Now that you’ve seen how radicals can be simplified using the properties of exponents, create a general product rule and a general quotient rule for nth degree radicals

The actual length of a cafeteria is 64 ft. Therefore, the option A is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, Austin used a scale that equaled 4 feet for every 1 inch depicted.

The scale drawing he made identified the cafeteria as being 16 inches in length.

Now, 4×16

= 64 feet

Therefore, the option A is the correct answer.

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y=f(x)

f(-6)

Answer : y=-6

The value of v in the variation is 21.1

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

Joint variation from p to s and v^2

So, we have

p = ksv^2

Substitute the known values in the above equation, so, we have the following representation

18 = k * 9 * 15^2

So, we have

k = 2/225

When s = 81 and p = 32, we have

32 = 2/225 * 81 * v^2

This gives

v^2 = 72000/162

So, we have

v = 21.1

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A dictionary with keys 'normalize' and 'alpha' and values [True, False] and [1, 10, 100] respectively can be used to perform a grid search.

Grid search is a technique used to find the optimal hyperparameters for a machine learning model. In the case of determining if normalization should be used and testing different values of alpha, we need to provide the algorithm with a range of values for each hyperparameter. This can be done using a dictionary.

The keys in the dictionary would be 'normalize' and 'alpha', representing the hyperparameters we want to search for. The values for 'normalize' would be [True, False], representing the options for normalizing the data or not. The values for 'alpha' would be [1, 10, 100], representing the different values of alpha to test.

This dictionary can then be passed as an argument to the grid search algorithm, which will then perform a search through all possible combinations of these hyperparameters, evaluating the performance of the model for each combination and determining the optimal set of hyperparameters.

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The positive externality of carpooling with friends is reduced traffic on the road. Hence, option C is the correct option.

Carpooling is a very useful method of reducing traffic as well as pollution and is quite simple as well. It involves the usage of only one common vehicle that can be used by people who commute to the same destination. It's helpful since it means a lot of people will use only one vehicle and hence, there will be less traffic and pollution.

In the given problem as well, since these friends are gonna carpool to work, they will use the same vehicle and so, lead to less traffic. So, option C is the correct option.

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The initial amount is 1250, rate is 13.5% and value of the function for t = 3 is 809

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Given that, an exponential function with rate of decay, h(t) = [tex]1250(0.865)^t[/tex]

Here we need to identify the initial amount, rate and the value of function when t = 3

The general formula of exponential decay is given by,

A = P(1-r)ⁿ

Where A is final amount

P is initial amount

r = rate of decay

n = years or time

Comparing with general formula,

P = 1250

1-r = 0.865

r = 1-0.865

r = 0.135

r % = 13.5

h(3) = 1250(0.865)³

= 809

Hence, the initial amount is 1250, rate is 13.5% and value of the function for t = 3 is 809

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350° and 350° - 360° are coterminal angles with magnitudes less than 2π.

What is coterminal?

In mathematics, two angles are called coterminal if they have the same magnitude (measure) but different orientations. This means that they represent the same angle but start from different points on the unit circle.

An angle is coterminal with another angle if it has the same magnitude but a different orientation. To find a positive angle less than 2π that is coterminal with a given angle, you can add or subtract multiples of 2π until you get an angle in the desired range.

For example, if the given angle is 350 degrees, you can subtract 2π from it to get a positive angle less than 2π:

350° - 360° = -10° + 360° = 350°

So, 350° and 350° - 360° are coterminal angles with magnitudes less than 2π.

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Random selection events.The two number of events involve selecting cards randomly from a deck and can thus be said to be random selection events.

The two events involve randomly selecting cards from a deck of cards. The first event is selecting a king, while the second event is replacing the king and selecting a queen. These two number of steps can be classified as random selection events, as the cards are chosen without any specific pattern or criteria. Random selection events involve selecting something at random, without any pre-defined criteria.

This can include flipping a coin, rolling a dice, or, in this case, selecting a card from a deck. Since the two events involve randomly selecting cards from a deck of cards, they can be classified as random selection events.

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The general solution of the differential equation is given by: [tex]y(x) = c1*sin(2x) + c2*cos(2x) + c3*x + c4*cos(x) + c5*sin(x) + c6*x^2[/tex]

1. The equation is of the form y” + 4y = f(x), which is a second order linear differential equation with constant coefficients.

2. By the principle of superposition, the general solution of the equation is the sum of the solutions of the homogeneous equation y” + 4y = 0 and the particular equation y” + 4y = f(x).

3. The homogeneous equation has two linearly independent solutions, [tex]y1 = sin(2x) and y2 = cos(2x)[/tex]

4. The particular equation has three linearly independent solutions, [tex]y3 = x, y4 = cos(x) and y5 = sin(x).[/tex]

5. Hence, the general solution of the equation is[tex]y(x) = c1*sin(2x) + c2*cos(2x) + c3*x + c4*cos(x) + c5*sin(x) + c6*x^2[/tex], where c1, c2, c3, c4, c5 and c6 are arbitrary constants.

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If b= the number of baseballs , then b-3 ,this algebraic expression represents the phrase, The number of baseballs minus 3 .

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

If b= the number of baseballs

now,

The number of baseballs minus 3

i.e. the number = b-3.

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The equation of the parabola is give as;

f (x) = x² − 2x − 8

Let y =  x² − 2x − 8

Complete the square on right sides of the equation.

y = (x - 1)² + 9

Comparing with the standard equation of the parabola.

y = a(x - h)² + k

Thus, vertex of the parabola are found as:

(h, k) = (1, - 9)

Since 'a' has a positive value, the parabola opens upwards.

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There are 2598960 different collections (hands) of 5 cards from a standard deck of 52 cards.

What is Combinations ?

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.

The number of different collections (hands) of 5 cards from a standard deck of 52 cards is calculated using combinations. In combinatorics, the number of ways to choose k items from a set of n items is given by the formula:

C(n, k) = n! / (k! (n-k)!)

where n! represents the factorial of n, which is the product of all positive integers less than or equal to n.

In this case, n = 52 and k = 5, so the number of different hands is:

C(52, 5) = 52! / (5! (52-5)!)

= 52! / (5! 47!)

= 2598960

Therefore, there are 2598960 different collections (hands) of 5 cards from a standard deck of 52 cards.

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The more appropriate measures of center and spread or the data set would be:

The median and interquartile range (IQR) should be used when analyzing data that has a non-normal distribution. They are particularly useful when working with data sets that contain outliers or skewness.

The median provides an indication of the central tendency of the data, representing the value that separates the data into two equal parts, with half the data being below and half the data being above that value. The IQR, on the other hand, provides information about the spread of the data and can be used to identify outliers.

The data here has the extreme figure of 24 which is an outlier and so not compatible with the mean. The median is therefore better. The interquartile range would be better for spread due to the outlier as well.

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The expression for the new cost of the shirt is 0.8p. Option B

Price discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product

To get the expression for the new cost of the shirt,

1 - 0.2 = 0.8

We then multiply the new percentage with the price to get the new price. And this can be expressed as: 0.8p

Hence, 0.8p is the new expression for the price discount

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After considering all his earnings and savings, we found that Chris started with $120 in his savings.

Let's assume that Chris saved x dollars. According to the equation, he spent half of his savings, so he spent 0.5 * x dollars on video games. After earning an additional $20 cutting grass, his total savings became 0.5 * x + 20 = 60. To solve for x, we can subtract 20 from both sides of the equation, which gives us 0.5 * x = 40.

Then, we can divide both sides of the equation by 0.5 to obtain x = 80. This means that Chris started with $80 in savings, which he then doubled by spending half of his savings and adding $20 earned from cutting grass, resulting in $120 in total savings.

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The pair of slopes of -3/4 and 4/3 represent perpendicular lines

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Two lines are said to be perpendicular if the product of their slope is -1.

Given two lines with slope of -3/4 and 4/3:

Product of their slope = (-3/4) * (4/3) = -1

The lines with slope of -3/4 and 4/3 is perpendicular

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So Condition 1 has reduced the possibilities for existing Enet = 0 positions to Region (I) (to the left of both charges) and Region (III) to the right of both charges.

The X-axis is sometimes known as the horizontal axis, and the Y-axis is the vertical axis.

There are a few main approaches to this issue. I'll explain it in terms of electric fields. This is due to the defining equation's ability to link the electrostatic force's expression, FE, to a region's net electric field, E:

FE = qE

where q is a charge that has been added to the electric field; in this case, it is a charge of 1 C. The only way FE can equal zero at some place when q is not zero (and q=0 would be a simple case, anyway) is if the net electric field E is zero at that location.

This is true regardless of the size and nature of the charge you were putting there.

Therefore, given this scenario, where can the net electric field E = 0? At every point in space surrounding the charge, each charge generates its own electric field, which either points in the direction of the charge (for negative charges) or away from the charge (for positive charges). The following equation determines the size of the electric field, |E|, produced by a point charge at a distance r from the charge:

|E| = kq/r2

At every point in space surrounding the two charges stated in the issue, an electric field is produced by one of them. The vector sum of the field from each charge present at a given point is the net electric field at that location. There are two requirements for the two fields to cancel each other out:

1. Each charge's electric fields must be directed in opposite directions.

2. Each charge's electric fields must be of equal strength.

We can examine the two situations independently. Since the first one (regarding directions) may frequently weed out a lot of potential responses through scrutiny, I frequently start there.

For instance, if you were to create a diagram with the two charges as indicated on the x-axis and then choose any location off of the x-axis, it would be clear that this position does not satisfy Condition 1. This is so that the (+)10 C charge's electric field will point away from the 10 C charge from that location. And from there, the -5 C charge's electric field will point in its direction. These two electric field vectors won't even coincide for any position off the x-axis. Since they cannot point in the same direction, even if their magnitudes are equal, they cannot cancel out. Thus, the third response from above is disproved.

Therefore, let's examine the x-axis. The electric fields for points on this line point in the same direction, so they could potentially point in different directions. But how is that even possible? We can divide a line with two charges into three regions: (I) to the left of both charges, (II) in the space in between the charges, and (III) to the right of both charges.

Therefore, So Condition 1 has narrowed the range of potential locations where Enet = 0 is present to Region (I) (to the left of both charges) and Region (III) (to the right of both charges).

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Answer:

x = 63° , y = 83°

Step-by-step explanation:

In a trapezium

each lower base angle is supplementary to the upper base angle on the same side , then

x + 117° = 180° ( subtract 117° from both sides )

x = 63°

the sum of the 3 angles in the outer triangle = 180° , that is

x + y + 34° = 180° ( substitute x = 63° )

63° + y + 34° = 180°

97° + y = 180° ( subtract 97° from both sides )

y = 83°

The probability distribution's mean and standard deviation, Y, will be 0.4899 and 0.699, respectively, based on the information provided.

A probability distribution is a statistical function that enumerates all the potential probabilities and values for a random variable within a certain range.

A key idea in statistics is the probability distribution. They are applied both theoretically and practically. Probability distributions can be used to compute critical regions for hypothesis tests and confidence intervals for parameter values, among other useful applications.

Each possible result of a random experiment or occurrence is shown by the probability distribution in statistics. It offers the odds of many potential events.

It should be noted that the likelihood that y will occur will follow the probability distribution given:

Let the given data be

Y                   0        1.         2

Probability  0.63.   0.25.   0.12

Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)

simplifying the above equation, we get

Mean = 0 + 0.25 + 0.25

Mean = 0.49

Let the variance be 0.4899.

standard deviation = ✓0.4899

Standard Deviation = 0.699

The complete question is:

Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution. If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F. (a) Construct the probability distribution of the random variable Y

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The type of correlation is determined by the relationship between variables in terms of the proportion of change between them that is multiple proportion.

A proportion is the relationship between two quantities, often expressed as a ratio or fraction.

"Simple correlation" refers to the relationship between two variables, where a change in one variable is associated with a change in the other variable in a consistent manner.

"Multiple correlation" refers to the relationship between three or more variables. In this type of correlation, the proportion of change in one variable is associated with the proportion of change in other variables.

"Zero correlation" refers to the absence of any relationship between two variables. In this type of correlation, there is no consistent proportion of change in one variable that is associated with a change in the other variable.

Therefore correct option is (b).

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The mass of  1 box of the weight of 20 boxes of apples is 84 kg.

Given that,

The weight of a single bag of apples = 350 grams.

No. of bags hold by one box = 12

The total weight of a single box is 12 x 350 grams = 4200 grams.

Now we multiply the weight of a single box (4200 g) by 20, which gives us 4200 g x 20 = 84,000 grams.

Since the final answer is asked in kilograms, we divide the weight in grams by 1000, which gives us 84,000 g ÷ 1000 = 84 kilograms.

Therefore, the total weight of 20 boxes of apples would be 84 kilograms.

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39.52 cm² of the surface area of the box​ increase.

Given data :

H = 31 cm

the surface area of the box​ increase ;

= 2( 31 x 8.7 + 31 x 16 + 16 x 8.7) + 2 ( 31.8 x 8.7 + 31.8 x 16 + 16 x 8.7 )

= 2 ( 8.7 + 16 ) x ( 31.8 - 31 )

= 2 x 24.7 x 0.8

= 39.52 cm²

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According to the given information, the mystery polygon is most likely a right trapezoid.

Li's mystery polygon has 4 sides and no pairs of parallel sides, which means it is a quadrilateral. Based on the angles given, 90 degrees, 63 degrees, 120 degrees, and 87 degrees, the mystery polygon is a trapezoid. A trapezoid is a quadrilateral with exactly one pair of parallel sides and no two angles that add up to 180 degrees.

A trapezoid with two right angles (90 degrees) is called a right trapezoid. Since Li's mystery polygon has one angle that measures 90 degrees, it is likely a right trapezoid. The other angles, 63 degrees, 120 degrees, and 87 degrees, do not match the angles of any other specific type of quadrilateral. Therefore, based on the information given, the mystery polygon is most likely a right trapezoid.

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The volume of the cylindrical shell will be 20 cubic unit using integration.

Integration is the process of calculating an integral. Integrals are used by mathematicians to compute a range of useful quantities, such as areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. Indefinite integrals are used for antiderivatives. Integration is one of the two primary calculus topics in mathematics, along with differentiation (which measure the rate of change of any function with respect to its variables).

An integral that has both the upper and lower boundaries is said to be definite. Only a real line may be used for X to lay. A Riemann Integral is another name for the Definite Integral.

n example of an Integral is:

f(x)dx, from a to b.

Indefinite integral

∫f(x)dx = F(x) + C

Where C is any constant and the function f(x) is called the integrand.

Now,

As we can see in image

Volume = ∫x³.dx from 1 to 3  Using integration formula

=x⁴/4

=81/4-1/4

=80/4

volume =20 cubic unit

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Answer:

y = $24,500 * (1 + 0.03x)

Step-by-step explanation:

Please find the attachment for detail

Answer:

26771.8115

Step-by-step explanation:

24500(1.03)=25235 then continue doing this 2 more times and you get 26771.8115

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/π), π/2 radians= π/2 × (180°/π) = 90° or 90 degrees. Therefore sinπ/2 = sin (90°) = 1. The Value of sinπ/2 is given as 1.

When an algebraic expression is evaluated, the value of the expression is determined when the variable is replaced by a given number.

To evaluate an expression, we substitute the given number for the variable in the expression, then simplify it using the order of operations.

Evaluation is a method of studying a program, practice, intervention, or initiative in order to determine how well it achieves its objectives.

Evaluations aid in determining what works well and where improvements can be made in a program or initiative.

Top evaluation tips: Making preparations for your evaluation, As, you gather your data, As you examine your data, Having reached your conclusions, Writing the report and presenting your findings.

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Answer:

a. $2,125

b. $2,000

Step-by-step explanation:

a. profit = 25%

[tex]\frac{x - 1700}{1700}[/tex] = 25%

Multiply 1700 to both sides

x - 1700 = 425

add 1700 to both sides

x = 2125

b. [tex]\frac{2500 - x}{x}[/tex] = 25%

multiply x to both sides

2500 - x = 0.25x

add x to both sides

2500 = 1.25x

1.25x = 2500

x = 2000

Answer:

55x+20

Step-by-step explanation:

Answer:

Simplification 5(11x+4)

Step-by-step explanation:

42x-23+13x+43

42x +20 + 13x

Combine like terms

42x+20+13x

55x+20

Common factor

55x+20

5(11x+4)

Yes, there is a proportional relationship between the number of bushels of wheat collected and the number of acres ploughed over the two days.

This can be seen by calculating the average number of bushels of wheat collected per acre for each day, and seeing if they are equal.

For the first day,

The average is 135 bushels / 5 acres = 27 bushels per acre.

For the second day,

The average is 216 bushels / 8 acres = 27 bushels per acre.

Since the two averages are equal, it can be concluded that there is a proportional relationship between the number of bushels of wheat collected and the number of acres ploughed.

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