Find all solutions to the equation in the interval [0, 2pi] Enter the solutions in increasing order. cosine of 2x = cosine of x

The value of the cosine of ∠L in triangle LMN is approximately 0.98 using Pythagorean Theorem.

To find the cosine of ∠L in triangle LMN, we first need to use the Pythagorean theorem to find the length of side LM, since only have the lengths of NM and LN:

[tex]LM^2 = LN^2 - NM^2\\LM^2 = 40^2 - 9^2\\LM^2 = 1521[/tex]

[tex]LM = \sqrt{1521}[/tex]

LM = 39

Now that we know the length of all three sides of the triangle, we can use the cosine rule to find the cosine of ∠L:

cos(L) = [tex](LM^2 + LN^2 - NM^2)[/tex] / (2 x LM x LN)

cos(L) = [tex](39^2 + 40^2 - 9^2)[/tex] / (2 x 39 x 40)

cos(L) = 0.975

Rounding to nearest hundredth:

cos(L) = 0.98

Therefore, the value of cosine of ∠L in triangle LMN is approximately 0.98.

The ratio of the neighbouring side to the hypotenuse is known as the cosine of an angle in a right triangle. As L is not a straight angle in this situation, its value must be determined using the cosine method. Whether a triangle is a right triangle or not, the cosine rule can be used to relate the lengths of its sides and angles.

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If every 2 inches of Yolanda's drawing represents 3 feet of the actual wall, we can use the scale factor to convert the dimensions of the drawing to the dimensions of the actual wall.

Since we are dealing with area, we need to square the scale factor.

2 inches : 3 feet

(2 inches / 3 feet)^2 = (2/36)² = 1/324

This means that every square inch of Yolanda's drawing represents 1/324 square feet of the actual wall.

If the area of the mural in Yolanda's drawing is A square inches, then the area of the actual mural is:

A (square inches) x (1/324) (square feet per square inch) = A/324 square feet

Therefore, to find the area of the actual mural in square feet, we need to first find the area of the mural in Yolanda's drawing and then divide by 324.

If the area of the mural in Yolanda's drawing is, for example, 500 square inches, then the area of the actual mural is:

500 (square inches) / 324 = 1.54 square feet (rounded to two decimal places)

Therefore, the area of the actual mural is 1.54 square feet.

[tex] \: \: [/tex]

Answer:

3200

Step-by-step explanation:

If we know the fact that :
1GB = 1000MB
We can form an equation to show that 16000MB divided by 5MB should give you your answer.
The answer you get is 3200.
This means that you can fit 3200 5 MB files into a 16GB flash drive.
Hoped this helped,
thank you

The calculated value of the surface area of the sphere is  676π

Given that

Radius, r = 13 inches

The formula for the surface area of a sphere is:

Surface area = 4πr^2

where r is the radius of the sphere

Substituting the given value of radius r = 13 inches, we get:

Surface area = 4π * 13^2

So, we have

Surface area = 676π

Hence, the surface area is 676π

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The number of different ways in which no song is liked by all three and there is at least one song liked by those two girls but disliked by the third is (b) 132 ways.

Let the song that is liked by Amy and Beth (but not Jo), Beth and Jo (but not Amy), and Amy and Jo (but not Beth), be denoted as : AB, BJ, and AJ.

Similarly, let the letters "A, B, J, and N" denote the song that is liked by only Amy, only Beth, only Jo, and none of them, respectively.

We know that there is at least 1 AB, BJ, and AJ, there must be 3 songs out of 4 songs which Amy, Beth, and Jo listened to.

The fourth song can be of any type : N, A, B, J, AB, BJ, and AJ (there is no ABJ because "no-song" is liked by all three),

So, we must find the number of ways to rearrange AB, BJ, AJ and a song from the set {N, A, B, J, AB, BJ, AJ}.

⇒ Case 1: Fourth song choices = N, A, B, J

All the four of choices for fourth song are different from the first 3 songs.

⇒ Number of ways to rearrange = 4! × 4 choices = 96.

⇒ Case 2: Fourth song choices = AB, BJ, AJ

All 3 of choices for fourth song repeat in the first three songs.

So, Number of ways to rearrange = (4!/2!) × 3 = 36,

So, total number of ways = 96 + 36 = 132.

Therefore, the required number of ways of arrangement is 132 ways, the correct option is (b).

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The given question is incomplete, the complete question is

Amy, Beth, and Jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. in how many different ways is this possible?

(a) 108

(b) 132

(c) 671

(d) 846

(e) 1105

To get from the number of eggs used to make a certain number of cookies to the number of eggs needed to make some other number of cookies, you would use a proportional relationship.

Let's say x represents the number of eggs used to make a certain number of cookies, y represents the number of cookies made, and z represents the number of eggs needed to make some other number of cookies.

Then, we can set up the proportion:

x eggs / y cookies = z eggs / (some other number of cookies)

We can then solve for z by cross-multiplying:

z eggs = x eggs * (some other number of cookies) / y cookies

This formula tells us how many eggs are needed to make the specified number of cookies, based on the number of eggs used and the number of cookies originally made.

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Answer:

Step-by-step explanation:

Answer:Radius = 21

Step-by-step explanation:

Volume of a sphere = 4/3 * pie * radius^3

12,348 pie = 4/3 * pie  radius ^3

12,348 = 4/3 * radius^3

(12,348 * 3)/ 4 = radius^3

9261 = radius^3

radius = 21

One real-world situation that could be modeled by the arithmetic sequence f(n) = 100 + 25n, for n ≥ 1, is the cost of a monthly subscription service for an online course.

An arithmetic sequence is a sequence of numbers where each term is found by adding or subtracting a constant value from the previous term. The constant value is called the common difference and determines the rate at which the sequence increases or decreases.

One real-world situation that could be modeled by the arithmetic sequence f(n) = 100 + 25n, for n ≥ 1, is the cost of a monthly subscription service for an online course.

Assuming that the initial cost of the service is $100 and the subscription fee increases by $25 every month, then the formula

=> f(n) = 100 + 25n

It can be used to calculate the cost of the subscription for any given month n.

For example, the cost of the subscription for the 5th month would be

f(5) = 100 + 25(5) = $225.

Similarly, the cost of the subscription for the 10th month would be

f(10) = 100 + 25(10) = $350.

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If the cost to fill a gas tank in 1995 is $15 then the cost to fill a gas tank in 2015 is equals to the $31.25.

Price Index is a effective method of comparing relative change in the price of a quantity with respect to its price in a reference year. This year which we use as a reference is called the base year and price index is ratio of the price of a product in a year to its price in the base year ( expressed in percentage ).

The cost to fill a gas tank in 1995 = $15

Price index in 1995 = 100.8%

price index in 2015 = 210.0%

In this case we want to determine the cost to fill a gas tank in 2015. Let the required cost value be x dolars. Using the formula, price index in 1995/price index in 2015 = reference value/ value in 2015

=> 100.8% /210% = 15/x

=> 2015 cost value, x =( 15 × 210 )/100.8

=> x = 3150/100.8

=> x = 31.25

Hence, required value is $31.25.

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Complete question:

If it cost $15 to fill a gas tank in 1995, how much would it cost to fill the same tank in 2015. 1995 index is 100.8%

2015 index is 210.0% round your answer nearest cent.

You can get a sense of what laptops are available, which brands are well-liked, and what specifications are shared by various models by looking through these three stores.

Amazon:

Go to Amazon's homepage and hover over the “Electronics” category in the top menu bar.

Click on “Computers & Accessories” in the dropdown menu.

Under “Laptops,” you can browse through the different categories such as “

2-in-1 Laptops," "Traditional Laptops," and "Gaming Laptops."

You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.

Best Buy:

Go to Best Buy's homepage and click on "Laptops & Computers" in the top menu bar.

You can browse through the different categories such as "Laptops," "Gaming PCs," and “Chromebooks.”

You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.

Dell:

Go to Dell's homepage and click on “Laptops & 2-in-1 PCs" in the top menu bar.

You can browse through the different categories such as "Consumer Laptops," "Gaming Laptops," and "Mobile Workstations.”

You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.

Therefore, By browsing through these three retailers, you can get an idea of what laptops are available, what brands are popular, and what features and specs are common across different models.

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Answer:

A

Step-by-step explanation:

A has a positive slope

Option A is the answer. The system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:

8c + 6v ≤ 70

8c + 6v ≤ 7016c + 20v ≥ 150

The cost of c gallons of chocolate ice cream is $8c, and the cost of v containers of vanilla ice cream is $6v. Krystal wants to spend no more than $70 on ice cream, so the inequality for the total cost of ice cream is:

8c + 6v ≤ 70

Krystal needs at least 150 servings of ice cream, and each gallon of chocolate ice cream provides 16 servings, while each container of vanilla ice cream provides 20 servings. The inequality for the total number of servings of ice cream is:

16c + 20v ≥ 150

Therefore, the system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:

8c + 6v ≤ 70

16c + 20v ≥ 150

Option A is the correct answer.

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The percentage increase/decrease of the DJIA over the week is a decrease of 6.53%.

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%".

A decreased percentage refers to the amount or rate by which a quantity or value has decreased from its original or initial value, expressed as a percentage of the original value.

According to given information:

To find the percentage increase/decrease of the DJIA over the week, we need to calculate the overall change in the index and express it as a percentage of the initial value.

Let's assume that the DJIA started the week at a value of 100. Then, the following changes would occur:

On Monday, it went down by 3.2%, so its value decreased to 96.8.

On Tuesday, it went up by 11.2%, so its value increased by 11.2% of 96.8, or 10.82, to reach 107.62.

On Wednesday, it went up by 0.7%, so its value increased by 0.7% of 107.62, or 0.75, to reach 108.37.

On Thursday, it went down by 4.8%, so its value decreased by 4.8% of 108.37, or 5.20, to reach 103.17.

On Friday, it went down by 9.4%, so its value decreased by 9.4% of 103.17, or 9.70, to reach 93.47.

Therefore, over the week, the DJIA decreased by 6.53% (from 100 to 93.47).

Rounding this to the nearest hundredth of a percentage, we get a decrease of 6.53%.

So, the percentage increase/decrease of the DJIA over the week is a decrease of 6.53%.

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Thus, the perimeter of the regular nonagon with centre O is found as: 78.57 units.

A closed, 2D structure with a finite number of line segments is referred to as a polygon. A polygon's number of vertices and its number of line segments are always identical. The perimeter of a closed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides.

P = (Side length) x n

The apothem of each of the 9 isosceles triangles that make up the regular nonagon is 12 cm.

The angle at the circle's centre is 360/9 = 40º.

Hence, the sides of the regular nonagon, if the apothem of a isosceles triangles is 12 cm.

2*12 tan (40/2) = 8.73 cm

Then the perimeter:

P = 9 x 8.73

P = 78.57 units

Thus, the perimeter of the regular nonagon with centre O is found as: 78.57 units.

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The probability of selecting three red balls or having three successes when drawing balls from the urn is 0.045, which is equivalent to 4.5%.

The probability of three successes can be calculated using the binomial probability distribution formula. Since there are only two outcomes for each ball drawn (success or failure), and the trials are independent, the binomial distribution applies.

The probability of drawing a red ball on the first attempt is 5/12. Since the ball is not replaced, the probability of drawing a red ball on the second attempt is 4/11. Similarly, the probability of drawing a red ball on the third attempt is 3/10.

To obtain the probability of three successes, we need to multiply these probabilities together:

P(three successes) = (5/12) x (4/11) x (3/10)

P(three successes) = 0.04545 or approximately 0.045

Therefore, the probability of drawing three red balls or three successes from the urn is 0.045 or 4.5%. This means that out of every 100 sets of three balls drawn, we can expect to get three red balls in approximately 4-5 sets.

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According to given information, the algebraic expression that represents the total number of quarters that Jake and Molly have is: 32 + q.

What is algebraic expression?

An algebraic expression is a mathematical phrase that contains numbers, variables, and arithmetic operations, such as addition, subtraction, multiplication, and division. It can also include exponents, roots, and other mathematical symbols.

The algebraic expression that represents the total number of quarters that Jake and Molly have is:

32 + q

where 32 represents the number of quarters that Jake has on his desk and q represents the number of quarters that Molly has in her purse.

Adding these two quantities together gives the total number of quarters that Jake and Molly have.

Therefore, the algebraic expression that represents the total number of quarters that Jake and Molly have is:

32 + q

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Based on the given frequency table, it takes between 150 and 160 minutes to fly from Denver to Atlanta on Delta Airlines for 25 out of 56 observations.

The table provides frequency data on flight times (in minutes) for the first week of March 2005 from Denver to Atlanta on Delta Airlines. The frequency table shows that there were 25 flights with a duration between 150 and 160 minutes, which is the most frequent flight duration. The flight times ranged from 140 to 190 minutes.

The frequency data can be used to construct a histogram that displays the distribution of flight times for the Denver to Atlanta route. The histogram can provide further insights into the distribution of flight times, such as whether the distribution is symmetric or skewed, and the location and spread of the data.

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--The complete question is, how long does it take to fly from denver to atlanta on delta airlines? the table below shows 56 observations on flight times (in minutes) for the first week of march 2005.

FROM      TO           FREQ

140         150            1

150         160            25

160         170            24

170         180            4

180         190            2--

Check the picture below.

so the center of the circle is the midpoint of that diameter, and its radius is half its length.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 -2}{2}~~~ ,~~~ \cfrac{ 7 -1}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 6 }{2} \right)\implies \stackrel{ center }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ r(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~4 - (-2)~~)^2 + (~~7 - (-1)~~)^2} \implies r=\sqrt{(4 +2)^2 + (7 +1)^2} \\\\\\ r=\sqrt{( 6 )^2 + ( 8 )^2} \implies r=\sqrt{ 36 + 64 } \implies r=\sqrt{ 100 }\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{3}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-3 ~~ )^2~~ = ~~10^2\implies {\large \begin{array}{llll} (x-1)^2+(y-3)=100 \end{array}}[/tex]

Answer:

A) Jeremy has the greater speed.  

B) y = 23x

C)  See graph

D) The slope is 23.  This means that Lauren can travel 23 miles in 1 hour.

Step-by-step explanation:

Part A:

Kevin's rate is 11.5 miles per hour.

Take two points, I used (2,23) and (4,46) to find the rate for Kevin.

Find the change in y over the change in x.  The y values are 46 and 23.  The x values are 4 and 2.  You find the change by subtracting

[tex]\frac{46-23}{4-2}[/tex] = [tex]\frac{23}{2}[/tex] = 11.5

Part B:

If Kevin's rate is 11.5, then Lauren's rate is 23

Part C:

See graph

 Part D :  

  The slope for C is 23.  This means that Lauren can ride 23 miles in one hour.

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The measure of angle y is 32°.

To find the measure of angle y, follow these steps:
1. Since the exterior angle to angle x is w, and w measures 100°, we can use the fact that the sum of an interior angle and its corresponding exterior angle is 180°.

So, angle x = 180° - 100° = 80°.
2. Now we know that a triangle has angles x, y, and z.

The sum of angles in a triangle is always 180°.

We have x = 80° and z = 68°,

so we can find angle y as follows:

y = 180° - (80° + 68°)

= 180° - 148°

= 32°.

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Answer:

4÷2=2

12÷2=6

6÷3=3

45÷9 =5

Step-by-step explanation:

48% of the people polled like playing golf.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

The percentage of people polled who like playing golf can be calculated by dividing the number of people who like golf (3,360) by the total number of people polled (3,360 + 3,640 = 7,000) and then multiplying by 100 to express the answer as a percentage:

(3360 ÷ 7000) x 100% = 48%

Therefore, 48% of the people polled like playing golf.

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The better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.

Everything in surveys revolves around asking the appropriate questions in the right ways since they are meant to elicit feedback. Many polls purposefully and unintentionally ask one-sided questions.

An objective question attempts to avoid using leading language and is fact-based rather than judgmental.

Biased questionnaire items use word choice and sentence structure in a way that affects how respondents react. This is sometimes done on purpose. This usually happens as a result of inadequate survey planning and assessment.

Here are a few advices.

Given query:

Thus, the better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.

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The association on the line is a negative linear assosciation and other solutions are shown below

To find the slope of the line passing through the given points, we use the slope formula

slope = (change in y) / (change in x)

Let's use the points (0, 90) and (8, 40) to find the slope:

slope = (40 - 90) / (8 - 0) = -50 / 8 = -6.25

The y-intercept is 90 i,e, when x = 0

The equation is represented as

y = mx + c

Where

m = slope and c = y when x = 0

So, we have

y = -6.25x + 90

The association on the line is a negative linear assosciation

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