3x − (2x² +1 − 8x) − (3x − 2x² + 7)

When Julie divides 98.6 by 12 , So by the rules of significant figures , the number that Julie should write down is  8.3  .

What are Significant Figures ?

The Significant figures can be defined as number of digits in a value, that is often a measurement, which contribute to degree of accuracy of value. The significant figures is counted from first non zero digit .

The Rule of Significant figures says that , when a number "a" that have 3 significant figures is divided by number "b" having 2 significant figures , then the quotient will have the minimum of the two significant figure that is 2 .

Here 98.6 is divided by 12 ,

the number 98.6 has 3 significant figures ; the number 12 has 2 significant figures ,

So , the result can have maximum of 2 significant figures ,

On dividing 98.6 by 12 , we get the result as 8.2166666..  ;

since the result can have at most 2 sig. figure , So , the result is 8.3 .

Therefore , Julie should write down 8.3   .

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1 is the quantity cosine of x to the power of two plus sine of x to the power of two divided by quantity cotangent of x to the power of two minus cosecant of x to the power of two

The given expression is as follows

(cos^2(x) + sin^2(x))/(cot^2(x) - csc^2(x))

This expression is equal to 1, because of the identity cos^2(x) + sin^2(x) = 1.

Cosecant is the reciprocal of sine, so csc^2(x) = 1/sin^2(x)

Cotangent is the reciprocal of tan, so cot^2(x) = 1/tan^2(x)

As tan^2(x) = sec^2(x) - 1, we can write the expression as:

1/(1/sin^2(x) - (sec^2(x) - 1))

Further on  simplifying this using the identity sec^2(x) = 1/cos^2(x) we get:

1/(1/sin^2(x) - (1/cos^2(x) - 1))

The denominator is now:

1/((sin^2(x) - cos^2(x))/cos^2(x)sin^2(x))

on Using the identity sin^2(x) + cos^2(x) = 1 we can simplify this as:

1/(cos^2(x)sin^2(x))

Canceling out the sin^2(x) and cos^2(x) we get 1

therefore  the final answer is 1.

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The artist should divide the region with vertical lines at x1 = 0.5000, x2 = 0.7500 and x3 = 1.0000 to get 3 pieces with equal areas.

Let the length of the region be l. Then, the area of the region = l x l = l^2

To divide the region into 3 equal areas, let the 3 divisions be at x1, x2, and x3 such that x1 < x2 < x3.

Then, the area of each division = (x2-x1) x l = l x (x2-x1) = l^2/3

Therefore,

l x (x2-x1) = l^2/3

or, x2 - x1 = l/3

Using this equation, we can find the values of x1, x2, and x3 that divide the region into 3 equal areas:

x1 = 0, x2 = l/3 and x3 = 2l/3

Therefore, for the given region, the artist should divide it with vertical lines at x1 = 0.5000, x2 = 0.7500 and x3 = 1.0000 to get 3 pieces with equal areas.

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Answer: For the first geometric sequence, the missing value is:

1 = -3/2, -2 = 7

To find the missing value, we can use the formula:

an = ar^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

So we know that:

a1 = 1, r = -3/2, n = 3

Plugging these values into the formula:

an = ar^(n-1)

an = 1 * (-3/2)^(3-1) = 1 * (-3/2)^2 = 1 * 9/4 = 9/4

So the missing value is 9/4.

For the second geometric sequence, the missing value is:

2 = 6, 7 = 192

To find the missing value, we can use the formula:

an = ar^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

So we know that:

a1 = 2, r = 7/6, n = 11

Plugging these values into the formula:

an = ar^(n-1)

an = 2 * (7/6)^(11-1) = 2 * (7/6)^10 = 2 * (7/6)^10 = 2 * 7^10 / 6^10 = 9261

So the missing value is 9261.

Step-by-step explanation:

No, it is not possible to construct a triangle with the sides 9.1cm ,8.3cm and 17.5cm because sum of the any two sides is not greater than the third side .

The side lengths are given as : 9.1cm ,8.3cm and 17.5cm  ;

we know that , the triangle is formed only when the sum of two sides of triangle is greater than third side .

applying this property , we get that ;

⇒ 9.1 + 8.3 = 17.4 > 17.5 ; False

⇒ 8.3 + 17.5 = 25.8 > 9.1 ; True

⇒ 9.1 + 17.5 = 26.6 > 8.3 ; True .

we can see that the sum of the sides 9.1 and 8.3 is 17.4 which is not greater than the third side (17.5) ,

Therefore , the triangle cannot be constructed .

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The inner triangle's area is equal to x2 - 9.The larger triangle has a surface area of (9x2 - 16) square units.8x2 - 7 is the necessary polynomial in terms of x.

The following is the formula for determining a rectangle's area:

A = LW

The length is L.

The width is W.

For the inner triangle, see (A)

Size = x - 3

Height = x +3

(x-3)(x+3) is the inner triangle's area.

x2-3x+3x+9 is the inner triangle's area.

Inner triangle's area is equal to x2 - 9.

B) Regarding the bigger triangle

Size = 3x-4

Height 3x + 4

A = (3x-4)(3x+4)

A = 9x²+12x-12x-16

A = (9 x 2 – 16) square units

Consequently, the larger triangle's area is (9x2 - 16) square units.

C) We will make the difference in the areas in order to describe the size of the region inside the bigger rectangle by outside the smaller rectangle as a polynomial in terms of x:

P(x) is equal to the smaller triangle's area minus the larger triangle's area.

P(x) = (9x² - 16) - (x² - 9)

P(x) = 9x² - 16 - x² + 9

P(x) = 9x² - x² - 16 + 9

P(x) = 8x² - 7

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Answer:

13.24 ft

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have:

Sinα=opposite/hypotenuse

α=62°

opposite=x

hypotenuse=15 ft

2. When you substitute the values into  Sinα=opposite/hypotenuse, you obtain:

Sinα=opposite/hypotenuse

Sin(62°)=x/15

3. You must clear "x", as below:

x=(15)(Sin(62°))

x=13.24 ft

The answer is. 13.24 ft

Answer:

We can solve the simultaneous equations by using substitution or elimination method. Here, we will use the substitution method:

x - 2y = 3 and x ^ 2 - y ^ 2 + 2x = 10

Solving the first equation for x, we get

x = 2y + 3

Now, substitute this value of x in the second equation

(2y + 3)^2 - y^2 + 2(2y + 3) = 10

Expanding the square on the left-hand side

4y^2 + 12y + 9 - y^2 + 4y + 6 = 10

Combining like terms

3y^2 + 16y + 3 = 0

Now, we can solve this equation by factoring or using the quadratic formula. Here, we will use factoring method:

3y^2 + 16y + 3 = 0

(3y + 3)(y + 1) = 0

So, y = -1 or y = -1

Now, we can substitute either value of y back into x = 2y + 3

For y = -1, x = 2(-1) + 3 = 1

For y = -1, x = 2(-1) + 3 = 1

So, the solutions of the simultaneous equations are x = 1 and y = -1 or x = 1 and y = -1

Answer:

If y = -5, x = -7

If y = -3, x = 2 1/3 or 7/3

Step-by-step explanation:

Alr alr,

x - 2y = 3

x = 2y + 3

Now, lets substitute that into the other equation,

x² - y² + 2x = 10

(2y + 3)² - y² + 2(2y+ 3) - 10 = 0

4y² + 9 + 12y - y² + 4y + 6 - 10 = 0

3y² + 16y + 5 = 0

3y² + 15y + y + 5 = 0

3y(y + 5) + y + 5 = 0

(3y + 1)(y + 5) = 0

y = -5, -1/3

Put both these values in the first equation, u will get,

x = 2y + 3

x = -10 + 3

x = -7

or

x = -2/3 + 3

x = 2 1/3

sorry for taking this long,

My internet gave out after I was about to add the answer.

pls mark as brainliest nevertheless. I don't know why i need it, but i need it. cheers

(7²)⁵ * 7⁴ is equal to the expression 7²ˣ⁵ ⁺ ⁴.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression (7²)⁵ * 7⁴

Since as per the rule of power we can add the power is base is same and also there is a rule if Power is the power of another power they will be multiplied

From the second rule

(7²)⁵ * 7⁴  = 7²ˣ⁵ * 7⁴

From the first rule of power

7²ˣ⁵ * 7⁴ = 7²ˣ⁵ ⁺ ⁴

therefore, (7²)⁵ * 7⁴ is equal to the expression 7²ˣ⁵ ⁺ ⁴.

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The answer of 21 tracks is accurate since, once the membership cost has been paid, the store charges $1.50 by each song. Since the monthly charge is a one-time expense, it is deducted from the $50 price cap.

The characteristic that every input is associated to approximately one output defines a function as a relationship between a series of inputs but a set of allowable outputs. A mapping from Here to there B will only be a function if every piece in set A has one end and only the image in set B. Let A & B have been any two non-empty sets.

The number of songs that may be downloaded with the specified budget is then calculated by dividing the remaining balance by the price of each song. The outcome is an analytic sequence because each song's price is set. The outcome is then rounded down to the closest whole number, which in this example is 21.

1. Take the $50 budget and deduct the $18 membership fee:

$50 - $18 = $32

2. Take the leftover amount and divide it by the price of each song:

$32 ÷ $1.50 = 21.33

3. To the nearest full number, round down:

21 songs

As a result, you may purchase 21 tracks for $50.

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The answer of the given conditions is 255/3 =83, 368/16 = 23 and 2 210/65 = 34.

What are the numerator and denominator?

For example, 4/5 is a fraction, and the line separating the numbers 4 and 5 is the fraction bar. Here the number above the fraction bar is the numerator, and the one below the fraction bar is the denominator. A numerator represents the number of parts out of the whole, which is the denominator.

3 divided by 255 is equal to 3/255.

16 divided by 368 is equal to 16/368.

65 divided by 2 210 is equal to 65/2210.

Note that for 2 and 3 the numerator and denominator have been swapped and the division is not correct, it should be 368/16 = 23 and 2 210/65 = 34

Hence, the answer of the given conditions are 255/3 =83, 368/16 = 23, and 2 210/65 = 34.

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We can see that the vertices, ko vertices and foci are related by the formula c2=a2+b2. This formula can also be rewritten as b2=c2-a2. This relationship is used to describe the equation given the coordinates of the hyperbolic foci and vertices.

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Therefore , the solution of the given problem of fraction comes out to be Stella makes 6 bows.

The definition of a fraction is a portion of a whole. A single object or a collection of objects might be the entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form.

Here,

Given :

Take the amount of ribbon and divide by the amount needed per bow

5 1/3÷ 1/3

Change the mixed number to an improper fraction

(5*1 +1)/3 ÷1/3

6/3 ÷1/3

Copy dot flip

6/3 * 3/1

6

Stella makes 6 bows.

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Using linear functions, we have that:

a) The equation for the line is: y = -500x + 5000

b) The prediction is 2250 sales with a price of $6.50.

The equation of a line is given by:

y = mx+ b

In which

Item a:

In this problem:

[tex]m = \frac{1500-2500}{7-5} = - \frac{1000}{2} = -500[/tex]

Thus:

y = -500x + b

Point (5,2500) means that when x=5, y = 2500, which we use to find b.

y = -500x + b

⇒2500 = -500* (5) +b

⇒2500 = -2500 +b

⇒b = 2500 +2500

⇒b = 5000

Thus

y = -500x + 5000

∴The equation for the line is: y = -500x + 5000

Item b:

y = -500*(6.5) + 5000

y = 2250

The prediction is 2250 sales with a price of $6.50.

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The coordinates of the new point after applying the given set of transformation is given by the ordered pair (0, -1).

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.

Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is given by this transformation rule:

(x, y)                                    →              (y, x)

Ordered pair A = (-4, -2)    →        Ordered pair A' = (-2, -4).

Next, we would apply a translation of 2 units to the right and 3 units up:

(x, y)                                    →              (x + 2, x + 3)

Ordered pair A' = (-2, -4)  →    (-2 + 2, -4 + 3)   →  Ordered pair A' = (0, -1).

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[tex]\displaystyle\\Answer:\ c.\ \frac{y-b}{x}[/tex]

Step-by-step explanation:

Given:  y=mx+b

y-b=mx+b-b

y-b=mx

Divide both parts of the equation by x:

[tex]\displaystyle\\\frac{y-b}{x}=m\\ Thus,\ m=\frac{y-b}{x}[/tex]

Jack's working is incorrect. To correctly find the product of 25 x 14.2 without a calculator, he should have used the distributive property of multiplication.

First, he should have broken down 25 into 20 and 5, which are easier numbers to multiply mentally. Then, he should have multiplied 14.2 by 20 to get 284, and 14.2 by 5 to get 71.

Finally, he should have added these two intermediate results, 284 and 71, to get the final answer of 25 x 14.2 = 355.

A correct working would be:

20 x 14.2 = 284

5 x 14.2 = 71

25 x 14.2 = 284 + 71 = 355

Therefore, Jack's final answer is incorrect, the correct answer is 355.

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So on solving the provided question we can say that [tex]\sqrt{2} , \sqrt{18} \\[/tex], [tex]5.\sqrt{5} \\[/tex] none of them are rational number.

Any number that can be expressed as a ratio (or fraction) of two integers is said to be rational. A rational number is a fraction that has a nonzero denominator. 1/2, 1/5, and 3/4 are examples of rational numbers. Additionally a rational number, "0" may be expressed in a variety of ways, including 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, etc. The number seven is logical. When two integers are divided, the result is known as a rational number. Divide the whole number 7 by the whole number 1 to obtain the rational number 7. Since two integers may be divided to yield 7, it is known as a rational number.

here, we have

[tex]\sqrt{2} , \sqrt{18} \\[/tex]

[tex]5.\sqrt{5} \\[/tex]

none of them are rational number

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Elasticidad es la forma de recobrar la forma original (banda elástica), dureza es la capacidad de resistir el rayado (mesa), permeabilidad es la propiedad de dejar pasar un liquido (camiseta) y tenacidad es la capacidad de resistir fuerzas.

Esta es una propiedad de un material que se puede definir como la capacidad de mantener su forma original o recobrar la forma después de una fuerza. Algunos ejemplos son cauchos, bandas elásticas, una licra.

Se refiere a la propiedad de un material para resistir el rayado y el corte. Materiales como los metales tienen esta propiedad, otro ejemplo de esto es una mesa pues no es fácil cortar o rayar la misma.

Se refiere a la capacidad de un material para permitir el paso de líquidos especialmente agua, por ejemplo una camiseta es muy permeable pero una bolsa de plástico no lo es.

Se refiere a la capacidad de resistencia si se somete el material a fuerzas. Un serrucho tiene gran tenacidad pues a pesar de someterlo a fuerza mecánica este la resiste.

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If you want to make 1/2 the recipe, then [tex]1\frac{11}{16}[/tex] tablespoon of sugar you need.

In the given question, a recipe calls for [tex]3\frac{3}{8}[/tex] tablespoons of sugar.

If you want to make 1/2 the recipe, then we have to find how much sugar you need.

As given that;

1 recipe = [tex]3\frac{3}{8}[/tex] tablespoons of sugar

Before solving the question, we convert the mixed fraction into simple fraction.

To convert in simple fraction we multiply 3 by 8 then we add 3 on the result of multiplication of 3 and 8.

1 recipe = 27/8 tablespoons of sugar

We have to find sugar need for making 1/2 recipe.

1/2 recipe = [tex]\frac{27}{8}\times\frac{1}{2}[/tex] tablespoons of sugar

1/2 recipe = 27/16 tablespoons of sugar

1/2 recipe = [tex]1\frac{11}{16}[/tex] tablespoons of sugar

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11423 be the number of dogs are at the rescue center.

An expression is combination of variables, numbers and operators.

A pet rescue center is creating a monthly food budget.

The center currently has two-thirds as many dogs as cats.

Each animal is fed 2 cans of food a day.

Dog food costs $0.08 per can, cat food costs $0.05  per can

The rescue center has budgeted a total  2581.8 of  for food for this .

2(0.08)x+2(0.05)y= 2581.8

Let x be the number of dogs.

cats be y.

2/3x =y

2(0.08)x+2(0.05)2/3x= 2581.8

0.16x+0.066x=2581.8

0.226x=2581.8

x=11423

Hence, 11423 be the number of dogs are at the rescue center.

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We can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling. not an SRS because the first sample was not balanced between men and women

an SRS?

the leader of a student organization wishes to form a committee that will consist of 5 of the 50 members.

he decides to take an SRS of size five from the members and those selected will comprise the committee.

he chooses an SRS of size five and all are men.

he would like to have some women on the task force, so he decides to take another SRS.

this time there are three women and two men in the sample, so he decides these five will form the committee.

we can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling.

an SRS because all members had the same chance of being in the final sample.

not an SRS because a sample consisting entirely of men is not allowed.

not an SRS because the first sample was not balanced between men and women.

we can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling. not an SRS because the first sample was not balanced between men and women.

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So on solving the provided question we cans say that  sides of a square are given as 18 units, area = 324 cm sq.

A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.

here,

sides of a square are given as 18 units

so area will be s^2 18*18 = 324 cm sq.

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The number of ways in which we can choose four members of the club to serve on the executive committee is 12650 ways.

The act of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the elements of a set if the set is already ordered. Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.

Given that the total number of members in the club is 25.

To choose four executive members for the committee we use the formula of combinations given as follows:

[tex]nCr = \frac{n!}{(n-r)! r!}[/tex]

Substituting the value of n= 25 and r = 4:

[tex]25C 4 = \frac{25!}{(25 -4)! 4!}\\\\\\25C 4 = 12650\\[/tex]

Hence, the number of ways in which we can choose four members of the club to serve on the executive committee is 12650 ways.

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Mrs Thomas' and Mr Carl's classes both have same lower ratio of A's to B's which expressed in the lowest term as 4:5 or fraction as 4/5

Ratio is used to compare values, and can be expressed as fractions.

Mrs Thomas' class have the ratio of students her students A's to B's as 16:20. And can be expressed as fraction in its lowest term as follows:

16:20 = 16/20

16:20 = 4/5

Mr Carl's class have the ratio of students her students A's to B's as 12:15. And can be expressed as fraction in its lowest term as follows:

12:15 = 12/15

12:15 = 4/5

Therefore, since the lowest form of Mrs Thomas' class and Mr Carl's class ratios of A's to B's are equal, then both class have equivalent lower ratio of A's to B's.

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0.1 is  Probability in Distribution Table X P(X).

What is Probability ?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                             Statistics describes the examination of events subject to probability.

Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.

now according to the properties of probability theory we know that sum of probabilities is 1.

so here to find the value of the probability of X coresponding to the value 53 we should use the following steps:

sum of given probabilities =(0.2+0.4+0.3) = 0.9

required probability = 1 - sum of given probabilities = 1 - 0.9 = 0.1

hence the complete probability table is

X P(X)

20 0.2

49 0.4

53 0.1

80 0.3

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Answer: .

Step-by-step explanation:

67.002 - 67.020 - 67.200

Answer:

67.002, 67.020, 67.200

Step-by-step explanation:

I think this is the answer

So, the fractional part of the regular passengers that are adult is 0.9404 or 94.04%.

We know that the cruise ship has 2,400 regular passengers, and that 120 of them are children and 23 are teenagers. To find the fractional part of the regular passengers that are adults, we need to subtract the number of children and teenagers from the total number of regular passengers.

First, add the number of children and teenagers: 120 + 23 = 143

Then, subtract this number from the total number of regular passengers: 2,400 - 143 = 2,257

This is the number of adult passengers. To find the fraction of adult passengers, divide the number of adult passengers by the total number of regular passengers and convert the result to a fraction.

2,257/2,400 = 0.9404

So, the fractional part of the regular passengers that are adult is 0.9404 or 94.04%.

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In using a counterexample, Sarah used a single example to show that a statement was False. This technique is unlike a direct proof, in which evidence is used to support a series of statements to show why a statement is True. A single example is enough to prove a statement true.

A counterexample is a specific example that contradicts a general statement or claim. In mathematics, a counterexample is used to disprove a conjecture, hypothesis or theory by providing an example that does not follow the rule or pattern that is being proposed. It is a method of proof by contradiction.

Counterexamples can also be used to show that a conjecture or assumption is not universally true. They are important tools in mathematics and logic, as they allow us to test the validity of statements and identify any exceptions or limitations.

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