I dont know how to solve this, can you please solve it for me?

Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

The required choice is true of an observational study B, C, and D.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
Option a is not true of an observational study. In an observational study, the researcher cannot control the variables of interest, unlike in a true experiment where the researcher can manipulate the variables.

Option b is true of an observational study. Since the researcher cannot control the variables of interest, the study is entirely based on observing the subjects and collecting data.

Option c is true of an observational study. The data collected in an observational study is similar to the data collected in a true experiment, and the same statistical methods can often be used to analyze both types of data.

Option d is true of an observational study. Since the researcher cannot control the variables of interest, they have to take advantage of natural variation in the variables to draw conclusions.

Thus, Options B, C, and D are correct.

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The roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

Using the quadratic formula to solve the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex],we have

[tex]x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\[/tex]

Therefore, the two roots of the quadratic equation in exact square root form are:

[tex]x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\[/tex]

Thus, the roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

A quadratic equation is a second-degree polynomial equation in one variable of the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.

The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.

The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:

[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]

where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).

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The other endpoint has its coordinate to be (4, -1).

Represent the coordinates of the other endpoint of the line segment be (x, y).

Since the midpoint of the line segment is (5, 1/2), we can use the midpoint formula to write an equation relating the coordinates of the two endpoints:

((6 + x)/2, (2 + y)/2) = (5, 1/2)

Simplifying this equation, we get:

(6 + x)/2 = 5

(2 + y)/2 = 1/2

Solving for x and y, we get:

x = 4

y = -1

Hence, the coordinates of the other endpoint of the line segment are (4, -1).

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Allison purchased lemons for $0.75 each.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph is showing.

Now, Two point on the line are (4, 3) and (8. 6)

Hence, Equation of line is,

⇒ y - 3 = (6 - 3) / (8 - 4) (x - 4)

⇒ y - 3 = 3/4 (x - 4)

⇒ 4 (y - 3) = 3 (x - 4)

⇒ 4y - 12 = 3x - 12

⇒ 4y = 3x

⇒ y = 3/4x

⇒ y = 0.75x

Where, y is cost and x is number of lemons.

Hence, Allison purchased lemons for $0.75 each.

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The statement A and statement B are supported by the data in the table. The solution has been obtained by studying the bar graph.

What is a bar graph?

Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.

We are given a graph showing grasshopper numbers before and after blue jays preyed on them.

From the graph, we can observe that there is no change in the number of green grasshoppers. This means that blue jays did not prey them.

Also, there is a great fall in the brown grasshoppers which means that they are most visible to the blue jays.

Hence, the statement A and statement B are supported by the data in the table.

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The complete question has been attached below

On solving the provided question we can say that The average rate equation of change of g(x) from x = -3 to x = 3 is -27.

A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.

Average Rate of Change = (g(b) - g(a)) / (b - a)

In this case, [tex]g(x) = -3x^3 + 3[/tex], and we need to find the average rate of change from x = -3 to x = 3.

So, we plug in the values of a=-3 and b=3 into the formula:

Average Rate of Change =[tex](g(3) - g(-3)) / (3 - (-3))[/tex]

[tex]= (-3(3)^3 + 3) - (-3(-3)^3 + 3)) / (6)\\= (-81 + 3) - (81 + 3)) / 6\\= (-78 - 84) / 6\\= -162 / 6\\= -27[/tex]

The average rate of change of g(x) from x = -3 to x = 3 is -27.

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Therefore , the solution of the given problem of unitary method comes out to be we have successfully created two groups of cards with the same sum.

After determining the dimensions of one tiny slice, multiply the sum by two to complete a work using unitary procedure. The unit variable methodology, which just requires an expression, can be used to distinguish a coded unit from a certain group or set of groups. 40 pens, for example, might cost Rs. 4,000, which would be equal to $1.01 and 4000 pounds. It's possible that one country will have total control over the method employed to do this. Virtually every living creature has a distinctive quality.

Here,

We can create two groups of cards with the same sum as follows:

Group 1: 1, 2, 5, 8, -4

Group 2: -2, -4, 5, 8, 2

To check that the two groups have the same sum, we can add up the values of each group:

Group 1 sum: 1 + 2 + 5 + 8 - 4 = 12

Group 2 sum: -2 - 4 + 5 + 8 + 2 = 9

We can see that the sum of Group 1 is 12, and the sum of Group 2 is 9. However, we want the sums to be the same. We can make them the same by adding 3 to the sum of Group 2, which gives:

Group 1 sum: 12

Group 2 sum: 12

Therefore, we have successfully created two groups of cards with the same sum, using as many cards as possible from the given set of card numbers.

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From the graph of system of linear inequality there may be other possible solutions, but (20, 100) is one that satisfies all the given constraints.

Let's first define our variables and their corresponding constraints:

Let a be the number of student tickets sold.

Let y be the number of adult tickets sold.

The total number of tickets sold cannot exceed 120, so we have the constraint

a + y ≤ 120 ...eq(i)

The minimum revenue required is $670, so we have the constraint          4a + 8y ≥ 670...eq(ii)

The drama club can sell at most 30 student tickets, so we have the constraint a ≤ 30.

The drama club must sell a minimum of 80 adult tickets, so we have the constraint y ≥ 80.

The last inequality is

y ≥ 80

To solve these inequalities graphically, we will plot the lines for each constraint on a coordinate plane and shade the region that satisfies all the inequalities. The shaded region will represent all possible combinations of student and adult tickets that meet the constraints.

First, let's plot the line for the a + y ≤ 120 constraint. We can rewrite this as y ≤ -a + 120 and plot the line y = -a + 120 on the coordinate plane:

The shaded region for this constraint is below the line and includes the origin.

Next, let's plot the line for the 4a + 8y ≥ 670 constraint. We can rewrite this as y ≥ (-1/2)a + 83.75 and plot the line y = (-1/2)a + 83.75 on the same coordinate plane:

The shaded region for this constraint is above the line.

Now, let's plot the constraint a ≤ 30. We can draw a vertical line at a = 30:

The shaded region for this constraint is to the left of the line.

Finally, let's plot the constraint y ≥ 80. We can draw a horizontal line at y = 80:

The shaded region for this constraint is above the line.

To find a possible solution, we need to find the point where all four shaded regions overlap. This point represents a combination of student and adult tickets that satisfies all the constraints. One such point is (20, 100), which means the drama club can sell 20 student tickets and 100 adult tickets to meet their requirements and raise at least $670 in revenue.

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Therefore, the probability that the first number divided by the second number is greater than zero is 1/3.

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.

Here,

Since we are returning the first tile to the bag before selecting the second one, the two selections are independent of each other.

There are two cases to consider:

Case 1: We select a positive number on the first draw.

The probability of selecting a positive number on the first draw is 2/3, since there are two positive numbers (-12 and 1) out of a total of three tiles.

Regardless of what number we select on the first draw, there is only one negative number (-2) in the bag, so the probability of selecting a negative number on the second draw is 1/3.

Therefore, the probability of selecting a positive number on the first draw and a negative number on the second draw (which results in a quotient greater than zero) is:

(2/3) x (1/3) = 2/9

Case 2: We select the negative number (-2) on the first draw.

The probability of selecting the negative number (-2) on the first draw is 1/3.

In this case, we must select the positive number on the second draw in order for the quotient to be greater than zero. There is only one positive number (1) in the bag, so the probability of selecting it on the second draw is 1/3.

Therefore, the probability of selecting the negative number (-2) on the first draw and the positive number on the second draw (which results in a quotient greater than zero) is:

(1/3) x (1/3) = 1/9

Since these are the only two cases that satisfy the condition, the overall probability is the sum of the probabilities of these two cases:

2/9 + 1/9 = 3/9 = 1/3

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Answer:

27.5

Step-by-step explanation:

(x – 3)2 = 49

(x – 3) = 49/2

(x – 3) = 24.5

x = 27.5

Therefore , the solution of the given problem of probability comes out to be  probability of  not experiencing either symptom is 0.05.

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.

Here,

To determine if the two symptoms are independent, we need to check if the probability of one symptom changes depending on whether the other symptom is present or not.

P(pain | swelling) = 40% / 75% = 0.533

P(pain | no swelling) = 20% / 25% = 0.8

Since the conditional probabilities are not equal, the two symptoms are dependent.

(c) The probability that the victim will experience at least one of these symptoms is the probability of experiencing pain, swelling, or both. This can be calculated as:

P(pain or swelling) = P(pain) + P(swelling) - P(pain and swelling)

= 60% + 75% - 40%

= 95%

So the probability of experiencing at least one of these symptoms is 95%.

(d) The probability that a victim will have intense pain given that they have swelling is the conditional probability:

P(pain | swelling) = 40% / 75%

= 0.533

So the probability of having intense pain given that there is swelling is 0.533.

(e) The probability that a victim will experience pain but not swelling can be calculated as:

P(pain and no swelling) = P(pain) - P(pain and swelling)

= 60% - 40%

= 20%

So the probability of having intense pain without swelling is 20%.

(f) The probability that a victim will not experience either symptom is the complement of the probability of experiencing at least one symptom:

P(neither pain nor swelling) = 1 - P(pain or swelling)

= 1 - 0.95

= 0.05

So the probability of not experiencing either symptom is 0.05.

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a) The probability that a survivor was male is:

142/450 = 0.315

b) The probability that a survivor was in the 2nd class is:

119/450 = 0.264

c) The probability that a survivor was a male, given that the person was in the 2nd class is:

25/119 ≈ 0.210

d) The probability that a survivor was a male and in the 2nd class is:

25/450 ≈ 0.056

e) The probability that a survivor was a male or in the 2nd class is:

P(male or 2nd class) = P(male) + P(2nd class) - P(male and 2nd class)

= 142/450 + 119/450 - 25/450

= 236/450

= 0.524

Now that we know k is 3/2, we can use the formula to find the value of y when x is 14:

y = (3/2)(14) = 21

Therefore, when x = 14, y = 21.

A variable is a number in mathematics that can change depending on the issue. Several statements and equations in mathematics use the generic letters x, y, and z. Or to put it another way, a variable is a symbol that denotes an unknowable numerical value. Assume that x + 5 = 10. The term "x" is used here.

Since y varies directly with x, we know that the ratio of y to x is constant. Let's call this constant k. Then we can write:

y = kx

To find k, we can use the first two rows of the table:

When x = 2, y = 3, so:

3 = k(2)

k = 3/2

When x = 10, y = 15, so:

15 = k(10)

k = 3/2 (which matches the previous calculation)

Now we can use k to find y when x = 14:

y = (3/2)(14) = 21

Therefore, when x = 14, y = 21.

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7 cars and 4 buses were used on the trip

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of cars used.

Let y be the number of buses used.

We know that there were a total of 11 vehicles used, so we can write an equation based on that:

x + y = 11

We also know that the total number of students who went on the trip is 155.

We can use this information to set up another equation:

5x + 30y = 155

This equation represents the fact that the total number of students in cars (5x) plus the total number of students in buses (30y) equals the total number of students (155).

Now we have two equations with two unknowns. We can solve for x and y using a method like substitution or elimination.

Let's use substitution. Solve the first equation for x in terms of y:

x + y = 11

x = 11 - y

Substitute this expression for x into the second equation:

5x + 30y = 155

5(11 - y) + 30y = 155

Simplify and solve for y:

55 - 5y + 30y = 155

25y = 100

y = 4

Now that we know y, we can use the first equation to find x:

x + y = 11

x + 4 = 11

x = 7

Therefore, there were 7 cars and 4 buses used on the trip.

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The best option is Location 2, which you can determine by adding up the points for each site using the information below.

The complete question is:

A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. Use the information below to calculate total points for each location and choose the best option. Round your answers to two decimal places.

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To make a batch of concrete with a total weight of 2200 pounds and a mix ratio of 5:4:2 for sand, gravel, and cement, we need 1000 pounds of sand, 800 pounds of gravel, and 400 pounds of cement.

We must utilise the ratio of sand, gravel, and cement in the mix, which is 5:4:2, to calculate the amount of each ingredient required for a batch of concrete with a total weight of 2200 pounds.

Let's use the number "5x" to represent the quantity of sand in the batch, where x is a proportionality constant. The batch's cement and gravel contents are then, respectively, "4x" and "2x," respectively.

The problem states that the batch weighs 2200 pounds in total. As a result, we may construct the equation shown below:

5x + 4x + 2x = 2200

By merging similar phrases to simplify the left side, we obtain:

11x = 2200

When we multiply both sides by 11, we get:

x = 200

Knowing the value of x allows us to calculate the quantity of each ingredient in the batch:

Sand weight is 5x, or 5 * 200, or 1000 pounds.

The gravel weight is 4x, or 4 * 200, or 800 pounds.

There are 400 pounds of cement, or 2x = 2 * 200.

Therefore we need 1000 pounds of sand, 800 pounds of gravel, and 400 pounds of cement to build a batch of concrete that weighs 2200 pounds overall and has a sand, gravel, and cement mix ratio of 5:4:2.

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Answer:

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

    |          /

    |        /

    |      /

    |    /

-----|------------------

    | /         \

    |/            \

    /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

   |          /

   |        /

   |      /

   |    /

-----|------------------

   | /         \

   |/            \

   /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

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The annual interest rate for the given compound interset is 6%

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.  

Given that, Rs.2250 is deposited for 2 years in an account, it amounts to Rs.2560 compounded annually.

A = P(1+r)ⁿ

2560 = 2250(1+r)²

2560 / 2250 = (1+r)²

1.13 = (1+r)²

Taking roots,

1+r = √1.13

r = 0.06

r = 6%

Hence, the annual interest rate for the given compound interset is 6%

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Answer:

Step-by-step explanation:

A. To plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane, we can use the standard form of the equation of a circle:

For x^2+y^2=4, the radius is 2 and the center is at the origin (0,0).

For x^2+y^2=1, the radius is 1 and the center is also at the origin (0,0)

B. To find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y), we can substitute the values of x and y from the original equation into the transformation rule. Let's take the point (2,0) as an example:

(1/2x,1/2y) = (1/22, 1/20) = (1,0)

Therefore, the point (2,0) will go to the ordered pair (1,0).

C. We can notice that x^2+y^2=1 is a smaller circle that is completely contained within x^2+y^2=4, which is a larger circle. The smaller circle is a dilation of the larger one using the origin as a center and a scale factor of 1/2. This means that every point on the smaller circle is half the distance from the origin as the corresponding point on the larger circle. In other words, the smaller circle is a scaled-down version of the larger one.

Answer:

Step-by-step explanation:

Let the first term of the geometric sequence be 'a' and the common ratio be 'r'.

We know that the 5th term is 729, so:

a * r^4 = 729

10th term is 3, so:

a * r^9 = 3

r^5 = 3/729

r^5 = 1/243

r = (1/243)^(1/5)

r = 1/3

a * (1/3)^4 = 729

a = 3^7

Therefore, the sequence is:

3^7, 3^6, 3^5, 3^4, 3^3, ...

The 12th term is:

3^2 = 9

Answer:

Step-by-step explanation:

First 3 + 4 is 7. Then for the red paint ( 3 ) , this is written.

= [tex]\frac{3}{7}[/tex] * 1400

Then calculated.

= [tex]\frac{3}{7}[/tex] * [tex]\frac{1400}{1}[/tex] = [tex]\frac{4200}{7}[/tex] = 600 ml for the red paint.

Then its easy to find the blue paint, either the long way ( above ) or...

= 1400 ml - 600 ml = 800 ml for blue paint.

Have a wonderful day! :-)

Therefore , the solution of the given problem of expressions comes out to be the simplified expression is 1/(5.6^2 * 3.4^11).

There is a requirement for mathematical operations as addition, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

To simplify the expression, we can combine the terms that have the same base, by adding their exponents. We have:

5.6^-5 * 3.4^-7 * 5.6^3 * 3.4^-4

= (5.6^-5 * 5.6^3) * (3.4^-7 * 3.4^-4) (rearranging the terms)

= 5.6^(-5 + 3) * 3.4^(-7 - 4) (adding the exponents)

= 5.6^-2 * 3.4^-11

= (1/5.6^2) * (1/3.4^11) (using the negative exponent rule)

= 1/(5.6^2 * 3.4^11) (multiplying the reciprocals)

Therefore, the simplified expression is 1/(5.6^2 * 3.4^11).

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The complete question is "

Simplify the expression so there is only one power for each base.

5.6^-5 * 3.4^-7 * 5.6^3 * 3.4^-4"

The solution of the given problem of expressions comes out to be the simplified expression is 1/(5.6² × 3.4¹¹).

There is a requirement for mathematical operations as addition, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an Expression. A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

To simplify the expression, we can combine the terms that have the same base, by adding their exponents. We have:

5.6⁻⁵ × 3.4⁻⁷ × 5.6³ × 3.4⁻⁴

= (5.6⁻⁵ × 5.6³) × (3.4⁻⁷ × 3.4⁻⁴ (rearranging the terms)

= [tex]5.6^{(-5 + 3)}}[/tex] × [tex]\math{3.4^{(-7 - 4)}}[/tex] (adding the exponents)

= 5.6⁻² × 3.4⁻¹¹

= (1/5.6²) × (1/3.4¹¹) (using the negative exponent rule)

= 1/(5.6² × 3.4¹¹) (multiplying the reciprocals)

Therefore, the simplified expression is 1/(5.6² × 3.4¹¹).

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The complete question is:

Simplify the expression so there is only one power for each base.

5.6⁻⁵ × 3.4⁻⁷ × 5.6³ × 3.4⁻⁴

Robin Nest's average daily sales were $1,644 based on credit sales and net receivables.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Average daily sales are the estimated amount of sales made daily in a year.

It can be found by the formula:

= Net credit sales / Number of days in the period

Solving gives:

= 600,000 / 365 days

= $1,644

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The complete question is given below.

Robin's Nest had net credit sales for the current period of $600,000 and average net receivables were $50,000. What is Robin's Nest's average daily sales

Answer:

Step-by-step explanation:

To obtain a polynomial of lowest degree with the given zeros and leading coefficient, we can use the fact that if a polynomial has a root of multiplicity m, then the factor (x - r)^m appears in the polynomial. Therefore, we can write:

f(x) = A(x + 1/4)^2(x - 2/3)

where A is a constant that we need to determine to satisfy the condition f(0) = 2.

To find A, we substitute x = 0 into f(x) and set the result equal to 2:

f(0) = A(0 + 1/4)^2(0 - 2/3) = -A/27 = 2

Solving for A, we find that A = -54.

Therefore, the polynomial f(x) is:

f(x) = -54(x + 1/4)^2(x - 2/3)

Answer: it

Step-by-step explanation:

A graph of the linear equation y = -1/2(x) in slope-intercept form is shown in the image attached below.

In Mathematics, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.

Next, we would use an online graphing calculator to plot the given linear function as shown in the graph attached below.

In conclusion, the slope of this linear function is equal to -1/2 and it represents a proportional relationship.

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9,600 kilobytes have been downloaded so far.

Kilobytes (KB) are a unit of digital information storage that is commonly used to measure the size of computer files and data. One kilobyte is equivalent to 1,000 bytes, or 2^10 (1024) bytes. Kilobytes are often used to describe small files and data sets, such as text documents, images, and audio files.

Kilobytes are part of a larger hierarchy of units used to measure digital information storage, which includes larger units such as megabytes (MB), gigabytes (GB), and terabytes (TB). In this hierarchy, each unit is 1,000 times larger than the previous one. For example, 1 MB is equivalent to 1,000 KB, 1 GB is equivalent to 1,000 MB, and so on.

Kilobytes are used in a variety of contexts, including computer storage, data transfer rates, and internet bandwidth. For example, the size of a typical email message might be measured in kilobytes, and the download speed of a file from the internet might be measured in kilobits per second (kbps).

Despite their relatively small size compared to larger units like gigabytes and terabytes, kilobytes remain an important unit of measurement in the digital world, as many files and data sets are still relatively small and easily manageable within this size range.

30% of 32,000 kilobytes can be found by multiplying 0.3 and 32,000:

0.3 × 32,000 = 9,600

So, 9,600 kilobytes have been downloaded so far.

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The time is about 122 years and 9 months after which there will be 15,000 dollars in the account.

Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.

Given:

An expression,

1[tex](e)^{0.034t}[/tex] model the balance, in thousands of dollars, where t is time.

(a).

0.034 represents the rate at which the function is expressed.

So,

0.034t = log(15000)

          t = log(15000)/0.034

          t =  122.826213502 in years.

          t = 122 years, 9 months.

Therefore,  t = 122 years, 9 months.

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