How are the rational and radical related?

The simplified form of the given expression is 3x+5y+4. Here only the constants are simplified since there are no like terms in the expression.

The given expression which is to be simplified is 6+3x-6+4+5y.

Here to simplify the given expression, we need to add or subtract the like terms.

In the given expression, the variables x and y.

They are unlike terms. So, we cannot add or subtract them. But there are three constants. Then, we can add or subtract them.

Thus, the simplified expression for the given expression is

6+3x-6+4+5y = 3x+5y+4

Here 6 and -6 are added so that we get 0.

Hence the answer is 3x+5y+4.

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Answer:

the range of possible weights for the letters is 98-105 ounces.

Step-by-step explanation:

To determine whether 101 ounces is a reasonable estimate for the weight of 25 letters that each weigh between 3.92 ounces and 4.2 ounces, we need to calculate the range of possible weights for the letters.

The minimum weight for the letters is 25 * 3.92 ounces = 98 ounces. The maximum weight for the letters is 25 * 4.2 ounces = 105 ounces. Therefore, the range of possible weights for the letters is 98-105 ounces.

Since 101 ounces falls within this range, it is a reasonable estimate for the weight of the letters.

Complex number equal to (5 + 12i) − (9i^2 − 6i), for i = √ -1 is 14 + 18i.

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and  ‘i’ is an imaginary number called “iota”. The value of i = (√-1)

Given number is (5 + 12i) − (9i^2 − 6i).

We know that i^2 = -1.

Using this we get number = 5+12i+9+6i

                                           = 14+18i

So the required number is 14 + 18i.

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Answer: (4, 10)

Step-by-step explanation:

The first number, 4, is the number on the x axis, the horizontal axis. The second number 0 is the number on the y axis, the vertical axis.

If you move up you would moving on the y axis, therefore the second number, 0, would change.

You moved 10 units so starting at 0 move up 10 units. 0 + 10 = 10

Now you're at (4, 10)

Answer:

Yes

Step-by-step explanation:

The pair of congruent angles needs to be included between the congruent sides. Since this is not the case, more information is needed.

The correct response is yes, the additional information is needed to show that ΔDEF is congruent to ΔGHJ by SAS congruency rule is whether the sides DE and GH, are congruent

The SAS (Side-Angle-Side) congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

The specified information for each triangle, starting from the indicated angle, and calling the sides in a clockwise direction, we get;

∠E, side EF and side DF in triangle ΔDEF are congruent to angle ∠H, side HJ, and side GJ

Therefore, the information from the diagram in the question are a nonincluded angle and two sides, SSA, which is not a condition for congruency.

The additional information needed to prove ΔDEF is congruent to ΔGHJ, by SAS are the sides DE and GH, which makes the angle ∠E and ∠H included angles.

Therefore, additional information is required;

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The pie chart is shown in the attached image. 30% of the pet owners responded with a price of $25

A pie chart is a circular graph that is divided into slices to illustrate numerical proportion

Given the data of 2,500 pet owners as shown below:

Number of People    Price

500                              $10

350                               $15

750                                $20

550                                $25

350                                 $0 (not interested)

To create a pie chart, you need to find the percentages of each price as follows:

For  $10:  percentage = 500/2500 × 100  = 20%

For  $15:  percentage = 350/2500 × 100  = 14%

For  $20:  percentage = 750/2500 × 100  = 30%

For  $25:  percentage = 550/2500 × 100  = 22%

For  $0:  percentage = 350/2500 × 1000  = 14%

Use the percentages to create a piechart as shown in the image attached

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Answer:

x=1,13

Step-by-step explanation:

(x – 7)^2 = 36

To solve for x take the square root of each side

sqrt((x – 7)^2) = sqrt(36)

x-7 = ±6

Splitting into two equations

x-7 = 6    x-7 = -6

Add 7 to all sides

x-7+7 = 6+7    x-7+7 = -6+7

x=13                          x=1

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(x - 7)^2 = 36}[/tex]

[tex]\mathsf{(x - 7)(x - 7) = 36}[/tex]

[tex]\mathsf{x^2 - 14x + 49 = 36}[/tex]

[tex]\text{SUBTRACT 36 to BOTH SIDES}[/tex]

[tex]\mathsf{x^2 - 14x + 49 + 49 = 36 + 49}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x^2 - 14x + 13 = 36 + 49}[/tex]

[tex]\mathsf{x^2 - 14x + 13 = 0}[/tex]

[tex]\text{FACTOR the LEFT SIDE of your equation}[/tex]

[tex]\mathsf{(x - 1)(x - 13) = 0}[/tex]

[tex]\text{SET the FACTORS to EQUAL to 0}[/tex]

[tex]\mathsf{Equation\ \#1.)\ \rightarrow x - 1 = 0}[/tex]

[tex]\mathsf{Equation\ \#2.)\ \rightarrow x - 13 = 0}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x = 1 \ or\ x = 13}[/tex]

[tex]\huge\text{Thus, your answer should be: } \boxed{\mathsf{x = 1 \ or\ x = 13}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Step-by-step explanation:

men = 2x

women = 3x

2x+3x=135

5x=135

x=27

27(2)=men

54 men

The surd expression 1 + [√2 / (3 - √2)²]  can be simplified as (61 + 11√2/ 49) where a is 61/49 and b is 11/49

When evaluating an expression, the first step is to identify the operators and operands in the expression. The operators are the symbols that direct the operation. The operands are the values or variables that the operators act upon. Once the operators and operands are identified, the expression can be evaluated by applying the order of operations to the expression. This includes performing operations inside parentheses first, then multiplication and division, followed by addition and subtraction.

In the case of a surd expression, the same process should be followed. However, it is important to note that surds can be simplified using the rules of indices. This means that surds with the same base value can be combined using addition and subtraction.

In the give problem, we have

1 + [√2 / (3 - √2)²] can be written in the form a + b√2

1 + [√2 / (3 - √2)²] can be simplified using a calculator to give us a value of;

1 + [√2 / (3 - √2)²] = (61 + 11√2/ 49)

In this expression, a = 61/49, b = 11/49

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The standard deviation is decreases then the graph of the normal z - score curve is increases.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

In mathematics, the Z score is used to quantify how many standard deviations the raw score deviates from or approaches the mean. Giving the z score are:

z = (x - μ ) / σ

Where,

x = raw score

μ = mean

σ = standard deviation

For a sample size,

z =  (x - μ ) / σ / [tex]\sqrt{n}[/tex]

The z score affects the area under the curve. The area under the curve increases as the z score increases and decreases as the z score decreases.

The standard deviation has an inverse relationship with the area under the curve (z score). The z score drops as the standard deviation rises, diminishing the area under the curve.

The area under the curve grows as the standard deviation is reduced because the z score increases.

Therefore,

The standard deviation is decreases then the graph of the normal z - score curve is increases.

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If a gardner plants 90 seedlings. the number of seedlings in each row is 3 more than twice the number rows then 43.5 number of rows are planted by the gardner.

Two or more expressions with an Equal sign is called as Equation.

Given,

Gardner plants 90 seedlings

The number of seedlings in each row is 3 more than twice the number rows.

We need to find the number of rows.

Let r be the number of rows

2r+3=90

Subtract 3 from both sides

2r=87

Divide both sides by 2

r=43.5

Hence, 43.5 number of rows are planted by the gardner.

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The probability that the resulting integer is divisible by 8 is 1/6

According to the question,

Nancy Rolled a six-sided die twice to generate two-digit integers

Total number of outcome by rolling a die = {1 , 2 , 3 , 4 ,5 ,6 }

If you roll twice then total number of outcomes becomes = 6 × 6

=> 36

We have to find  the probability that the resulting integer is divisible by 8

Number of two - digit integer divisible by 8 = 16 , 24 , 32 , 48 , 56 , 64

that is 6  

So, Probability = Number of favorable outcomes / total number of outcomes

=> 6 / 36

=> 1/6 is required probability

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Answer:

The middle of A and C

Step-by-step explanation:

Definition of Midpoint

kiloliter

One thousand liters is called a kiloliter. A kiloliter is equal to 264.172 gallons. One liter is equal to 0.264172, so if you want to find how many gallons there are in 1 kiloliter, just multiply 0.264172 by 1000

Answer:

1000 liters  

Step-by-step explanation:

Answer: slope = -1

Step-by-step explanation:

count number down vs number it takes to get back to the line.

For example, 1 down, 1 across

The value of y will be 104 using direct proportion property between x and y.

What is direct proportion ?

Direct proportion is the relation between two quantities where ratio of these two is equal to a constant.

It is represented by proportional symbol , "∝"

Let's consider constant is m.

For given que,

As y and x are in direct proportion,

y ∝ x

or x ∝ y

eliminating the proportionality,

y = x*m where m is any constant.

y/x = m

Given when y = 64 , then x = 8

So, m = 64/8

          = 8

And when x = 13 then y = ?

y/13 = 8

y = 13*8

  = 104

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Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.

Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.

Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.

Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.

Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.

Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.

Q7 there is less spread for larger sample than that of lower sample.

The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution.

Based on the data they have available, sampling distributions are useful tools used by researchers to estimate and draw conclusions about a wider population of interest.

Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.

Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.

Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.

Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.

Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.

Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.

Q7 there is less spread for larger sample than that of lower sample.

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Following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.

In mathematics, an integral assigns numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data.

Integration is the action of locating integrals.

So, the number of automobiles that cross an intersection each hour is:

r(t) = 400 + 800t - 120t²

Integration should be carried out to establish the number of cars traveling through the intersection between 6 am and 8 am.

[tex]\begin{aligned}\int_{t_1}^{t_2} r d t & =\int_0^2 400+800 t-120 t^2 d t \\& =\left[400 t+400 t^2-40 t^3\right]_0^2 \\& =400 \times 2+400 \times 2^2-40 \times 2^3 \\& =800+1600-320 \\& =2080\end{aligned}[/tex]

Therefore, following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.

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Correct question:
The traffic flow rate (cars per hour) across an intersection is r ( t ) = 400 + 800 t − 120 t 2 , where t is in hours, and t =0 is 6am. How many cars pass through the intersection between 6 am and 8 am?

The expected number of defective shirts produced by the factory on Friday is of:

42 shirts.

The expected number of defective shirts produced by the factory on Friday is obtained as the multiplication of the sample proportion by the total number of shirts produced on Friday.

The manager of a clothing factory checks a random sample 500 shirts for defects he finds that 8 are defective, hence the sample proportion is given as follows:

p = 8/500 = 0.016.

The factory produces 2625 shirts on Friday, hence the expected number of defective shirts is given as follows:

E(X) = 0.016 x 2625 = 42 shirts.

The problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the expected number of defective shirts produced by the factory on Friday.

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The perpendicular bisector of the line is option c)

The bisector of the angle YXZ is option B)

The perpendicular from point Z to the line XY is option G)

What is perpendicular bisector?

A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.

We are asked to find the perpendicular bisector on the line XY

Now this means a segment dividing segment XY in two equal parts and intersecting XY at right angle

Hence This description match with option C)

Hence The perpendicular bisector of the line is option c)

Similarly,

The bisector of Angle YXZ will be the line which divides the angle in two equal parts

This description matches with option B)

Hence the correct option is option B)

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By solving a linear equation we will see that the value of x is 10.

Remember that for any triangle, the sum of all internal angles is always equal to 180°.

Here only look at triangle BCD, we know that:

m∠DBC = m∠ABC = 3x

m∠BCD = m∠ACB + m∠ABD = 2x + 65°

m∠ADC = 65°

Now we can write the linear equation as:

3x + 2x + 65° + 65° = 180°

5x + 130° = 180°

5x = 180° - 130°

5x = 50°

x = 50°/5 = 10°

The value of x is 10.

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Answer:

Below

Step-by-step explanation:

.046 is lost each year meaning  (1 - .046) remains

A(t) = 300 ( 1 - .046)^t        will show milligrams remaining after 't' years (where t is the years since 2004)

The expression can be rewritten as, by taking the common factor, 9 x³y³(2x - 4y), so option C is correct.

Common factors are those that apply to two or more different integers. To put it another way, a common factor is a number that will divide a group of two numbers exactly.

Given:

18 x⁴y³− 36x³y⁴

Factorize the above expression,

9 × 2 x⁴y³ - 9 × 4x³y⁴

Take common 9 x³y³

9 x³y³(2x - 4y)

Therefore, the expression can be rewritten as, by taking the common factor, 9 x³y³(2x - 4y).

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Divide by the norm of 1+i and apply De Moivre's theorem to find that (1 +i)^20 = − 1024 in standard form.

De Moivre's theorem presents a formula for calculating powers of complex numbers. By first studying what occurs when we multiply a complex number by itself, we may have a better understanding of de Moivre's theorem. This demonstrates that when squaring a complex number, the argument is multiplied by two and the absolute value is squared.

DeMoivre's Theorem, which unites complex numbers with trigonometry, is one of the most significant and practical theorems in the study of complex numbers. Obtaining correlations between trigonometric functions of various angles is also useful. The famous mathematician De Moivre, who made several contributions to the subject of mathematics, particularly in the fields of probability theory and algebra, is honored in the name of the theorem. The solution is attached below.

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Answer: 7

Step-by-step explanation: You would multiply 70 by 10 to get 700, then divide it by 100 to get 7. So, it would be 7 dollars.

Answer: 7

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

16/64 (divide the numerator and denominator by 4)

-> 4/8 (divide the numerator and denominator by 4)

-> 1/2

Therefore by solving the question from the equation we get ,total money he has now is $(m+100)/2

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.

Here,

He got $m for his birthday

therefore he spent half the money the money left =m/2

and he got extra $50

Thus

total money he has now is = m/2 +50

or m+100/2

Therefore ,total money he has now is $(m+100)/2

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Area to the right of 125 is 0.0475 and area to the left of 125 is 0.9525 .

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The area of a shape is the space enclosed within the perimeter or the boundary of the given shape.

Here, μ = 100, σ = 15 and x = 125. We need to compute P(X >= 125). The corresponding z-value is calculated using Central Limit Theorem.

z = (x - μ)/σ

z = (125 - 100)/15 = 1.67

z = 1.67

Therefore,

P(X >= 125) = P(z <= (125 - 100)/15)

= P(z >= 1.67)

= 1 - 0.9525

= 0.0475

Area to the right of 125 is 0.0475 and area to the left of 125 is 0.9525 .

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a) The amount of ounces in 8 liters is of: 270.5 ounces.

b) The number of containers needed is of: 90 containers.

A proportion is a fraction of a total amount, which serves as an unit rate in the context of a problem, used along basic arithmetic operations such as multiplication or division, to find the desired measures in the context of a problem.

The number of ounces per liter is given as follows:

33.814 ounces.

Hence the number of ounces in eight liters is given as follows:

8 x 33.814 = 270.5 ounces.

Each container has three ounces, hence the number of containers is obtained as follows:

270.5/3 = 90 containers.

(as the total amount is of 270.5 ounces, and each container is composed by three ounces, hence the proportion was applied).

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The sum of the area of the rectangle has an area of 5x + 22 ft²rectangle b has an area of 8x - 2  ft² is  13x + 20  ft².

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 area of a rectangle, A = 5x+22 ft²,

The area of a rectangle, B = 8x-2 ft²,

Calculate the sum of the areas as shown below,

A + B = 5x + 22 + 8x - 2

A + B = 13x + 20  ft²

Therefore, the sum of the area of the rectangle has an area of 5x + 22 ft²rectangle b has an area of 8x - 2  ft² is  13x + 20  ft².

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