, if we choose a = 0, then ab = 0 which is a rational number. Therefore, our assumption that for all rational numbers a and irrational numbers b, ab is irrational is false.

Hence, by contradiction, we can conclude that there exist a rational number a and an irrational number b such that ab is rational.

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Let,

Now,

The probability is:

→ \(P(xq) = 0.35\times 0.15\)

             \(= 0.0525\)

→ \(P(yp) = (1-0.35)\times 0.85\)

             \(= 0.65\times 0.85\)

             \(= 0.5525\)

hence,

The likelihood that perhaps the factory's carbon emissions were well within the allowable range:

= \(\frac{0.5525}{(0.5525+0.0525)}\)

= \(\frac{0.5525}{0.605}\)

= \(0.9132\)

Thus the above response is right.

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Answer: 0.098%

Step-by-step explanation:

The $2.25 must the theatre charge per ticket in order to maximize their revenue.

For the stated question.

Let the revenue generated be 'R'.

The price of ticket after reduction of $1 = x.

Total tickets  = 100

Using the revenue equation;

Revenue = (Number of ticket)X(price per ticket)

R =  (100 - 10x)(15 + x)

R =  1500 - 10x² -150x + 100x

R =  1500 - 10x² -50x

For the maximum revenue-

x = -b/2a = 50/2(-10)

x = -50/20 = -2.25

Thus, the $2.25 must the theatre charge per ticket in order to maximize their revenue.

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Answer: I am here to nswer

Step-by-step explanation: so first to this then do another thing

The variables considered in a chi-squared test used to evaluate a contingency table is; A categorical variable

Reason:

A contingency table is a frequency table showing two variables

simultaneously. In an investigation of a communicable infection the two

variables in the table can be handwashing and the contracting the disease

The variables in a contingency table are categorical variables

A categorical variable is a qualitative variable that can have a limited

number of defined values and are assigned to the subjects of the study

based observation or experimental treatment

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Given the equation:

We will find the intercepts of the given equation.

The x-intercept is the value of (x) when y = 0

So, substitute with y = 0 and solve the equation to find (x)

So, the x-intercept = -2

The y-intercept is the value of (y) when x = 0

So, substitute with x = 0 and solve the equation to find (y):

So, the y-intercept = 2

El resultado de esta división es 0.010

Para solucionar la operación matemática debemos realizar los siguientes pasos:

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\(\implies {\blue {\boxed {\boxed {\purple {\sf {Numerator\:=\:25 }}}}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {Denominator \:=\:56}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\( \: \frac{ - 3}{7} + \frac{7}{8} \)

Since the denominators are unequal, we find the L.C.M (lowest common multiple) for both denominators.

The L. C. M for 7 and 8 is 56.

Now,

➺\( \: \frac{ - 3 \times 8}{7 \times 8} + \frac{7 \times 7}{8 \times 7} \)

➺\( \: \frac{ - 24}{56} + \frac{49}{56} \)

Now that the denominators are equal, we can add them.

➺\( \: \frac{ - 24 + 49}{56} \)

➺\( \: \frac{ 25}{56} \)

Therefore, the numerator is \(\boxed{ 25 }\) and the denominator is \(\boxed{ 56 }\).

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{ヅ}}}}}\)

Answer:

C The probability of rolling a number less than 6 is the same for both number cubes.

Step-by-step explanation:

The answer is, C . The probability of rolling a number less than 6 is the same for both number cubes.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

the red cube has the following numbers on the faces 1,1,2,2,5,6

the blue number cube has the following numbers on the faces 1,2,2,3,4,6

hence, The answer is, C . The probability of rolling a number less than 6 is the same for both number cubes.

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Answer:

One solution

Step-by-step explanation:

At a sales level of $15,000, the two options yield the same salary.

To find the sales level at which the two options yield the same salary, we need to set the two salaries equal to each other and solve for sales:

2500 + 0.09x = 3100 + 0.05x

where x is the sales level.

Simplifying this equation, we get:

0.04x = 600

x = 15000

If the sales are less than $15,000, the first option with a lower base salary but a higher commission rate would be more favorable, while if sales exceed $15,000, the second option with a higher base salary but a lower commission rate would be more favorable.

It's worth noting that the decision between the two options depends on more than just the sales level. Other factors, such as the type of work, job security, and benefits, should also be considered when making a decision.

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Answer: \(C(t) = 120(1-0.30)^t\)

Step-by-step explanation:

Exponential equation for decay:\(y= A(1-r)^t\), where A = initial value, r= decay rate , t= time.

As per given, A = 120ml , r= 0.30

\(C(t) = 120(1-0.30)^t\)

Hence, the required function that gives the medicine's concentration in milligrams per liter, C(t), t hours after the medicine was injected.

\(C(t) = 120(1-0.30)^t\)

Answer:

Step-by-step explanation:

Let's solve each problem one by one:

1. Adam has $2 and is saving $2 each day. Brodie has $8 and is spending $1 each day. After how many days will each person have the same amount of money?

Let's assume the number of days is represented by 'x'.

Adam's money after 'x' days = $2 + $2x

Brodie's money after 'x' days = $8 - $1x

To find the number of days when they have the same amount of money, we set up an equation:

$2 + $2x = $8 - $1x

Simplifying the equation:

$2x + $1x = $8 - $2

$3x = $6

x = $6 / $3

x = 2

Therefore, after 2 days, Adam and Brodie will have the same amount of money.

Answer: A. 5x + 4 = 3x - 2 (incorrect)

2. A number increased by 8 is equal to twice the same number increased by 7.

Let's represent the number by 'x'.

Equation: x + 8 = 2x + 7

Solving the equation:

x - 2x = 7 - 8

-x = -1

x = 1

Therefore, the number is 1.

Answer: D. x + 8 = 2x + 7 (correct)

3. Spot weighs 6 pounds and gains one pound each week. Buddy weighs 2 pounds and gains 2 pounds each week. After how many weeks will the puppies weigh the same?

Let's represent the number of weeks by 'x'.

Spot's weight after 'x' weeks = 6 + 1x

Buddy's weight after 'x' weeks = 2 + 2x

To find the number of weeks when they weigh the same, we set up an equation:

6 + 1x = 2 + 2x

Simplifying the equation:

x - 2x = 2 - 6

-x = -4

x = 4

Therefore, after 4 weeks, Spot and Buddy will weigh the same.

Answer: A. x + 6 = 2x + 2 (incorrect)

4. Five less than two times a number is equal to 4 less than the same number.

Let's represent the number by 'x'.

Equation: 2x - 5 = x - 4

Solving the equation:

2x - x = -4 + 5

x = 1

Therefore, the number is 1.

Answer: B. 2x - 5 = x - 4 (correct)

5. Ann has an empty cup and adds 1 ounce of water per second. Bob has 12 ounces of water and drinks 2 ounces per second. After how many seconds will they have the same amount of water?

Let's represent the number of seconds by 'x'.

Ann's water after 'x' seconds = 1x ounces

Bob's water after 'x' seconds = 12 - 2x ounces

To find the number of seconds when they have the same amount of water, we set up an equation:

1x = 12 - 2x

Simplifying the equation:

1x + 2x = 12

3x = 12

x = 12 / 3

x = 4

Therefore, after 4 seconds, Ann and Bob will have the same amount of water.

Answer: A. -2x + 12 = -x + 6 (incorrect)

6. Tom has

12 candies and eats 2 each minute. Sue has 6 candies and eats 1 every minute. After how many minutes will they have the same number of candies?

Let's represent the number of minutes by 'x'.

Tom's candies after 'x' minutes = 12 - 2x

Sue's candies after 'x' minutes = 6 - 1x

To find the number of minutes when they have the same number of candies, we set up an equation:

12 - 2x = 6 - 1x

Simplifying the equation:

-2x + 1x = 6 - 12

-x = -6

x = 6

Therefore, after 6 minutes, Tom and Sue will have the same number of candies.

Answer: A. -2x + 12 = -x + 6 (correct)

Therefore, the closest point to P in the subspace W is approximately (0.259, 0.309, -0.581).

To find the closest point to a given point in a subspace spanned by a set of vectors, we can use the projection formula. Let's denote the given point as P and the subspace as W, spanned by the vectors v₁ and v₂.

The projection of P onto W can be calculated using the formula:

projᵥ(P) = ((P·v₁) / (v₁·v₁)) * v₁ + ((P·v₂) / (v₂·v₂)) * v₂,

where · represents the dot product.

In this case, the given point P is (4, 4, 8) and the subspace W is spanned by the vectors v₁ = (5, 1, -2) and v₂ = (-6, 28, -2).

First, we need to calculate the dot products and the denominators for the projection formula:

P·v₁ = 4 * 5 + 4 * 1 + 8 * (-2) = 20 + 4 - 16 = 8,

P·v₂ = 4 * (-6) + 4 * 28 + 8 * (-2) = -24 + 112 - 16 = 72,

v₁·v₁ = 5 * 5 + 1 * 1 + (-2) * (-2) = 25 + 1 + 4 = 30,

v₂·v₂ = (-6) * (-6) + 28 * 28 + (-2) * (-2) = 36 + 784 + 4 = 824.

Now we can substitute these values into the projection formula to find the closest point to P in the subspace W:

projᵥ(P) = (8 / 30) * (5, 1, -2) + (72 / 824) * (-6, 28, -2).

Calculating each component separately:

projᵥ(P) = (8/30) * (5, 1, -2) + (9/103) * (-6, 28, -2),

projᵥ(P) = (40/150, 8/30, -16/30) + (-54/824, 252/824, -18/824),

projᵥ(P) = (40/150 - 54/824, 8/30 + 252/824, -16/30 - 18/824),

projᵥ(P) = (32760/123000 - 810/123000, 6520/123000 + 31500/123000, -49280/123000 - 22140/123000),

projᵥ(P) = (31950/123000, 38020/123000, -71420/123000),

projᵥ(P) ≈ (0.259, 0.309, -0.581).

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If it rained on Monday, Tuesday, Thursday and Friday Last week then probability of rain would be 4/7 as there are 7 days in a week.

Total days in week = total outcome = 7days
Possible outcome = 4
P(rain) = 4/7

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Answer:

5 basketballs and 2 soccer balls

Step-by-step explanation:

5 times 20= 100

2 times 18= 36

equals 136

4 basketballs and 6 soccer balls- wrong-185

2 basketballs and 7 soccer balls-wrong-166

6 basketballs and 5 soccer balls- wrong- over 200

Answer:

The Inequality Equation is

20b + 18s <_ 150

5 Basketballs and 2 Soccer Balls

Step-by-step explanation:

$50.15

Step-by-step explanation:

100%->$43.70

1%->$43.70÷100≈0.43

15%->$0.43×15=$6.45

115%->$50.15 (ans)

nkt sure if correct but.. yeah

The prediction we can make is that there were about 169 principals in attendance at the conference. The answer is D.

A type of ratio known as proportions describes the size of one segment of a group in relation to the size of the group as a whole, or population.

If 80 people represent a certain percentage of the total attendance, then we can use that same percentage to estimate the number of principals in attendance. Specifically:

percentage of principals in exhibit room = 15/80 = 0.1875

percentage of total attendance in exhibit room = 80/900 = 0.0889

If we assume that the percentage of principals in the exhibit room is similar to the percentage of principals in the entire conference, then we can set up the following proportion:

0.1875 / x = 0.0889 / 900

where x represents the total number of principals in attendance.

here, Solve for x, then:

x = 169

Therefore, the prediction we can make is that there were about 169 principals in attendance at the conference. The answer is D.

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