. An integer a is said to be a type 0 integer if there exists an integer n such that a3n. An integer a is said to be a type 1 integer if there exists an integer n such that a-3n 1. An integer a is said to be a type 2 integer if there exists an integer m such that a - 3m + 2. * (a) Give examples of at least four different integers that are type 1 integers (b) Give examples of at least four different integers that are type 2 integers (c) By multiplying pairs of integers from the list in Exercise (9a), does it appear that the following statement is true or false? If a and b are both type 1 integers, then a b is a type 1 integer.

Answer:

[tex]x=16y^2-5[/tex]

Step-by-step explanation:

Lets solve for x.

[tex]\frac{\sqrt{x+5} }{4} =y[/tex]

Multiply both sides of the equation by 4.

[tex]\sqrt{x+5}=4y[/tex]

Eliminate the square root on the left side raising both sides of the equation to the power of 2.

[tex]\sqrt{x+5}^2=(4y)^2[/tex]

The square root and the exponent on the left side cancel out leaving us with

[tex]x+5=(4y)^2[/tex]

Distribute the exponent on the right side.

[tex]x+5=4^2y^2[/tex]

Simplify.

[tex]x+5=16y^2[/tex]

Subtract 5 from both sides.

[tex]x=16y^2-5[/tex]

By finding the Greatest Common Factor we can conclude that the possible dimensions of the sports field are a width of 70 yards and a length 9-6d yards.

There are two theories needed to solve the problem:

Dimensions of an object are defined as a measure of length, width, or height extended in a certain direction.

The Greatest Common Factor (GCF) of two or more numbers is the largest number that can be evenly divisible by these numbers.

We can assume that the sports field is a rectangle since we know that:

- the width is at least 50 yards

- the area is (630-420d) yard square

To find the dimension of the sports field, we have to find the GCF of 490 and 210, by enumerating their prime factors and multiplying those factors both numbers have in common.

490 = 2 × 5 × 7 × 7

210 = 2 × 5 × 3 × 7

So the GCF is 2 × 5 × 7 = 70

This GCF depicts one of the dimensions of the sports field, which we denote as d₁.

By substituting the value of one dimension, the value of another dimension (d₂) can be obtained:

Area = d₁ x d₂

d₂ = Area / d₁

    = (630-420d) / 70

    = 9-6d

Thus we can conclude that the possible dimensions of the sports field are width 70 yards and length 9-6d yards.

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Answer:

1, 3, 5, 7 and 19

Step-by-step explanation:

to find the first 4 terms, substitute n = 1, 2, 3, 4 into the rule, then

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 - 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

the first 4 terms are 1, 3, 5, 7

to find the 10th term , substitute n = 10 into the rule

a₁₀ = 2(20) - 1 = 20 - 1 = 19

His pay to play this game per draw is $0.1413

0.015 of an event is a measurement of how likely an event can occur as an outcome of a random experiment.

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.

Given;

Money mark recieves for diamond=$0.45

Money mark recieves for queen=$0.60

Money mark recieves for queen of diamonds=$0.80

Now,

Probability of getting a diamond = 13/52

Price of one heart =$0.45

Pay for one heart = 13/52×0.45=$0.1125

Probability of getting a queen =4/52

Price of one queen =$0.60

Pay for one queen =4/52×$0.60=$0.0115

Probability of getting a queen of diamonds =1/52

Price of one queen =$0.80

Pay for one queen =1/52×$0.80=$0.015

Total pay for one draw= $0.1125+$0.0115+$0.0173=$0.015

=0.1413

Therefore, the pay per draw by probability will be $0.1413

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Answer:

sorry, No answer I have no idea for this

Answer:

Step-by-step explanation:

As you see in the X coloum they have already given you the number for x. So what you do is plug in -2 for x. so it would be 6(-2)+3y=18. it will be -12+3y=18. Put like terms on the same side. Meaning you would add 12 to both sides. it will end up being 3y=30. Divide both sides by 3 so the variable can stay alone and that would mean y=10. So when x=-2, y=10. You can always plus it back in the equation to double check if the answer is right. 6(-2)+3(10)=18. Do the same thing for the remaining ones and youre all set!!! Hope th

If n=2k  (means even value) is always possible to dissect a rectangle into n right triangles.

Dissect means to separate a dead person's or animal's body into its component for closer examination.

Dissect is to consider or talk about the specifics of something in order to fully comprehend it.

To dissect is to separate into components.

For n=2, it is easy to show that it is possible (just insert the diagonal).

For n=3, it is not possible ( I tried on some examples but not able to do it).

For n=4, it is possible first make two rectangle from the original rectangle then use the case of n=2

So if n=2k  (means even) then it is always possible.

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Step-by-step explanation:

5^(2x-1) = 1/125

5^2x = 5/125 => (1/25) = 5^2x

5^-2=5^2x

equating both sides

-2=2x

X=-1

hope this helps you.

There is a 0.2209 = 22.09% probability that three students will arrive during a randomly chosen office hour.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

According to our question-

The number of successes is x.

The Euler number is e = 2.71828.

is the average over the specified range.

When a professor of statistics sets an office hour for student assistance, she discovers that on average, 3.3 students show up.

It follows that

Determine the likelihood that three students will arrive during a randomly chosen office hour.

So, P(X = 3).

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The smaller of the numbers, given the ratio and the larger number, can be found to be 393.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

The ratio is given such that it is 5 : 3 . What this means is that for every 3 of the smaller number, there is 5 of the larger number.

Given that the larger number is 655 therefore, the smaller number would be:

= ( Ratio of smaller number x Larger number ) / Ratio of larger number

Ratio of smaller number = 3

Ratio of larger number = 5

Larger number = 655

The smaller number is:

= ( 3 x 655 ) / 5

= 1, 965 / 5

= 393

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The FG slope is 1/5 and the HJ slope is -2. Because slopes are not connected to one another, they are neither parallel nor perpendicular.

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). A slope is the steepness of a hill. The same is true for a line's steepness. The slope is defined as the ratio of the vertical change between two places, known as the rise, to the horizontal change between those same two points, known as the run.

Here,

F(3, 1), G( 8, 2), H(2, 4), and J(1, 6)

a. FG=2-1/8-3

=1/5

HJ=6-4/1-2

=-2

b. Since slopes are not related to each other it is neither parallel nor perpendicular.

The slope of FG is 1/5 and slope of HJ is -2. Since slopes are not related to each other it is neither parallel nor perpendicular.

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Answer: "-99"

Step-by-step explanation:

You should begin evaluating the given expression from the innermost part.

So, you should find the s(5) firstly. And then, you should use this value for the other function to find r(s(5)).

If you calculate s(5) ==> (-2) * (5)^2 + 1 = -49

This means that the question is asking what is r(-49), indeed.

If you finally calculate r(-49) ==> 2 * (-49) - 1 = -99

The answer is -99.

To calculate the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10, we can use a normal approximation to the binomial distribution.

First, we need to calculate the mean and standard deviation of the proportion of mixed couples in a sample of 200.

The mean is calculated as:

mean = n * p

where n is the sample size (200) and p is the proportion of mixed couples in the population (assumed to be .10).

So: mean = 200 * .10 = 20

The standard deviation is calculated as:

standard deviation = sqrt(n * p * (1-p))

where n is the sample size (200), p is the proportion of mixed couples in the population (assumed to be .10), and sqrt is the square root function.

So: standard deviation = sqrt (200 * .10 * .90) = sqrt (18) = 4.24

We can use the standard normal distribution to calculate this probability. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. We can convert our random variable X to a standard normal variable using the following formula:

Z = (X - mean) / standard deviation

So: Z = (X - 20) / 4.24

To find the probability that X is greater than .10, we can use a standard normal table or calculator to find the probability that Z is greater than (X - 20) / 4.24

This probability is 0.48, so the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than .10 is 48%.

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Answer:

9.68

Step-by-step explanation:

x*(x-4)=55; x approximately equals 9.68

The correct expression for the given error interval is; 12.5 cm ≤ l ≤ 13.4

Error intervals are defined as the limits of accuracy when a number has been rounded or truncated. These error intervals are the range of possible values that a number could have been before it was rounded or truncated.

Now, we can also say that Error interval is the range of values (between the upper and lower bounds) in which the precise value could possibly be.

Now, since the precise value is given as 13 cm after approximation to the nearest centimeter, then the lower bound will be 12.5 because it is the lowest number that can be approximated to 13. Meanwhile the upper bound will be 13.4 cm as it is the largest values that can be approximated to 13 cm. Thus, the inequality is;

12.5 cm ≤ l ≤ 13.4

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The subtraction of the expression 27 g^7 k^3 z^4 - 9 g^2 K^5 z is 18(g⁷k³z⁴ - g²k⁵z)

Algebraic expressions are described as expressions that are known to consist of terms, coefficients, constants, variables and factors.

They are also described as expressions composed of arithmetic operations, such as;

It is also important to note that index forms are mathematical representation of variables or values too large or small in more convenient forms.

From the information given, we have the expression;

27 g^7 k^3 z^4 - 9 g^2 K^5 z

Subtract the coefficient

18(g⁷k³z⁴ - g²k⁵z)

Hence, the value is 18(g⁷k³z⁴ - g²k⁵z)

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(4x + 5) + (2x - 7)

4x + 5 + 2x - 7

6x - 2

The point that is equidistant of the points (7, 3) and (13, -1) is (3.33, -9)

Remember the distance between two points (x₁, y₁) and (x₂, y₂) can be written as:

distance = √( (x₂ - x₁)² + ( y₂ -  y₁)²)

We want to find a point (x, y), that lies on the line y = -9 that is equidistant to  (7, 3) and (13, -1)

We can rewrite our point as (x, -9)

And the distances to the given points are:

distance = √( (x - 7)² + ( -9 - 3)²)

distance = √( (x - 13)² + ( -9 + 1)²)

These distances must be equal, (that is what equidistant means) so we can write:

√( (x - 7)² + ( -9 - 3)²) = √( (x - 13)² + ( -9 + 1)²)

Now we can remove the square root and simplify the equation:

(x - 7)² + ( -9 - 3)² =  (x - 13)² + ( -9 + 1)²

(x - 7)² + 144 = (x - 13)² + 64

x^2 - 14x + 49 + 144 = x^2 - 26x + 169 + 64

-14x + 26x = 169 + 64 - 49 - 144

12x = 40

x = 40/12

x = 3.33

The point is (3.33, -9)

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The height of the tree is 381.05 ft.

The given distance between the man and the tree's base is 220 feet.

Let the tree's height be x feet.

A group of figures known as the trig ratios is characteristic of each angle.

They can be defined when the angle is in a right triangle.

as in this:

Angle's tangent (tan): (opposite leg) divided by (adjacent leg)

Angle's cotangent (cot): (adjacent leg) divided by (opposite leg)

To see the summit of the tree, we must now gaze up at a 60-degree angle.

in the form of a trigonometric ratio,

Tan60= perpendicular/base

√3=x/220 (Tan60 = √3)

x= 220×√3

x= 381.05 ft

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(x^2  - 5x -  14 = 0) has the solution set as F: "x = 7 , -2" .

Solve the equation by factorization method.

x^2 - 5x - 14 = 0

x^2 -  7.x + 2.x - 14 = 0

taking x common from the frist two terms and +2 common from the last two terms.

[ x(x - 7 ) PLUS (+) 2 (x -7) ] = 0

[( x - 7) . (x + 2)] = 0

x - 7 = 0 , &   x + 2  =0

x = 7  , & x = -2

Thus the solution is x = 7 and x = -2.

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If set of ordered pairs (1,8.50) , (3,25.50) , (5,42.50) , (6,51) , (7,59.50) represents cost of tickets for school play , it means that the function that represents the relationship between the number of tickets and the cost for ticket is  [tex]y = 8.5\times x[/tex] .

The Ordered Pairs are given as : (1,8.50) , (3,25.50) , (5,42.50) , (6,51) , (7,59.50) ;

the input represents the number of ticket and

the output represents the total cost of number of tickets ,

So , the domain is = { 1 , 3 , 5 , 6 , 7 } ;

and the range for this function is = {8.50 , 25.50 , 42.50 , 51 , 59.50 } ;

Considering the first pair ,

when the number of ticket is 1 , then the cost is 8.50 ,

for second pair when the number of ticket is 3 , then the cost is 25.50 ;

So , we can say that the cost of 1 ticket is = 8.50 ;

if x represents number of tickets , and y represents the cost for that tickets , then  function that can represent given situation is [tex]y = 8.5\times x[/tex] .

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Suppose X and Y are two random variables that have the same distribution. Does

P[X≤ t∣ Y=a]

be necessarily equal to

P[Y≤ t∣ X=a]?

Note that if X and Y are bivariate normal with correlation ρ and each is marginally N(μ,σ2), then it is necessarily true because both conditional distributions would be

N(μ+ρ(a−μ),(1−ρ2)σ2).

A simple counter example:

P(X=1,Y=2)=13P(X=2,Y=3)=13P(X=3,Y=1)=13

Then P(X≤1|Y=2)=1, but P(Y≤1|X=2)=0.

Because it is interesting to look at the general pattern.

The wanted property is a kind of symmetry,

so we should look for some asymmetrical joint distribution for X,Y).

Si if (X,Y) has a permutable distribution in the sense that (X,Y) and (Y,X) have the same distribution,

so that for the joint cumulative we have F(x ,y)=F(y ,x) for all (x ,y), then the sought-after property will hold.

Let us use copulas. Let F be the joint CDF (cumulative distribution function) and

C(u ,v)=P(F(x)≤ u ,F(Y)≤v)

By the Fréchet– Hoefdding copula bounds (see linked wiki article above) we have

W(u ,v)≤C(u ,v)≤M(u ,v)

where W(u ,v)=max(u+v−1,0) and M(u ,v)=min(u ,v). Both W,M are copulas. W describes the anti-monotonic case X=U,Y…

Not necessarily true. Let X and Y be discrete random variables that take the values in {1, 2, 3} each with probability 13;

i.e. they have a discrete uniform distribution. Consider the joint probability mass function represented by the matrix below where the element in row i and column j is P[X=i , Y=j]:

160⎡⎣⎢331461221154⎤⎦⎥

Note that all rows and columns add up to 13 and therefore the marginal distributions are the discrete uniform as stated. Now calculate the conditional probability

P[X≤2∣Y=1]=360+360360+360+1460=310.

On the other hand,

P[Y≤2∣X=1]=360+660360+660+1160=920.

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Answer:

-9

Step-by-step explanation:

-7x = 63

Divide both sides by -7.

-7x/-7 = 63/-7

Simplify.

x = -9

Follow directions and input only the -9

[tex]-7x=63[/tex]

1. Divide both sides by -7.

[tex]\frac{-7x}{-7} = \frac{63}{-7}[/tex]

[tex]x=-9[/tex]

-9 would be your answer.

Answer:

16x feet

Step-by-step explanation:

A scale of 1/4" = 4' means that every 1/4 inch on the drawing or map represents 4 feet in the actual measurement. To find the actual length of a line on the drawing or map, you need to multiply the length of the line in inches on the drawing by the denominator of the scale, and then divide by the numerator of the scale.

The formula is:

Actual length = (length on the drawing or map x scale denominator) / scale numerator.

In this case, the length on the drawing or map is x inches, and the scale is 1/4" = 4'.

So the actual length is: (x inches x 4') / 1/4" = 16x feet

Therefore, the actual length of the line on the drawing or map is 16x feet.

The length of AD is 70.26.

A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.

The volume of a pyramid with a square base is given as:

Volume = 1/3 x base area x height

We have,

ΔBCD

Tan 33 = BC/BD

0.65 = 37/BD

BD = 37/0.65

BD = 56.92

Now,

ΔABD

Sin 54 = BD/AD

0.81 = 56.92/AD

AD = 56.91/0.81

AD = 70.26

Thus,

The length of AD is 70.26.

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The third side of the right angle triangle is 5 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, using Pythagoras's theorem,

6² - (√11)² = b²

36 - 11 = b²

b² = 25

square root both sides of the equation

b = √25

b = 5 units

Therefore.

third side = 5 units.

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Answer: 126 marbles

Step-by-step explanation:

Let the marbles with Sam be x

so, marbles with Ravi will be 4x

we know total marbles are 630 which means

    x + 4x = 630

      x     =  126

so marbles with Sam & Ravi will be 126 & 504.

To make marbles equal each should have 315 marbles.

So, Ravi has to give 315 - 126 = 189 marbles to Sam.

Answer:

Option 2

Step-by-step explanation:

The data is not periodic, so the model is not is not a trigonometric equation.

Setting [tex]x=0[/tex] eliminates Option 1.

Therefore, Option 2 is the only remaining option

Answer:

d. y = 5x/2 + 1, y = 5x/2 + 7

Step-by-step explanation:

Both lines have the same slope (5/2) , so they are parallel.

The supplied figure's half is tipped downward; therefore, to make them symmetric, we must translate the figure upwards. Anden consider the negative image.

In mathematics, symmetry is the quality of an object being split into two identical, mirrored parts. What does axis of symmetry mean? The term "axis of symmetry" refers to a hypothetical line that can fold or divide an item into two identical mirror halves. If two halves can fit together, then anything is symmetrical. Drawing a mirror line in the center and making sure both halves are the same will allow you to determine the shape's symmetry. To put it another way, symmetry is when two things are facing one another or when two things have mating pieces that revolve about an axis.

The supplied figure's half is tipped downward; therefore, to make them symmetric, we must translate the figure upwards. Anden consider the negative image. We obtain the translational and reflective symmetry.

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