let a and be positive integers satisfying (ab+1)/(a+b) < 3/2. The maximum possible value of (a^3b^3+1)/(a^3+b^3) is p/q. where p and q are relatively prime positive integers. Find p+q.

Answer:

1.478 x 10^2 AU

Step-by-step explanation:

To convert this distance to astronomical units (AU), we can use the fact that 1 AU is approximately equal to 93 million miles.

So, 13.8 billion miles is approximately:

13.8 billion miles / 93 million miles/AU = 147.8 AU

In scientific notation, this distance would be written as: 1.478 x 10^2 AU

(a) The average rate of change over the interval [2, 5] is given by (f(5) - f(2)) / (5 - 2), which is equal to (24 - 16) / (5 - 2) = 8 / 3 = 2.67.

(b) The average rate of change over the interval [3.8, 4] is given by (f(4) - f(3.8)) / (4 - 3.8), which is equal to (19 - 19.6) / (4 - 3.8) = -0.6 / 0.2 = -3.

The average rate of change over a given interval [a, b] is a measure of how much the value of a function changes on average as the input changes over that interval. It is calculated as the difference between the value of the function at the endpoints of the interval divided by the difference of the corresponding inputs.

Formally, the average rate of change over the interval [a, b] is given by:

f_avg = (f(b) - f(a)) / (b - a)

where f is the function being evaluated and f_avg represents the average rate of change.

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The type of sampling used in this example is Convenience sampling.

Convenience sampling is a type of non-probability sampling in which the sample is selected based on the ease of access or availability of the subjects. The sample is selected based on the researcher's convenience, and it does not use a random selection process.

In this case, the reporter chose to interview people in his own apartment building because it was convenient for him and he had easy access to them.

The other options you listed are:

a) Cluster sampling, which is a form of probability sampling in which the sample is selected by first dividing the population into smaller groups or clusters, and then selecting a random sample of those clusters.

b) Voluntary response sampling, which is a type of non-probability sampling where individuals choose to participate in the study.

c) Systematic sampling, which is a form of probability sampling in which the sample is selected by choosing a random starting point and then selecting every nth subject from the population.

d) Attempted census, which is when the researcher tries to include all members of a population in the sample.

Therefore, The type of sampling used in this example is Convenience sampling.

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Answer:

The total number of planes landing at O’Hare Airport categorized by type.

Differentiating the expression [tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex] with respect to x will be [tex]16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]

We are given with

[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]

Here we will be using the chain rule. According to the chain rule, we will first have to solve the parentheses as a variable. Then we will have to solve the expression within the parenthesis

First, we will differentiate [tex](4x-7)^4[/tex] keeping [tex](7x+8)^5[/tex] constant. Here we will first assume [tex](4x-7)[/tex] as one variable and differentiate using the formula d/dx[x^n] then we will differentiate 4x - 7 to get just 4. They would be multiplied by one another

Hence we get

[tex]4 X4(4x-7)^3(7x+8)^5[/tex]

[tex]16(4x-7)^3(7x+8)^5[/tex]

Now, we will keep [tex](4x-7)^4[/tex] constant and differentiate [tex](7x+8)^5[/tex] and adding it up we get

[tex]16(4x-7)^3(7x+8)^5 + 5X7(4x-7)^4(7x+8)^4[/tex]

[tex]= 16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]

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Complete Question

[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]

Answer: If x-1 is a factor of f(x) = 3x^3+kx-13, then f(x) can be written as (x-1)g(x) for some polynomial g(x). This means that f(1) = 0.

We can substitute x = 1 into f(x) to get f(1) = 3(1)^3 + k(1) - 13 = 3 + k - 13 = 0.

Therefore k - 10 = 0, so k = 10

So the value of k is 10.

Step-by-step explanation:

The unknown side AC will be equal to 2.33.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that a right triangle ABC. Angle ACB is a right angle. Angle ABC is twenty-five degrees. The side AC is unknown. Side BC is five units.

The unknown side will be calculated as:-

tan(25) = P / B

tan(25) = AC / BC

AC = BC x tan(25)

AC = 5 x tan(25)

AC = 2.33

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Answer: The height of the ball (in meters) after t seconds is given by the equation h = 2 + 5t - 5t^2. We can use this equation to find the values of t for which the ball's height is 3 meters.

We need to find the values of t that make h = 3, so we can substitute 3 for h in the equation:

3 = 2 + 5t - 5t^2

Then we can solve for t by moving all the terms to one side of the equation and factoring it:

-5t^2 + 5t - 1 = 0

And we can use the quadratic formula to find the solutions of this equation:

t = (5 +/- sqrt(5^2 - 4*(-1)(-1)))/ 2(-1)

t = (5 +/- sqrt(25 + 4))/ -2

t = (5 +/- sqrt(29))/ -2

The solutions of this equation are t = (5 +/- sqrt(29))/ -2

Since the time, t, is a real value the square root of 29 should be positive.

The values of t for which the ball's height is 3 meters are not real values, so there's no time when the ball's height is 3 meters.

Step-by-step explanation:

Answer:

Answer in attached photo.

Step-by-step explanation:

Solution in attached photo, do take note the standard form of an equation is:

y = mx + c,

where m is the gradient and c is the y-intercept.

Answer: (x– 8)2= 4(1)(y+ 3); vertex: (8, –3); opens upward

Smallest = 16, median=22, largest value of data=26 , interquartile range=Q3-Q1=23-19=4.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

We have the data 19 22 22 26 23 24 21 16 16, and we have to calculate smallest, Q1, median ...

First rearrange the data 16,16,19,21,22,22,23,24,26

So, Smallest = 16

Median of the data = middle number of data=22

Q1=middle of smallest and median=19

Q3=23

largest value of data=26

range= 19-26

interquartile range=Q3-Q1=23-19=4

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The amount Jacob has to pay in a month where he used x GB over the limit is  y=25+20x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Jacob has a smart phone data plan that costs $25 per month that includes 5 GB of data, but will charge an extra $20 per GB over the included amount.

Amount Jacob has to pay in a month where he used 4 GB over the limit is

25+4×20

= $105

Amount Jacob has to pay in a month where he used x GB over the limit is

y=25+20x

Where, y is total amount of money

Hence, the amount Jacob has to pay in a month where he used x GB over the limit is  y=25+20x.

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Answer:

Step-by-step explanation:

I don’t know just 5 point

After the raise, Tyler's brother will make $14 x 1.05 = $14.70 per hour.

Answer:

14 x 1.05 = 14.70

Step-by-step explanation:

The depiction of 35% as a fraction is 7/ 20, and option D is the correct answer.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given that the chance of getting hit by the ball is 35%.

35 % = 35/100

Simplifying the fraction:

35/100 = 7/ 20

Hence, depiction of 35% as a fraction is 7/ 20, and option D is the correct answer.

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Answer:

Yes, one gallon is enough

Step-by-step explanation:

16ft x 12ft = 192ft

If one gallon covers 250 square feet then she will have enough for another 58ft remaining

The cost of one muffin after taxes is $2.56. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

For all the real numbers, there are four basic mathematical operations which are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

Let cost of one muffin after taxes be 'x'

We are given that there were six friends and each person ordered a small cup of coffee and a muffin.

The total for the order, including taxes, was $38.10

Also, the cost of a small coffee is $3.79 after taxes.

So, we get

⇒ 6(3.79 + x) = 38.10

⇒ 22.74 + 6x = 38.10

⇒ 6x = 15.36

⇒ x = $2.56

Hence, the cost of one muffin after taxes is $2.56.

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Based on the information, we can infer that of the 250 adults surveyed, 190 wanted the park to be expanded and 60 did not want the park to be expanded.

To complete the table we must take into account the available information. In this case, they are only referring to the adults who wanted the park to be expanded:

According to the above, if we add these two values we would have a group of 190 adults who want the park to be expanded. So the number of adults who do not want the park to be expanded would be 60.

Finally, if there are 60 people who do not want the park to be expanded, we can infer that there may be 30 who are parents and 30 who are not parents.

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The triangles abc and cda are congruent by sss congruence criteria.

The full form of CPCT is Corresponding parts of Congruent triangles. After proving triangles congruent, the remaining dimension can be predicted without actually measuring the sides and angles of a triangle. Different rules of congruency are as follows. SSS (Side-Side-Side)

SSS (Side-Side-Side) :-If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

so, sides

AB=CD

BC=DA

AC=CA

Hence by SSS (Side-Side-Side) the triangles are congruent.

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Kathy’s and Mark's investments worth will be $1248000 and $312000.

From the information, Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35.

Let Mark = x

Kathy = 4 × x = 4x

The equation to represent this will be:

4x + x = 1560000

5x = 1560000

Divide

x = 1560000 / 5

x = 312000

Mark contributed $312000

Kathy contributed

= 312000 × 4

= 1248000

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Answer: To find the distance the child travels, we can use the arc length formula: s = r * θ, where s is the arc length, r is the radius of the circle, and θ is the angle of rotation in radians. Since the merry-go-round has a radius of 3m and rotates through 120 degrees, we can convert the angle to radians by multiplying by pi/180.

120 degrees * pi/180 = 2pi/3 radians

Now we can plug in the values into the arc length formula:

s = r * θ

s = 3 * (2pi/3)

s = 2pi

The distance the child travels is 2pi meters, which is the circumference of the circle.

Step-by-step explanation:

it would take 29.5 hours the second airplane to overtake the first.

speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.

Given, Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour.

So, in 3 hours first airplane will reach at;

Distance = speed *time

Distance = 590 * 3

Distance travels by first airplane in 3 hours will be = 1770 km

Since, Relative speed of given two planes = 650 - 590

Relative speed of given two planes = 60 km/hour

To reach 1770 km it would take  = 1770/60 hours

Thus,

To reach 1770 km it would take  = 29.5 hours

therefore, it would take 29.5 hours the second airplane to overtake the first.

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Probability of less than 50 % democrats for the example based on sample proportion is equal to 0.1562.

Sample size 'n' = 100

Registered voters  'p' = 55%

                                    = 0.55

σ = √ p( 1- p )/ n

  = √0.55( 0.45)/ 100

  = 0.04975

Mean 'μ' = 55%

               = 0.55

Probability of getting less than 50% democrats in a sample size of 100 voters

X = 0.5

Z = ( X - μ ) / σ

  = ( 0.5 - 0.55) / 0.4975

 = -1. 005

 = -1.01

p-value pf -1.01 is equal to 0.156248

Therefore, the probability of getting 50% democrats for the given sample size id equal to 0.1562. The given example represents sample proportion.

The above question is incomplete , the complete question is :

In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?

Is this an example of a sample proportion OR a sample mean?

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Based on the data displayed in the histogram, the percentage of students who study 2 or more hours for the midterm is 88%.

A histogram is a graphical representation of data that shows the distribution of a dataset. It is used to show the frequency or the relative frequency of different values within a set of data. It is a bar chart that displays the data in a continuous format, with the bars touching each other.

Based on the histogram, the number of students studying 2 or more hours for the exam are:

= 9 + 6 + 3 + 2 + 1 + 1

= 22 students

While the total number of students studying is :

= 3 + 9 + 6 + 3 + 2 + 1 + 1

= 25 students

The percentage of students study to or more hours can be determined by dividing the number of students studying 2 or more hours with the total number of students studying multiply by 100.

percentage = 22/25 x 100

percentage = 0.88 x 100

percentage = 88%

Therefore, 88% of students study to or more hours for the midterm.

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It is useful to determine the predictive accuracy of a choice model and hence option c is correct for confusion matrix

the misclassification error rate for the following xlminer confusion matrix and the accuracy value of the confusion matrix is 10.82% .

In the field of machine learning, specifically the problem of statistical classification (in unsupervised learning, it is typically referred to as a matching matrix), a confusion matrix, also known as an error matrix, is a specific table structure that enables visualizing the performance of an algorithm.

The literature describes both iterations of the matrix, where each row represents instances in an actual class and each column represents instances in a predicted class. Since it is straightforward to tell whether the system is combining two classes, the name was chosen (i.e. commonly mislabeling one as another).

accuracy is given by the formula :

Accuracy(%) = (true positive + true negative)/(positive + negative)

Here TP true positive =10

and TN true negative is 8.2

hence accuracy = (10+8.2) / (1+0)  %

Accuracy = 10.82%

Therefore the accuracy value of the confusion matrix is 10.82% .

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Answer:

Step-by-step explanation:

[tex]-63y^2+27y[/tex]

[tex]-63yy+27y[/tex]

[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]

[tex]9y\left(-7y+3\right)[/tex]

Answer:

m∠ABD = 111

Step-by-step explanation:

69 + x = 180

x = 111

Answer:

< ABD  = 111 °

Step-by-step explanation:

< ABD and < DBE form a straight line which is 180 degrees

< ABD + < DBE = 180

< ABD + 69= 180

< ABD  = 180 -69

< ABD  = 111

Answer:

1.5 is more than -1.5

Step-by-step explanation:

Positive numbers, like 1.5, are always greater than negative numbers, like -1.5

Answer:

[tex]m=-\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\Delta y=-1,\,\Delta x=2\\\rightarrow \frac{\Delta y}{\Delta x}=\frac{-1}{2}=-\frac{1}{2}[/tex]

[tex]\Delta[/tex] represents change in both variables, so we calculate the slope this way.

Answer:

m=-1/2

Step-by-step explanation:

Use slope formula: [tex]m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]

divide the lateral height in half, Height squared lateral height squared is subtracted from height squared, the answer from step three, and find its square root. The radius of the cone is the outcome.

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Therefore , the solution of the given problem of volume comes out to be 9,003.75π cubic cm.

The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume. The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.

Here,

Given :

=> 15 cm is the AB

=> radius = 49/2 = 24.5 cm

The radius of base is 24.5 cm

and

the volume of frustrum:

=> π(24.5)(24.5)(15)

=> 9,003.75π cubic cm

Therefore , the solution of the given problem of volume comes out to be

9,003.75π cubic cm.

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Answer:

6 divided by 2/3 = 9

Step-by-step explanation:

Steven cuts the 6 ft long rope by 2/3 to make 9 pieces and the answer is mathematically correct, via calulcator

Answer:

(a) 45

(b) 10

(c) 70

Step-by-step explanation:

(a) The number of teachers who teach science but not humanities is:

Number who teach science - Number who teach both subjects

==> 60 - 15 = 45

(b) The number of teachers who teach humanities but not science is:

Number who teach humanities - Number who teach both subjects

==> 25 - 15 = 10

(c) The number who teach humanities or science is Number who teach humanities + number who teach science  - number who teach both

60 + 25 - 15 = 70

There are 30 teachers who teach neither humanities nor science = 100 - 70