Find sin(17π/12) exactly.


I think it has to do something with splitting 17π/12 into π/3 + π/4 + 5π/6 and then using the sin/cos angle sum identities. Though when I tried this, it got complicated really quickly, so I'm not sure if this is the method I should be using.

The coefficient of the equation A = 5.4 x 10⁸ is c = 5.4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the coefficient of the equation be c

A = 5.4 x 10⁸   be equation (1)

On simplifying the equation , we get

Group coefficients together and exponents together to multiply the numbers in the scientific notation

So , A = c x bˣ

where c is the coefficient

Substituting the values in the equation , we get

The value of c = 5.4

Therefore , the value of c is 5.4

Hence , the coefficient is 5.4

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Answer:

False

Step-by-step explanation:

The first value given is the numerator even if its greater than the denominator.

Answer:

[tex]p+166=249[/tex]; [tex]p=83[/tex] pages

Step-by-step explanation:

The number of pages that need to be read plus the 166 pages already read must add to 249.

Answer:

[tex]2m=45[/tex]

Step-by-step explanation:

He earned twice as much washing cars, which is [tex]2m[/tex]. This is given to be equal to 45.

The annual interest rate would have to be about 0.57% in order to earn $1200 in interest in 3.5 years. Rounded to two decimal places, the annual interest rate would have to be about 0.57%.

What is an annual interest rate?

The annual interest rate is the percentage of the principal (the initial amount of money invested or borrowed) that is charged as interest on a loan or earned on an investment over a period of one year. It is used to calculate the amount of interest that will be earned or charged over a given period of time.

To determine the annual interest rate that an account would have to offer in order to earn $1200 in interest in 3.5 years, we need to use the following formula:

rate = (interest / principal) * (1 / time)

Where the rate is the annual interest rate, interest is the amount of interest earned, the principal is the amount of money invested, and time is the length of time in years.

Plugging in the given values, we get:

rate = ($1200 / $60000) * (1 / 3.5)

= 0.02 * (1 / 3.5)

= 0.00571428571

Hence, the annual interest rate would have to be about 0.57% in order to earn $1200 in interest in 3.5 years. Rounded to two decimal places, the annual interest rate would have to be about 0.57%.

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The maximum length or width we can increase so that it will not exceed the capacity of AC  is 100 feet.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

The volume AC can cool, v = 40000 feet³,

The dimensions of the room are 75 feet × 50 feet × 8 feet.,

Calculate the volume of the room as shown below,

Volume = 75 feet × 50 feet × 8 feet

Volume = 30000 feet³

The remaining margin of volume = 40000 - 30000

The remaining margin of volume = 10000 feet³

Thus, the maximum dimension we can increase in length and width is 100 feet.

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The area of the figure having two semicircles and a parallelogram is equal to 173.01 square inches. The correct option is A.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle. The space occupied by the parallelogram in a two-dimensional plane is called the area of the parallelogram.

Given that the radius of the semicircle is 6 inches and the height of the parallelogram is 5 inches.

Calculate the area of two semicircles,

Area = π / 2r² +  π / 2r²

Area = πr²

Area = ( π x 6² )

Area = 113.09 square inches

Calculate the area of a parallelogram,

Area = B x H

Area = 12 x 5

Area = 60 square inches

The total area of the figure,

Total area = 113.09 + 60

Total area = 173.01 square inches

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The possible locations for the walkway bridge are 1, 5, and 6.

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

Given

The function can model a section of a roller coaster:

F(x) = x⁵ - 5x⁴ - 31x³ + 113x² + 282x - 360.

We have to find the possible locations for the walkway bridge.

Now, we factorize the given function

F(x) = x⁵ - 5x⁴ - 31x³ + 113x² + 282x - 360

F(x) = (x-1)(x+3)(x+4)(x-5)(x-6)

then, x - 1 = 0, x+3 = 0, x+4 = 0, x-5 = 0, x-6 = 0

x = 1, -3, -4, 5, 6, becausex>0

s0, x = 1, 5, 6

Hence, the possible locations for the walkway bridge are 1, 5, and 6.

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The best description of the distribution is bimodal with a gap.

Here in the plot, we can see that there are two peaks and it implies that there are two modes.

This can be seen in a histogram as a distinct gap between two cohesive groups of bars. When two clearly separate groups are visible in a histogram, you have a bimodal distribution. Literally, a bimodal distribution has two modes, or two distinct clusters of data

We can see that there is a gap between the two modes. So the best description of the distribution is bimodal with a gap.

The following dot-Plot shows the bimodal with a gap.

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Answer: seth made 3 banana bread and 2 bananas where left over

Step-by-step explanation:

so draw 11 bananas circle three until you are left with less than three

count how many circles have three bananas which is 3 circles

now count how many bananas are not in a circle which is 2

i have adhd so i'm not good at explaining things so yeah hope this helps

:)

a) The deviation from the mean for each term is given as follows:

b) The sum of all deviations obtained in part a is of 378.

The deviation from the mean of each term is given by the absolute value of the difference between each term and the mean.

Hence, for example, the absolute deviation of 27 from the mean of 108 is given as follows:

|27 - 108| = |-81| = 81.

(the absolute value of a number is the number without the signal).

For a number greater than the mean of 108, the deviation of 243 from the mean is given as follows:

|243 - 108| = |135| = 135.

Then the sum of all deviations obtained in part a is given as follows:

81 + 63 + 45 + 0 + 54 + 135 = 378.

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Answer:

A glide.

Step-by-step explanation:

The image is a shift or a glide.

Reflection is either changes the arrow direction the other direction.

A glide reflection is both.

Lauren’s reasoning does not make sense, as the lcm of 2 and 8 is 8.

In this question we have been given Lauren uses a treadmill every 2 days and the weight machines every 8 days.

She used a treadmill on March 2 and will use the weight machines on March 8.

But she says that the first time she will use both a treadmill and the weight machines in March is March 16 because the LCM of 2 and 8 is 16.

First we find and list multiples of each number until the first common multiple is found. And that would be the least common multiple.

Multiples of 2:

2, 4, 6, 8, 10, 12

Multiples of 8:

8, 16, 24

Therefore, LCM(2, 8) = 8 and Lauren is incorrect.

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Answer:

[tex]223093\pi/187500[/tex]

Step-by-step explanation:

[tex]V=\frac{1}{3}\pi r^2 h=(\pi/3)(1.31^2)(2.08)=223093\pi/187500[/tex]

The measure of each of the other two angles is 72° and 36°.

What is vertex angle?

The angle created by two lines or rays intersecting at a location is known as the vertex angle. The sides of the angle are formed by these two rays. In other terms, vertex angle refers to the angle contained within a certain vertex and is expressed in degrees.

let the vertex angle is 36°

the other two angles are equal

let the angle be x

sum of angle in triangle is 180

x + x + 36 = 180

2x = 180 - 36

2x = 144

x = 144/2

x = 72

largest angle is 72°

smallest angle is 36°

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Delilah is baking cupcakes for her brother's birthday party. She has already made 14 cupcakes and is making 2 cupcakes per hour. How many cupcakes will she have in 10 hours? How many hours does it take to make 20 cupcakes?

It would take Laine 20.83 minutes to read 25 pages at the same rate.

Assuming that Laine was able to read 200 pages in 240 minutes at a consistent rate, it would take her 25 minutes to read 25 pages. To figure out how long it would take Laine to read 25 pages, we need to use a proportion.

Let x represent the time it will take Laine to read 25 pages.

200/240 = 25/x

Cross multiply to solve for x:

240x = 5000

Divide both sides by 240:

x = 20.83 minutes

Therefore, it would take Laine 20.83 minutes to read 25 pages at the same rate.

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There are 10240 bacteria after 3 hours.

Initial population = 20

Time period = 3 hours

Time period in minutes = 3 hours x 60 minutes = 180 minutes

Number of doublings = 180 minutes / 20 minutes = 9 doublings

Final population = 20 x 2^9

Final population = 20 x 512

Final population = 10240

Bacteria doubling is the process in which one bacterial cell divides into two identical daughter cells. This process is known as binary fission and is the primary way bacteria reproduce. During this process, a single bacterium first replicates its single chromosome, which is then partitioned into two identical parts. The single cell then divides into two daughter cells, each containing one of the replicated chromosomes. This process is incredibly fast and can occur in as little as twenty minutes.

Bacterial doubling is an important process, as it allows bacteria to rapidly increase in number and spread. In optimal conditions, a single bacterial cell can divide into two daughter cells every twenty minutes, and this can continue for many generations. For this reason, bacteria can quickly become abundant in a given environment and pose a potential threat to human health. Fortunately, antibiotics are often able to help control bacterial doubling and limit the spread of certain bacteria.

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The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.

We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.

According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by

x = (-b +/- √(b² - 4ac)) / (2a)

In this formula, if we add "ax² = y," we obtain

x = (-0 +/- √(0² - 4ay)) / (2a)

which simplifies to

x = √(-4ay) / (2a)

If a = 4, the equation becomes

x = √(-16y) / 8

The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.

The equation has a single solution provided by any other value of a.

x = √(-4ay) / (2a)

For example, if a = 3, the equation becomes

x = √(-12y) / 6

Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.

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Answer:

A.

Step-by-step explanation:

5 x 14 = 70

x^1 x x^7 = 8

y^0 x y^5 = 5

To find the z-score for a given systolic blood pressure reading, we need to use the z-score formula:

z = (x - mu) / sigma

where z is the z-score, x is the raw score, mu is the mean, and sigma is the standard deviation.

In this case, we are given that mu = 121 and sigma = 15. We can use this information to find the z-score for each of the given blood pressure readings:

A. For a blood pressure reading of 142, we have:

z = (142 - 121) / 15

= 21 / 15

= 1.4

Therefore, the z-score for a blood pressure reading of 142 is approximately 1.4, to the nearest tenth.

B. For a blood pressure reading of 130, we have:

z = (130 - 121) / 15

= 9 / 15

= 0.6

Therefore, the z-score for a blood pressure reading of 130 is approximately 0.6, to the nearest tenth.

C. For a blood pressure reading of 103, we have:

z = (103 - 121) / 15

= -18 / 15

= -1.2

Therefore, the z-score for a blood pressure reading of 103 is approximately -1.2, to the nearest tenth.

Answer: 42 parcels total.

each parcel contains 6 tins of beans in each parcel, 4 chocolate bars, and 7 packets of soup.

Answer:

The number of packages is 42.

The contents of each package is 4 chocolate bars, 6 tins of beans, 7 packets of soup.

Step-by-step explanation:

We need to find the greatest common factor (GCF) of the three numbers to find the number of packages.

168 = 2³ × 3 × 7

252 = 2² × 3² × 7

294 = 2 × 3 × 7²

GCF = 2 × 3 × 7 = 42

The number of packages is 42.

168/42 = 4

252/42 = 6

294/42 = 7

The contents of each package is 4 chocolate bars, 6 tins of beans, 7 packets of soup.

The probability that the weight of the box less than 27 kilogram is 0.375

The figure shows the probability distribution shows the weights x, in kilograms, of boxes being shipped from a certain factory.

Then a shipped box is randomly chosen

The probability is the ratio of the number of favorable outcomes to the total number of outcome

The probability = Number of favorable outcomes / Total number of outcomes

Number of possible weights = 8 weights

Number weights less than 27 kilogram = 3

Substitute the value in the equation of probability

The probability = 3/8

Divide the numbers

= 0.375

Therefore, the probability is 0.375

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Therefore, the margin of error for the 90% confidence interval is 1.32. This means that you can be 90% confident that the true population mean falls within a range of 1.32 around the sample mean.

To find the margin of error for a 90% confidence interval, you can use the following formula:

margin of error = z * standard deviation / sqrt(n)

Where z is the z-score for the desired level of confidence (in this case, 90%), standard deviation is the standard deviation of the sample, and n is the sample size (in this case, 120).

Plugging in the values, you get:

margin of error = 1.645 * 9.1 / sqrt(120)

= 1.645 * 9.1 / 11.1

= 14.72 / 11.1

= 1.32

The middle of the set of values is represented by the mean. This value is the mean of all values in the data collection. In statistics, the middle quantity, referred to as the mean, is known as the average.

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No, The two expression you wrote is not true. Because expression are equivalent when values are substituted in for variables. So, both expression gave same answer. Then we can say equivalent expression.

What is expression?

Expression is a finite of symbols that are formed in accordance with dependent rule. It is a number, a variable and combination of variables or symbols. It can be possible by multiply, divide, subtraction and addition.

What is equivalent expression?

Equivalent expression that always work same but look different. When equivalent expression simplified they give same answer. If all the terms in the two expression are identical then we can expression are equivalent.

NOW we have expression

ax +3b

3b+xc

ax+3b=3b+xc

ax=xc

The two expression can only be equivalent if ax=xc it mean that a is equal to c. which is not true. So, they are not equivalent.

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Answer:

Step-by-step explanation:

First, they want you to recall that in a right triangle,  that you know the angle y, because you know two of the angles already.   and you know the total is 180°  around a triangle.  There is a lot you're supposed to remember.   Anyway,  

180 = y + 62+90

180-62-90 = y

28 = y

see??

z =  the same length, as triangle  IHK on the same segment

z= 1

Answer:

y= 1/2x

Step-by-step explanation:

If y is 2 and x is 4

2= 1/2 (4)

2 = 2

The measurement of m∠2 = 47°.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that m∠PQR = 75° and m∠1 = 28°.

From the figure ∠PQS = m∠1 and ∠SQR = m∠2

The angle ∠PQR can be written as the sum of two angles.

∠PQR = ∠PQS + ∠SQR

∠PQR = m∠1 + m∠2

Putting m∠PQR = 75°  and  m∠1 = 28°:

75° = 28° + m∠2

Subtract 28° from both sides:

m∠2 = 75° - 28°

m∠2 = 47°

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Check the picture below.

[tex]\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x[/tex]