9p^2q^7-2p^5q^6 ⋅ 4p^7q

Answer:

  x = ln(4) ≈ 1.3862944

Step-by-step explanation:

You apparently want the solution to the equation 2e^(2x) -2e^x -24 = 0.

This is effectively a quadratic in e^x. Dividing by 2, we get ...

  (e^x)^2 -(e^x) -12 = 0

Factoring gives ...

  ((e^x) -4)((e^x) +3) = 0

Solutions will be the values of x that make the factors zero.

  e^x -4 = 0   ⇒   e^x = 4   ⇒   x = ln(4)

  e^x +3 = 0   ⇒   e^x = -3   ⇒   x = ln(-3) . . . . not defined for real numbers

The only real solution is x = ln(4) ≈ 1.3862944.

__

Additional comment

In the complex numbers, the other solution is x = ln(-3) = ln(3) +πi.

The bank that Ashley will earn more interest with, given the annual interest and monthly interest offered, is Bank #1.

To find the bank that is offering her better interest on her savings, which in other words means the bank that Ashely will earn more with, convert the monthly interest to an annual figure.

This is called the Equivalent Annual Rate or EAR and when compared to the annual interest rate offered by Bank #1, we get a clearer picture of which bank has the better rate.

The Equivalent Annual Rate is found as:

= ( 1 + interest / number of periods in year) ^ number of periods in year - 1

= ( 1 + 0. 3% ) ¹² - 1

= 3. 66%

This means that Bank A will give Ashley the better interest at 4.6 %.

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The general form of the equation Kareem can use to represent the data include the following: B. y = ab^x.

Generally speaking, an equation is a linear equation when the first difference between the y-values of an equation are the same. Additionally, an equation is an exponential equation when the common ratio between y-values of an equation are the same.

Furthermore, an equation is a quadratic equation when the second difference between the y-values of an equation are the same.

For the first difference between the y-values, we have:

First difference = 1/4 - 1/8 = 1/8

First difference = 1/2 - 1/4 = 1/4

Therefore, this equation is not a linear equation.

Next, we would determine the common ratio between y-values;

Common ratio = 1/4/(1/8) = 2

Common ratio = 1/2/(1/4) = 2

Therefore, this equation is not an exponential equation with the general form of y = ab^x.

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Answer:

B

Step-by-step explanation:

28 different even numbers can be formed using 1,2,3,4 and 5 that are less than 500.

To form the even number from a combination of five different numbers 1 to 5 and the even number less that will be formed from such a combination are less than 500. Therefore, in this scenario, 28 different event numbers will be formed. The cases to formed the even number from 1,2,3,4 and 5 are given below:

Case 1: There is only one digit in the number.

The only even integers in this situation are 2 and 4, adding up to a total of 2.

Case 2: There are exactly two digits in the number.

In this instance, the first digit must be one of the other four permitted digits and the last digit must be either 2 or 4, for a sum of 2*4=8.

Case 3: There are exactly three digits in the number.

In this instance, the middle digit must be one of the other four permitted digits, and the last digit must either be 2 or 4.

The total will be 2*3*2=12 if the middle digit is not 5, which means the first digit must be one of two digits other than the final two digits and 5.

As a result, there exist 28 even numbers with the digits 1, 2, 3, and 5 that are less than 500.

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The choice that represents the correct similarity statement is A. EFGH = IJKL

When it comes to Euclidean geometry, two objects are said to be similar if they have the same shape or the same shape as each other's mirror image. One can be created from the other more precisely by uniformly scaling, possibly with the addition of additional translation, rotation, and reflection.

If two figures share the same shape, congruent corresponding angles (which means the angles in the same places of each shape are the same), and equal scale factors, they are said to be "similar figures."

In this case, or can be seen that the rectangles are similar as they have same angles. The correct option is A.

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Answer:

5 hours

Step-by-step explanation:

100t + 80t = 900

First, you can add 100t to 80t because they are both like terms.

100t + 80t = 900

180t = 900

Now you multiply,

when t = 2,

180*2 = 360

when t = 4,

180*4 = 720

When t = 5,

180*5 = 900

So, it will take them 5 hours to make 900 papers

Nick's taxable income will be $(x - 390).

Given is that Nick is paid every other week. He has 390$ taken out of each paycheck for federal taxes.

Assume that his income without tax is ${x}. Then, his taxable income will be -

taxable income = original income - federal tax

taxable income = $(x - 390)

Therefore, Nick's taxable income will be $(x - 390).

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This asking for solutions to the energy equation for fully developed laminar Newtonian flow in a circular tube of radius R.

(a) The energy equation (Eq. 113.2-1) is given with the viscous dissipation terms not neglected.

(b) For the isothermal wall problem (T = T, at r = R for 2 >0 and at z = 0 for all r), the asymptotic expression for T(r) at large z is T-T, = [1-() (113.2-2) 4K

(c) For the adiabatic wall problem (q, = 0 at r = R for all z > 0), an asymptotic expression for large z is given by T-T, = (44v,max/pĈ,RO)2 + for) (113.2-4) and then integrate the resulting equation for fr) to obtain 4 доллах T-T; 2 + pĈ R² (113.2-5) after determining the integration constant by an energy balance over the tube from 0 to z. These solutions are only valid for large z and the complete solutions for small z are not provided in the question.

This expression of temperature for a fluid flowing through a circular tube, considering two different conditions of the walls (isothermal and adiabatic) and for large values of distance. The solutions are only asymptotic and only for large values of distance.

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The coordinates of point B on the line is (-1/2, 19/4)

From the question, we have the following parameters that can be used in our computation:

Point A is at (-2,4) and point C is at (4,7).

Also, we have the ratio of AB to AC to be 1 : 3

The partition involves dividing the line into subsegments

This means that

(x, y) = (-2, 4) and (4, 7)

m : n = 1 : 3

The coordinates of the partition are calculated as:

Point = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

Point = 1/(1 + 3) * (1 * 4 + 3 * -2, 1 * 7 + 3 * 4)

Evaluate the products

So, we have the following representation

Point = 1/4 * (-2, 19)

Evaluate the quotients

Point = (-1/2, 19/4)

Hence, the coordinate of the partition is (x,y) = (-1/2, 19/4)

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Considering f(x) = 3^x. the graph of each function compares to f as follows

1. g(x) = 3^(x + 4) : translation 4 units to the left

2. h(x) = (1/4)^(x - 5) : vertical stretch by a factor of 12 and translation 5 units to the right.

3. j(x) = 3^(x + 6) - 2 : translation 6 units to the left and 2 units down

Translation say x units to the left is represented by positive x units while to the right is represented by negative x values. the left and right translation is restricted to the x values.

Translation say x units up is represented by positive x units while to the down is represented by negative x values. the top and down translation is restricted to the y values or the function itself.

Using the problem, comparing f(x) = 3^x and g(x) = 3^(x + 4) the difference is +4 hence it results to moving 4 units to the left

Comparing f(x) = 3^x and h(x) = (1/4)^(x - 5)

A factor of 12 is used to to make 1/4 equal to 3 since 1/4 * 12 = 3. this is called a vertical stretch

then (x - 5) is translation of 5 units to the right

Comparing f(x) = 3^x and j(x) = 3^(x + 6) - 2

(x + 6) is a translation 6 units to the left while the -2 represents a translation 2 units down since it is negative 2.

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After simplifying the total cost is $78

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas. The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given, that each pair of wings is made with 3/4 yard of fabric. Since the fabric costs $8 per yard. Therefore:

1) 3/4 x $8 will give us the cost of the amount required for 3/4 yard of fabric.  3/4 x $8 = $6 each

2) Now, we are told that Mr. Townsend needs to make 13 pairs of butterfly wings and as such:

Amount needed to make 13 pairs is expressed as; 3/4 x $8 x 13 = $78

3) Treat 1 yard of fabric like the fraction 4/4.

Now, if this 1 fabric is equal to $8, then it means that 3/4 of the fabric will be $6. That is for one pair of butterfly wings, there's 13 of those so multiply $6 by 13.

This is easier  because we know how much 1 fabric costs, but we don't know what 3/4 of it does, so we treat 1 yard of fabric as the fraction 4/4.

4) Simplifying the expression gives: $78

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The linear function corresponding to the line in the graph will be y = 200x - 120000.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given data,

A linear function is given as,

y = mx + c

Here m is the slope and c is the y-intercept.

The slope m will be as follows,

Slope m = (600 - 400)/(1 - 0)

m = 200

Put m = 200 and (600,0)

0 = 200(600) + c

c = -120000

Thus, the linear equation will be as,

y = 200x - 120000

Hence "y = 200x - 120000 is the linear function that corresponds to the line in the graph.".

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The probability that at least 8 out of 9 participants will correctly identify the tap water is 0.0195.

From the information, a blind taste test will be conducted with 9 volunteers to determine whether people can taste the difference between bottled water and tap water

Let x be the number of people that correctly identify tap water.

The probability that at least 8 out of 9 participants will correctly identify the tap water will be:

P(x ≥ 8) = P(x = 8) + P(x = 9)

= ⁹C₈ × 0.5⁸ × 0.5^(9-8) + 9C9 × 0.5⁹ × 0.5^(9 - 9)

= 0.0195

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A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?

Answer:

  see attached

Step-by-step explanation:

You want a graph of the equation y = -5x +2.

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x=0. In the equation, the y-intercept is the constant: +2.

The slope of the line is the coefficient of x. It is the ratio of "rise" to "run." The equation tells you the slope is -5. This means the line drops 5 units for each unit to the right.

Another point on the line will be (0, 2) +(1, -5) = (1, -3).

The line can be drawn through these points: (0, 2) and (1, -3).

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It will take 3 passes to sort this array.

The bubble sort makes multiple passes through a list. It compares adjacent items and exchanges those that are out of order. Each pass through the list places the next largest value in its proper place. In essence, each item “bubbles” up to the location where it belongs.

Bubble sort repeatedly steps through the list to be sorted , compares each pair of an adjacent items and swap them if they are in wrong order.

The pass through the list is repeated until no swap are needed, which indicated that the list is sorted.

Array element : 4 5 6 7

Bubble sort will take maximum n-1 passes to completely sort array of n elements. So here array size is 4,

It will take 3 passes to sort this array.

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The table represents a linear function while the graph represents a nonlinear function.

Linear functions are functions where the relationship between the independent variable (x) and the dependent variable (y) is a straight line. This means that the graph of a linear function is a straight line and the slope (or rate of change) of the line is constant.

On the other hand, nonlinear functions are functions where the relationship between the independent variable (x) and the dependent variable (y) is not a straight line. The graph of a nonlinear function is often a curve, and the slope (or rate of change) of the curve can vary.

In the table, the rate of change is -3 and variables are moving constantly with one increasing and the other decreasing, which makes it a linear function.

The graph is a nonlinear function as the graph is a curve.

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The domain of the points (3, 2) and (-5, 2) are all real numbers.

The Range of the points (3, 2) and (-5, 2) is only the value of y = 2.

What is the domain and range of the function?

The domain of a function is the set of all input values (independent variable) for which the function is defined and produces a valid output (dependent variable). The range of a function is the set of all possible output values (dependent variable) that the function can produce for all valid input values (independent variable).

The domain and range of a set of points in a coordinate plane refer to the set of all possible x-values and y-values, respectively.

The domain of the points (3, 2) and (-5, 2) are all real numbers. So, the domain can be represented as (-inf, inf)

The range of the points (3, 2) and (-5, 2) is only the value of y = 2. So, the range can be represented as {2}

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The absolute value model |x - 30| = 10 represents the time required for Jack to fold his laundry. (Correct choice: D)

Absolute values are functions used in mathematics that represents the magnitude of a number, whose definition is summarized below:

In this case, we must determine an absolute value model that contains the maximum and minimum times required by Jack to fold his laundry, This is represented by the following model:

|x - a| = b

Where:

If we know that a = 30 min and b = 10 min, then the absolute value model is:

|x - 30| = 10

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Answer:

Step-by-step explanation:

-36

Answer:

Graphing, Substitution, and Elimination.

Step-by-step explanation:

Graphing: Graphing is the best method to use when introducing a new student to solving systems of two equations in two variables because it gives them a visual to recognize what they are looking for. Graphing is less exact and often takes more time than the other methods. I only recommend graphing to find a solution if the problem comes with a graph already drawn and the intersection appears to be on an exact coordinate.

Substitution: Substitution gives the advantage of having an equation already written for the second variable when you find the first one. Substitution is best used when one (or both) of the equations is already solved for one of the variables. It also works well if one of the variables has a coefficient of 1.

Elimination: Elimination is the method that I use almost every time. If you are not sure which method to use, I recommend that you use elimination. Elimination is best used when both equations are in standard form (Ax + By = C). Elimination is also the best method to use if all of the variables have a coefficient other than 1.

I hope this gives you some idea about which method you should use. All three methods will give the same solution. Also, you should always check your answer in both equations to make sure it is correct.

The line segment joining the points (1/2, -2) and (1, 1) cuts the line 3x + 4y = 7 at the point of intersection of the line defined by the points and the line 3x + 4y = 7.

To find the ratio of the line segment at this point of intersection, we first need to find the point of intersection. We can do this by solving the system of equations defined by the line 3x + 4y = 7 and the line defined by the points (1/2, -2) and (1, 1).

Once we have the point of intersection (x,y), we can use the following formula to find the ratio:

(x - 1/2) : (y + 2) = (x2 - x1) : (y2 - y1) = (x - x1) : (y - y1)

Where (x1, y1) and (x2, y2) are the coordinates of the two points defining the line segment

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1) The number of miles that they travelled each day is; 4²/₃ miles

2) The total distance that they will travel here is; 42 miles

1) We are told that the Miller family paddles  the same distance each day throughout the course of 3 days, traveling a total of 14 miles.

Thus;

Total number of miles = 14 miles

Total number of days = 3 days

Thus number of miles that they travelled each day = 14/3 = 4²/₃ miles

2) Now, we are told that they want to go half their daily distance each day. Thus;

Number of miles per day = 14/2 = 7 miles

Total number of days = 2 * 3 = 6 days

Thus, the total distance that they will travel = 7 * 6 = 42 miles

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The probability density function is:

f(x,y) = 11k(1-x^2) for 0 ≤ y ≤ 1-x^2, and 0 elsewhere.

1. Determine the region of integration:

The region of integration is the area bounded by y = 1 - x2 and y = 0.

2. Calculate the area of the region:

The area of the region is given by the following integral:

A = ∫0∞∫0(1−x2)dxdy

3. Determine the normalizing constant:

The normalizing constant k is given by the following equation:

k = 1/A

4. Calculate the probability density function:

The probability density function is given by the following equation:

f(x,y) = 11k(1-x^2) for 0 ≤ y ≤ 1-x^2, and 0 elsewhere.

The probability density function is 11k(1-x^2) for 0 ≤ y ≤ 1-x^2, and 0 elsewhere. This is calculated by determining the region of integration, calculating the area of the region, finding the normalizing constant k and then calculating the probability density function.

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To conduct this simulation, we will first generate a random number between 0 and 1 for each of the four children in each trial. If the random number is less than 0.15, we will consider that child to have contracted the disease.Here is how we can do this using the random number table you provided:Trial 1:

Child 1: 0.14 (does not get the disease)

Child 2: 0.06 (gets the disease)

Child 3: 0.11 (does not get the disease)

Child 4: 0.13 (does not get the disease)Trial 2:

Child 1: 0.12 (does not get the disease)

Child 2: 0.08 (does not get the disease)

Child 3: 0.05 (gets the disease)

Child 4: 0.10 (does not get the disease)Trial 3:

Child 1: 0.09 (does not get the disease)

Child 2: 0.01 (gets the disease)

Child 3: 0.03 (gets the disease)

Child 4: 0.06 (gets the disease)...Trial 20:

Child 1: 0.14 (does not get the disease)

Child 2: 0.12 (does not get the disease)

Child 3: 0.05 (gets the disease)

Child 4: 0.07 (gets the disease)Based on this simulation, we can estimate the average number of children who will get the disease by taking the total number of children who got the disease across all 20 trials and dividing by the total number of trials. This comes out to be approximately 1.5 children.To calculate the probability of two of the children getting the disease, we count the number of trials where exactly two of the children got the disease, and divide by the total number of trials. In this simulation, this occurs in 5 trials out of 20, so the probability is 5/20 = 0.25.To calculate the probability of at least two of the children getting the disease, we count the number of trials where at least two of the children got the disease, and divide by the total number of trials. In this simulation, this occurs in 8 trials out of 20, so the probability is 8/20 = 0.4.

Answer:

Step-by-step explanation:

First, reverse the first and second number and change the operation to division. Now you have 22 / 59 or      (22/1) / (59/1)                                 Now just flip the second number and multiply the numbers.

(22/1) x (1/59)= 22/59

You cannot simplify anymore so that is the answer!

The total cost of all the items after the discount is $26.98.

A discount makes the price of a good or service cheaper. After a discount is applied, the carrying price of the item drops. If the discount is 5%, the price of the items declines by 5%.

Total cost after the discount = (100 - discount) x total cost of all the items

Total cost after the discount  = (100 - 5)% x $28.40

Total cost after the discount  = 95% x $28.40

Total cost after the discount  = 0.95 x $28.40

Total cost after the discount  = $26.98

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Taking the square of both sides to change the subject of formula, the value of x is 16y² - 5

By transferring all other terms to the other side of an equation, changing the subject of a formula is a technique for manipulating algebra that is used to isolate a variable on one side of an equation. It is also referred to as "rearranging" or "transposing" a formula.

In order to simplify expressions, solve word problems, or solve equations, it can be helpful to change the subject of a formula.

It's crucial to keep in mind that altering a formula's subject can also alter the function's domain, which could be limited to a particular range of values.

In short, changing a formula's subject allows you to isolate a variable that is on one side of an equation by transferring all other terms to the opposite side of the equation. It's sometimes referred to as "rearranging" or "transposing" a formula. It's a helpful method for resolving equations.

In the given question;

y = √(x + 5) / 4

Square both side;

y² = x + 5 / 16

16y² = x + 5

x = 16y² - 5

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We evaluated the function and we got

                                 [tex]h(-2)=-14\\h(0)=0\\h(2)=6[/tex]

Let us evaluate that function for [tex]x = -2[/tex]

 We can substitute the value of [tex]x[/tex] in the given expression      

                                      [tex]h(-2)=5(-2)-(-2)^{2}[/tex]

                                                 [tex]=-10-4\\=-14[/tex]

                                      [tex]h(-2)=-14[/tex]

Now, we can evaluate the function for [tex]x=0[/tex]

Let's substitute the value of [tex]x[/tex] in the given expression

                              [tex]h(0)=5(0)-0^{2} \\h(0)=0[/tex]

Now, we can evaluate the function for [tex]x=2[/tex]

Let's substitute the value of [tex]x[/tex] in the given expression

                              [tex]h(2)=5(2)-2^{2} \\h(2)=10-4\\h(2)=6[/tex]

Hence, we evaluate the function

            [tex]h(-2)=-14\\h(0)=0\\h(2)=6[/tex]

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The piecewise function is f(x) = {f(x)=2x, if x≤2

f(x) = {f(x)=2, if x>-4.

Piecewise functions are functions that have multiple pieces, or sections. They are defined piece by piece, with various functions defining each interval. Piecewise functions can be split into as many pieces as necessary. Each piece behaves differently based on the input function for that interval. Pieces may be single points, lines, or curves.

From the graph,

Domain of one part of line is x>-4 and domain of other part of the line is x≤2.

For increasing part of line m=4/2 =2

Which is intersecting y-axis at (0, 0), so y-intercept is c=0

Then, the function is y=2x+0

So, f(x)=2x

For the second part of line in III quadrant, slope=m=0

Substitute m=0 and (x, y)=(-1, 2) in y=mx+c, we get

2=0(-1)+c

c=2

So, equation is y=2

Now, the piecewise function is

f(x) = {f(x)=2x, if x≤2

f(x) = {f(x)=2, if x>-4

Therefore, the piecewise function is f(x) = {f(x)=2x, if x≤2

f(x) = {f(x)=2, if x>-4.

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