write 5.67 x 10^2 in standard notation

Answer:

(-4)3/(-4)-12

-12/48

-1/4

Step-by-step explanation:

PEMDAS

do multiplication then division

The probability of throwing a sum less than or equal to 3 is 1/216

Probability:

It is defined as an event that can be calculated by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

If we are talking three six-sided dice each marked 1 through 6, and fairly weighted so every side is of equal probability, then there is only 1 combination that sums to less than 3: 1 1.

Meanwhile, there are 6 possible rolls on the first die, and for each, 6 possible rolls on the second and third die, so 6*6*6=216 total possible rolls.

There is only one probability to get a sum less than or equal to 3 (1,1,1)

P(x<=3)=1/216

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Answer:

Part A

Step-by-step explanation:

Answer:

1.5558 x 10^4

Step-by-step explanation:

move decimal four places over

The estimated marginal effect of x on y when x is equal to 100 is 1.

Option B is the correct answer.

We have,

To determine the estimated marginal effect of x on y, we need to take the derivative of y with respect to x.

\(\hat y\) = 5 + 20√x.

Taking the derivative with respect to x,

d(\(\hat y\)) / dx = d(5 + 20√x) / dx

Since the derivative of a constant term (5) is 0.

Using the chain rule, the derivative of √x is (1/2√x),

d(\(\hat y\)) / dx = 20 * (1/2√x) = 10 / √x

Now, we can substitute x = 100 into the derivative:

d(\(\hat y\)) / dx = 10 / √100 = 10 / 10 = 1

Therefore,

The estimated marginal effect of x on y when x is equal to 100 is 1.

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The best estimate for the solution to the system of linear equations among the given ordered pairs is (-4, 2 1/2).

In the context of a system of linear equations, the solution represents the values of the variables that satisfy all the equations simultaneously. To determine the best estimate for the solution, we need to evaluate each ordered pair and see which one satisfies the given system.

By substituting the values of the ordered pairs into the equations of the system, we can determine if they satisfy the equations or not. Among the given options, when substituting (-4, 2 1/2) into the system of linear equations, it is likely to result in a solution that satisfies all the equations.  Therefore, it is important to consider the specific equations and the context of the problem to determine the best estimate for the solution.

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When examining the problem and purpose portions of a research study, the important question to ask is (option d) Is the objective of the study clearly stated?

Given,

What should I look for while  reviewing the problem and purpose sections of a research article?

To do this, we suggest reading the content numerous times before criticizing it, making notes, and adding annotations. Be sure to take notes while you read on crucial elements such as the thesis, purpose, research questions, hypotheses, methods, evidence, significant findings, tone, and publishing information.

Here,

The pertinent question when reviewing the problem and purpose sections of a research article is (option d) Is the objective of the study clearly stated?

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As an AI language model, my purpose is to provide information and assist with answering questions to the best of my knowledge and abilities.

I can help you understand quadratic equations and provide guidance on how to solve them. Quadratic equations are second-degree polynomial equations in the form of ax^2 + bx + c = 0, where 'a', 'b', and 'c' are constants. To solve a quadratic equation, you can use various methods such as factoring, completing the square, or using the quadratic formula. If you have specific quadratic equations you would like assistance with, please provide the equations, and I'll do my best to guide you through the solution steps. Remember, understanding the concepts and solving the problems yourself will ultimately help you learn and retain the knowledge.

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Answer: The length, breadth, and height of the rectangular prism are:

Length = 3x + y cm

Breadth = 2x + 2y cm

Height = 3y cm

The volume of the rectangular prism is given by the formula:

Volume = Length x Breadth x Height

Substituting the values, we get:

Volume = (3x + y) x (2x + 2y) x (3y)

Simplifying the expression, we get:

Volume = 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3

Therefore, the volume of the rectangular prism is 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3 cubic cm.

Step-by-step explanation:

The maximum possible number of handshakes at the party can be calculated using the formula n(n-1)/2, where n is the number of people attending. This formula is derived from the fact that each person can shake hands with every other person except themselves.

Let's assume that there are n people attending the party. In order to maximize the number of handshakes, we want each person to shake hands with every other person except themselves.

Now, let's consider the first person. They can shake hands with (n-1) other people, as they cannot shake hands with themselves. Similarly, the second person can shake hands with (n-1) other people, but they have already shaken hands with the first person, so they can only shake hands with (n-1)-1 = (n-2) remaining people.

Following this pattern, the third person can shake hands with (n-1)-2 = (n-3) people, the fourth person can shake hands with (n-1)-3 = (n-4) people, and so on. The last person, the nth person, can shake hands with (n-1)-(n-2) = 1 person.

By summing up the number of handshakes for each person, we get (n-1) + (n-2) + (n-3) + ... + 1, which is the sum of the first (n-1) natural numbers. This sum can be calculated using the formula n(n-1)/2.

Therefore, the maximum possible number of handshakes at the party is n(n-1)/2.

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Answer:

No solution

Step-by-step explanation:

Let's solve your system by elimination.

−2x+14y=−29;x−7y=19

Multiply the second equation by 2, then add the equations together.

(−2x+14y=−29)

2(x−7y=19)

Becomes:

−2x+14y=−29

2x−14y=38

Add these equations to eliminate x:

0=9

The positive solution is the one that makes sense in this context, so the answer is: \(b - c = √(169 + 4a(a - x^2 - 30))\)This is the amount by which the long dimension is longer than the short dimension.

Let's start by finding the area of the original square of fabric with side length "a":

Area of original square \(= a^2\)

Next, let's say she added "b" units of fabric to one side and "c" units of fabric to the other side. Then the dimensions of the final quilt would be:

Long dimension  \(= a + b\)

Short dimension  \(= a + c\)

To do this, we can use the fact that the sum and product of the roots of a quadratic equation  \(ax^2 + bx + c = 0\) are given by -b/a and c/a, respectively.

So if we rearrange the equation above to the form  \(ax^2 + bx + c = 0\) , we have:

\(a^2 + (b + c)a + bc - x^2 - 13x - 30 = 0\)

The sum of the roots is (b + c)/a, which in this case is:

\(b + c = -(-13) = 13\)

And the product of the roots is bc/a, which is:

\(bc/a = a^2 - x^2 - 30\)

Now we have two equations with two unknowns (b and c):

\(b + c = 13\)

\(bc/a = a^2 - x^2 - 30\)

We can solve for "b" and "c" by substituting the first equation into the second equation to eliminate one of the variables:

\(b = 13 - c\)

\(bc/a = a^2 - x^2 - 30\)

\((c - 13)c/a = a^2 - x^2 - 30\)

\(c^2 - 13c = a(a - x^2 - 30)\)

\(c^2 - 13c - a(a - x^2 - 30) = 0\)

This is a quadratic equation in "c", which we can solve using the quadratic formula:

\(c = (13 ± √(169 + 4a(a - x^2 - 30))) / 2\)

We want to find the difference between the long and short dimensions, which is:

\(b - c = 13 - 2c\)

So we can substitute the expression for "c" above to get:

\(b - c = 13 - (13 ± √(169 + 4a(a - x^2 - 30))) = ±√(169 + 4a(a - x^2 - 30))\)

Therefore, The positive solution is the one that makes sense in this context, so the answer is: \(b - c = √(169 + 4a(a - x^2 - 30))\)This is the amount by which the long dimension is longer than the short dimension.

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Interp2 is a MATLAB function that can be used to resize arrays of different sizes. This function is especially useful when we want to change the dimensions of an array without losing any important data.

An array is a collection of values or elements arranged in a specific order. When we want to resize an array, we essentially want to change its shape, but keep the same amount of data. This can be tricky when dealing with arrays of different sizes, because we need to find a way to map the data from one array onto another.

Interp2 helps us do this by using interpolation. Interpolation is a mathematical technique that allows us to estimate values between known data points. In the context of array resizing, interpolation is used to estimate the values of the new array based on the values of the old array.

To use interp2 to resize arrays, we need to provide it with the following inputs:

The old array (the array we want to resize)

The new size of the array (the dimensions of the new array)

The method of interpolation (how we want to estimate the values of the new array)

For example, let's say we have an array A that is 4x4, and we want to resize it to a 6x6 array. We can use interp2 as follows:

B = interp2(A, 6, 6, 'cubic');

In this case, we are telling interp2 to resize the array A to a 6x6 size using cubic interpolation. The resulting array B will have the same amount of data as A, but will be reshaped to fit the new dimensions.

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Answer:

(x)^2 + (y+8)^2 = 36

Step-by-step explanation:

The standard form for an equation for a circle is

(x-h)^2 + (y-k)^2 = r^2  where ( h,k) is center of the circle and r is the radius

(x-0)^2 + (y- -8)^2 = 6^2

(x)^2 + (y+8)^2 = 36

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

A bond is a debt security, meaning that it represents a loan made by an investor to a borrower (typically a corporation or government). The bond issuer promises to pay interest to the bondholder, usually at regular intervals, and to repay the principal when the bond matures.

So, a statement that could describe the returns from a bond is:

"Bonds typically provide a steady stream of income in the form of interest payments, but the return on investment is generally lower than that of stocks."

Another statement that could describe the returns from a bond is:

"Bonds are considered to be a relatively safe investment option, but they are not as profitable as stocks in terms of returns."

In general, bonds are considered to be less risky than stocks, but they also typically offer lower returns.

Answer: B

Step-by-step explanation:

Answer:42%

Step-by-step explanation:

The percentage of student attendees saw an action movie is 52.38%..

The percentage calculation is a calculation which is done with respect to number 100.

Student that watched the comedy movie is 70.

Student that watched the action movie is 77.

Therefore, the total number of students present in that movie theater were (70 + 77) = 147.

Therefore, the percentage of students those saw the action movie is

= (77/147) × 100% = 52.38%.

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Answer:

\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)

Step-by-step explanation:

Answer:

]-3,7[

Step-by-step explanation:

the domain is from -3 to 7

Answer:

15

Step-by-step explanation:

5bc = 5(-3)(-1) = -15(-1) = 15

The maximum profit per day is $600, and the soft-drink vendor must sell 1,500 cans to achieve this maximum profit.

The profit function for the soft-drink vendor is given by P(x) = -0.001x^2 + 3x - 1800. To find the maximum profit per day and the number of cans to sell for maximum profit, follow these steps:

1. Identify the quadratic function: In this case, it's P(x) = -0.001x^2 + 3x - 1800.

2. Find the vertex of the parabola, which represents the maximum profit point. The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a and b are the coefficients of the quadratic function (a = -0.001, b = 3).

3. Calculate the x-coordinate of the vertex: x = -3 / (2 * -0.001) = -3 / -0.002 = 1500.

4. Substitute the x-coordinate back into the profit function to find the maximum profit: P(1500) = -0.001(1500)^2 + 3(1500) - 1800 = $600.

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The probability that a woman is having one child of each sex is 0.2548.

The probability of having two children of the same gender (either both girls or both boys) can be calculated by multiplying the probability of having a girl or a boy is (which is 1/2 or 0.5) by itself twice, as each child is independent of the other:

0.5 × 0.5 = 0.25 (probability of having either two girls or two boys)

Since the total probability of having two girls or two boys is 0.5048 as given in the question, the probability of having one child of each sex is: 0.5048 - 0.25 = 0.2548.

Therefore, the probability that a woman with two children has one child of each sex is 0.2548

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Mean for start of school year is 6.5; Mean for end of school year is 7.2.

Median for start of school year is 6.5; Median for end of school year is 7.

To find the means, list out each data value given for each dot plot and calculated the mean.

Mean for start of school year:

We have, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9

Mean = ( 4 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 9)/14

= 91/14

Mean ≈ 6.5

Mean for end of school year:

We have, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9

Mean = ( 5 + 5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 9 + 9 + 9)/14

= 101/14

Mean ≈ 7.2

Median represents the middle data value in a data set, therefore:

Median for start of school year = ( 6 + 7)/2 = 6.5

Median for end of school year = ( 7 + 7)/2 = 7

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Answer:

B  Hope it helps

Step-by-step explanation:

Answer:

I would say B

Step-by-step explanation:

It sounds like the right answer

\(\boxed{\underline{\bf \: ANS WER}}\)

\( \sf \frac{6}{x} = 18 \\ \)

Variable x cannot be equal to 0 as division by zero is not defined. Multiply both sides of the equation by x.

\( \sf \: 6=18x \)

Swap sides so that all variable terms are on the left-hand side.

\( \sf \: 18x=6 \)

Divide both sides by 18.

\( \sf \: x=\frac{6}{18} \\ \)

Reduce the fraction \( \sf\frac{6}{18}\) to its lowest terms by extracting and cancelling out 6.

\( \sf \: x=\frac{1}{3} \\ \)

\( \sf \: x=\frac{1}{3}\approx \boxed{\underline{0.33... }}\\ \)

______

Hope it helps.

ᏒᎯᎨᏁᏰᎾᏯᏕᎯᏝᎿ2222

To find the average rate of change of a function over an interval, we need to calculate the slope of the secant line connecting the points on the function at the two endpoints of the interval.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of a secant line, we can calculate the slope by using the formula:

m = (y2 - y1) / (x2 - x1)

For the function y = x^2 + 4x - 1, we can plug in the values of x and y at the two endpoints of the interval, (-4 and 1), to find the slope of the secant line:

m = [(1)^2 + 4(1) - 1] - [(-4)^2 + 4(-4) - 1] / (1 - (-4))

Simplifying this expression, we get:

m = (1 + 4 - 1) - (16 + 16 - 1) / (-3)

This simplifies to:

m = -20 / -3

Therefore, the average rate of change of the function y = x^2 + 4x - 1 over the interval -4 ≤ x ≤ 1 is 6.5.

A positively skewed distribution is due to an extremely large number.

A positively skewed distribution is a type of distribution in which the majority of the data values are clustered towards the left side of the distribution, with a tail extending to the right. This means that there are relatively more smaller values in the dataset than larger values. In a positively skewed distribution, the mean of the dataset is typically larger than the median, and the mode may not be a good representation of the central tendency of the data. This is because the presence of a long tail on the right-hand side of the distribution pulls the mean towards the higher values, while the median remains closer to the center of the dataset. Some common examples of positively skewed distributions include income distributions, where there are a few extremely high earners that skew the data towards the right, and test scores, where there may be a few students who perform extremely well and pull the average higher than the median.

Here,

A positively skewed distribution occurs when the tail of the distribution extends to the right, and the majority of the data is clustered towards the left side of the graph. This means that there are relatively more smaller values in the dataset than larger values. One common cause of positive skewness is the presence of extremely large values, also called outliers, in the dataset. These large values pull the mean of the dataset towards the right, resulting in the tail of the distribution stretching in that direction.

Therefore, out of the options provided, the correct answer is "an extremely large number."

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Answer:

Ok so its -3;3

Step-by-step explanation: