Distributive Method
(2x+3)(x

Answer:

C. 0.0067

Step-by-step explanation:

6.7*10^-3

Write in standard form.

This question pertains to scientific notation, a way to easily express really large or really small numbers.

You'll first notice that 10 has a negative exponent. This tells you that the number is going to be smaller than 10.

This is because 10^-3 translates to 1/10^3 based on exponent rules

With that, you know that your equation is 6.7/10^3

You can simplify that to:

\(\frac{6.7}{10^{3} }\)

\(\frac{6.7}{1000}\)

0.0067

In case you didn't know how I got there, 10^3 simply means 10 multiplied by itself 3 times.

The other method would be to look at your answer choices. Since we have a negative exponent, we can eliminate D.

Next, since we have a positive coefficient (6.7), we can eliminate A and B.

That leaves us with the answer C. 0.0067

A model that attempts to approximate or determine outcomes based on multiple parameters and known relationships expressed as mathematical algorithms or parametric equations is called a mathematical model.

A mathematical model is a representation of a real-world system or phenomenon using mathematical equations. It is a tool used to analyze and predict the behavior of complex systems by expressing the relationships between various variables. Mathematical models can be applied in various fields, including physics, economics, engineering, and social sciences.

These models involve identifying the relevant parameters and variables, establishing the mathematical relationships between them, and formulating equations or algorithms to represent these relationships. By manipulating and solving these equations, researchers can simulate scenarios, predict outcomes, and gain insights into the behavior of the system under study.

Mathematical models can take different forms, such as deterministic or stochastic, linear or nonlinear, continuous or discrete. They provide a quantitative framework to explore the impact of different inputs, understand the interplay between variables, and make predictions about the system's behavior.

The use of mathematical models enables researchers to test hypotheses, optimize processes, make informed decisions, and understand complex systems that may be challenging to study directly through experimentation.

A mathematical model is a powerful tool that allows researchers to approximate or determine outcomes by expressing relationships between variables through mathematical equations or algorithms. It provides a quantitative framework to analyze, predict, and understand the behavior of complex systems in various fields of study.

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Answer:

7

Step-by-step explanation:

subtract the cost of the bat from the budget and you get 58

divide the amount left by the cost of balls and you get 7.73.

you can not buy half of a ball so your answer is 7

If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h  .

A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.

We have to find the rate at which the radius is changing after 6.5 hours.

So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.

Volume Of Sphere is  V = (4/3)πr³ and dV/dt = -11 ft³/h ;

So,  dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt)  ;

derivative of volume formula with respect to "r", we get:

⇒ dV/dr = 4πr²   ;

Substituting the given values in chain rule equation, we get:

⇒ -11 = (4/3)πr² × dr/dt  ;

⇒ dr/dt = -11/((4/3)πr²)

For  rate of change of the radius when t = 6.5 hours, we find the radius at that time.

The initial volume of the snowball = 260 ft³.

After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be:  V = 260 - (11 × 6.5) = 188.5 ft³   ;

So , V = (4/3)πr³

⇒ 188.5 = (4/3)πr³

⇒ r³ = (188.5 × 3 / (4π))   ;

≈ 3.55ft

Now we substitute r = 3.55 feet

⇒ dr/dt = -11/[(4/3)π(3.55)²]  ;

⇒ dr/dt ≈ -0.208 ft/h  ;

Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing  .

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Answer: Its -10 :)

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

on edge it works

Answer:

Hypotneuse is 2.5 cm.

Step-by-step explanation:

Hyp^2=Sum of the squares of the other two sides
a^2 = b^2+ c^2
hyp^2 = (2)^2 + (1.5)

hyp^2 = 4 + 2.25

hyp^2=6.25

Apply sq. root on both sides

hyp = 2.5 cm

Could you get a closer picture?

Answer:

1.54 and 1.7 I believe

Step-by-step explanation:

Answer:

The full steel tire is 1.76 pounds and the lighter wheel is 1.54 pounds

Step-by-step explanation:

To find how many pounds each tire is, divide the weight in grams by 453.592

Full steel tire:

800/453.592 = 1.76 pounds

Lighter wheel:

700/453.592 = 1.54 pounds

So, the full steel tire is 1.76 pounds and the lighter wheel is 1.54 pounds

Answer:

The difference of 0.5 is not significant because the re-randomizations show that it is within the range of what could happen by chance.

Step-by-step explanation:

For the means which are given as 5.375 and 4.875 respectively, for a difference of 0.5.

The best conclusion for Jorge to make based on the data is that - The difference of 0.5 is not significant because the re-randomizations show that it is within the range of what could happen by chance

A source of money that allows individuals to pay for goods and services later is called consumer credit and an advantage of this source of money is that there are no interest charges.

Consumer credit, also known as consumer debt, enables the consumers to incur debt or borrow money and to defer repayment of that money over time. It allows consumers to buy goods without having to pay for them in cash at the time of purchase. Examples of consumer credit include credit cards, student loans, etc. Among the advantages of using consumer credit is that there is no interest charge to borrow the money for a certain period of time until the due date.

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The critical points are (0, 0) and (1/2, 1/8).

To find the critical points of the function f(x, y) = 8x^3 + y^3 - 6xy + 2, we need to find the points where the partial derivatives of f with respect to x and y are equal to zero.

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

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Answer:

Session A = 1.25 hours

Session B = 0.5 hours

Step-by-step explanation:

Given

Plans: A and B

Friday can be expressed as: 4A + 8B

Saturday can be expressed as: 2A + 3B

Total Time:

Friday = 9 hours

Saturday = 4 hours

Required

Determine time for each session (A and B)

The question illustrates simultaneous equation and the equations are;

\(4A + 8B = 9\)

\(2A + 3B = 4\)

Multiply the second equation by 2

\(2(2A + 3B = 4)\)

\(4A + 6B = 8\)

Subtract this from the first equation:

\((4A + 8B = 9) - (4A + 6B = 8)\)

\(4A - 4A + 8B -6B = 9 - 8\)

\(8B -6B = 1\)

\(2B = 1\)

Solve for B

\(B= \frac{1}{2}\)

\(B = 0.5\ hours\)

Substitute \(B= \frac{1}{2}\) in \(2A + 3B = 4\)

\(2A + 3(\frac{1}{2}) = 4\)

\(2A + \frac{3}{2} = 4\)

Solve for 2A

\(2A = 4 - \frac{3}{2}\)

\(2A = \frac{8 - 3}{2}\)

\(2A = \frac{5}{2}\)

Solve for A

\(A = \frac{5}{2} * \frac{1}{2}\)

\(A = \frac{5}{4}\)

\(A = 1.25\ hours\)

Answer:

(f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11 in standard form.

Step-bystep-Explanation:

To find (f - g)(x), we need to subtract the function g(x) from the function f(x) by subtracting the corresponding terms.

Given:

f(x) = 3x^5 + 6x^2 - 5

g(x) = 2x^4 + 7x^2 - x + 16

To find (f - g)(x), we subtract each term of g(x) from the corresponding term of f(x):

(f - g)(x) = (3x^5 - 2x^4) + (6x^2 - 7x^2) + (-5 - (-x)) - 16

Simplifying this expression, we get:

(f - g)(x) = 3x^5 - 2x^4 + 6x^2 - 7x^2 + (5 + x) - 16

Combining like terms, we have:

(f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11

Therefore, (f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11 in standard form.

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The age of Lisa and Myra now is 35 years old and 5 years old, respectively.

To determine how old each person now, use algebraic expression and equation.

Let x = current age of Lisa

y = current age of Myra

If the sum of Lisa's age and Myra's age is 40, then we can express it as:

x + y = 40

x = 40 - y

If in 10 years, Lisa will be 3 times as old as Myra, then we can express it as:

x + 10 = 3(y + 10)

x + 10 = 3y + 30

x - 3y = 20

Substitute the equation for x into the 2nd equation and solve for y.

x - 3y = 20

(40 - y) - 3y = 20

40 - 4y = 20

4y = 20

y = 5

Substitute the value of y into the equation for x and solve.

x = 40 - y

x = 40 - 5

x = 35

Therefore, Lisa is 35 years old while Myra is 5 years old.

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The Blu-ray movie will cost approximately $36.42 in 5 years with an inflation rate of 12% and continuous compounding.

To calculate the future cost of the Blu-ray movie in 5 years with an inflation rate of 12% and continuous compounding, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

A = Future value

P = Present value

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time period in years

In this case, the present value (P) is $19.99, the inflation rate (r) is 12% or 0.12, and the time period (t) is 5 years. Substituting these values into the formula, we get:

A = 19.99 * e^(0.12 * 5)

Calculating the exponent first:

0.12 * 5 = 0.6

Then:

e^0.6 ≈ 1.82212

Finally:

A = 19.99 * 1.82212 ≈ 36.42

Using the formula for continuous compound interest, we calculated that a Blu-ray movie that costs $19.99 today will cost approximately $36.42 in 5 years, assuming an inflation rate of 12% and continuous compounding.

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The equation for temperature change is T = -1.5t + 29 and the number line is plotted.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

Let T represent the temperature in degrees Celsius, and let t represent the time in hours after lunchtime.

Then write an expression for the situation as follows:

T = -1.5t + 29

Here, -1.5t represents the decrease in temperature per hour, since the temperature is dropping at a rate of 1.5 degrees Celsius per hour.

Adding 29 to -1.5t gives the initial temperature of 29 degrees Celsius at lunchtime.

To illustrate this situation on a number line diagram, we can plot the temperature T as a function of time t.

The diagram would have time t on the horizontal axis and temperature T on the vertical axis.

Label the point (0, 29) on the diagram to represent the temperature at lunchtime, and the point (x, 16) to represent the temperature at sunset, where x is the number of hours after lunchtime.

Then draw a straight line connecting these two points to represent the linear relationship between temperature and time.

The line slopes downward from left to right, indicating that the temperature is decreasing over time.

Therefore, the number line diagram is plotted.

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On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

Hi, Laura! ;)

They want to know the center of a distribution. Another word for center is middle. When you have a set of numbers, you can find the middle by calculating the mean, the "average" of the data set.

1) Add all the numbers: 12,8 + 5,7 + 7,9 + 1,3 + 3,2 + 2,8 = 33,7

2) Divide the sum by the quantity of numbers, which is 6:  33,7 / 6 = 5,616

The closest number to 5,616 is 5,62.

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

Now let's answer your second question.

1) First step is to find out how many possible outcomes you have. It is the

number of raffle tickets in the box: 200.

2) Then, let's define the number of tickets that are prizes: 4 + 8 + 16 = 28.

The probability of selecting a prize ticket is the number of prize tickets divided by all the raffle tickets in the box: 28 / 200 = 0,14.

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Good luck, Laura! :)

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Let's simplify step-by-step.

5c2c+7+c−282c+7

=5c3+7+c+−282c+7

Combine Like Terms:

=5c3+7+c+−282c+7

=(5c3)+(c+−282c)+(7+7)

=5c3+−281c+14

Answer:

=5c3−281c+14

Hope this helped!

(I hope this is what u asked for :)

Answer:

y=\(\frac{1}{3}\)x+8

This will return `True`, since all the elements in `set1` are also present in `set2`.

True.

The `issubset()` method in Python can be used to determine if a set is a subset of another set. It returns `True` if all the elements of the first set are also present in the second set, and `False` otherwise.

For example, if we have two sets `set1 = {1, 2, 3}` and `set2 = {1, 2, 3, 4, 5}`, we can use the `issubset()` method to check if `set1` is a subset of `set2` as follows:

```

set1.issubset(set2)

```

This will return `True`, since all the elements in `set1` are also present in `set2`.

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Answer:

15 is a composite number. 15 = 1 x 15 or 3 x 5. Factors of 15: 1, 3, 5, 15. Prime factorization: 15 = 3 x 5

Step-by-step explanation:

Answer:

15= 3 x 5

Step-by-step explanation:

                            15

                        /      /

                      5   x    3

3 and 5 both multiply together to make 15

Answer:

x>-7/3, x<-1

Step-by-step explanation:

Hope this helped!!!

Answered by NONE other than the #QUEEN herself!!

The last or 3rd figure attached below shows how to draw a perpendicular to a line from a point on the line.

As shown in the last figure attached below ,to draw a perpendicular take a point on line and draw an arc of equal length on the both side  and extend both arc, the point at which both arc intesect is now the 2nd point now connect the point on line and the second point the straight line drawn is  the perpendicular to the line from the point .

The last figure attached below is the best description of the above statement so it is the best possible method to draw perpendicualr from a point on the line.

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Complete question:

Which figure shown below illustrates the construction of a perpendicular to a line from a point on the line.

Answer:

x=10

Step-by-step explanation:

2/3+5/6x=9

5/6x=8 1/3

5/6x=25/3

5x=50

x=10

Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

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The simplified value of log 64 (with base 10) is approximately 2.5.

To solve the logarithm equation log 64, we need to determine the base of the logarithm. Assuming the base is 10 (common logarithm), we can rewrite the equation as: log₁₀ 64

The logarithm function asks the question: "To what power must we raise the base (10) to obtain the given number (64)?" In this case, we need to find the exponent that produces 64 when the base 10 is raised to that power.

To simplify, we recall that 10 to the power of 2 is equal to 100:

10² = 100

Similarly, 10 to the power of 3 is equal to 1000:

10³ = 1000

Since 64 is between 10² and 10³, we can conclude that the exponent will be between 2 and 3. We can estimate that the exponent is closer to 2.5.

Thus, the simplified value of log 64 (with base 10) is approximately 2.5.

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Answer:

B. Evidence

Step-by-step explanation:

Reference: like when your drawing something and you want to make sure that you draw the hair the same way some other person did.

Cite: That’s when you give the credits to someone or something 90% sure

Hope this helps :)

Answer:

C. y = -x

Step-by-step explanation:

the slope is -1 so in the formula y= mx + b

b is 0 and m is -1

so plug it in and you get y = -x

An article appearing in a certain journal included the following acrylamide content for five brands of biscuits. 344 , 294, 333, 276, 248. The mean acrylamide level (in nanograms/gram) is 299.

In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values. It is commonly referred to as the average.

To calculate the mean, all the data values are added together, and then this sum is divided by the number of data points in the dataset. The formula for calculating the mean is:

mean = (sum of values) / (number of values)

To calculate the mean acrylamide level, we need to add up all the acrylamide levels for the five brands of biscuits and divide the sum by the total number of brands.

Sum of acrylamide levels = 344 + 294 + 333 + 276 + 248 = 1495

Total number of brands = 5

Mean acrylamide level = (Sum of acrylamide levels) / (Total number of brands) = 1495 / 5 = 299

Therefore, the mean acrylamide level is 299 nanograms/gram.

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