To construct frequency and relative frequency distributions, count number of students for each major and divide by total number of students (30) to find the relative frequency.
Use the frequency and relative frequency data to create a bar chart and a pie chart to visualize the data. To construct a frequency distribution and bar chart for the thirty students in the School of Business, we need to count the number of occurrences of each major and create a table. For example, if 9 students chose Management as their major, 9 would be the frequency for Management. We can then plot the frequencies on a bar chart, with each major on the x-axis and its frequency on the y-axis. The bar chart visually represents the distribution of the data.
A relative frequency distribution is a frequency distribution expressed as a proportion or percentage of the total number of observations. To create a relative frequency distribution, we divide each frequency by the total number of students (30 in this case) and multiply by 100%. The relative frequencies can then be used to construct a pie chart, where each major is represented as a wedge or slice of the pie, proportional to its relative frequency. The pie chart visually represents the distribution of the data as a whole.
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let $k$ be the product of all factors $(b - a)$ (not necessarily distinct) where $a$ and $b$ are integers satisfying $1 \le a < b \le 20$. find the greatest positive integer $n$ such that $2^n$ divides $k$.
The greatest positive integer [tex]$n$[/tex] such that [tex]$2^n$[/tex] divides [tex]$k$ is $n = 4$[/tex].
[tex]$k = (2 - 1)(3 - 1)(4 - 1)...(20 - 1)$[/tex]
We can rewrite [tex]$k$[/tex] as [tex]$k = 2^1 \cdot 3^1 \cdot 4^1 \cdot ... \cdot 20^1$[/tex], and then use the formula [tex]$2^n \mid (p_1^{\alpha_1} \cdot p_2^{\alpha_2} \cdot p_3^{\alpha_3} \cdot ... \cdot p_m^{\alpha_m})$ $\iff$ $2^n \mid p_1^{\alpha_1}$[/tex] and [tex]$2^n \mid p_2^{\alpha_2}$[/tex] and[tex]$2^n \mid p_3^{\alpha_3}$ and ... and $2^n \mid p_m^{\alpha_m}$[/tex]
Since all of the exponents [tex]$\alpha_1, \alpha_2, \alpha_3, ..., \alpha_m$[/tex] are equal to 1, we can simplify this to: [tex]$2^n \mid p_1$ and $2^n \mid p_2$ and $2^n \mid p_3$ and ... and $2^n \mid p_m$[/tex]
In this case, [tex]$p_1 = 2$, $p_2 = 3$, $p_3 = 4$[/tex], and so on, so [tex]$2^n$[/tex] must divide all of the prime numbers from 2 to 20 in order for it to divide k. The highest power of 2 that divides all of these prime numbers is [tex]$2^4$[/tex], so the greatest positive integer n such that [tex]$2^n$[/tex] divides [tex]$k$ is $n = 4$[/tex].
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This morning Haidar noticed that her dog, Aldi, seemed unwell. She took him to the vet, where he was diagnosed with an ear infection. The veterinarian prescribed an antibiotic called amoxicillin to help Aldi feel better. Haidar will give Aldi 150 mg of the antibiotic once each day for 10 days. Each time Haidar gives Aldi his next dose of medication, 40% of the previous dose remains in his bloodstream. Use what you know about recursive sequences and iteration to explore the mathematics related to this scenario.
Use your response to question 1 to write a recursive definition for the amount of medication in Aldi’s bloodstream after each dose of medication. Is your definition arithmetic, geometric, or neither? Explain.
PLEASE MAKE SURE TO ADD THE DEFINITION :)
The solution is , 225 mg remain in Aldi bloodstream.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
150mg of amoxicillin was given daily for 10 days equals 1,500
of the 1500-40% =600mg
so, we get,
600mg divided by 4 days
= 225mg still in blood stream
Hence, The solution is , 225 mg remain in Aldi bloodstream.
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What kind of angle is this
A car dealership has been keeping detailed records of the colors of cars sold during the current year. This chart shows the probabilities for each color.
What is the probability that for the next two cars sold, the first will be black and the second will be silver?
The requried probability that for the next two cars sold, the first will be black and the second will be silver is 41%.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
To find the probability that a customer will purchase a silver or white car, we add the probabilities of each individual color:
silver = 23%
white = 18%
silver or white = 23% + 18% = 41%
So, the probability that a customer will purchase a silver or white car is 41%.
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What fraction of Kaitlins family have green or brown eyes?
The fraction of Kaitlins family have green or brown eyes is 5/8
How to determine the fractionThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Green = 3/8
Brown = 2/8
This means that
Green or Brown = 3/8 + 2/8
Evaluate the like terms
Green or Brown = 5/8
Hence, the fraction is 5/8
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determine if the ordered pair (6, 4) is a solution to the inequality
Y > -1/2x + 7 
Yes, because (6, 4) is above the line
No because (6, 4) is below the line
Yes, because (6, 4) is on the line
No, because (6, 4) is on the line
The ordered pair (6, 4) is not a solution to the inequality Y > - (1/2)x + 7 as,
No, because (6, 4) is below the line.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality Y > - (1/2)x + 7.
Form for the ordered pair (6, 4) we have,
4 > - (1/2)×4 + 7.
4 > - 2 + 7.
4 > 5 which is not true.
Therefore, The ordered pair is not a solution to the inequality.
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25 POINTS!! PLEASE HELP!! i only need the answers for the circled problems
18. With a deposit of $375 in a savings account earning 2.75% interest compounded annually, the interest for the given amounts of time is as follows:
a) $10.31b) $54.48c) $270.16.How is the interest computed?Compound interest operates on a system of computing interest to accumulated interest, unlike the simple interest system.
To find the interest for the given periods, we can use an online finance calculator, which also shows the future value (compounded present value).
We can also manually compute the interest, using the FV table or factor and deducting the present investment from the future value.
Compounded Interest for 1 Year:N (# of periods) = 1 year
I/Y (Interest per year) = 2.75%
PV (Present Value) = $375
PMT (Periodic Payment) = $0
Results:
FV = $385.31
Total Interest = $10.31 ($375 x 2.75%)
Compounded Interest for 5 Years:N (# of periods) = 5 years
I/Y (Interest per year) = 2.75%
PV (Present Value) = $375
PMT (Periodic Payment) = $0
Results:
FV = $429.48
Total Interest = $54.48
Compounded Interest for 20 Years:N (# of periods) = 20 years
I/Y (Interest per year) = 2.75%
PV (Present Value) = $375
PMT (Periodic Payment) = $0
Results:
FV = $645.16
Total Interest = $270.16
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Question Completion:18: You deposit $375 in a savings account that earns 2.75% interest compounded yearly. Find the interest earned by the account after the given amounts of time.
a) 1 year
b) 5 years
c) 20 years
a counting process {nt} is a pp if and only if it is a renewal process in which the interarrival times have an exponential distribution function.
True. A counting process {N(t)} is a Poisson process(PP) if and only if it is a renewal process in which the interarrival times have an exponential distribution function.
A counting process is a mathematical model used to count the number of events that occur over time. A Poisson process is a specific type of counting process in which the number of events occurring in any given time interval is independent of the number of events that have occurred in any previous interval.
A renewal process is a type of counting process in which the arrival of events resets the process so that the future events are independent of the past events. The interarrival time between two events in a renewal process is the time between the arrival of one event and the arrival of the next.
Complete Question:
T/F. a counting process {nt} is a pp if and only if it is a renewal process in which the interarrival times have an exponential distribution function.
m∠CFG = 129o and m∠HFD = 93o, find each missing measure.
The measure of each angle ∠EFG, ∠HFD, DFG, GFC, and CFE will be 36°, 93°, 51°, 129°, and 51°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Angle ∠CFG and angle ∠HFD are vertically opposite angles. Then we have
y + 93° = 129°
y = 36°
Angle ∠EFC and angle ∠CFG are supplementary angles. Then we have
x + 129° = 180°
x = 51°
Then the measure of each angle ∠EFG, ∠HFD, DFG, GFC, and CFE will be 36°, 93°, 51°, 129°, and 51°, respectively.
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The missing diagram is given below.
For the pair of functions, find the indicated sum, difference, product, or quotient. f(x) = x² + 1, g(x) = 9x + 5 Find (fg)(x).
Answer:The product of the two functions, f and g, is given by fg(x) = (x² + 1)(9x + 5). This can be expanded to give fg(x) = 9x³ + 14x² + 5x + 5.
Step-by-step explanation:
In the Fall 2011 STA 2023 Beginning of the Semester Survey, students were asked how many parties they attended every week and how many text messages they sent per day. The researcher decided to make the number of parties attended per week the explanatory variable and the number of text messages sent per day the response variable. The least squares regression line for this relationship is y-hat = 64.96 + 25.41x. Interpret the y-intercept if appropriate. 1000 2002 Legend Fitted line Parties Do not interpret. The predicted number of text messages per day for someone who has not attended a party this week is 64.96. The predicted number of text messages per day for someone who has not attended a party this week is 25.41. The predicted number of parties attended this week for someone that hasn't sent any text messages is 64.96. The predicted number of parties attended this week for someone that hasn't sent any text messages is 25.41.
The predicted number of text messages sent per day for someone who has not attended a party this week is 64.96 and the predicted number of text messages sent per day for someone who has attended one party this week is 90.37 (64.96 + 25.41).
The least squares regression line is a mathematical formula that is used to predict the response variable (in this case, the number of text messages sent per day) based on the explanatory variable (the number of parties attended per week). The formula for the least squares regression line is y-hat = b0 + b1x, where y-hat is the predicted response variable, b0 is the y-intercept, b1 is the slope, and x is the explanatory variable. In this example, the y-intercept is 64.96 and the slope is 25.41. This means that the predicted number of text messages sent per day for someone who has not attended a party this week is 64.96 and the predicted number of text messages sent per day for someone who has attended one party this week is 90.37 (64.96 + 25.41).
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The mean of the diameter of the rubber ball is 12cm with a standard deviation of 0.2 cm. Define the random variable X in words. X =
Therefore , the solution of the given problem of standard deviation comes out to be Random variable X is 30.
Define standard deviation.
Statistics uses variance as a metric for variability. It evaluates the square root of the average deviation between the data values and the mean. It includes all data points in its calculations, unlike some other statistical measures of variability, by comparing each value to the mean. Variances can happen for internal or external causes, and they might involve things like human mistake, unrealistic expectations, and shifting business or economic conditions.
Here,
Given:
=> radius of rubber ball=12/2 = 6cm
Standard deviation = 0.2cm
Random variable X:
=> 6/0.2
=> 30
Therefore , the solution of the given problem of standard deviation comes out to be Random variable X is 30.
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PLEASE HELP 10 points
Examine the figure below, what is a = ?
The value of 'a' in the figure is, 6
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
In the figure,
⇒ ∠MLK = 15a°
⇒ ∠MJK = 180°
Now, We know that;
In a circle;
⇒ ∠MLK = 1/2 ∠MJK
Substitute given values, we get;
⇒ 15a = 1/2 (180°)
⇒ 15a = 90°
⇒ a = 90/15
⇒ a = 6
Thus, The value of a = 6
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the numbers 1, 2, 3, 4, 5, 6, 7, and 8 are randomly written on the faces of a regular octahedron so that each face contains a different number. the probability that no two consecutive numbers, where 8 and 1 are considered to be consecutive, are written on faces that share an edge is where and are relatively prime positive integers. find .
The probability of no two consecutive numbers written on the faces that share an edge is given by P = (7! - 16) / (2 * 8) = 105/16.
The probability of no two consecutive numbers written on the faces that share an edge is given by the formula P = (n–1)!/(2n), where n is the number of faces (in this case 8). Applying this formula, the probability of no two consecutive numbers written on the faces that share an edge is P = 7!/16 = 105/16. Therefore, the answer is 105/16.
To calculate this probability, we must first consider the number of ways in which the numbers can be written on the faces of the octahedron so that no two consecutive numbers appear on faces that share an edge. There are 7! (7 factorial, i.e. 1 * 2 * 3 * 4 * 5 * 6 * 7) total ways in which the numbers can be written on the faces, but among these, there are some arrangements in which two consecutive numbers appear on faces that share an edge. To find the number of these arrangements, we can consider the number of ways in which the numbers can be written on the faces of the octahedron so that two consecutive numbers appear on faces that share an edge. There are 8 pairs of consecutive numbers, and for each pair, there are 2! (2 factorial, i.e. 1 * 2) ways in which the two numbers can be written on faces that share an edge. Thus, the total number of ways in which two consecutive numbers appear on faces that share an edge is 8 * 2! = 16.
Therefore, the probability of no two consecutive numbers written on the faces that share an edge is given by P = (7! - 16) / (2 * 8) = 105/16.
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For this project, you will submit the Python script you used to make your calculations and a summary report explaining your findings.
Python Script: To complete the tasks listed below, open the Project Two Jupyter Notebook link in the Assignment Information module. Your project contains the NBA data set and a Jupyter Notebook with your Python scripts. In the notebook, you will find step-by-step instructions and code blocks that will help you complete the following tasks:
Hypothesis tests for a population parameter
Hypothesis tests for a population mean
Hypothesis test for a population proportion
Hypothesis test for the difference between two population parameters
Hypothesis test for difference between two population means
Summary Report: Once you have completed all the steps in your Python script, you will create a summary report to present your findings. Use the provided template to create your report. You must complete each of the following sections:
Introduction: Set the context for your scenario and the analyses you will be performing.
Hypothesis tests for the population mean: Discuss all steps of the hypothesis tests and interpret your results.
Hypothesis test for the population proportion: Discuss all steps of the hypothesis test and interpret your results.
Hypothesis test for the difference between two population means: Discuss all steps of the hypothesis test and interpret your results.
Conclusion: Summarize your findings and explain their practical implications.
IVE GOT THE PYTHON SCRIPT COMPLETED JUST NEED HELP WITH THE SUMMARY REPORT ALL PYTHON SCRIPT DATA IS BELOW
Assigned team
game_id year_id fran_id pts opp_pts elo_n opp_elo_n game_location game_result
0 199511030CHI 1996 Bulls 105 91 1598.2924 1531.7449 H W
1 199511040CHI 1996 Bulls 107 85 1604.3940 1458.6415 H W
2 199511070CHI 1996 Bulls 117 108 1605.7983 1310.9349 H W
3 199511090CLE 1996 Bulls 106 88 1618.8701 1452.8268 A W
4 199511110CHI 1996 Bulls 110 106 1621.1591 1490.2861 H W
My team
game_id year_id fran_id pts opp_pts elo_n opp_elo_n game_location game_result
0 201210300MIA 2013 Celtics 107 120 1586.1121 1666.3193 A L
1 201211020BOS 2013 Celtics 88 99 1566.8929 1520.3861 H L
2 201211030WAS 2013 Celtics 89 86 1571.9491 1435.2531 A W
3 201211070BOS 2013 Celtics 100 94 1574.5995 1432.6027 H W
4 201211090BOS 2013 Celtics 100 106 1562.3982 1541.7600 H L
Mean Relative Skill of your team in the years 2013 to 2015 = 1456.78
Mean Points = 98.04897959183674
T Stat = -17.47, P Value = 0.0000
Reject the null hypothesis
Proportion of games won by your team when scoring more than 80 points in the years 2013 to 2015 = 0.4506
Mean Relative Skill of the assigned team in the years 1996 to 1998 = 1739.8
Mean Relative Skill of your team in the years 2013 to 2015 = 1456.78
The results of the hypothesis tests indicate that the difference in mean relative skill between the assigned team and my team is significant.
Hypothesis tests for the population mean:
The first hypothesis test was performed to test the mean relative skill of the assigned team and my team. The mean relative skill of the assigned team was found to be 1739.8 and the mean relative skill of my team was found to be 1456.78. The hypothesis test was performed to test the difference between the two means. The t-statistic was calculated to be -17.47 and the p-value was found to be 0.0000. Based on the results, the null hypothesis was rejected.
Hypothesis test for the population proportion:
The second hypothesis test was performed to test the proportion of games won by my team when they scored more than 80 points. The proportion was found to be 0.4506. The hypothesis test was performed to test the difference between the proportion of games won and the null hypothesis value of 0.5. The p-value was found to be significant, which means that the proportion of games won by my team when scoring more than 80 points is significantly different from 0.5.
Hypothesis test for the difference between two population means:
The third hypothesis test was performed to test the difference between the mean points scored by my team and the assigned team. The mean points scored by my team was found to be 98.0489 and the mean points scored by the assigned team was not calculated in this project.
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Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5}
B = {1, 3, 5, 7}
How many elements are in (A' ∪ B)' ?
describe the x-values at which f is differentiable. (enter your answer using interval notation.) f(x)
The x-values at which the function f(x) is differentiable are all real numbers, excluding those values where the derivative is undefined. This can be expressed using interval notation as (-∞, -4) ∪ (-4, 0) ∪ (0, 4) ∪ (4, ∞).
The function mentioned is a continuous function on the interval 4 < x < 5, h(x), which is described in the table provided. This function has a vertical asymptote at 4 and 5, meaning that its values approach positive or negative infinity at these points.
The function's domain is 4 < x < 5, meaning that it is defined and can take a value for any x within this interval. The function's range is not specified, so it can take any value for an x within the given interval. Additionally, the function is differentiable for all values of x within the given interval, meaning that its rate of change can be calculated using derivatives.
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15, 15 moved 10 units down on a graph
Answer: if you are on a graph and go down 15 it would be
Step-by-step explanation:
15 minus 10 equals
K
What is the minimum number of pitches that a baseball player who pitches a complete game can make in a
regulation 9-inning baseball game?
The minimum number of pitches that a baseball player who pitches a complete game can make in a regulation 9-inning baseball game is given as follows:
27 pitches.
How to obtain the minimum number of pitches?The minimum number of pitches is obtained applying the proportions in the context of this problem.
Each baseball game is composed by nine innings, and for each inning the pitching team must get three outs.
Hence the number of outs in a baseball game is given as follows:
9 x 3 = 27 outs.
The minimum number of pitches for one out is of one pitch, hence the minimum number of pitches for an entire game is given as follows:
1 x 27 = 27 pitches.
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Find the distance along an arc on the surface of the earth that subtends a central angle of 4 minutes (1 minute = 1/60 degree). The radius of the earth is 3960 miles. Round to the thousandths. (3 decimal places)
The distance along an arc on the surface of the earth is 4.605miles
What is length of an arc?Given an angle and the diameter of a circle, we can calculate the length of the arc using the formula: Arc Length = ( 2 * pi * radius ) * ( angle / 360 ) Where pi = 22/7, diameter = 2 * radius, angle is in degree.
1 minutes = 1/60 degree
4 minutes = 1/60 × 4
4 minutes = 1/15 °
l = tetha/360 × 2πr
l = 1/15 × 1/360 × 2 × 3.14 × 3960
l = 24868.8/5400
l = 4.605miles
therefore the distance along the surface of the earth by the arc is 4.605miles
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Can you help please
Answer: 1/3
Step-by-step explanation:
5/15 = 1/3
10/30 = 1/3
6/18 = 1/3
9/27 = 1/3
2/6 = 1/3
30 points can someone help please
Answer:
[tex]y = 4[/tex]
Step-by-step explanation:
Since each box is the same, that means Box A = Box B, which means 8y+1=6y+9
[tex]8y + 1 = 6y + 9[/tex]
Now to get y's on one sides of the equal sign and numbers on the other.
First we can subtract 1 from each side to get
[tex]8y = 6y + 8[/tex]
Next we'll subtract 6y from both sides
[tex]2y = 8[/tex]
Lastly, we divide both sides by 2
[tex]y = 4[/tex]
Answer:
y=4
Step-by-step explanation:
set up the equation like 8y+1=6y+9.
subtract the one to the other side to get the 8y isolated.
8y=6y+8
subtract6 6y from 8y.
2y=8
divide to find y.
y=4
Heritage Company uses a job-order costing system to assign costs to jobs. It had no work in process or finished goods inventories on hand at the beginning of May. The table below provides data concerning the only three jobs worked on in May.
Job X Job Y Job Z
Direct labor hours 200 80 120
Direct materials $ 4,800 $ 1,800 $ 3,600
Direct labor $ 2,400 $ 1,000 $ 1,500
Jobs X and Y were completed in May; however, only 150 of the 200 units included in Job X were sold in May, whereas all 100 of Job Y’s units were sold in May. Job Z was not completed by the end of the month.
Overhead costs are applied to jobs based on direct labor-hours and the predetermined overhead rate is $45 per direct labor-hour. The company’s total applied overhead always equals its total actual overhead.
Required:
Compute the amount of overhead cost that would have been applied to each job during May.
Compute the work in process inventory that would be reported in the company’s May 31 balance sheet.
Compute the finished goods inventory that would be reported in the company’s May 31 balance sheet.
Compute the cost of goods sold that would be reported in the company’s income statement for May.
a) The amount of overhead cost that would have been applied to each job during May, based on the predetermined overhead rate, was as follows:
Job X Job Y Job Z
Overhead applied $9,000 $3,600 $5,400
b) The work-in-process inventory reported in the company's May 31 balance sheet was $10,500 for Job Z only.
c) The finished goods inventory that would be reported in the company’s May 31 balance sheet was $4,050.
d) The cost of goods sold that would be reported in the company's income statement for May was $14,500.
What is the predetermined overhead rate?The predetermined overhead rate is the rate per unit at which overhead costs are applied to production units or jobs.
The predetermined overhead rate is the quotient of the total budgeted overhead cost divided by the relevant total cost driver units (e.g. direct labor hours).
Predetermined overhead rate = $45 per direct labor-hour
Job X Job Y Job Z
Direct labor hours 200 80 120
Direct materials $4,800 $1,800 $3,600
Direct labor 2,400 1,000 1,500
Overhead applied 9,000 3,600 5,400
($45 x 200) ($45 x 80) ($45 x 120)
Production costs $16,200 $6,400 $10,500
Unit costs of Job X $81 ($16,200/200)
Sold units of Job X = 150
Unsold units of Job X = 50 (200 - 150)
Work in process inventory = Job Z's total cost.
Finished Goods Inventory = $4,050 ($81 x 50)
Cost of Goods Sold = $14,500 ($6,400 + $81 x 100)
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show that each conditional statement in exercise 12 is a tautology using the fact that a conditional statement is false exactly when the hypothesis is true and the conclu- sion is false.
From conditional statements, there can be built a Tautology.
According to the question, when the Hypothesis is true and the conclusion is false, the result will be false. And that's correct.
But when a conditional statement can a Tautology, given the fact that not always a conditional statement will return the logical value of truth? Look at this example below:
1)James is from Orlando and he lives in Florida. Therefore, James is from Orlando.
2)James is from Orlando and he does not live in Florida. Therefore, James is from Orlando.
3)James is not from Orlando and lives in Florida. Therefore, James is from Orlando.
4)James is not from Orlando and he does not live in Florida. Therefore, James is from Orlando.
What we have above is symbolic for:
p∧q→p
And this is tautological, since no matter, what we have line 2 for p∧q, q being false it does not change the value for false, in any way for the whole proposition p∧q→p. What gives us a Tautology?
This, p∧q→p can be rewritten as p∧q⇒p.
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Is the question below
(one solution)
(infinite number of solutions) or
(no solution)
Answer:
One Solution
Step-by-step explanation:
The graph shows two lines crossing each other once, therefore meaning there is only one solution in this graph.
pls help will mark brainliest asapb
When pentagon ABCDE is translated 2 units down, dilated by a scale factor of 1/2 units and reflected over the x-axis, it will map into pentagon FGHIJ. This proves that the pentagons are similar.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The transformations to this problem are given as follows:
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Answer questions 14-16.
Answer:
14. D
15. angle 2= 125 angle 6= 55
16. yes, because if corresponding angles are congruent, then the lines are parallel.
Step-by-step explanation:
14. alternant exterior are outside of the parallel lines. angle HBF and angle ABD are not.
15. corresponding angles are congruent. angle 5 is the vertical angle of angle 2, meaning that they are congruent. angle 6 are linear pair, meaning they equal to 180. 180-125 is 55, which is the angle measure for angle 6.
Lian is making a banner for the school gym. She cut three pieces of fabric into congruent isosceles triangles, as shown. Trigonometric area formula: Area = 1/2absin(c) To the nearest square inch, how much fabric will she use to make all three triangles? 139 square inches 172 square inches 417 square inches515 square inches
The nearest square inch gives a total of 61 square inches of fabric used to make all three triangles.
The trigonometric area formula is used to calculate the area of a triangle. The formula is Area = 1/2absin(c), where a and b are the lengths of two sides of the triangle, and c is the angle between the two sides. In this case, Lian is making three congruent isosceles triangles, so all three triangles have the same base and height, and the same angle at the vertex. Therefore, the area of each triangle is the same. The base and height of the triangle can be calculated using the side lengths, and the angle can be calculated using the theorem of cosines. For example, the base of the triangle is 11 cm, the height is 8 cm, and the angle at the vertex is 62 degrees. Therefore, the area of each triangle is 1/2*11*8*sin(62) = 52 square cm. Multiplying this by three gives a total area of 156 square cm. Converting this to square inches gives 156*0.3937 = 61.4 square inches. Rounding to the nearest square inch gives a total of 61 square inches of fabric used to make all three triangles.
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Which of the following ordered pairs lies on the graph of y = 1/2x?
The ordered pair that lie on the graph of y = 1/2 x are A and B - (0, 0), (1, 2)
What is a line equation?
The equation of a line can be constructed using the slope of the line and a point on the line. Let's learn more about the line's slope and the crucial point on the line in order to better understand how the equation for a line is created. The line's inclination with respect to the positive x-axis is measured by its slope, which can be expressed as an integer number, a fraction, or the tangent of the angle it makes with the x-axis. The point is the intersection of the x and y coordinates in the coordinate system.
The line's equation is as follows:
y = 1/2 x
To check which ordered pair lie on the graph of the given equation of line, we substitute the values of x and y coordinate in the equation.
1. (0, 0)
y = 1/2 x
0 = 1/2 (0)
True.
2. (1, 2)
y = 1/2 x
1 = (1/2) (2) = 1
True
3. (2, 1)
y = 1/2 x
2 = 1/2 (1)
False
4. (3, 4)
y = 1/2 x
3 = (1/2) (4) = 2
False
5. (4, 2)
y = 1/2 x
4 = (1/2)(2) = 1
False
Hence, the ordered pair that lie on the graph of y = 1/2 x are A and B.
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Complete question -
Which of the following ordered pairs lies on the graph of y = 1/2x?
1. (0, 0)
2. (1, 2)
3. (2, 1)
4. (3, 4)
5. (4, 2)