Given the equation 2x − 5 = 8, which order of operations completely solves for x? (1 point)

The central limit theorem requires a sample size of at least 30 be used to ensure that the sample means are normally distributed. Correct option is B.

The central limit theorem is a fundamental concept in statistics that describes the behavior of sample means as the sample size increases.

It states that, under certain conditions, the sampling distribution of the means of a random sample of size n will approach a normal distribution, regardless of the shape of the population distribution from which the sample is drawn.

The central limit theorem does not require the use of any specific sampling technique or resampling method, such as the bootstrap method. Rather, it applies to any random sample that is selected from a population, as long as the sample size is sufficiently large.

The commonly accepted rule of thumb is that the sample size should be at least 30 in order for the central limit theorem to apply. This is because a sample size of 30 or more is generally considered large enough to ensure that the sample means are normally distributed, regardless of the shape of the population distribution.

Therefore, the correct answer to the question is (b) a sample size of at least 30 be used to ensure that the sample means are normally distributed.

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To find the volume of the solid generated by revolving the region bounded by the graphs of the equations, either the disk method or the shell method can be used.

When finding the volume of a solid generated by revolving a region around a line, we have two methods at our disposal: the disk method and the shell method.

1. Disk Method:

The disk method involves dividing the region into infinitesimally thin disks perpendicular to the axis of rotation. The volume of each disk can be calculated using the formula for the volume of a cylinder (V = πr^2h), where r represents the radius of the disk and h represents its height. By summing up the volumes of all the disks, we obtain the total volume of the solid.

2. Shell Method:

The shell method, on the other hand, involves dividing the region into infinitesimally thin cylindrical shells parallel to the axis of rotation. Each shell has a thickness of Δx, where x is the variable that defines the boundaries of the region. The volume of each shell is calculated by multiplying the height of the shell (given by the difference in the y-values of the two bounding curves) by the circumference of the shell (given by 2πx). By summing up the volumes of all the shells, we obtain the total volume of the solid.

Both methods yield the same result for the volume of the solid. The choice between the two methods depends on the shape of the region and the convenience of integrating with respect to either x or y.

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Answer:

x=30

Step-by-step explanation:

dive 3x both sides then u should get 10

Answer:

D.

Step-by-step explanation:

Because its three times as much as 42 so its opposite of multiplication so its division with is also 3x=42 and to solve that you divide 3x by 3 and just get x then you divide 42 and 3 and u get your answer( im not gonna do the math lol)

Answer:

Step-by-step explanation:

-5 - 2(3x - 4) = 3(x - 4) + 6

-5 - 6x + 8 = 3x - 12 + 6

-6x + 3 = 3x - 6

3 = 9x - 6

9 = 9x

1 = x

Answer: x =1

Step-by-step explanation:

-5-2(3x-4) = 3(x-4) +6   Apply the distributive property to break it down.

-5-6x+8 = 3x -12 +6   Combine like terms

-6x + 3 = 3x - 6        Add 6x to both sides

+6x         +6x

3 = 9x  -6       Add 6 to both sides

+6        +6

9=9x             Divide both sides by 9

x= 1

2 grams = 2000 milligrams

Conversion between different units of measurement of the same quantity is called as conversion of units.

The process of conversion depends on the specific situation and the precision and accuracy of measurement.

Conversions from one unit to another should be exact, without changing the precision of the first. This is sometimes called soft conversion. It does not involve changing of the physical configuration of the unit being calculated.

'g' is the same as grams and similarly 'mg' is the same as milligrams.

Thus, when asked to convert 2 g to mg, as in the given question,

first multiply the value in grams by the conversion factor '1000'.

So, 2 grams = 2 × 1000 = 2000 milligrams.

A gram is larger unit than a milligram.

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can you write the question correctly

Answer:

Finish the question and ill be glad to help!

Step-by-step explanation:

The type of error that explains the variability in the results between groups is "random error."Explanation:Random error is the variability between the groups' results due to the imprecision of the measuring instrument or technique.

It is caused by minor differences in the experimental conditions that are unpredictable and can not be controlled or accounted for in the experiment. Random error can lead to imprecise results that fluctuate from the main answer, which means that it is not biased towards one particular direction.The other type of error that is commonly known is "systematic error" which is characterized by consistent errors that occur in a specific direction due to the method or instrument used.

Systematic error is due to the inaccuracy of the measuring instrument or incorrect experimental design, and it can affect the accuracy of the main answer. Mistakes or human errors, on the other hand, are due to human error, such as incorrect calculations or transcriptions, and are not part of the sources of errors.

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The sum of the interior angles of a regular polygon of 12 sides is 1800°

A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The sum of the all the interior angles of a polygon with 'n' number of sides is given by the formula,

Sum of all the angles = (n-2) × 180°

Since the number of sides in the polygon is 12, the sum of the angles will be,

Sum = (12-2) × 180° = 10 × 180° = 1800°

Hence, the sum of the interior angles of a regular polygon of 12 sides is 1800°.

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Answer: 88 square inches

Step-by-step explanation:

Answer:

Richard is older

Step-by-step explanation:

We can set up an inequality for both statements.

Let r equal Richard's age and s equal Sylvia's age.

"I am older than my wife."

Since Richard is speaking, the inequality would look like this:

r > s

This means Richard is older than Sylvia.

"I am younger than my husband."

Since Sylvia is speaking, the inequality would look like this:

s < r

This means that Sylvia is younger than Richard.

We can flip one inequality to "see" them from the same perspective.

Let's use s < r

To make it so that we can see the relationship from Richard's perspective, flip the entire inequality.

s < r

to

r > s

The inequality from the first quote is identical to this one!

Therefore, Richard is older than Sylvia.

Connect the points where the first arc crosses the triangle's base and the second arc intersects the base of the triangle with the straightedge to create the triangle's third side, BC.

Generally, To accurately construct triangle ABC, you will need a straightedge (such as a ruler) and a protractor. Here are the steps to follow:

Use the straightedge to draw a straight line segment of length 8 cm, which will represent side AB. This line segment will be the base of the triangle.

Place the point of the protractor at one end of the line segment and draw an arc that intersects the other end of the line segment.

Measure the angle formed by the line segment and the arc using the protractor. The measure of this angle should be 70 degrees.

Without changing the position of the protractor, draw another arc that intersects the first arc and the base of the triangle.

Use the straightedge to connect the point where the second arc intersects the base of the triangle to the point where the first arc intersects the base of the triangle. This will form the third side of the triangle, AC.

Finally, use the straightedge to draw the third side of the triangle, BC, by connecting the point where the first arc intersects the base of the triangle to the point where the second arc intersects the base of the triangle.

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Answer:

y = (17/4)x + (3/4)

Step-by-step explanation:

Formula we use,

→ y = mx + b

Now the slope-intercept form is,

→ y = mx + b

→ 4y - 5x = 12x + 3

→ 4y = 12x + 5x + 3

→ y = (17x + 3)/4

→ y = (17/4)x + (3/4)

Thus, answer is y = (17/4)x + (3/4).

Answer:

y = \(\frac{17}{4}\) x + \(\frac{3}{4}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4y - 5x = 12x + 3 ( add 5x to both sides )

4y = 17x + 3 ( divide through by 4 )

y = \(\frac{17}{4}\) x + \(\frac{3}{4}\) ← in slope- intercept form

The coordinates of the polynomial p(x) = -32 - 24x - 40x^2 relative to the basis B = {2 + 2x^2, 10 + 4x + 10x^2 - 14 - 8x - 16x^2} are [p(x)]_B = [-31, 3].

To find the coordinates of the polynomial p(x) = -32 - 24x - 40x^2 relative to the basis B = {2 + 2x^2, 10 + 4x + 10x^2 - 14 - 8x - 16x^2} for P₃, we need to express p(x) as a linear combination of the basis vectors.

We set up the equation:

p(x) = c₁(2 + 2x²) + c₂(10 + 4x + 10x² - 14 - 8x - 16x²)

Expanding and simplifying:

p(x) = 2c₁ + 2c₂x² + 10c₂ + 4c₂x + 10c₂x² - 14c₂ - 8c₂x - 16c₂x²

Now we equate the corresponding coefficients of the same powers of x on both sides of the equation:

-32 - 24x - 40x² = 2c₁ + 10c₂ + (-16c₂) x² + (4c₂ - 8c₂)x

We can now compare coefficients:

2c₁ + 10c₂ = -32

-16c₂ = -24

4c₂ - 8c₂ = -40

From the second equation, we find c₂ = 3. Substituting this value into the first and third equations:

2c₁ + 10(3) = -32

2c₁ + 30 = -32

2c₁ = -32 - 30

2c₁ = -62

c₁ = -31

Therefore, the coordinates of p(x) = -32 - 24x - 40x² relative to the basis B are [p(x)]_B = [-31, 3].

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The standard deviation of x for scores on the Critical Reading part of the test is approximately 18.26.

To find the standard deviation of x for scores on the Critical Reading part of the test, we can use the formula:

\(σ(x) = σ / √n\)

where σ is the population standard deviation and n is the sample size.

Plugging in the values given in the question:

\(σ(x) = 100 / √30\)

≈ 18.26

Therefore, the standard deviation of x for scores on the Critical Reading part of the test is approximately 18.26.

(b) Using the same formula, we can find the standard deviation of x for scores on the Mathematics part of the test:

\(σ(x) = 100 / √60\)

≈ 12.91

So, the standard deviation of x for scores on the Mathematics part of the test is approximately 12.91.

(c) Again, using the same formula, we can find the standard deviation of x for scores on the Writing part of the test:

\(σ(x) = 100 / √90\)

≈ 10.58

Hence, the standard deviation of x for scores on the Writing part of the test is approximately 10.58.

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Answer:

473 or 472, depends on how you round

Step-by-step explanation:

378/4 = 94.5

94.5 x 5 = 472.5

The number of votes she gets will be 473.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4.

Then the number of votes she gets that will be

→ 378 x 5 / 4

→ 378 x 1.25

→ 472.5 ≅ 473

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a) The probability that a single student randomly chosen from all those taking the test scores 23 or higher is 0.3557

b) The probability that the mean score x of these students is 23 or higher is 0.0043

What is Probability?

Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event.

Given that ,

mean = \mu = 21.1

standard deviation = \sigma = 5.1

a) P(x ≥ 23 ) = 1 - P(x ≤ 23)

= 1 - P[(x - \mu) / \sigma ≤ (23-21.1) /5.1 ]

= 1 - P(z ≤ 0.37)

= 1 - 0.6443 = 0.3557

Probability= 0.3557

b) n = 50

mu\bar x = \mu = 21.1

σbar x = σ / \\(\sqrt{n}\) = 5.1/ \\(\sqrt{50}\) = 0.7212

P(\bar x ≥ 23) = 1 - P(\bar x ≤ 23 )

= 1 - P[(\bar x - \mu\bar x ) / \sigma\bar x ≤ (23 - 21.1) / 0.7212 ]

= 1 - P(z ≤ 2.63)

= 1 - 0.9957 = 0.0043

Probability = 0.0043

a) The chance of a single student picked at random from all those taking the test scoring 23 or higher is 0.3557.

b) The chance that the mean x of these students is 23 or greater is 0.0043.

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Answer:

function is the correct answer

Answer:

an = a1 + (n - 1 ) d (Function)

Step-by-step explanation:

This is the formula that will be used when we find the general (or nth) term of an arithmetic sequence. So it is function

Given

a=15

b=11

c=21

Find

all angles of the triangle

Explanation

Using law of cosine to find angle A

Similarly

Final Answer

option (b) is correct

Answer:

multiplying by 2.3 is the opposite

Answer:

Step-by-step explanation:

Given the radius of the base of the cone is 5 cm and the height of the cone is 12 cm, we can find the volume of the toy as follows:

Volume of the cone:

The volume of a cone can be found using the formula: V = (π * r^2 * h) / 3, where r is the radius and h is the height of the cone.

Plugging in the values, we get:

V = (π * 5^2 * 12) / 3 = 100π cm^3

Volume of the hemisphere:

The volume of a hemisphere can be found using the formula: V = (4/3) * π * r^3, where r is the radius of the hemisphere.

Plugging in the values, we get:

V = (4/3) * π * 5^3 = (4/3) * π * 125 = 500π / 3 cm^3

Total volume of the toy:

The total volume of the toy is equal to the sum of the volume of the cone and the volume of the hemisphere:

V = 100π + 500π / 3 = (100 + 500 / 3) * π = 600π / 3 cm^3

So, the total volume of the toy is 600π / 3 cubic centimeters.

Answer:

6.64*10^(-9) moles of oxygen.

Step-by-step explanation:

If we have N molecules, the number of moles is given by:

n = N/Nₐ

where Nₐ is the Avogadro's number:

Nₐ = 6.02214076*10^23

In 2.000*10^15 molecules of sulfur dioxide, we have:

n = (2.000*10^15)/(6.02214076*10^23) = 3.32*10^(-9) moles of sulfur dioxide.

Now, sulfur dioxide has two oxygens and a single sulfur.

Then a mole of sulfur dioxide has two moles of oxygen and a single mol of sulfur.

Then in 3.32*10^(-9) moles of sulfur dioxide, we have twice that amount moles of oxygen, or:

2*3.32*10^(-9) = 6.64*10^(-9) moles of oxygen.

For the first payment, the interest payment is $1,330 and the principal repayment is $2,715.39.

To calculate the annual loan payments, we need to use the formula for an amortized loan:

Payment = (Loan Amount * Interest Rate) /\((1 - (1 + Interest Rate)^{-Number of Payments}\)

Substituting the values given in the problem, we get:

Payment = ($19,000 * 0.07) / \((1 - (1 + 0.07)^{-5}\)

Calculating this out gives us a payment of $4,045.39 per year.

To calculate the amount of the first payment that will be applied to interest and principal repayment, we need to use the following formula:

Interest Payment = Remaining Balance * Interest Rate

Principal Payment = Payment - Interest Payment

We can use these formulas to calculate the interest and principal payments for the first year. First, we need to find the remaining balance after the first payment is made. We can do this using the following formula:

Remaining Balance = Initial Balance - Principal Payment

Plugging in the values given in the problem, we get:

Interest Payment = $19,000 * 0.07 = $1,330

Principal Payment = $4,045.39 - $1,330 = $2,715.39

Remaining Balance = $19,000 - $2,715.39 = $16,284.61

So, for the first payment, the interest payment is $1,330 and the principal repayment is $2,715.39.

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Answer:

V = pi * R^2 * h

R = (V / (pi * h))^1/2 = (141.3 / (3.14 * 5))^1/2 = 3 cm

The radius of the cylinder is 3 cm.

Given,

The volume of the cylinder is 141.3 cubic centimeters.

We need to find what is the approximate radius of the cylinder.

Use 3.14 for the approximation of pi.

It is given by:

V = π r² h

h = height of the cylinder

r = radius of the cylinder.

We have,

V = 141.3 cm³

π = 3.14

h = 5 cm

V = π r² h

141.3 = 3.14 x r² x 5

141.3 / 3.14 x 5 = r²

r² = 9 cm²

r = 3 cm

Thus the radius of the cylinder is 3 cm

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The Z-score corresponding to a right tail area of 0.32 is approximately 0.75 (rounded to two decimal places).

Find the Z-score such that the area under the standard normal curve to the right is 0.32 Click the icon to view a table of areas under the normal curve. The approximate Z-score that corresponds to a right tail area of 0.32 is 0.7517 (Round to two decimal places as needed.)

The given area is a right-tail area, so we will find the value of Z that corresponds to 0.68 of the standard normal curve.

Step-by-step explanation:

The area under a standard normal curve is 1. The Z-score corresponding to the right-tail area of 0.32 is 0.7517 (rounded to four decimal places).Since this is a right-tail area, we will use the positive version of the Z-score (the negative version of the Z-score corresponds to a left-tail area).

Therefore, the Z-score corresponding to a right tail area of 0.32 is approximately 0.75 (rounded to two decimal places).

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Answer:

\(\huge\boxed{x=3}\)

Step-by-step explanation:

\(\text{Solve the equation for 'x'.}\\\\\\2(4x-3)-8=4+2x\\\\8x-6-8=4+2x\\\\8x-14=4+2x\\\\8x-14+14=4+14+2x\\\\8x=18+2x\\\\8x-2x=18+2x-2x\\\\6x=18\\\\\frac{6x=18}{6}\\\\\boxed{x=3}\\\\\\\boxed{\text{The correct answer should be: } X= 3}\\\\\\\text{Hope this helps you!}\)

Answer:

Lets mark the unmarked angle as angle A and the base of the building as BC

We can use tan to find this

tan=opposite/adjacent

by knowing the 2 interior angles we can calculate the measure of A sicne the interior angles of any triangle add up to 180

52+90+A=180

142+a=180

38=a

tan(38)=BC/300

300 tan(38)=bc

using a calculator we see that bc=234.385689 or 234meters rounded

Step-by-step explanation: