what is the maximum possible value of a sine ratio? in two or more complete sentences, explain your answer

The explicit formula for the arithmetic sequence 40, 37, 34, 31 is given as follows:

[tex]a_n = 40 - 3(n - 1)[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the explicit formula presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In the sequence, each term is the previous term subtracted by three, hence the common difference is given as follows:

d = -3.

The first term is of:

[tex]a_1 = 40[/tex]

Hence the explicit formula is given as follows:

[tex]a_n = 40 - 3(n - 1)[/tex]

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The consecutive integers for the two roots are:

17) 14 < √214 < 15

18) 7 < ∛441 < 8

17) First, we want to find two consecutive integers such that √214 lies between them.

To do so, we just need to find two consecutive integers such that when we square them, one is smaller than 214, and the other is larger than 214.

For example:

13*13 = 169

14*14 = 196

15*15 = 225

Now we can see that:

14² < 214 < 15²

If we apply the square root we get:

14 < √214 < 15

Thes are the two integers.

18) Now we want to do the same thing, but this time with:

∛441

This time we need to cube our numbers.

7*7*7 = 343

8*8*8 = 512

These are the two integers such that:

343 < 441 < 512

Now we can apply the cube root to get:

∛343 <∛ 441 < ∛512

7 < ∛441 < 8

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Answer: [tex](x+1)^2+y^2=117[/tex]

Step-by-step explanation:

The radius of the circle is [tex]\sqrt{(-1-(-4))^2 +(\sqrt{108}-0)^2}=\sqrt{117}[/tex].

Using the center-radius form for the equation of a circle, the equation is [tex](x+1)^2+y^2=117[/tex].

Answer:

[tex](x+1)^2+y^2=117[/tex]

Step-by-step explanation:

Equation of the circle: (x - h)² + (y - k)² = r²

(x, y) – any point in the circle

(h, k) – the center of the circle

r – the radius of the circle

(-4, √108) – (x , y)

(-1, 0) – (h, k)

r – ?

[tex](x-h)^2+(y-k)^2=r^2\\\\((-4)-(-1))^2+((\sqrt{108})-(0))^2=r^2\\\\(-4+1)^2+(\sqrt{108}-0 )^2=r^2\\\\(-3)^2+(\sqrt{108} )^2=r^2\\\\9+108=r^2\\\\r^2=117\\\\r^2=9*13\\\\\sqrt{r^2}=\sqrt{9*13} \\\\r=3\sqrt{13}[/tex]

Now that we know what's the r value:

[tex](x - (-1))^2+(y-0)^2=(3\sqrt{13} )^2\\\\(x+1)^2+y^2=9*13\\\\(x+1)^2+y^2=117[/tex]

Answer:

JK = 10 , JL = 14

Step-by-step explanation:

• opposite sides of a parallelogram are congruent

(6)

JK = ML , that is

3x - 2 = x + 6 ( subtract x from both sides )

2x - 2 = 6 ( add 2 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Then

JK = 3x - 2 = 3(4) - 2 = 12 - 2 = 10

• the diagonals of a parallelogram bisect each other

(7)

JL = 2 × JA = 2(2x - 1) = 4x - 2 ( substitute x = 4 )

JL = 4x - 2 = 4(4) - 2 = 16 - 2 = 14

If there are currently 250,000 square miles of rainforest, then number of square miles of rainforest will happen in n years is, f = 250000(0.73)ⁿ

So option B is correct

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

The rainforest is currently decreasing at a rate of 27% per year

There are currently 250,000 square miles of rainforest

The number of square miles of rainforest will happen in n years = ?

The expression for remaining rainforest is,

after 1 year

f = 250000(1 - 0.27)

after 2 year

f = 250000(1 - 0.27)(1 - 0.27)

after 3 year

f = 250000(1 - 0.27)(1 - 0.27)(1 - 0.27)

Similarly

after n year

f = 250000(1 - 0.27)ⁿ

f = 250000(0.73)ⁿ

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On solving the provided question, we can say that the probability that at least two students pick the same integer is = 10/10 = 1

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

here,

number of favorable  outcome = 1,2 ; 2,3; 3,4; 4,5; 5,6; 6,7; 7,8;8,9;9,10; 1,10

number of total outcome = 10

probability = 10/10 = 1

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For given circle value of arc KT will be 147m.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Circumference of circle=2πr

Now,

as for a given circle when the vertex of angle falls outside of circle

then (larger arc-smaller arc/2)=angle

Therefore,  55=(KT-37)/2

KT=110+37

KT=147m

Hence,

              Value of arc KT will be 147m.

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The monomial that completes the expression hence it is the square of a binomial is given as follows:

9p².

The square of a binomial is modeled as follows, considering that the binomial can be either a sum or a subtraction.

The expression for this problem is given as follows:

x - 42pq + 49q².

In which x is the monomial.

Hence the system of equations to obtain the values of the parameters a and b are given as follows:

Hence the parameter b is obtained as follows:

[tex]b = \sqrt{49q^2}[/tex]

b = 7q.

The parameter a is obtained as follows:

2ab = 42pq

14aq = 42pq

14a = 42p

a = 42p/14

a = 3p.

Hence monomial that makes the expression that square of a binomial is given as follows:

a² = (3p)² = 9p².

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P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are if we are unclear about how an event will turn out. Statistics refers to the study of occurrences subject to probability.

According to the question

a) Assuming that X is the random variable that takes the place of the number of defectives and has a normal distribution with a mean of 10 ounces and a standard deviation (σ) of 0.15.

The random variable's values deviate from the mean by 1, causing them to either exceed or fall short of (10 + 0.15) and (10-0.15)

= 10.15 or 9.85.

The following formula may be used to determine the likelihood that there will be either more or lesser defects than the range of 10.15 to 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P [tex](\frac{9.85-10}{0.15} < \frac{X-10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(1) - φ(-1)

Now we calculate the value of z for z = 1 and z = -1; we have: 0.841345 and 0.158655 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.841345 - 0.158655)

P( X < 9.85 or X > 10.15 ) = 0.31713

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

b) It is possible to lower the process standard deviation to 0.05 by making modifications to the process design.

The following formula may be used to determine the likelihood that the number of defectives is either larger than 10.15 or lesser than 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P  [tex](\frac{9.85-10}{0.15} < \frac{X-10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(3) - φ(-3)

Now we calculate the value of z for z = 3 and z = -3; we have: 0.99865 and 0.00135 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.99865 - 0.00135)

P( X < 9.85 or X > 10.15 ) = 0.00271

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

(c) What is the benefit of increasing the number of standard deviations from the mean for process control limits by minimizing process variation?

As we can see from the reduction from a to b above, the key benefit of minimizing process variance is that it will decrease the likelihood of receiving a defective item.

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The volume of the ice cream cone is 100.48 in³.

The volume of the basketball is 267.95 in³.

The volume of the can of corn is 169.56 in³

To find the volume of the ice cream cone, use the formula for the volume of cone, which is given by:

V = (1/3)πr²h

r = 4 in and h = 6 in

V = 1/3 × 3.14 × 4² × 6 = 100.48 in³

To find the volume of the basketball, use the formula for the volume of sphere, which is given by:

V = (4/3)πr³, where r = 4 inches

V = (4/3) × 3.14 × 4³ = 267.95 in³

To find the volume of the can of corn, use the formula for the volume of cylinder, which is given by:

V = πr²h, where r = 3 in and h = 6 in

V =  3.14 × 3² × 6 = 169.56 in³

code: HG DA CF

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Answer:

3[tex]x^{2}[/tex](3+1)

Step-by-step explanation:

The HCF is 3[tex]x^{2}[/tex] hence it will go outside the brackets.

Answer:

3x^2(3+1)

^2 means squared or two to the exponential power.

Step-by-step explanation:

The general solution of the given differential equation is: y = c_1 e^x + (1/x)∫xe^x dx.

A general solution is a comprehensive approach that is applicable to a wide variety of situations and problems. It is usually used to solve complex problems that have multiple variables and factors. General solutions often involve a combination of strategies, techniques, and processes that can be adapted to fit a particular context. In some cases, general solutions may require a combination of both traditional and modern methods. The goal of a general solution is to provide an effective, efficient, and sustainable solution to an issue.

The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution, so the answer is NONE.

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After translating the sentence into an equation using n to represent the unknown number and solving the equation the unknown number is 5.5.

In the given question, we have to translate the sentence into an equation using n to represent the unknown number. Then solve the equation for n. the quotient of a number divided by 11 is 0.5.

Let the number is n. So

n/11 = 0.5

Now solving the expression to find the value of n.

Multiply the 11 on both side, we get

n = 0.5×11

n = 5.5

Hence, the unknown number is 5.5.

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Answer:

h = 6/7

Step-by-step explanation:

h minus four sevenths equals two sevenths

minus means -

equals means =

h - four sevenths = two sevenths

four sevenths means 4/7

two sevenths = 2/7

h - 4/7 = 2/7

add 4/7 to both sides to isolate h

h = 6/7

Answer: h =6/7

Step-by-step explanation: 4/7 + 2/7 = 6/7 so h - 4/7 = 2/7 h = 6/7

The standard error of the mean is approximately for 225 elements with variance of 900 is 1.4847.

In contrast to range and interquartile range, variance is a measure of dispersion that considers the spread of all data points in a data collection. It is the most commonly used measure of dispersion, along with the standard deviation, which is essentially the square root of the variance. The calculations for variance are listed below. Variance can be stated as follows for ungrouped data: Population (Xi X)2N is the variance for a population of size N. The variance is calculated as the total of the squared departures from the mean. The variance of population data is denoted by 2 (read as sigma squared), whereas the variance of sample data is marked by s2.

Here,

For 225 items with a variation of 900, the standard error of the mean is roughly 1.4847.

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Property which represents the one half of the figure exactly same as the rest half of the same figure is known as the line of symmetry.

As given in the question,

Therefore, property used to define the one half of the figure is exactly same as the other half is known as line of symmetry.

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Based on the solution to a system of equations,  with John having four more than twice as many baseball cards as Caleb, and altogether the boys owning 286 baseball cards, Caleb alone has 94.

A system of equations or simultaneous equations is two or more equations solved simultaneously or concurrently.

Let the number of baseballs Caleb owns = c

Let the number of baseball John has = 2c + 4

The total number of baseball = 286

c + 2c + 4 = 286

3c = 282

c = 94

Thus, Caleb has 94 baseballs while John has 192 baseballs.

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The formula for expected value is E(p) = Σ [p(x) * x] where x are the possible values of p and p(x) is the probability of x.

Without the probability distribution of p, it is impossible to determine the expected value of p.

The expected value (also known as the mathematical expectation or mean) of a random variable is a measure of the central tendency of the variable's possible values. The expected value of a discrete random variable p is the sum of the product of each possible value of the variable and its corresponding probability.

To find the expected value of p, you would need to know the probability distribution of the variable, which tells you the likelihood of each possible value of p. The probability distribution would typically be provided in a problem statement, or can be determined through experimentation or survey data.

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The volume of the figure is V = (1/2)xy*h.

The volume of an oblique prism can be found by multiplying the area of its base by its height.

Since the bases of the prism are right triangles, we can use the formula for the area of a right triangle, which is (1/2)base*height.

If we assume that the base is the right triangle with legs x and y, and the height of the prism is h. The volume of the prism can be calculated as:

V = (1/2)xy*h

Note that this formula is valid only if the prism is a right triangular prism and the bases are right triangles, otherwise we would need more information to calculate the volume.

Thus, The volume of the figure is V = (1/2)xy*h.

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Answer:

x=-36

Step-by-step explanation:

To do this we do the inverse of the equaison which is 9×-4 and the answer to that is -36

Answer: slope is 1 or m=1

Step-by-step explanation:

Answer: 55%

Step-by-step explanation:

The question says that Toronto FC lost 12 of 40 games and drew in 15% of the total games they played. To find the percentage of the games they won, you need to subtract the percentage of games they lost and the percentage of games they drew from 1 since all possibilities add up to 1.

% of games won = 1 - (% of games lost + % of games drawn)

First, Toronto FC lost 12 of 40 games. This means that they lost 12/40 of all games, and this can be simplified to be

3/10

Which is 0.3, or 30%.

Now the questions said that Toronto FC drew in 15% of all games, which means that using the equation from earlier, we can find the percentage of games won.

% of games won = 1 - (30%+15%)

= 1-0.45

= 0.55

Therefore, Toronto FC won in 55% of their games.

The probability that at least two dice show 3 in the fraction form will be 1/9.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The total number of events is given as,

Total event = 6 x 6

Total event = 36

The favorable events are given as,

Favorable events = 4 {(1, 1), (1, 2), (2, 1), (2, 2)}

Then the probability that at least two dice show a 3 will be given as,

P = 4 / 36

P = 1/9

The probability that at least two dice show 3 in the fraction form will be 1/9.

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There are many types of functions and each type of function has its own characteristics. This implies that their graph has also its own characteristics.

Based on the graph, the absolute value function has a "V-Shaped" graph.

Every absolute value graph makes a “V”-shaped figure. It consists of two parts: one with a negative slope and one with a positive slope. The point of their intersection is called the vertex. An absolute value graph is symmetrical, meaning that it can be folded in half on its line of symmetry.

An absolute value graph has a distinct V-shape. It is symmetric about the vertical line which passes through its vertex. The vertex of an absolute value function is the point at which the graph changes direction. Since the graph of y=|x-1|+1 changes direction at (1,1), this point is the vertex.

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Answer:

Yes it’s functions, because for each input there is an output.

The value of z at the end of the procedure is 84.

The term procedure in math is defined as a sequence of mathematical operations carried out in order.

Here we have given that if x was 20 and y was 2.

And here we need to find the value of z.

Here let us consider the the equation of z can be written according to the theorem it can be written as,

=> z = 4x + y²

Here we know the values of x and y then the value of z is calculated as,

=> z  = 4(20) + 2²

When we simplify the equation, then we get,

=> z = 80 +  4

=> z = 84.

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Each piece of room or house length and width should be inverted to be scaled. For instance, a rectangle measuring 66" by 7" might be used to depict a dresser that is 5' by 2' at a scale of 14" = 1'.

A table that is 4' by 4' would also be 1" by 1" in size. [7] When measuring furniture that isn't square or rectangular, make the smallest square or rectangle the item might possibly fit and then use those dimensions. For instance, to represent a wingback chair that is 2' 6" wide and 2' deep, use a 5/8" by 1" rectangle.

Next, draw a rough outline of the chair inside the rectangle. On a piece of graph paper that is blank, draw the furnishings. Use graph paper without the room's floor plan drawn on it.

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The correct answer to the given question is an option (C) -the size of the confidence interval increases.

In statistics, the confidence interval for the population means signifies the range in which it could lie at a given confidence level. The confidence interval is usually approximated by using the standard deviation, mean, and sample size of a representative sample drawn from population data.

The margin of error is given by:

= (Z-score * Standard error)

= [tex]\frac{Z -score * Standard deviation}{\sqrt{Sample Size} }[/tex]

Now, the width of a confidence interval is given by:

=(2 * Margin of error)

From the above formulae, it can be inferred that the width of the confidence interval is directly connected to the margin of error, which in turn is directly related to the confidence level or Z-score. Hence, if we change the 95% confidence interval estimate to a 99% confidence interval, the size of the confidence interval will increase.

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The complete question is:

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect:

A. the size of the confidence interval to decrease.

B. the sample size to increase.

C. the size of the confidence interval to increase.

D. the size of the confidence interval to remain the same.

The simple interest for 4 years is Rs 960 and at the end of 4 years, the total amount in the bank account is Rs 2160.

Simple interest is calculated by multiplying the principal amount (initial deposit) by the interest rate and the number of years. In this case, the principal amount is Rs 1200 and the interest rate is 20% per annum (or 0.20) and the number of years is 4.

Simple Interest = Principal x Rate x Time

Simple Interest = 1200 x 0.20 x 4 = 960

So the simple interest for 4 years is Rs 960

To calculate the total amount at the end of 4 years, we add the simple interest to the original deposit.

Total Amount = Principal + Simple Interest

Total Amount = 1200 + 960 = 2160

So, at the end of 4 years, the total amount in the bank account is Rs 2160

Therefore, the simple interest for 4 years is Rs 960 and at the end of 4 years, the total amount in the bank account is Rs 2160.

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Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.

What is radian ?

A radian is a unit of measurement for angles. It is defined as the ratio of the length of an arc of a circle to the radius of that circle. One radian is approximately 57.3 degrees. Radians are often used in mathematics, physics, and engineering because they allow for a more natural way of measuring angles and help simplify certain calculations.

To find the bearing, we can use the formula ,

Bearing = atan2(East, North)

Where East is the number of miles east of the airport and North is the number of miles north of the airport.

The atan2 function is a variation of the arctangent function, which returns the angle (in radians) whose tangent is the quotient of its two arguments. This function is defined for all real arguments and returns a value between -π and π.

So you can convert the bearing from radians to degrees using the formula ,

degrees = bearing * (180/π)

Pilot should take reverse bearing, calculated using atan2(East,North),converted in degrees.

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