transform the equation formulated into standard form ax²+bx+c=0​

The marked price of the television is Rs. 20,000.

The market price is the current price at which a good or service can be purchased or sold.

Here, let the marked price of the television be Rs. x

          Discount = 16% on MP

          VAT = 13% additional on MP

          Total paid amount = Rs. 18984

Now, according to question;

     MP X (1 - Discount) X (1 + VAT) = 18984

              x (1 - 0.16)(1+0.13) = 18984

              x = 18984/(0.84 X 1.13)

              x = 18984 / 0.9492

              x = 20,000

Thus, the marked price of the television is Rs. 20,000.

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ANOVA is a more appropriate and efficient method for evaluating mean differences when an experiment consists of three or more treatment conditions, as it provides a more robust and reliable analysis than multiple t-tests, while also reducing the risk of Type I errors.

The principal reason why you should use ANOVA (Analysis of Variance) instead of several t-tests to evaluate mean differences when an experiment consists of three or more treatment conditions is that multiple t-tests accumulate the risk of a Type I error.

A Type I error is the rejection of a true null hypothesis, which means that you have falsely concluded that there is a significant difference between the treatment groups when there is actually no difference. When conducting multiple t-tests, the probability of making a Type I error increases with the number of tests performed. In other words, if you perform multiple t-tests, the overall probability of making at least one Type I error increases, and this can lead to incorrect conclusions.

ANOVA is a statistical technique that allows you to compare the means of three or more treatment groups simultaneously while controlling the probability of making a Type I error. ANOVA compares the variance between groups to the variance within groups to determine if the differences between the treatment groups are statistically significant. By using ANOVA instead of multiple t-tests, you can reduce the overall risk of making a Type I error while still evaluating the mean differences between the treatment groups.

Therefore, ANOVA is a more appropriate and efficient method for evaluating mean differences when an experiment consists of three or more treatment conditions, as it provides a more robust and reliable analysis than multiple t-tests, while also reducing the risk of Type I errors.

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Answer:

What statements =?

Step-by-step explanation:

The trigonometric functions sine and cosecant have a positive sign.

In this problem we must determine what trigonometric functions associated with a vector of the form (x, y) have a positive sign. This can be done by computing on each function:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

If we know that x = - 12 and y = 5, then the values of the trigonometric functions are, respectively:

sin θ = 5 / √[(- 12)² + 5²]

sin θ = 5 / 13

cos θ = - 12 / √[(- 12)² + 5²]

cos θ = - 12 / 13

tan θ = - 5 / 12

sec θ = - 13 / 12

csc θ = 13 / 5

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Answer:

<ACB = \(65^{o}\) and <BAC = \(50^{o}\)

Step-by-step explanation:

The given triangle is an isosceles triangle. Thus its two sides are equal and base angles are equal.

So that;

<ACB = <ABC

<ACB = \(65^{o}\) (property of an isosceles triangle)

Then,

<ABC + <ACB + <BAC = \(180^{o}\)

\(65^{o}\) + \(65^{o}\) + <BAC = \(180^{o}\)

130 + <BAC = \(180^{o}\)

<BAC = \(180^{o}\) - \(130^{o}\)

          = \(50^{o}\)

<BAC = \(50^{o}\)

Thus, <ACB = \(65^{o}\) and <BAC = \(50^{o}\).

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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Answer:

Your Ans

1.03

Hope this Helpful

x, y, and z are pairwise independent because any two of them are independent. x, y, and z are not mutually independent because their joint distribution does not factor into the product of their marginal distributions.

To show that the random variables x, y, and z are pairwise independent but not mutually independent, we need to examine the definitions of these concepts and demonstrate the properties.

Pairwise Independence:

Two random variables are said to be pairwise independent if any two of them are independent, regardless of the dependence on the third variable.

Mutual Independence:

Three random variables are said to be mutually independent if each pair of them is independent and their joint distribution factors into the product of their marginal distributions.

Now let's analyze x, y, and z based on these definitions.

Pairwise Independence:

To show that x, y, and z are pairwise independent, we need to demonstrate that any two of them are independent, regardless of the dependence on the third variable.

a) x and y:

Since x and y are independent Bernoulli(1/2) random variables, their outcomes do not affect each other. Therefore, x and y are independent.

b) x and z:

We need to consider the joint distribution of x and z. Let's examine all possible combinations:

If x = 0, then regardless of the value of y, z will be 0. Hence, P(x = 0, z = 0) = P(x = 0)P(z = 0) = (1/2)(1) = 1/2.

If x = 1, then z will be 1 only when y = 1. Therefore, P(x = 1, z = 1) = P(x = 1, y = 1) = P(x = 1)P(y = 1) = (1/2)(1/2) = 1/4.

If x = 1, then z will be 0 when y = 0. Therefore, P(x = 1, z = 0) = P(x = 1, y = 0) = P(x = 1)P(y = 0) = (1/2)(1/2) = 1/4.

If x = 0, then regardless of the value of y, z will be 0. Hence, P(x = 0, z = 0) = P(x = 0)P(z = 0) = (1/2)(1) = 1/2.

From the above calculations, we can see that P(x, z) = P(x)P(z) for all possible combinations of x and z. Therefore, x and z are independent.

c) y and z:

Similar to the analysis above, we can calculate the joint probabilities:

If y = 0, then regardless of the value of x, z will be 0. Hence, P(y = 0, z = 0) = P(y = 0)P(z = 0) = (1/2)(1) = 1/2.

If y = 1, then z will be 1 only when x = 1. Therefore, P(y = 1, z = 1) = P(y = 1, x = 1) = P(y = 1)P(x = 1) = (1/2)(1/2) = 1/4.

If y = 1, then z will be 0 when x = 0. Therefore, P(y = 1, z = 0) = P(y = 1, x = 0) = P(y = 1)P(x = 0) = (1/2)(1/2) = 1/4.

If y = 0, then regardless of the value of x, z will be 0. Hence, P(y = 0, z = 0) = P(y = 0)P(z = 0) = (1/2)(1) = 1/2.

From the above calculations, we can see that P(y, z) = P(y)P(z) for all possible combinations of y and z. Therefore, y and z are independent.

We have shown that any two random variables among x, y, and z are independent. Hence, x, y, and z are pairwise independent.

Not Mutually Independent:

To demonstrate that x, y, and z are not mutually independent, we need to show that their joint distribution does not factor into the product of their marginal distributions.

To do this, let's consider the joint distribution of x, y, and z. We can analyze all possible combinations:

If x = 0 and y = 0, then z will be 0. Hence, P(x = 0, y = 0, z = 0) = P(x = 0)P(y = 0)P(z = 0) = (1/2)(1/2)(1) = 1/4.

If x = 1 and y = 1, then z will be 1. Hence, P(x = 1, y = 1, z = 1) = P(x = 1)P(y = 1)P(z = 1) = (1/2)(1/2)(1/2) = 1/8.

However, if we examine the joint probability P(x = 0, y = 0, z = 1), we find that it is not equal to P(x = 0)P(y = 0)P(z = 1). In this case, P(x = 0, y = 0, z = 1) is 0 because z can only be 0 when x and y are both 0. Therefore, P(x = 0, y = 0, z = 1) ≠ P(x = 0)P(y = 0)P(z = 1).

Since the joint distribution does not factor into the product of the marginal distributions for all possible combinations, x, y, and z are not mutually independent.

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The correct answer is: c) 1/3, 5/3 The cosine function has a period of 2π, meaning it repeats every 2π radians.

To find the solutions for x in the equation 12cos(2x) + 10 = 16, we can solve it algebraically. Let's begin:

12cos(2x) + 10 = 16

Subtract 10 from both sides:

12cos(2x) = 6

Divide both sides by 12:

cos(2x) = 1/2

Now, we want to find the two smallest positive solutions for cos(2x) = 1/2. The cosine function has a period of 2π, meaning it repeats every 2π radians. We are looking for solutions in the range of 0 to 2π.

The cosine function has values of 1/2 at two specific angles: π/3 and 5π/3.

So, we can set up the following equations:

2x = π/3 and 2x = 5π/3

Solving for x in each equation:

For 2x = π/3:

x = π/6

For 2x = 5π/3:

x = 5π/6

Thus, the two smallest positive solutions for x in the equation 12cos(2x) + 10 = 16 are x = π/6 and x = 5π/6.

Therefore, the correct answer is:

c) 1/3, 5/3

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Answer:

Cost of 1 goggles = $20

Cost of 1 mask = 15

Step-by-step explanation:

Given:

Cost of 2 goggles and 1 mask = $55

Cost of 1 goggles and 2 mask = $50

Find:

Cost of each goggles and mask

Computation:

Assume;

Cost of 1 goggles = a

Cost of 1 mask = b

So,

2a + b = 55.....EQ1

a + 2b = 50.......EQ2

EQ1 x 2

4a + 2b = 110 ......EQ3

EQ3 - EQ2

3a = 60

a = 20

Cost of 1 goggles = $20

a + 2a = 50

20 + 2b = 50

2b = 30

b = 15

Cost of 1 mask = 15

.

We will see that the total number of ways in which we can distribute 20 different prizes among 180 people is:

C =  6.818e46

Here we need to count how many selections do we have. Each prize will be a selection, so we have 20 selections.

Now we need to count the numbers of 6for each selection.

For the first prize, there are 180 options.

For the second prize, there are 179 options (because one person already got a prize).

For the third prize, there are 178 options.

And so on.

The total number of combinations is given by the product between the numbers of options:

C = 180*179*178*...*161*160 = 6.818e46

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Answer:

2

Step-by-step explanation:

The Intial value, also know as the y-intercept, is where the line crosses line y.

Therefore, looking at the graph, your initial value is 2.

The values of the missing sides and angles using trigonometric ratios are:

b = 7.06

c = 3.76

C = 28°

The six trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent.

The symbols used for them are:

sine: sin

cosine: cos

tangent: tan

cosecant: csc

secant: sec

cotangent: cot

The trigonometric ratios are defined as the ratio of the sides in right triangles.

Using trigonometric ratios, we have:

b/8 = sin 62

b = 8 * sin 62

b = 7.06

Similarly:

c/8 = cos 62

c = 8 * cos 62

c = 3.76

Sum of angles in a triangle is 180 degrees. Thus:

C = 180 - (90 + 62)

C = 28°

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After seven years, making deposits of $470.00 at the end of each month with a compound interest rate of 10.8% compounded monthly, the total amount would be approximately $905.49.

To calculate the amount of deposits made at the end of each month after seven years with a compound interest rate of 10.8% compounded monthly, we can use the formula for compound interest:

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

where:

A is the final amount,

P is the initial deposit amount,

r is the interest rate,

n is the number of times the interest is compounded per year, and

t is the number of years.

In this case, the initial deposit amount (P) is $470.00, the interest rate (r) is 10.8% (or 0.108 as a decimal), the interest is compounded monthly (n = 12), and the time period (t) is 7 years.

Plugging in these values into the formula, we get:

A = $470.00 * (1 + 0.108/12)^(12*7).

Using a calculator or software, we can evaluate this expression:

A ≈ $905.49.

Therefore, after seven years of making monthly deposits of $470.00 with a compound interest rate of 10.8% compounded monthly, the total amount would amount to approximately $905.49.

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The correct answer is c. Numerical data are easier to collect.

Numerical data and qualitative data (e.g., text responses) are both important in research, but they have different strengths and uses. Numerical data is often preferred for certain reasons, but one of the reasons it is not preferred over qualitative data is that numerical data is easier to collect.

Here's why the other options are not the correct answer:

a. Statistics can be used with numerical data to determine if hypotheses are supported: This is a valid reason why numerical data is preferred. Statistics can be applied to numerical data to analyze and draw conclusions, which helps researchers determine if their hypotheses are supported.

b. Numerical data are more objective and easier to interpret: This is another valid reason why numerical data is preferred. Numerical data is often more objective and easier to interpret compared to qualitative data, which can be subjective and open to interpretation.

d. Numerical data can be used in significance testing: This is also a valid reason why numerical data is preferred. Significance testing, which is used to determine if the results of a study are statistically significant, is often done with numerical data.

To summarize, while numerical data is preferred in research for reasons such as its compatibility with statistical analysis and its objectivity, it is not preferred over qualitative data because it is easier to collect.

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The 68% confidence interval for the true proportion of garter snakes that are over 20 inches in length is (0.20, 0.30).

A 68% confidence interval for the true proportion of garter snakes that are over 20 inches in length can be calculated using the sample proportion (p′), the sampling standard deviation (σp′), and the z-score for a 68% confidence level. Here are the steps:

1. Identify the given values: p′ = 0.25 and σp′ = 0.05.
2. Look up the z-score for a 68% confidence level, which is approximately 1 standard deviation away from the mean. Therefore, the z-score is 1.
3. Calculate the margin of error (ME) by multiplying the z-score by the sampling standard deviation: ME = 1 × 0.05 = 0.05.
4. Calculate the lower and upper bounds of the confidence interval:
  - Lower bound = p′ - ME = 0.25 - 0.05 = 0.20.
  - Upper bound = p′ + ME = 0.25 + 0.05 = 0.30.

So, the 68% confidence interval for the true proportion of garter snakes that are over 20 inches in length is (0.20, 0.30).

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Answer: (0.2, 0.3)

Step-by-step explanation:

By the Empirical Rule, a 68% confidence interval corresponds to a z-score of z=1.  Substituting the given values p′=0.25 and σp′=0.05, a confidence interval is

(p′−z⋅σp′,p′+z⋅σp′)(0.25−1⋅0.05,0.25+1⋅0.05)(0.25−0.05,0.25+0.05)(0.20,0.30)

Answer:

182.4

this website deleted my paragraph... TLDR; 182.4 is the answer

Answer:

The answer is 2

Step-by-step explanation:

Y2-Y1/X2-X1

4-2/2-1

4-2 ( 2 )

2-1 ( 1 )

2/1 ( 2 )

The estimate for the sum of the numbers is 230, and the actual sum of the numbers is 209.

To estimate the sum of the numbers, we can round each number to the nearest ten and then add them together. When rounding off to the nearest tens, we look at the number at the tenth position. If it is five and above, we round it off to the next nearest tens number and if it is below five, we round it off to the previous nearest tens number.

76 rounds to 80   since 6 is above 5
6 rounds to 10 since 6 is above 5
25 rounds to 30 since 5 is located at 5 and above interval
5 rounds to 10 since 5 is located at 5 and above interval
10 rounds to 10 since 0 is below 5
87 rounds to 90 since 7 is above 5

So, the estimate for the sum of the numbers is: 80 + 10 + 30 + 10 + 10 + 90 = 230

To find the actual sum of the numbers, we simply add them together without rounding:

76 + 6 + 25 + 5 + 10 + 87 = 209

The complete question is: 76. 6 25. 5 10. 87 =

What was Sela's estimate and what is the actual sum of the number?

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Answer:

20:10 10 hours

Step-by-step explanation:

10:5 * 2 = 20:10 or 10:5 / 5 : 2:1 * 20 = 20:10

The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)

Parametric vector form:

If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:

x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.

A common parametric vector form uses the free variables as the parameters s1 through sm

Given is a system of equations

We are to solve them in parametric form.

x1 + 3x2 + x3 = 0 --------(1)

-4x1 + 9x2 + 2x3 = 0 ---------(2)

-3x2 - 6x3 = 0--------(3)

From equation(3)

-3x2=6x3

x2=-2x3

substitute in equation(1) and equation(2)

x1+3(-2x3)+x3=0

x1-6x3+x3=0

x1-5x3=0

x1=5x3

So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.

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The area of the house is the amount of space on the house.

The area of the addition is given as:

\(Area = x^2 + 10x - 200\)

Expand

\(Area = x^2 + 20x - 10x - 200\)

Factorize

\(Area = x(x + 20) - 10(x + 20)\)

Factor out x + 20

\(Area = (x -10)(x + 20)\)

The width of the addition is x - 10.

Hence, the length of the addition is x + 20

The dimension of the original house is

x + 20 by x + 10

So, the area is:

\(Area =(x + 20)(x + 10)\)

Expand

\(Area =x^2 + 20x + 10x + 200\)

This gives

\(Area =x^2 + 30x + 200\)

Hence, the area of the original house is \(x^2 + 30x + 200\)

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Answer: the ancient Romans

Step-by-step explanation:

Answer:

Step-by-step explanation:

jefferson thompson made the numberal numerebaals

-11

Answer: D) y=2x-11

Answer:

x ≤ -27

Step-by-step explanation:

\(\frac{x}{-9}\) ≥ 3

to isolate the 'x' we need to multiply each side by -9

whenever you multiply or divide an inequality by a negative you must reverse the inequality symbol, therefore:

x ≤ -27