suppose that you want to construct a 95% confidence interval for estimating a population mean. how does the margin of error with a sample size of 100 compare with the margin of error with a sample size of 1,600, if both samples have the same standard deviation?

Answer:

<ICJ

Step-by-step explanation:

Vertical angles are congruent.

Answer: <ICJ

Answer: ∠JCI

Step-by-step explanation:

   ∠JCI and ∠FCE are vertical angles. We know that vertical angles are congruent, so the answer to this question is;

            ∠JCI

In conclusion Sample: A subset of the population, which could be a randomly selected group of home runs hit during one week in July of the 2014-2015 baseball season, used to estimate the average number of home runs hit during that week.

What does average number mean?

Average number is a measure of central tendency that is calculated by adding up a set of numbers and dividing the sum by the total number of numbers in the set. It is also known as the mean.

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Complete question:

What is the population and sample in a study of the number of home runs hit during one week in July of the 2014-2015 baseball season?

Population: The population in this study would be all home runs hit during one week in July of the 2014-2015 baseball season by all players and teams in the league.

Sample: The sample in this study would be a subset of the population, such as the home runs hit during one week in July of the 2014-2015 baseball season by a specific team or a specific player.

The required cost of 34 inches of wire as per the cost of 23 inches of wire is 92 cents is equals to 136 cents.

Let x be the cost (in cents) of 34 inches of wire.

We know that 23 inches of wire costs 92 cents,

Use a proportion to solve this problem,

23 inches / 92 cents = 34 inches / x cents

To solve for x, apply cross-multiply and simplify,

⇒ 23 inches × x cents = 92 cents × 34 inches

⇒ 23x = 3128

⇒ x = 3128/23

⇒ x ≈ 136.00 cents

Therefore, the cost of 34 inches of wire will be approximately 136 cents.

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Answer:

Step-by-step explanation:

The sum of the units 3 ft. 9 in, 4 ft. 7 in. and  10 ft. 3 in. is 18 ft. 7 in.

To add these lengths, we need to first convert all the measurements to the same units.

Let's convert everything to inches.

3 ft. 9 in. = (3 x 12) + 9 = 45 in.

4 ft. 7 in. = (4 x 12) + 7 = 55 in.

10 ft. 3 in. = (10 x 12) + 3 = 123 in.

Now we can add the lengths:

45 in. + 55 in. + 123 in. = 223 in.

We have 223 inches in total.

To convert this back to feet and inches, we can divide by 12 to get:

18 ft. 7 in.

So the final answer is 18 ft. 7 in.

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For this situation, the example size is 45 and the standard deviation is 3.1 inches, which is known. Hence, a one-example t-test is fitting for testing the scientist's hypothesis about the normal length of salmon getting back to generate from the Alaskan waterway.

The proper test for the scientist's hypothesis that the typical length of salmon getting back to generate from an Alaskan river is not exactly the verifiable normal length of 24 inches is a one-example t-test for a populace mean.

This is on the grounds that the specialist is looking at the example mean length (22 inches) to a realized verifiable populace mean (24 inches), and needs to decide whether the contrast between the two means is measurably huge. A one-example t-test is utilized to contrast an example mean with a realized populace mean and is suitable when the example size is little and the populace standard deviation is obscure.

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The slope of the line that passes through (2, 5) and (−1, 5) will be 0.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope of (2, 5) and (−1, 5),

Slope = (5 - 5)/(-1 - 2) = 0

Hence "The slope of the line that passes through (2, 5) and (−1, 5) will be 0".

The correct option is A.

y  ≥ -3

The range is defined as the set of possible outputs, so just look at the vertical axis, you can see it goes from x = -3 up, then the range is just the set of all values larger than -3

it is written as:

y  ≥ -3

The correct option is a-.

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The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

A numerical expression is characterized as the assortment of numbers factors and works by utilizing operations like expansion, deduction, multiplication, and division.

Considering that;

The expression is,

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

Presently, We can place x and y in the above expression as;

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

⇒ [- 5/(- 2 - 1) ] (- 4) - [-5×-2 + (- 3)]/(- 1)

⇒ [ - 5/ - 3 ] (- 4) - [10 - 3]/(- 1)

⇒ - 20/3 + 7

⇒ 1/3

In this way, The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

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A negative answer makes no sense because y is an angle and cannot be negative. As a result, we can conclude that there is no solution because the specified angles do not form a proper triangle.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

The total of a triangle's angles is 180 degrees. As a result, we may begin by locating the missing angle in the triangle containing the angle denoted by y:

Angle missing = 180° - 40° - y = 140° - y

y + 160° + 30° = 180°

Mixing like terms and calculating y:

y = 180° - 160° - 30° = -10°

A negative answer makes no sense because y is an angle and cannot be negative. As a result, we can conclude that there is no solution because the specified angles do not form a proper triangle.

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It will take approximately 1.386*t days until only 1/2 ounces of element X remain.

If the half-life of element X is t days, it means that after every t days the amount of element X will be reduced by half.

Initially, we have a 1-ounce sample of element X.

After t days, the amount of element X remaining will be 1/2 ounces.

After 2t days, the amount of element X remaining will be (1/2)*(1/2) = 1/4 ounces.

Similarly, after 3t days, the amount of element X remaining will be (1/2)(1/2)(1/2) = 1/8 ounces.

After n*t days, the amount of element X remaining will be (1/2)^n ounces.

We want to find the value of n such that (1/2)^n = 1/2^(n/2) ounces.

Taking the logarithm of both sides, we get:

n*log(1/2) = (n/2)*log(1/2)

Simplifying, we get:

n = 2*log(2) = 1.386

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Step-by-step explanation:

all he have to do is you substitute the expressions correctly

The experimental probability closest to the theoretical probability is O.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.

Each letter should have the same probability of occurring since there are 15 of each.

There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability of 15/75 = 1/5 of being drawn.

This means one would expect a theoretical frequency of 1250/5 = 250, i.e. any given letter should get drawn 250 times.

Hence, the experimental probability closest to the theoretical probability is O.

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The result (f•g)(12) = 382 represents the overall cost of catering the event when 12 fewer guests than 100 attend.

In mathematics, a function is a rule that gives each input value in a set a distinct output value. It is a relationship between a collection of inputs and a set of potential outputs, where each input has a single, precise counterpart in each possible outcome. f(x) = x2, where f is the function, x is the input, and x2 is the output, is a common function notation used to represent functions. Functions are used to model and analyse interactions between variables in many branches of mathematics as well as in many fields of science and engineering.

given

We must first locate the composite function f(g(x)) before substituting x = 12 to calculate (f•g)(12):

430 - 4x = f(g(x)) = f(100 - x) = 30 + 4(100 - x)

Thus, 430 - 4x = (f•g)(x) = f(g(x)).

If we replace x with 12, we get:

(f•g)(12) = 430 - 4

(12) = 382

Interpretation: Taking into account the cost per guest as modelled by f(x) = 30 + 4x and the number of attendees as modelled by g(x) = 100 - x, the result (f•g)(12) = 382 represents the overall cost of catering the event when 12 fewer guests than 100 attend.

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Answer: 7 meters

Step-by-step explanation:

1. Identify the given information: Circumference = 14 pi meters

2. Use the formula for calculating the circumference of a circle: Circumference = 2 pi * radius

3. Rearrange the formula to solve for the radius: Radius = (Circumference) / (2 pi)

4. Substitute the given information into the formula: Radius = (14 pi meters) / (2 pi)

5. Calculate the radius: Radius = 7 meters

The speed of the wind is 10km/hr.

What is the speed?

A scalar quantity, speed is defined as the size of the change in an object's location over time or the size of the change in an object's position per unit of time.

Here, we have

Given: An airship flies 150km with the wind and then turns around and flies back, taking 6 hours and 15 minutes for the round trip.

We have to find the speed of the wind if the speed of the airship in calm weather is 50 km/hr.

150 = (50-c)(6.25-t)

6.25-t = 150/(50-c)

(6.25×50 - 6.25c -150)/(50-c) = t

t = (162.5 - 6.25c)/(50-c).....(1)

150=(50+c)t  

t = 150/(50+c)

Now, we put the value of t in equation (1) and we get

150/(50+c) = (162.5 - 6.25c)/(50-c)

150 = (50+c) (162.5 - 6.25c)/(50-c)

150 = (50+c)(162.5 - 6.25c)/(50-c)

150 = (8125 - 312.5c +162.5c - 6.25c²)/(50-c)

7500 - 150c = 8125 - 312.5c + 162.5c - 6.25c²

7500 - 150c = 8125 - 150c  - 6.25c²

7500 = 8125 - 6.25c²

8125 - 6.25c² - 7500 = 0

6.25c² - 625 = 0

c² = 100

c = 10

Hence, the speed of the wind is 10km/hr.

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The Scatterplot has no correlation.

What is scatterplot?

Data visualization that depicts the relationship between two numerical variables is known as a scatterplot. The values for the two variables are used to depict each member of the dataset as a point with ( x , y ) coordinates that correspond to those values.

We know that A positive correlation between the variables is present when the y variable tends to grow as the x variable increases and a negative correlation is when x variables increase but y variable decreases.

No correlation means there is no clear relationship between two variables.

In the given scatter plot represent the relationship between month and cost.

Here for 6 months cost is $0.5 , for 7 months cost is $1 and for 5 months  cost is also $1. Then there is no clear relationship between month and cost.

Hence the scatterplot has no correlation.

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The probability of a SRS of 45 students spending an average of between $600 and $700 is approximately 0.9871.

We can use the central limit theorem to approximate the distribution of the sample mean from a normal population. Since the population standard deviation is known and the sample size is large enough (n = 45), we can use the normal distribution to approximate the sampling distribution of the sample mean.

The formula for the standard error of the mean is:

SE = σ/√n

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

Plugging in the values, we get:

SE = 120/√45 ≈ 17.89

Now, we need to standardize the sample mean using the z-score formula:

z = (x - μ) / SE

Where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.

For the lower bound of 600:

z = (600 - 650) / 17.89 ≈ -2.79

For the upper bound of 700:

z = (700 - 650) / 17.89 ≈ 2.79

Using a standard normal distribution table or calculator, we can find the area between these two z-scores:

P(-2.79 < z < 2.79) ≈ 0.9871

Therefore, the probability that a SRS of 45 students will spend an average of between 600 and 700 dollars is approximately 0.9871, or 0.98710 rounded to five decimal places.

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In conclusion, the chance of having HIV, assuming a positive test result, is 0.4%. It is important to remember that this number could vary depending on the accuracy and false positive rate of the test, as well as the number of people infected with HIV in the given area.

Assuming you tested positive for HIV, the chance of having the virus is higher than 2.5%, since the test has a false positive rate of 2.5%.

Out of the 10,000 people, 250 are likely to test positive, of which only one person actually has the virus. This means that the actual chance of having HIV, assuming a positive test result, is 1 in 250 or 0.4%.

It is important to note that this calculation only applies to the specific case of the 10,000 people in question, and the false positive rate of the test. Different tests have different levels of accuracy and false positive rate, which could alter the result. Furthermore, the number of people infected with HIV may differ significantly in different areas, which could also change the probability.

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Using composite figures, we can find the value of area as:

In the 1st image,

Area of 1st triangle =70m².

Area of 2nd triangle = 24unit².

Area of 3rd triangle = 30unit².

In the 2nd image,

Area of the composite figure = 144unit²

In the 3rd image,

Area of the trapezium = 54unit².

The area of composite shapes refers to the space any composite shape occupies. The composite shape is a shape made by combining a few polygons together to generate the required shape. Certain geometric forms, such as triangles, squares, quadrilaterals, etc., can be combined to create other geometric forms. Dividing a composite item into straightforward forms like a square, triangle, rectangle, or hexagon will allow you to compute its area.

In the 1st image,

Base of 1st triangle = 14m

Height of triangle = 10m.

Area of 1st triangle = 1/2 × b × h

= 1/2 × 14 × 10

= 70m².

In the 2nd triangle,

Base = 12

Height = 4

Area = 1/2 × b × h
= 1/2 × 12 × 4

= 24unit².

In the 3rd triangle,

Base = 12

Height = 5

Area = 1/2 × b × h

= 1/2 × 12 × 5

= 30unit².

Coming to the 2nd image we have a composite figure,

We have a rectangle with length = 9 and breadth = 6.

We have a triangle with base = 9 and height = 6.

And we have a trapezium with opposite sides as, a = 6, b = 15 with a height = 6.

So, the total area will be area of rectangle + area of triangle + area of trapezium.

= (9 × 6) + (1/2 × 9 × 6) + ((6+15)/2 × 6)

= 54 + 27 + 63

= 144unit².

Coming to the last image:

From the graph we can see that the polygon is a trapezium.

The height of the trapezium = 6 units.

Opposite sides,

a = 7 and b = 11.

So, area of trapezium = (a+b)/2 × h

= (7+11)/2 × 6

= 18/2 × 6

= 54unit².

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The graph should show a parabolic shape, opening upwards. The points are (0,0), (0.5, 2.5), (1,5), (1.5, 22.5), and (2,20).

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output.

Using the table provided, we can fill in the values for distance traveled:

Given function d=5t²

Putting t=0, d=0

t=0.5, d=1.25

t=1, d=5

t=1.5, d=11.25

t=2, d=20

Hence, d(meters) are 0,1.25,5,11.25 and 20.

To plot this data on a coordinate plane, we can use the values of t as the x-coordinates and the values of d as the y-coordinates.

The graph should show a parabolic shape, opening upwards. The points (0,0), (0.5, 2.5), (1,5), (1.5, 22.5), and (2,20) should be plotted and connected with a smooth curve.

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To sum up, the sampling distribution of the mean can be assumed to be approximately normal when the sample size is greater than 30 or the population is normally distributed.

The sampling distributions of means are always approximately normally distributed.

The correct option is: approximately normally distributed.

When the size of the sample is greater than 30 or the population is normally distributed, the sampling distribution of the mean is said to be approximately normally distributed.

This is true, whether the population is symmetrical or not, and the sampling distribution of the mean is symmetrical when the sample size is at least 30. .

If the population is symmetrical, then the sampling distribution of the mean will be symmetrical regardless of the sample sizes.

The other options are not true for the sampling distribution of the mean.

The distribution of the means would be positively skewed or negatively skewed if the distribution of the population was not symmetrical.

It's not the case that the distribution of the means is more variable than the population from which the samples were drawn.

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Based on proportions, the numbers of students in the senior form and junior form are 615 and 885, respectively.

Proportion refers to the equation of two ratios.

Proportion is a fractional value depicted using ratios, percentages, fractions, and decimals.

The percentage of senior form students in the school = 41%

The percentage of junior form students = 59% (100% - 41%)

The additional percentage of junior over senior students = 18% (59% - 41%)

The additional number of junior form students over the seniors = 270

Proportionately, if 18% = 270, the total number of students (both junior and senior) = 1,500.

Therefore, the number of senior and junior students is as follows:

Check:

The difference in the numbers = 270 (885 - 615)

Thus, using proportions, we can state that there are 1,500 students in the school, consisting of 615 seniors and 885 juniors.

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Answer:

Step-by-step explanation you have to do this

Answer:

Saanvi recorded the number of math problems she did for homework each night for 10 days.

Step-by-step explanation:

An angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.

Vertex, the intersection of two lines, is used to measure angles. Internal angles are created by the sides of geometric shapes like triangles and rectangles.

With the triangles that are presented, prove the angle bisector theorem:

There will be equality in the side ratios.

AB / BC = AD / DC

AB = 9 ; BC = 11.7 AD = 3.6

Put the values.

9/11.7 = 3.6 / AD

AD = 3.6*11.7 / 9

AD = 4.68

Thus, an angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.

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The relationship between the angle of elevation and the angle of depression between two points is that they are alternate interior angles and are equal when measured from the same horizontal line.

The angle of elevation and the angle of depression are related to each other as follows. The angle of elevation is the angle between the horizontal line and the line of sight when an observer is looking upwards to an object. The angle of depression is the angle between the horizontal line and the line of sight when an observer is looking downwards to an object.

The two angles are complementary, which means that they add up to 90 degrees. This is because the horizontal line and the line of sight form a right angle.

So, if the angle of elevation is x degrees, then the angle of depression is (90 - x) degrees, and vice versa.

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When creating a 96% confidence interval from a simple random sample (SRS) of 16 observations, the critical value to be used is 2.120.

A confidence interval is a range of values for an unknown population parameter, such as the population mean or population proportion. Confidence intervals are usually stated as a range of values with a level of confidence that the population parameter is contained in the interval.

Let's examine the components of a confidence interval to understand what it is:

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Answer:<HBG

Step-by-step explanation:

Adjacent means next to in this situation so it would be the angle next to it.

A larger sample size will result in a more reliable estimate of the population mean, lowering the variability and resulting in a higher F-ratio, which will result in the null hypothesis being rejected. As a result, both options A and B are correct.

Here we want to find,

the likelihood of rejecting the null hypothesis using anova is increased by which.

To increase the likelihood of rejecting the null hypothesis using ANOVA, a decrease in SSWITHIN and an increase in sample sizes are needed.

In statistics, analysis of variance (ANOVA) is a technique for comparing the means of two or more samples. ANOVA is an extension of the t-test and z-test methods, which can be used to compare only two means.

ANOVA compares the variation within the groups to the variation between the groups to see whether or not there is a statistically significant difference between them.

The null hypothesis ([tex]H_0[/tex]) in ANOVA is that the means of all groups are equal, while the alternative hypothesis (Ha) is that at least one group's mean is different from the others.

In ANOVA, a low value of SSWITHIN is desirable because it reflects that the data points are clustered around their respective means.

As a result, ANOVA will result in a higher F-ratio, which means that the null hypothesis will be rejected.

So, both a and b options are correct.

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Answer:

2/7 or 4/14

Step-by-step explanation:

we add all the people in the various electives and get 14.

then, we put 4 over 14 to get 4/14, which simplifies to 2/7 people.

I hope this helps!

Good luck for future math questions!

~Cain