need answer right nowwwww

Answer:

Step-by-step explanation:

\(Given \ f (p,q) = 8qe^{-p} + 4pe^{-q} \ where \ P_o(0,0) \\ \text{thus the gradient of f is: } \\ \\ \bigtriangledown f(p,q) = \Big(\dfrac{\partial f}{\partial p}, \dfrac{\partial f}{\partial q} \Big) \\ \\ \dfrac{\partial f}{\partial p} = -8qe^{-p} + 4pe^{-q} \\ \\ \dfrac{\partial f}{\partial p} = 8qe^{-p} - 4pe^{-q} \\ \\ Then: \bigtriangledown f(p.q) = (-4qe^{-p}+ 8qe^{-q}, 4qe^{-p}- 8qe^{-q}) \\ \\ f(0,0) = (-4*(0)e^{-0}+ 8*(0)e^{-(0)}, 4*(0)e^{-(0)}- 8*(0)e^{-(0)}) \\ \\ = (0+8,4-0) = (8.4)\)

\(\Big| \Big | \bigtriangledown f(0,0) = \sqrt{(8)^2+4^2} \\ \\ = \sqrt{64+16} \\ \\ = \sqrt{80}\)

\(\mathbf{the \ direction \ of \ maximum \ change \ is }= \mathbf{\sqrt{80}} \\ \\ \mathbf{direction }(8,4)\)

Answer:

Yes

Yes

No

Step-by-step explanation:

Given value x = -2;

    Problem, is the expression a positive number ?

A. -2(x - 2)

  if x = -2

     -2(-2 - 2)

     = -2 (-4)

     = 8

Yes

B.  -3x(5 - 4x)

   if x = -2

     -3 x -2(5  - 4(-2))

    = 6 (5 + 8)

     = 6 x 13

     = 78

Yes

C. x + 6x

if x = -2

    -2 + 6(-2)

   = -2 - 12

   = - 14

No

Increasing the value from 3 to 6 can potentially change the mode of a dataset. The mode represents the most frequently occurring value(s) in a dataset. If there are no repeated values or if the repeated values remain the same, then increasing the value from 3 to 6 will not change the mode. If there are new values introduced or if the frequency of certain values changes as a result of increasing the value, then the mode may indeed change.

1. Identify the initial dataset: Take note of the dataset where the mode is currently determined based on a value of 3.

2. Determine the mode: Calculate the mode of the dataset when the value is 3. The mode represents the most frequently occurring value(s) in the dataset.

3. Increase the value to 6: Modify the dataset by increasing the value from 3 to 6.

4. Analyze the dataset: Examine the modified dataset to observe any changes in the frequency distribution of values.

5. Compare the modes: Calculate the mode of the modified dataset with the value of 6 and compare it to the initial mode.

6. Assess changes: If the mode remains the same, it implies that the most frequently occurring value(s) in the dataset did not change. However, if the mode differs from the initial mode, it indicates that the increase from 3 to 6 has affected the frequency distribution and altered the most frequently occurring value(s).

7. Determine the impact: Analyze the specific changes in the dataset that led to the mode alteration. Identify any newly introduced values or shifts in the frequency of existing values.

8. Conclude: Based on the comparison of the initial mode and the mode with the increased value, determine whether increasing from 3 to 6 has changed the mode and describe the nature of the change.

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Answer:

\(v=1/3\pi r^2h\)

\(v=1/3(3.14(7)^2(7)\)

\(v=359.01 ~units^3\)

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

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Answer:

Answer: 2b+3 = 7

=================================================

Work Shown:

b = unknown number

2b = 2 times a number

2b+3 = the sum of 2 times a number and 3

2b+3 = 7, since the expression above is set equal to 7

Step-by-step explanation:

The division of 7x³ - 25x² + 17x - 7 by x - 3 will have a quotient of 7x² - 4x + 5 and a remainder of 8 using synthetic division.

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall divide 7x³ - 25x² + 17x - 7 by x - 3 as follows;

7x³ divided by x equals 7x²

x - 3 multiplied by 7x² equals 7x³ - 21x²

subtract 7x³ - 21x² from 7x³ - 25x² + 17x - 7 will give us -4x² + 17x - 7

-4x² divided by x equals -4x

x - 3 multiplied by -4x equals -4x² + 12x

subtract -4x² + 12x from -4x² + 17x - 7 will give us 5x - 7

5x divided by x equals 5

x - 3 multiplied by 5 equals 5x - 15

subtract 5x - 15 from 5x - 7 will give result to a remainder of 8

Therefore by synthetic division, 7x³ - 25x² + 17x - 7 divided by x - 3 will result to a quotient of 7x² - 4x + 5 and a remainder of 8.

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Answer:

Cross multiplication

Step-by-step explanation:

The simplified form of the rational expression \((7x)/(14x^6)\) is \(1/(2x^6).\)

To simplify the rational expression \((7x)/(14x^6)\), we can begin by simplifying the numerator and denominator separately.

In the numerator, 7x, we can see that both 7 and x have a common factor of 7. So, we can rewrite the numerator as 7 × x = 7x.

In the denominator, \(14x^6\), we can see that both 14 and x^6 have a common factor of \(2x^6\).

So, we can rewrite the denominator as

\(14 \times x^6 = 2 \times 7 \times x^6 = 2 \times 7x^6.\)

Now, we can simplify the rational expression by canceling out the common factors in the numerator and denominator:

\((7x)/(14x^6) = (7x)/(2 \times 7x^6) \\= (7x)/(2 \times 7 \times x^6) \\= (cross(7x))/(2 \times cross(7) \times x^6) \\= 1/(2x^6)\)

Therefore, the simplified form of the rational expression\((7x)/(14x^6)\) is \(1/(2x^6).\)

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Answer:

\(g(f(x)) = x^{[2]} +[-1]\)

Step-by-step explanation:

Given

\(f(x) = x^2\)

\(g(x) =x -1\)

Required

\(g(f(x))\)

We have:

\(g(x) =x -1\)

Replace x with f(x):

\(g(f(x)) = f(x) -1\)

Substitute \(f(x) = x^2\)

\(g(f(x)) = x^2 -1\)

Hence:

\(g(f(x)) = x^{[2]} +[-1]\)

Answer:

50% or 1/2 Could be 100% but i think it is 50%

Step-by-step explanation:

Because Changing the coin will make no difference.

The probability of getting heads is same as the probability of tails which is \(\frac{1}{2}\).

What is the probability?

The concept of probability is used to assign a numerical description to the likelihood of occurrence of an event.

Probability can be defined as the number of favorable outcomes divided by the total number of possible outcomes of an event.

Here given that,

The \(10\) tosses of a coin were all heads, and you switch to a new coin.

So, the probability of getting all heads is \(2^{-n}\)

And we have \(n=10\),

Then, the probability of getting the heads is

\((^{n}C_k)(\frac{1}{2})^k(\frac{1}{2})^{n-k}=2^{-n}(^nC_k)\)

Hence, the probability of getting heads is same as the probability of tails which is \(\frac{1}{2}\).

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The new coordinates after translating 2 units right and 1 unit down are D'(-3,0), H'(-2,4) and S'(1,1) respectively.

Given, triangle DHS has the coordinates D(-5, 1), H(-4, 5) and S(-1, 2). Now, we have to find the coordinates of D'H'S' if DHS is translated 2 units right and 1 unit down.

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.

To translate the point P(x,y), 'a' units right and 'b' units down, use P′(x+a,y-b).

Now, let's proceed to solve the question according to above listed points accordingly.

D(-5, 1), H(-4, 5) and S(-1, 2), these coordinates are translated 2 units right and 1 unit down. So, we will simply add 2 to the x-coordinate of the points and will subtract 1 from the y-coordinate.

Let's translate D, H and S accordingly into D', H' and S'.

D(-5,1)⇒ D(-5+2, 1-1)⇒ D'(-3,0)

H(-4,5)⇒ H(-4+2, 5-1)⇒ H'(-2,4)

S(-1,2)⇒ S(-1+2, 2-1)⇒ S'(1,1)

Therefore, the new coordinates after translation are D'(-3,0), H'(-2,4) and S'(1,1) respectively.

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The size of the Matrix is a 3 x 3 matrix.

The matrices have the same diagonals

\(s^{2} = \left[\begin{array}{ccc}1&0&0\\9&1&0\\0&9&1\end{array}\right]\)

\(s^{3} \left[\begin{array}{ccc}1&0&0\\27&1&0\\0&27&1\end{array}\right]\)

From the solution of the matrix we can see that the diagonal has remained unchanged all through. The diagonals at S, S2 and S3 is the same as 1

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number one take the second

Answer:

A) congruent triangles

Step-by-step explanation:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

The collection, description, analysis, and drawing of conclusions from quantitative data are all included in the area of statistics, which is a branch of applied mathematics. Probability theory, linear algebra, and calculus of differential and integrals are some of the core mathematical concepts in statistics.

Descriptive statistics were used in the statement.

Descriptive statistics is a branch of statistics that deals with the collection, presentation, and summary of data. It is used to describe and summarize the main features of a data set, such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., range, variance, standard deviation).

In this case, the statement is simply reporting a single value, the average credit card debt for college students in 2008. This is an example of a descriptive statistic because it is a summary measure that describes a characteristic of the population or sample under study.

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Descriptive statistics were used in the statement.

Descriptive statistics is a branch οf statistics that deals with the analysis, descriptiοn, and summarizatiοn οf data. It invοlves the use οf variοus statistical measures, such as measures οf central tendency (mean, median, and mοde), measures οf dispersiοn (standard deviatiοn, variance, range), and graphical representatiοns (histοgrams, bοx plοts, scatter plοts, etc.) tο describe the features οf a dataset.

Descriptive statistics were used in the statement. The statement is simply describing the average credit card debt fοr cοllege students in 2008. Descriptive statistics are used tο describe οr summarize a dataset οr pοpulatiοn, while inferential statistics are used tο draw cοnclusiοns οr make predictiοns abοut a larger pοpulatiοn based οn a sample οf data. Since the statement οnly prοvides infοrmatiοn abοut a specific grοup οf cοllege students in 2008, it dοes nοt invοlve making any inferences οr predictiοns beyοnd this grοup.

Hence, Descriptive statistics were used in the statement.

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The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.

The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.

The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.

An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.

In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

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Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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Answer:

-6

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

b

Answer:

Step-by-step explanation:

Given the system of equation;

kx - y = 2 ------------------- 1

6x - 2y = 3 -------------------- 2

Rewriting the equations in the format ax+by+c = 0

Equation 1 becomes kx - y - 2 = 0

Equation 2 becomes 6x - 2y - 3 = 0

where a₁ = k, b₁ = -1 and c₁ = -2  and a₂ = 6, b₂ = -2 and c₂ = -3

For the system of equation to have a unique solution the following must be true;

a₁/a₂ ≠ b₁/b₁

Substituting the coefficients into the condition, we will have;

k/6 ≠ -1/-2

k/6 ≠ 1/2

Cross multiplying we will have;

2k ≠ 6

k ≠ 6/2

k ≠ 3

This means that k can be any other real values except 3 for the system of equation to have a unique solution.

Answer:

It is false

Step-by-step explanation:

It is false because 12 has the factors of 2 and 4 but 8 is not a factor of 12.

The statement is false. If a number has 2 and 4 as factors, it doesn't mean that it has 8 as a factor.

The fact that a number has 2 and 4 as factors, doesn't mean that the number will have 8 as a factor. For example, 4 and 12 have both 2 and 4 as factors but don't have 8 as a factor

Therefore, the fact that a number has 2 and 4 as factors doesn't mean that it has 8 as a factor.

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Answer:

  (a)  y = x/8

  (b)  y = 7/8

Step-by-step explanation:

You want a direct variation equation that relates x and y, given y = 2 when x = 16.

The equation for direct variation is usually written in the form ...

  y = kx

where k is the constant of proportionality.

The value of k can be found from ...

  k = y/x . . . . divide by x

For the given values, k is ...

  k = 2/16 = 1/8

The direct variation equation is ...

  y = (1/8)x

The value of y for x=7 is found by substituting 7 for x in the equation above:

  y = (1/8)·7

  y = 7/8

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Answer:

12:30 P.M.

Step-by-step explanation:

Emily took 30 minutes to make the dough and 1 hour to bake all of the cookies. In total, that's 30 minutes + 1 hour = 90 minutes (1 hour and 30 minutes). If it were 1:30 P.M. when Emily took the last batch of cookies out of the oven, then 90 minutes before that would be 1:30 P.M. - 90 minutes = 12:30 P.M. So, Emily started making the cookies at 12:30 P.M.

Answer:

0.0045 = 0.45% probability that less than two of them ended in a divorce

Step-by-step explanation:

For each marriage, there are only two possible outcomes. Either it ended in divorce, or it did not. The probability of a marriage ending in divorce is independent of any other marriage. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

55% of marriages in the state of California end in divorce within the first 15 years.

This means that \(p = 0.55\)

Suppose 10 marriages are randomly selected.

This means that \(n = 10\)

What is the probability that less than two of them ended in a divorce?

This is

\(P(X < 2) = P(X = 0) + P(X = 1)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{10,0}.(0.55)^{0}.(0.45)^{10} = 0.0003\)

\(P(X = 1) = C_{10,1}.(0.55)^{1}.(0.45)^{9} = 0.0042\)

\(P(X < 2) = P(X = 0) + P(X = 1) = 0.0003 + 0.0042 = 0.0045\)

0.0045 = 0.45% probability that less than two of them ended in a divorce

Reflection over a line

We are given the drawing of a triangle ABC, and it's required to reflect it across the line x = 1. We have completed the figure with all the information we need to perform the task. Note the line x = 1 passes through point A, this point maps to itself.

Reflecting a point across a given line means to project is as if the line was a mirror and our point maps to a point that is at the same distance to the mirror.

For example, point B is 3 units away from the mirror, thus we map it to a point located 3 units 'behind the mirror', that is at x = -2.

The original triangle, the mapped triangle, and the line of reflection are shown in the figure below:

Summarizing:

Point A(1, 2) maps to itself A'(1, 2)

Point B(4, 2) maps to B'(-2, 2)

Point C(2,4) maps to C'(0, 4)

Answer:

y = -8/3x + 8

Step-by-step explanation:

Step 1:  Identify which values we have and need to find in the slope-intercept form:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.

Step 2:  Find m, the slope of the line:

Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:

0 = m(3) + 8

0 = 3m + 8

-8 = 3m

-8/3 = m

Thus, the slope is -8/3.

Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.

Optional Step 3:  Check the validity of the answer:

Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:

Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:

0 = -8/3(3) + 8

0 = -24/3 + 8

0 = -8 = 8

0 = 0

Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;

8 = -8/3(0) + 8

8 = 0 + 8

8 = 8

Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.