Point F is on line segment EG. Given EG = 20 and EF = 18, determine the
length FG.

Answer:

cos (-85°)

Step-by-step explanation:

\( \cos(275 \degree) \)

since cosine is in fourth quadrant:

\( \cos(275 \degree) = \cos( \{360 \degree - 275 \degree \}) \\ = \cos( - 85 \degree) \)

-85° is the angle between –180° and 0° that has the same cosine value as 275°.

Cosine is the trigonometric function that is equal to the ratio of the side adjacent to the acute angle in a right angled triangle.

Mathematically,

            Cos = Base/Hypotenuse

Now, to calculate cos(275) we have to first determine the quadrant of the given angle.

Since our angle is greater than 270 and less than or equal to 360, it is located in the Quadrant IV.

In the Quadrant IV, the values of cos are always positive.

275 is an obtuse angle so we can write,

Cos(275) = Cos{360+(-85)}

∵ Cos(360+θ) = Cosθ

∴ Cos{360+(-85)} = Cos(-85)

⇒ Cos(275) = Cos(-85)

The required answer is cos(275) = cos(-85)

Hence, -85° is the angle between –180° and 0° that has the same cosine value as 275°.

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Answer:

See Explanation

Step-by-step explanation:

The question is not clear. However, I will treat the question as:

\((26)x = 1\)

\((50)x = 1\)

and:

\((2^6)^x = 1\)

\((5^0)^x = 1\)

Solving: \((26)x = 1\)  and  \((50)x = 1\)

\((26)x = 1\)

Divide both sides by 26

\(x = \frac{1}{26}\)

\((50)x = 1\)

Divide both sides by 50

\(x = \frac{1}{50}\)

Solving \((2^6)^x = 1\) and \((5^0)^x = 1\)

\((2^6)^x = 1\)

Express 1 as 2^0

\((2^6)^x = 2^0\)

Remove bracket

\(2^{6x} = 2^0\)

Cancel out 2

\(6x = 0\)

Divide both sides by 6

\(x = \frac{0}{6}\)

\(x = 0\)

\((5^0)^x = 1\)

Express 1 as 5^0

\((5^0)^x = 5^0\)

Cancel out 5^0

\(x = 1\)

Answer:

C

Step-by-step explanation:

This scenario is best described as an example of an experimental study or a randomized controlled trial. In this study, the researchers are investigating the benefits of a new driver training scheme and specifically examining whether the outcome differs between two groups: learners under 25 years old and learners over 25 years old.

The study follows an experimental design by randomly assigning participants to different groups: half of the participants are under 25 years old, and the other half are over 25 years old. Within each group, further randomization takes place where half of the participants are selected to participate in the new training program.

By comparing the results between the group that received the training program and the group that did not, the researchers can assess the effectiveness and potential differences in outcomes based on age. This experimental approach allows for controlled comparisons and helps draw conclusions about the impact of the training program on different age groups of learner drivers.

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complete question

This scenario is best described as an example of a randomized controlled trial (RCT) or an experimental study. In this study, the researchers aim to determine the benefits of a new driver training scheme and whether it has different outcomes for over-25 years old learner drivers compared to under-25 years old learner drivers. The study involves a group of 80 learner drivers, with half being under 25 years old and half being over 25 years old. Within each age group, half of the participants are randomly selected to participate in the new training program, while the other half serve as the control group. The results of the study are recorded and compared between the groups. By randomly assigning participants and having a control group, the researchers can assess the effectiveness of the training program and analyze any differences in outcomes based on age.

Answer:

y = 6

Step-by-step explanation:

Given a parallelogram ABCD with diagonals AC and BD.

Kindly refer to the diagram attached for the given parallelogram.

\(AE=2x\\BE=y+10\\CE=x+2\\DE=4y-8\)

To find:

The value of y = ?

Solution:

First of all, let us consider a property of parallelogram and its diagonals.

The intersecting point of diagonals of a parallelogram bisect the diagonals in two equal parts.

Let us consider the given parallelogram ABCD which has its diagonals BD and AC intersecting at point E.

As per the property stated above:

AE = CE and

DE = BE

Putting the values of AE, CE, DE and BE as given in the question statement and solving for \(x\) and \(y\):

\(2x = x+2\\\Rightarrow \bold{x = 2}\)

and

\(y+10=4y-8\\\Rightarrow 4y-y = 10+8\\\Rightarrow 3y=18\\\Rightarrow y =\dfrac{18}{3}\\\Rightarrow \bold{y= 6}\)

So, the answer is:

y = 6

To find the general solution of the given higher-order differential equation y''' − 6y'' − 7y' = 0, we first need to find the characteristic equation by assuming that y = e^(rt), where r is a constant. Substituting this into the differential equation, we get r^3 - 6r^2 - 7r = 0.

Factoring this, we get r(r - 7)(r + 1) = 0. So the roots of the characteristic equation are r1 = 0, r2 = 7, and r3 = -1.

Therefore, the general solution of the differential equation is y(t) = c1 + c2e^(7t) + c3e^(-t), where c1, c2, and c3 are constants that can be determined using initial or boundary conditions.

In summary, the general solution of the given higher-order differential equation y''' − 6y'' − 7y' = 0 is y(t) = c1 + c2e^(7t) + c3e^(-t), where c1, c2, and c3 are constants.

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(b) (iii) Factory 0 is better than all other factories (i.e., it is less likely to produce defective fidget spinners).

(c) (iii)Factory 0 is better than all other factories (i.e., it is less likely to produce defective fidget spinners).


(b) Nat chose the value of a to be 0.3 because she knows that factory 0 produces fewer defective fidget spinners than factory 1. This means that factory 0 is better, or less likely to produce defective fidget spinners, which is why the value of a is closer to 0 than 1.

(c) Nat chose the values of a and B to be 1 and 5 for factory 0, and 5 and 1 for factory 1, because she knows that factory 0 is better, or less likely to produce defective fidget spinners, than factory 1.

The values of a and B are used to determine the probability of a fidget spinner being defective from each factory, with a lower value of a and a higher value of B indicating a lower probability of a defective fidget spinner.

Therefore, the values of a and B for factory 0 indicate a lower probability of a defective fidget spinner than the values of a and B for factory 1.

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Answer:

Step-by-step explanation:

Use the simple interest formula

Where interest = Principal * Rate * Time

A = $1,840.00

I = A - P = $240.00

Equation:
A = P(1 + rt)


Calculation:
First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year.

Solving our equation:
A = 1600(1 + (0.05 × 3)) = 1840
A = $1,840.00

The total amount accrued, principal plus interest, from simple interest on a principal of $1,600.00 at a rate of 5% per year for 3 years is $1,840.00.

The required equivalent pairs are C and D which we gοt by sοlving the expressiοn fοrmed.

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne math prοcedure, and a sentence. It's pοssible tο multiply, divide, add, οr subtract with this mathematical prοcedure. An expressiοn's fοrm is as fοllοws: Expressiοn: (Math Operatοr, Number/Variable, Math Operatοr)

Accοrding tο questiοn:

We have given fοllοwing expressiοn, check which οf the fοllοwing are equivalent.

A) \(12^{(1/7)\)and \((\sqrt{12)^{7\)

Here  \(12^{(1/7)\) and  \((\sqrt{12)}^{7\) are nοt equal.

B) \((\sqrt[3]{125} )^7\)and (125)^(3/7)

Here 125^(7/2) and \(125^{(3/7)\) are nοt equal

c) \(8^{(9/2)\) and \((\sqrt8)^9\)

Here \(8^{(9/2)\) and \((\sqrt8)^9\)bοth are equal.

D) \(4^{(5/2)\) and  \((\sqrt4)^5\)

Here \(4^{(5/2)\) and  \((\sqrt4)^5\) are equal.

Thus, required equivalent pairs are C and D.

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Answer:

It took Mr. Holloway 28 weeks to make 7 guitars.

Step-by-step explanation:

The question is incomplete, but if we are trying to find out how many weeks it would take him to make 7 guitars then the answer would be 28.

First you have to find out how many weeks it takes him to make 1 guitar.

8 ÷ 2 = 4 (4 weeks to make 1 guitar)

Then you have to multiply 4 by 7 since it takes 4 weeks to make 1 guitar.

4 * 7 = 28 (28 weeks to make 7 guitars)

Answer:

28 weeks

Step-by-step explanation:

Answer: Ask three before me please!

Step-by-step explanation:

a. When evaluating a model, we use R2 as a parameter for performance assessment.

b. If model A has a higher MAPE but model B has a higher R2, we choose the model with the higher R2 for better overall performance.

c. For accuracy measures, we typically use MAPE (Mean Absolute Percentage Error) due to its interpretability and ability to capture relative errors.

When evaluating a model's performance, it is crucial to choose the appropriate parameters to assess its accuracy and reliability. In the case of MAPE (Mean Absolute Percentage Error) and R2 (Coefficient of Determination), the choice between them depends on the specific evaluation goals.

The R2 parameter is commonly used for evaluating models because it measures the proportion of the dependent variable's variance that can be explained by the independent variables. R2 provides insights into how well the model fits the data and captures the relationship between the input features and the target variable. Therefore, R2 is a suitable parameter to use when evaluating a model.

When comparing two models, if model A has a higher MAPE but model B has a higher R2, it is advisable to choose the model with the higher R2 value. This is because R2 indicates the proportion of variance explained, suggesting that model B performs better in capturing the underlying patterns and predicting the target variable.

Although model A may have a lower relative error (MAPE), it is crucial to prioritize the model's ability to explain and predict the target variable accurately.

Among MAPE, MAD (Mean Absolute Deviation), and MSD (Mean Squared Deviation), MAPE is commonly preferred as a parameter for accuracy measures. MAPE calculates the average percentage difference between the predicted and actual values, making it interpretable and easily understandable.

It captures relative errors and enables comparisons across different scales and datasets. MAD and MSD, on the other hand, measure absolute and squared errors, respectively, but they do not account for the relative magnitude of the errors. Hence, MAPE is a more suitable parameter for accuracy measures.

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For given triangle, the length of BX is 10 cm.

What is triangle?

A triangle is a geometric shape that consists of three sides and three angles. It is one of the most fundamental and commonly studied shapes in geometry.

To find the length of BX, we can use the formula for the area of a triangle:

Area = (base * height) / 2.

We are given the areas of triangles ADX and BCX, as well as the lengths of AX and DX.

Area of triangle ADX = \(36 cm^2\)
Area of triangle BCX = \(65.61 cm^2\)
AX = 8.6 cm
DX = 7.2 cm

Let's start by finding the height of triangle ADX. We can use the formula:

\(36 cm^2\) = (BX * 7.2 cm) / 2

Simplifying the equation:

\(36 cm^2\) = (BX * 3.6 cm)

Dividing both sides by 3.6 cm:

BX = \(36 cm^2\) / 3.6 cm
BX = 10 cm

Therefore, the length of BX is 10 cm.

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The vector that describes each translation is given as follows:

a) Shape C to Shape D: (10, -5).

b) Shape D to Shape C: (-10, 5).

The four translation rules are defined as follows:

From shape C to shape D in item a, the translation is given as follows:

Hence the vector is given as follows:

(10, -5).

For shape D to shape C in item b, we just change the signal of the components of the vector, hence:

(-10, 5).

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Shyla spent $30.94 on the fabric to cover the box, considering the dimensions and the cost per square inch.

To calculate the cost of the fabric, we need to find the surface area of the box. A rectangular prism has six rectangular faces, and each face's area can be found by multiplying its length by its width. The dimensions given in the figure are length = 11 inches, height = 7 inches, and width = 8 inches. The surface area of the box is calculated as follows:

Surface Area = 2 * (length * width + height * width + height * length)

= 2 * (11 * 8 + 7 * 8 + 7 * 11)

= 2 * (88 + 56 + 77)

= 2 * 221

= 442 square inches

The cost of the fabric is then found by multiplying the surface area by the cost per square inch, which is 7¢:

Cost of Fabric = Surface Area * Cost per Square Inch

= 442 * 0.07

= $30.94

Therefore, Shyla spent $30.94 on the fabric to cover the box.

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The interquartile range for the data set are

Andre

Interquartile Range: = 2

For Lin

Interquartile Range = 8

For Noah

Interquartile Range = 8

For Andre

Min: 25 the minimum number

Q1: 27 (the third position)

Median: 28 (the sixth position)

Q3: 29 (the 9th position)

Max: 30 (the maximum number)

Interquartile Range: Q3 - Q1 = 29 - 27 = 2

For Lin

Min: 20 the minimum number

Q1: 21 (the third position)

Median: 28 (the sixth position)

Q3: 29 (the 9th position)

Max: 32 (the maximum number)

Interquartile Range: Q3 - Q1 = 29 - 21 = 8

For Noah

Min: 13 the minimum number

Q1: 15 (the third position)

Median: 20 (the sixth position)

Q3: 23 (the 9th position)

Max: 25 (the maximum number)

Interquartile Range: Q3 - Q1 = 23 - 15 = 8

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Answer:

the value of x in this problem is 9

According to the graph, it is found that the percent of apartment residents who pay less than $700 per month is given by:

B. 75%

It states that:

Hence, for less than $700, we have that:

5% + 25% + 45% = 75%.

Thus option B is correct.

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Answer:

19

Step-by-step explanation:

Call made in the 3rd month = total calls made - calls made in the first month - call made in the 2nd month

56 - 24 - 13 = 19 calls

The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

For new customers, there is an additional one-time $150 service fee.

Now, Let the number of months of service = x

And, the total amount paid in dollars by an customer = y

Hence, The correct linear equation is,

⇒ y = 150x

Thus, The value of linear equation which representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an customer is,

⇒ y = 150x

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Answer: b2 should be 5 i believe

Step-by-step explanation:

Answer:

B∨2 = 5

Step-by-step explanation:

Hope this helps!

Answer:

\(x + y = 301\\y = 6x\)

Step-by-step explanation:

\(x + y = 301\\6x = y\\x + (6x) = 3017x = 301\\x = 43\\43 + (43(6)) = 301\\y = 258\)

Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.

To solve for the mileages at which company A will charge less than company B, we can set up the following inequality:
A < B
where A is the cost of renting from company A and B is the cost of renting from company B. We can plug in the given information to get:
x ≤ A
x > B = y + 40z
where x is the number of miles driven, y is the initial fee for company B, and z is the additional cost per mile for company B.
Now we can substitute the given values to get:
x ≤ A
x > y + 40z
For company A, the cost is a flat rate with unlimited mileage, so A is just the cost listed for one day of rental. Let's say that cost is $100.
For company B, the initial fee is $50 and the additional cost per mile is $0.25. So:
y = 50
z = 0.25
Now we can plug in these values and solve for x:
x ≤ 100
x > 50 + 40(0.25)
x > 65
Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.

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If a simple random sample of 31 observations was taken from a large population. The sample mean equals 5 then the five is a point estimate

Total number of population = 31 observations

Sample mean of the population = 5

Sample mean is the average value of the sample that is selected from a large population of data.

The point estimate is defined as the single value estimate of the parameter. Point estimate is usually use when we have to choose single value from a larger population, that should be the best estimate to represents the parameter.

Here the sample mean of population is 5

Therefore, five is a point estimate

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Step-by-step explanation:

f(x)=8(5x-2)

interchanging the role of x&y

x=8(5y-2)

f-1(x)=(x+16)/10

The value of \(f^{-1}(x)\) for the given function f(x) = 8(5x - 2) will be  \(f^{-1}(x)\) =(x + 16)/40.

A function's inverse can be thought of as a reverse of the function.

For instance, if y = f(x), then x = f will be the inverse (y).

It implies that we must swap x and y in the inverse function.

As per the given,

f(x)=8(5x-2)

Interchange the variable y and x as,

⇒ x = 8(5y - 2)

⇒ x+16=401y

⇒ y = (x+16)/40

Put y =  \(f^{-1}(x)\)

\(f^{-1}(x)\) =(x + 16)/40

Hence "The value of \(f^{-1}(x)\) for the given function f(x) = 8(5x - 2) will be  \(f^{-1}(x)\) =(x + 16)/40".

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Answer:

the first set

Step-by-step explanation:

y = 8x − 2

to see which of the following represent the right input and out put substitute the amount of x in the equation and see it you get the same output .

x        y=8x-2              y

0       8(0)-2               -2

1         8(1)-2               6

2        8(2)-2              14

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8