Use Figure 1 to evaluate the trigonometric function.

A right triangle with side a of length 13 opposite of angle A, and side b of length 6 opposite of angle B.

Answer:

[tex]\frac{x}{x+3}[/tex]

Step-by-step explanation:

[tex]\frac{x(x-3)}{(x+3)(x-3)}[/tex]

[tex]\frac{x}{x+3}[/tex]

The simplified expression of the fraction in its simplest form is -12a¹¹r⁻³

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

\frac{3a^9r^{-3}}{-4(a^2)^{-1}}

Rewrite the above expression properly

So, we have the following representation

3a⁹r⁻³/(-4a²)⁻¹

Evaluate the expression in bracket

So, we have the following representation

3a⁹r⁻³/(-4a²)⁻¹ = 3a⁹r⁻³ * (-4a²)

Remove the brackets

This gives

3a⁹r⁻³/(-4a²)⁻¹ = 3a⁹r⁻³ * -4a²

Evaluate the products

So, we have the following representation

3a⁹r⁻³/(-4a²)⁻¹ = -12a¹¹r⁻³

Hence, the the fraction expression in its simplest form is -12a¹¹r⁻³

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Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).

DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).

Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).

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Answer:

x- intercept = - 8 , y- intercept = 6

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

3x - 4(0) = - 24

3x = - 24 ( divide both sides by 3 )

x = - 8 ← x- intercept

to find the y- intercept let x = 0 in the equation and solve for y

3(0) - 4y = - 24

- 4y = - 24 ( divide both sides by - 4 )

y = 6 ← y- intercept

Answer:

Dan has 42 quarters and 25 dimes.

Step-by-step explanation:

63 degrees is the angle.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angle triangle.

The opposite side length is 85 and the adjacent side is 38.

Opposite side=85

Adjacent side=38.

Calculate Opposite/Adjacent

= 85/38= 2.236

Which is tanθ=2.236

Now tan inverse on both the sides

θ=tan⁻¹2.236

θ=tan⁻¹2

θ=63 degrees.

Hence, the angle is 63 degrees.

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Answer:

To find the difference between the elevations of City A and City B, we need to subtract the elevation of City A from the elevation of City B. Since City A is located 15 meters below sea level, and City B is located 43 meters above sea level, the difference between their elevations is $43 - (-15) = 43 + 15 = 58 meters. Therefore, the difference between the elevations of City A and City B is 58 meters.

The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).

Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.

Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.

The image of the translation is (9,-2).

The point is given as: P = (-6, -4)

The image of the point is: P' = (-2, 3)

The translation rule is calculated as:

T = x - 2 - (-6), y+3-(-4)

so,  T = x + 4, y + 7

So, the image of (5, -1) is:

the Image of the translation = 5 + 4, -1 + 7

Hence, the image of the translation is (9, 6).

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(a) There are 36 ways to select 8 apartments randomly by cluster sampling method.

(b) Throughout this process, we obtain floors 3, 4, 6, or 3, 6, which do not have sample flats with children, and as a result, the sample will not accurately reflect the population.

(a) Given the building has 9 floors which are taken as N=9 clusters.

Each floor has 4 apartments.

It is to select 8 apartments by cluster sampling method.

That is to select a sample of size any n=2 floors(clusters) by cluster sampling method out of the population of N=9 clusters.

By simple random sampling without replacement, there are NCn = 9C2 =36 ways to select 2 clusters.

Hence, there are 36 ways to select 8 apartments randomly by cluster sampling method.

(b) The main benefit of stratified sampling over cluster sampling is that the sample obtained using this method will unquestionably include representations of both features, i.e., apartments with and without children as a full representative of the population.

In contrast, there is no guarantee that the sample of flats with and without children from the cluster sampling approach will accurately reflect both qualities. Sometimes throughout this process, we obtain floors 3, 4, 6, or 3, 6, which do not have sample flats with children, and as a result, the sample will not accurately reflect the population.

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The right question is given beow:

Answer:

f - 36

-3f - 23

are your prime polynomials.

Answer:

Step-by-step explanation:

log base (2) of (x^2 +5) = (3) can also be described as 2^3 = x^2 + 5

simplify: 8 = x^2+5

Subtract 5 from each side: 3 = x^2

square root: x = sqrt(3)

Answer:

Step-by-step explanation:

[tex]log(2)^{(x^2+5)}=3\\[/tex]

[tex]2^3 =x^2+5\\8-5=x^2\\x^2=3\\x=\pm\sqrt{3}[/tex]

15% discount; 6% sales tax in-store. Online retailer: $5 discount; $8.99 for delivery.

$5 off offer that can only be used online and a physical shop. Only the actual store is subject to the 5% sales tax. The online retailer charges a fixed $6.99 shipping fee.

Let's say the entire amount spent was $100.

In a physical store, 100 times 15% equals 15 off.

100 - 15 = 85 is the item's reduced cost.

85 x 6% is 5.1 sales tax.

85 + 5.1 = 90.10 as a whole price

Internet shop:

Discounted cost of item: 100 - 5 = 95

95 plus 8.99 is 103.99 in total.

15% discount; 6% sales tax in-store.

Online retailer: $5 discount; $8.99 for delivery.

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Answer:

Step-by-step explanation:

When any value of x, other than 0, is multiplied by itself the result will ALWAYS be a POSITIVE value. Therefore, equations in the form x square =p, where p is GREATER THAN 0, will have 2 SOLUTIONS.

The probability that the first success occurs on trial number n = 3 is 0.032

Given:

probability of success on a single trial p = 0.80

trial number, n = 3

Recall the formula for the Geometric Probability Distribution

P(n) = p(1 - p)ⁿ⁻¹

where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial

P(n) = p(1 - p)ⁿ⁻¹

P(3) = 0.8(1-0.8)³⁻¹

P(3) = 0.8(0.2)²

P(3) = 0.032

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The statement of the problem has already made a lot of decisions for us. We are told to use three global variables of type int[]. The variables must be static, and I have chosen to make them private, so the declarations become:

private static int[] firstNumbers;  // The first numbers in all ten questions.

private static int[] secondNumbers; // The second numbers in all ten questions.

private static int[] user answers;   // The user's answers to the ten questions.

Note that these declarations are not in any subroutine. These statements only create variables, not arrays. We still need to create three arrays of length 10. The arrays can be created using the new operator. This initialization could in fact be combined with the declaration of the variables:

private static int[] firstNumbers = new int[10];

private static int[] secondNumbers = new int[10];

private static int[] userAnswers = new int[10];

Another possibility would be to create the three arrays at the beginning of the main() routine. In fact, I chose to create them in the subroutines where they are first used.

The program has three stages -- create the problems, administer the quiz, and grade the quiz -- and we are told to write a subroutine to do each stage. The main program simply has to call the subroutines:

public static void main(String[] args) {

   createQuiz();

   administerQuiz();

   gradeQuiz();

}

This is an example of using subroutines to break up a large task into several simpler subtasks, so that programming each subtask becomes a separate problem. The subroutines are short and not too hard to write. Looking at administerQuiz() as an example, note that the user's answers have to be stored in the array, the user answers so that they can be used when grading the quiz. I create the array itself before asking any questions and then store the user's responses in the array as they are read by the user. On the other hand, the arrays that hold the numbers that occur in the questions have already been created and filled before administerQuiz() is called. Here's the subroutine:

private static void administerQuiz() {

   userAnswers = new int[10];

   for (int i = 0; i < 10; i++) {

       int questionNum = i + 1;

       System.out.printf("Question %2d:  What is %2d + %2d  ? ",

                     questionNum, firstNumbers[i], secondNumbers[i]);

       userAnswers[i] = TextIO.getlnInt();

   }

}

A couple notes about the output: I wanted to number the questions 1, 2, ..., 10, but the elements of the arrays are numbered 0, 1, ..., 9. This means that the question number that I output has to be one more than the array index. Also, all the numbers that occur in my program are either one or two digits. By allowing exactly two digits for each number in the output, I can get everything to line up neatly. Here's the I/O for a sample run of the program:

Welcome to the addition quiz!

Question  1:  What is 40 + 14  ? 54

Question  2:  What is 18 + 38  ? 46

Question  3:  What is 21 + 31  ? 52

Question  4:  What is 18 + 36  ? 54

Question  5:  What is 43 + 12  ? 55

Question  6:  What is 21 + 17  ? 38

Question  7:  What is 33 + 25  ? 58

Question  8:  What is 39 + 21  ? 70

Question  9:  What is  1 + 25  ? 26

Question 10:  What is 39 + 26  ? 65

Here are the correct answers:

  Question  1:  40 + 14  =  54.  You were CORRECT.

  Question  2:  18 + 38  =  56.  You said 46, which is INCORRECT.

  Question  3:  21 + 31  =  52.  You were CORRECT.

  Question  4:  18 + 36  =  54.  You were CORRECT.

  Question  5:  43 + 12  =  55.  You were CORRECT.

  Question  6:  21 + 17  =  38.  You were CORRECT.

  Question  7:  33 + 25  =  58.  You were CORRECT.

  Question  8:  39 + 21  =  60.  You said 70, which is INCORRECT.

  Question  9:   1 + 25  =  26.  You were CORRECT.

  Question 10:  39 + 26  =  65.  You were CORRECT.

You got 8 questions correct.

Your grade on the quiz is 80.

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The two linear equations have the same slope, -2/3, and different y-intercepts, thus, the lines are parallel.

A general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two linear equations are parallel if both lines have the same slope and different y-intercepts.

And two lines are perpendicular if the product between the slopes is equal to -1.

In this case, we have the two linear equations:

y= -(2/3)*x - 3

y= -(2/3)*x + 6

So you can see that both linear equations have the same slope -2/3 and different y-intercepts, thus, the lines are parallel.

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The complete answer: A domain is a set of input data in a relationship.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

An input value and an output value are matched in a relation.

A relation is a function where each input value yields one and only one output value.

Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,

while the range is the set of output values.

The domain of a function or relation is the set of all possible independent values that it can have.

Therefore,  a domain is a set of input data in a relationship.

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All the real numbers except 1 make the two expressions equal. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expressions are given below.

[(x - 1)(x - 6)] / [4(x - 1)] and (x - 6) / 4

Simplify the expression [(x - 1)(x - 6)] / [4(x - 1)], then we have

⇒ [(x - 1)(x - 6)] / [4(x - 1)]

⇒ (x - 6) / 4

But at x = 1, the expression [(x - 1)(x - 6)] / [4(x - 1)] is not defined.

All the real numbers except 1 make the two expressions equal. Then the correct option is A.

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Step-by-step explanation:

[tex]1. \: \: 3x +4 y = 8.50[/tex]

[tex]2. \: \: 5x + 8y = 14.50[/tex]

times equation 1 by 2

[tex]3. \: \: 6x + 8y = 17[/tex]

3-2 eliminates y variable

[tex]x =2.50[/tex]

[tex]y = 0.25[/tex]

The total interest paid on the loan repayable over three months weekly at 2.85% per week is $3,584.96.

The total interest can be computed using an online finance calculator.

The result is then added to the late payment fees.  The default payment fee is the product of $600 and 5.

N (# of periods) = 14 weeks (3 x 4 + 2)

I/Y (Interest per year) = 2.85%

PV (Present Value) = $50,000

PMT (Periodic Payment) = $4,000

Results:

Sum of all periodic payments = $56,000.00

Total Interest = $584.96

Late payment charge = $3,000 ($600 x 5)

Total interest and late charge = $3,584.96

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Assume that the borrower repays $4,000 weekly.

Conditional problems are problems that involve one or more conditions that must be met in order for a certain action to be taken or a certain result to be obtained. The temperature of the solution in degrees Fahrenheit after x hours, is y = 1.5x - 100.

The required details for Conditional problems in given paragraph

This function models the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. The initial temperature of the solution is 100 °F, and the temperature decreases by 1.5 °F for each hour that passes. Therefore, the temperature of the solution after x hours can be found by subtracting 1.5x degrees from the initial temperature of 100 degrees.

For example, if we plug in x = 2 into the function, we get y = 1.5 * 2 - 100 = 3 - 100 = -97, which means that the temperature of the solution after 2 hours is -97 °F.

The other options listed are not correct because they do not correctly model the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. Option A is incorrect because it adds 1.5x degrees to the initial temperature, rather than subtracting it. Option B is incorrect because it adds 100 degrees to the temperature, rather than subtracting it. Option C is incorrect because it multiplies the initial temperature by 1.5x, rather than subtracting 1.5x degrees from it. Option D is incorrect because it adds 1.5 to the temperature, rather than subtracting 1.5x degrees from it.

what are conditional problems?

Conditional problems are often expressed using words like "if," "then," or "when." For example, a conditional problem might involve finding the value of a variable x if it satisfies a certain condition, such as "If x is greater than 5, then x is even." In this case, the problem specifies that x must be greater than 5 in order for it to be even.

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From the given the vector function , T(t) = (2V2, ez, -2e-2t) N(t) = (2e-2t, -2V2, ez)(b) Use this formula to find , curvature. k(t) = (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)

(a) To find the unit tangent and unit normal vectors, we use the following formula:

T(t) = (1/|r'(t)|) * r'(t)

N(t) = (1/|r'(t)|) * (r'(t) x r"(t))

where r'(t) is the first derivative of the vector function and r"(t) is the second derivative of the vector function.

For the given vector function, r'(t) = (9, -4sin(t), 4cos(t)).

Therefore, |r'(t)| = sqrt(81 + 16sin2(t) + 16cos2(t))

To find r"(t), we take the derivative of r'(t), which is (0, -4cos(t), -4sin(t)).

Thus, T(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (9, -4sin(t), 4cos(t))

and N(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (0, -4cos(t), -4sin(t)).

(b) To find the curvature, we use the following formula:

k(t) = |r'(t) x r"(t)| / |r'(t)|3

For the given vector function, r'(t) = (2V2, ez, -2e-2t) and r"(t) = (0, -2V2, -ez).

Therefore, k(t) = |(2V2, ez, -2e-2t) x (0, -2V2, -ez)| / |(2V2, ez, -2e-2t)|3

= (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)

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It is true that when difference on dependent variable is attributed to effect of that variable through statistical hypothesis testing then it is unlikely that the difference would occur by chance alone

A formal assertion about the nature of a phenomenon made within the constraints of a statistical model is known as a statistical hypothesis.

Statistical hypothesis is a description of the makeup of a population. A population parameter is frequently used to express it.

There are two statistical hypotheses used in hypothesis testing. The above-described null hypothesis (H0) is the first.

If it turns out that the null hypothesis is statistically invalid, an alternative hypothesis (Ha) for each H0 will be given preference. Depending on the research hypothesis, the Ha may be directed or nondirectional.

About the statement in the question,

It is improbable that an observed difference between two groups on the dependent variable would occur by chance alone when the difference is explained by the effect of the dependent variable through statistical hypothesis testing.

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We have evidence that this is not a symmetrical die, the standardized residuals is 9.5689

The die is tossed 1000 times

Given the observed value

x1 = 163

x2=178

x3=142

x4= 150

x5 = 183

x6 = 184

The mean = 163 + 178 + 142 + 150 + 183 + 184 / 6

= 1000 /6

= 166.67

Next we have to find the value of (observed value - Expected value)^2 / Expected value

x1 = (163-166.67)^2 / 166.67 = 0.081

x2 = (178-166.67)^2 / 166.67 = 0.7659

x3 = (142-166.67)^2 / 166.67 = 3.6598

x4 = (160 -166.67)^2 / 166.67 = 1.673

x5 = (183 - 166.67)^2 /  166.67 =  1.5938

x6 = (184-166.67)^2 / 166.67 =   1.7954

The standardized residuals = 0.081 + 0.7659 + 3.6598 +1.673 +1.5938 +1.7954 = 9.5689

Therefore, this is not a symmetrical die

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The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

Given that:

Total surface area of the rectangular box or cuboid = 100 cm²

A rectangular box with largest volume is a cube.

The total surface area of a cube = 6 times square of one edge length.

Let the edge length = given dimensions; x, y, z

So,

x = y = z

6x^2 = 100

x^2 = 100 / 6

x = √ 100 / 6

x = 10 / √ 6 cm

x = 2.449 cm

Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

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The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.

Given :

emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 %  .

Freshmen = 0.85

sophomores = 0.80

it is clearly visible that the freshmen or sophomores is greater than the 40 % .

Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.

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Answer:

  2x² +5

Step-by-step explanation:

You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.

The area is the product of length and width, so the width will be ...

  A = LW

  W = A/L = (2x³ +6x² +5x +15)/(x +3)

The cubic expression can be factored by grouping, so we have ...

  Area = (2x³ +6x²) +(5x +15)

  = 2x²(x +3) +5(x +3)

  = (2x² +5)(x +3)

Then the width is ...

  [tex]\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}[/tex]

The width of the rectangle is 2x² +5.

<95141404393>

Answer:

1/3

Step-by-step explanation:

Every third multiple of 20 is a multiple of 15.

The Slope intercept form of equation passing through points ( 1 , 3 ) and having slope 3 is y = 3x

In mathematics, formulating an equation for a line in the form y = mx + b is known as slope intercept form. The m stands for the line's slope, and the b for the y-intercept. When you need to find a point on a line or solve for y given x, you utilize the slope intercept form.

According to the given information

Form of the slope intercept: y = mx + b

It goes through some points ( 1 , 3 )

Slope of the line given m = 3

Put x = 1 and y = 3 and m = 3 in slope intercept form equation

3 = 3( 1 ) + b

b = 0

Hence

Put the value of b = 0 in y = mx + c

y = 3x

The Slope intercept form of equation passing through points ( 1 , 3 ) and having slope 3 is y = 3x

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