what is the sum of a and b?

To prove that 3x ≤ y, assume the opposite, that is, 3x > y, rearrange the inequality substitute x < 2y and simplify, contradict the given condition that x < 2y, therefore, concluding that 3x ≤ y.

Start by assuming the opposite, that is, 3x > y.

From the given inequality,\(7xy \leq 3x^2 + 2y^2,\), we can rearrange to get:
\(7xy - 3x^2 \leq 2y^2\)

We can substitute \(x < 2y\) into this inequality:
\(7(2y)x - 3(2y)^2 \leq 2y^2\)

Simplifying, we get:
\(y(14x - 12y) \leq 0\)

Since y is a real number, this means that either y ≤ 0 or 14x - 12y ≤ 0.

If y ≤ 0, then 3x ≤ y is trivially true.

If 14x - 12y ≤ 0, then we can rearrange to get:
3x ≤ (12/14)y
3x ≤ (6/7)y
3x < y (since we assumed 3x > y)

But this contradicts the given condition that x < 2y, so our assumption that 3x > y must be false.

Therefore, we can conclude that 3x ≤ y.

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Question:

Find the probability of getting a doublet in a throw of a pair of dice.

Answer:

The probability is 1 out of 6.

Explanation:

There are a total of 6 possibilities that you get a doublet, which is {1, 1}, {2, 2}, {3, 3}, {4, 4}, {5, 5}, and {6, 6}.

The total possibilities of throwing a dice are 6 possibilities for the first dice, and 6 possibilities for the second dice. Which results in a total of 6 × 6 = 36 possibilities available.

Probability = Possibilities of getting doublet ÷ Total possibilities = 6 ÷ 36 = 1 ÷ 6.

Hopefully this answer will help you.

The argument "All cats are mammals. I am a mammal. Therefore, I am a cat" is fallacious and can be shown as such using set theory and a Venn diagram.

Let's represent the sets using a Venn diagram:

   -------------

   |    Mammals   |

   -------------

       /       \

      /         \

     /           \

----          ----

| Cats |        | You |

----          ----

In the Venn diagram, the circle labeled "Mammals" represents the set of all mammals, and the circle labeled "Cats" represents the set of all cats. The region where the circles overlap represents the set of mammals that are also cats.

According to the argument, "All cats are mammals," which means that the set of cats is entirely contained within the set of mammals. This relationship is correctly represented in the Venn diagram.

The argument also states, "I am a mammal," which means that you are part of the set of mammals. In the Venn diagram, your position would be within the circle labeled "Mammals" but outside the circle labeled "Cats."

The fallacy occurs when the argument concludes, "Therefore, I am a cat." This conclusion is not valid because being a mammal does not automatically make you a cat. The Venn diagram clearly shows that there is a region within the set of mammals that is not within the set of cats.

To summarize, the fallacy in the argument arises from incorrectly inferring that being a mammal automatically implies being a cat. The Venn diagram visually demonstrates that being a mammal is a broader category that encompasses various animals, including cats, but being a mammal alone does not make one a cat.

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Answer:

(Answer in picture)

Answer: 71  1/2$

Step-by-step explanation:

From the given information , the hawk's speed increased by 0.84 ft/s from t=3 to t=9.

To find the change in speed of the hawk from t=3 to t=9, we need to integrate the acceleration function over the given time interval. The acceleration function is given as a(t) = 0.2 + 0.14t ft/s^2.

First, let's find the velocity function by integrating the acceleration function:

v(t) = ∫ a(t) dt = ∫ (0.2 + 0.14t) dt = 0.2t + 0.07t^2 + C,

where C is the constant of integration. We can determine the value of C by considering the initial condition. Since we want the speed at t=3, we can use the initial speed given.

Given that v(0) = 3 ft/s (initial speed), we substitute t=0 and v(0)=3 into the velocity function:

3 = 0.2(0) + 0.07(0^2) + C

C = 3.

Thus, the velocity function becomes:

v(t) = 0.2t + 0.07t^2 + 3.

To find the change in speed from t=3 to t=9, we evaluate the velocity function at these time points:

v(3) = 0.2(3) + 0.07(3^2) + 3 = 0.6 + 0.63 + 3 = 4.23 ft/s,

v(9) = 0.2(9) + 0.07(9^2) + 3 = 1.8 + 5.67 + 3 = 10.47 ft/s.

The change in speed is the difference between these two values:

Change in speed = v(9) - v(3) = 10.47 - 4.23 = 6.24 ft/s.

The hawk's speed increased by 6.24 ft/s from t=3 to t=9.

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Answer:

43720

Step-by-step explanation:

It was right on delta math

Answer:

The answer is 118.

Step-by-step explanation:

You would plug in 6 for x. You would then do 18 times 6 to get 108. Then you would add 10 to 108 to get 118.

Answer:

Given

f(x)= 18x+10

f(6)=18(6)+10

f(6)=108+10

f(6)=118

Step-by-step explanation:

to solve this problem you will need to insert 6 every place there is an X in the equation, and then follow the order of operations.

The system of the equation doesn't give the solution at (-3, -6).

-4x+y = 6

solve for y

\(-4x+y =6\\y= 6+4x\)

5x-y =21

substitute the value of y in equation 2,

\(5x-(6+4x) =21\\5x -6 -4x =21\\5x -4x=21+6\\x = 27\)

Substitute the value of x in equation 2,

\(5x-y =21\\5(27)-y =21\\135-y = 21\\-y=21-135\\-y = -114\\y=114\)

We can see that the solution of the two equations is at (27, 114). Also, it can be verified by plotting the line on the graph.

Hence, the system of the equation doesn't give the solution at (-3, -6).

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The amount of cars that have been sold more this year compared to the previous year is given as follows:

3,600 cars.

The amount of cars that have been sold more this year compared to the previous year is obtained applying the proportions in the context of the problem.

The amount of cars sold this year is given as follows:

11/13 x 27300 = 23,100 cars.

The amount of cars sold on the previous year is given as follows:

15/21 x 27300 = 19,500 cars.

Hence the difference is given as follows:

23100 - 19500 = 3,600 cars.

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The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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a) The feasible set can be represented as a straight line with a negative slope on a graph.

b) The preferred choice point is (15, 15).

c)  With an entrance fee of $9, the new feasible set shifts vertically upwards.

d)  The change in entrance fee reduced the amount of leftover cash in the feasible set.

a) The x-axis represents the number of pizza slices, and the y-axis represents the leftover cash. The line starts at the point (0, 60) and intersects the x-axis at (20, 0). This means that you can buy a maximum of 20 pizza slices with $60, and if you don't buy any pizza, you will have $60 left.

b) This point represents buying 15 slices of pizza, which costs $45, and having $15 left. It is the preferred choice because it allows for a balance between enjoying pizza and not exhausting all the cash. It provides both a substantial amount of pizza and a reasonable amount of leftover cash.

c) The line now starts at (0, 51) and intersects the x-axis at (20, 9). This means that with the entrance fee, you can buy a maximum of 20 pizza slices and have $9 left.

d) It means that you have less cash available after buying pizza slices. The new preferred choice would likely shift downwards to a point that allows for a reasonable number of pizza slices while still leaving enough money to cover the entrance fee.

The change in entrance fee makes it necessary to consider the balance between the number of pizza slices and the available cash more carefully to ensure you can afford the entrance fee and still enjoy a satisfying amount of pizza.

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To find the PMF for X(T), we first find the conditional distribution of X(t) given T = t, which is a Poisson distribution with parameter λt. Then, we multiply this conditional distribution by the density function of T, which is μe^(-μt), and integrate over all possible values of t.

The probability mass function (PMF) for X(T), where Xt is a Poisson process with parameter λ and T is exponentially distributed with parameter μ, can be expressed in two steps. First, we need to find the conditional probability distribution of X(t) given T = t for any fixed t. This distribution will be a Poisson distribution with parameter λt. Second, we need to find the distribution of T. Since T is exponentially distributed with parameter μ, its probability density function is fT(t) = μe^(-μt) for t ≥ 0. To find the PMF for X(T), we can multiply the conditional distribution of X(t) given T = t by the density function of T, and integrate over all possible values of t. This will give us the PMF for X(T).

Now, let's explain the answer in more detail. Given that T = t, the number of events in the time interval [0, t] follows a Poisson distribution with parameter λt. This is because the Poisson process has a constant rate of λ events per unit time, and in the interval [0, t], we expect on average λt events to occur.

To obtain the PMF for X(T), we need to consider the distribution of T as well. Since T is exponentially distributed with parameter μ, its probability density function is fT(t) = μe^(-μt) for t ≥ 0.

To find the PMF for X(T), we multiply the conditional distribution of X(t) given T = t, which is a Poisson distribution with parameter λt, by the density function of T, and integrate over all possible values of t. This integration accounts for the uncertainty in the value of T.

The resulting PMF for X(T) will depend on the specific form of the density function fT(t), and the Poisson parameter λ. By performing the integration, we can derive the expression for the PMF of X(T) in terms of λ and μ.

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Convergent series:A series is said to be convergent when the limits of the series converge to the finite possible value for the series.

Consider a series

Sn=a1+a2+a3+a4+........+an

this form a new series as ,

Sn(n=1 to infinity)=

=s.

It is important that the partial sum of series, there should be a limit existed and that is finite in nature then only the series converges.

The geometric series gives a proper idea of how the limit decides the convergent and divergent nature.

A series in which the individual term, approaches zero then series is convergent in nature but not for all time.

The series,

A convergent series is a series for which limits exist.

If the sequence of the partial sum is a convergent sequence.

G(r,c)=  r+c

where r≠1 then series converges.

Divergent series:

A series is an infinite series that does not converge at  any point,

had an infinite sequence of partial sums with no finite limit.

A series where the individual sum does not approaches zero diverges.

For e.g.

This series diverges.

Or harmonic series which diverges.

Where is limit tends to infinity, eventually series added up to infinity means no exact answer will be there.

For summing the divergent series  there method is:

FT

extrapolation methods.

Abelian theorems

Regularity, linearity, and stability test for the series.

If this test is checked then we will get to know which series diverges and converges.

It is not possible to determine whether a series converges or diverges based on its sum alone. The sum of a series can be finite, infinite, or undefined, but it does not provide information on whether the series converges or diverges. Other mathematical tests, such as the ratio test or the integral test, are used to determine whether a series converges or diverges.

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Answer: 624 ft^3

work is in the image i attached

Answer:

7

Step-by-step explanation:

The data value that corresponds to the 46th percentile is 10.

To find the data value that corresponds to the 46th percentile, we need to arrange the given data in ascending order and then identify the value at the desired percentile.

Arranging the data in ascending order:

7, 12, 14, 16, 19, 19, 19, 25, 25, 27, 28, 28, 34, 37, 38, 40, 53, 69, 92, 115, 200

Since we have 21 data values, the 46th percentile corresponds to the (46/100) * 21 = 9.66th value.

To find the corresponding data value, we round up the decimal value to the nearest whole number, which is 10.

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Answer:

13 1/2 hours

Step-by-step explanation:

4/6=9/x then find the rate and solve

Answer:

4 times 3 = 12

1/3 times 3 = 1

12 + 1 = 13

Answer:

The expressions are:

2. \(60h+20\ minutes\)

3. \(2+\frac{x}{60}\ hours\)

4. \(y+0.75\ hours\)

Step-by-step explanation:

The given expressions have to be converted into algebraic expressions.

So,

2. Write an algebraic expression for the total number of minutes in h hours and 20 minutes.

Here,

h is a variable that can have any value but the 20 minutes will remain same with any number of hours.

If h is for hour, the number of minutes in h hours will be: \(60*h = 60h\)

And there are also 20 minutes so the algebraic expression is:

\(60h+20\ minutes\)

3. Write an algebraic expression for the total number of hours in 2 hours and x minutes.

In order to convert minutes into hour, the minutes are divided by 60

So converting x minutes into hour means

\(x\ minutes = \frac{x}{60}\ hours\)

There are 2 hours already so the expression will be:

\(2+\frac{x}{60}\ hours\)

4. Write an algebraic expression for the total number of hours in y hours and 45 minutes.

Converting 45 minutes to hours by dividing by 60

\(45\ minutes = \frac{45}{60}\ hours = 0.75\ hours\)

The expression is:

\(y+0.75\ hours\)

Hence,

The expressions are:

2. \(60h+20\ minutes\)

3. \(2+\frac{x}{60}\ hours\)

4. \(y+0.75\ hours\)

Answer:

16 miles

Step-by-step explanation:

3.2 miles per minute for 5 minutes

3.2*5=16

16 miles

Answer:

11 1/12

Step-by-step explanation:

The model used by Victor in the linear equation is incorrect,

The parameters are that;

Victor saved: $89.25

Cost of the bicycle = $129.85

Thus, to find the amount extra that he will need to purchase the bicycle, the equation model should be;

$89.25 + x = $129.85

This can be expressed in words as;

The amount of money he already has saved + the amount of money he still requires = the total price of the bike.

An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle

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Complete question is;

Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor writes the equation below to help him determine the additional amount that he needs to solve to have enough to buy the bicycle.

89.25 + 129.85 = x

Does Victor's equation correctly model the problem?

The inequality that can be used to solve for x, the height of the wall, is \(x^2 + 15x - 166 ≤ 0.\)

To solve for x, the height of the wall, we need to set up an inequality based on the combined area of the wall and the paintings.

The area of the wall can be represented as (15 + x) ft multiplied by the width x ft, which gives us an area of (15 + x) * x square feet.

The combined area of the wall and the three paintings is the area of the wall plus the sum of the areas of the three paintings, which are each 3 ft by 4 ft. So the combined area is (15 + x) * x + 3 * 4 * 3 square feet.

We want the combined area to be at most 202 square feet, so we can set up the following inequality:

\((15 + x) * x + 3 * 4 * 3 ≤ 202\)

Simplifying the inequality:

(15 + x) * x + 36 ≤ 202

Expanding the terms:

15x + x^2 + 36 ≤ 202

Rearranging the terms:

\(x^2 + 15x + 36 - 202 ≤ 0x^2 + 15x - 166 ≤ 0\)

Now we have a quadratic inequality. We can solve it by factoring or by using the quadratic formula. However, in this case, since we are looking for a range of values for x, we can use the graph of the quadratic equation to determine the solution.

By graphing the quadratic equation y =\(x^2 + 15x\)- 166 and finding the values of x where the graph is less than or equal to zero (on or below the x-axis), we can determine the valid range of x values.

Therefore, the inequality that can be used to solve for x, the height of the wall, is \(x^2 + 15x - 166 ≤ 0.\)

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The graph of the first five terms can be seen in the image at the end.

We know that we have an arithmetic sequence:

3, -10, -23, -36

The common difference is what we get when we subtract two consecutive terms, we will get:

d = -36 - (-23) = -3

Then the recursive relation is:

a(n) = a(n - 1) - 13

At the moment we know:

a(1) = 3

a(2) = -10

a(3) = -23

a(4) = -36

Then fifth term will be:

a(5) = a(4) - 13 = -36 - 13 = -49

Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).

The graph can be seen in the image below:

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Part a)Given, utility function of the consumer as:U(x1, x2) = log(x1) + log(x2)X1 ≤ 0.5Let p2 = 1 and m = 1, and p1 is unknown. The consumer has a budget constraint as: p1x1 + p2x2 = m = 1Now we have to find the minimal p1 such that the consumer consumes x1 strictly less than 0.5.

We need to find the value of p1 such that the consumer spends the entire budget (m = 1) on the two goods, but purchases only less than 0.5 units of the first good. In other words, the consumer spends all his money on the two goods, but still cannot afford more than 0.5 units of good 1.

Mathematically we can represent this as:

p1x1 + p2x2 = 1......(1)Where, x1 < 0.5, p2 = 1 and m = 1

Substituting the given value of p2 in (1), we get:

p1x1 + x2 = 1x1 = (1 - x2) / p1Given, x1 < 0.5 => (1 - x2) / p1 < 0.5 => 1 - x2 < 0.5p1 => p1 > (1 - x2) / 0.5

Now we know, 0 < x2 < 1.So, we will maximize the expression (1 - x2) / 0.5 for x2 ∈ (0,1) which gives the minimum value of p1 such that x1 < 0.5.On differentiating the expression w.r.t x2, we get:d/dx2 [(1-x2)/0.5] = -1/0.5 = -2

Therefore, (1-x2) / 0.5 is maximum at x2 = 0.

Now, substituting the value of x2 = 0 in the above equation, we get:p1 > 1/0.5 = 2So, the minimal value of p1 is 2.Part b)Now, we have to show mathematically that whether the threshold on p1 found in Part a increases/decreases/stays the same when p2 increases.

That is, if p2 increases then the minimum value of p1 will increase/decrease/stay the same.Since p2 = 1, the consumer’s budget constraint is given by:

p1x1 + x2 = m = 1Suppose that p2 increases to p2′.

The consumer’s new budget constraint is:

p1x1 + p2′x2 = m = 1.

Now we will find the minimal p1 denoted by pi, such that the consumer purchases less than 0.5 units of good 1. This can be expressed as:

p1x1 + p2′x2 = 1Where, x1 < 0.5

The budget constraint is the same as that in Part a, except that p2 has been replaced by p2′. Now, using the same argument as in Part a, the minimum value of p1 is given by:

p1 > (1 - x2) / 0.5.

We need to maximize (1 - x2) / 0.5 w.r.t x2.

As discussed in Part a, this occurs when x2 = 0.Therefore, minimal value of p1 is:

pi > 1/0.5 = 2

This value of pi is independent of the value of p2′.

Hence, the threshold on p1 found in Part a stays the same when p2 increases.

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Answer:

d. 46.19

Step-by-step explanation:

y=124.85(0.37)

to figure out the percent decrease, subtract the percent from 100. then divide by 100 to get a decimal. multiply that decimal by the original cost to get the answer.

In these options, 0ption D that is, Multicollinearity, is not an assumption of the regression model.

The regression model is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. There are several assumptions associated with the regression model, which should be satisfied for accurate and reliable results.

Option A, Linearity, assumes that there is a linear relationship between the independent variables and the dependent variable. It implies that the relationship can be represented by a straight line.

Option B, Independence, assumes that the observations or data points used in the regression model are independent of each other. This means that the value of one observation does not depend on or influence the value of another observation.

Option C, Homoscedasticity, assumes that the variance of the errors or residuals in the regression model is constant across all levels of the independent variables. It implies that the spread or dispersion of the residuals is consistent.

Option D, Multicollinearity, is not an assumption of the regression model. Multicollinearity refers to a high correlation between independent variables in the regression model, which can cause issues in estimating the individual effects of the independent variables.

Therefore, the correct answer is D) Multicollinearity, as it is not an assumption of the regression model.

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In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

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Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3