what is the solution to the equasion 1/2x + 3= 2/3x + 1​

The thickness of each sheet of paper is 0.0012mm.

To find the thickness of each sheet of paper answer in millimeters​.

The act of measuring geometry applied to the computation of lengths, areas, or volumes from given dimensions or angles.

Given that:

A ream of A4 paper contain 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm.

To convert cm in mm.

3742.2cm=37422 mm

Surface 1 sheet:

(297mm) X 210mm) =

62370\(mm^{2}\)

Volume 1 sheet:

37422mm : 500 =

74.844mm

Thickness of 1 sheet:

74.844mm : 62370mm =

0.0012mm

So, the thickness of each sheet of paper is 0.0012mm.

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Answer:

The domain is all real numbers, x, such that x ≤ 4/3.

The range is all real numbers, y, such that y ≥ 0.

Step-by-step explanation:

The domain is the set of values that can be substituted for x.

The expression inside the square root cannot be negative; therefore, it must be zero or positive.

4 - 3x ≥ 0

-3x ≥ -4

x ≤ 4/3

The domain is: x ≤ 4/3

The range is the set of value that can be substituted for y.

When all numbers of the domain are used for x, and then the square root is taken, the smallest value that the square root can have is zero. Therefore, y can be all real numbers greater than or equal to 0.

The range is: y ≥ 0

Using the Pythagorean theorem, the length of the water slide is approximately 24.7 meters.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental idea in geometry that asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle= the sum of the squares of the other two sides. In equation form, it is as follows:

a² + b² = c²

Now,

Using the Pythagorean theorem, we can find the length of the water slide as follows:

Length of the slide = √(23² + 9²) meters

Length of the slide = √(529 + 81) meters

Length of the slide = √610 meters

Length of the slide ≈ 24.7 meters (rounded to the nearest tenth)

Therefore, the length of the water slide is approximately 24.7 meters.

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The missing reasons are

1. Corresponding Angle

2. Alternate Exterior Angle

We know, if a line intersects two parallel lines, the corresponding interior angles on the same side of the transversal will be congruent (equal).

1. Since CL || EK

Then, by the property of parallel line

<BFJ = <ADF (Corresponding Angle)

2. Since CL || EK

Then, by the property of parallel line

<EBH= <LDM (Alternate Exterior Angle)

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Work Shown:

We'll divide the total 5/8 evenly among the 6 cousins.

(5/8) ÷ 6 = (5/8) ÷ (6/1)

(5/8) ÷ 6 = (5/8) * (1/6)

(5/8) ÷ 6 = (5*1)/(8*6)

(5/8) ÷ 6 = 5/48

Each cousin gets 5/48 of the aunt's assets.

So for instance, if the aunt had $48,000 in assets, then each cousin gets (5/48)*(48,000) = 5000 dollars.

------------------

An alternative approach:

Draw 6 rectangles side by side that represent the 6 cousins. Then divide each rectangle into 8 pieces, with 5 pieces shaded. The yellow pieces represent the amount given to the cousins. For any given rectangle, 5/8 of it is shaded yellow. Refer to the diagram below.

Overall we have 6*8 = 48 pieces.

The first cousin gets 5 yellow pieces out of 48 total. The same applies to the other five cousins. So this is a visual way to arrive at the answer 5/48.

Answer:

  JL = 78

Step-by-step explanation:

The shorter segment is a midline, so is half the length of the longer one.

  2(5x-16) = 4x +34

  5x -16 = 2x +17 . . . . . divide by 2

  3x = 33 . . . . . . . . . . add 16-2x

  x = 11 . . . . . . . . . . divide by 3

Then segment JL is ...

  JL = 4x +34 = 4(11) +34 = 44+34

  JL = 78

The distance, which is determined by integrating the velocity function over the specified time interval, is calculated as 2.98 and 2.58.

We will use left Riemann sum and right Riemann sum to obtain an overestimate and an underestimate. The definite integral, which in this case is a distance, can also be approximated using the average of these estimates.

1 ) The distance the bug crawls obtained by integrating the velocity function v(t) = 4/1+t over the inclined time interval is

\(\int\limits^1_0 \, \frac{4}{1+t} dt.\)

Splitting the interval [0, 1] into sub intervals of length Δt = 0.2, we get the Riemann sum L and the right Riemann sum R:

L = ∑⁴ v(ti) Δt

L = (0.2) (v(0) + v(0.2) + v(0.4) + v(0.6) + v(0.8))

L ≈ 2.98

R = ∑⁵ v(ti) Δt

R = (0.2) (v(0.2) + v(0.4) + v(0.6) + v(0.8) + v(1.0))

R ≈ 2.58

2 )The average of these two Riemann sums gives us a new estimate for the distance :

AVG = (2.98 + 2.58)/2

=2.78.

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Answer:

Circumference:   C = 7.5π m.  This is approximately 23.56 m

Total fencing cost:  $215.76

Step-by-step explanation:

Ashton walks along the diameter of the garden, which is 7.5 m.

The circumference formula C = πd yields C = 7.5π m.  This is approximately 23.56 m, which we must round up to 24 m, and which calls for 24 - 1 m pieces at $8.99 each.

The desired fencing would cost (24 m)($8.99/m), or $215.76

To evaluate the given expressions without using a calculator: (a) sin(sin^(-1)(-21)), (b) sin^(-1)(sin(-3π)), and (c) tan(sin^(-1)(cos(-3π)).

(a) The expression sin(sin^(-1)(-21)) involves the arcsine function (sin^(-1)) applied to -21. Since the arcsine function gives the angle whose sine is a given value, sin^(-1)(-21) does not have a real solution. Therefore, the expression sin(sin^(-1)(-21)) is undefined.

(b) The expression sin^(-1)(sin(-3π)) involves the arcsine function applied to sin(-3π). The sine function is periodic with a period of 2π, so sin(-3π) is equal to sin(-π), which is 0. Thus, sin^(-1)(sin(-3π)) evaluates to 0.

(c) The expression tan(sin^(-1)(cos(-3π))) involves the tangent function applied to sin^(-1)(cos(-3π)). The cosine function is also periodic with a period of 2π, so cos(-3π) is equal to cos(-π), which is -1. Evaluating sin^(-1)(-1), we find that sin^(-1)(-1) is equal to -π/2. Therefore, tan(sin^(-1)(cos(-3π))) evaluates to tan(-π/2), which is undefined.

The evaluations are as follows: (a) undefined, (b) 0, and (c) undefined.

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the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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For the absolute value equation |2 x+1|-14=9

x = 11

Given, absolute value equation is

|2 x+1|-14=9

|2 x+1|-14 + 14 = 9+14

2x + 1 = 23

2x + 1-1 = 23-1

2x = 22

x = 11

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(2x + 3) (x^2 - 6x + 9)

Answer:

Integers are 48, 49, 50

Step-by-step explanation:

x+(x+1)+(x+2) = 147

3x + 3 = 147

3x = 147-3

x = 144 / 3 = 48

Variables with values that are determined by chance are called random variables (option a).

Random variables are variables whose values are determined by chance or randomness. They are often used in probability theory and statistics to model uncertain or unpredictable phenomena. The values of random variables can come from various sources, such as the outcome of a random experiment, the result of a random process, or the measurement of a random quantity.

Random variables can take on different types of values, including numerical values (such as integers or real numbers) or categorical values (such as "heads" or "tails" in a coin toss). The possible values that a random variable can take are known as its sample space.

Random variables are commonly denoted by capital letters, such as X, Y, or Z. Each value in the sample space of a random variable is associated with a probability or likelihood of occurring, which can be described using a probability distribution. The probability distribution provides information about the likelihood of different outcomes or values of the random variable.

Random variables are fundamental in many areas of mathematics, statistics, and science. They play a crucial role in understanding and modeling uncertainty, making predictions, analyzing data, and making informed decisions in various fields, including finance, engineering, biology, and social sciences.

The complete question is:

Variables with values that are determined by chance are called _______.

a) random variables.

b) erratic variables.

c) specialized.

d) inconsistent variables.

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Answer:

n= -1.2

Step-by-step explanation:

I think because if you use slope equation to find the slope which is 3/5 and then you use point slop equation to find out what the equation would be. y=3/5x and then you substitue y for 18 and solve/simplify the equation to get -1.2.

Answer:

x = 10 so D

Step-by-step explanation:

-4 + x = 6

add 4 both sides to get the x by itself

so 4 + 6 = 10

then the final answer is  x = 10

Answer:

You have a negative 4 being added to the variable. To solve you need to use the opposite operation (what is the opposite of addition?)

For example:

7 = -3 + h

Subtraction -3 from each side.

7 -(-3) = -3- (-3) + h

10 = h

Step-by-step explanation:

a survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools The U.S. Population Census is an example of a census

Census means the procedure of counting, calculating and recording the number and information about the members of the nation's.

Generally, population census are conducted every 10 years although some nations conduct their's every 5 years.

The primary objective of population census is to know the total size of the population of a country.

Population census also enable the government to appropriate resources fairly based on the number of people in a geographical area.

In conclusion, the U.S. population census is the only example of census.

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a. Z-score formula

where,

• x: observed value

• μ: mean

• σ: standard deviation

Substituting with x = $275, μ = $280, and σ = $20, we get:

In terms of the z-score, we need to find

From the table:

Then, the percentage of customers that has daily balances of more than $275 is:

b. Substituting with x = $243, μ = $280, and σ = $20 into the z-score formula, we get:

In terms of the z-score, we need to find:

From the table, the percentage of customers that has daily balances of less than $243 is:

c. Substituting with x₁ = $241 and x₂ = $301.60, μ = $280, and σ = $20 into the z-score formula, we get:

In terms of the z-score, we need to find:

From the first table:

From the second table:

Therefore, the percentage of its customers' balances between $241 and $301.60 is:

Answer:

um yes the top one cannot be 50°

Step-by-step explanation:

Answer:

No correct answer

Step-by-step explanation:

height = volume/ area

height= 69/36= 1.667in

5 in.

I just did this one, and this was the answer.

The linear expression that is not equivalent to the other three is D) (-5x-1)+(6x + 7).

A linear expression is an algebraic expression which is composed of constants, variables, and coefficients that are related by only addition and multiplication operations. It usually takes the form of ax + b, where 'a' and 'b' are constants and 'x' is a variable. Linear expressions can be used to describe various mathematical and physical phenomena, such as the slope of a line or the volume of a cylinder.

This linear expression is not equivalent to the other three because it does not have the same coefficient for the x terms and the constant terms. The other three expressions all have the same coefficients for the x terms and the constant terms, making them equivalent.

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Answer:

umm it's a piecewise function and I think the graph is correct I don't really understand what you mean by what is the "graph" of the following function since the graph is already there...

Step-by-step explanation:

∠3 is congruent to ∠1. Hence, proved.

Two angles are said to be complementary angles if they add up to 90 degrees. In other words, when complementary angles are put together, they form a right angle (90 degrees).

Given that, ∠3 and ∠2 are complementary; m∠2 + m∠3 = 90°---------(I)

From the given figure,

m∠1 + m∠2 = 90°---------(II)

From the given equation (I) and (II), we get

m∠1 + m∠2=m∠2 + m∠3

m∠1 ≅ m∠3

Hence, proved.

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The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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Answer:

h ≤ 70 I'm pretty sure I could be wrong

The correct inequality for the maximum height, h, of a fighter pilot is h ≤ 77.

Given that the height of the fighter pilot (h) must be less than or equal to 77 inches.

The symbol "≤" represents "less than or equal to," and 77 inches is the maximum allowable height for a fighter pilot.

The inequality h ≥ 77 would be incorrect since it states that the height of the fighter pilot should be greater than or equal to 77 inches, which would not be a maximum height requirement.

Similarly, the inequality h ≤ 70 would also be incorrect as it would imply a height limit of 70 inches, which is lower than the actual maximum height allowed.

Lastly, h ≥ 70 would not be suitable as it would permit heights greater than or equal to 70 inches, potentially exceeding the specified maximum height of 77 inches.

In conclusion, the correct inequality to represent the maximum height of a fighter pilot is h ≤ 77, ensuring that their height does not exceed 77 inches.

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Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

The average rate of change is the slope of the line between the points

     ( -4, f(-4) ) and ( 4, f(4) )

f(-4) = 16 + 40 + 5 = 61

f(4) = 16 - 40 + 5 = 19

The slope (AKA average rate of change) is then

    \(m =\dfrac{19-61}{4-(-4)}=\dfrac{-42}{8} = -\dfrac{21}{4}\)

Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.

A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.

Here,

The z value at the 90 percent confidence interval is 1.645.

t ≥ z*s/√n

5≥1.645*62/√n

√n≥20.398

√n≥20.4

n≥416.16

The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.

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