I need help on this question!!!!

The change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

To quantify the change in the area of the surface of a cube when its side length triples from s units to 3s units, we can set up an integral.

Let's denote the side length of the cube as "x". The initial side length is "s" and the final side length is "3s". We want to find the change in surface area, which is the difference between the final surface area and the initial surface area.

The surface area of a cube with side length "x" is given by 6x², as each face of the cube has an area of x² and there are 6 faces.

The change in surface area can be calculated as:

ΔA = ∫(6x²) dx,

where the integral is taken from the initial side length "s" to the final side length "3s".

Now let's evaluate the integral:

∫(6x²) dx = 2x³ + C,

where C is the constant of integration.

To find the change in surface area, we substitute the limits of integration:

ΔA = [2x³]s to 3s

= 2(3s)³ - 2s³

= 2(27)s³ - 2s³

= 52s³

Therefore, the change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

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Answer:

\(y _{1} - y = m(x _{1} - x) \\ \\ 5 - y = 3(x - 9) \\ \\ 5 - y = 3x - 27 \\ - y = 3x - 27 - 5 \\ - y = 3x - 32 \\ y = - 3x + 32\)

I hope this help

Answer:

a

Step-by-step explanation:

Answer:

A 7.85 cm2 should be right

The number of ways it is possible for the gold, silver, and bronze medals to be awarded is 1320 ways

Permutation are related to arrangement and combination has to do with selection.

If there are 12 teams, each representing a different country and the possible awards are gold, silver, and bronze medals, the number of ways they can be selected is given as:

12P3 = 12!/(12-3)!

12P3 = 12!/9!

12P3 = 12 * 11 * 10

12P3 = 1320 ways

Hence the number of ways it is possible for the gold, silver, and bronze medals to be awarded is 1320 ways

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Complete question is;

A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 1850 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Answer:

Car 1 consumed 30 gallons of gas.

Car 2 consumed 20 gallons of gas.

Step-by-step explanation:

Let x be number gallons consumed by car 1

Let y be number of gallons consumed by car 2

We are told that total gas consumption of 50 gallons. Thus;

x + y = 50 - - - - - eq(1)

We are told that the first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas and they went a combined total of 1850 miles. Thus;

35x + 40y = 1850 - - - - eq2

Let's make y the subject in eq(1),

y = 50 - x - - - - eq(3)

Putting 50 - x for y in eq 2 gives;

35x + 40(50-x) = 1850

35x + 2000 - 40x = 1850

-5x + 2000 = 1850

-5x = -150

x = 150/5

x = 30 gallons

Substitute 30 for x into eq 3,we have;

y = 50 - 30

y = 20 gallons

Thus;

Car 1 consumed 30 gallons of gas.

Car 2 consumed 20 gallons of gas.

The probability that exactly 4 flights will arrive on time is 0.2508.

Answer:The probability that exactly 4 flights will arrive on time is 0.2508.The probability of a single flight arriving on time is 0.8. As a result, the probability of a single flight arriving late is 0.2. As a result, in a sample of 14 Southwest flights, the number of flights that arrive on time is represented by the random variable X, which follows a binomial distribution with n = 14 and p = 0.8.P(X = 4) = (14 C 4)(0.8)4(0.2)10= 1001 × 0.4096 × 0.00098= 0.4012%≈ 0.2508 (to 4 decimal places)The probability that exactly 4 flights will arrive on time is 0.2508. The 0.4096 in the formula is the probability that there will be 4 flights that arrive on time, while the (14 C 4) is the number of ways to pick 4 flights out of 14 flights without considering their sequence. The 0.00098 is the probability that there will be 10 flights that arrive late, assuming there are 4 flights that arrive on time.

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This retirement planning scenario involves saving a fixed amount per year, earning a specified interest rate, and determining the final retirement account balance, lump-sum investment amount, annual withdrawal in retirement, and required interest rate for a specific savings goal. The details are as follows:

a. retirement account balance of approximately $536,144.37

b. The lump sum required would be approximately $60,319.79.

c. With an account balance of $536,144.37, the annual withdrawal would be approximately $46,914.90.

d.  It would take approximately 16 years until the savings are depleted.

e. Through trial and error, it can be determined that an interest rate of approximately 10.47% is needed to achieve the desired savings goal.

a. The retirement account balance on the day of retirement can be calculated by using the formula for the future value of an ordinary annuity. In this case, saving $4,500 per year for 35 years with an annual interest rate of 5.5% will result in a retirement account balance of approximately $536,144.37.

b. To achieve the same retirement savings goal with a lump-sum investment today, the present value of an ordinary annuity formula can be used. The lump sum required would be approximately $60,319.79.

c. Assuming a retirement duration of 17 years and a desire to exhaust the savings with the 17th withdrawal, the annual withdrawal can be calculated using the formula for the annuity payment. With an account balance of $536,144.37, the annual withdrawal would be approximately $46,914.90.

d. If the decision is made to withdraw $90,000 per year in retirement, the number of years until the savings are exhausted can be determined using the formula for the number of periods in an annuity. It would take approximately 16 years until the savings are depleted.

e. If the maximum affordable annual saving is $900 and the goal is to retire with $1,000,000, the required interest rate can be calculated using the formula for the rate of return. Through trial and error, it can be determined that an interest rate of approximately 10.47% is needed to achieve the desired savings goal.

These calculations provide insights into the financial aspects of retirement planning and can help individuals make informed decisions about their savings, investments, and withdrawal strategies based on their specific goals and constraints.

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Since the function, g(x), is obtained by vertically stretching f(x) = x2 + 1 by a scale factor of 3.The option that is the correct expression for g(x) is option C: g(x) = 3x² + 3

In the above case,  we shall multiply the base function by the scale factor when stretching a function vertically. As a result, we have g(x) = 3 f. (x). Don't forget to share 3 to each term in f. (x).

g(x) = 3(x² + 1)

=3x² + 3

As a result, the appropriate formulation for g(x) is 3x² + 3.

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See complete question below

The function, g(x), is obtained by vertically stretching f(x) = x2 + 1 by a scale factor of 3. Which of the following is the correct expression for g(x)?

 g(x) = 3x² + 1

g(x) = x² + 3

g(x) = 3x² + 3

g(x) = 3(x + 1)2

Answer:

≈ 50 ft²

Step-by-step explanation:

Area of circle:

Given:

Then:

Alisha can choose either shop based on personal preference or other factors like turnaround time or quality of service, as both options have the same charge for her order of 120 T-shirts.

Let's define the variables for the two print shops:

- For Smith's T-Shirt Shop:

 - Let x be the number of T-shirts ordered.

 - Let S(x) be the total charge from Smith's T-Shirt Shop.

- For Brilliant Print Shop:

 - Let y be the number of T-shirts ordered.

 - Let B(y) be the total charge from Brilliant Print Shop.

Now let's write the functions for the total charges:

For Smith's T-Shirt Shop:

- For 0 ≤ x ≤ 100: S(x) = 12x

- For 101 ≤ x ≤ 200: S(x) = 10x

- For x ≥ 201: S(x) = 8x

For Brilliant Print Shop:

- For 1 ≤ y ≤ 100: B(y) = 200 + 14y

- For 101 ≤ y ≤ 200: B(y) = 10y

- For y ≥ 201: B(y) = 8y

To compare the two options, let's evaluate the charges for Alisha's order of 120 T-shirts:

For Smith's T-Shirt Shop:

- For 101 ≤ x ≤ 200: S(120) = 10 * 120 = $1,200

For Brilliant Print Shop:

- For 101 ≤ y ≤ 200: B(120) = 10 * 120 = $1,200

Both shops charge the same amount for 120 T-shirts, which is $1,200. Therefore, Alisha can choose either shop.

Now let's compare the key features of the graphs of the functions for both shops:

Smith's T-Shirt Shop:

- Initial Value: The total charge starts at $0 when no T-shirts are ordered.

- End Behavior: As the number of T-shirts ordered increases, the total charge decreases. The rate of decrease changes at 100 and 200 T-shirts.

Brilliant Print Shop:

- Initial Value: The total charge has a flat fee of $200 when ordering 1-100 T-shirts.

- End Behavior: As the number of T-shirts ordered increases, the total charge decreases. The rate of decrease changes at 100 and 200 T-shirts.

Both shops have different pricing structures, but they both decrease the total charge as the number of T-shirts ordered increases. Smith's T-Shirt Shop has a tiered pricing structure, while Brilliant Print Shop has different rates for different ranges. The key difference is that Brilliant Print Shop has a flat fee for the first range of T-shirts (1-100).

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17.85

so what i did is i took 20 divided by 3 = 7

than i did

2.55 x 7 = 17.85

answer:

____________________________________________________________17.85

Please mark brainlist if this helps!

The total cost of 20 toy cars is 17 dollars.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, at the toy store, 3 toy cars cost $2.55.

Here, cost of 1 toy car = 2.55/3

= 0.85

Cost of 20 cars = 20×0.85

= $17

Therefore, the cost of 20 toy cars is 17 dollars.

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Answer:

x=36

Step-by-step explanation:

The angles in a triangle must add to 180 degrees.

Therefore,

x+65+79=180

Add 65 and 79

x+144=180

We want to solve for x. In order to do this, we have to get x by itself. 144 is being added to x (+144)The opposite of addition is subtraction, so subtract 144 from both sides(-144)The +144 and -144 will cancel out, and leave x by itself.

x+144-144=180-144

x=180-144

x=36

Let’s check our answer. Add all the angles together, and make sure they equal 180 degrees.

x+65+79

We know x is equal to 36, so we can substitute it in

36+65+79

180

The 3 angles add to 180, so we know that x=36

Answer:

-4.65< -4 and 2/5

Step-by-step explanation:

To solve, this we can convert the fraction -4 and 2/5 into a decimal so that the values can be more easily compared. When we do this, we get the result that -4 and 2/5 equals -4.4. Now we can clearly see which value is greater because they are written in the same form:

-4.65<-4.4

-4.65<-4 2/5

Answer:

<

Step-by-step explanation:

You have to convert the mixed number by multiplying the whole number by the denominator, adding the numerator, and dividing the sum by the denominator.

4x5=20

20+2=22

22÷5=4.4

-4.65 < -4.40

When identifying the parts of a packaged data model that apply to your organization, you should first start with understanding your Organization's specific needs and requirements.

This involves the following steps:

1. Assess your organization's business processes and goals, which helps in identifying key areas where data modeling can enhance decision-making and performance.

2. Analyze existing data sources and systems to understand the current data landscape, including its structure, relationships, and data quality.

3. Identify the critical data elements that align with your organization's needs, such as customer information, sales data, or financial data. These elements form the foundation of your data model.

4. Determine the relevant industry-standard data models or frameworks that can serve as a starting point for your organization's data model. This may include industry-specific models or general models applicable to a variety of businesses.

5. Evaluate the suitability of the selected packaged data model for your organization by comparing its features, flexibility, and scalability with your specific requirements.

6. Customize the chosen data model to fit your organization's unique processes, data structures, and business rules, ensuring that it accurately represents your data environment.

7. Implement and maintain the data model, regularly updating it to reflect changes in your organization's processes, data sources, or business objectives.

By following these steps, you will effectively identify and apply the parts of a packaged data model that best suit your organization's needs, enabling improved decision-making and performance.

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Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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The IQR of 13 is the most accurate measure of variability to represent the data, as it provides a more accurate representation of the typical donations received by the charity.

The range is the difference between the highest and lowest values in a dataset.

In this case, the range is,

⇒ 49 - 10 = 39.

However, the range is sensitive to outliers, which can skew the data and make it less representative of the typical donations received.

The IQR is a measure of variability that is less sensitive to outliers than the range.

It is the difference between the third quartile (Q3) and the first quartile (Q1) of the dataset.

In this case, Q1 = 42

and Q3 = 49,

so the IQR is ,

IQR = 49 - 42

IQR = 7.

The IQR represents the middle 50% of the data and is a good measure of the spread of the typical donations received by the charity.

Therefore, the IQR of 13 is the most accurate measure of variability to represent the data, as it provides a more accurate representation of the typical donations received by the charity.

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Complete question is,

A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data. 10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59

Which measure of variability should the charity use to accurately represent the data? Explain your answer.

A: The range of 13 is most accyrate to use since the data is skewed

B: The IQR of 49 is most accurate to use to show that they need more money.

C:The range of 49 is the most accurate to use to show that they have plenty of money

D: The IQR of 13 is the most accurate to use since the data is skewed​

Answer:

1 25/ 26

2 3/4

3 35/24

6 9/2

8 2/5

Step-by-step explanation:

Answer:

Red

Step-by-step explanation:

Answer:

$46.88 and $28.13

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

To solve a part-part ratio problem, we need to follow these steps:

If two people share some money in the ratio 3:5 and one person gets $75, you can find out two possible values with the amount of money the other person gets by doing this:

The total number of parts in the ratio is:

The value of one part is:

The amount of money the other person gets is either:

Or:

Therefore the two possible values are $46.88 and $28.13.

The equation to represent the cost (C) of frozen yogurt in terms of the number of ounces (x) is: C = 0.30x + 1.00

Ounces are a unit of measurement for weight or mass commonly used in the United States and some other countries. There are different types of ounces, but the most common ones are:

When measuring weight or mass in ounces, it is important to specify the type of ounce being used to avoid confusion. For example, if a recipe calls for 4 ounces of sugar, it is not clear whether it refers to avoirdupois ounces or fluid ounces, which could result in the wrong amount of sugar being used.

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The expected number of claims made by people under 25 years of age is 5.74.

For this problem, we can use the binomial distribution which states that the probability of success (p) is equal to the proportion of people under 25 making claims (82%) and the probability of failure (q) is equal to the proportion of people over 25 making claims (1 - 82% = 18%).

The expected number of claims made by people under 25 is equal to the total sample size (7) times the proportion of people under 25 making claims (0.82) so the expected number of claims made by people under 25 is 7×0.82 = 5.74.

Hence, the expected number of claims made by people under 25 years of age is 5.74.

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Answer:

-118

Step-by-step explanation:

y = 3 = -118(x + 6)  Distributive property

y + 3 = -118x - 708  Subtract 3 from both sides

y = -118x - 711

The number before the x is the slope: -118            

Answer:

13

Step-by-step explanation:

We can write the following inequality to find the answer:

7x + 3 < 100 (where x is our answer and x is an integer)

7x < 97

x < 13.86

The largest integer value of x that satisfies this inequality is x = 13 so we know that our answer will be 13.

The probability that a random point on AK will be on BF is 3/7.

We have,

On the number line, there are 21 points.

And,

There are 9 points between B and F.

Now,

The probability that a random point on AK will be on BF.

= Number of points between B and F / Total number of points

= 9 / 21

= 3 / 7

Thus,

The probability that a random point on AK will be on BF is 3/7.

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Answer:

3x=15 the x is 5

10+5=15

10 quarters

5 dimes

Step-by-step explanation:

Answer:

Yes . Divide by 10 for 10/20 to get 1/2.

10/10= 1

20/10= 2

10/20= 1/2

The area of the hub cap is \(493.765sq.cm\) when the circumference of the hub cap of a tire is \(78.81cm\).

What is the circumference?

The boundary of a specific area or geometric figure, esp of a circle. the length of a closed geometric curve, esp of a circle. The circumference of a circle is equal to the diameter multiplied by \(\pi\).

Here given that,

The circumference of the hub cap of a tire is \(78.81\) centimeters.

As we know, the area of circle is :-

Area of circle \(=\pi r^2\)

Circumference of circle = \(2\pi r\)

So,

Circumference \(=2\pi r\)

\(78.81=2(3.14)r\\\\78.81=6.28r\\\\r=\frac{78.81}{6.28}\\\\r=12.54\)

Therefore, the Area aof circle = \(\pi r^2\)

\(=(3.14)(12.54)^2\\\\=(3.14)(157.25)\\\\=493.765\)sq.cm.

Hence, the area of the hub cap is \(493.765sq.cm.\)

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Answer:

108.75 square meter.

Step-by-step explanation:

   \(\sf \boxed{\text{\bf Surface area of pentagonal pyramid = $ \bf \dfrac{5}{2}*b*(a + s)$}}\)

  Here,  b is the base length of the pyramid. b = 3 m

              a is the apothem of the pyramid. a = 3.5 m

              s is the slant height of the pyramid. s = 11 m

     \(\sf Surface \ area = \dfrac{5}{2}*3*(11 + 3.5)\)

                         \(\sf = \dfrac{5}{2}*3*14.5\\\\ = 108.75 \ m^2\)