The value of test statistic is -5.83.
Define statistics?statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics. statistic = (sample proportion - hypothesized proportion)/ standard error.
What is decimal system?The decimal system is a number system that uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent all possible numbers. It is also known as the base-10 system because each digit represents a power of 10. For example, in the number 123, the digit 3 represents 10^0 (which is 1), the digit 2 represents 10^1 (which is 10), and the digit 1 represents 10^2 (which is 100). The decimal system is widely used in everyday life and is the most common number system used around the world.
Here, the sample proportion is 0.9 (90% of 1146 adults said they have a cell phone), and the hypothesized proportion is 0.97 (the claim that fewer than 97% of adults have a cell phone).
The standard error can be calculated as:
standard error = sqrt[(hypothesized proportion * (1 - hypothesized proportion)) / sample size]
Substituting the values, we get:
standard error = [tex]\sqrt{(0.97*0.03)/1146}[/tex] = 0.012
Now, substituting all the values in the formula for the test statistic, we get:
test statistic = (0.9 - 0.97) / 0.012 = -5.83
Rounding to two decimal places, the value of the test statistic is -5.83.
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What is the value of x
in the equation, 5(x+2)+4x=6x+1
?
Responses
x=−3
, x is equal to negative 3
x=−1
, x is equal to negative 1
x=1
, x is equal to 1
x=3
, x is equal to 3
The value of x that satisfies the equation is x = -3. So the answer is x = −3, or "x is equal to negative 3"
What is the value of xin the equation, 5(x+2)+4x=6x+1?To solve the equation, we can begin by simplifying both sides using the distributive property and combining like terms:
5(x+2) + 4x = 6x + 1
5x + 10 + 4x = 6x + 1
9x + 10 = 6x + 1
Next, we can isolate the variable x on one side of the equation by subtracting 6x and 1 from both sides:
9x + 10 - 6x - 1 = 0
3x + 9 = 0
3x = -9
x = -3
Therefore, the value of x that satisfies the equation is x = -3. So the answer is x = −3, or "x is equal to negative 3"
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Answer: the awnser is x = -2 I just got x = -3 wrong
Step-by-step explanation:
trust
Please help me! My teacher gave us this and has only taught us about rectangles, not rhombi. My classmates and I are very confused
Step-by-step explanation:
It is important to know that the diagonals of a rhombus are PERPINDICUALR bisectors of each other . Opposite angles are equal and adjacen angles sum to 180 degrees .
Then remember alternate angles are equal and there are 180 degrees inside of a triangle .....then you should be able to solve these...here is the first one
What is the meaning of [tex]\pi (i-j)/n[/tex]?
A regular polygon with n vertices' angle in radians between two consecutive axes of symmetry is referred to by the formula π(i - j) /n in the definition of the dihedral group D.
A regular polygon with n vertices' angle in radians between two consecutive axes of symmetry is referred to by the formula π(i - j) /n in the definition of the dihedral group D.
What is a subgroup?A group G's subgroups are its subsets that are also groups that fall under the same operation as G. The same axioms of G—closure, associativity, identity, and inverse—are satisfied by a subgroup, which is a subset of G that does the same. The identity element of G must be present in a subgroup, and for any element g, the inverse of g must also be present. Every pair of components g1 and g2 in the subgroup must also have their product, g1g2, present in the subgroup.
A regular polygon with n vertices' angle in radians between two consecutive axes of symmetry is referred to by the formula π(i - j) /n in the definition of the dihedral group D.
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What is the least whole number that rounds to 570 when rounded to the nearest ten?
What is the greatest whole number that rounds to 570 when rounded to the nearest ten?
Use the number pad to enter your answers in the boxes.
Least number:
Greatest number:
Answer:
Least: 565
Greatest: 574
Step-by-step explanation:
564 would round down to 560 and 575 would round to 580
Helping in the name of Jeus.
The least whole number that rounds to 570 when rounded to the nearest ten is 570. The greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
Explanation:To find the least whole number that rounds to 570 when rounded to the nearest ten, we need to look at the digit in the tens place. In this case, the tens digit is 7. Since the number can only round up or down, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 570 than to 580, we can round down to 570. Therefore, the least whole number that rounds to 570 when rounded to the nearest ten is 570 itself.
On the other hand, to find the greatest whole number that rounds to 570 when rounded to the nearest ten, we again need to look at the digit in the tens place. Since the tens digit is 7, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 580 than to 570, we can round up to 580. Therefore, the greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
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Given cos A = 3/10 and tan A < 0 , find sin A .
Answer: Since we know that cos A = 3/10, we can use the Pythagorean identity to find sin A:
sin^2 A + cos^2 A = 1
sin^2 A = 1 - cos^2 A
sin A = sqrt(1 - cos^2 A)
Substituting cos A = 3/10, we get:
sin A = sqrt(1 - (3/10)^2)
sin A = sqrt(1 - 9/100)
sin A = sqrt(91)/10
Since we also know that tan A < 0, we know that the sine and tangent of A have opposite signs, and therefore sin A is negative.
Therefore:
sin A = -sqrt(91)/10
Step-by-step explanation:
Find the area of the figure. Round to the nearest hundredth when necessary.
6in
14in
26in
15in
The answer is 1,764 in^2
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answer: option (a) and option (e).
Step-by-step explanation:
Answer:
(a) and (e) are correct
Step-by-step explanation:
(a) x² + (y - 3)² = 6²
(b) x² + (y - 5)² = (√6)²
(c) (x - 4)² + y² = 6²
(d) (x + 6)² + y² = 12²
(e) x² + (y + 8)² = 6²
The general equation of a circle is:
(x - a)² + (y - b)² = r², where (a, b) represents the x-y coordinates of the centre, and r represents the radius.
Hence, by process of elimination, the options that have a diameter of 12 units and therefore, a radius of 6 units, are (a), (c), and (e).
Therefore, the correct choices are (a), and (e), as (c) has a circle centre of (4,0) and does not lie on the y-axis.
A group of six student's in Mrs. Turner's class is working on a project. The number of hours that each student worked is shown below.
3 hours
5 hours
4 hours
4 hours
2 hours
5 hours
Which statement describes the mean number of hours worked?
The statement that describes the mean number of hours worked through which the relation is satisfied is The mean is the highest number or hours worked by any students in the group
What about mean?
In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is often called the arithmetic mean, and it is calculated by adding up all the values in the set and then dividing the result by the total number of values.
The formula for the mean is:
mean = (sum of all values) / (total number of values)
For example, suppose we have a set of four numbers: 2, 5, 8, and 11. To find the mean of this set of numbers, we add them up and divide by the total number of values:
mean = (2 + 5 + 8 + 11) / 4
mean = 26 / 4
mean = 6.5
Therefore, the mean of this set of numbers is 6.5. The mean is a commonly used measure of central tendency in statistics and data analysis, and it provides a way to summarize the general trend or average of a data set.
According to the given information:
Mean of the given condition is,
⇒ [tex]\frac{3 + 5 + 4 + 4 + 2 + 5}{6}[/tex]
⇒ [tex]\frac{23}{6}[/tex]
⇒ 3.83 mean of the given condition.
So, it indicate that The mean is the highest number or hours worked by any students in the group.
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7.) Adult tickets for Disney on Ice are $6.50 while a child's ticket is only $2.50. At Tuesday night's
performance, 435 people were there in attendance. The box office brought in $1667.50 for that evening.
How many of each type of ticket were sold?
Answer:
Adult tickets: 145
Child tickets: 290
Step-by-step explanation:
Let x = adults; y = children
[tex]\left \{ {{x + y=435} \atop {6.50x+2.50y=1667.50}} \right.[/tex]
=> x = adults = 145
y = children = 290
At a local play, student tickets cost $6 each and adult tickets cost $11 each. If ticket sales were $3,000 for 400 tickets, how many students attended the play?
120
180
220
280
Answer:
If ticket sales were $3,000 for 400 tickets then 280 students attended the play.
Step-by-step explanation:
Consider the statement “If you are under age 17, then you cannot attend this movie.”
a. Write the converse.
b. Write the inverse.
c. Write the contrapositive.
a. The converse, inverse and contrapositive are "If you cannot attend this movie, then you are under age 17.", "If you are over age 16, then you can attend this movie." and "If you can attend this movie, then you are not under age 17."
Writing the other versions of the statementThe original statement is an example of a conditional statement, which is a statement of the form "if A, then B." The part that comes after "if" is called the hypothesis, and the part that comes after "then" is called the conclusion.
To find the converse of the statement, we switch the hypothesis and conclusion. The converse of a conditional statement may or may not be true. In this case, the converse is not true.
To find the inverse of the statement, we negate both the hypothesis and conclusion. The inverse of a conditional statement may or may not be true. In this case, the inverse is not true.
To find the contrapositive of the statement, we switch and negate both the hypothesis and conclusion. The contrapositive of a conditional statement is always true if the original statement is true. In this case, the contrapositive is true.
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Class: Algebra 2
I need help with these Natural Logarithms problems!!!!!
I will give lots of points!!!!
The solutions are: x = ln(2) for 2eˣ = 4, x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.
Solving equations using natural logarithmTo solve these equations using natural logarithm, we can use the following rules:
If a = eᵇ, then b = ln(a).If ln(aᵇ) = b ln(a).Using these rules, we can solve the given equations as follows:
2eˣ = 4
Divide both sides by 2 to get
eˣ = 2.
Take the natural logarithm of both sides to get
ln(eˣ) = ln(2).
Using rule 1 above, we can simplify ln(eˣ) to x, and we get
x = ln(2).
e⁴ˣ = 25
4x = ln(25).
Divide both sides by 4 to get
x = ln(25)/4.
eˣ = 72
Take the natural logarithm of both sides to get
x = ln(72).
e³ˣ = 124
Take the natural logarithm of both sides to get
3x = ln(124).
Divide both sides by 3 to get
x = ln(124)/3.
For the second set of equations, we use the same rule as above
So, we have
ln(x - 3) = 2
x - 3 = e²
x = e² + 3.
x ≈ 10.389.
Therefore, the solution is x ≈ 10.389.
ln(2t) = 4
2t = e⁴
t = 0.5 * e⁴
t ≈ 27.299.
Therefore, the solution is t ≈ 27.299.
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in the number below, how many times greater is the number represented by the digit in the thousands place than the number represented by the digit in the hundreds place?
57,762
Answer:
Ten times greater
Step-by-step explanation:
700 x 10 = 7000
Answer:
it will be ten times greater
Step-by-step explanation:
Smoky Mountain Corporation makes two types of hiking boots—the Xtreme and the Pathfinder. Data concerning these two product lines appear below:
Xtreme Pathfinder
Selling price per unit $ 115.00 $ 84.00
Direct materials per unit $ 65.50 $ 54.00
Direct labor per unit $ 13.60 $ 8.00
Direct labor-hours per unit 1.7 DLHs 1.0 DLHs
Estimated annual production and sales 33,000 units 61,000 units
The company has a traditional costing system in which manufacturing overhead is applied to units based on direct labor-hours. Data concerning manufacturing overhead and direct labor-hours for the upcoming year appear below:
Estimated total manufacturing overhead $ 1,756,500
Estimated total direct labor-hours 117,100 DLHs
Required:
1. Compute the product margins for the Xtreme and the Pathfinder products under the company’s traditional costing system.
2. The company is considering replacing its traditional costing system with an activity-based costing system that would assign its manufacturing overhead to the following four activity cost pools (the Other cost pool includes organization-sustaining costs and idle capacity costs):
Estimated
Overhead Cost Expected Activity
Activities and Activity Measures Xtreme Pathfinder Total
Supporting direct labor (direct labor-hours) $ 526,950 56,100 61,000 117,100
Batch setups (setups) 790,000 440 350 790
Product sustaining (number of products) 400,000 1 1 2
Other 39,550 NA NA NA
Total manufacturing overhead cost $ 1,756,500
Compute the product margins for the Xtreme and the Pathfinder products under the activity-based costing system.
3. Prepare a quantitative comparison of the traditional and activity-based cost assignments.
Answer: Product margins under traditional costing system:
Xtreme:
Selling price per unit = $115.00
Direct materials per unit = $65.50
Direct labor per unit = $13.60
Manufacturing overhead rate = Total manufacturing overhead / Total direct labor-hours = $1,756,500 / 117,100 DLHs = $15.00 per DLH
Direct labor-hours per unit = 1.7 DLHs
Manufacturing overhead per unit = $15.00 per DLH × 1.7 DLHs = $25.50
Total cost per unit = $65.50 + $13.60 + $25.50 = $104.60
Product margin per unit = Selling price per unit – Total cost per unit = $115.00 – $104.60 = $10.40
Pathfinder:
Selling price per unit = $84.00
Direct materials per unit = $54.00
Direct labor per unit = $8.00
Manufacturing overhead rate = Total manufacturing overhead / Total direct labor-hours = $1,756,500 / 117,100 DLHs = $15.00 per DLH
Direct labor-hours per unit = 1.0 DLHs
Manufacturing overhead per unit = $15.00 per DLH × 1.0 DLHs = $15.00
Total cost per unit = $54.00 + $8.00 + $15.00 = $77.00
Product margin per unit = Selling price per unit – Total cost per unit = $84.00 – $77.00 = $7.00
Product margins under activity-based costing system:
Xtreme:
Selling price per unit = $115.00
Direct materials per unit = $65.50
Direct labor per unit = $13.60
Manufacturing overhead rate:
Supporting direct labor cost pool rate = Supporting direct labor cost pool / Supporting direct labor-hours = $526,950 / 56,100 DLHs = $9.39 per DLH
Batch setups cost pool rate = Batch setups cost pool / Number of setups = $790,000 / 440 setups = $1,795.45 per setup
Product sustaining cost pool rate = Product sustaining cost pool / Number of products = $400,000 / 2 products = $200,000 per product
Direct labor-hours per unit = 1.7 DLHs
Supporting direct labor cost per unit = $9.39 per DLH × 1.7 DLHs = $15.93
Batch setups cost per unit = $1,795.45 per setup × (33,000 units / 440 setups) = $135.96
Product sustaining cost per unit = $200,000 / 33,000 units = $6.06
Total cost per unit = $65.50 + $13.60 + $15.93 + $135.96 + $6.06 = $237.05
Product margin per unit = Selling price per unit – Total cost per unit = $115.00 – $237.05 = –$122.05
Pathfinder:
Selling price per unit = $84.00
Direct materials per unit = $54.00
Direct labor per unit = $8.00
Manufacturing overhead rate:
Supporting direct labor cost pool rate = Supporting direct labor cost pool / Supporting direct labor-hours = $526,950 / 56,100 DLHs = $9.39 per DLH
Batch setups cost pool rate = Batch setups cost pool / Number of setups = $790,000 / 350 setups = $2,257
Compute the product margins for the Xtreme and the Pathfinder products under the activity-based costing system:
Xtreme:
Direct materials per unit $ 65.50
Direct labor per unit $ 13.60
Manufacturing overhead per unit (Supporting direct labor) $ 8.94 (($526,950 ÷ 56,100 DLHs) × 1.7 DLHs)
Manufacturing overhead per unit (Batch setups) $ 23.15 (($790,000 ÷ 440 setups) × 1 setup ÷ 33,000 units)
Manufacturing overhead per unit (Product sustaining) $ 0.61 (($400,000 ÷ 1 product) ÷ 33,000 units)
Total cost per unit $ 111.80
Selling price per unit $ 115.00
Product margin per unit $ 3.20
Pathfinder:
Direct materials per unit $ 54.00
Direct labor per unit $ 8.00
Manufacturing overhead per unit (Supporting direct labor) $ 6.88 (($526,950 ÷ 61,000 DLHs) × 1.0 DLHs)
Manufacturing overhead per unit (Batch setups) $ 3.78 (($790,000 ÷ 350 setups) × 1 setup ÷ 61,000 units)
Manufacturing overhead per unit (Product sustaining) $ 0.33 (($400,000 ÷ 1 product) ÷ 61,000 units)
Total cost per unit $ 72.99
Selling price per unit $ 84.00
Product margin per unit $ 11.01
Quantitative comparison of the traditional and activity-based cost assignments:
Product Xtreme Pathfinder
Traditional Costing System Product Margin per unit $ 31.90 $ 22.40
Activity-Based Costing System Product Margin per unit $ 3.20 $ 11.01
Difference $ 28.70 $ 11.39
Under the traditional costing system, the product margin for the Xtreme is $31.90, while the product margin for the Pathfinder is $22.40. Under the activity-based costing system, the product margin for the Xtreme is $3.20, while the product margin for the Pathfinder is $11.01. The difference between the two costing systems is significant, with the traditional system overstating the product margin for the Xtreme by $28.70 and understating the product margin for the Pathfinder by $11.39. This is due to the fact that the traditional system assigns overhead based solely on direct labor-hours, which does not accurately reflect the actual cost drivers of the manufacturing overhead. The activity-based costing system provides a more accurate reflection of the costs of producing each product.
Step-by-step explanation:
14. Type the correct answer in each box.
A41 represents the element at the line 4 and column 1, which is the same for B41.
When two matrices are added or subtract, we add or subtract the elements at the same position.
The elements are:
A41 = 7.B41 = 2.Hence:
(A - B)41 = 7 - 2 = 5.(A + B)41 = 7 + 2 = 9.When a matrix is multiplied by a constant, each element is multiplied by a constant, hence:
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1267.1 ml = L
pls help
1267.1 ml = 1.2671 L.
What are liter and milliliter?A little amount of liquid is measured in milliliters. You can utilize liters for larger amounts of liquid. One milliliter, or 1 ml, is equal to one liter. Milliliter can be written as ml or mL.
Large amounts of liquid are measured in liters. Kg is the unit for measuring mass, m is the unit for measuring length, and km is the unit for measuring distance among the ones provided.
To convert milliliters (ml) to liters (L), we divide the number of milliliters by 1000:
1267.1 ml ÷ 1000 = 1.2671 L
Therefore, 1267.1 ml is equal to 1.2671 L.
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1267.1mL is equal to 1.2671 L.
What does equal refers to?The term "equal" is used to indicate that two values or expressions have the same numerical value or meaning. When we say that two quantities are equal, we mean that they are exactly the same in terms of their value or magnitude. This is denoted by the symbol "=". For example, if we say that 2 + 3 = 5, we mean that the sum of 2 and 3 is exactly equal to 5. Similarly, if we say that x + 4 = 10, we mean that the value of x that satisfies this equation is exactly equal to 6. The concept of equality is fundamental to many areas of mathematics, including algebra, calculus, and geometry.
1L =1000mL
1mL=(1/1000)L
Therefore 1267.1 mL= (1267.1/1000)L
So, 1267.1 mL= 1.2671L
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Need help Asap please 2 Question
Type the correct answer in each box. Round your answers to the nearest hundredth.
This is the original two-way frequency table that describes ninth graders and tenth graders' favorite season of the year.
Based on the table, complete the two-way relative frequency table based on the total number of students surveyed.
Two-Way Frequency Table
The two-way frequency table can be filled in the following way and to the nearest hundredth frequency as follows:
0.26, 0.13, 0.18, 0. 05, 0.63
0.10, 0.08, 0.16, 0.04, 0.37
0.36, 0.21, 0.34, 0.10, 1.00
How to complete the two-way frequency tableTo complete the two-way frequency table, we can start with the spring value wherein the total values for Ninth graders and tenth graders is 0.26 + 0.10 = 0.36.
For summer, the total value for ninth graders and tenth graders = 0.13 + 0.08 = 0.21.
For fall, the total value for ninth and tenth graders equals 0.18 + 0.16 =0.34.
For winter the total value for ninth and tenth graders = 0.05 + 0.04 = 0.09.
The sum for girls is 0.63 and the sum for boys is 1 - 0.63 which equals 0.37.
Note that to get the values, we divide the individual values with the total values. For instance, the value of ninth graders in summer is 28/219 which equals 0.13.
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0.13
0.16
0.37
0.21
0.34
0.09
Step-by-step explanation: To get each relative frequency, divide each data value in the first table by the total number of people in the survey.
Edmentum Answer
Fresh Produce, Inc. buys white button mushrooms for $0.87 a pack. The selling price is $1.50 a pack. What is the markup rate based on the selling price?
5 points
30%
22%
45%
42%
The markup rate based on the selling price is 42%.
What is markup rate?Markup rate is the percentage of the selling price that is added to the cost price to determine the final selling price. It is calculated as (selling price - cost price) / cost price x 100%.
In the given question,
The markup rate based on the selling price is:
Markup rate = ((Selling price - Cost price) / Selling price) x 100%
Markup rate = (($1.50 - $0.87) / $1.50) x 100%
Markup rate = (0.63 / 1.50) x 100%
Markup rate = 42%
Therefore, the markup rate based on the selling price is 42%.
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PLSSS HELP ME ITS DUE TOMORROW!!!!!
HELP! I ONLY HAVE 5 MINS LEFT! You and 15 other people are at a party. The host tells you that they have placed one special item in a bag with 16 items total. The host says that there is an 80% chance that the special item is still in the bag, and a 20% chance that it was taken out.
The host passes the bag around and each person selects an item at random. You decide to keep your item hidden while everyone else shows theirs, and no one finds the special item. What are the odds that the special item is in your item?
Answer:
67.5%
Step-by-step explanation:
There is a 67.5% chance that the special item is in your bag.
The initial probability that the special item is in the bag is 80%.
The probability that the special item is not in the bag is 20%.
The probability that the special item is not in any of the other 15 bags is 15/16 * 14/15 * 13/14 * ... * 3/4 * 2/3 = 1/2.
The probability that the special item is in at least one of the other 15 bags is 1 - 1/2 = 1/2.
The probability that the special item is in your bag is 80% * 1/2 = 67.5%.
Here is a breakdown of the probabilities:
* The special item is in the bag: 80%
* The special item is not in the bag: 20%
* The special item is in one of the other 15 bags: 1/2
* The special item is in your bag: 67.5%
ANSWER Quick Due in 5 minutes!!!!!!
The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 18, with an IQR of 16 Bus 47, with an IQR of 24 Bus 18, with a range of 16 Bus 47, with a range of 24
IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers.
Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.
WHAT IS IQR?An indicator of statistical dispersion used to describe the variability of a dataset is the interquartile range (IQR). It is derived by subtracting a dataset's 75th percentile (Q3) from its 25th percentile (Q1). When compared to other measures of variability like range, the IQR represents the middle 50% of the data and is less susceptible to outliers.
We must contrast the measurements of variability for the two buses in order to determine which one is more reliable. We can utilize range and interquartile range as measurements of variability. (IQR).
The range of a dataset is the difference between its maximum and minimum values.
The range for Bus 18 is 16 (22 - 6), whereas the range for Bus 47 is 24. (28 - 4).
As a result, Bus 47's range is greater than Bus 18's.A measure of variability that is less impacted by outliers than the range is the interquartile range (IQR). It is determined as the difference between a dataset's third and first quartiles (Q3 and Q1, respectively).
The IQR is 16 for Bus 18 (Q3 - Q1 = 22 - 6)
The IQR for Bus 47 is 24 (Q3 - Q1 = 28 - 4"). Bus 18 therefore has a lower IQR than Bus 47.IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers. Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.
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1/2 of 50 of 1/4 of ?
Answer:
[tex] \frac{1}{2} \times 50 \times \frac{1}{4} = 50 \times \frac{1}{8} = \frac{25}{4} = 6 \frac{1}{4} [/tex]
Select Repeating or Nonrepeating to correctly classify each decimal.
The correct Repeating or Non-repeating decimals are-
Repeating - 2.23(bar) , 3.426(bar) , 4.321321....
Non-repeating - 1.01011
Explain about the Repeating or Non-repeating decimals:As fractions and decimals both represent portions of a whole, many decimals can be expressed as fractions. "Rational numbers" are defined as decimals that can be expressed as fractions. "Irrational numbers" are decimals that cannot be expressed as a fraction.
A decimal number that never ends and never repeats itself is known as a non-terminating, non-repeating decimal.Such decimals are irrational numbers since they cannot be expressed as fractions.Repeating decimals: The decimals which will not end and the number will repeat again and again.
Repeating - 2.23(bar) , 3.426(bar) , 4.321321....
Non-repeating: These decimals will not have the repeating numbers after the decimal poins.
Non-repeating - 1.01011
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Hurry please combine Leon’s results and Celia’s results to find the experimental probability of spinning a 4
The experimental probability of spinning a 4 will equals to 0.3.
How to find the experimental probability of spinning a 4?Outcome Tally Frequency
1 IIII 4
2 III 3
3 IIIIIIII 7
4 IIIIII 6
Total 20
The probability of spinning a 4:
= 6/20
= 3/10
= 0.3
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please help and please show step by step :)
(3,4) , (5,80) ,(7,188)
(10,245), (13,305)
(1,9), (2,15), (4,87) , (6,279)
for each data set above
a)State the degree of the interpolant
b) Write each system of the equations that must be solved to find the interpolant
c) Find the Vandermonde matrix corresponding to the system of equations
a) The degree of the interpolant is 3.
b) Required system of equations are
[tex]a_0 + 3a_1 + 9a_2 = 4 \\ a_0 + 5a_1 + 25a_2 = 80 \\ a_0 + 7a_1 + 49a_2 = 188 \\ a_0 + 10a_1 = 245 \\ a_0 + 13a_1 = 305 \\ a_0 + a_1 + a_2 + a_3 = 9 \\ a_0 + 2a_1 + 4a_2 + 6a_3 = 15 \\ a_0 + 4a_1 + 16a_2 + 36a_3 = 87 \\ a_0 + 6a_1 + 36a_2 + 216a_3 = 279[/tex]
c) Required Vandermonde matrix corresponding to the system of equations are [ 1 3 9; 1 5 25; 1 7 49], [1 10; 1 13], [1 1 1 1; 1 2 4 6; 1 4 16 36; 1 6 36 216].
a) How to determine the degree of the interpolant?
To determine the degree of the interpolant, we count the number of data points in each set, subtract one, and take the minimum of the resulting values. This is because a polynomial of degree n can exactly interpolate n+1 distinct data points.
For the first set, we have 3 data points, so the interpolant can have degree at most 2.
For the second set, we have 2 data points, so the interpolant can have degree at most 1.
For the third set, we have 4 data points, so the interpolant can have degree at most 3.
b) How to find the interpolant for each set?
To find the interpolant for each set, we need to solve a system of equations. Let f(x) be the interpolant for each set, and let [tex]x_i[/tex] be the x-coordinate of the ith data point, and yi be the corresponding y-coordinate. Then we need to find the coefficients [tex]a_0, a_1, ..., a_n[/tex] such that [tex]f(x_i) = a_i(x_i)^n + a_{i-1}(x_i)^{(n-1)} + ... + a_1 \times x_i + a_0 = y_i[/tex] for i = 1, 2, ..., m, where m is the number of data points in the set. This gives us m equations in n+1 unknowns.
For the first set,
[tex]a_0 + 3a_1 + 9a_2 = 4 \\ a_0 + 5a_1 + 25a_2 = 80 \\ a_0 + 7a_1 + 49a_2 = 188[/tex]
For the second set,
[tex]a_0 + 10a_1 = 245 \\ a_0 + 13a_1 = 305[/tex]
For the third set,
[tex]a_0 + a_1 + a_2 + a_3 = 9 \\ a_0 + 2a_1 + 4a_2 + 6a_3 = 15 \\ a_0 + 4a_1 + 16a_2 + 36a_3 = 87 \\ a_0 + 6a_1 + 36a_2 + 216a_3 = 279[/tex]
c) The Vandermonde matrix corresponding to the system of equations is an m x (n+1) matrix V, where the ith row is [tex] [x_i^n, x_i^{(n-1)}, ..., x_1, 1] [/tex] for i = 1, 2, ..., m. The columns of the matrix correspond to the coefficients of the interpolant.
For the first set,
V = [ 1 3 9; 1 5 25; 1 7 49]
For the second set,
V = [1 10; 1 13]
For the third set,
V = [1 1 1 1; 1 2 4 6; 1 4 16 36; 1 6 36 216]
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A bakery owner wants to keep his bakery open a few more hours every evening. He wants to
conduct a survey to determine whether extending the bakery's hours would be what customers
want. Which survey method would likely produce the most representative sample?
A. Ask 20 of the bakery's employees as they arrive for work.
B. Ask the first 20 customers who enter the bakery tomorrow.
C. Ask 20 of the bakery's regular suppliers as they make deliveries.
D. Ask 20 customers as they visit the bakery over the course of a day.
"Ask 20 customers as they visit the bakery over the course of a day." would likely produce the most representative sample.
What is sample?In statistics, a sample refers to a group of individuals or objects that are selected from a larger population and used to represent that population for the purpose of statistical analysis and inference. A sample is often used because it is impractical or impossible to examine every member of the population, so a smaller group is chosen that is expected to be representative of the larger population. The goal of sampling is to obtain accurate and reliable information about the population by studying the characteristics of the sample.
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A baseball team has the starting and relief pitchers shown in the table. The manager selects a pitcher at random. Find the probability that the pitcher is left-handed.
Pitchers on Baseball Team (Table)
Pitchers Number
Left-handed starters 1
Right-handed starters 4
Left-handed relievers 2
Right-handed relievers 1
Okay, here are the steps to find the probability the randomly selected pitcher is left-handed:
1) There are 1 left-handed starter, 4 right-handed starters, 2 left-handed relievers and 1 right-handed reliever.
2) In total, there are 1 + 4 + 2 + 1 = 8 pitchers.
3) Of the 8 pitchers, 1 + 2 = 3 are left-handed.
4) So the probability the randomly selected pitcher is left-handed = (3/8) = 3/8 = 0.375
Therefore, the probability that the randomly selected pitcher from the team is left-handed is 0.375.
Let me know if you have any other questions!
Which missing x-value would make the table a function?
we can replace the second occurrence of x = -2 with x = 1:
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
For the table to be a function, each x-value must correspond to a unique y-value. To determine the missing x-value, we need to find if there are any repeated x-values with different y-values.
The x-value 3 is paired with y-values -3 and -1, which means that the table is not a function. Therefore, we need to replace one of the x-values that appears twice with a different value.
Since x = 0 is already paired with y = 5, we cannot use 0 as the replacement. The only other x-value that appears more than once is x = -2. Therefore, we can replace one of the occurrences of x = -2 with a different value.
For example, we can replace the second occurrence of x = -2 with x = 1:
x y
3 -3
1 4
-2 -1
-2 -2
0 5
Now each x-value corresponds to a unique y-value, so the table represents a function.
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Write an Algebraic Equation for each problem (include a let statement) and use it to solve the world problem
On number is eight less than five times another. If the the sum of the two numbers is 28, find the two numbers.
The smaller number is __.
The larger number is __.
The smaller number is 6 .
The larger number is 22
To solve this problem
Let's let x be the smaller number and y be the larger number.
From the problem, we know that one number is eight less than five times the other, so we can write:
y = 5x - 8
We also know that the sum of the two numbers is 28, so we can write:
x + y = 28
Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.
Let's solve the first equation for x
x = (y + 8)/5
Now we can substitute this expression for x into the second equation:
(y + 8)/5 + y = 28
Multiplying both sides by 5 to eliminate the fraction, we get:
y + 8 + 5y = 140
Combining like terms, we get:
6y + 8 = 140
Subtracting 8 from both sides, we get:
6y = 132
Dividing both sides by 6, we get:
y = 22
Now we can use the equation y = 5x - 8 to solve for x:
22 = 5x - 8
Adding 8 to both sides, we get:
30 = 5x
Dividing both sides by 5, we get:
x = 6
Therefore, the smaller number is 6 and the larger number is 22.
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Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline.
B is wrong
The average rate of change in fuel consumption per year from 1995 to 1997 will be option c.) 4 gallons per year
What is average rate of change?The average rate of change, sometimes referred to as the average rate of variation, is a measurement of the average rate of change of a quantity over a certain period of time or space. It is frequently used in physics, mathematics, and other academic fields to explain how quickly one quantity changes with relation to another.
For given problem,
[tex]\text{Average fuel consumption per year per passenger car in 1995} = 530\; gallons[/tex]
[tex]\text{Average fuel consumption per year per passenger car in 1997} = 538\; gallons[/tex]
[tex]\text{Change in fuel consumption } \delta g= 538 - 530 = 8 \;gallons[/tex]
[tex]\text{Change in years} \; \delta t= 1997 - 1995 = 2 \;years[/tex]
We can now determine the average annual change in fuel consumption:
[tex]\text{Average rate of change} = \text{Change in fuel consumption} /\text{ Change in years}[/tex]
[tex]\delta g/ \delta t[/tex]= [tex]8\; gallons / \;2 \;years= 4 \;gallons\; per\; year[/tex]
Hence, 4 gallons per year is the accurate average rate of change in gasoline usage per passenger automobile between 1995 and 1997. This shows that, on average, fuel efficiency declined throughout this time for passenger cars in the United States, with average gasoline usage rising.
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