i need this answerd ASAP ill give brainliest to whoever solves it first along with 3
40 points​

To solve the equation 7 sin(2x) = 6 for the two smallest positive solutions A and B, we can use algebraic techniques and trigonometric properties.

The solutions A and B are approximately equal to A ≈ 0.287 and B ≈ 1.569, respectively.

To explain the solution, let's begin by rearranging the equation: sin(2x) = 6/7. Since the range of the sine function is between -1 and 1, the equation has solutions only if 6/7 is within this range. We can find the corresponding angles by taking the inverse sine (arcsin) of 6/7. Using a calculator, we find that the arcsin(6/7) is approximately 0.942.

However, this gives us only one of the solutions. To find the other solution, we can use the periodicity of the sine function. We know that sin(θ) = sin(π - θ), where θ is the angle in radians. Therefore, the second solution is π - 0.942, which is approximately 2.199. However, since we're looking for the smallest positive solutions, we need to consider only the values between 0 and 2π. Thus, the two smallest positive solutions are A ≈ 0.287 and B ≈ 1.569.

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Answer:

6.25.

Step-by-step explanation:

25 divided by 4 is 6.25.

a) The forecast is approximately miles. b) the Mean Absolute Deviation (MAD) based on the forecast is approximately miles. c) The forecast for year 6 is approximately miles. d) the last forecast is 3,468 miles.

a) To calculate the forecast for year 6 using a 2-year moving average, we take the average of the mileage for years 5 and 4. This provides us with the forecasted value for year 6.

b) The Mean Absolute Deviation (MAD) for the 2-year moving average forecast is calculated by taking the absolute difference between the actual mileage for year 6 and the forecasted value and then finding the average of these differences.

c) When using a weighted 2-year moving average, we assign weights to the most recent and previous periods. The forecast for year 6 is calculated by multiplying the mileage for year 5 by 0.40 and the mileage for year 4 by 0.60, and summing these weighted values.

The MAD for the weighted 2-year moving average forecast is calculated in the same way as in part b, by taking the absolute difference between the actual mileage for year 6 and the weighted forecasted value and finding the average of these differences.

d) Exponential smoothing involves assigning a weight (α) to the most recent forecasted value and adjusting it with the previous actual value. The forecast for year 6 is calculated by adding α times the difference between the actual mileage for year 5 and the previous forecasted value, to the previous forecasted value.

In this case, with α=0.20 and a forecast of 3,100 miles for year 1, we perform this exponential smoothing calculation iteratively for each year until we reach year 6, resulting in the forecasted value of approximately 3,468 miles.

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The average annual growth rate of the population for this time period was approximately 3.53%.

What is average annual growth ?

Average annual growth refers to the average rate at which a quantity or value increases or decreases over a period of time, usually measured in terms of percentage per year. It is commonly used to describe the growth or decline of economic indicators such as Gross Domestic Product (GDP), population, income, and investments.

To calculate the average annual growth rate, we use the following formula:

\(average annual growth rate = (Ending Value / Beginning Value)^{1/Number of Years} - 1\)

where:

"Ending Value" is the value of the quantity at the end of the period.

"Beginning Value" is the value of the quantity at the beginning of the period.

"Number of Years" is the length of the period in years.

According to the question:
We can use these values to calculate the average annual growth rate of the population. To do this, we can use the formula:

\(average annual growth rate = (final population / initial population)^{(1/number of years)} - 1\)

Using the given values, we can calculate the average annual growth rate as follows:

For the period from 2010 to 2011:

average annual growth rate = \((15,939 / 15,400)^{1/1} - 1 = 0.0356 or 3.56%\)

For the period from 2011 to 2012:

average annual growth rate =\((16,497 / 15,939)^{1/1} - 1 = 0.0352 or 3.52%\)

For the period from 2012 to 2013:

average annual growth rate =\((17,074 / 16,497)^{1/1} - 1 = 0.0350 or 3.50%\)

Therefore, the average annual growth rate of the population for this time period was approximately 3.53%.

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The population in 2022, if the trend continues, would be approximately 32,825. The answer is (c).

What is exponential function?

An exponential function is a mathematical function in which an independent variable appears in the exponent.

To determine the population in 2022 if the trend continues, we can use the exponential growth model:

P(t) = P0 * \((1+r)^{t}\)

where P0 is the initial population, r is the annual growth rate, and t is the number of years.

To find the annual growth rate, we can use the formula:

r = \((P1/P0)^{1/n}\) - 1

where P1 is the final population, P0 is the initial population, and n is the number of years.

Using the given data, we can calculate the annual growth rate:

r = \((17,074/15,400)^{1/3}\) - 1

r = 0.0572

So the exponential growth model for the population is:

P(t) = 15,400 * \((1 + 0.0572)^{t}\)

To find the population in 2022, we can substitute t = 12 (since we want to find the population after 12 years):

P(12) = 15,400 * \((1 + 0.0572)^{12}\)

P(12) ≈ 32,825

Therefore, the population in 2022, if the trend continues, would be approximately 32,825. The answer is (c).

To determine which of the following equations best models the exponential function of this situation, we can compare the given equations with the exponential growth model we derived:

P(t) = 15,400 * \((1 + 0.0572)^{t}\)

(a) \(15,4000(1.965)^{x}\)

This equation does not match the form of the exponential growth model. The base of the exponent is greater than 1, which would indicate exponential growth, but the exponent is not in the correct form.

(b) \(15,4000(0.035)^{x}\)

This equation has a base between 0 and 1, which would indicate exponential decay, not growth.

(c) \(15,4000(0.965)^{x}\)

This equation has a base between 0 and 1, which would indicate exponential decay, not growth.

(d) \(15,4000(1.035)^{x}\)

This equation has a base greater than 1, which would indicate exponential growth, and the exponent is in the correct form. However, the coefficient is incorrect.

Therefore, the equation that best models the exponential function of this situation is (d) 15,4000(1.035)^x.\(15,4000(1.035)^{x}\)

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No, the F-test statistic cannot be less than 1 when it represents the larger of two sample variances.

The F-distribution is always a positive distribution with a range of values greater than zero. The F-test value is always greater than or equal to 0, but it is not always less than or equal to 1.

The numerator, representing the bigger sample variance, is always greater than or equal to the denominator, representing the smaller sample variance. Consequently, the F-ratio, which is the ratio of the larger to the smaller variance, is always greater than or equal to 1. Thus, an F-test statistic that is less than 1 is mathematically incorrect.

Therefore, an F-test statistic is always a positive number that is greater than or equal to zero and greater than or equal to 1. This is because the numerator of an F-distribution is always greater than or equal to the denominator.

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The inequality compares the left (l), right (r), and trapezoidal (t) sum approximations of the area under the curve is C. r < t < l.

From the information given, it should be noted that f'(x) is negative. Therefore, L > R. Also since f"(x) is negative, T > R.

f(x) = 2 cos 2x.

f'(x) = -4 sin 2x

f"(x) = -8 cos 2x

Therefore, the inequality compares the left (l), right (r), and trapezoidal (t) sum approximations of the area under the curve is r < t < l

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>>> alist = [2, 3.5, 7, 9]. It can be find out by using concept of sorting and basic knowledge of programming.

What is sorting?

A sorting algorithm in computer science is a method for organising the items on a list. The most frequently utilised ordering systems are lexicographical and numerical, both in ascending and descending order. The effectiveness of other algorithms (like search as well as merge algorithms) which require input data being in sorted lists must be maximised, so efficient sorting is crucial. Additionally, canonicalizing data and creating output that is readable by humans both benefit from sorting.

i.e. either in ascending or descending order.

Here , sort() is a function that is used to sort the given list "alist".

By default sort() arranges in ascending order.

Given elements of list = 9, 2, 3.5, 7

So, ascending order = 2, 3.5, 7, 9

So, >>>alist = [2, 3.5, 7, 9]

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See attachment for math work and answer.

Note: The triangle next to y and x in the fraction is read: "delta y divided by delta x."

It means the difference of the y terms divided by the difference of the x terms.

Answer:

its not a solution

Step-by-step explanation:

substitute  the points

3(-2) + 7(-3) = 14

-6 - 21 = 14?

-27 = 14 X

Answer:

is there a picture

Step-by-step explanation:

Answer:b

Step-by-step explanation:did it

Answer:

why does it say the answer is 165 on top?

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

2

Step-by-step explanation:

the - means you have to subtract to add. so subtract 3 over 4 and you get 2

\(\text{L.H.S}\\\\=\dfrac{1}{\sin^2 A} - \dfrac1{\tan^2 A}\\\\\\=\dfrac{1}{\sin^2 A}- \dfrac{1}{\tfrac{\sin^2 A}{\cos^2 A}}\\\\\\=\dfrac{1}{\sin^2 A} - \dfrac{\cos^2 A}{\sin^2 A}\\\\\\=\dfrac{1 - \cos^2 A}{\sin^2 A}\\\\\\=\dfrac{\sin^2 A}{\sin^2 A}\\\\\\=1\\\\=\text{R.H.S}\\\\\text{Proved.}\)

Probability of selecting a female student from the given number of students is equal to 0.5217.

As given in the question,

Number of female students in algebra class = 48

Number of male students in algebra class = 44

Total Number of students in algebra class = 48 + 44

                                                                  = 92

Total number of outcomes = ⁹²C₁

Number of favourable outcomes = ⁴⁸C₁

Probability of selecting a female student

= (Number of favourable outcomes) / (Total number of outcomes )

= ⁴⁸C₁ /  ⁹²C₁

= 48 / 92

= 12/23

= 0.5217

Therefore, the probability of selecting a female students from the given number of male and female students is equal to 0.5217.

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Answer:

d

Step-by-step explanation:

hiiiiiiii

Answer:

Area = 36

Perimeter = 26

Step-by-step explanation:

Area = (4*2)+(7*4) = 8+28 = 36

Perimeter = 6+4+2+3+(6-2)+(3+4) = 10+5+4+7 = 15+11 = 26

Answer:

Perimeter: 26

Area: 36

Step-by-step explanation:

Perimeter:

6 + 4 + 2 + 3 + 4 + 7

10 + 5 + 11

15 + 11

26

Area:

(6 x 4) + (3 x 4)

24 + 12

36

The actual length of the bus is 45 feet.

Given that, a scale drawing of a school bus has a scale of 1/2 inch to 5 feet.

Scale factor is a number by which the size of any geometrical figure or shape can be changed with respect to its original size.

Here, \(4\frac{1}{2} = \frac{9}{2}\)

Let the actual length of the bus be x.

Now, the proportion is

1/2 : 5 :: 9/2 : x

⇒ x/2 = 45/2

⇒ x = 45 feet

Therefore, the actual length of the bus is 45 feet.

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The parametric equations for the curve are:

x = -5t^3 - 3t

y = t

To find parametric equations for the curve x = -5y^3 - 3y, we can set y as the parameter and express x in terms of y.

Let y = t, where t is the parameter.

Substituting y = t into the equation x = -5y^3 - 3y:

x = -5(t^3) - 3t

The interval for the parameter values depends on the context or specific requirements of the problem. If no specific interval is given, we can assume a wide range of values for t, such as all real numbers.

So, the correct answer is:

A. x = -5t^3 - 3t, y = t

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Given:

Equation of line is \(y=3x-7\).

To find:

The equation of line which is parallel line to \(y=3x-7\) and passes through (3,5) in function notation.

Solution:

Slope intercept form of a line is

\(y=mx+b\)

where, m is slope and b is y-intercept.

On comparing the equation \(y=3x-7\) with slope intercept form, we get

\(m=3\)

So, slope of given line is 3.

Slope of parallel lines are same. Thus, the slope of parallel line is also 3.

Point slope form of a line is

\(y-y_1=m(x-x_1)\)

where, m is slope.

The parallel line passes through (3,5) with slope 3. So, the equation of line is

\(y-5=3(x-3)\)

\(y-5=3x-9\)

Add 5 on both sides.

\(y=3x-9+5\)

\(y=3x-4\)

Function notation of this equation is

\(f(x)=3x-4\)

Therefore, the equation equation in function notation is \(f(x)=3x-4\).

The absolute maximum value occurs at x = -2, where f(x) is 20.

Therefore, the answer is E. -2.

Here, we have,

To find the absolute maximum value of the function f(x) = x³ - 3x² + 12 on the closed interval [-2, 4], we need to evaluate the function at the critical points within the interval and at the endpoints.

Evaluate f(x) at the critical points:

To find the critical points, we take the derivative of f(x) and set it equal to zero:

f'(x) = 3x² - 6x

Setting f'(x) = 0 and solving for x:

3x² - 6x = 0

3x(x - 2) = 0

From this equation, we find two critical points: x = 0 and x = 2.

Evaluate f(x) at x = 0:

f(0) = (0)³ - 3(0)² + 12 = 12

Evaluate f(x) at x = 2:

f(2) = (2)³ - 3(2)² + 12 = 2

Evaluate f(x) at the endpoints of the interval:

Evaluate f(x) at x = -2:

f(-2) = (-2)³ - 3(-2)² + 12 = 20

Evaluate f(x) at x = 4:

f(4) = (4)³ - 3(4)² + 12 = -8

Now, we compare the function values at the critical points and endpoints to determine the absolute maximum value:

f(-2) = 20

f(0) = 12

f(2) = 2

f(4) = -8

The absolute maximum value occurs at x = -2, where f(x) is 20.

Therefore, the answer is E. -2.

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Answer:

y = x^2 - 2x - 8

Step-by-step explanation:

First we can put it into vertex form, the vertex is at (1, -9)

y = a ( x − h )^2 + k .

y = 1 (x - 1)^2 - 9

Then distribute:

y = x^2 - 2x + 1 - 9

y = x^2 - 2x - 8

Answer:

A = [84]in^2

Step-by-step explanation:

5 x 3 = 15

4 x 2 = 16

9 + 4 = 13 x 4 = 52

52 + 15 + 16 = 84in

There are 70,560 possible divisions of 8 new teachers among 4 schools. The total number of divisions of 8 new teachers among 4 schools is therefore:65,536 - 4 = 70,560

To calculate the total number of divisions of 8 new teachers among 4 schools, you can use the formula for combinations with repetition:

n^r

where n is the number of schools (4) and r is the number of teachers (8).

4^8 = 65,536

However, this formula does not take into account the possibility of one or more schools having no teachers assigned to them. To account for this, you can subtract the number of combinations where one or more schools have zero teachers assigned, which is calculated using the formula for combinations without repetition:

nCr = n! / r!(n - r)!

where n is the number of schools (4) and r is the number of teachers (8).

4C8 = 4! / 8!(4 - 8)! = 4! / 8!(-4)! = 4! / 8!(4)! = 4 / 1 = 4

The total number of divisions of 8 new teachers among 4 schools is therefore:

65,536 - 4 = 70,560

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Answer:

Does the answer help you?

The number of possibilities in a lottery where they pick three balls out of an urn with 10 balls numbered 1 to 10 is calculated using the concept of combinations. A combination is a way to select items from a larger set, where the order of the items doesn't matter.

In this case, the total number of items in the set is 10, and we need to select 3 items. The formula for the number of combinations of "n" items taken "k" at a time is given by:

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

Where "n!" means "n factorial," which is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Using this formula, we can calculate the number of combinations of 3 items taken from a set of 10:

C(10, 3) = 10! / (3! (10-3)!) = 10! / (3! 7!) = (10 x 9 x 8) / (3 x 2 x 1) = 120

So, there are 120 possible combinations of 3 balls that can be selected from an urn with 10 balls numbered 1 to 10. This means that there are 120 different ways that the three balls could be drawn, and each one is equally likely.

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9514 1404 393

Answer:

  \(f^{-1}(x)=\dfrac{\sqrt[3]{3x+12}}{3}\)

Step-by-step explanation:

For function ...

  \(y=f(x)\)

sometimes we know y, but we want to find the corresponding value x. That is, we would like to have an inverse function:

  \(x=f^{-1}(y)\)

Here, I have said the input to the inverse function is the value of y for which we want the corresponding value of x.

__

Normally, we write the inverse function basically the same way we write the function. The input is named x, and the output is named y. We can swap the variable names for input and output either before or after we find the equation that relates them.

Perhaps you can see that finding the inverse function

  \(x=f^{-1}(y)\)

amounts to solving the function relation y = f(x) for x. If we interchange variables first, it is the same as solving x = f(y) for y.

__

To find the inverse, we can interchange the variables and solve for y.

  \(x=f(y)=9y^3-4\\\\x+4=9y^3\qquad\text{add 4}\\\\\dfrac{x+4}{9}=y^3\qquad\text{divide by 9}\\\\\dfrac{3x+12}{27}=y^3\qquad\text{make the denominator a cube; multiply by 3}\\\\y=\dfrac{\sqrt[3]{3x+12}}{3}\qquad\text{take the cube root}\\\\\boxed{f^{-1}(x)=\dfrac{\sqrt[3]{3x+12}}{3}}\)

_____

The graph of the inverse of a function is the reflection of the graph of the function across the line y=x. The given function and the inverse we found are graphed in the attachment. The dashed line is y=x.