how to do this question plz ​

Answer:

0.5

Step-by-step explanation:

The function (f · g)(x) is equal to: 4x^5 - 16x^3 + x^2 - 4

To find the product of two functions f(x) and g(x), we need to multiply them term by term, i.e.,

(f · g)(x) = f(x) * g(x)

Let's start by multiplying the two functions:

f(x) * g(x) = (0.5x^2 - 2) * (8x^3 + 2)

Expanding the brackets, we get:

f(x) * g(x) = 4x^5 + x^2 - 16x^3 - 4

So the value of the function (f · g)(x) is:

(f · g)(x) = 4x^5 - 16x^3 + x^2 - 4

Therefore, the function (f · g)(x) is equal to:

4x^5 - 16x^3 + x^2 - 4

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Factoring the expression \(x^{6} - y^{6}\) is\((x^{3} +y^{3})(x^{3}-y^{3})(x^{2}+y^{2}+xy)(x^{2}+y^{2}-xy)\)

Given expression = \(x^{6}-y^{6}\)

= \((x^{3})^{2} - (y^{3})^{2}\)

Now, using the formula \(a^{2}-b^{2} = (a+b) (a-b)\)

= \((x^{3}-y^{3})(x^{3}+y^{3})\)

Here, using the formulas

\(x^{3}-b^{3} = (a-b)(a^{2}+b^{2}+ab)\) and \(a^{3} + b^{3} = (a+b)(a^{2}+b^{2} -ab)\)

Therefore, \((x^{3} +y^{3})(x^{3}-y^{3})(x^{2}+y^{2}+xy)(x^{2}+y^{2}-xy)\)

When a number or other mathematical object is expressed as the sum of several factors, usually smaller or easier versions of the same kind, this is referred to as factorization. When an expression has been fully factorized, it must be enclosed in brackets by removing the factors with the highest common denominator. The simplest method of factorization is to find the phrase's highest common factor among all of its terms. The highest common factor (HCF) should be placed in front of any brackets.

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Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length (1p 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35°. The search area is approximately 1.49 mi².

The search area of the sunken ship can be found by using the formula for the area of a triangle, which is given by A = (1/2) * a * b * sin(C), where a and b are the lengths of the adjacent sides of the triangle, and C is the angle between those sides.

Given that the adjacent sides have lengths of 1.75 miles and 1.32 miles, and the angle between them is 35°, we can substitute these values into the formula: A = (1/2) * 1.75 * 1.32 * sin(35°)

Evaluating the expression:

A ≈ (1/2) * 1.75 * 1.32 * 0.5736

A ≈ 1.493 mi²

Rounding the result to the nearest hundredth, the search area of the sunken ship is approximately 1.49 mi².

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Solution

For this case we can do the following:

a+ b= 15

b=3a

Replacing in the first equation we got:

a + 3a = 15

4a = 15

a = 15/4

b= 45/4

Then we can find the value of y on the following way:

y= a *tan 60 = 15/4 * tan 60

AC is the greatest side, therefore is hypotenuse. AB and BC are legs.B is 90 deg as the two legs cross at this point.

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec).

Ratios:

   sin = opposite / hypotenuse

   cos = adjacent / hypotenuse

   tan = opposite / adjacent

BC is opposite to A and adjacent to C

AB is adjacent to A and opposite to C

sin A = cos C = 8/10 = 4/5

cos A = sin C = 6/10 = 3/5

tan A = cot C = 8/6 = 4/3

tan C = cot A = 6/8 = 3/4

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Answer:

-46

Step-by-step explanation:

first multiply

add

and last subtract

Answer:

\(d = 10\)

Step-by-step explanation:

Distance formula

\(d =\sqrt{(x_2-x_1)^{2} + (y_2-y_1)^{2} }\)        ------------ (1)

Here

\((x_1, y_1) = (6, 2) \ \ \ and \ \ \ (x_2, y_2) = (5, 9)\)

Substituting values in equation (1)

\(d =\sqrt{(5-6)^{2} + (9-2)^{2} }\)

\(d =\sqrt{(-1)^{2} + (7)^{2} }\)

\(d = \sqrt { 50 }\)

\(d=7.07\)

the nearest tenth is 10

The form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.

what is decision boundaries.?

Decision boundaries refer to the dividing lines or regions that separate different classes or categories in a classification problem. They are determined based on the features or attributes of the data and the classification algorithm being used. The decision boundary serves as a threshold or criterion for assigning new or unseen data points to specific classes based on their feature values.

To derive the decision boundaries in the given case, more specific information or context is needed. Decision boundaries are determined based on the specific classification or grouping criteria and the underlying data distribution. Please provide additional details or specifications regarding the problem or classification task.

Regarding the conditional maximum likelihood estimator (MLE) of θ, more information is required to proceed with the derivation. The MLE involves finding the parameter value that maximizes the likelihood function based on the observed data and any relevant assumptions or models. Please provide the specific context, assumptions, and the form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.

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The product of binomial is 10n² - 3n - 18

A specific kind of expression is a polynomial. A mathematical statement without the equals symbol (=) is called an expression.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Given:

(2n- 3)(5n + 6)

Now, we have to multiply the binomial

(2n- 3)(5n + 6)

= 2n x 5n + 2n x 6 - 3 x5n - 3x 6

=10n² + 12n - 15n - 18

= 10n² - 3n - 18

Hence, the product of binomial is 10n² - 3n - 18.

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The two possible temperatures for the other town are 8°C (2°C + 6°C) and -4°C (2°C - 6°C).

Given that the difference in temperature between the two towns is 6°C and the temperature in one of the towns is 2°C, we can determine the possible temperatures for the other town. Since the difference is 6°C, we can add or subtract this difference to/from the known temperature of 2°C to find the potential temperatures.

Adding the difference of 6°C to 2°C gives us 8°C, which represents a warmer temperature in the other town. On the other hand, subtracting the difference of 6°C from 2°C gives us -4°C, indicating a colder temperature in the other town.

Therefore, the two possible temperatures for the other town are 8°C (warmer) and -4°C (colder), considering the given information.

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Answer:

\(D=\sqrt{29}\)

Step-by-step explanation:

The teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

In order to help the students understand that the triangle is equivalent to half a square, the teacher can adopt different methods, including the following:

1. Drawing diagrams of the triangle and the square to show the comparison. The teacher can draw diagrams of a triangle and a square on the board and label the different parts.

They can then show the students that a triangle can be created by halving the square diagonally. This way, the students will be able to visualize the comparison and understand it better.

2. Demonstrating the concept practically. The teacher can also demonstrate the concept by using physical objects such as paper or cardboard.

They can show the students how to create a triangle by folding a square diagonally and cutting it along the fold. This way, the students will be able to see the practical application of the concept.

3. Using real-world examples. The teacher can also use real-world examples to help the students understand the concept better.

For example, they can show the students pictures of tents or rooftops that are shaped like triangles and explain how they are related to squares.

4. Conducting group discussions. The teacher can conduct group discussions where the students can share their understanding of the concept and ask questions.

This way, the students will be able to learn from each other and clarify any doubts they may have.

Overall, the teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

The key is to use different approaches that cater to different learning styles and to encourage the students to participate actively in the learning process.

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Answer:

36.25

Step-by-step explanation:

If you want to find the rate to anything, divide the measurements by the time.

29/8= 36.25

The probability that it will rain both days is \(\frac{1}{4}\).

According to the question

Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.

Assuming that the chance of rain is independent of the day

Probability is the chance that some event will happen.

It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.

Probability = Number of ways it can occur/Total number of outcomes

Probability of rain on first day = 1/2

Probability of rain on second day = 1/2

Then

Probability of rain on both days = \(\frac{1}{2}\) × \(\frac{1}{2}\) = 1/4

Hence,

The probability that it will rain both days is \(\frac{1}{4}\).

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Answer:

how is your day

Step-by-step explanation:

Answer:

x= 16.6ft

Step-by-step explanation:

a. The degree of the polynomial is 6.

b. Factoring the equation, we have:

x6 - 49x^4 = x^4(x^2 - 49) = x^4(x - 7)(x + 7)

a.The degree of the polynomial equation x^6 - 49x^4 = 0 is 6. This is determined by the highest exponent of x in the polynomial, which is 6.

b. The two roots of multiplicity 1 can be found by factoring the equation as x^4(x^2 - 49) = 0. Setting each factor equal to zero, we have x^4 = 0 and x^2 - 49 = 0.

From x^4 = 0, we find the root x = 0 with multiplicity 4.

From x^2 - 49 = 0, we get (x - 7)(x + 7) = 0. Therefore, the roots x = 7 and x = -7 each have multiplicity 1.

In summary, the equation x^6 - 49x^4 = 0 has a degree of 6, and the roots with multiplicity 1 are x = 0, x = 7, and x = -7.

So the roots of the equation are:

x = 0 (multiplicity 4)

x = 7 (multiplicity 1)

x = -7 (multiplicity 1)

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In 2012, the population of a city was 5.77 million, and it experienced an exponential growth rate of 2.03% per year.

Over time, the city's population grew exponentially due to the compounded effect of the growth rate. The exponential growth formula can be used to calculate the population at a given year. By applying the formula, we can determine the population of the city after a certain number of years. To calculate the population after a specific number of years, we can use the formula P = P₀ * (1 + r/100)^t, where P₀ is the initial population, r is the growth rate, and t is the number of years. In this case, we substitute P₀ = 5.77 million, r = 2.03%, and t = the desired number of years. For example, if we want to find the population after 5 years, we can substitute these values into the formula: P = 5.77 million * (1 + 2.03/100)^5. By calculating this expression, we can determine the population of the city after 5 years. This exponential growth model provides a way to estimate how the population of the city might have increased over time based on the given growth rate.

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In the context of an independent t-test (2 sample t), the notation "41-H2" represents the alternative hypothesis.

In an independent t-test, we compare the means of two independent groups to determine if there is a significant difference between them. The null hypothesis (H0) states that there is no significant difference between the means of the two groups. The alternative hypothesis (H1 or HA) states that there is a significant difference between the means.

The notation "41-H2" refers to the alternative hypothesis, which is represented by HA or H1. The alternative hypothesis can take different forms depending on the research question and the expected relationship between the groups. For example, it could be "HA: μ1 ≠ μ2" for a two-tailed test, indicating that the means of the two groups are not equal. Alternatively, it could be "HA: μ1 > μ2" or "HA: μ1 < μ2" for a one-tailed test, indicating that the mean of one group is greater or less than the mean of the other group, respectively.

To summarize, the notation "41-H2" specifically represents the alternative hypothesis in the context of an independent t-test (2 sample t), indicating a significant difference between the means of the two groups being compared. It does not represent the null hypothesis, two-tail hypothesis, or one-tail hypothesis.

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Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

==========================================================

Explanation:

There are two methods you could use. The first method involves the remote interior angle theorem. This says the remote interior angles (the two y angles) add to the exterior angle (130)

y+y = 130

2y = 130

y = 130/2

y = 65

--------

Or we could find the interior angle that is adjacent to the 130 degree angle. This is 180-130 = 50 degrees. So this is the top interior angle of the triangle. For any triangle, the three interior angles always add to 180

angle1+angle2+angle3 = 180

y+y+50 = 180

2y+50 = 180

2y = 180-50

2y = 130 ... from here on out, the steps are the same as above

y = 130/2

y = 65

So this helps show how the remote interior angle theorem is set up

Responda:

15cm

Explicação passo a passo:

Volume de uma pirâmide = Área da Base × Altura / 3

Dado

Volume = 2100m³

Altura da pirâmide = 30m

Vamos obter a área base primeiro, substituindo o valor dado na fórmula.

2100 = B (30) / 3

2100 = 30B / 3

2100 = 10B

10B = 2100

Divida os dois lados por 10

10B / 10 = 2100/10

B = 210cm²

Como a base é um quadrado

área da base quadrada = 210cm²

L² = 210

L = √210

L = 14,49cm

C ≈ 15cm

Portanto, a medida da borda de sua menor base é de aproximadamente 15 cm

The given exponential growth model that approximates the population of Capital City is given by P(t) = 68,532(1.03)^t for t in years, where t = 0 represents January 1, 1950.What was the population of Capital City in 1960.

The given exponential growth model is,P(t) = 68,532(1.03)^tLet's substitute t = 10, since t represents the number of years after 1950 till 1960, thus we get,P(10) = 68,532(1.03)^10= 68,532 x 1.344 = 92,127.648

Thus, the population of Capital City in 1960 is approximately 92,128 people. The given exponential growth model that approximates the population of Capital City is given by P(t) = 68,532(1.03)^t for t in years, where t = 0 represents January 1, 1950.What was the population of Capital City in 1960.

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All of the following are measures of central tendency except the range

Mean

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

The mode, median, and mean are the three primary metrics for assessing central tendency. These metrics each give a different indication of the average or central value in the distribution.

Mode

The highest frequency of data and how many times the element is repeated in the data set is known as the mode value.

Median

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average.

Mean, median and mode are different measures of center in a numerical data set. They each try to summarize a dataset with a single number to represent a typical data point from the dataset.

When there are extremes in the sequences that might affect the average of the numbers the median is sometimes employed instead of the mean.

Thus, all of the following are measures of central tendency except the range

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The probability that Anthony, Brian, and Chantal are in the same lab group today is approximately 0.8703, or about 87.03%.

There are 15 students in total, so there are 15 ways to choose the first student, 14 ways to choose the second student (since one has already been chosen), and 13 ways to choose the third student (since two have already been chosen). However, since the lab groups are identical, we need to divide by the number of ways to arrange the group of three students, which is 3! = 6. Therefore, the total number of ways to choose a group of three students is:

15 x 14 x 13

6

Simplifying this expression gives:

(15 x 14 x 13) / 6 = 455

There are 5 lab groups, and we want to find the probability that Anthony, Brian, and Chantal are all in the same group. There are 3 ways to choose which group they will be in, and then we need to choose 2 more students to join them, which can be done in:

12 x 11

2

ways, since there are 12 students remaining to choose from after we have chosen Anthony, Brian, and Chantal, and we need to choose 2 more students to join them. Therefore, the total number of ways that Anthony, Brian, and Chantal can be in the same group is:

3 x (12 x 11) = 396

Finally, we can calculate the probability by dividing the number of favorable outcomes (i.e., Anthony, Brian, and Chantal are in the same group) by the total number of possible outcomes:

P(Anthony, Brian, Chantal in same group) = 396 / 455

≈ 0.8703

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Answer:6,000 is the answer

Step-by-step explanation: