Use a double-angle identity to find the exact value of each expression. sin 60⁰

Answer:

182,490

      x60

_______

10949400

Answer:

10949400

Step-by-step explanation:

if you break it down into it units you will have 100 thousands, 80 thousands, 2 thousands, 4 hundreds, 9 tens, and 0 ones now if we do 60 times each one of theses uints we would get  6000 thousands, 4800 thousands, 120 thousand, 24 hundreds, 54 tens, and 0 ones add these all together and you would get 10,949,400 :))

The required number of multiplications using a single composite transformation matrix for k transformations of n points is n × k.

In computer graphics, composite transformation matrices are used to transform points and shapes. These matrices are created by combining multiple transformations into a single matrix, allowing for efficient processing of large amounts of data. The number of multiplications required to perform a composite transformation depends on the number of points being transformed and the number of transformations being applied.

If there are n points and k transformations, then the required number of multiplications is n × k.

This is because each point needs to be multiplied by the composite transformation matrix k times.

Therefore, the total number of multiplications is n × k.

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Answer:7.5

Step-by-step explanation:

6*0.25=7.5

The equivalent radian measure of 540° is calculated to be 3π using the relation between degree and radian.

The value of 180° is equivalent to π radian.

π radian= 180°

as we know that

180° = π radian

1° = π/180 radian

540° = 540* π/180

3π radian

therefore, The equivalent radian measure of 540°  is 3π.

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Answer:

d on edge

Step-by-step explanation:

Equations with three variables that are linear. Ax + by + cz = r is referred to as a linear equation in three variables.

A linear equation is one that has the form y=mx+b in algebra. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

equations with three variables that are linear. Ax + by + cz = r is referred to as a linear equation in three variables if all four variables—a, b, c, and r—are real values and not equal to 0.

(The x, y, and z are the "three variables"). The coefficients of the equation are designated by the numerals a, b, and c.

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The value of (x + 4)² will be x² + 8x + 16

The value of (7x + 5y)² will be 49x² + 70xy + 25y²

The value of (4x + 5y)² will be 16x² + 40xy + 25y²

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

The value of (x + 4)² will be:

(x + 4)²

= (x + 4)(x + 4)

= x² + 4x + 4x + 16

= x² + 8x + 16

(7x + 5y)² will be:

= (7x + 5y)(7x + 5y)

= 49x² + 35xy + 35xy + 25y²

= 49x² + 70xy + 25y²

(4x + 5y)² will be:

= (4x + 5y)(4x + 5y)

= 16x² + 20xy + 20xy + 25y²

= 16x² + 40xy + 25y²

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Answer: 30.85%.

Step-by-step explanation:

Let X denotes the score of  random student.

Given: \(\mu = 50\) and \(\sigma=10\)

We assume that scores are normally distributed.

Then , the probability that a a student score higher than 55:

\(P(X>55)=P(\dfrac{X-\mu}{\sigma}>\dfrac{55-50}{10})\\\\=P(Z>0.5) \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.5)\\\\=1-0.6915\ [\text{By p-value table for z}]\\\\= 0.3085\)

Hence, the percent of students have a higher score than hers is 30.85%.

The maximum profit is $5000, which can be achieved by planting 50 acres of corn and 0 acres of wheat.

This is a linear programming problem that can be solved using the simplex method. We can define two decision variables

x1: the number of acres of wheat to be planted

x2: the number of acres of corn to be planted

The objective is to maximize the profit, which can be expressed as

maximize 80x1 + 100x2

The constraints are:

4x1 + 16x2 <= 800 (limit on labor hours)

20x1 + 40x2 <= 2400 (limit on capital)

x1, x2 >= 0 (non-negativity constraint)

We can rewrite the constraints in the form of inequalities:

x2 <= 50 - 0.25x1

x2 <= 60 - 0.5x1

x1, x2 >= 0

The first two constraints are derived by dividing the labor and capital constraints by the respective coefficients of x2 and x1.

The feasible region is bounded by the x-axis, y-axis, and the two lines given by the above inequalities. It is a convex polygon with vertices at (0,0), (0,50), (20,30), and (40,0).

To find the maximum profit, we need to evaluate the objective function at each vertex of the feasible region and choose the one with the highest value. This can be done as follows

At (0,0), the profit is 0.

At (0,50), the profit is 5000.

At (20,30), the profit is 3400.

At (40,0), the profit is 3200.

Therefore, the maximum profit is $5000

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We are given that the expected value of X, the amount in claims collected by a randomly chosen policy holder, is $77, and the standard deviation of X, denoted as O(X), is $57.

To find the standard deviation of Y, O(Y), we use the properties of variances and standard deviations. Firstly, note that Y = 54 + 1.03X. The expected value of Y, E(Y), can be calculated as E(Y) = E(54 + 1.03X) = 54 + 1.03E(X) = 54 + 1.03 * 77 = $135.81.

To find the standard deviation of Y, we use the fact that the standard deviation of a constant times a random variable is equal to the absolute value of the constant multiplied by the standard deviation of the random variable. In this case, we have Y = 54 + 1.03X, so O(Y) = |1.03| * O(X) = 1.03 * $57 = $58.71.

The standard deviation of Y, O(Y), is approximately $58.71. This means that the amount in claims for a randomly chosen new customer can be expected to deviate from the expected value, $135.81, by around $58.71 on average.

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Answer:

Step-by-step explanation:

abc = 1

We have to prove that,

\(\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1\)

We take left hand side of the given equation and solve it,

\(\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}\)

Since, abc = 1,

\(\frac{1}{c}=ab\) and c = \(\frac{1}{ab}\)

By substituting these values in the expression,

\(\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}\)

                                       \(=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}\)

                                       \(=\frac{1+b+ab}{1+b+ab}\)

                                       \(=1\)

Which equal to the right hand side of the equation.

Hence, \(\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1\)

In the given problem, we have to find the value of |2.5a - 36|, where ã = (–4, −8) and ☎ = (–2, −6).

Then, subtract 36 from the obtained value and find its absolute value. Given ã = (–4, −8)and☎

= (–2, −6)

=> 2.5a

= 2.5(–4, −8)

= (–10, −20)|2.5a – 36|

= |(–10, −20) – 36|.

Given ã = (–4, −8)and☎

= (–2, −6)So, to get 2.5a, multiply ã by 2.5:2.5(–4, −8) = (2.5 × –4, 2.5 × −8) = (–10, −20).

Now, subtract 36 from the obtained value of 2.5a. We get:–10 − 36 = −46 and −20 − 36 = −56Thus, we get, |2.5a – 36|

= |-46, -56|

= 2√5 Thus, the answer is 2√5.

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Therefore, the expression that equals 3B - 3C in standard form is -21x² - 6x + 24.

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated or simplified to obtain a single value or another expression. In algebra, expressions are often used to represent mathematical relationships or formulas, and can be manipulated using various algebraic techniques such as factoring, expanding, simplifying, and solving for unknown variables. Expressions are also used in calculus, probability theory, and many other branches of mathematics to describe mathematical models and relationships.

Here,

We can start by substituting the expressions for B and C into the expression for 3B - 3C and simplifying:

3B - 3C = 3(-3x - 7x²) - 3(-x² - 8 - x)

= -9x - 21x² + 3x² + 24 + 3x

= -21x² - 6x + 24

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Answer:

it is when it can make a mathematical statement

The probability that the sample mean will be larger than 49 is approximately c. 0.8554.

To calculate the probability, we need to standardize the sample mean using the formula Z = (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X = 49, μ = 52, σ = 20, and n = 50. Substituting these values into the formula, we get:

Z = (49 - 52) / (20 / √50) ≈ -1.0607

Next, we can use a standard normal distribution table or calculator to find the probability that Z is larger than -1.0607. The corresponding probability is approximately 0.8554.

Therefore, the correct answer is c. 0.8554.

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Answer  -3

Step-by-step explanation:

Answer:

The ones you have chosen are correct

Step-by-step explanation:

:)

The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

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The diameter of the figure is given as 3.1 cm

The diameter of a cylinder is a straight line that passes through the center of the circular base and connects two points on the circumference of the base. It is a measurement that helps determine the size of the cylinder.

The diameter is equal to twice the radius of the cylinder's base. In other words, if the radius of the base is denoted as 'r', then the diameter is equal to 2r.

The length of the line is 3.1 cm

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Answer:

66%

Step-by-step explanation:

The experimental probability of winning 5 or more tickets is 90%

To do this, we simply add the probability values of the bars that have a value of 5 or more

So, we have:

P(x >= 5) = (5 + 8 +17 + 19 + 20 + 21)%

Evaluate the sum

P(x >= 5) = 90%

Hence, the experimental probability of winning 5 or more tickets is 90%

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\(\huge\bold\green{answer}\)

\(\\ \sf\longmapsto \: a( + 2 + 3) + b( - 3 - 1) + c( + 3 - 2) + d( - 4 + 2) \\ \)

\(\\ \sf\longmapsto \: + 5a - 4b + c \: - 2d \: \)

Answer:

=-2a-3b+3c-4d+3a-b-2c+2d

collect like terms

=-2a+3a-3b-b+3c-2c-4d+2d

=a-4b+c-2d

Answer:

22 cm

Step-by-step explanation:

Simply count the number of square units of each side, then add them up. (each square unit = 1 cm)

4+4+2+3+2+7

= 22 cm

Answer:

Step-by-step explanation:

-125/4

-124/4=-31

-31 1/4

The polynomial function f(x)=x²(x+2) in terms of end behavior approaches positive infinity as x approaches positive and negative infinity, the x-intercepts are at x = 0 and x = -2, the y-intercept is at the origin, the zeros are x = 0 (with multiplicity 2) and x = -2, there can be a maximum of 2 turning points.

a) The end behavior of the graph of the function is y approaches positive infinity as x approaches positive infinity and y approaches positive infinity as x approaches negative infinity.

b) The x-intercepts of the graph occur when f(x) = 0, which are x = 0 and x = -2. The y-intercept occurs when x = 0, which is y = 0.

c) The zeros of the function are x = 0 (with multiplicity 2) and x = -2. The lesser zero of multiplicity 2 means the graph touches the x-axis at x = 0. The greater zero of multiplicity 1 means the graph crosses the x-axis at x = -2.

d) The maximum number of turning points on the graph of the function is 2 (a whole number).

e) Graphing the function would require plotting points and connecting them to form the graph, taking into account the x-intercepts, y-intercept, end behavior, and turning points.

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Answer:

56 degrees

Step-by-step explanation:

Hello there!

Remember the sum of the angles in a triangle is equal to 180

so to find the missing angle we subtract the given angles from 180

180 - 34 - 90 = 56

so we can conclude that the measure of the missing angle is 56 degrees

Note: the little square at the bottom left of the triangle indicates that the angle is a right angle. The measure of a right angle is 90 degrees so thats where the 90 came from

Answer:

hope it help you

The number of elements in set A or set B is 14.

Set A contains 3 letters and 3 numbers, for a total of 6 elements. Set B contains 5 letters and 8 numbers, for a total of 13 elements. There is 1 number that is common to both sets, so we need to subtract  1 to avoid double-counting. This gives us a total of 14 elements in set A or set B.

To arrive at this answer, we can use the following steps:

Find the number of elements in set A.

Find the number of elements in set B.

Find the number of elements that are common to both sets.

Subtract the number of elements that are common to both sets from the sum of the number of elements in set A and set B.

The answer is the number of elements in set A or set B.

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Answer:

7/12

Step-by-step explanation:

Total = 10W+14R

probability of red = R/total

10+14 = 24 so total = 24

R = 14

14/24

reduce (divide by two on the top and bottom)

14/2

-------

24/2

= 7/12

Answer:

7 bananas

Step-by-step explanation: