The term of an AP is 75 and the 25th is also 75. Find the common difference and the sum of the 100terms

The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0680. So, the correct answer is option d.

Calculate the sample proportion:

The formula (p) = x/n, where x is the sample size (163) and n is the number of successes (96), yields the sample proportion.

Therefore, the sample proportion is 96/163 = 0.5896.

Calculate the standard error:

The formula SE(p) yields the sample proportion's standard error = √[p(1-p)/n], where n is the sample size, and p is the sample proportion.

Consequently, the sample proportion's standard error is as follows:

SE(p) = √[0.5896(1-0.5896)/163] = 0.037

Calculate the margin of error:

The margin of error is given by the formula ME = z × SE(p), where SE(p) is the standard error of the sample proportion and z is the z-score corresponding to the desired level of confidence.

The z-score for a 95% confidence interval is 1.96.

As a result, the error margin is:

ME = 1.96 × 0.037 = 0.0680

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Answer:

Eqation a and 15

Step-by-step explanation:

because 5 pears all cut into thirds is 15 slices 5 times 3 is 15

The length of XZ in circle C is equal to the √34. This can be found using the Pythagorean theorem and the fact that XZ is a radius of the circle.

As WZ and XR are diameters, they intersect at the center of the circle, which we'll call point O.

Since WX is a chord of the circle, we can use the perpendicular bisector of WX, which passes through O, to find the length of XZ.

Let's call the midpoint of WX point M. Then OM is perpendicular to WX and bisects it.

So we have two right triangles, OXM and MXZ. We know that OM = 5 and XM = 3 (half of WX).

Using the Pythagorean theorem, we can find the length of OX:

OX² = OM² + MX²

OX² = 5² + 3²

OX² = 34

OX = √(34)

Since XZ is also a radius of the circle, we have XZ = OX = √(34).

Therefore, the measure of XZ in circle C is √(34).

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The mean of the game is 9

To find the mean of a game with two possible outcomes, we need to multiply the value of each outcome by its probability and then add the results.

Let X be the random variable representing the outcome of the game. The first outcome has a value of 5 and a probability of 0.2, while the second outcome has a value of 10 and a probability of 0.8.

Thus, the expected value or mean of the game can be calculated as:

E(X) = (0.2 x 5) + (0.8 x 10)

= 1 + 8

= 9

Therefore, the mean of the game is 9

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The calcuated value of the proportionality constant (y to x) is 15

To find the proportionality constant between the distance and time, we can use the formula:

proportionality constant = y/x

where y is the distance and x is the time.

From the graph, we know that when x = 1, y = 15. Therefore, the proportionality constant can be calculated as follows:

proportionality constant = y/x = 15/1 = 15

So, the proportionality constant between the distance and time is 15.

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The value of k is given as follows:

k = 2.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For this problem, we have that the parameters are given as follows:

Hence the equation to obtain k is given as follows:

[tex]\sin{45^\circ} = \frac{\sqrt{2}}{k}[/tex]

[tex]\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{k}[/tex]

k = 2.

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The answer of the given question based on the circle is ,  the answer is option (d) 8/3π.

In geometry, an arc is  portion of circumference of a circle. It is  curved line that connects two points on  circle. The length of arc is proportional to the angle that it subtends at the center of the circle.

Since EFB is a straight line and EB is a diameter of the circle, angle EFB subtends the entire circle at F. Therefore, the angle subtended by arc EFD is the difference between the angles subtended by arcs EF and EB.

Arc EF subtends a full circle at F, so its angle is 2π radians. Arc EB subtends a straight angle at F, so its angle is π radians.

Therefore, the angle subtended by arc EFD is:

2π - π = π

The length of arc is given by formula L = rθ, where r is  radius of  circle and θ is  angle (in radians) subtended by  arc at  center of  circle.

In this case, r = 4 and θ = π, so the length of the arc corresponding to angle EFD is:

L = rθ = 4π

Therefore, the answer is (d) 8/3π.

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Answer:

x² - 4 = 0

Step-by-step explanation:

choices: x² - 4 = 0, x² = -4, 3x² + 12 = 0, 4x² = 16, 2(x-2)² = 0

to find x= -2, 2

x² - 4 = 0

(x + 2) (x - 2) = 0

x = -2, 2

We have shown that the left-hand side of the equation is equal to the right-hand side of the equation, and the trigonometric identity is proved.

We have,

(cos 2x + cos 4x)/(cos 2x - cos 4x)

We can use the identity cos 2A = 1 - 2sin² A to rewrite cos 4x as:

cos 4x = 1 - 2sin² 2x

Then, substituting this into the expression, we get:

(cos 2x + 1 - 2sin² 2x)/(cos 2x - 1 + 2sin² 2x)

Using the identity sin² A = 1 - cos^2 A, we can rewrite sin² 2x as:

sin² 2x = 1 - cos² 2x

Substituting this into the expression, we get:

(cos 2x + 1 - 2(1 - cos² 2x))/(cos 2x - 1 + 2(1 - cos² 2x))

Simplifying the numerator and denominator separately, we get:

(2cos² 2x + 1)/(2cos² 2x - 1)

Using the identity cot A = 1/tan A, we can rewrite tan 3x as:

tan 3x = sin 3x/cos 3x

We can then use the identity sin 3A = 3sin A - 4sin^3 A and

cos 3A = 4cos³ A - 3cos A to rewrite sin 3x and cos 3x as:

sin 3x = 3sin x - 4sin³ x

cos 3x = 4cos³ x - 3cos x

Substituting these expressions into the right-hand side of the equation, we get:

cot 3x/tan x = (cos x/sin x)/(3sin x - 4sin³ x)/(cos x)

Simplifying by multiplying the numerator and denominator by the reciprocal of the fraction in the denominator, we get:

cot 3x/tan x = (cos x/sin x) * (cos x)/(3sin x - 4sin^3 x)

Multiplying the two fractions together, we get:

cot 3x/tan x = cos^2 x/(sin x(3 - 4sin^2 x))

Using the identity 1 - cos^2 A = sin^2 A, we can rewrite cos^2 x as:

cos^2 x = 1 - sin^2 x

Substituting this into the expression, we get:

cot 3x/tan x = (1 - sin^2 x)/(sin x(3 - 4sin^2 x))

Simplifying the numerator and denominator separately, we get:

cot 3x/tan x = (1/sin x) x (1 + sin x)/(3 - 4sin^2 x)

Using the identity 1 + sin A = 1/cos A, we can rewrite the expression as:

cot 3x/tan x = (1/sin x) x (1/cos x)/(3 - 4sin^2 x)

Finally, using the identity cot A = cos A/sin A, we can rewrite the expression as:

cot 3x/tan x = cos x/(sin x(3 - 4sin^2 x))

Therefore,

We have shown that the left-hand side of the equation is equal to the right-hand side of the equation, and the trigonometric identity is proved.

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The table of ordered pairs is completed below

Here is the completed table and plotted points:

Point x y (x,y)

A 4 9 (4,9)

B 6 3 (6,3)

C 1 3 (1,3)

D 8 7 (8,7)

E 8 9 (8,9)

To plot these ordered pairs on a coordinate plane, we need to draw the x and y axes, and label the units on each axis.

Then we can plot each point by starting at the origin (0,0) and moving horizontally (to the right if x is positive, or to the left if x is negative) and vertically (up if y is positive, or down if y is negative) to the corresponding point.

The points plotted on the coordinate plane are attached

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Complete the table. Then, plot the ordered pairs on the coordinate plane. Make sure to label each point with its corresponding letter.

              x                y       (x, y)

A            4                9

B            6                3

C            1                3

D            8                7

E             8                9

The area of the replaceable is [tex]15[/tex] square inches.

The area of a regular hexagon, we can use the formula:

[tex]A = (3\sqrt3 / 2) \times s^2[/tex]

Where A is the area of the hexagon and s is the length of one of its sides.

To find the area of the replaceable head, we can split it into two shapes: a rectangle and a triangle.

The rectangle has a length of 10 mm and a width of 12 mm, so its area is:

Area of Rectangle [tex]= length \times width = 10 mm \times 12 mm = 120 mm^2[/tex]

The triangle has a base of  [tex]12 mm[/tex] and a height of [tex]6 mm[/tex], so its area is:

Area of Triangle [tex]= 1/2 \times base \times height = 1/2 \times 12 mm \times 6 mm = 36 mm^2[/tex]

To find the total area of the replaceable head, we add the area of the rectangle and the area of the triangle:

Total Area =Area of Rectangle  +  Area of Triangle [tex]= 120 mm^2 + 36 mm^2 = 156 mm^2[/tex]

Therefore, the area of the replaceable head is   [tex]156[/tex]mm².

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Answer:

Step-by-step explanation:

q – 3 = 7 q

-3=6q

q=-1/2

2p=2p

{p∈IR}

The equation of the given circle is;Option D; x² + y² = 9

The general formula for the equation of a circle is expressed as;

(x - h)² + (y - k)² = r²

Where;

We are told that;

Circle is at the origin with coordinates (0, 0)

r = 3

Substitute the known values in the above equation, so, we have the following representation

(x - 0)² + (y - 0)² = 3²

Evaluate the exponents and open the brackets

x² + y² = 9

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The equation of the circle is; Option D: x² + y² = 9

The general formula for expressing the equation of a circle is :

(x - h)² + (y - k)² = r²

Where;

(h, k) is the coordinate of the center of the circle

r is the radius of the circle

From the given image of the circle, we see that the center of the circle is at the origin. Thus, the coordinates of the center of the circle is (0, 0)

We also see that from the origin to the circumference is 3. Thus:

r = 3

Plugging in the relevant values into the circle equation, we have:

(x - 0)² + (y - 0)² = 3²

Simplifying further gives us:

x² + y² = 9

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Answer:

the required answer is 1 and -5

Therefore, C) The median for Felicia's data is bigger than the median for Gabriella's data is the claim best supported by the data in the box plots.

Basketball is a team sport played by two teams of five players each on a rectangular court. The objective of the game is to score points by shooting a ball through a hoop, which is located 10 feet high on a backboard at each end of the court.

In statistics, quartiles are values that divide a dataset into four equal parts, with each part comprising 25% of the data. The three quartiles that divide the data into four equal parts are the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). The second quartile (Q2) is the same as the median of the dataset.

From the given box plots, we can see that Felicia's maximum number of points scored in one game is 28 and Gabriella's maximum is 24. Therefore, statement A is false.

The range of the data for Felicia is from 6 to 28, which is 22. The range of the data for Gabriella is from 10 to 24, which is 14. Therefore, statement B is false.

The median for Felicia's data is approximately 19 and the median for Gabriella's data is approximately 16. Therefore, statement C is true.

The first quartile for Felicia's data is approximately 12 and the first quartile for Gabriella's data is approximately 11. Therefore, statement D is false.

Thus, the statement best supported by the information in the box plots is C) The median for Felicia’s data is greater than the median for Gabriella’s data.

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The area of the rectangle is 48 in².

The area of the triangle is 24 in².

The area of the triangle is half the area of the rectangle.

To calculate the area of a rectangle, we multiply the length of the rectangle by its width. And to calculate the area of a triangle we multiply the base of the triangle to the height of the triangle and divide by 2.

To calculate the area of the rectangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute into equation 1

Also, the area of the triangle is given by the formula below

Where:

Substitute into equation 2

Hence, the area of the triangle is half the area of the rectangle.

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The probability that a lightbulb will last between 1,950 and 2,050 hours is 0.84, or 84%.

To solve this problem, we need to find the probability that the lifespan of a lightbulb will fall between 1,950 and 2,050 hours.

First, we need to standardize the distribution using the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For x = 1,950 hours:

z = (1,950 - 1,975) / 25 = -1

For x = 2,050 hours:

z = (2,050 - 1,975) / 25 = 3

Now, we need to find the area under the standard normal distribution curve between z = -1 and z = 3. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = 3 is 0.9987. Therefore, the area between z = -1 and z = 3 is:

0.9987 - 0.1587 = 0.84

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The weights in a weighted moving average are selected by: Trial and error, Fitting to a regression line, Guessing, Experience.

The methods for selecting weights in weighted moving averages are trial and error, fitting to a regression line, and experience.

When selecting weights for weighted moving averages, the following methods can be used:
Trial and error:

Testing different weight combinations to find the best fit for the data.
Fitting to a regression line:

Analyzing the relationship between the data points and assigning weights accordingly.
Experience:

Using prior knowledge and understanding of the data or similar situations to determine appropriate weights.

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 Trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.

With weighted moving averages, the weights can be selected using various methods. Here are the applicable methods from your given options:

1. Trial and error fitting: Weights can be selected by testing different combinations of weights and observing their impact on the accuracy of the model.

2. Fitting to a regression line: Weights can be determined by fitting a regression line to the data and using the coefficients of the regression line as the weights.

3. Experience: Domain knowledge or past experience with similar data can help in selecting appropriate weights.

In summary, trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.

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Count the significant digits in the number.

Since there are no captive zeros or trailing zeros, only the two non-zero digits (3 and 6) are significant.

The time measurement 0.0036 seconds has 2 significant digits.

Significant digits in the time measurement 0.0036 seconds, let's first define what significant digits are and then determine the number of significant digits in the given measurement.
Significant digits are the meaningful digits in a number that contribute to its precision.

These digits help to reduce any ambiguity when reporting measurements.
To determine the significant digits in the number 0.0036 seconds:
Identify non-zero digits.
All non-zero digits (1-9) are always considered significant.

The non-zero digits are 3 and 6.
Identify leading zeros.
Leading zeros are the zeros that appear before the first non-zero digit.

These zeros are not considered significant.

The leading zeros are the three zeros before the 3.
Identify trailing zeros.
Trailing zeros are the zeros that appear after the last non-zero digit.

If the number has a decimal point, these zeros are considered significant.

There are no trailing zeros.
Identify captive zeros.
Captive zeros are the zeros that appear between non-zero digits.

These zeros are always considered significant.

There are no captive zeros.
Count the significant digits in the number.

Since there are no captive zeros or trailing zeros, only the two non-zero digits (3 and 6) are significant. So, the time measurement 0.0036 seconds has 2 significant digits.

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y = (-4/3)x + 1 this line will intersect point (3,-3) and be perpendicular to the line y = (3/4)x + 5.

y = (3/4)x + 5

Compare with the standard form of equation y = mx +c

3/4 is the slope.

The negative reciprocal of the slope is used to obtain a perpendicular slope.

-4/3 is the perpendicular slope.

Let's rewrite the equation: y = (-4/3)x + b

Remember that b is the line's y-intercept base. If the line must pass straight through the point (3, -3), we must determine the location of the base.

To accomplish this, we just enter our point into the formula and solve for our base.

-3 = (-4/3)(3) + b

Now calculate b: b = (-4/3)(3) + 3

b = -4 + 3 b = 1

You now get the final equation: y = (-4/3)x + 1 now that you have the base.

This line will intersect point (3,-3) and be perpendicular to the line y = (3/4)x + 5.

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Complete question:

write an equation passing through the point that is perpendicular to(3,-3); y= 3/4 x+5

After rounding 475.189 to the nearest hundredth we get 475.19 .

Rounding of a number is a process of approximating the original number to some decimal points resulting the original number to shorten up for more explicit representation.

Rules of rounding a number to its nearest hundredth is,

The original number would be rounded up to two decimal places as it represents to its hundredth decimal place.

If the digit after the second decimal place of the original number is greater than (equals to) 5 then we round up the number, by increasing the previous place value digit by 1.

And if the digit after the second decimal place of the original number is lesser than 5 then we round down the number, by decreasing the previous place value digit by 1.

Here in 475.189 the digit after second decimal is 9 which is greater than 5, hence we round up the number by increasing the previous value (that is, second decimal digit)  by 1 we get 475.19 (to the nearest hundredth).

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The length of side BD which is the altitude of the triangle is 2√(70)

The length of BD is solved using similar triangles. This is defined by triangles formed from triangle ABC and they include

Let the altitude be h, hence we have the formula of the proportions as

AD / h = h / DC

plugging the values gives

20 / h = h / 14

h^2 = 20 * 14

h = √(20 * 14 )

h = √(280)

h = 2√(70)

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The best description of the area under the normal curve that would be used to approximate binomial probability is 'Area to the left of 46.5'.

To approximate the binomial probability, we can use the normal distribution as an approximation for the binomial distribution when the sample size is large enough, and the probability of success is not too close to 0 or 1. The mean of the normal distribution is equal to the mean of the binomial distribution, which is np, and the standard deviation of the normal distribution is equal to the square root of npq, where q is the probability of failure.

In this case, the number of DVDs that may malfunction follows a binomial distribution with parameters n = 319 and p = 1/100, where 1/100 is the probability of a DVD malfunctioning. Therefore, the mean of the binomial distribution is np = 3.19, and the standard deviation is [tex]\sqrt{npq}[/tex] = [tex]\sqrt{3.19*0.99}[/tex] ≈ 1.77.

To find the probability that at most 46 out of 319 DVDs will malfunction, we need to find the area under the normal curve to the left of 46.5 (since we are interested in the probability of at most 46 malfunctions, which includes 46.5 as well). Therefore, the answer is 'Area to the left of 46.5'.

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A. Here's a sketch of a horizontal pipe at a maximum slope (1/2 inch per foot) and a minimum slope (1/4 inch per foot):   / / / / / / / / / / / / / / / / / / /

 / / / / / / / / / / / / / / / / / / /

/ / / / / / / / / / / / / / / / / / /

/ / / / / / / / / / / / / / / / / / /

The pipe on the left has a slope of 1/4 inch per foot, while the pipe on the right has a slope of 1/2 inch per foot.B. To determine the minimum and maximum angles, we need to use trigonometry. If we let the angle that the pipe makes with the horizontal be θ, then we have:Minimum angle: tan(θ) = 1/48 (since 1/4 inch per foot is equivalent to 1 inch of drop over 48 inches of horizontal distance) θ ≈ 1.2 degreesMaximum angle: tan(θ) = 1/24 (since 1/2 inch per foot is equivalent to 1 inch of drop over 24 inches of horizontal distance) θ ≈ 2.4 degreesSo the minimum angle is approximately 1.2 degrees and the maximum angle is approximately 2.4 degrees.C. To determine if the slope of Enrico's pipe is acceptable, we need to calculate the slope of the pipe in inches per foot. Enrico's pipe runs a horizontal distance of 172 inches and drops 6 inches. The slope is:Slope = Drop / Horizontal distance = 6 / 172Slope = 0.0349 inches per inchTo convert this to slope in inches per foot, we multiply by 12:Slope = 0.4188 inches per footSince this slope is between the acceptable range of 1/4 inch per foot and 1/2 inch per foot, Enrico's pipe slope is acceptable.


Correct me if I am wrong

A. Sketch of a pipe at slop 1/4 inch per foot and a horizontal pipe at slope 1/2 inch per foot attached below. B. the minimum and maximum angle are approximately 14.0 degrees and 26.6 degrees, respectively. C. Yes, pipe slope is acceptable according to the given criteria.

B. Determine the minimum and maximum angles:

To find the angle, use the tangent function. The tangent of an angle is equal to the ratio of the height to the horizontal distance travelled.

Minimum angle:

Tangent of the angle= 1/4 inch per foot

Tangent of the angle = 0.25 inches per foot

Minimum angle (in degrees) = arctan(0.25)

Minimum angle ≈ 14.0 degrees

Maximum angle:

Tangent of the angle = 1/2 inch per foot

Tangent of the angle = 0.5 inches per foot

Maximum angle (in degrees) = arctan(0.5)

Maximum angle ≈ 26.6 degrees

C. Enrico's drain pipe:

Horizontal distance travelled  = 172 inches

Drop from the horizontal = 6 inches

Slope of the pipe = Drop / Run

Slope of the pipe = 6 / 172

Slope of the pipe ≈ 0.0349 inches per inch

To convert the slope to inches per foot:

Slope = 0.0349 × 12

Slope ≈ 0.4188 inches per foot

Hence, sketch of a pipe at slop 1/4 inch per foot and a horizontal pipe at slope 1/2 inch per foot attached below, the minimum and maximum angle are approximately 14.0 degrees and 26.6 degrees, respectively, and yes, pipe slope is acceptable according to the given criteria.

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The integer conversion specifier that would display the hexadecimal digit "a" is "x".
d) x

To display the hexadecimal digit "a" using an integer conversion specifier.
The "x" specifier is used for displaying an integer value in hexadecimal format with lowercase letters (i.e., a, b, c, etc.), while "X" would display the value in uppercase letters (i.e., A, B, C, etc.).

Options "H" and "h" are not standard integer conversion specifiers for displaying hexadecimal values.

Hence d) x is correct.

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Ana will hit the water 3 seconds after diving.

We need to solve for when her height is 0. We can set h(x) = 0 and solve for x:

-5(x+1)(x-3) = 0

This expression equals zero when either (x+1) = 0 or (x-3) = 0. Solving for these values gives:

x+1 = 0 or x-3 = 0

x = -1 or x = 3

The negative value for x doesn't make sense in this context since it represents a time before Ana even jumped off the board, so we can ignore it.

Therefore, Ana will hit the water 3 seconds after diving.

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Answer:

Step-by-step explanation:

x = [tex]\sqrt{12^{2}+9^{2} }[/tex]

x = 15

Answer: 3x²-2x+5=0

You subtract the 2x and add 9 from both sides to get 3x²-2x+9=0

Answer:

3x^2−2x+5=0

Step-by-step explanation:

3x^2-4=2x-9

first you gotta add 9 to both sides

3x^2+5=2x

then you gotta subtract 2x from both sides

3x^2-2x+5=0

-SpoOky

Answer:

C. -1.7

Step-by-step explanation:

-4.2 - x = -2 2/4

-2 2/4 = -10/4 = -2.5

-4.2 - x = -2.5

-x = 1.7

x = -1.7

So, the answer is C. -1.7

If a random sample of 20 gas stations was selected to estimate the gas prices. The type of error that could have occurred is a type I error, which is the rejection of a true null hypothesis. The probability of making a type I error is equal to the level of significance (α), which is 10% in this case. So, there is a 10% chance of making a type I error in this test.

To test if the true average gas price is under $3.50, we can use a one-tailed t-test with a null hypothesis of:

H0: μ >= $3.50

And an alternative hypothesis of:

Ha: μ < $3.50

where μ is the true population mean gas price.

Using a t-test with a sample size of 20, we can calculate the t-value as:

t = (x -bar - μ) / (s / sqrt(n))

where x-bar is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (3.40 - 3.50) / (0.22 / sqrt(20))

t = -2.03

Looking up the t-distribution table with degrees of freedom (df) = 19 and a 10% alpha level (α = 0.10), we find the critical t-value as -1.325.

Since our calculated t-value (-2.03) is less than the critical t-value (-1.325), we reject the null hypothesis in favor of the alternative hypothesis. Therefore, we can conclude that there is sufficient evidence to suggest that the true average gas price is under $3.50.

The type of error that could have occurred is a Type I error, which is rejecting a true null hypothesis. In this case, it means that we conclude that the true average gas price is under $3.50 when it's actually not. The probability of making a Type I error is equal to the alpha level, which is 10% in this case. So there's a 10% chance that we falsely reject the null hypothesis.

Learn more about type 1 error here:https://brainly.com/question/29854786

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