Please help me, I am confused on how to do this problem.

Find the exact value, cos(-pi/12). Use the half angle strategy.

Answer:

y = 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes , then

slope of line AB is m = 2

line AB crosses the y- axis at (0, 4 ) ⇒ c = 4

y = 2x + 4 ← equation of line AB

Answer:

To evaluate the composite functions (f◦g), (g◦f), (f◦f), and (g◦g), we need to substitute one function into the other and simplify the resulting expression.

(a) (f◦g)(4):

To find (f◦g)(4), we need to first find g(4) and then substitute it into f(x):

g(4) = 7 - 1/2(4)^2

= 7 - 8

= -1

Now we substitute g(4) = -1 into f(x):

(f◦g)(4) = f(g(4))

= f(-1)

= 3(-1)^2 - 2

= 1

Therefore, (f◦g)(4) = 1.

(b) (g◦f)(2):

To find (g◦f)(2), we need to first find f(2) and then substitute it into g(x):

f(2) = 3(2)^2 - 2

= 10

Now we substitute f(2) = 10 into g(x):

(g◦f)(2) = g(f(2))

= g(10)

= 7 - 1/2(10)^2

= -43

Therefore, (g◦f)(2) = -43.

(c) (f◦f)(1):

To find (f◦f)(1), we need to find f(f(1)):

f(1) = 3(1)^2 - 2

= 1

Now we substitute f(1) = 1 into f(x):

(f◦f)(1) = f(f(1))

= f(1)

= 1

Therefore, (f◦f)(1) = 1.

(d) (g◦g)(0):

To find (g◦g)(0), we need to find g(g(0)):

g(0) = 7 - 1/2(0)^2

= 7

Now we substitute g(0) = 7 into g(x):

(g◦g)(0) = g(g(0))

= g(7)

= 7 - 1/2(7)^2

= -17/2

Therefore, (g◦g)(0) = -17/2.

The total number of employees is 112.

Explain numbers

Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.

According to the given information

Let's use x to represent the total number of employees.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.

So, we can set up the following proportion:

4/9 = x/(x - 140)

To solve for x, we can cross-multiply and simplify:

4(x - 140) = 9x

4x - 560 = 9x

560 = 5x

x = 112

Therefore, the total number of employees is 112.

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Is the graph increasing, decreasing, or constant: C. Constant.

In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.

In conclusion, the above is constant, rather than increasing or decreasing.

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The expression x^4 + 5x^2 - 8 in quadratic form is: (x^2 + 8)(x^2 - 1)

It should be noted that to express the given expression x^4+5x^2 - 8 in quadratic form, we need to identify a suitable substitution that will allow us to rewrite the expression as a quadratic in a new variable.

One possible substitution is to let u = x^2, so that we can write:

x^4 + 5x^2 - 8 = u^2 + 5u - 8

We can then factor this quadratic expression as:

u^2 + 5u - 8 = (u + 8)(u - 1)

Substituting back u = x^2, we get:

x^4 + 5x^2 - 8 = (x^2 + 8)(x^2 - 1)

Therefore, the expression x^4 + 5x^2 - 8 in quadratic form is:

(x^2 + 8)(x^2 - 1)

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The probability of drawing a marble that is green or even-numbered is  28/35

The total number of marbles in the jar is 35, of which 10 are blue, 12 are green, and 13 are red.

We need to find the probability of drawing a marble that is green or an even number.

First, let's find the number of even-numbered marbles.

Out of 35 marbles, 17 of them are even-numbered (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34).

There are 12 green marbles, and 17 even-numbered marbles,

Therefore, there are 12 + 17 - 1 = 28 marbles that are either green or even-numbered.

The probability of drawing a marble that is green or even-numbered is

28/35

So the probability of drawing a marble that is green or even-numbered is  28/35

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x ≤ 4, -2≤ y ≤ 2  are the domain and range of the graph of this function.

What is the domain and domain of the function in the graph?

Another way to identify domains and feature sets is with graphs. Domain refers to the set of possible input values, so a chart's domain consists of all input values ​​displayed on the x-axis.

                                    A range is the set of possible output values ​​plotted on the y-axis. To find the domain and domain of the equation y = f(x), find the value of the independent variable x for which the function is defined. 

y = f(x)

according to the graph value of y

 x ≤ 4,

-2≤ y ≤ 2

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Answer: 104%

Step-by-step explanation: 26% times 4 years

Solving the system of equations using matrices is : = -66, y = 163, and z = 11.

To solve this system of equations using matrices, we can write it in the form AX = B, where:

A = coefficient matrix

X = variable matrix (containing x, y, and z)

B = constant matrix (containing the constants on the right-hand side of each equation)

So, we have:

| 2  -1  3 |   | x |   | 180 |

| -4  2  3 | x | y | = | 225 |

| 3  -4  0 |   | z |   | 270 |

We can solve for X by multiplying both sides of the equation by the inverse of A:

X = A^-1 * B

First, we need to find the inverse of A. We can do this by using the formula:

A^-1 = (1 / det(A)) * adj(A)

where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16

| 2  -1  3 |

| -4  2  3 |

| 3  -4  0 |

The cofactor matrix is:

| 2  9  6 |

| 12  0  -2 |

| 13  -9  8 |

Taking the transpose of the cofactor matrix gives us the adjugate of A:

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

So, we have:

A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *

| 2  12  13 |

| 9  0  -9 |

| 6  -2  8 |

Multiplying A^-1 by B gives us:

| x |   | -66 |

| y | = | 163 |

| z |   | 11  |

Therefore, x = -66, y = 163, and z = 11.

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Answer: The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?

Step-by-step explanation:

To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.

Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.

The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.

Answer:

Yasmine estimated the difference to be 82. The actual difference is 81.91.

Step-by-step explanation:

The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.

So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be

(88 - 6) = 82.

The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.

Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.

The equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

The equation of a circle with center (a,b) and radius r is given by the equation:

(x - a)^2 + (y - b)^2 = r^2

Using the given values, the equation of the circle with center (1/2, 0) and radius 2 is:

(x - 1/2)^2 + (y - 0)^2 = 2^2

Expanding and simplifying, we get:

(x - 1/2)^2 + y^2 = 4 - 1/4

Therefore, the equation of the circle is:

(x - 1/2)^2 + y^2 = 15/4

So, the equation of the circle is (x - 1/2)^2 + y^2 = 15/4.

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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to√(0.861(1.0.861)/410) = 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

What is a proportion?

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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Angle A equals 41.81°

c:

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Answer:

B

Step-by-step explanation:

The equation of the function g(x) is g(x) = 1/2x²

If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.

Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).

To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):

[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]

So, we have

a = 1/2

Recall that

g(x) = f(ax)

So, we have

g(x) = f(1/2x)

This means that

g(x) = 1/2x²

Hence. the function is g(x) = 1/2x²

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Step-by-step explanation:

the answer is 115 remainder 1

The correct option is: No. Because the interval does not contain $35, the manager would not be issued the bonus.

An interval refers to a range of values between two points on a numerical scale. It can be represented by two numbers, called endpoints, and includes all the values that lie between these endpoints.

The two common types of intervals are closed intervals and open intervals.

According to the given information:

In a confidence interval, the range of values within which the true population parameter (in this case, the mean amount of money each customer spends per visit) is likely to fall is estimated. A 95% confidence interval means that there is a 95% probability that the true population parameter falls within the interval.

In this case, the confidence interval is ($10.53, $31.89), which means that we are 95% confident that the true mean amount customers spend per visit falls between $10.53 and $31.89. Since the interval does not contain $35, it is not reasonable to believe that the manager will receive a bonus, as the estimated mean amount spent per visit is below $35 according to the confidence interval.

The correct answer is: No. Because the interval does not contain $35, the manager would not be issued the bonus.

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Answer:

k = 10

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ MYZ is an exterior angle of the triangle , then

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

----------------------

Exterior angle of a triangle is equal to the sum of remote interior angles.

In the given picture, the exterior angle is 115°, and remote interior angles are (4k + 5)° and (6k + 10)°.

Set up equation and solve for k:

Therefore the value of k is 10.

The correct answer is: Decrease total assets and net income.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.

When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.

Therefore, the correct answer is: Decrease total assets and net income.

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The option that is true about the equations for these two lines iis that they represent the same lines.

The trick to questions like this is to get both equations into the slope-intercept form.  That is done for our first equation (y = 3x + 5).  However, for the second, some rearranging must be done:

5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5

Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.

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Two lines are described by the equations:

y = 3x + 5 and 5y – 25 = 15x

Which of the following is true about the equations for these two lines?They represent perpendicular lines.

None of the other answers

They represent non-perpendicular, intersecting lines.

They represent the same lines.

They represent parallel lines.

Answer:

28°

Step-by-step explanation:

If the angles are supplementary, they add up to 180°.

(3x) + (2x + 40) = 180

5x + 40 = 180

     - 40   - 40

5x = 140

x = 28°

Answer:

One possible rational function that satisfies the given properties is:

r(x) = (x-2)(x-6) / [(x-3)(x-5)]

Step-by-step explanation:

x-intercepts at (2,0) and (6,0)

The x-intercepts are the points where the function crosses the x-axis, i.e., where the function value is zero. Since we are given that the function has x-intercepts at (2,0) and (6,0), we know that the function can be factored as:

r(x) = A(x-2)(x-6)

where A is a constant that we need to determine.

A hole at x=1 and vertical asymptotes at x=5 and x=3

A hole in a rational function occurs when there are factors in the numerator and denominator that cancel out, leaving a "hole" in the graph. In this case, we are given that there is a hole at x=1, which means that there must be a common factor of (x-1) in both the numerator and denominator. So, we can write:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))

where B is another constant that we need to determine.

We are also given that there are vertical asymptotes at x=5 and x=3, which means that the denominator must have factors of (x-5) and (x-3) that do not cancel out with any factors in the numerator. So, we can write:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5)) = [A(x-2)(x-6)] / [(B(x-1))(x-3)(x-5)]

End behavior given by x → ∞ ,f(x) → 1 and x → -∞ ,f(x) → 1

The end behavior of a rational function is determined by the degree of the numerator and denominator. Since the numerator and denominator in this case have the same degree (3), we know that the end behavior is given by the ratio of the leading coefficients, which is A/B. We are told that the end behavior approaches 1 as x approaches infinity or negative infinity, so we can set A/B = 1 and solve for A in terms of B:

A/B = 1, so A = B

Putting it all together

We now have enough information to write the equation for the rational function with the given properties:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))

Using A = B, we get:

r(x) = A(x-2)(x-6) / [A(x-1)(x-3)(x-5)]

Canceling out the common factor of (x-1) in the numerator and denominator, we get:

r(x) = (x-2)(x-6) / [(x-3)(x-5)]

which is the equation for the desired rational function.

We can say that f(x) has a local maximum at A and a local minimum at B.

A function is a mathematical rule that assigns a unique output value to each input value. It describes the relationship between the input and output variables.

Critical numbers of a function are the values of the independent variable where the derivative is zero or undefined, indicating possible extrema or inflection points.

According to the given information:

To find the critical numbers of the function f(x), we need to find the values of x where f'(x) = 0 or f'(x) is undefined.

f(x) = cos(x) + √2/2

f'(x) = -sin(x)

Setting f'(x) = -sin(x) = 0, we get sin(x) = 0, which is true for x = nπ, where n is an integer. However, we only need to consider the values of x in the interval [0,2].

For n = 0, x = 0 is a critical number.

For n = 1, x = π is a critical number.

For n = 2, x = 2π is not in the interval [0,2], so we don't need to consider it.

Therefore, the critical numbers of f(x) in the interval [0,2] are A = 0 and B = π.

To find the nature of the critical points, we need to find the second derivative of f(x).

f''(x) = -cos(x)

Evaluating f''(x) at A and B, we get:

f''(A) = -cos(0) = -1, which means that f(x) has a local maximum at A.

f''(B) = -cos(π) = 1, which means that f(x) has a local minimum at B.

Therefore, we can say that f(x) has a local maximum at A and a local minimum at B.

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Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Vertex form of a quadratic function:

f(x) = a(x – h)² + k, where a, h, and k are constants.

The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).

(h,k) are the vertex of parabola.

From the given graph:

f(b) is the given function:

Vertex (h,k) = (8, 4)

Thus, h= 8 and k = a = 1, x = b.

Put the values in quadratic function:

f(b) = 1(b – 8)² + 4

f(b) = (b – 8)² + 4

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

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The fraction of Earth that is not made up of ocean = 1/4.

The numbers we are familiar with are whole numbers, such as 1, 2, and so on.

Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.

In essence, a fraction explains how a portion of a group interacts with the entire group.

Given that-

The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water

The fraction of Earth that is not made up of ocean = 1 - 3/4

The fraction of Earth that is not made up of ocean = (4 - 3)/4

The fraction of Earth that is not made up of ocean = 1/4

Thus, the fraction of Earth that is not made up of ocean = 1/4.

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Complete question:

Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?​

Answer:

1

Step-by-step explanation:

1/3 + 8/12 ⬅️(factor out by common factor, 4)

= 1/3 + 2/3

=1+2/ 3

=3/3 or 1