Solve for x: 5x+2(3x+7)=3(x-6)

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

C

Step-by-step explanation:

2m + 3m = 5m

9m - 5m = 4m

11m - 6m = 5m

Therefore, the expression 11m - 6m is equivalent to 2m + 3m

(as they both equal 5m)

Answer:

C. The expression 11m - 6m is equivalent to 2m + 3m.

Step-by-step explanation:

9m - 5m = 4m

11m - 6m = 5m

2m + 3m = 5m

Answer:

LHS.= Sin 2x /( 1 + cos2x )

We have , sin 2x = 2 sinx•cosx

And. cos2x = 2cos^2 x - 1

i.e . 1+ cosx 2x = 2cos^2x

Putting the above results in the LHSwe get,

Sin2x/ ( 1+ cos2x ) =2 sinx•cosx/2cos^2x

=sinx / cosx

= Tanx

.•. sin2x/(1 + cos2x)= tanx

Step-by-step explanation:

Jason is right while Gabby is wrong because, two congruent rectangles are similar, but two similar rectangles may not be congruent.

For two figures to be considered similar, the following criterion must be satisfied:

This means the only criterion necessary for two figures to be considered congruent is that they must have the same shape but not necessary the same size. i.e. equal corresponding angles and the same ratio of corresponding lengths.

On the other hand, for two figures to be considered congruent, the following must be satisficed:

This implies that they must have the same shape and size.

Thus, if two rectangles have the 4 pairs of corresponding angles that are congruent, they are said to be similar.

The diagram of two similar rectangles is shown in the image attached below.

Therefore, Jason is right: all rectangles are similar.

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If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.

Answer:

3h - 15g

Step-by-step explanation:

All you have to do is multiply 3 by h, and 3 by 5g, but you have to keep the subtraction, so it would be 3h - 15g

Answer:The third one is!!

Step-by-step explanation:

The commutative property of addition says that changing the order of addends does not change the sum. Here's an example: 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+4

The inequality tha calculates the possible values of x is x < 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

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Answer:

\(\displaystyle \large \boxed{ \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}=-\dfrac{1}{2}}\)

Step-by-step explanation:

Hello, please consider the following.

\(\sqrt{(x^2-1)}-x\\\\=\sqrt{x^2(1-\dfrac{1}{x^2})}-x\\\\=x\left( \sqrt{1-\frac{1}{x^2}}-1\right)\)

For x close to 0, we can write

\(\sqrt{1+x}=1+\dfrac{1}{2}x-\dfrac{1}{8}x^2+o(x^2)\\\\\ \text{x tends to } +\infty \text{ means }\dfrac{1}{x} \text{ tends to 0}\\\\\text{So, when }\dfrac{1}{x}\text{ is close to 0, we can write.}\\\\\sqrt{1-\dfrac{1}{x^2}}=1-\dfrac{1}{2}\dfrac{1}{x^2}-\dfrac{1}{8}\dfrac{1}{x^4}+o(\dfrac{1}{x^4})\)

So,

\(x\left( \sqrt{1-\frac{1}{x^2}}-1\right)\\\\=x(1-\dfrac{1}{2}\dfrac{1}{x^2}+o(\dfrac{1}{x^2})-1)\\\\=-\dfrac{1}{2x}+o(\dfrac{1}{x})\)

It means that

\(\displaystyle \lim_{x \rightarrow +\infty} {x\left(\sqrt{x^2-1}-x\right)}\\\\=\lim_{x \rightarrow +\infty} {-\dfrac{x}{2x}}=-\dfrac{1}{2}\)

Thank you

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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Answer:

8.302

Step-by-step explanation:

cos(41)x/11

since x is on top then just multiply

cos(41)(11)

x=8.302 round it how u like

Answer:

8.3

Step-by-step explanation:

It has been awhile since I have done this so I may be a bit rusty.

a = (sin(A)⋅b) / sin(B)  =  (sin(49.00∘)⋅11.00)   /  (sin(90.00∘))    =    8.30

Answer:

Step-by-step explanation:

You paid C dollars for an item that you sold at a 6% profit.

F = 1.06C

Answer:

-6

Step-by-step explanation:

\(y = 7x - 6 \\ \\ equating \: it \: with \\ \\ y = mx + b \\ \\ b = - 6 \\ y - intercept = - 6\)

It is true that the quadrilateral EFGH is a trapezoid but not an isosceles trapezoid

The coordinates are given as:

Start by calculating the slopes of the parallel sides (i.e. sides FG and EH) using the following slope formula

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m_{FG} = \frac{3-0}{2 +2}\)

\(m_{FG} = \frac{3}{4}\)

\(m_{EH} = \frac{1 +5}{5 +3}\)

\(m_{EH} = \frac{6}{8}\)

Reduce the fraction

\(m_{EH} = \frac{3}{4}\)

By comparison, the slopes of the parallel sides are equal (i.e 3/4)

Next, calculate the side lengths of the slant sides (i.e. EF and GH) using the following distance formula

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}\)

So, we have:

\(d_{EF} = \sqrt{(-2 +3)^2+ (0+5)^2 }\)

\(d_{EF} = \sqrt{26}\)

\(d_{GH} = \sqrt{(5 -2)^2 + (1 - 3)^2}\)

\(d_{GH} = \sqrt{13}\)

By comparison, the side lengths of the slant sides are not equal

Because the slant sides do not have congruent side lengths, and the slopes of the parallel sides are equal; then the quadrilateral EFGH is a trapezoid but not an isosceles trapezoid

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Answer:

Distance between Nauru and Galapagos islands = 11525 Km to the nearest Km

Step-by-step explanation:

The angle between the two Islands is given as X

X = (180 - 166.56) + (180 - 90.30)

X = 13.44° + 89.70°

X = 103.14

Distance between the islands = length of the arc with angle X subtended at the center of the earth of radius R.

Length of arc = (X/360) × 2πR

Where, R, radius of the earth = 6400 Km

Length of arc = (103.14/360) × 2π × 6400 Km

Length of arc = 11525.48 Km

Therefore, distance between Nauru and Galapagos islands = 11525 Km to the nearest Km

Answer:

9. he bought 9.

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Step-by-step explanation:

The volume of a cube is 17 cubic inches.

The formula used to find the volume of a cube is given by :

\(V=x^3\)

x is the side of the cube

\(x=(V)^{1/3}\\\\x=(17)^{1/3}\\\\x=2.57\ \text{inches}\)

The fraction that cannot be written in the form of p/q is irrational no. If the cube root a number is not possible, then the length is considered to be irrational.

Answer:

x = 21

eliminate the denominator of 4

you can do this buy multiplying both sides by 4

x -9 = 12

x = 21

Answer:

z³=27

³√z³=³√27

z=3

Step-by-step explanation:

z³=27

³√z³=³√27

z=3

Answer:

the answer is 3

if you want the answer with complex number the Answer will be (-3i⁶)

because (-3)³ equal -27

and (i⁶)³ its i¹⁸ and the same time its i² so its -1

Answer:

2/3, or 66.7%

Step-by-step explanation:

There are 2 options for the first digit (3 or 4).

After the first digit is selected, it cannot be repeated, so there are 2 options left for the second digit.

After the first two digits are selected, there is only 1 option for the third digit.

So there are 4 permutations greater than 300.

The total number of permutations is 3! = 6.

So the probability is 4/6 = 2/3.

o show that 4.57 (5 and 7 recurring) is equal to 4 and 19/33, we can use algebraic equations. First, let x = 4.57 (5 and 7 recurring), then we multiply both sides by 100 to get 100x = 457.5757... Next, we subtract x from 100x to get 99x = 453. Thus, x = 453/99. We can simplify this fraction by dividing both the numerator and denominator by 3, giving us 151/33. Finally, we can write 151/33 as a mixed number, which is 4 and 19/33. Therefore, we have shown that 4.57 (5 and 7 recurring) is equal to 4 and 19/33 using algebraic equations.

Answer:

-7

Step-by-step explanation:

The full coordinate is (-7,3) the dot is on the line between -6 and -8

Answer:

-7

Step-by-step explanation:

x = 3

y = -7

the answer is just -7

Answer:

P(X ≥ 125) = 0.9812

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the normal distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\lambda\) is the mean in the given interval, which is the same as the variance.

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The Poisson can be approximated to the normal, with \(\mu = \lambda, \sigma = \sqrt{\lambda}\)

Let μ = 2.5 every minute

This is the mean of the Poisson, so \(\lambda = 2.5n\), in which n is the number of minutes.

P(X ≥ 125) over an hour

An hour has 60 minutes, so \(n = 60, \lambda = 2.5*60 = 150, \sigma = \sqrt{150} = 12.25\)

Using continuity correction, this is \(P(X \geq 125 - 0.5) = P(X \geq 124.5)\), which is 1 subtracted by the pvalue of Z when X = 124.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{124.5 - 150}{12.25}\)

\(Z = -2.08\)

\(Z = -2.08\) has a pvalue of 0.0188

1 - 0.0188 = 0.9812

So

P(X ≥ 125) = 0.9812

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Answer:

4\(y^{\frac{3}{2} }\)

Step-by-step explanation:

using the rule of exponents/ radicals

\(\sqrt[n]{a^{m} }\) = \(a^{\frac{m}{n} }\)

then

4 \(\sqrt{y^{3} }\)

= 4\(y^{\frac{3}{2} }\)

Answer:

divide 99 by 5

99/5= 19.8

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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