The minimum wage set by the government at $7.50 per hour does not result in a pay cut for unskilled workers, as it is below the equilibrium wage of $8.00 per hour.
The wage rate remains unchanged, and the labor market remains in balance.
The statement is false.
False.
The equilibrium wage in the market for unskilled labor is $8.00 per hour, which means that the market naturally sets the wage rate at this level, based on the forces of supply and demand.
The government then sets a minimum wage at $7.50 per hour.
Since the minimum wage is below the equilibrium wage, it does not directly impact the wage rate for unskilled workers.
The equilibrium wage represents the point at which the supply of labor (the number of workers willing to work at a given wage) equals the demand for labor (the number of workers that employers are willing to hire at a given wage).
In this case, both workers and employers are satisfied with the $8.00 per hour wage, and the labor market is balanced.
The government sets a minimum wage below the equilibrium wage, it essentially sets a wage floor that is not binding. Employers are still willing to pay the equilibrium wage of $8.00 per hour, and workers are still willing to accept this wage.
The wage for unskilled workers remains at $8.00 per hour, and there is no pay cut of 50 cents per hour.
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2a. complete the table for values for the equation y=3x+4 X0 1 2 Y b. Plot the coordinates from the table. Join them with a straight line. Extend your straight line to y=-2 d. Write three pairs of negative x- and y-coordinates that lie on the line y = 3x + 4. 4 5x
Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).
what is coordinates ?A set of numbers known as coordinates describes a point or object's location in a given space or coordinate system. When representing a spot's location in a plane or three-dimensional space, coordinates are frequently expressed as x or triples in mathematics. Depending also on system being utilised, several values can be used to represent coordinates, although often, integers or real numbers are used to express them.
given
We can substitute negative values for x and solve for y to obtain three pairs of negative x and y coordinates that lie on the line y = 3x + 4.
With x = 1, y = 3(-1), plus 4, equals 1. Hence, one set of negative x and y coordinates is (-1, 1).
Y = 3(-2) + 4 = -2 when x is equal to 2. In light of this, another set of negative x- and y-coordinates is (-2, -2).
Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).
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please help me with this question
Answer:
Step-by-step explanation:
The answer is attached below. There isn't much explanation for this. You just translate the word problem into a mathematical inequality.
PLEASE HELP ASAP WITH EXPLANATION AND ANSWER
Answer: 3.45meters
Step-by-step explanation:
To find the range of the length of pipe that the plumber can cut, we need to write an absolute value inequality that expresses the condition that the length of the pipe must be within 0.09 meters of the required length. Let's call the required length L.
The plumber can cut a pipe that is within 0.09 meters of the required length, so the length of the pipe must be between L - 0.09 and L + 0.09. We can express this as:
|3.36 - L| ≤ 0.09
To solve this inequality, we need to consider two cases: when 3.36 - L is positive and when it is negative.
Case 1: 3.36 - L ≥ 0
In this case, the absolute value of 3.36 - L is equal to 3.36 - L. So we can write:
3.36 - L ≤ 0.09
Solving for L, we get:
L ≥ 3.36 - 0.09
L ≥ 3.27
Therefore, if 3.36 - L is positive, the length of the pipe must be greater than or equal to 3.27 meters.
Case 2: 3.36 - L < 0
In this case, the absolute value of 3.36 - L is equal to -(3.36 - L), or L - 3.36. So we can write:
L - 3.36 ≤ 0.09
Solving for L, we get:
L ≤ 3.36 + 0.09
L ≤ 3.45
Therefore, if 3.36 - L is negative, the length of the pipe must be less than or equal to 3.45 meters.
Putting these two cases together, we get:
3.27 ≤ L ≤ 3.45
Therefore, the range of the length of pipe that the plumber can cut is between 3.27 meters and 3.45 meters.
If I have this sequence 2, 4, 6, . .. I can describe the rule as add 2
For each sequence below, describe the rule and write the
next two terms.
a)
b)
-9, -7,-5,
The rule is
4, -10, -16,
The rule is
susie has a rectangular garden that is 10 feet by 12 feet she plants flowers in a circular shape with a radius of 4 feet if Susie only wants to fertilize the space outside the flowers how many square feet will she fertilize.
She will fertilize 69.76 square feet outside of the circular flowers.
How many Sq ft will Susie fertilize outside the circular flowers?In order to get the area that she will fertilize outside of the circular flowers, we will calculate area of the entire rectangular garden and the area of the circular flowers.
The area of the rectangular garden is:
[tex]= 10 ft * 12 ft\\= 120 sq ft[/tex]
The area of the circular flowers is:
[tex]= \pi r^2\\= 3.14 * 4^2\\= 50.24 sq ft[/tex]
To find area to be fertilize outside of the circular flowers, we will subtract these area which gives us:
[tex]= 120 sq ft - 50.24 sq ft\\= 69.76 sq ft[/tex]
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5) What is the correct definition of a resume?
Question 5 options:
a letter listing all former employers, salaries and positions the applicant has ever had
a document listing detailed reasons why the applicant wants to work for the company and why he should be chosen
a letter serving as a sample of the applicant's writing skills and communication style
a document describing the applicant's experience, strengths, skills, education, and other qualifications
Answer:
The correction definition of a resume is a document describing the applicant's experience, strengths, skills, education and other qualifications.
A recipe calls for 23\frac{2}{3}
3
2
cup of brown sugar. Marilyn is making 5 batches. How many cups of brown sugar should Marilyn use?
Marilyn needs 3 and 1/3 cups of brown sugar to make 5 batches of the recipe.
To find the total amount of brown sugar Marilyn needs, we need to multiply the amount required for one batch by the number of batches.
One batch requires 2/3 cup of brown sugar. To find the amount required for five batches, we can multiply 2/3 by 5.
2/3 * 5 = 10/3
So Marilyn needs 10/3 cups of brown sugar to make 5 batches of the recipe. However, it's usually easier to work with mixed numbers or whole numbers.
To convert the fraction 10/3 to a mixed number, we divide the numerator (10) by the denominator (3) and get a quotient of 3 with a remainder of 1. So:
10/3 = 3 1/3
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find the median mode and range for each set of data 23,87,19,34,37,87,5,14,100,26
The mean, median, mode and range are 42.2, 30, 87 and 95 respectively.
What is mean, mode median and range?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Therefore mean = (23+87+19+34+37+37+5+14+100+26)/10
= 422/10 = 43.2
The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
median = 26+34/2 = 60/2 = 30
Mode is the number with the highest frequency
Therefore, the mode is 87
Range Is the difference between the highest and the lowest
= 100-5 = 95
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Sovle each of the followig eqations and mark it on a number line
|3z-2|=1
The solutions to the equation are z = 1 and z = 1/3. We can mark these solutions on a number line is {1/3, 1}.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
We can solve this equation by considering two cases:
Case 1: 3z-2 = 1
Solving for z, we get:
3z-2 = 1
3z = 3
z = 1
Case 2: 3z-2 = -1
Solving for z, we get:
3z-2 = -1
3z = 1
z = 1/3
Therefore, the solutions to the equation are z = 1 and z = 1/3. We can mark these solutions on a number line as follows:
The solution set is {1/3, 1}.
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To obtain certification for a certain occupation, candidates take a proficiency exam. The exam consists of two sections, and neither section should be more difficult than the other. To investigate whether one section of the exam was more difficult than the other, a random sample of 50 candidates was selected. The candidates took the exam and their scores on each section were recorded. The table shows the summary statistics
The test statistic for the appropriate test to determine if there is a significant mean difference between the percent correct on the two sections for all candidates similar to the one in the investigation is given by t = 75 - 65 / [8 / √(50)], option (A) is correct.
The appropriate test to determine if there is a significant mean difference between the percent correct on the two sections is a two-sample t-test assuming equal variances.
The test statistic for this hypothesis test can be calculated using the formula:
t = x' / ([tex]s{p}[/tex] × √n')
where x' is the sample means for the first and second sections, respectively, [tex]s{p}[/tex] is the pooled standard deviation, and n' is the sample sizes for the first and second sections.
Using the information given in the question, we can calculate the values needed for the test statistic:
x₁ = 75, x₂ = 65, s₁ = 10, s₂ = 5, n' = 50
x’ = x₁ - x₂ = 75 - 65 = 10
The pooled standard deviation is given by [tex]s_{p}[/tex] = 8
We can calculate the test statistic:
t = (x') / [[tex]s_{p}[/tex] / √(n)]
t = 75 - 65 / [8 / √(50)]
Further simplifying:
t = 10 / [8 / √(50)]
t = 8.8356
Hence, option (A) is correct.
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– The question is incomplete, The complete question is:
To obtain certification for a certain occupation, candidates take a proficiency exam. The exam consists of two sections, and neither section should be more difficult than the other. To investigate whether one section of the exam was more difficult than the other, a random sample of 50 candidates was selected. The candidates took the exam and their scores on each section were recorded.
The summary of the statistics are as follows:
-For the first section, Mean Percent Correct is 75 and Standard Deviation Percent Correct is 10
-For the second section, Mean Percent Correct is 65 and Standard Deviation Percent Correct is 5
-The difference is, Mean Percent Correct is 10, and the pooled Standard Deviation Percent Correct is 8
Which of the following is the test statistic for the appropriate test to determine if there is a significant mean difference between the percent correct on the two sections (first minus second) for all candidates similar to the one in the investigation?
A) t = 75 - 65 / (8 / √(50))
B) t = 75 - 65 / [√(10² / 50 + 5² / 50)]
C) x² =(75 - 70)² / 70 + (65-70)² / 70
D) x² = (75-70)² / 65 + (65-70)² / 65
i need help feeling in the blank
The circumference of a circle is proportional to its diameter. The constant of proportionality for this relationship is pi (π). Therefore, we can use the equation C = πd (where C is the circumference and d is the diameter) to determine the circumference of a circle.
What is piPi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159, but its decimal representation goes on infinitely without repeating.
The radius of a circle is half the length of its diameter. Therefore, the relationship between diameter and radius is that the diameter is twice the length of the radius, or d = 2r.
If given the diameter of a circle, you can calculate its radius by dividing the diameter by 2 (r = d/2). Conversely, if given the radius of a circle, you can calculate its diameter by multiplying the radius by 2 (d = 2r).
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I need some help please
yes very cool math problem
An angle measures 51.8 degrees less than the measure of it’s complementary angle, what is the measurement of each angle?
the answer to the problem is that one angle measures 19.1 degrees and its complementary angle measures 70.9 degrees.
How to solve the question?
Let's first define the problem. Complementary angles are two angles whose sum is 90 degrees. Let x be the measure of one of the angles, then the measure of its complementary angle is 90 - x. According to the problem, one angle measures 51.8 degrees less than its complementary angle, so we can write:
x = (90 - x) - 51.8
Simplifying this equation, we get:
2x = 90 - 51.8
2x = 38.2
x = 19.1
Therefore, one angle measures 19.1 degrees and its complementary angle measures 90 - 19.1 = 70.9 degrees.
We can check that these angles are indeed complementary by verifying that their sum is 90 degrees:
19.1 + 70.9 = 90
So the answer to the problem is that one angle measures 19.1 degrees and its complementary angle measures 70.9 degrees.
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Rafael finished the Boston Marathon ( 26. 2 miles) in 4. 75 hours. At this pace, how long would it take him to run a 50 mile marathon in Washington D. C?
It would take Rafael approximately 9.05 hours to run a 50-mile marathon in Washington D.C. at the same pace he ran the Boston Marathon.
What is distance?
Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.
To solve this problem, we can use the concept of the average speed or pace, which is given by the formula:
pace = time / distance
where pace is the time it takes to cover one unit of distance (e.g., one mile), time is the time taken to cover the distance, and distance is the distance covered.
We can rearrange this formula to find the time it would take to cover a given distance at a given pace:
time = pace * distance
Using this formula, we can find the pace at which Rafael ran the Boston Marathon:
pace = time / distance
pace = 4.75 hours / 26.2 miles
pace = 0.181 hours/mile
Now we can use this pace to find the time it would take Rafael to run a 50-mile marathon:
time = pace * distance
time = 0.181 hours/mile * 50 miles
time = 9.05 hours
Therefore, it would take Rafael approximately 9.05 hours to run a 50-mile marathon in Washington D.C. at the same pace he ran the Boston Marathon.
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Find the value of X.
The angle x subtended by the arc of the circle between the two tangents is 130 degrees.
What is tangent?In trigonometry, the tangent (often abbreviated as tan) is a mathematical function that describes the ratio of the length of the side opposite to an angle in a right-angled triangle to the length of the adjacent side.
According to given information:The formula 50=180-x represents the fact that the angle between two tangents drawn to a circle from an external point is equal to the difference of the angles subtended by the tangents in the opposite segment of the circle.
Using this formula, we can solve for x as follows:
50 = 180 - x (given)
x = 180 - 50 (subtracting 50 from both sides)
x = 130 (simplifying)
Therefore, the angle x subtended by the arc of the circle between the two tangents is 130 degrees.
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A company is designing a new cylindrical water bottle. The volume of the bottle will be 220 cm cubed 3. The height of the water bottle is 8. 9 cm. What is the radius of the water bottle? Use 3. 14 for π
The radius of the cylindrical water bottle is approximately 2.34 cm.
The company designing the water bottle has given us the volume of the bottle, which is 220 cm³, and the height of the bottle, which is 8.9 cm. We can use the formula for the volume of a cylinder to relate the radius, height, and volume of the water bottle. The formula is:
Volume of a cylinder = π × radius² × height
We are given the volume of the cylinder as 220 cm³ and the height as 8.9 cm, so we can substitute these values into the formula to get:
220 = π × radius² × 8.9
To solve for the radius, we need to isolate it on one side of the equation. We can start by dividing both sides by π × 8.9:
220 ÷ (π × 8.9) = radius²
Now, we can take the square root of both sides to find the value of the radius:
√(220 ÷ (π × 8.9)) = radius
Using 3.14 for π, we can simplify the expression to get:
radius ≈ 2.34 cm
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Find the area of the shaded region for each composite figure. Round your answer to the nearest tenth, if necessary.
The area of the composite figure for this problem is given as follows:
A = 90 in².
How to obtain the area of the composite figure?The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.
The right triangle has a side length of 5 in and an hypotenuse of 13 units, hence the missing side is given as follows:
5² + x² = 13²
25 + x² = 169
x² = 144
x = 12.
Thus the entire base is of:
12 + 4 = 16 in.
Then the figure is composed as follows:
Rectangle of dimensions 3 in and 16 in.Right triangle of sides 12 in and 8 - 3 = 5 in.Rectangle of dimensions 4 in and 3 in.Hence the area is given as follows:
A = 3 x 16 + 0.5 x 12 x 5 + 4 x 3
A = 90 in².
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i dont understand what this means if yall want to help
Answer: Just simply replace the letter with the number that it equals in the equation. Then solve the equation using PEMDAS order of operations, (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction).
Step-by-step explanation:
3 / 1/4 using multiplication
Answer:
12
Step-by-step explanation:
to divide by a fraction use the acronym K.C.F or keep change flip to re-arrange the problem.
[tex]\frac{3}{\frac{1}{4} }[/tex] can be re-written as
[tex]\frac{3}{1} *\frac{4}{1}[/tex]
or 3*4 which equals 12
Question 1-1
The table shows values of y relative to values of x in a proportional relationship. What is the constant of proportionality for this relationship?
X Y
6 24
8 32
10 40
12 48
Answer:
y = 4x
Step-by-step explanation:
To find the constant of proportionality, we need to calculate the ratio of y to x for any two corresponding values in the table.
Let's choose the first set of values: x = 6, y = 24.
y/x = 24/6 = 4
So the constant of proportionality is 4.
We can check this for the other sets of values as well:
- for x = 8, y = 32: y/x = 32/8 = 4
- for x = 10, y = 40: y/x = 40/10 = 4
- for x = 12, y = 48: y/x = 48/12 = 4
In each case, the ratio of y to x is equal to 4, so the constant of proportionality is indeed 4. Therefore, the relationship between x and y is:
y = 4x
Answer:10 40
Step-by-step explanation:
please answer only if you know the answer.
The dimensions of the net for the cube lampshade which fits into the sheet of plastic with dimensions 20 cm by 15 cm indicates;
5. The area of each square of (5 cm)² on the sheet of plastic, indicates that the area of the net comprising of six squares is 150 cm²
6. The percentage of the plastic sheet wasted is 50%
What is a cubic shape?
A cubic shape is a shape that consists of six square faces, twelve edges and eight vertices. The area of each square face of side length s = Side length, s × Side length, s.
5. The surface area of the net in the figure can be calculated by finding the sum of the area of the squares within the area of the net.
The number of squares in the figure are 6 squares
The area of each square = (5 cm)²
The area of the sheet of plastic = 20 cm × 15 cm = 300 cm²
The area of the net containing six squares is therefore;
Area = 6 × (5 cm)² = 150 cm²
The surface area of the net is 150 cm²6. The amount of plastic sheet wasted can be obtained by finding the difference between the area of the plastic and the area of the net
Area of the sheet of plastic = 20 cm × 15 cm = 300 cm²
Area of the net = 150 cm²
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Select the correct answer.
Exponential function f is represented by the table.
x -2 -1 0 1 2
f(x) -46 -22 -10 -4 -1
Function g is represented by the equation.
Which statement correctly compares the two functions on the interval [-1, 2]?
A. Both functions are increasing, but function g increases at a faster average rate.
B. Only function f is increasing, and only function f is negative.
C. Both functions are increasing, but function f increases at a faster average rate.
D. Only function f is increasing, but both functions are negative.
The statement that correctly compares the two functions on the interval [-1, 2] is A. Both functions are increasing, but function g increases at a faster average rate.
How to explain the functionFor function f, as x increases from -2 to 2, we can see that the corresponding values of f(x) also increase, but at a decreasing rate. This is because the function is exponential and approaching a horizontal asymptote as x goes to infinity. Therefore, f(x) is increasing, but at a decreasing rate.
For function g, we don't have enough information to determine if it's increasing or not, since only its equation is given. The correct option is A.
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Which factors affect the resistance of a material? Select three options.
Olength
current
thickness
O temperature
voltage
Answer:
They are length, thickness and temperature
HELP IS VERY MUCH APPRECIATED
1.75 in or 1 3/4 in (which ever form you need it in)
youre given the diameter and so to find radius, you simply divide the diameter by 2.
Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
The correct answer is option c) A circle graph, also known as a pie chart, would be the best graphical representation for the teacher's data on the subject preferences of the 100 students in the school.
What is graphical representation?
A graphical representation is a way of presenting data or information visually using charts, graphs, diagrams, or other visual aids. It helps to convey complex information in an easy-to-understand manner, enabling the viewer to quickly grasp the main points and trends.
A circle graph, also known as a pie chart, would be the best graphical representation for the teacher's data on the subject preferences of the 100 students in the school.
A circle graph can effectively display the relative proportions of different categories in a data set, making it a useful tool for showing the distribution of categorical data such as subject preferences.
A stem-and-leaf plot is more suitable for displaying numerical data, while a histogram and box plot are typically used for showing the distribution of continuous data.
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The manager of a local nursery wants to know which types of plants his customers buy most often. What is the population from which the manager should choose a sample to answer her question?
A. The first 25 adults who come into the nursery during one business day.
B. The list of customers who purchased plants from the nursery.
C. Every adult who enters the nursery during one business day.
D. Subscribers to a gardening magazine.
The population from which the manager should choose a sample to answer her question is: B. The list of customers who purchased plants from the nursery.
How to distinguish between population and sample?A population is a term that goes by the definition of it being the entire group that we specifically intend to get conclusions about. Meanwhile, we ca sample is defined as the specific group that you will collect data from. The size of the given sample is normally always less than that of the total size of the given population. In research, it is noticed that a population doesn't always mean we are referring to people.
Now, we are told that the manager wants to know which types of plants his customers buy most often.
Looking at the options, the most appropriate population from which a sample could be gotten from is the list of customers who purchased plants from the nursery.
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Also they all should be one step equations: integers
Answer: 3. is 13
4. is 36
5. is 21
6. is 15
7. is 21
8. is 2
9. is 6
10. is 45
Step-by-step explanation:
the letters are there to just confuse you. i promise its all right <-- the answers
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h(x)= 6/x-h+k
Oh no! He seems to be missing some parts though. He was "robbed" of his asymptotes!
Luckily, he can remember what they were:
1. This functions vertical asymptote was x = 4.
2. This functions horizontal asymptote was y = -15.
Please recreate this function with those identifying features! Please make sure it looks like the function at the beginning of this problem.
At a function x = 4 has a vertical asymptote and at y = -15 has a horizontal asymptote.
What are asymptotes?The general form of a function is x= a and y = b.
f(x) = (kx + m) / (x - a) + b
k and m are constants.
We require a factor of (x - 4) in the denominator to get a vertical asymptote at x = 4. It is necessary for the fraction to approach -15 when x approaches positive or negative infinity in order to obtain a horizontal asymptote at y = -15.
One potential function that meets these specifications is:
H(x) = 6/(x - 4) - 15 + k
where k is a constant that establishes the function's vertical shift (i.e., its value at x = 0).
By entering a point on the graph, such as the x-intercept (where y = 0), the value of k can be determined:
0 = 6/(x - 4) - 15 + k
15 - k = 6/(x - 4)
x - 4 = 6/(15 - k)
x = 6/(15 - k) + 4
We may enter this value of x into the original equation to find k since y = 0 at the x-intercept:
0 = 6/((6/(15 - k) + 4) - 4) - 15 + k
0 = 6/(6/(15 - k)) - 15 + k
0 = 15 - k - 15 + k
The x-intercept and asymptotes are unaffected by the value of k, and any value of k will result in a function with the same asymptotes. K does, however, have an impact on the function's vertical shift.
We can select a value for k and then search for a specific function that has the specified asymptotes.
For instance, if we select k = 0, we obtain:
H(x) = 6/(x - 4) - 15
This function has the same shape as the original function H(x) presented in the problem and asymptotes at x = 4 and y = -15, respectively.
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Alvin's new bag of 50 marbles of different
designs spilled in his backpack. On the way
home from school, he randomly selects one
marble from the backpack, records the
result, puts the marble back in the bag,
and selects again. Here are his results:
jasper, galaxy, cat's-eye, rainbow,
galaxy, sunburst, galaxy, cat's-eye,
sunburst, jasper
Based on the data, estimate how many of
the marbles in Alvin's backpack are galaxy
marbles.
If necessary, round your answer to the
nearest whole number.
Answer: 7
Step-by-step explanation:
i did it a weird way
During the 1999 and 2000 baseball seasons, there was much speculation that the unusually large number of home runs that were hit was due at least in part to a livelier ball. One way to test the "liveliness" of a baseball is to launch the ball at a vertical surface with a known velocity and measure the ratio of the outgoing velocity of the ball to. The ratio is called the coefficient of restitution. Following are measurements of the coefficient of restitution for 40 randomly selected baseballs.
The balls were thrown from a pitching machine at an oak surface.
0. 6248 0. 6237 0. 6118 0. 6159 0. 6298 0. 6192 0. 6520 0. 6368 0. 6220 0. 6151 0. 6121 0. 6548 0. 6226 0. 6280 0. 6096 0. 6300 0. 6107 0. 6392 0. 6230 0. 6131 0. 6223 0. 6297 0. 6435 0. 5978 0. 6351 0. 6275 0. 6261 0. 6262 0. 6262 0. 6314 0. 6128 0. 6403 0. 6521 0. 6049 0. 6170 0. 6134 0. 6310 0. 6065 0. 6214 0. 6141
Suppose that any baseball that has a coefficient of restitution that exceeds 0. 630 is considered too lively.
Based on the available data, what proportion of the baseballs in the sampled population are too lively?
Find a 95% lower confidence bound on this proportion. Assume population is approximately normally distributed
Approximately 30% of the sampled baseballs are too lively based on a cutoff coefficient of restitution of 0.630. The 95% lower confidence bound on this proportion is 0.154.
To find the proportion of the baseballs in the sampled population that are too lively, we need to count the number of baseballs in the sample that have a coefficient of restitution greater than 0.630 and divide by the total sample size
Number of baseballs with coefficient of restitution > 0.630 = 12
Total sample size = 40
Proportion of baseballs in the sample that are too lively = 12/40 = 0.3 = 30%
To find a 95% lower confidence bound on this proportion, we can use the formula
lower bound = p - zsqrt(p(1-p)/n)
where p is the sample proportion, z is the z-score associated with the desired confidence level (95% confidence level has a z-score of 1.96), and n is the sample size.
Substituting the values, we get:
lower bound = 0.3 - 1.96sqrt(0.3(1-0.3)/40) ≈ 0.154
Therefore, we can be 95% confident interval that at least 15.4% of the baseballs in the population are too lively.
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