Answer:
[tex]\large\boxed{\textsf{First Angle = 40}^{\circ}}[/tex]
[tex]\large\boxed{\textsf{Second Angle = 60}^{\circ}}[/tex]
[tex]\large\boxed{\textsf{Third Angle = 80}^{\circ}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the measurement of 3 unknown angles. We are given that}[/tex]
[tex]\textsf{a Triangle is the shape, meaning that there are 3 angles total.}[/tex]
[tex]\large\underline{\textsf{What is a Triangle?}}[/tex]
[tex]\textsf{A Triangle is a 3-sided shape with 3 angles. Sometimes, these can be congruent.}[/tex]
[tex]\textsf{Because a Triangle has 3 angles, the sum of the angles' measurements is equal}[/tex]
[tex]\textsf{to 180}^{\circ}.[/tex]
[tex]\large\underline{\textsf{Forming an Equation;}}[/tex]
[tex]\textsf{We know that the first angle is not stated to relate to any other angles, hence}[/tex]
[tex]\textsf{let's call this angle \boxed{\tt x.}}[/tex]
[tex]\textsf{The Second Angle is 20 more than the first angle, or x. This is represented as}[/tex]
[tex]\boxed{\tt x + 20.}[/tex]
[tex]\textsf{The Third Angle is twice the measurement of the first angle. This is represented}[/tex]
[tex]\textsf{as;} \ \boxed{\tt 2x.}[/tex]
[tex]\textsf{Remember that these angles add up to 180}^{\circ}, \ \textsf{hence their combined sum is}[/tex]
[tex]\textsf{identified.}[/tex]
[tex]\underline{\textsf{Our Equation;}}[/tex]
[tex]\boxed{\tt x^{\circ} + x^{\circ} + 20^{\circ} + 2x^{\circ} = 180^{\circ}}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{Let's begin by solving for x. Afterwards we can find the measures of all the angles}[/tex]
[tex]\textsf{by Substitution.}[/tex]
[tex]\underline{\textsf{Solving for x;}}[/tex]
[tex]\tt x^{\circ} + x^{\circ} + 20^{\circ} + 2x^{\circ} = 180^{\circ}[/tex]
[tex]\textsf{We first should consider that there are like terms in this equation. All the x's can}[/tex]
[tex]\textsf{combine together since they're alike.}[/tex]
[tex]\tt \boxed{\tt x^{\circ} + x^{\circ}} + 20^{\circ} + \boxed{\tt 2x^{\circ}} = 180^{\circ}[/tex]
[tex]\underline{\textsf{This results as;}}[/tex]
[tex]\tt 4x^{\circ} + 20^{\circ}= 180^{\circ}[/tex]
[tex]\textsf{Our next step should be isolating x, this involves removing 20 from the left side.}[/tex]
[tex]\textsf{This involves using the Properties of Equalities which state that whenever a}[/tex]
[tex]\textsf{constant is used to manipulate an equation, the expressions still show equality.}[/tex]
[tex]\textsf{For our problem, using the Subtraction Property of Equality, when we subtract}[/tex]
[tex]\textsf{20 from both sides of the equation, then the equation remains equal.}[/tex]
[tex]\underline{\textsf{Subtract 20 from both sides of the equation;}}[/tex]
[tex]\tt 4x^{\circ} + 20^{\circ} - 20^{\circ} = 180^{\circ} - 20^{\circ}[/tex]
[tex]\tt 4x^{\circ} = 160^{\circ}[/tex]
[tex]\textsf{Using the Division Property of Equality, we are able to divide each side by 4 to}[/tex]
[tex]\textsf{remove the coefficient of 4 from x.}[/tex]
[tex]\tt \frac{4x^{\circ}}{4} = \frac{160^{\circ}}{4}[/tex]
[tex]\large\boxed{\tt x = 40^{\circ}}[/tex]
[tex]\large\underline{\textsf{Finding the Unknown Angles;}}[/tex]
[tex]\textsf{We know that the measure of x is 40, which represents the measure of the first}[/tex]
[tex]\textsf{angle.}[/tex]
[tex]\large\boxed{\textsf{First Angle = 40}^{\circ}}[/tex]
[tex]\textsf{We know that the second angle is 20 more than the first angle. Knowing that}[/tex]
[tex]\textsf{the first angle is 40, the sum is 60.}[/tex]
[tex]\large\boxed{\textsf{Second Angle = 60}^{\circ}}[/tex]
[tex]\textsf{We know that the third angle is twice the measure of the first angle. This means}[/tex]
[tex]\textsf{40 is multiplied by 2, which gives us a product of 80.}[/tex]
[tex]\large\boxed{\textsf{Third Angle = 80}^{\circ}}[/tex]
I need help simplifying this expression
The expression simplified is 5³ = 125
How to simplify the expression?Remember that in products the exponents add up and in quotients the exponents are reduced.
Then we can write the numeartor as:
5⁻³*5⁸ = 5⁻³⁺⁸ = 5⁵
Now the quotient becomes:
5⁵/5² = 5⁵⁻² = 5³
That is the expression simplified.
Learn moer about exponents at:
https://brainly.com/question/847241
#SPJ1
hich component of an expert system uses forward and backward chaining to manipulate a series of rules?
The inference engine in an expert system will use both forward and backward chaining as needed to manipulate the rules and make decisions based on the available data and the desired outcome.
To address your question concisely:
The component of an expert system that uses forward and backward chaining to manipulate a series of rules is called the Inference Engine.
An expert system is composed of three primary components: the Knowledge Base, the Inference Engine, and the User Interface.
The Knowledge Base contains the domain-specific facts and rules that the system relies on to solve problems.
The User Interface facilitates communication between the user and the system.
The Inference Engine is responsible for reasoning and drawing conclusions based on the knowledge stored in the Knowledge Base.
It applies logical techniques such as forward and backward chaining to manipulate and evaluate rules.
In forward chaining, the Inference Engine begins with the available data and applies rules to deduce new information or conclusions.
This approach is data-driven, as it starts with facts and moves towards conclusions.
In backward chaining, the Inference Engine starts with a goal or hypothesis and works backward to find supporting evidence or facts.
This approach is goal-driven, as it begins with a desired conclusion and looks for rules that can lead to it.
By employing both forward and backward chaining, the Inference Engine is able to effectively analyze and manipulate rules to provide accurate and reliable solutions to problems within the domain of the expert system.
For similar question on chaining.
https://brainly.com/question/14574494
#SPJ11
By using both forward and backward chaining, the inference engine can efficiently evaluate complex sets of rules and make accurate decisions based on the available data.
The inference engine component of an expert system uses forward and backward chaining to manipulate a series of rules. Forward chaining involves starting with initial data and applying rules to draw a conclusion, while backward chaining involves starting with a goal and working backward to find the necessary data and rules to reach that goal.
By using both forward and backward chaining, the inference engine can efficiently evaluate complex sets of rules and make accurate decisions based on the available data.
The component of an expert system that uses forward and backward chaining to manipulate a series of rules is called the "inference engine". The inference engine applies logical reasoning to deduce new information based on the provided facts and rules in the knowledge base, ultimately assisting in problem-solving and decision-making processes.
to learn more about data click here:
https://brainly.com/question/30459199
#SPJ11
Question 1-13
A ball is hit straight up in the air from a certain height from the ground. The height of the ball from the ground, H (t), in feet, as a function of time, t, in seconds, can be modeled by the equation
shown.
H ( = -44? + 167+ 1
Select all the true statements.
The ball reaches the maximum height att = seconds
The ball reaches the maximum height at r = 2 seconds.
The maximum height reached by the ball is 13 feet from the ground.
The maximum height reached by the ball is 17 feet from the ground.
The ball is hit straight up in the air from 1 feet height from the ground.
The ball is hit straight up in the air from 4 feet height from the ground.
Answer: H(t) = -16t^2 + vt + h
Step-by-step explanation:
The equation that models the height of a ball hit straight up in the air from a certain height from the ground is given by:
H(t) = -16t^2 + vt + h
where H(t) is the height of the ball at time t, v is the initial velocity of the ball, and h is the initial height of the ball.
The equation you provided is incomplete. Could you please check and provide me with the correct equation so that I can help you better?
Question 5
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
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
Question 7
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
Question 10
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Answer:
B
B
A
B
D
C
Step-by-step explanation:
5. B
65 = teachers
15 = principal
65/80 = 81.25
If there's is a total of 900 people, find 81.25 (number of teachers)
=731.25
=731
6. B
The best graphical representation for the teacher's data would be a histogram. A histogram is a graph that displays the distribution of continuous data, such as the number of students who prefer a particular subject. It shows the frequency of each interval, or bin, of values.
A stem-and-leaf plot is typically used for small datasets and displays each data point. A circle graph, also known as a pie chart, is used to show how different parts make up a whole and is not appropriate for showing the distribution of preferences among the students. A box plot, also known as a box-and-whisker plot, is used to display the distribution of data, but it may not be as useful for showing the specific frequencies of each preference as a histogram would be.
7) A
There's an image for it I attached
8) B
The correct circle graph that represents the data in the table is option B) circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.
In the given table, the number of visitors for each type of transportation is given. To create a circle graph, we need to convert the given numbers to percentages. Then, we can use these percentages to determine the angle of each section in the circle graph.
Using the given numbers, we can calculate the percentage of visitors for each transportation type as follows:
Walk: (120/300) x 100 = 40%
Bicycle: (24/300) x 100 = 8%
Car Service: (45/300) x 100 = 15%
Bus: (30/300) x 100 = 10%
Subway: (81/300) x 100 = 27%
Option B) correctly represents these percentages in a circle graph.
9) D
The best prediction about the scoops of ice cream the college will need is option D) The college will have about 1,440 students who prefer ice cream.
To make this prediction, we need to use the information given in the table and assume that the entire student body has the same preferences as the sample of 225 students.
According to the table, 81 out of 225 students prefer ice cream.
To estimate the number of students who prefer ice cream in the entire student body of 4,000 students, we can use proportions.
81/225 = x/4000
Multiplying both sides by 4000, we get:x = 81/225 x 4000 = 1,440
Therefore, the college will have about 1,440 students who prefer ice cream, and they will need to prepare that many scoops.
10) C
The drive-thru that typically has more wait time is option C) Super Fast Food, because it has a larger median.
The median is the middle value when a set of data is arranged in order. In this case, the median wait time for Super Fast Food is 12 minutes, and the median wait time for Burger Quick is 15.5 minutes.
This means that half of the customers at Super Fast Food waited less than 12 minutes, while half of the customers at Burger Quick waited less than 15.5 minutes.
Therefore, the wait time at Super Fast Food is typically shorter than at Burger Quick.
The mean, on the other hand, is influenced by outliers or extreme values, and it is not as robust a measure of central tendency as the median. Therefore, we cannot determine which drive-thru typically has more wait time based on the mean alone.
pleasee help I don’t understand how to do this
The area within the floor plan that Mutt can roam is determined as 37.7 m².
What is the area that Mutt can roam?
The total possible area that Mutt can roam is calculated as follows;
A = πr²
where;
r is the radius if the circle = length of Mutt's leash = 6 mA = π (6 m)²
A = 113.1 m²
The area outside the 120⁰ is calculated as follows;
θ = 360 - 120
θ = 240⁰
A = 240⁰/360 x 113.1 m²
A = 75.4 m²
The area that Mutt can roam is calculated as follows;
A = 113.1 m² - 75.4 m²
A = 37.7 m²
Learn more about area here: https://brainly.com/question/25292087
#SPJ1
A fair die will be rolled 12
times. What is the probability that 1
, 2
, or 3
is rolled at most 9
times? Round your answer to four decimal places
The probability of getting 1, 2, or 3 at the most 9 times after rolling a fair die 12 times is given by 0.9807.
Probability that 1, 2, or 3 is rolled at most 9 times,
Consider all the possible outcomes of rolling a fair die 12 times.
Count the number of outcomes where 1, 2, or 3 is rolled at most 9 times.
Use the complementary probability,
Probability that 1, 2, or 3 is rolled more than 9 times,
Then subtract that probability from 1 .
Let X be the number of times 1, 2, or 3 is rolled in 12 rolls.
Then X follows a binomial distribution with n=12 and p=1/2,
Since there are 3 favorable outcomes out of 6 possible outcomes on each roll.
The probability that 1, 2, or 3 is rolled more than 9 times can be calculated as follows,
P(X > 9) = P(X = 10) + P(X = 11) + P(X = 12)
= (¹²C₁₀) (1/2)^10 (1/2)^2 + (¹²C₁₁) (1/2)^11 (1/2)^1 + (¹²C₁₂) (1/2)^12 (1/2)^0
= 66/2^12 + 12/2^12 + 1/2^12
= 79/2^12
Probability that 1, 2, or 3 is rolled at most 9 times is,
P(X ≤ 9)
= 1 - P(X > 9)
= 1 - 79/2^12
= 4017/2^12
Rounding this to four decimal places gives,
P(X ≤ 9) ≈ 0.9807
Therefore, the probability that 1, 2, or 3 is rolled at most 9 times is approximately 0.9807.
Learn more about probability here
brainly.com/question/11075616
#SPJ4
can someone help me asap? It’s due today
The type of sampling the principal can use is systematic sampling.
What is systematic sampling?Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in a university, you could survey a sample of 50 students.
Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval.
Therefore , with the definition of systematic sampling, it is best for the principal to use a method of systematic sampling for the procedure.
learn more about systematic sampling from
https://brainly.com/question/14333907
#SPJ1
The measure of angle G is 20° what fraction of a complete circle is the measure of angle G
The angle G is (1/18) th {or (20/360)th } fraction of complete circle.
The angle G is measured to be 20°.
We know, the total angle of a complete circle is 360°.
Thus, by simple fraction we can say,
The angle G fraction of complete circle is = 20° / 360°
Simplifying we get, the angle G fraction of complete circle is = 1/18
Hence the angle G is (1/18 )th fraction of a complete circle.
In mathematical term, fractions are defined as a part of the whole. In other words, fraction is referred to the ratio of the value observing to the whole set of values.
To know more about fraction here
https://brainly.com/question/10354322
#SPJ4
a number c increased by 3 is less than or equal to -18
Please help me so i can finish my homework
Answer:
[tex]\frac{1}{4}[/tex]w + 3
Step-by-step explanation:
Helping in the name of Jesus.
The relationship between the mass m in kilograms of an organism and its metabolism P in Calories per
day can be represented by P = 73.3m³. Find the metabolism of an organism that has a mass of 16 kilograms.
Answer:
The relationship between the mass m in kilograms of an organism and its metabolism p in calories per day can be represented by p = 73.3m³ . To find the metabolism of an organism that has a mass of 16 kilograms, we can substitute m = 16 into the equation:
p = 73.3m³ p = 73.3(16)³ p = 73.3(4096) p = 299,648 calories per day
Therefore, an organism with a mass of 16 kilograms has a metabolism of 299,648 calories per day.
I hope that helps!
Step-by-step explanation:
An organism with a mass of 16 kilograms has a metabolism of 299,708.8 Calories per day according to the given relationship.
We can use the given formula to find the metabolism P of an organism with a mass of 16 kilograms:
P = 73.3m³
where m = 16 kg
Substituting the value of m:
P = 73.3(16)³
P = 73.3(4096)
P = 299,708.8 Calories per day.
Learn more about kilograms here:
https://brainly.com/question/28844288
What is the common differences for
3, 7, 11, 15, 19, 23
Step-by-step explanation:
Each term goes UP by 4 from the one before it
common difference, d = 4
. Which jar of pasta has the greatest unit price?
Answer:
Jar 2 has the greatest unit price. B is correct.
Step-by-step explanation:
Jar 1: $1.60/16 oz = 10¢/ounce
Jar 2: $2.40/20 oz = 12¢/ounce
Jar 3: $2.64/24 oz = 11¢/ounce
Jar 4: $2.88/32 oz = 9¢/ounce
Jar 2 has the greatest unit price, so the correct answer is B.
Tyler struggled with his math class early in the year, but he has been working to improve his scores. There is one test left, and he is hoping that his final average test score will be 75. What score will Taylor need to get on Test 6 to finish the year with an average score of 75?
Tyler will need to score an 85 on Test 6 to finish the year with an average score of 75.
To calculate the score that Tyler needs to get on Test 6 to achieve an average score of 75, we need to use the following formula
(average score) = (total points earned / total number of tests)
Let's assume that Tyler has taken five tests so far, and his total points earned are X. Also, let's assume that Test 6 is worth Y points.
Therefore, the equation becomes:
75 = (X + Y) / 6
Multiplying both sides by 6, we get:
X + Y = 450
Now, let's say Tyler's scores on his first five tests are as follows
Test 1: 65, Test 2: 72, Test 3: 70, Test 4: 78 and Test 5: 80
To find out how many points Tyler has earned so far (X), we simply add up his scores on the first five tests
X = 65 + 72 + 70 + 78 + 80
X = 365
Substituting this value of X in the equation we derived earlier, we get
365 + Y = 450
Solving for Y, we get:
Y = 85
Learn more about average score here
brainly.com/question/7471517
#SPJ4
when the underlying distribution of interval scores is violently skewed the appropriate correlational technique should be
The appropriate correlational technique when the underlying distribution of interval scores is violently skewed would be:
b. Spearman's rank correlation coefficient
When the distribution of interval scores is violently skewed, meaning that the data is not normally distributed and may have extreme values or significant departures from normality, Pearson's correlation coefficient (option a) may not be appropriate as it assumes a linear relationship between variables and normality of data.
Instead, Spearman's rank correlation coefficient (option b) is a more appropriate choice. Spearman's rank correlation coefficient is a non-parametric method that does not assume normality of data and is based on the ranks of data rather than the actual values. It measures the strength and direction of monotonic association between variables, making it suitable for data that may not meet the assumptions of Pearson's correlation coefficient.
Learn more about “ correlational technique “ visit here;
https://brainly.com/question/30034221
#SPJ4
Complete Question
When the underlying distribution of interval scores is violently skewed, the appropriate correlational technique should be:
a. Pearson's correlation coefficient
b. Spearman's rank correlation coefficient
c. Kendall's tau
d. Point-biserial correlation coefficient
e. Phi coefficient
The appropriate correlational technique when the underlying distribution of interval scores is violently skewed depends on the type of data and the research question, and may include non-parametric tests such as Spearman's rank correlation coefficient.
When the underlying distribution of interval scores is violently skewed, the appropriate correlational technique depends on the type of data and the research question.
If the data is bivariate (two variables) and both variables are continuous, then the appropriate correlational technique would be Spearman's rank correlation coefficient, which is a non-parametric test that measures the strength and direction of the association between two variables.
Spearman's rank correlation coefficient is used when the data is not normally distributed or when the relationship between the variables is not linear.
On the other hand, if one or both of the variables are dichotomous or categorical, then a different correlational technique may be more appropriate.
For example, if one variable is dichotomous and the other is continuous, a point-biserial correlation coefficient may be used.
If both variables are categorical, a chi-square test of independence or Cramer's V may be used.
It is important to note that the appropriateness of a particular correlational technique depends on the specific characteristics of the data and research question.
Therefore, it is recommended to consult with a statistician or data analyst to determine the most appropriate technique for a particular study.
For similar question on non-parametric.
https://brainly.com/question/29692466
#SPJ11
Jody's team scored 26, 25, 34, 28, and 32 points at the last five basketball games.
What does the mean number of points Jody's team scored represent?
Responses:
A mean of 29 means that the data values are relatively close together and Jody's team scored around 29 points each game.
A mean of 29 points means that the data is very spread out.
A mean of 29 points means that Jody's team scored exactly 29 points in each of the last 5 games.
Answer: A
Step-by-step explanation:
you place in a dark bag 24 marbles. 12 marbles are red, 5 marbles are blue and 7 marbles are yellow. you select 2 random marbles (one after the other without putting the first back in). what is the probability that the marbles have the same color?
The probability of selecting two marbles with the same color is approximately 0.27 or 27%.
To work out the likelihood that the two marbles drawn have similar variety, we can utilize the accompanying advances:
In the first place, we compute the likelihood of drawing a red marble on the principal pick: 12/24 = 1/2.
On the off chance that the main marble drawn is red, there will be 11 red marbles left clinched, out of a sum of 23 marbles. So the likelihood of drawing one more red marble on the subsequent pick is 11/23.
Likewise, in the event that the principal marble drawn is blue, there will be 4 blue marbles left clinched, out of a sum of 23 marbles. So the likelihood of drawing one more blue marble on the subsequent pick is 4/23.
Furthermore, on the off chance that the main marble drawn is yellow, there will be 6 yellow marbles left taken care of, out of a sum of 23 marbles. So the likelihood of drawing one more yellow marble on the subsequent pick is 6/23.
To get the complete likelihood of drawing two marbles of similar variety, we want to add the probabilities of every one of these cases:
(1/2) x (11/23) + (5/24) x (4/23) + (7/24) x (6/23) = 55/138 or roughly 0.398 or 39.8%.
In this way, the likelihood of drawing two marbles of a similar variety is roughly 39.8%.
To learn more about numerical on probability, refer:
https://brainly.com/question/30736519
#SPJ4
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.
y= -2x^2+145x−1051
As a result, the corporation can earn a maximum profit of **$1,292** to the nearest dollar
WHAT IS PROFIT?Profit is a financial gain that occurs when the revenue from a company activity is more than the costs, costs, and taxes required to support the activity. To put it another way, profit is what is left over after all costs have been subtracted from revenue1.
For instance, if a business sells widgets for $100 apiece and the cost of production is $50 each widget, the profit would be $50. The business would make $10,000 in total income and incur $5,000 in total costs if it sold 100 widgets. There would be $5,000 in total profit.
Using the given equation y=-2x²+145x1051 we can utilise the procedures below to get the greatest profit the corporation may make:
1. Using the equation x = -b/2a, where a = -2 and b = 145, determine the x-coordinate of the parabola's vertex.
2. To determine the highest possible value of y, substitute this x value into the equation.
These actions result in:
x = -b/2a = -145/(2×(-2)) = 36.25
When we enter this x value into the equation, we obtain:
y = -2(36.25)² + 145(36.25) - 1051 ≈ $1,292
As a result, the corporation can earn a maximum profit of **$1,292** to the nearest dollar.
To know more about profit visit:
brainly.com/question/29987711
#SPJ1
Find the three trigonometric ratios . If needed, reduce fractions.
The trigonometric ratios with respect to the angle C are:
sin(C) = 15/17, cos(C) = 8/17, tan(C) = 15/8, cosec(C) = 17/15, sec(C) = 17/8, cot(C) = 8/15
What is trigonometric ratios?Trigonometric ratios are ratios of the sides of a right triangle used to calculate angles and side lengths.
The three main ratios are sine, cosine, and tangent, which are defined as the ratios of the opposite, adjacent, and hypotenuse sides.
Using the right triangle ABC, we can find the trigonometric ratios with respect to angle C:
sin(C) = opposite/hypotenuse = AB/AC = 15/17
cos(C) = adjacent/hypotenuse = BC/AC = 8/17
tan(C) = opposite/adjacent = AB/BC = 15/8
cosec(C) = 1/sin(C) = AC/AB = 17/15
sec(C) = 1/cos(C) = AC/BC = 17/8
cot(C) = 1/tan(C) = BC/AB = 8/15
To know more about right triangle visit:
https://brainly.com/question/15101552
#SPJ1
consider the following data set when answering questions 9-12. in a study of jury behavior, participants were provided details about a trial in which the defendant was obviously guilty. although group 2 was told the same details as group 1, they were also told that some evidence had been withheld from the jury by the judge. later the participants were asked to recommend a jail sentence in years. the length of sentence suggested by each participant is presented below. group 1 scores: 4 4 3 2 5 1 1 4 group 2 scores: 3 7 8 5 4 7 6 8 what is the null hypothesis for this test? the groups will differ in their suggested sentences the second group will have a longer mean sentence than group one the second group will have a shorter mean sentence than group one the 2 groups will not differ in terms of their suggested sentences
The null hypothesis for this test is that the 2 groups will not differ in terms of their suggested sentences.
The null hypothesis is a statement that there is no difference between the two populations or variables being tested.
It can be thought of as the "default" position, which assumes that any observed difference is due to chance.
The null hypothesis is usually written in a way that it can be tested and rejected or not rejected through statistical analysis.
The null hypothesis for this test is that the two groups will not differ in terms of their suggested sentences.
This means that any difference between the groups in their suggested sentences is due to chance and not a difference in the population or variables being tested.
This hypothesis can be tested and rejected or not rejected through statistical analysis.
If the two groups do differ in their suggested sentences then the null hypothesis will be rejected and it will be concluded that the difference is not due to chance but rather due to a difference in the population or variables being tested.
For similar question on hypothesis:
https://brainly.com/question/6984941
#SPJ11
In triangle ∆ABC, m<A = 33°, m<C = 58°, and AB = 25 in. What is AC to the nearest tenth of an inch?
1. 16.1 in.
2. 38.9 in
3. 42 in.
4. 12 in.
The length of AC using the laws of sines is 29.5 inches
Calculating the length of ACWe can use the law of sines to solve this problem.
The law of sines states that in any triangle ∆ABC:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides opposite to the angles A, B, and C, respectively.
In this case, we know that m<A = 33°, m<C = 58°, and AB = 25 in.
We need to find AC, which is opposite to angle A.
Let's use the law of sines to solve for AC:
AC/sin(B) = AB/sin(C)
Where
B = 180 - 33 - 58
B = 89
So, we have
AC/sin(89°) = 25/sin(58°)
This gives
AC = 29.5 in. (rounded to the nearest tenth)
Therefore, the answer is 29.5 inches
Read more about triangles at
https://brainly.com/question/19387653
#SPJ1
A store is offering a 30% discount on shirts. A shirt at the store has an original cost of $25. What is the cost of the shirt, in dollars, after the discount?
The cost of the shirt, in dollars, after the 30% discount is $17.50.
What is discount?
A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. Discounts can be offered for a variety of reasons, such as to attract customers, increase sales, or clear out inventory. Discounts can be expressed as a percentage or a fixed amount, and they can be applied at the time of purchase or deducted from an invoice or bill. Discounts are often used in sales promotions, marketing campaigns, and loyalty programs to incentivize customers to buy or use a product or service.
If a store is offering a 30% discount on shirts that cost $25 originally, then the discount amount is:
30% of $25 = 0.30 x $25 = $7.50
The discount amount is $7.50, so the new price of the shirt after the discount is:
$25 - $7.50 = $17.50
Therefore, the cost of the shirt, in dollars, after the 30% discount is $17.50.
To know more about discount visit:
https://brainly.com/question/1548141
#SPJ1
use the 60 mutual funds in the table above to conduct the hypothesis test. what is the p value? p value is (to 4 decimals)
Welch's two-sample t-test indicates that the average of Load Return's population is significantly greater than the average of No Load Return's population, with a large effect size.
The null hypothesis (H0) that the two population means are equal is rejected as the p-value (0.005) is less than the chosen significance level (α=0.05). This indicates that the chance of a Type 1 error is small, and the alternative hypothesis (H1) that the average of Load Return's population is greater than the average of No Load Return's population is supported.
The test statistic (T=-2.646) falls outside the 95% critical value accepted range, which further supports the rejection of H0. The effect size (0.68) is considered large, indicating that the difference between the two population means is substantial.
Learn more about p-value
https://brainly.com/question/13786078
#SPJ4
Complete Question:
use the 60 mutual funds in the table below to conduct the hypothesis test. what is the p value? p value is (to 4 decimals)
Is 20/√40 the same as 1/√2
Answer:
Step-by-step explanation:
[tex]\sqrt{40}[/tex] = [tex]\sqrt{4}[/tex] x [tex]\sqrt{10}[/tex] = [tex]2\sqrt{10[/tex]
[tex]\frac{20}{2\sqrt{10} }[/tex] = [tex]\frac{10}{\sqrt{10} }[/tex]
[tex]\frac{10}{\sqrt{10} } * \frac{\sqrt{10} }{\sqrt{10} } = \frac{10\sqrt{10} }{10} = \sqrt{10} }[/tex]
[tex]\frac{1}{\sqrt{2} } = \frac{1}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{2} }{2}[/tex]
From the above since [tex]\frac{20}{\sqrt{40} }[/tex] is not equal to [tex]\frac{1}{\sqrt{2} }[/tex] it implies that they are not the same
16. pen problems a. a rectangular pen is built with one side against a barn. two hundred meters of fencing are used for the other three sides of the pen. what dimensions maximize the area of the pen? b. a rancher plans to make four identical and adjacent rectan- gular pens against a barn, each with an area of 100 m2 (see figure). what are the dimensions of each pen that minimize the amount of fence that must be used?
a. The dimensions that maximize the area of the pen are 33 meters by 100 meters.
b. The dimensions of each rectangular pen that minimize the amount of fence used are 10sqrt(2) meters by 10sqrt(2) meters.
a. To maximize the area of the rectangular pen, we need to find the dimensions that use up all 200 meters of fencing, except for the side that is against the barn. Let the length of the pen be x and the width be y. Then we have:
Perimeter of the pen = 2x + y = 200 - x (since one side is against the barn)
Simplifying this equation, we get:
3x + y = 200
Area of the pen = xy
Now we can express y in terms of x using the equation above:
y = 200 - 3x
Substituting this into the expression for area, we get:
A(x) = x(200 - 3x) = 200x - 3x^2
To maximize the area, we need to find the value of x that makes A(x) as large as possible. We can do this by taking the derivative of A(x) with respect to x and setting it equal to 0:
A'(x) = 200 - 6x
200 - 6x = 0
x = 33.33
Since we can't have a fractional length, we choose x = 33 meters (rounded to the nearest meter). Then y = 200 - 3x = 100 meters.
b. Let the dimensions of each rectangular pen be x and y. Then we have:
Area of each pen = xy = 100
Perimeter of each pen = 2x + 2y
We want to minimize the amount of fence used, which is equal to the total perimeter of all four pens. So, we need to find the dimensions that minimize the total perimeter subject to the constraint that the area of each pen is 100. We can use Lagrange multipliers to solve this problem:
L(x, y, λ) = 2x + 2y + λ(xy - 100)
Taking the partial derivatives with respect to x, y, and λ, we get:
∂L/∂x = 2 + λy = 0
∂L/∂y = 2 + λx = 0
∂L/∂λ = xy - 100 = 0
Solving these equations simultaneously, we get:
x = y = sqrt(200/λ)
xy = 100
Substituting the first equation into the second equation, we get:
sqrt(200/λ)^2 = 100
λ = 2
Substituting λ = 2 back into the first equation, we get:
x = y = sqrt(200/λ) = 10sqrt(2)
for such more question on dimensions
https://brainly.com/question/28107004
#SPJ11
shuffle a deck of cards and t urn over t he first card. \i\fhat is t he sample space of t his experiment? how many outcomes are in t he event t hat t he first card is a heart?
If we shuffle a deck of cards ,turn over first card, then
(a) "Sample-Space" of this experiment is set of all 52 cards.
(b) Number of outcomes in event that the first card is a heart is 13 .
Part (a) : The "Sample-Space" of this experiment refers to all possible outcomes that occur when "first-card" from a shuffled deck of cards is turned over.
In a "standard-deck" of 52 playing cards, the sample space consist of all 52 cards, which includes 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace - 10, Jack, Queen, King).
So, the sample space of this experiment will be set of all 52 possible cards that could be turned over as "first-card".
Part (b) : The event that "first-card" is a heart will consist of all outcomes where the first card turned over is a heart.
In a "standard-deck" of 52 "playing-cards", there are 13 hearts (Ace of Hearts, 2 of Hearts, 3 of Hearts, ..., 10 of Hearts, Jack of Hearts, Queen of Hearts, and King of Hearts).
Therefore, there are 13 outcomes in the event .
Learn more about Sample Space here
https://brainly.com/question/30206035
#SPJ4
The given question is incomplete, the complete question is
Shuffle a deck of cards and turn over the first card.
(a) What is the sample space of this experiment?
(b) How many outcomes are in the event that the first card is a heart?
Samuel rotated PLUTO 90° clockwise about the origin to generate P'L'U'T'O'.
with vertices at P (2,-3), L'(-2,-5), U'(-6,-1), T'(-2,3), and O'(1,1). What
are the coprdinates for PLUTO?
The coordinates for PLUTO are P(3,2), L(5, -2), U(1, -6), T-3, -2) and O(-1, 1)
When a figure is rotated 90 degrees clockwise about the origin, its new coordinates are found by switching the x and y values of each point and then negating the new x value. This means that if a point had coordinates (x, y) in the original figure, its new coordinates in the rotated figure would be (-y, x).
Using this information, we can find the coordinates of each vertex of PLUTO by working backwards from the coordinates of the vertices of P'L'U'T'O'. For example, the coordinates of P can be found by negating the y-coordinate of P' and switching the x and y values. Applying this formula to P'(2,-3) gives us P(3,2).
Similarly, the coordinates of L can be found by negating the y-coordinate of L' and switching the x and y values. Applying this formula to L'(-2,-5) gives us L(5,-2).
Then for the other coordinates are calculated based on then we get the following,
U'(-6,-1) is U(1, -6)
T'(-2,3) is (-3, -2)
and O'(1,1) is (-1, 1).
To know more about coordinates here
https://brainly.com/question/27749090
#SPJ4
wants to know if there is a difference in the average annual household income between those who own their own homes and those who rent. she has measured household income on a ratio scale, based on the annual take-home pay of residents. what statistical test should she use to examine this difference?
Use an independent samples t-test to compare annual household income between homeowners and renters, considering within-group variability and determining statistical significance.
To look at the distinction in the normal yearly family pay between the people who own their own homes and the individuals who lease, a suitable factual test to utilize would be an autonomous examples t-test.
This test is utilized to think about the method for two autonomous gatherings, for this situation, the gathering of property holders and the gathering of tenants.
As the family pay is estimated on a proportion scale, the t-test can be utilized to decide whether there is a huge distinction in the method for the two gatherings, considering the changeability inside each gathering.
The consequences of the t-test will give a p-esteem, which can be utilized to decide the factual meaning of any distinctions tracked down between the two gatherings.
To learn more about annual household income, refer:
https://brainly.com/question/28865006
#SPJ4
Leo subscribes to a monthly app service that charges him $6 for one month, and each app he purchases costs $0. 90. Lara subscribes to a service that charges $1. 50 per app with no additional monthly fee. After how many apps will they have the same monthly bill?
Iam do not understand what do you mean 1335690964225753897426908224 1335690964225753897426908224 88 9 109 250 10 10 XL 220 10 10 30 250 30 30 30 400
which method uses an arithmetic mean to forecast the next period? group of answer choices naive. exponential smoothing. none of the above moving averages. adaptive filtering.
The method that uses an arithmetic mean to forecast the next period is "moving averages".
Which method is suitable for arithmetic mean?The method that uses an arithmetic mean to forecast the next period is the "moving averages" method.
In this method, the average of the past observations is calculated, and this average is used as the forecast for the next period.
The number of past observations used in the calculation of the moving average depends on the specific variant of the method being used.
Learn more about arithmetic mean
brainly.com/question/13000783
#SPJ11