Please solve all of these!

Please Solve All Of These!
Please Solve All Of These!
Please Solve All Of These!
Please Solve All Of These!

Answers

Answer 1

The answers are:

a)the number we're looking for is [tex]2^{(-97.5)}[/tex], or approximately [tex]1.629 x 10^{(-30)}.[/tex]

b)the value of a is -13.

c) there were 61 people in the line before the second round of people squeezing in.

What is algebra?

Algebra involves solving equations and manipulating expressions to find the value of unknown quantities. It involves working with numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

11. We can solve this problem by using the properties of exponents and algebra.

Let the number we're looking for be x. Then, we can write the equation:

x * 8⁶⁵ = 16⁵⁰

We can simplify the right side of the equation by using the property:

[tex]a^2 = (a^{1/2})^2[/tex]

So, we have:

[tex]16^{50} = (2^4)^{50} = 2^{(4*50)} = 2^{200}[/tex]

Now we can substitute this into the equation:

[tex]x * 8^{65} = 2^{200}[/tex]

We can simplify the left side of the equation by using the property:

[tex]a^n * b^n = (ab)^n[/tex]

So, we have:

[tex]x * (8^2)^{32.5} = (2^3)^{32.5} = 2^{(3*32.5)} = 2^{97.5}[/tex]

Now we can substitute this into the equation:

[tex]x * 64^{32.5} = 2^{97.5}[/tex]

We can simplify the left side of the equation by using the property:

[tex]a^{(n/2)} = (a^n)^{(1/2)}[/tex]

So, we have:

[tex]x * (2^6)^{32.5} = x * 2^{(6*32.5)} = x * 2^{195}[/tex]

Now we can substitute this into the equation:

[tex]x * 2^{195} = 2^{97.5}[/tex]

We can simplify both sides of the equation by dividing by [tex]2^{195}[/tex]:

[tex]x = 2^{97.5} / 2^{195}[/tex]

[tex]x = 2^{(-97.5)}[/tex]

Therefore, the number we're looking for is [tex]2^{(-97.5)}[/tex], or approximately [tex]1.629 x 10^{(-30)}.[/tex]

12. We can find the equation of the line using the two given points and then use the fact that the line passes through the origin to solve for a.

First, we can find the slope of the line using the two given points:

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

slope = (3 - 9) / (40 - (2a + 50))

slope = -6 / (-2a - 10)

slope = 3 / (a + 5)

Now we can use the point-slope form of the equation of a line to write the equation of the line passing through the two given points:

y - 9 = (3 / (a + 5))(x - (2a + 50))

Simplifying this equation, we get:

y - 9 = (3x / (a + 5)) - (6a + 150 / (a + 5))

Now we can use the fact that the line passes through the origin to solve for a:

When x = 0, y = 0, so we can substitute these values into the equation:

0 - 9 = (3(0) / (a + 5)) - (6a + 150 / (a + 5))

-9(a + 5) = 6a + 150

Expanding and simplifying:

-9a - 45 = 6a + 150

-15a = 195

a = -13

Therefore, the value of a is -13.

14. Bree can organize her trip in different ways depending on how many countries she decides to visit. If she visits only one country, there is only one way to organize her trip. If she visits two countries, she can either choose to visit the second country or skip it, which gives her 2 possible ways to organize her trip. If she visits three countries, she has 2 options for the second country and 2 options for the third country (visit or skip), giving her a total of 2x2 = 4 ways to organize her trip. Following this logic, we can create a table to show the number of ways Bree can organize her trip for different numbers of countries:

Number of countries | Number of ways to organize a trip

1                                        1

2                                       2

3                                       4

4                                       8

5                                      16

6                                      32

7                                      64

Therefore, Bree can organize her trip in a total of 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127 ways.

13. Let's start by working backward. After the second round of people squeezing in, there are 121 people in the line. Let's call the number of people in the line before the second round "x". Then we can set up an equation to represent this situation:

121 = x + (x-1)

The reason we have x-1 in the equation is that between each pair of people in the original line, one person squeezed in during the first round, so we have one less gap between people in the new line.

Simplifying the equation, we get:

121 = 2x - 1

Adding 1 to both sides, we get:

122 = 2x

Dividing both sides by 2, we get:

x = 61

Therefore, there were 61 people in the line before the second round of people squeezing in. But before the first round, there were also gaps between people, so the actual initial number of people in the line is one more than the number of gaps. Since there are x-1 gaps between x people, there were 60 gaps and therefore 61 initial people in the line.

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Related Questions

What is the conversion of 64kg in pounds?

Answers

The conversion of 64kg in pounds  is equivalent to approximately 141.09568 pounds.

The kilogram (kg) is the SI unit of mass. It is equal to the mass of the international prototype of the kilogram. This prototype is a platinum-iridium international prototype kept at the International Bureau of Weights and Measures. One kg is approximately equal to 2.20462262184878 pounds.One pound, the international avoirdupois pound, is legally defined as exactly 0.45359237 kilograms.

To convert 64 kilograms to pounds, you can use the conversion factor of 1 kilogram = 2.20462 pounds.

Therefore,64 kilograms = 64 x 2.20462 pounds

= 141.09568 pounds (rounded to 5 decimal places)

So, 64 kilograms is equivalent to approximately 141.09568 pounds.

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how to convert 40 pounds in kg?

Answers

As per the conversion, the weight of 40 pounds is equivalent to a weight of 18.14 kilograms.

Converting measurements can sometimes be a tricky task, especially when we need to convert from one unit to another. One common conversion that we often encounter is the conversion of pounds to kilograms. In this guide, we will explain step by step how to convert 40 pounds into kilograms.

First, we need to understand the basic unit of measurement for both pounds and kilograms. Pounds are a unit of measurement commonly used in the United States and the United Kingdom to measure weight. Kilograms, on the other hand, are the standard unit of measurement for weight in the International System of Units (SI).

To convert 40 pounds to kilograms, we need to use the following formula:

1 pound = 0.45359237 kilograms

Using this formula, we can calculate the equivalent weight in kilograms for 40 pounds. We simply multiply 40 by 0.45359237 to get:

40 x 0.45359237 = 18.14374948 kilograms

So, 40 pounds is equivalent to 18.14374948 kilograms (rounded off to the nearest hundredth) we get 18.14 kilograms.

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what is logarithmic differentiation calculator online

Answers

A logarithmic differentiation calculator is an online tool used to calculate the derivative of a function using logarithmic differentiation.

A logarithmic separation mini-computer is a web-based instrument that utilizes logarithmic separation to work out the subordinate of a capability. Logarithmic separation is a procedure used to separate capabilities that are challenging to separate utilizing customary techniques. The cycle includes taking the normal logarithm of the two sides of the capability, then separating utilizing the principles of logarithms and the chain rule. The subsequent articulation can be streamlined to give the subsidiary of the first capability. An internet based logarithmic separation number cruncher robotizes this interaction, permitting clients to enter a capability and accept its subsidiary. This can be helpful for understudies and experts in fields like math, physical science, and designing, who need to rapidly and precisely work out subsidiaries of perplexing capabilities. There are numerous logarithmic separation number crunchers accessible on the web, some of which additionally give bit by bit clarifications of the interaction used to compute the subsidiary.

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what is average read speed?

Answers

The average read speed is defined as the rate at which a person can read and comprehend written text

The average read speed refers to the rate at which a person can read and comprehend written text. This is typically measured in words per minute (wpm). According to studies, the average reading speed for adults is around 200 to 300 wpm, although this can vary depending on factors such as reading proficiency, familiarity with the material, and reading conditions.

Factors that can affect reading speed include:

Word length and complexity: Longer and more complex words can slow down reading speed.

Font size and style: Smaller fonts and difficult-to-read styles can also slow down reading.

Reading experience: Frequent readers tend to have higher reading speeds than occasional readers.

Comprehension level: Reading speed can decrease if the reader is trying to understand difficult or technical material.

It's important to note that while reading speed is a useful metric, it's not always the most important factor in reading. Comprehension and retention of the material are also crucial, so it's important to find a balance between reading speed and comprehension.

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assuming she worked at a constant rate, how many rows had been completed before elena started working?

Answers

If she is working at a constant rate, 12 rows had been completed before Elena started working.

To determine the number of rows that were completed before Elena started working, we need to find the equation of the line that represents the relationship between the number of rows completed and the time taken.

We can use the two given points (14, 19) and (20, 22) to find the slope of the line:

slope = (change in rows) / (change in time) = (22 - 19) / (20 - 14) = 3 / 6 = 1/2

Next, we can use the slope and one of the points to find the y-intercept of the line using the point-slope form of a line:

y - 19 = (1/2)(x - 14)

y - 19 = (1/2)x - 7

y = (1/2)x + 12

Now that we have the equation of the line, we can use it to find the number of rows completed when x (time) is equal to 0, which represents the point when Elena started working:

y = (1/2)(0) + 12 = 12

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The given question is incomplete, the complete question is :

Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting.

Assuming she worked at a constant rate, how many rows had been completed before Elena started working?

how to convert 50cm to in

Answers

50cm is equal to 19.685 inches.

Measurement is a crucial aspect of our lives, and it helps us to determine the quantity, size, or amount of things. Different units of measurement are used to measure various objects, and it is essential to know how to convert from one unit to another. In this article, we will discuss how to convert 50cm to inches, which are both commonly used measurements.

To convert 50cm to inches, we need to know the conversion factor between centimeters and inches. One inch is equal to 2.54 centimeters, which means that we can convert centimeters to inches by dividing the measurement by 2.54.

So, to convert 50cm to inches, we need to divide 50 by 2.54. We can do this using a calculator or by long division.

50 / 2.54 = 19.685 inches

In this case, we have learned how to convert 50cm to inches, which involves dividing the measurement by 2.54.

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Solve |h+3|<5. Write the solution set using set-builder notation.

Answers

Answer:

To solve the inequality |h + 3| < 5, we need to consider two cases, depending on whether the expression inside the absolute value bars is positive or negative:

Case 1: h + 3 >= 0

If h + 3 >= 0, then we can remove the absolute value bars without changing the inequality:

h + 3 < 5

Subtracting 3 from both sides, we get:

h < 2

So the solution for this case is h < 2.

Case 2: h + 3 < 0

If h + 3 < 0, then the inequality becomes:

-(h + 3) < 5

Multiplying both sides by -1 (and reversing the inequality), we get:

h + 3 > -5

Subtracting 3 from both sides, we get:

h > -8

So the solution for this case is h > -8.

Putting these two solutions together, we have:

-8 < h < 2

Therefore, the solution set in set-builder notation is:

{h | -8 < h < 2}

Daniel is selecting a sock from his drawer at random. if daniel does this 60 times, what is reasonable prediction for the number of times he will get a completely striped sock?

Answers

Reasonable prediction for the number of times he will get a completely striped sock is 15 times.

What is random used for?

Random numbers are used to construct probability samples from a population and make statistical inferences from a survey, and also to decide which treatment should be applied to the various physical units in an experiment.

Daniel is selecting a sock from his drawer at random.

If Daniel does this 60 times.

To determine the reasonable prediction for the number of times he will get a completely striped sock.

Now,

There are 8 socks in total, including 2 stripped socks.

So, the probability of picking a stripped socks at random is 2/8 = 1/4

60 times × 1/4 = 15 × 4 times × 1/4

                       = 15 times

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what is 1/2 cup butter?

Answers

As per weight measurement, half cup of butter is equal to 113 grams or eight tablespoons of butter. In ounces it is actually 4oz.

An object's weight serves as a gauge for its weight. Weight is expressed in common units of measurement. The weight of an object can be measured with tools using the gram and kilogram. The metric system that is universally accepted as a reference for measurements is called the International System of Units. The kilogram is the SI unit for mass or weight.

A common unit of measurement for cooking volume is the cup, which is used to determine serving and cooking sizes. Normal conversion: 1 cup = 8 liquid ounces = 1/2 pint. 16 fluid ounces divided by 2 cups equals one pint. 4 cups are equivalent to 32 fluid ounces, 2 pints, and 1 quart. 8 cups equal 64 fluid ounces, or 4 pints.

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What is the income threshold for self-employed workers to file a return?

Answers

Answer:

$400 or more

Step-by-step explanation:

im pretty sure:)

draw each quadrilateral

with a pair of opposite sides parrarel but not congruent

with a pair of opposite sides congruent not parrarel

with 2 pairs of congruent angles

with one right angle

with two consecutive congruent sides

Answers

The answers to each type of quadrilateral given below.

What is Quadrilateral?

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Given:

A quadrilateral with a pair of opposite sides parallel but not congruent is a Trapezium.

A quadrilateral with a pair of opposite sides congruent not parallel

is isosceles trapezoid.

A quadrilateral with 2 pairs of congruent angles is a parallelogram.

A quadrilateral with one right angle is right quadrilateral. .

A quadrilateral with two consecutive congruent sides is Kite.

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help me please i will mark you as brainiest if you get this answer right

Answers

Answer:

a = √c²-b²

Step-by-step explanation:

Sup bro,

The correct answer is a = √c²-b²

Give an example of a matrix A and a vector b such that the solution set of Ax=b is a line in R3 that does not contain the origin.

Answers

an example of a matrix A and a vector b such that the solution set of Ax=b is a line in R3 that does not contain the origin will be= 1 0 0 0 ,0 1 0 0 , 0 0 0 0]

[tex]AX = \left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\4\\2&\end{array}\right][/tex]

and b = [tex]\left[\begin{array}{ccc}6\\14\\30&\end{array}\right][/tex]

the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}6\\14\\30&\end{array}\right][/tex]

we shall reduced the augmented matrix [A;B] to echelon form by applying elementary row transformation only.

operating  [tex]R_{2} , R_{2} - R_{1} , R_{3} ,R_{3} -R_{1}[/tex]

[tex][A:B] = \left[\begin{array}{ccc}1&1&1\\0&1&2\\0&3&6\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}6\\8\\24&\end{array}\right][/tex]

operating [tex]R_{3} , R_{3} - 3R_{2}[/tex]

      ≈ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}6\\8\\0&\end{array}\right][/tex]

which is the row echelon form of the matrix [A:B].

A matrix that has gone through the Gaussian end is supposed to be in column echelon form or, all the more appropriately, "decreased echelon form" or "line diminished echelon form." Such a matrix has the accompanying qualities:

1. Every one of the zero columns are at the lower part of the matrix

2. The main passage of each nonzero column after the first happens to one side of the main section of the past line.

3. The main passage in any nonzero column is 1.

4. All sections in the segment above and under a main 1 are zero.

One more typical meaning of echelon form just requires zeros beneath the main ones, while the above definition additionally requires them over the main ones.

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Check all that apply that describe the graph of the inequality: y2 - 2x + 3
slope: -2
slope: 2
dotted/dashed line
solid line
shade above
shade below
y-intercept of 3

Answers

The correct options for the inequality y ≥ -2x + 3 are:

slope: -2solid lineshaded abovey-intercept of 3How to describe the graph of the inequality?

Here we have the next inequality:

y ≥ -2x + 3

First, we can see that the symbol "≥" is used, then the points on the line are solutions, and thus, the line must be a solid line.

Also, y is larger or equal than that, so we need to shade the region above.

Finally, the line is y = -2x + 3

So the slope is -2 and the y-intercept is 3.

These are the characteristics of the inequality

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How many more hours did Bryce practice piano than guitar? If there is no whole number, place a 0 in the box. (Rest of question is in image)

Answers

The total time of the guitar session will be 7¹/₂ hours.

What is a scatter plot?

A scatter plot is a plot mathematical chart or graph that depicts the relationships by the use of dots and shows the two numeric variables.

The dots are positioned on each horizontal and vertical value for an individual. They are used for observing the relationship between the variables. The graph shows are positive but nonlinear association.

The total time will be calculated as:-

T = ( 3) x ( 1 / 4 ) + (4) x (1 / 2 ) + ( 5 ) x ( 3 / 4 ) + 1

T = 3/4 + 4 / 2 + 15 / 4 + 1

T = 3 / 4 + 2 + 15 / 4 + 1

T = 18 / 4 + 3

T = 15 / 2

T = 7¹/₂ hours.

Therefore, the total time will be 7¹/₂  hours.

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What is the unit rate for 30 millimeters every 4 hours

Answers

Answer:

30 X 4=yhhvvihddthjgyujjnbbbvvvukgdddsxgjooi

If joe wants to burn 250 calories in 54 and he does the treadmill for 5 cal/min and does the bike for 4cal/min what is the equation
Treadmill is represented by T
Bike represent by B

Answers

Answer:

Step-by-step explanation:

Konnor wants to burn  while exercising for  at the gym. On the treadmill, he can burn . On the stationary bike, he can burn . If t represents the number of  on the treadmill and  represents the number of  on the stationary bike, what expression represents the number of Calories that Konnor can burn on the stationary bike?

a.6

b.4

c.2

what is negative z score table

Answers

A table used to find the area under the standard normal distribution to determine the probability of a z-score being less than a given value.

A negative z-score table is a tool used in statistics to find the probability of a z-score being less than a certain value. A z-score is a measure of the number of standard deviations an observation or data point is above or below the mean of a dataset.

The standard normal distribution is a bell curve with a mean of zero and a standard deviation of one. The negative z-score table lists the area under the curve to the left of a negative z-score, which can be used to calculate probabilities. The table is used by finding the corresponding row and column for the desired z-score and reading the probability from the table.

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1. What are the Math 1 essential skills and/or concepts relevant to this task?

2.Name the strategy you will use to solve the problem:

3. Describe the strategy:

Justify your thinking. (This means: justify the strategy or justify your final solution.)

Answers

The number of solutions in the equation is One solution

The number of solutions in the equation

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

The graph

On the graph, we have two lines that intersect at a point

This means that the number of solutions is one

The essential skills

Here, the skills needed are:

Being able to solve a system of equations using graphsUnderstanding the concept of a unique solution of equations

The strategy used to solve the problem

The strategy to solve the problem is to use the graph method to solve the system of linear equations and check if the resulting solution satisfies all the equations in the system.

If it does, then the system has one unique solution.

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the angles opposite the congruent sides of an isosceles triangle are congruent. find the value of x in the triangle. show all your work.

Answers

The measure of angle x in the isosceles triangle is 40 degrees.

Let's call the two congruent sides of the isosceles triangle "a" and the remaining side "b". Since the angle opposite one of the congruent sides (let's call it "a") is 70 degrees, the other angle opposite "a" must also be 70 degrees due to the property of isosceles triangles. Let's call this angle "y".

So we have two angles that add up to 140 degrees (70 + 70 = 140). We also know that the sum of the angles in any triangle is always 180 degrees. Therefore, we can find the measure of angle "x" as follows:

x + y + 70 = 180

Substituting y = 70, we get:

x + 70 + 70 = 180

Simplifying the equation, we get:

x + 140 = 180

Subtracting 140 from both sides, we get:

x = 40

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The given question is incomplete, the complete question is :

The angles opposite the congruent sides of an isosceles triangle are congruent. find the value of x in the triangle. show all your work.

Tell whether $(2,\ 3)$ is a solution of $x+y<7$

Answers

Answer: It is not

Step-by-step explanation: If you graph the equation you can see that it is not a solution and doesn't line up.

What is the conversion of 72 into feet?

Answers

After converting 72 inches into inches, we will get it as: 72 inches equal to 6 feet.

Length conversion is the process of converting length measurements between different units.

The metric system uses length units like kilometres (km), metres (m), centimetres (cm), and so on.

As we know,

1 Foot equal to 12.000005 Inches.

But actually, we can consider it as:

The 12 inches is equal to 1 foot.

We have to convert the 72 inches into feet,

So, We will simply divide the value of given inches by 12

Thus, we will get it as:

72 inches = (72/12) feet = 6 feet

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The complete question may be:

What is the conversion of 72 inches into feet?

What are the steps you take to find the área of a compound figure?

How do you show your work when finding area of compound figure?

Answers

Answer:

1. Divide the compound figure into parts whose areas can be calculated. These parts must be simple shapes such are rectangles, triangle, circles, etc. for which there is a formula, and the dimensions (length, width, height, radius, etc.) must be shown or can be calculated.

2. Calculate the area of each part.

3. Add all areas together.

I need some help on this question please, thank you.

Answers

Answer:

37cm^2

Step-by-step explanation:

Area of rectangle = Length × Width

This shape needs to be split then you simply work out the area of each shape and add it.

Shape 1: 3cm × 5cm = 15cm^2

Shape 2: 2cm × 11cm = 22cm^2

Now add them together: 15cm^2 + 22cm^2 = 37cm^2

a researcher is interested in average first semester change in weight (gain or loss) for students at a local college. thus, they record the individual change in weight for a small group of 25 freshman from this college during their first semester. then, the researcher calculates the average change in weight during the first semester among these 25 students. the average is an example of a

Answers

In the given scenario, the average is an example of a Parameter.

Statistic:  

In statistics, a statistic is a numerical value or measure that is calculated from a sample of data. Statistics are used to summarize and describe the characteristics of a sample.

Variable:

a variable is a symbol or letter that represents a quantity or value that can change or vary. Variables are used to describe relationships between quantities and to represent unknown values or values that can take on different values in different situations.

Parameter:

In statistics, a parameter is a characteristic of a population. A population refers to the entire group of individuals, objects, or events that we want to study. A parameter is a numerical value that describes some aspect of the population, such as its mean, variance, or proportion.

For example, if we want to study the average height of all students at a university, then the population is all the students at the university, and the parameter of interest is the population's mean height

Constant:

A constant is a value that does not change. In mathematics, constants are often used to represent fixed values or quantities that do not depend on other variables or parameters.  

Here we have

A researcher record the individual change in weight for a small group of 25 freshmen from this college during their first semester.

Then, the researcher calculates the average change in weight during the first semester among these 25 students.  

By the given information,

In the given scenario, the average is an example of a Parameter.        

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Evan volunteers on the weekend at the Central Library. As a school project, he decides to record how many people visit the library, and where they go. On Saturday, 433 people went to The Youth Wing, 335 people went to Social Issues, and 367 went to Fiction and Literature.
On Sunday, the library had 600 total visitors. Based on what Evan had recorded on Saturday, about how many people should be expected to go to Fiction and Literature? Round your answer to the nearest whole number.

Answers

Answer: Rounding to the nearest whole number, we can estimate that about 194 people should be expected to visit the Fiction and Literature section on Sunday.

Step-by-step explanation:

To estimate how many people to expect in the Fiction and Literature section on Sunday, we can assume that the proportion of visitors to each section remains the same as it was on Saturday.

First, we need to calculate the total number of visitors on Saturday:

433 (Youth Wing) + 335 (Social Issues) + 367 (Fiction and Literature) = 1135

Next, we can find the proportion of visitors to the Fiction and Literature section:

367 (Fiction and Literature) / 1135 (total visitors on Saturday) ≈ 0.323

We can use this proportion to estimate the number of visitors to the Fiction and Literature section on Sunday:

0.323 (proportion of visitors to Fiction and Literature) x 600 (total visitors on Sunday) ≈ 194

Rounding to the nearest whole number, we can estimate that about 194 people should be expected to visit the Fiction and Literature section on Sunday.

Hi , please help ( see images)

Answers

This is a word problem and the value of the unknown number is equal to 5.5.

We can write algebraically the second question as 3(x - 1).

Simplifying fully 15xy ÷ 15xy = 1/y

Word problems in mathematics

Word problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.

Let us represent the unknown number with the letter x so that we derive the equation;

2x - 2 = 9

we add 2 from both sides of the equation

2x - 2 + 2 = 9 + 2

2x = 11

divide through by the coefficient of x which is 2

2x/2 = 11/2

x = 5.5.

Using x as the unknown, we can write the statement in the second question as 3(x - 1).

15xy ÷ 15xy = 1/y

Therefore, the value of the unknown number for the word problem is equal to 5.5

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Answer:

in order from last to first

3y

(x-1)3

x2-2=9

Step-by-step explanation:

(I also included the image for your previous question))

what is the greatest common factor of 42 126 and 210?

Answers

The greatest common factor (GCF) of 42, 126, and 210 is 42.

To find the GCF, you can use several methods such as prime factorization or the Euclidean algorithm. One way to find the GCF using prime factorization is to express each number as a product of its prime factors:

42 = 2 × 3 × 7

126 = 2 × 3² × 7

210 = 2 × 3 × 5 × 7

Then, identify the common prime factors and their smallest exponent across all three numbers. In this case, the common prime factors are 2, 3, and 7. The smallest exponent of 2 is 1, the smallest exponent of 3 is 1, and the smallest exponent of 7 is 1. Therefore, the GCF is

= 2 × 3 × 7

= 42

Another method to find the GCF is the Euclidean algorithm, which involves finding the remainder of dividing the larger number by the smaller number repeatedly until the remainder is zero. The GCF is the last nonzero remainder. However, in this case, the prime factorization method is simpler and quicker.

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Sai borrowed $390 from his mum to buy a phone. His mum says she will reduce his debt by 5% of what he owes at the end of each month, provided he keeps his room tidy. If he manages to keep his room tidy for three months, what does he owe her at the end of that period?​

Answers

The amount owed at the end of that period is given as follows:

$334.

What is an exponential function?

An exponential function is modeled as follows:

y = ab^x.

In which:

a is the value of y when x = 0.b is the rate of change.

For a decreasing exponential function, the rate of change b is given as follows:

b = 1 - r.

In which r is the decay rate.

The parameters for this problem are given as follows:

a = 390, r = 0.05, b = 0.95.

Hence the function giving the amount owed after x months is given as follows:

y = 390(0.95)^x.

After three months, the amount owed is given as follows:

y = 390(0.95)^3

y = $334.

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Answer:

$334.37

Step-by-step explanation:

At the start, Sai owes his mum $390. After the first month, his mum reduces his debt by 5% of $390, which is 0.05 x $390 = $19.50. So at the end of the first month, he owes his mum $390 - $19.50 = $370.50.

After the second month, his mum reduces his debt by 5% of $370.50, which is 0.05 x $370.50 = $18.53. So at the end of the second month, he owes his mum $370.50 - $18.53 = $351.97.

After the third month, his mum reduces his debt by 5% of $351.97, which is 0.05 x $351.97 = $17.60 (rounded to the nearest cent). So at the end of the third month, he owes his mum $351.97 - $17.60 = $334.37.

Therefore, Sai owes his mum $334.37 at the end of three months.

Sin descuento, esta casaca cuesta $80 por lo que luiscomenta. Voy acomprar la casac, ya que por ella pagaré solo $55 luego del descuento. ¿es correcto lo que dice luis? ¿por qué? explica tu respuesta

Answers

No es posible determinar si lo que dice Luis es correcto sin conocer el porcentaje de descuento aplicado en la compra de la casaca.

Si el precio original de la casaca es de $80 y después de aplicar un descuento el precio final es de $55, entonces se puede determinar el porcentaje de descuento utilizando la fórmula:

descuento = (precio original - precio final) / precio original

descuento = (80 - 55) / 80 = 0.3125 = 31.25%

Si el porcentaje de descuento es del 31.25%, entonces Luis tiene razón en su afirmación de que está comprando la casaca con un descuento. Sin embargo, si el porcentaje de descuento es diferente, entonces su afirmación podría ser incorrecta.

Por lo tanto, es importante conocer el porcentaje de descuento para determinar si lo que dice Luis es correcto o no.

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