2. Is the set of rational expressions closed under multiplication? Explain
(p(x)/q(x)) (r(x)/s(x))

The three double-angle identities are :

1.[tex]$\cos(2\theta) = \cos^2\theta - \sin^2\theta$[/tex]

2. [tex]$\sin(2\theta) = 2\sin\theta\cos\theta$[/tex]

3. [tex]$\tan(2\theta) = \frac{2\tan\theta}{1-\tan^2\theta}$[/tex]

The three double angle identities are equations that relate the cosine, sine, and tangent of twice an angle to the cosine, sine, and tangent of the original angle. these identities are useful in trigonometry, as they make it possible to express a double angle in terms of its simpler  angle components.

The first identity states that the cosine of twice an angle is equal to the square of the cosine of the original angle, minus the square of the sine of the original angle. the second identity, states that the sine of twice an angle is equal to twice the product of the sine and cosine of the original angle.

The third  identity states that the tangent of twice an angle is equal to twice the tangent of the original angle, over one minus the square of the tangent of the original angle,

To know more about tangent  refer to the link brainly.com/question/19064965

#SPJ4

Answer:

2

Step-by-step explanation:

p/2-5

You can use PEMDAS to help:

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

So, first we have to substitute 14 for p to get:

14/2-5

Next, comes division before subtraction, so we can rewrite the equation as this:

(14/2)-5

7-5

=2

The measure of angle A to the neasrest degree is 46°.

Th figure in the image is a right triangle.

To solve for angle A, we use trigonometric ratio

Cosine = adjacent / hypotenuse

Plug in the values and solve for A.

cosA = 7.8/11.2

Take the cos inverse

A = cos⁻¹( 7.8/11.2 )

A = 46°

Therefore, angle A is 46 degrees.

Learn more about trigonometric ratio here: brainly.com/question/28016662

#SPJ1

In the triangle QRS, the length of QS is 12 inches

Triangles are a fundamental shape in geometry, and understanding them is critical for many mathematical calculations.

In this case, triangle QRS and XYR are similar triangles, so we can use the ratio of XY to XR to calculate the length of QS.

Mathematically, this ratio can be expressed as:

=> XY / XR = QS / QY.

Thus, if we plug in the values of XY (8 inches) and XR (5 inches) into the equation, we get:

=> 8 / 5 = QS / 12.

We can then solve for QS by multiplying both sides of the equation by 12 and dividing by 8. This gives us the following result:

=> QS = (8 × 12) / 8 = 12 inches.

To know more about triangle here.

https://brainly.com/question/8587906

#SPJ4

A line's slope might be zero, positive, negative, or undefinable. The slope of a horizontal line is zero because it does not climb vertically (y1 y2 = 0), but the slope of a vertical line is unknown because it does not run horizontally (x1 x2 = 0).

The slope (m = 3.5 is positive) and y-intercept (b = 4) of the line y = 3.5x + 4 are both positive. This indicates that the y-intercept, or point (0, 4), is where the line crosses.

A line on a plane with no upward or downward slope is known as a line with zero slope in mathematics and computer science.

To know more about Slope visit:

brainly.com/question/29019604

#SPJ1

The income plainness of demand for eatery reflections is Income plainness = 200/ 20 = 10

Chance is a way of expressing a volume as a bit of 100. It's frequently denoted using the percent symbol(), which represents" per hundred". For illustration, 25 is original to25/100 or0.25 as a numeric.

By question-

The income plainness of demand measures the responsiveness of the volume demanded of a good or service to a change in income, all other effects being equal .However, it means that the good is a normal good, and the volume demanded increases as income increases, If the income plainness is positive. However, it means that the good is an inferior good, and the volume demanded diminishments as income increases, If the income plainness is negative.

In this case, John's pay increased by 20 percent, and the average number of eatery reflections he consumed increased from one a week to three a week. We can calculate the income plainness of demand for eatery reflections as follows

Income plainness = chance change in volume demanded/ chance change in income

The chance change in volume demanded is

( 3 reflections per week- 1 mess per week)/ 1 mess per week) x 100 = 200

The chance change in income is 20

thus, the income plainness of demand for eatery reflections is

Income plainness = 200/ 20 = 10

Since the income plainness is positive and lesser than 1, we can conclude that eatery reflections are a luxury good for John. Option( b) is the correct answer.

To learn more about demand:

https://brainly.com/question/29703449

#SPJ1

Based on an equation, the weight of each train is as follows:

An equation is an algebraic statement of the equality of two or more mathematical expressions.

An equation uses the equation symbol (=) to differentiate it from a mathematical expression that combines values, variables, constants, and numbers with mathematical operands.

The total weight of Train A and Train B = 225 tons

Let the weight of Train B = x tons

Let the weight of Train A = x + 27 tons

2x + 27 = 225

2x = 198

x = 99

Train A = 126 tons (99 + 27)

Train B = 99 tons

Learn more about equations at https://brainly.com/question/2972832.

#SPJ1

I believe the answer is: 83 square inches.

"How so?"

First step:

11 x 5 + 7 x 4 = ?

Now, multiply.

11 x 5 = 55

Multiply once again.

7 x 4 = 28

Now add.

55 + 28 = 83.

I apologize if this is incorrect. I hope you have a lovely day! :)

Answer:

What is the area of this figure?

Step-by-step explanation:

You're welcome.

a. The coordinates after the rotation are: D(-5, 4) → D' (5, -4), E(3, 6) → E'(3, -6), and F(4, 2) → F'(4, -2) b. The general rule below that describes the rotation are: (x, y) → (x, -y).

According to the definition of a transformation in mathematics, a transformation is a geometric shape or formula that has been altered, mapping the shape or formula from its preimage, or initial position, to its image, or after-transformation position. Because transforming a function to a different space offers a fresh viewpoint on the issue, scientists and mathematicians employ transformations to simplify a problem. Scientists frequently shift a function, manipulate it, and then transform it back to its original place because this fresh perspective can make computations easier in the new space than in the old one.

a. The coordinates after the rotation are:

D(-5, 4) → D' (5, -4)

E(3, 6) → E'(3, -6)

F(4, 2) → F'(4, -2)

b. The general rule below that describes the rotation are:

(x, y) → (x, -y)

Learn more about transformation here:

https://brainly.com/question/18065245

#SPJ1

To solve this system of equations by elimination, we need to eliminate one of the variables (either x or y) by adding or subtracting the equations.

In this case, we can eliminate x by multiplying the first equation by 2 and subtracting it from the second equation:

2x - 6y = 12    (original second equation)

-2(x - 3y = 7)  (original first equation multiplied by -2)

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

0x - 12y = -2

Now we have a new equation, 0x - 12y = -2, that relates only to y. Solving for y, we get:

0x - 12y = -2

-12y = -2

y = 1/6

Substituting this value of y back into either of the original equations, we can solve for x:

x - 3y = 7

x - 3(1/6) = 7

x - 1/2 = 7

x = 7 + 1/2

x = 15/2

Therefore, the solution to the system of equations is x = 15/2 and y = 1/6.

To know more about equations:

brainly.com/question/29657983

#SPJ1

Answer:      (-4,-8)

Step-by-step explanation:

The given statement "Two vectors are linearly dependent if and only if they are collinear" is true because one is a scalar multiple of the other.

Two vectors are linearly dependent if and only if one of them is a scalar multiple of the other. This means that if you have two vectors, say v and w, then there exists a scalar c such that v = cw or w = cv.

If v and w are collinear, then they lie on the same line and one is a scalar multiple of the other. Specifically, if v = (a, b) and w = (c, d) are collinear, then there exists a scalar k such that v = kw, which means that a = kc and b = kd.

Conversely, if v and w are linearly dependent, then one is a scalar multiple of the other, which means that they lie on the same line and are collinear.

Learn more about vectors here

brainly.com/question/30326376

#SPJ4

Since the rectangular prism holds exactly 24 unit cubes, the volume of the prism is equal to 24 cubic units.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

Generally speaking, the volume of a rectangular prism is directly proportional to the number of unit cubes. Based on the information provided above, we can reasonably infer and logically deduce that volume of this rectangular prism is equal to 24 cubic units because it holds exactly 24 unit cubes.

Read more on prism here: brainly.com/question/21012007

#SPJ1

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Lets take two points from this line, (4,9) and (2,6).

Method 1: Count the slope

We can use [tex]\frac{rise}{run}[/tex] to count the slope.

Counting the slope, we get [tex]\frac{3}{2}[/tex].

Method 2: Slope formula

We can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex] to calculate the formula.

Lets plug in the coordinates and solve.

[tex]\frac{6-9}{2-4}[/tex]

[tex]\frac{-3}{-2} = \frac{3}{2}[/tex]

The lengths of the missing sides are: y = 7.0 * sqrt(2) and x = 7.0 * sqrt(2)

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

According to the 45-45-90 triangle theorem, the two legs of a 45-45-90 triangle are congruent and the hypotenuse is the square root of 2 times the length of the legs. Therefore, if the side opposite the 45-degree angle is 7, then the other leg is also 7.

Let's label the hypotenuse as h. We know that h is the side opposite the right angle, so h = x. Using the Pythagorean theorem, we can find the length of x:

[tex]x^2 = 7^2 + 7^2x^2 = 98x = sqrt(98) = 7.0 * sqrt(2)[/tex]

So the length of the hypotenuse is 7.0 * sqrt(2).

Now let's find the length of the side opposite the other 45-degree angle, which we'll label as y. Since the two legs are congruent, y is also equal to 7.0 * sqrt(2).

Therefore, the lengths of the missing sides are: y = 7.0 * sqrt(2) and x = 7.0 * sqrt(2)

To learn more about Triangle from given link.

brainly.com/question/30599944

#SPJ1

400kg is equivalent to 881.848 lbs

One of the most common conversions you may need to make is from kilograms (kg) to pounds (lbs). This conversion is important, especially when dealing with weights and measurements in science, engineering, and everyday life. In this article, we will guide you on how to convert 400kg to lbs using a conversion factor.

The first step in converting 400kg to lbs is to understand the relationship between these two units of measurement. A conversion factor is a ratio that expresses the relationship between two different units of measurement. In this case, we will use the conversion factor for kg to lbs.

The conversion factor for kg to lbs is 2.20462. This means that one kilogram is equivalent to 2.20462 pounds. To convert 400kg to lbs, we simply need to multiply 400kg by the conversion factor.

400kg x 2.20462 = 881.848 lbs

In conclusion, converting 400kg to lbs is a straightforward process that can be done by using the appropriate conversion factor. With this knowledge, you can confidently make conversions from kilograms to pounds and vice versa in the future.

To know more about conversion factor here.

https://brainly.com/question/30166433

#SPJ4

The restaurant sold 25 calzones and 21 slices. Our answer as an ordered pair is (25, 21).

To solve this problem, we can use a system of equations. Let x be the number of calzones sold and y be the number of slices sold. We can create two equations based on the information given:

1) x + y = 46 (the total number of calzones and slices sold)

2) 9x + 6y = 351 (the total money collected)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:

y = 46 - x

Now we can substitute this expression for y into the second equation:

9x + 6(46 - x) = 351

Simplifying and solving for x:

9x + 276 - 6x = 351

3x = 75

x = 25

Now we can substitute this value of x back into the first equation to find y:

25 + y = 46

y = 21

So the restaurant sold 25 calzones and 21 slices. Our answer as an ordered pair is (25, 21).

For more information about system of equations, visit:

https://brainly.com/question/13729904

#SPJ11

Answer:

Answer:

Associates=7

Partners=10

Step-by-step explanation:

Let the number of associates be x while partners be y. Since they are a total of 17 then

x+y=17

Therefore, x=17-y

Also considering the charges then

800x+1800y=23600

Subsituting x with 17-y then

800(17-y)+1800y=23600

13600-800y+1800y=23600

1000y=10000

Y=10

X=17-y=17-10=7

THE minimum score required to be in the top 4% of exam scores is 87.08 points, which is option A. To determine the minimum score required to be in the top 4% of exam scores, we can use the standard normal distribution and the Z-score formula.

First, we need to find the Z-score associated with the top 4% of exam scores. The Z-score represents the number of standard deviations above or below the mean a particular value falls. We can use a standard normal distribution table or calculator to find that the Z-score corresponding to the top 4% is approximately 1.75.

Next, we can use the Z-score formula to find the minimum score required to achieve a Z-score of 1.75:

Z = (X - μ) / σ

where X is the minimum score required, μ is the mean of exam scores, and σ is the standard deviation of exam scores.

Rearranging the formula to solve for X, we get:

X = Z {multiply} σ + μ

Plugging in the values we have, we get:

X = 1.75 {multiply}6.1 + 76.4

X = 87.08

Therefore, the minimum score required to be in the top 4% of exam scores is 87.08 points, which is option A.

Note that this assumes that the distribution of exam scores is approximately normal, which is often the case for large samples. If the sample size is small or the distribution is significantly non-normal, this method may not be as accurate.

To know more about normal distribution click here:

brainly.com/question/29509087

#SPJ4

Answer:

Step-by-step explanation: 40% you take the 10 salmon plates and divide it by the 25 specials the restaurant had 10/25=.40

Answer:

means

Step-by-step explanation:

The first term and the fourth term of a proportion are called extreme terms, and the second term and the third term are called means.

The probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have the XBB.1.5 variant is approximately 0.2277 and the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the XBB.1.5 variant is approximately 0.9987.

(a) Let X be the number of people out of 20 who have the XBB.1.5 variant. X follows a binomial distribution with parameters n=20 and p=0.7. We need to find the probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have this specific variant, which can be expressed as P(X ≤ 12).

Using a binomial distribution table or a calculator, we can calculate:

P(X ≤ 12) = ΣP(X=k), for k=0 to 12

P(X ≤ 12) =  0.2277

Therefore, the probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have the XBB.1.5 variant is approximately 0.2277.

(b) Let Y be the number of patients tested until exactly 5 are found to have the XBB.1.5 variant. Y follows a negative binomial distribution with parameters r=5 and p=0.7. We need to find the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the new variant, which can be expressed as P(Y ≥ 8).

Using the negative binomial distribution formula, we can calculate:

P(Y ≥ 8) = ΣP(Y=k), for k=8 to infinity

P(Y ≥ 8) = Σ [(k-1) choose (r-1)] p^r (1-p)^(k-r), for k=8 to infinity

This is a tedious calculation to do by hand, but we can use a calculator or software to find that P(Y ≥ 8) ≈ 0.99872

Therefore, the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the XBB.1.5 variant is approximately 0.9987.

Learn more on binomial distribution here;

https://brainly.com/question/9325204

#SPJ1

Answer: x = -11

Step-by-step explanation:

[tex]\frac{-x+10}{3} = 7[/tex]

⇒-x+10 = 7x3
⇒-x+10 = 21
⇒-x = 21-10
⇒-x = 11
∴ x = -11

It is important to consider scholarships and grants before loans to pay for higher education because Scholarships and grants are free money that do not need to be paid back. That is option A.

Scholarship and grants are defined as payments that are being granted to an individual upon an academic achievement which usually involves a stipulated amount of money.

Scholarship and grants are important due to the following reasons:

Learn more about scholarship here:

https://brainly.com/question/25298192

#SPJ1

The product of -1 and -3/4 is 3/4, and the quotient of -3/4 divided by 1/-3 is 9/4.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

Here are some multiplication and division sentences that make the product and quotient of -3/4:

Multiplication:

-1 × (-3/4) = 3/4

In this multiplication sentence, we're multiplying -1 by -3/4. The product of these two values is 3/4. We can also think of this as "negative times negative is positive" - when we multiply two negative numbers, we get a positive result.

Division:

(-3/4) ÷ (1/-3) = 9/4

In this division sentence, we're dividing -3/4 by 1/-3. To divide by a fraction, we can multiply by its reciprocal. So we can rewrite this as (-3/4) × (-3/1), which simplifies it to 9/4.

So, the product of -1 and -3/4 is 3/4, and the quotient of -3/4 divided by 1/-3 is 9/4.

Learn more about the quotient here:

brainly.com/question/27796160

#SPJ1

Step-by-step explanation:

6 notebooks = $d

1 notebook = $?

So

1 notebook price = $d ÷ 6

Answer:

Step-by-step explanation:

n represents the number of notebooks

d represents the cost of a notebook

n = d            one notebook = d dollars

9n = 9d        multiply both sides by 9

So the probability of getting four cards of the same rank and one other card is approximately 0.00096, or about 1 in 1,040.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. The probability of an event happening can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, the probability of rolling a six on a fair six-sided die is 1/6, because there is only one favorable outcome (rolling a six) out of six possible outcomes (rolling a one, two, three, four, five, or six). Probability theory is widely used in mathematics, statistics, physics, engineering, economics, and many other fields to model and analyze uncertain situations and make predictions based on incomplete or imperfect information. It has many practical applications, such as in insurance, gambling, risk assessment, and scientific research.

Here,

To calculate the probability of getting four of a kind and one other card, we need to count the number of possible hands that satisfy this condition and divide it by the total number of possible hands.

First, we need to count the number of possible hands that contain four of a kind and one other card. There are 13 ranks in a deck of cards, and for each rank, there are 48 ways to choose four cards of that rank and 4 ways to choose one card of another rank (there are 4 cards of each rank in a deck). Therefore, the total number of hands that contain four of a kind and one other card is:

13 x 48 x 4 = 2,496

Next, we need to count the total number of possible hands of five cards that can be chosen from a deck of 52 cards without replacement. This is given by the formula:

52 choose 5 = 2,598,960

Therefore, the probability of getting four of a kind and one other card is:

2,496 / 2,598,960 = 0.00096 (rounded to 5 decimal places)

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

The correct expression that represents the number of bracelets you have after h hours would be:60 = 28 + 5h. option A (28 + 5h  ) is correct.

Based on the given information, the correct expression that represents the number of bracelets you have after h hours would be:

60 = 28 + 5h

This is because you start with 28 bracelets and make 5 bracelets every hour. So after h hours, you would have made 5h bracelets, and the total number of bracelets you have would be:

Total number of bracelets = Starting number of bracelets + Number of bracelets made

Total number of bracelets = 28 + 5h

If you substitute h = 6 into the equation, you can see that after 6 hours, you would have made 5 x 6 = 30 bracelets, and the total number of bracelets you would have is:

for such more question on hours

https://brainly.com/question/10929133

#SPJ4  

Question

You need 60 bracelets for a craft fair. You begin with 28 bracelets and make 5 bracelets each hou a. Choose an expression that represents the number of bracelets you have after h hours.

A. 28 + 5h                                     B. 60 + 28h

C. 60 + 5h                                     D. 5 + 60h

Answer:

Hi! In order to determine which answer is correct, remember that if an ordered pair is a solution of the inequality, then the ordered pair will satisfy the inequality. Let's plug each of these ordered pairs into the inequality.

A. 5, 0

Substitute 5 and 0 for x and y.

[tex]0 > \frac{3}{5} (5) - 2[/tex]

0 > 1 is not true. Therefore, A is NOT correct.

B. 0, -2

Substitute 0 and -2 for x and y.

[tex]-2 > \frac{3}{5} (0) -2[/tex]

-2 > -2 is not true. Therefore, B is NOT correct.

C. 1, 1

Substitute 1 and 1 for x and y.

[tex]1 > \frac{3}{5} (1) - 2[/tex]

1 > [tex]-\frac{7}{5}[/tex] is true. Therefore, C. 1, 1 is CORRECT.

D. -5, -6

Substitute -5 and -6 for x and y.

[tex]-6 > \frac{3}{5} (-5) - 2[/tex]

-6 > -5 is not true. Therefore, D is NOT correct.

Hope this helps!

According to the conversion, 55 kg is equal to approximately 121.25 lbs.

In the world of mathematics, measurement plays a vital role in determining the quantity, weight, and size of any object. The standard units of measurement are different in various countries, and knowing how to convert from one unit to another is essential.

The question posed is, "What is 55 kg in lbs?" Here, 'kg' is a unit of mass, commonly used in the metric system, whereas 'lbs' stands for pounds, which is a unit of weight in the Imperial system. To convert from kg to lbs, we need to multiply the given value by a conversion factor.

1 kg is equal to 2.20462 pounds. Hence, we can use this conversion factor to convert 55 kg to lbs as follows:

55 kg x 2.20462 lbs/kg = 121.2542 lbs (rounded off to two decimal places)

In conclusion, understanding measurements and being able to convert from one unit to another is a fundamental aspect of mathematics. In this case, we used the conversion factor of 2.20462 lbs/kg to convert 55 kg to lbs.

To know more about measurement here.

https://brainly.com/question/4725561

#SPJ4

Answer:

if ur asking who removes the president from office it's the constitution