What is the new surface area and volume of a 2cm length of a cube if it is enlarged with 5 scale factor

Answer:

4x² - 12x + 9

4a² - 10a + 25

Step-by-step explanation:

If you want to have some fun with math, you should try to find perfect square trinomials. These are polynomials that look like this:

a² + 2ab + b² = (a + b)²

or

a² - 2ab + b² = (a - b)²

They are called perfect square trinomials because they are the squares of binomials. For example, x² + 2x + 1 is a perfect square trinomial because it is the same as (x + 1)².

How do you spot a perfect square trinomial? Here are some tips:

- The first and last terms must be perfect squares. For example, 4x² and 9 are perfect squares because they are 2x times 2x and 3 times 3.

- The middle term must be double the product of the square roots of the first and last terms. For example, 6x is double of 2x times 3, which are the square roots of 4x² and 9.

Let's practice with some examples:

4x²- 12x + 9

This is a perfect square trinomial because:

- The first and last terms are perfect squares: 4x² = (2x)² and 9 = (3)²

- The middle term is double the product of the square roots of the first and last terms: -12x = 2 * -2x * 3

We can write this polynomial as (2x - 3)².

16x² + 24x - 9

This is not a perfect square trinomial because:

- The first and last terms are perfect squares: 16x² = (4x)² and 9 = (3)²

- The middle term is not double the product of the square roots of the first and last terms: 24x ≠ 2 * -4x * -3

We cannot write this polynomial as a square of a binomial.

4a² - 10a + 25

This is a perfect square trinomial because:

- The first and last terms are perfect squares: 4a² = (2a)² and 25 = (5)²

- The middle term is double the product of the square roots of the first and last terms: -10a = 2 * -2a * -5

We can write this polynomial as (2a - 5)².

36b² - 24b - 16

This is not a perfect square trinomial because:

- The first and last terms are perfect squares: 36b² = (6b)² and 16 = (4)²

- The middle term is not double the product of the square roots of the first and last terms: -24b ≠ 2 * -6b * -4

We cannot write this polynomial as a square of a binomial.

Now you know how to find perfect square trinomials. They are fun, right?

The polynomials that are perfect square trinomials are:

a. 4x² - 12x + 9 = (2x - 3)^2 c. 4a² - 10a + 25 = (2a - 5)²

Taking the quotient between the total amount and the amount needed for each serving, we can see that she can make 12 servings.

To see how many individual servings can Keisha make, we need to take the quotient between the total amount of nuts that she has and the amount that she needs for each serving.

The total amount she has is:

T = (4 + 1/2) cups.

Each serving needs:

S = (3/8) cups.

Taking the quotient we will get:

N = (4 + 1/2)/(3/8)

N = (4.5)/(3/8) = 12

She can make 12 individual servings.

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Answer:

3/8

Step-by-step explanation:

To solve this problem, we need to perform division. We can convert the mixed fraction 4 1/2 into an improper fraction: 4 1/2 = (4 x 2 + 1)/2 = 9/2. Then we can divide 9/2 by 3/8:

(9/2) ÷ (3/8) = (9/2) x (8/3) = 12

Therefore, Keisha can make 12 individual servings of nuts by dividing 4 1/2 cups of nuts into 3/8 cup servings.

The mean with the outlier is 20.2.

The median with the outlier is 18.

The mean without the outlier is 17.6.

The median without the outlier is also 18.

To find the middle, we must first sort the dossier from shortest to capital:

3, 7, 9, 12, 14, 18, 20, 21, 24, 31, 35, 68

When a set of 12 numbers is orderly, the middle is the middle profit. If skilled are an even number of variables, the middle is the average of two together middle principles.

(accompanying deviation) Median = 18

To decide the mean outside the deviation, first away it and therefore recalculate the mean utilizing the staying principles:

20 + 3 + 9 + 21 + 24 + 14 + 18 + 7 + 35 + 12 + 31 = 194

There are now 11 principles, that wealth:

The mean (no outliers) is 194/11 = 17.6.

To reckon the middle outside the oddity, we must organize the staying principles in the following order:

3, 7, 9, 12, 14, 18, 20, 21, 24, 31, 35

When a set of 11 numbers is orderly, the middle is the middle worth. If skilled are an even number of variables, the middle is the average of two together middle principles.

Median (no outliers) = 18

As a result, the mean accompanying the aberration is 20.2 and the middle is 18. The mean, forbidding the oddity, is 17.6, and the middle, forbidding the deviation, is still 18.

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The probability that a randomly selected student is not a master's student or a senior is 0.75 or 75%.

The probability that a randomly selected student is either a master's student or a senior is 25%. Therefore, the probability that a randomly selected student is not a master's student or a senior is 75%.

To calculate the probability that a randomly selected student is not a master's student or a senior, we can subtract the probability that a randomly selected student is either a master's student or a senior from 1.

P(not a master's student or senior) = 1 - P(a master's student or senior)

P(not a master's student or senior) = 1 - 0.25

P(not a master's student or senior) = 0.75

Therefore, the probability that a randomly selected student is not a master's student or a senior is 0.75 or 75%.

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The slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis is 3/4.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = 27/36

Slope (m) = 3/4.

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a. The value for m based on the information in the expression is 15.

b. The value for s based on the information is 21.

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The value for m based on the information is:

= 38 - 23

= 15.

b. The value for s based on the information is:

= 59 - 38

= 21.

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The members of each set are A = {2, 3, 5, 7, 11, 13, 17} and B = {}

A n B = {}

A u B = {2, 3, 5, 7, 11, 13, 17}

The members of each set

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

U = (1,2,3,4,.... 18)

A = {Prime numbers)

B = (Odd numbers greater than 31)

This means that the universal set is from 1 to 18

So, we have

A = {2, 3, 5, 7, 11, 13, 17}

B = {}

The sets of the following

A n B: This is the elements common in both sets

So, we have A n B = {}

A u B: This is the list of all elements without repetition

So, we have A u B = {2, 3, 5, 7, 11, 13, 17}

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complete question:

U

=(1,2,3,4,.... 18); A= {Prime numbers) and B= (Odd numbers greater than 31. a) If A and B are subsets of the universal set, &, list the members of A and B Find the set b) c) i) AnB ii) AUB i) Illustrate U, A and B on a Venn diagram. ii) Shade the region for prime factors of 18 on the Venn diagram.

​

The surface area and volume of the polyhedron are mathematically given as:

SA=160 Sqr Units

V=105 cubic units

This is further explained below.

We have,

Generally, The surface area of a three-dimensional object is equal to the total of areas of all of its faces, also known as surfaces. A cuboid has six faces that are rectangular in shape.

Add together the areas of each of the cube's six sides to get the surface area of the cube. To get the surface area of the prism, we may additionally label its length (l), width (w), and height (h), and then use the formula surface area = length (l) times width (w) times height (h).

To refresh your memory, the surface area of an item is the entire area of the exterior surfaces of the three-dimensional object or the total sum of the area of the faces of the object.

In other words, the surface area of an object is its "face area." It is expressed in terms of square units as a measurement.

In conclusion, Generally, the Surface area is mathematically given as

SA= 9+35+35+33+36+12

SA=160 Sqr Units

Generally, the equation for Volume is mathematically given as

V=(11*9)+6

V=99+6

V=105 cubic units

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The two consecutive integers from the equation are 5 and 6.

We have,

Two consecutive integers:

x and  (x + 1)

To solve for the integers, you need to use the equation you found and solve for x:

x (x + 1) = 3 (x + x + 1) - 3

Simplifying:

x^2 + x = 6x + 3 - 3

x^2 - 5x = 0

Now you can factor out x:

x(x - 5) = 0

So,

x = 0 or x = 5.

Two consecutive integers,

x can't be 0. So the first integer is 5, and the next consecutive integer is 6.

Therefore,

The two consecutive integers are 5 and 6.

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Note that the value of integers m and n are   m =  5 and n  = 3.   Understand that there are other   ways one can solve this.

We begin by trying different values of m and n that satisfy the given equation.

If we let m = 5 and n = 2, then:

m² - n² = 5² - 2² = 25 - 4 = 21

So m = 5 and n = 2 is one possible solution to the equation m² - n² = 21.

Recal that an equation is simply a math expression that is uxed to codify real world situations or sometimes, ficticious ones.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

I need to find the value of m and n

m² - n² = 21

The coordinates of vertex R are (1, y3), where y3 is the y-coordinate of vertex R.

If x=1 is the line of symmetry of triangle PQR, then the x-coordinate of vertex R must be equal to 2 times the x-coordinate of the midpoint of side PQ. This is because the midpoint of a line segment is equidistant from the endpoints, and the line of symmetry passes through the midpoint.

Let's denote the coordinates of vertex P as (x1, y1), the coordinates of vertex Q as (x2, y2), and the coordinates of vertex R as (x3, y3). We can use the midpoint formula to find the coordinates of the midpoint of side PQ:

Midpoint of PQ = ((x1 + x2)/2, (y1 + y2)/2)

Since x=1 is the line of symmetry, we know that x3 = 2(x1 + x2)/2 - x3, which simplifies to x3 = x1 + x2 - x3. Solving for x3, we get:

2x3 = x1 + x2

x3 = (x1 + x2)/2

This tells us that the x-coordinate of vertex R is equal to the x-coordinate of the midpoint of side PQ. Since the line of symmetry is vertical and passes through x=1, we know that the x-coordinate of vertex R is 1.

Therefore, the coordinates of vertex R are (1, y3), where y3 is the y-coordinate of vertex R. To determine y3, we need more information about the triangle or its vertices. Without this additional information, we cannot determine the coordinates of vertex R.

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If x=1 is the line of symmetry of triangle PQR, what are the coordinates of vertex R?

Answer:

The maker of a cell phone screen protector would like to estimate the proportion of customers who file a warranty claim. To do so, they select a random sample of 200 customers and determine that the 96% confidence interval for the true proportion of customers who file a warranty claim to be 0.15 to 0.28.

Step-by-step explanation:

Kevin must work at least 9 hours babysitting to meet his requirements.

Let's call the number of hours Kevin works babysitting "x". We know that he works 3 hours walking dogs, so the total number of hours he works in a week is x + 3.

We also know that he must earn at least $90, so we can set up the following inequality:

8x + 6(3) ≥ 90

Simplifying this inequality, we get:

8x + 18 ≥ 90

Subtracting 18 from both sides, we get:

8x ≥ 72

Dividing both sides by 8, we get:

x ≥ 9

Therefore, Kevin must work at least 9 hours babysitting to meet his requirements.

To check that this is a valid solution, we can calculate his total earnings for the week:

Total earnings = 8x + 6(3) = 8x + 18

If he works 9 hours babysitting and 3 hours walking dogs, his total earnings will be:

Total earnings = 8(9) + 6(3) = 72 + 18 = $90

In summary, the minimum number of whole hours Kevin must work babysitting to meet his requirements is 9. This is found by solving an inequality based on his earnings and the number of hours he can work in a week, and then checking that the solution meets his requirements.

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Based on the residual plot, is the linear model appropriate is option (D). Yes, half of the residuals are positive and half are negative.

The residual plot is one that can be a scatterplot of the residuals (the contrasts between the observed  values as well as the predicted values) against the indicator variable. The reason of this plot is to check the presumption that the errors are randomly conveyed and have steady fluctuation over the run of the indicator variable.

In the event that the linear show is fitting for the information, the residuals ought to be randomly scattered around the flat line at zero. The reality that half of the residuals are positive and half are negative indicates that there's no systematic bias within the predictions.

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The test statistic is -2.50, which represents a significant deviation from the null hypothesis. The critical value at the 5% level of significance is -1.645.

The value of the statistical hypothesis testing (-2.50) is less than the critical value at the 5% level of significance (-1.645). Therefore, we reject the null hypothesis (H;u = 10) and conclude that the population mean appears to be less than 10 at the 5% significance level

In statistical hypothesis testing, the null hypothesis (H0) represents the default assumption about the population parameter under investigation, while the alternative hypothesis (Ha) represents a deviation from the null hypothesis that we want to investigate. In this case, the null hypothesis is H0: μ = 10, and the alternative hypothesis is Ha: μ < 10, where μ is the population mean.

The test statistic is a value calculated from the sample data that measures how much the sample data deviates from the null hypothesis. The critical value is a value from the standard normal distribution that defines the rejection region for the null hypothesis based on the chosen significance level.

In this problem, the test statistic is -2.50, which represents a significant deviation from the null hypothesis. The critical value at the 5% level of significance is -1.645, which defines the rejection region for the null hypothesis. Since the test statistic falls within the rejection region, we reject the null hypothesis and conclude that the population mean appears to be less than 10 at the 5% significance level.

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The correct answer is (e) Model View Controller.

MVC is a design pattern commonly used in software engineering, particularly in web development frameworks such as Java Spring and Struts. In the context of Java, MVC stands for Model View Controller, which is a design pattern that separates an application into three interconnected components:

- The Model represents the data and the business logic of the application.
- The View represents the user interface, and is responsible for rendering the data to the user.
- The Controller acts as an intermediary between the Model and the View, and handles user input and updates to the Model.

The Model and View components are decoupled and can be developed independently, while the Controller component handles the communication between them. This separation of concerns makes it easier to maintain and modify the application, and also allows for code reuse.

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The  standard deviation of X is 3.46.

the mean of X is 30.

Given that 60% of American adults prefer saving over spending, the probability of selecting an adult who prefers saving is p = 0.6.

The number of American adults out of a random sample of 50 who prefer saving to spending, X, follows a binomial distribution with parameters n = 50 and p = 0.6.

The mean of a binomial distribution is given by μ = np, so in this case, μ = 50 x 0.6 = 30. Therefore, the mean of X is 30.

The standard deviation of a binomial distribution is given by σ = √(np(1-p)), so in this case, σ = √(50 x 0.6 x 0.4) = 3.46 (rounded to two decimal places). Therefore, the standard deviation of X is 3.46.

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The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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

This means that

Initial, a = 250 bacterial cultures.

Rate = 3

So, the recursive formulas is

f(n) = 3f(n - 1), where f(1) = 250

For the explicit formula, we have

f(n) = 250(3)ⁿ‐¹

Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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A large-scale bakery needs an oven that can accommodate around 933 units of bread to produce 4000 units per hour with a 14-minute baking time.

We need to find the oven capacity to produce 4000 units of bread per hour while taking into account the 14-minute baking time.

Convert the baking time to hours
14 minutes = 14/60 = 7/30 hours
Calculate the number of baking cycles per hour
1 hour / (7/30 hours per cycle) = 30/7 cycles per hour
Calculate the number of bread units needed per baking cycle
4000 units per hour / (30/7 cycles per hour) = 4000 * (7/30) = 2800/3 ≈ 933.33 units per cycle
Round to the nearest integer
The required oven capacity is approximately 933 units of bread that can be baked simultaneously.

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When using Ridge Regression, it is important to choose the right value of \lambda» that balances between the model's complexity and its ability to generalize well to new data.

This process is known as hyperparameter tuning. One common approach is to use cross-validation to evaluate the model's performance for different values of \lambda» and select the one that gives the best balance between bias and variance. It is important to note that the optimal value of \lambdaλ may vary depending on the specific dataset and the nature of the problem being solved. Therefore, it is important to experiment with different values of \lambdaλ and choose the one that provides the best results.
To select the appropriate value of λ (lambda) to use for Ridge Regression, you should follow these steps:

1. Define a range of λ values to test. It's common to use a logarithmic scale, such as 10^(-4), 10^(-3), 10^(-2), ..., 10^4.
2. Perform k-fold cross-validation for each λ value in the range. K-fold cross-validation involves splitting the dataset into k equally sized subsets (folds), training the model on k-1 folds, and validating the performance on the remaining fold. Repeat this process k times, with each fold serving as the validation set once.
3. Calculate the average cross-validation error for each λ value. This error is often measured using mean squared error (MSE) or root mean squared error (RMSE).
4. Choose the λ value that yields the lowest average cross-validation error. This λ value will provide a balance between fitting the data and controlling the complexity of the model to prevent overfitting.
By following these steps, you can select an appropriate λ value for Ridge Regression that balances model complexity and predictive performance.

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If $500 is invested at an interest rate of 8.25% that is compounded monthly for 13 years. The amount invested is $1455.99.

Using this formula to find the amount of the investment

A = P(1 + r/n)^(nt)

Where:

A = Amount

P = Principal = $500

r = Interest rate = 8.25%

n = Number of times

t = Number of years = 13

Let plug  in the formula

A = 500(1 + 0.0825/12)^(12*13)

A = $1,455.99

Therefore the amount is $1,455.99.

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One way to approach the problem of communality in factor analysis is to increase the number of factors included in the analysis. This can help to account for more of the variance in the observed variables and reduce the overall communality. Another approach is to identify and remove any variables that have high levels of communality, as these may not be contributing unique information to the factor analysis and may be better analyzed separately.

To address the problem of communality in factor analysis, two common approaches are:

1. Extraction Method: One approach is to choose an appropriate extraction method, such as Principal Components Analysis (PCA) or Maximum Likelihood Estimation (MLE). These methods aim to estimate communalities more accurately by considering the shared variance between variables.

2. Rotation Technique: Another approach is to apply rotation techniques like Varimax or Oblimin. These methods simplify the factor structure and improve interpretability, which can help identify meaningful communalities among variables more effectively.

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Answer: Let's denote the number of toy cars that Thomas had at first as T, and the number of toy cars that they were given each as x.

After they were given an equal number of toy cars, Zack had twice the number of toys cars as he had at first, which means that Zack had 2x toy cars.

Also, we know that 2/3 of Zack's toy cars were now 1/2 of Thomas's toy cars, so we can write:

2/3 * 2x = 1/2 * (T + x)

Multiplying both sides by 3/2:

2x = 3/4T + 3/4x

Simplifying:

5/4x = 3/4T

Since Zack has 36 more toy cars than Thomas now, we can write:

2x - x = T + x - 36

Simplifying:

x = T/3 + 12

We can now substitute x in the second equation:

5/4(T/3 + 12) = 3/4T

Multiplying both sides by 12:

5T/4 + 60 = 9T/4

Subtracting 5T/4 from both sides:

T/2 = 60

T = 120

So Thomas had 120 toy cars at first, and they were given a total of:

2 * x + T + 2x - (T + x) = 3x + 2T = 3(T/3 + 12) + 2T = 5T + 108 = 708

Toy cars altogether.

The probability of picking a free-game ticket from the first container is 6/10, or 0.6. The probability of picking a 20-free-tokens ticket from the second container is 5/8, or 0.625.

To find the probability of both events occurring, you multiply the probabilities together:

0.6 x 0.625 = 0.375

So the probability of picking a free-game ticket and a 20-free-tokens ticket is 0.375, or 37.5%.

The table is completed as follows:

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

For the function y = 2x², the numeric values are given as follows:

For the function y = 2^x, the numeric values are given as follows:

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After 8 years, the amount in the account will be approximately $7,228.62.

To calculate the future value of an investment, we can use the formula for compound interest:

Future Value = Principal * (1 + Interest Rate)^Time

In this case, the principal (initial investment) is $4,700, the interest rate is 5.3% (or 0.053 as a decimal), and the time is 8 years. Plugging these values into the formula:

Future Value = 4700 * (1 + 0.053)^8

Calculating the future value:

Future Value = 4700 * (1.053)^8 ≈ $7,228.62

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Answer:

Step-by-step explanation:

1/2 ton is 1000 pounds

1/4 pound is 4 ounces

2 1/2 pounds is 40 ounces

[tex]\sqrt[4]{567x^9 y^{11}} ~~ \begin{cases} 567=3\cdot 3\cdot 3\cdot 3\cdot 7\\ \qquad ~~ ~ 3^4\cdot 7\\ x^9=x^{4+4+1}\\ \qquad ~x^4\cdot x^4\cdot x\\ y^{11}=y^{4+4+3}\\ \qquad ~~ y^4\cdot y^4\cdot y^3 \end{cases}\implies \sqrt[4]{3^4\cdot 7 \cdot x^4\cdot x^4\cdot x\cdot y^4\cdot y^4\cdot y^3}[/tex]

[tex]\left( 3^4\cdot 7 \cdot x^4\cdot x^4\cdot x\cdot y^4\cdot y^4\cdot y^3\right)^{\frac{1}{4}}\implies 3^{\frac{4}{4}}\cdot 7^{\frac{1}{4}}\cdot x^{\frac{4}{4}}\cdot x^{\frac{4}{4}}\cdot x^{\frac{1}{4}}\cdot y^{\frac{4}{4}}\cdot y^{\frac{4}{4}}\cdot y^{\frac{3}{4}}[/tex]

[tex]3\cdot 7^{\frac{1}{4}}\cdot x\cdot x\cdot x^{\frac{1}{4}}\cdot y\cdot y\cdot y^{\frac{3}{4}}\implies 3x^2y^2\cdot 7^{\frac{1}{4}}x^{\frac{1}{4}} y^{\frac{3}{4}} \implies 3x^2y^2(7xy^3)^{\frac{1}{4}} \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x^2y^2\sqrt[4]{7xy^3} \end{array}}~\hfill[/tex]