Evaluate 6(2x + 5y) if x = 3 and y = 4

To solve the equation cos²x + sin x = 1, we can use the trigonometric identity cos²x = 1 - sin²x. By substituting this identity into the equation, we get:

1 - sin²x + sin x = 1

Combining like terms, we get:

1 - sin²x = 0

Solving for sin x, we get:

sin x = 1

However, the sine function has a range of [-1, 1], so the only solution in the interval [0, 2π] is sin x = 1, which corresponds to x = π/2. So the solution to the equation cos²x + sin x = 1 in the interval [0, 2π] is x = π/2.

For all n that is higher than or equal to 4, this statement is true.

By taking the cubes of both sides of the inequality, we can demonstrate this.

log2(n3) = [tex]3\sqrt{n}[/tex]

n^(3/2) <= 3 * log2(n) (n)

Since log2(n) > 2 for n >= 4, we can write:

3 * 2 * (log2(n)) = 3 * n where n(3/2) = 3 * log2(n)

This suggests that:

[tex]\sqrt{n} =( \frac{3}{n{log 2}} + n) (n)[/tex]

We come to the conclusion that the square root of n will eventually be less than or equal to log2(n3) for all n higher than or equal to 4 since the right-hand side of this inequality approaches zero as n goes to infinity. The assertion is accurate as a result.

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Answer:

C. it decreases the removal of carbon dioxide from the atmosphere

Answer:

Step-by-step explanation:

it decreases the production of ozone in the atmosphere

The most appropriate approach of probability to determine the probability of having a snow on Christmas is Relative frequency approach or Empirical probability.

The Empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment.

The most appropriate approach of probability to determine the probability of getting a red colour if you play on multicolour roulette is Classical approach of probability.

In classical probability, all the outcomes have equal odds of happening. For example, rolling a dice or tossing a coin. The formula of classical probability is as follows: P(A)= f/N; where, P(A)= classical probability, f= frequency or the number of favourable outcomes and N= Number of total possible outcomes.

The most appropriate approach of probability to determine the probability of Catalonia becoming an independent state is Subjective probability.

Subjective probability is a type of probability derived from an individual's personal judgment or own experience about whether a specific outcome is likely to occur. It contains no formal calculations and only reflects the subject's opinions and past experience.

The most appropriate approach of probability to determine the probability of being involved in a car accident is Relative frequency approach or Empirical probability.

The Empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment.

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The probability that Anthony is on time for work and takes the train is 0.76.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: the probability that Anthony is on time for work is 0.90. the probability that Anthony takes the train to work is 0.80. given that Anthony takes the train to work, the probability that he is on time is 0.95.

We let

A: Anthony being on time for work

B: Anthony will take the train to work

P(A) = 0.9

P(B) = 0.8

P(A/B) = 0.95

P(Anthony is on time for work and takes the train):

P(A∩B) = P(A/B). P(B)

P(A∩B) = 0.95×0.8

P(A∩B) = 0.76

Hence, the probability that Anthony is on time for work and takes the train is 0.76.

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The work required to stretch the spring from its natural length to a distance of 9 inches beyond its natural length is 2.25 lb-ft.

The problem involves calculating the work required to stretch a spring from its natural length to a distance of 9 inches beyond its natural length, given that a force of 192 lb is required to hold the spring stretched 3 ft beyond its natural length.

To solve the problem, we use the formula for the work done by a force that varies with distance, which is given by:

W = (1/2) k (x2^2 - x1^2)

where W is the work done, k is the spring constant, x1 is the initial distance, and x2 is the final distance.

In this case, the initial distance is the natural length of the spring, which is 0 ft, and the final distance is 9/12 ft. To find the spring constant, we use the fact that a force of 192 lb is required to hold the spring stretched 3 ft beyond its natural length, which gives us:

192 = k * 3

Solving for k, we get k = 64 lb/ft.

Substituting the values into the formula, we get:

W = (1/2) * 64 * (9/12)^2

Simplifying, we get:

W = 2.25 lb-ft

This calculation shows how the work done by a force that varies with distance can be calculated using the spring constant and the distances involved.

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Answer: 4.) 9.4 inches, 5.) 12.6 inches

Step-by-step explanation:

4.) So basically one revolution is going around a circle which will be finding the circumference. The equation to finding the circumference is    (2)x(pi)x(radius) so if the diameter is 3 inches then half of that is 1.5 inches which is the radius. Multiply 1.5 times pi and 2 which is 9.4 inches.

5.) Same thing multiply the radius which is 2 times 2 and pi. The answer is 12.6.

[tex]32^5[/tex] - [tex]16^5[/tex] + [tex]2^{19}[/tex] is divisible by 63.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]32^5[/tex] - [tex]16^5[/tex] + [tex]2^{19}[/tex]

= 33554432 - 1048576 + 524288

= 33030144

Now,

33030144 ÷ 63

= 524288

Thus,

It is divisible by 63.

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Answer:-3, 2

Step-by-step explanation:

Step-by-step explanation:

first open the bracket

200+320=520

then multiple the answer with 250

thus: 250×520=130,000

130,000

Step-by-step explanation:

first calculate the bracket 200 + 320 =520

than multiply it by 250. 250 x 520 = 130,000

Histogram 1 is positively skewed, and Histogram 2 is symmetric, which is a true statement about the distributions represented by the histograms.

An illustrated display of data points arranged into user-specified ranges is called a histogram. By taking several data points and organising them into logical ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an easily understood graphic.

Among graphing tools, the histogram is widely used. It is utilised to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

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Answer:

C) Histogram 1 is negatively skewed, and Histogram 2 is positively skewed.

Step-by-step explanation:

When most of the data on a histogram is gathered to the right, then the distribution is negatively skewed. If most of the data is gathered to the left, then the distribution is positively skewed.

Assuming you are going off of these Histograms:

C is the correct answer.

Answer: 22 units²

Step-by-step explanation:

Just count the squares, its faster than breaking this into individual quadrilaterals.

22 squares, so the Area is 22 units²

a) The change in total cost for each book printed is $15.

b) The cost to get started (Before any books are printed) is $110

Overall, understanding the relationship between the number of copies printed and the total cost of publishing a book can help publishers and authors make important financial decisions.

a) The change in total cost for each book printed is represented by the slope of the equation.

In this case, the equation is in slope-intercept form

=> y = mx + b, where m is the slope and b is the y-intercept.

The slope of the equation 15x+1100=y is 15.

This means that for every additional book printed (x), the total cost (y) will increase by $15.

So, the change in total cost for each book printed is $15.

b) The cost to get started, before any books are printed, is represented by the y-intercept of the equation. In this case, the y-intercept is 1100.

This means that the cost to get started, before any books are printed, is $1100.

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The values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.

According to the stem leaf plot the first digit is the stem and the second digit is the leaf.

Hence, the values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.

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Ryan purchased 3 ties and 4 shirts for $500 Earl purchased 6 ties and 7 shirts at the same store for $920.00 then  the total cost of 1 tie and 1 shirt is $153.33.

What is system of equations?

A system of equations is a set of two or more equations that are solved simultaneously to find the values of the variables that satisfy all the equations in the system. The solution of the system is the set of values of the variables that satisfy all the equations. There are different methods to solve a system of equations, such as substitution, elimination, and matrix methods.

Let x be the cost of 1 tie and y be the cost of 1 shirt.

From the problem, we can set up a system of equations:

3x + 4y = 500 (equation 1)

6x + 7y = 920 (equation 2)

To solve for x and y, we can use elimination method. Multiply equation 1 by 2 and subtract it from equation 2:

6x + 7y = 920

(6x + 8y = 1000)

-y = -80

Therefore, y = 80. We can substitute y = 80 into equation 1:

3x + 4(80) = 500

Simplifying the equation, we get:

3x = 220

So, x = 220/3 = 73.33 (rounded to two decimal places).

Therefore, the total cost of 1 tie and 1 shirt is $73.33 + $80 = $153.33.

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A rectangular piece of cardbord has 3D dimensions.

Rectangles are enclosed 2-D shapes with four sides, four corners, and four right angles.Equal and parallel opposite sides make up a rectangle.

The rectangle's properties are listed below:

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For this data, the IQR is a superior measure of variability because it is less than the range. The greatest way to quantify variability is the IQR, and that number is 11.

The interquartile range (IQR) in descriptive statistics is a measurement of statistical dispersion, or the spread of the data. The IQR is also known as the middle 50%, the fourth spread, or the H-spread. The difference between the data's 75th and 25th percentiles is how it is defined.

The median (middle value) of the lower half and upper half of the data should be found first in order to determine the interquartile range (IQR). The quartile 1 (Q1) and quartile 3 values are these (Q3). The IQR is the difference between Q3 and Q1.

From the given stem-and-leaf plot, we can see that the lowest score is 5, and the highest score is 23. Therefore, the range of the data is:

Range = highest value - lowest value = 23 - 5 = 18

We also need to find the quartiles to calculate the IQR. The median (Q2) of the data is 18, which is the value that separates the lower 50% of the scores from the upper 50%. To find Q1 and Q3, we can split the lower and upper halves of the data, respectively, and find their medians.

The lower half of the data is: 5, 10, 13, 17, 18. The median of this half is (13 + 17)/2 = 15.

The upper half of the data is: 24, 26, 28. The median of this half is 26.

Therefore, Q1 = 15 and Q3 = 26, and the IQR is:

IQR = Q3 - Q1 = 26 - 15 = 11.

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Answer:

IQR 18.5

Step-by-step explanation:

I took the test

The probability that at least one component does not function properly when 2 components are randomly selected from 8 is 1/4, or 0.25.

The total number of ways to select 2 components from 8 is:

C(8,2) = 8! / (2! (8-2)!) = 28

Now, let's find the probability that at least one component does not function properly. We can find this probability by subtracting the probability that both components function properly from 1.

The probability that the first component functions properly is 7/8, since there are 7 working components out of 8. The probability that the second component also functions properly, given that the first component does, is 6/7, since there are 6 working components left out of 7. Therefore, the probability that both components function properly is:

(7/8) * (6/7) = 6/8 = 3/4

So the probability that at least one component does not function properly is:

1 - 3/4 = 1/4

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Answer:

2 • (10ab + 35a - 12b2 - 42b)

Step-by-step explanation:

(20ab + 70a - 84b) - (23•3b2)

20ab + 70a - 24b2 - 84b =

2 • (10ab + 35a - 12b2 - 42b)

Answer:

73°

Step-by-step explanation:

Vertical angles are congruent.  They have the same measurement.

Answer:

1.             The volume of the composite figure is 10,164 [tex]cm^3[/tex].

2.            The measure of ∠BCM is 59°.

3.            The area of the given figure is 823.5 [tex]in^2[/tex].

4.            The area of the given figure is 60 [tex]yd^2[/tex].

5.            The area of the following figure is 22.5 [tex]m^2[/tex].

Step-by-step explanation:

1.             In order to make finding the composite figure's volume easier, we can separate the figure into two rectangular prisms, find the volume of each, and add them together. If we make a horizontal cut across the top of the large rectangular prism, we would have two rectangular prisms: One with the dimensions 23 cm × 10 cm × 42 cm, and one with the dimensions 3 cm × 4 cm × 42 cm. Their respective volumes would be 9,660 [tex]cm^3[/tex] and 504 [tex]cm^3[/tex]. Therefore, the composite figure's volume is 9,660 + 504 = 10,164 [tex]cm^3.[/tex]

2.           As ∠BCH and ∠MCD are vertical angles, we can conclude that 4g + 109 = 5g + 106. Based on this information, g is equivalent to 3, meaning both ∠BCH and ∠MCD have an angle measure of 121°. Since both angles form a straight angle with ∠BCM, we know that 121° plus the angle measure of ∠BCM is equivalent to 180°. Therefore, we can conclude that ∠BCM = 180 - 121 = 59°.

3.         In order to make finding the area of the given figure easier, we can split the figure into three shapes: two rectangles and a triangle. The area of the large rectangle is 12 × 54 = 648 [tex]in^2[/tex], the area of the smaller rectangle is 12 × 9 = 108 [tex]in^2[/tex], and the area of the triangle is 15 × 9 × [tex]\frac{1}{2}[/tex] = 67.5 [tex]in^2[/tex]. Therefore, the area of the entire figure would be 648 + 108 + 67.5 = 823.5 [tex]in^2[/tex].

4.         Like questions 1 and 3, we can cut the figure into a triangle, a rectangle, and a parallelogram in order to find the entire area easier. The area of the rectangle is 11 × 4 = 44 [tex]yd^2[/tex], and the area of the triangle is 5 × 4 × [tex]\frac{1}{2}[/tex] = 10 [tex]yd^2[/tex]. As for the parallelogram, it's important to note that in order to find the area of a parallelogram, you only need to multiply the length and the height together as you would for a rectangle. This is because you can cut any parallelogram and reshape it into a rectangle with the same dimensions, therefore the area of the parallelogram would be 3 × 2 = 6 [tex]yd^2[/tex]. Lastly, the area of the entire given figure would be 44 + 10 + 6 = 60 [tex]yd^2[/tex].

5.       Lastly, we are given a triangle and asked to find its area. An important information to keep in mind is that as long as you know a base length and the vertical height to that corresponding side, the formula to calculate the area of a triangle would still be [tex]\frac{1}{2} bh[/tex]. In the given triangle, the base length is 9 meters, and the vertical height is 5 meters. Therefore, the area of the following figure would be 22.5 [tex]m^2[/tex].

Have a great day! Feel free to let me know if you have any more questions :)

The unknown angle in the cyclic quadrilateral is as follows:

m∠B = 121 degrees.

In a cyclic quadrilateral, the sum of a pair of opposite angles is 180° (supplementary). The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's find the angle m∠B in the cyclic quadrilateral.

m∠D = 59 degrees

m∠A = 33 degrees

Therefore,

m∠B = 180 - m∠D

This is because the angle m∠B is opposite to the angle m∠D.

Hence,

m∠B = 180 - 59

m∠B = 121 degrees.

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A regular polygon with an interior angle of 172 degrees has 20 sides.

The formula to find the measure of an interior angle of a regular polygon is:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

Setting the equation equal to 172 and solving for n, we get:

172 = (n-2) x 180 / n

172n = 180n - 360

8n = 360

n = 45

Therefore, the regular polygon has 45 sides, but since the question asks for a regular polygon, all sides must be equal and all interior angles must be congruent. The only regular polygon that satisfies these conditions with an interior angle of 172 degrees is a regular 20-sided polygon.

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Answer:

B

Step-by-step explanation:

the zeros are the values of x on the x- axis where the graph crosses.

the graph crosses the x- axis at x = 3 and x = 6

then

the zeros are x = 3 and x = 6

Answer: Sure, I can help you with that!

Let's assume that the height of the cylinder is h and its radius is r. The volume of the cylinder can be calculated using the formula:

V = πr^2h

Similarly, let's assume that the length, width and height of the cuboid are l, w and h respectively. The volume of the cuboid can be calculated using the formula:

V = lwh

As the volume of the cylinder and the cuboid are the same, we can set the two expressions equal to each other:

πr^2h = lwh

Now, let's assume that the radius of the cylinder is equal to the length of the cuboid (r = l). This means that:

πl^2h = lwh

Solving for h, we get:

h = (πl^2)/w

Finally, substituting the value of h back into the original equation:

πr^2h = πl^2h = lwh

πr^2 = lwh/w = lw

r^2 = lw

r = sqrt(lw)

So, the value of x (the radius of the cylinder) can be found by knowing the length (l) and width (w) of the cuboid. To two decimal places, x = sqrt(lw).

Step-by-step explanation:

This is a probability problem. To find the probability of removing two blue counters, we need to calculate the number of possible outcomes of removing two blue counters out of seven counters (3 blue and 4 yellow).

The number of possible outcomes of removing two blue counters is 3C2 = 3! / (2! * (3-2)!) = 3.

So, the probability of removing two blue counters is 3/7C2 = 3/21.

To find the probability of X being equal to 2, we need to calculate the probability of removing two blue counters.

Therefore, the probability of X being equal to 2 is 3/21.

The area of the aperture storing light is 0.196 [tex]m^{2}[/tex].

Mathematical figures which have a set of pre defined properties are known as shapes. For example, Square shape is a mathematical figure who has four sides and all of them are equal in length and all the four corner of square have an angle of 90 degree. Similarly if there a figure who  has been formed by the help of four lines of equal length but the corners are not 90 degrees then it will be Rhombus and not Square.

Now for the given question:

Diameter of the mirror=50 cm

we convert dia. unit in meter as area is asked in meter.

Dia.= [tex]\frac{50}{100}[/tex]

      = [tex]\frac{1}{2}[/tex]

Area of a circle=π× [tex](\frac{dia}{2} )^{2}[/tex]

               =π×[tex](\frac{1}{4} )^{2}[/tex]

Area= π/16

π=3.14

Area=[tex]\frac{3.14}{16}[/tex]

       = 0.196 [tex]m^{2}[/tex]

Hence area of the aperture is 0.196 [tex]m^{2}[/tex].

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If the measure of <2 is 5 less than 4 times the measure of <1. The measure of angle <1 is 37 degrees, and the measure of angle <2 is   143 degrees. The measure of angle <3 is 55 degrees.

Let's call the measure of angle <1 "x".

From the problem, we know that:

4 times the measure of angle <1 is equal to the measure of angle <2 plus 5:

4x = measure of angle <2 + 5

So the measure of angle <2 is 4x - 5.

Next, we know that the measures of all angles in a triangle must add up to 180 degrees.

Therefore, we have:

x + (4x - 5) + measure of angle <3 = 180

Expanding and simplifying:

5x - 5 + measure of angle <3 = 180

5x + measure of angle <3 = 185

5x = 185

Finally, solving for x:

x = 37

So the measure of angle <1 is 37 degrees, and the measure of angle <2 is 4 * 37 - 5 = 143 degrees. The measure of angle <3 is 185 - 5x = 185 - 5 * 37 = 55 degrees.

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We draw the conclusion that perhaps the actual probability of the die falling on the 4th position is between 0.398 and 0.562, with a 90% confidence level. The die appears to be fair since this contains 0.5.

It is predicated on the probability that something might happen. The concept of probability relies mainly on the justification for probability. A coin is tossed, for instance, and the hypothetical likelihood of receiving a head is 1 in 2.

P(A) = f / N determines probability, which quantifies the possibility of an event happening. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.

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