Select the correct answer.
Which expression is equivalent to sin (2x) cos x?

Answer:

Based on the information given, it seems like Messi and Ronaldo were asked to shoot the ball at two targets, target 1 and target 2, and the points they earned would be based on which target they hit.

In Test 1, Messi's first shot followed the equation 3(3x-4) = 24. To determine which target he hit, we need to solve for x. Using algebra, we can simplify the equation to 9x - 12 = 8, and then add 12 to both sides to get 9x = 20. Dividing both sides by 9, we find x = 2.2. Since x represents the number of points earned, this means Messi earned 2.2 points with this shot.

For Messi's second shot, the equation is 6.8 (2.3x + 5.7) = 132.6. To solve for x, we can start by dividing both sides by 6.8 to get 2.3x + 5.7 = 19.5. Subtracting 5.7 from both sides, we find 2.3x = 13.8. Dividing both sides by 2.3, we find x = 6.

In Test 2, Ronaldo's first shot followed the equation (6y-18) = 12. To solve for y, we can add 18 to both sides to get 6y = 30, and then divide both sides by 6 to get y = 5. This means Ronaldo earned 5 points with this shot.

For Ronaldo's second shot, the equation is 8.2 (-5) = -16.4. To solve for y, we need to determine the value of x. Since the equation is just a constant times a negative number, we can simplify it to 8.2 * -5 = -41. This means Ronaldo earned -41 points with this shot.

It's important to note that negative points are not possible in this scenario, as the targets only have positive point values.

Step-by-step explanation:

The population of chickadees in the region is 8,400 and the population of blue jays is 3,600.

percentage, a relative value indicating hundredth parts of any quantity.

First, we can find the population of chickadees by multiplying the population of phoebes by 0.7 (100% - 30%):

Population of chickadees = 0.7 x 12,000 = 8,400

Next, we can find the population of blue jays by multiplying the population of phoebes by 0.3:

Population of blue jays = 0.3 x 12,000 = 3,600

Therefore, the population of chickadees in the region is 8,400 and the population of blue jays is 3,600.

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Answer:

Step-by-step explanation:

The correct answer is C: The vertices always lie on the circle.

In Poincaré's system, an equilateral triangle is a unique type of triangle in which all three sides are equal in length and all three angles are equal to 60 degrees. Since the vertices of an equilateral triangle lie on the circumference of a circle, it can be said that the vertices always lie on the circle.

The other options, A and B, are also true for equilateral triangles in Poincaré's system, but option C is the best answer because it directly addresses the question of where the vertices lie.

In Poincaré's system, a geometric model of non-Euclidean geometry, the vertices of an equilateral triangle are points that lie on the circumference of a circle.

Here's how this can be demonstrated step by step:

Draw a circle with a center point and a circumference.

Choose three points on the circumference of the circle and connect them with lines to form an equilateral triangle.

Measure the angles at each vertex using a protractor or by counting the number of degrees along the circumference of the circle. In an equilateral triangle, all three angles will be equal to 60 degrees.

Measure the sides of the triangle. In an equilateral triangle, all three sides will be equal in length.

Since the vertices of the triangle are points on the circumference of the circle, it can be concluded that the vertices always lie on the circle.

It is important to note that in Poincaré's system, the relationships between the vertices, sides, and angles of a triangle are different from those in Euclidean geometry. However, an equilateral triangle in Poincaré's system still follows the basic definition of an equilateral triangle, with all sides equal in length and all angles equal to 60 degrees.

The f -intercepts and r -intercepts of the function are (0, 180) and (6, 0), (-6, 0),(5, 0)

The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.

Assume that we've got: y = f(x)

At y-axis, we've got x = 0, so putting it will give us the y-intercept.

Thus, y-intercept of y = f(x) is y = f(0)

We are given that;

The function is  f ( r ) = ( r − 6 ) ( r + 3 ) ( r − 1 )

Now,

Substituting r=0 for f -intercept

f(0) = (0-6)(0+6)(0-5)

f(0) = 180

The f-intercept is (0, 180);

Solving for the r-intercepts;

Set the function equal to 0.

0 = (r-6)(r+6)(r-5)

(r-6) = 0

r = 6

(r+6) = 0

r = -6

(r-5) = 0

r = 5

Therefore, the r-intercepts will be (6, 0), (-6, 0), and (5, 0)

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Answer: no

Step-by-step explanation:

the  solution of the given equation will be x =1

What is a System of Equations?

A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.

The given equation x -5 = -4

add +5 in both side we get

x = -4+5

x=1.

Hence the solution of the given equation will be x =1

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The reflected function across the {x} - axis would be -

g(x) = -2/5 (10)ˣ.

If the function f(x) is reflected across the {x} - axis, then the new function g(x) becomes -

g(x) = - f(x)

Given is the function as -

f(x) = 2/5 (10)ˣ

We can write the reflected function as -

g(x) = - f(x)

g(x) = - {2/5 (10)ˣ}

g(x) = -2/5 (10)ˣ

Therefore,  the reflected function across the {x} - axis would be -

g(x) = -2/5 (10)ˣ.

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If the r-value, or correlation coefficient, of a data set is 0.934, the

coefficient of determination to three decimal places is:  A. 0.872.

The coefficient of determination (R-squared) is the square of the correlation coefficient (r) and represents the proportion of the variance in the dependent variable (y) that can be explained by the independent variable (x).

So, to find the coefficient of determination, we need to square the correlation coefficient:

R-squared = r^2

= 0.934^2

= 0.872 (Rounded to three decimal places)

Therefore, the answer is (A) 0.872.

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The graph of the quadratic function y = x² - 5 is given by the image presented at the end of the answer.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function is given as follows:

y = x².

Which is concave up with vertex at the origin.

The translated function is given as follows:

y = x² - 5.

Meaning that the function was translated 5 units down, hence the vertex is at (0,-5) and the roots are plus/minus square root of 5.

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The correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a transformation that maps polygon ABCD to polygon A'B'C'D',

We are asked to select the correct composition of similarity transformations,

According to the graph, there is a scale factor of 1/2 which is smaller than 1,

Also, the polygon is dilating and then reflected.

Hence, the correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

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The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3

a. log(2^100) = 100 log(2) ≈ 30.103

b. log(100^2) = 2 log(100) = 2 log(10^2) = 2 × 2 = 4

c. log(3.0862.062) = log(3.086) + log(2.062) ≈ 0.488 + 0.316 = 0.804

(Note: The multiplication of 3.086 and 2.062 can be done using a calculator.)

d. log(55^(-3.1)) = -3.1 log(55) ≈ -3.1 × 1.740 = -5.394

e. log(5/1) = log(5) - log(1) ≈ 0.699 - 0 = 0.699

f. log(1/5) = log(1) - log(5) ≈ 0 - 0.699 = -0.699

g. log(1/81^2) = log(1) - 2 log(81) = -2 log(9^2) = -2 × 2 log(9) ≈ -2 × 0.954 = -1.908

(Note: We can use the property that log(a^b) = b log(a) to simplify the expression.)

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The values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:

AC² = 3² + 12² {Pythagoras rule}

AC = √(9 +144)

AC = √153

AC = 12.3693

tanα = 12/3 {opposite/adjacent}

α = tan⁻¹(4) {cross multiplication}

α = 75.9638

tanθ = 3/12 {opposite/adjacent}

θ = tan⁻¹(1/4){cross multiplication}

θ = 75.9638

Therefore, the values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.

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Answer:

Step-by-step explanation:

(-4 - 8)/(5 + 1)= -12/6 = -2

Option C

The PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths, without having any tickets left over.

We need to find a number that is divisible by at least 3, but less than 10.

We can start by listing out the multiples of 3 and see which one is closest to 1,932:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

3 × 6 = 18

3 × 7 = 21

3 × 8 = 24

3 × 9 = 27

We can see that the closest multiple of 3 to 1,932 is 1,932 ÷ 3 = 644. This means that if the PTO split the tickets into 644-ticket batches, they would have 3 equal booths of 644 tickets each.

We can check whether 644 is also divisible by 4, 5, 6, 7, 8, or 9, as those numbers are less than 10. We can see that 644 is not divisible by 4 or 5, but it is divisible by 6, 7, 8, and 9. This means that the PTO could also split the tickets into 6, 7, 8, or 9 ticket booths, with each booth having an equal number of tickets.

Therefore, the PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths.

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Using Venn diagram, 49 students participated in only music, 29 students participated in only sports, and 156 students were involved in either music or sports.

Let's use a Venn diagram to represent the information given:

We know that there are 200 students in total, and we can use the information given to fill in the numbers in the Venn diagram.

a.

127 students were involved in music, including 78 who were also involved in sports, so 127 - 78 = 49 students participated in only music.

b.

78 students participated in both music and sports, so 78 - 49 = 29 students participated in only sports.

20 students did not participate in either activity.

c.

The total number of students involved in music or sports is the sum of the number of students in each circle: 49 + 29 + 78 = 156.

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The scale factor of dilation is 4/9

From the question, we have the following parameters that can be used in our computation:

The triangles

Given that the right is the scaled copy of the left

We have the following representation

Scaled factor = Right/Left

Substitute the known values in the above equation, so, we have the following representation

Scaled factor = 4/9

Hence, the scale factor is 4/9

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7x² + 48xy - 7y² is the simplified expression

Polynomial is an equation described as the sum of terms in the form of

k[tex]x^n[/tex].

where,

k and n =  positive integers.

Example:

2x³ + 4x² + 3x + 5 is a polynomial.

We have,

(x + 7y) (7x − y)

Distribute the addition over subtraction.

x (7x - y) + 7y (7x - y)

7x² - xy + 49xy - 7y²

Add like terms.

7x² + 48xy - 7y²

We can not further simplify.

So,

7x² + 48xy - 7y² is the final expression.

Thus,

7x² + 48xy - 7y² is the simplified expression

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The complete question.

Find the product (x+7y) (7x−y)

The student spends x hours tutoring, so y = 15.50x + 35, where x is the number of hours of tutoring and y is the total cost. Therefore, the total cost for a student who receives tutoring for two hours is $66.

According to the dictionary definition, a tutor is a person who provides one-on-one or occasionally small-group teaching. The goal of tutoring is to enable students to help themselves, or to support or mentor them until they reach the point at which they are self-sufficient learners and no longer require a tutor.

Tutors have the ability to, and frequently do, teach students new things. However, when comparing tutoring with teaching, what is being taught  is the main difference. Teachers are meant to teach students new content, and tutors teach students how to learn new content.

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Answer:

Step-by-step explanation:

1. YES

2. NO

3.NO

4. YES

1. This is because only some shoes are new not all of them.\

2. There are some new shoes so it is wrong.

3. Not all of them are new

4. Not every shoe is new because there are some old shoes.

The product of a non-zero rational and an irrational number is always irrational number.

To prove this statement:

Let x be a rational number and y be an irrational number.

Let xy=a.

Let us assume that a is rational.

Since, a is rational it can be expressed as  p/q , where p and q are integers.

Let x= m/n , where m and n are integers.

Now, xy=a

[tex]\frac{my}{n} = \frac{p}{q}[/tex]

On cross multiplying we get,

y = pn/qm​

Now, pn and qm are integers.

Hence, pn/qm is a rational number.

However, y is irrational.

Hence, our assumption is incorrect.

Hence, the product of a non-zero rational and an irrational number is always an Irrational number.

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1,755 cm² icings are needed for one cake.

The correct option is (C).

What is the area of the circle?

The area of a circle is the amount of space enclosed within the circle. It is a measure of the size of the circle, and it is determined by the distance from the center of the circle to its edge (which is the radius). The formula for the area of a circle is:

A = πr²

The surface area of the circular top of the cake can be found using the formula for the area of a circle:

A = πr^2

where A is the area of the circle, and r is the radius. For the red velvet cake, the radius is 13 cm, so the area of the circular top of the cake is:

A = 3.14 x 13^2 = 530.66 cm^2 (rounded to two decimal places)

To find the surface area of the curved side of the cake, we need to find the circumference of the circular base and multiply it by the height of the cake. The circumference can be found using the formula:

C = 2πr

where C is the circumference and r is the radius. For the red velvet cake, the circumference of the circular base is:

C = 2 x 3.14 x 13 = 81.64 cm (rounded to two decimal places)

So, the surface area of the curved side of the cake is:

A = C x h = 81.64 x 15 = 1224.60 cm^2 (rounded to two decimal places)

Therefore, the total surface area of the cake that needs to be iced (excluding the circular bottom) is:

530.66 + 1224.60 = 1755.26 cm^2 (rounded to two decimal places)

Rounding to the nearest square centimeter, we get that approximately 1755 cm^2 of icing is needed for one red velvet cake at the Bisecting Bakery.

Therefore, 1,755 cm² icings are needed for one cake.

The correct option is (C).

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The system of equations defined by the supply and demand models solved for equilibrium price is $9 and equilibrium quantity is 3000 units

Supply:

p=0.003x

x = p/0.003

x = 1/0.003p

Demand:

p= -0.008x+330

-0.008x = p - 330

x = (p - 330)/-0.008

Equilibrium price

Equate supply and demand price

0.003x = -0.008x+330

0.003x + 0.008x = 330

0.011x = 330

x = 330/0.11

x = 3,000

Substitute into

p=0.003x

p = 0.003(3000)

p = $9

Consequently, the equilibrium quantity and price is 3000 units and $9

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Answer:

1

Step-by-step explanation:

f(x) = 3x^3+kx+9, and the remainder when f(x) is divided by x+2 is -17, then what is the value of k=1

Answer:

(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.

(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.

Answer:

(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.

(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.

Answer:

C) 175.

Step-by-step explanation:

Sure, here's a step-by-step solution:

Let's call the number of employees at the agency "x".

If 80% of the employees have more than 12 days of unused sick leave, that means 0.8 * x employees have more than 12 days of unused sick leave.

We know that 0.8 * x = 140, so we can solve for x by dividing both sides of the equation by 0.8:

x = 140 / 0.8

Simplifying, we get:

x = 175

So there are 175 employees who work at the agency, and the answer is C) 175.

The required value of the given expression which satisfy it is b = 3/5.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

We have,

3 - 2(b - 2) = 2 - 7b

= 3 - 2b - 4 = 2 - 7b

= 5b = 3

= b = 3/5

Thus, required value of the b for the given function is b = 3/5.

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Answer:

Step-by-step explanation:

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