Angle D of △DEF is congruent to ∠G of △GHJ. Angle E is congruent to ∠H. Side DE is congruent to side HJ. Can you prove that the two triangles are congruent? Explain your answer.
No image attached.
Answers
Answer:
No
Step-by-step explanation:
"Looking" at our triangles
If Angle D is congruent to Angle G, and angle E is congruent to Angle H, lets call those the first and second vertices of each triangle. If we're trying to prove the triangles congruent, we're trying to prove Triangle DEF is congruent to Triangle GHJ (in that order, since we're already given that the first and second angles correspond between triangles).
Could these triangle be congruent? Yes! As a quick example, imagine two Equilateral triangles with side lengths 5. They are congruent, and they do have the first angle and second angle corresponding pairs congruent, and one of those sides from triangle 1 does match the length of one of the sides in triangle 2. ...and they are congruent triangles.
The problem with the given scenario is that the side they give for triangle 1 (between vertex 1 and 2) is not the corresponding side of triangle 2 (between vertex 2 and 3). This makes it so that we cannot guarantee that the triangles are congruent.
As can be seen in the attached image, I've made Side DE length 2, and put it on a coordinate plane so it's easy to see. Side HJ is also definitely length 2. Clearly, those triangles are not congruent.
When would triangles be congruent?
Going back to the definition of congruent triangles, three corresponding angles and three corresponding sides must be congruent. That's 6 pairs of parts needed to be proven congruent to prove triangles congruent!
Fortunately, there are a number of theorems that can be proven to lessen the amount of pairs of parts needed to be proven congruent and still guarantee that the resulting triangles must be congruent.
There are exactly 5 cases:
SSSSASASAAASHLIt looks like a bunch of alphabet soup, but notice that all of them require 3 pieces of information (even HL, which is Hypotenuse-Leg... since there's a Hypotenuse, it must be a right triangle, so there are a pair of corresponding congruent right angles that are congruent that they don't talk about)
In order to remember which items work, remember that you MUST know 3 parts, and think about all of the way you could know 3 parts:
Scenario 1: Have all 3 side pairs (SSS)
There is only one way that all three sides can be equal, and yes, that is one of the triangle congruence shortcuts.
Scenario 2: Have 2 side pairs & 1 angle pair
There are two option here.
two sides and the angle between them (SAS), ortwo sides and an angle NOT between them (...nope).Two sides with the angle between them is SAS (note the angle is between them).
Two sides with the angle not between them is ... (well, that can get you in trouble). Conveniently, that is NOT one of the triangle congruence theorems. So, stay out of trouble, and don't use this for triangle congruence.
Interestingly, HL, is a special case of this "trouble case". Note that if you have the Hypotenuse and a leg, that's two Sides. The right Angle is NOT the angle between those two sides (because the hypotenuse is always across from the right angle). When that angle is 90 degrees, then the set of two sides and the angle not between them DOES work as sufficient to prove triangle congruence, and it's the only time that it's sufficient.
Scenario 3: Have 1 Side and 2 Angles
Again, there are two option here:
two Angles and the Side between them (ASA), ortwo Angles and a Side NOT between them (AAS).In either scenario, this is sufficient to prove the triangles are congruent.
Scenario 4: Have all 3 angles (AAA)
This definitely won't be enough to prove congruence. Zoom in. It's got the same angles, but not the same lengths.
So, only 5 short ways to prove triangles are congruent, and all of them require 3 parts of one triangle corresponding to 3 parts of another, each of the 3 pairs must be congruent.
Related Questions
A block of metal has a volume of 4 cm³, and a density of 19.58 g/cm³. Work out the mass of the block of metal. Give your answer correct to 2 decimal places.
Answers
The block of metal with a 4 cubic cm volume and density of 19.58 g/cm³ has a mass of 78.32 g.
Density refers to a dimension that is it is the mass per unit volume. The density of an object is not affected by the volume or the mass of the object.
It is a unitless quantity. Density is affected by the nature of the substance as well as the temperature. It is expressed as below:
ρ = m/v
where ρ is the density
m is the mass
v is the volume
Given:
ρ = 19.58 g/cm³
v = 4 cm³
19.85 = m / 4
m = 19.58 * 4
= 78.32 g
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Suppose that the production of basic cell phones has become fully automated and firms can produce any number of cell phones at a constant per-unit cost of $46. 3rd attempt Part 1 (3 points) What is the cost of producing 10 cell phones? What is the cost of producing 20 cell phones? What is the cost to produce y cell phones? Choose one: A. 46y OB. 102 О С. а OD 10221
Answers
Answer:
Since the cost of producing one cell phone is $46, the cost of producing 10 cell phones is 10 times the cost of producing one, which is:
10 x $46 = $460Similarly, the cost of producing 20 cell phones is 20 times the cost of producing one, which is:
20 x $46 = $920Therefore, the cost to produce y cell phones is:
y x $46 = $46yTherefore, the correct answer is A. 46y.
which of the following type(s) of unemployment are most associated with an economy that is experiencing dynamic growth and technological progress?
Answers
An economy experiencing dynamic growth and technological progress is more likely to have structural unemployment, as workers may need to retrain and acquire new skills to keep up with changes in the economy and earn higher wages.
Dynamic growth and technological progress often lead to changes in the way goods and services are produced, which can have significant impacts on the labor market. In some cases, new technologies may displace workers who lack the skills necessary to operate or maintain them. This can lead to frictional or cyclical unemployment as workers search for new jobs or wait for the economy to recover.
However, in the long run, technological progress is more likely to result in structural unemployment, which occurs when there is a mismatch between the skills of workers and the requirements of available jobs. As technology advances, workers in some industries may need to retrain or acquire new skills to remain competitive in the labor market.
For example, workers in manufacturing may need to learn how to operate and maintain new automated machinery, while those in information technology may need to keep up with the latest programming languages and software development frameworks. In such cases, workers who are unable or unwilling to acquire these new skills may become structurally unemployed, while those who are able to adapt may be in high demand and earn higher wages.
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someone plsss help me !!! like asap
Answers
The value of the variable 'x' will be 8, 8.1, 9, and 13.
Given that:
Inequality, - x ≤ - 8
Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Simplify the inequality, then we have
- x ≤ - 8
x ≥ 8
The value of 'x' is greater than or equal to 8.
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A man saves 3/ 10 of his income and pays 1/6 of the remainder as rent .Find what fraction of his income is left for other purposes.
Answers
Answer: 7/12
Step-by-step explanation:
1. The remainder is 7/10.
2. He pays 1/6 of the remaining amount as rent; this is the rent he pays.
3. His usage total is 3/10 + 7/60 = 25/60, or 5/12.
If you folded a 90 degree angle in thirds how many degrees is this angle?
Answers
Answer:
30°
Step-by-step explanation:
If you folded a 90 degree angle in thirds how many degrees is this angle?
folding in thirds the value is 1/3 of 90, therefore 90 : 3 = 30°
I need help on this question it is the last one please help
Answers
Answer:
Step-by-step explanation:
a. 45mph
135miles ÷ 3hrs = 45mph
b. 44mph
22m x 2 = 44mph
c. 30mph
1/4 = 15 mins
7.5mins x 4 = 30mph
d. 50mph
100/3 miles = 2/3hr
xmiles (x = number of miles) = 1h
we use cross multiplying and use x to find the miles
2x = 100 x 1
3 3
2x = 100
x = 50mph
e. 65mph
speed = 97.5 miles half an hour
You roll a die and spin the spinner. How many outcomes are possible?
Answers
Answer: 24
Step-by-step explanation:
6 sides on the dice. 4 sections on the spinner.
6 times 4 = 24
24 possible outcomes.
answer this question please if it is visible
Answers
The matching of charges of the given polyatomic ions are as listed below:
Hydroxide: OH⁻ (charge of -1)Carbonate: CO₃²⁻ (charge of -2)Sulfate: SO₄²⁻ (charge of -2)Ammonium: NH₄⁺ (charge of +1)Nitrate: NO₃⁻ (charge of -1)What can one determine the polyatomic charge?The polyatomic charge of a molecule or ion can be determined by adding up the charges of its constituent atoms and accounting for any additional charges present in the molecule or ion.
1. Determine the number of valence electrons for each atom in the polyatomic ion or molecule.
2. Write the Lewis structure for the molecule or ion, including the formal charges for each atom.
3. Add up the formal charges on all atoms in the molecule or ion to determine the overall charge.
4. Alternatively, you can use the oxidation state of each atom in the molecule or ion to calculate the overall charge.
For example, let's consider the sulfate ion, SO₄²-.
1. Sulfur has 6 valence electrons, and each oxygen has 6 valence electrons.
2. The Lewis structure for SO₄²- is:
O
|||
S-O
|||
O
Each oxygen has a -1 formal charge, and sulfur has a +2 formal charge.
3. The overall charge of the sulfate ion is (-1) x 4 + (+2) = -2.
4. Alternatively, we can use the oxidation state of each atom in SO₄²- to calculate the overall charge. The oxidation state of sulfur is +6, and each oxygen is -2. Therefore, the overall charge of the sulfate ion is (+6) + (-2 x 4) = -2.
So, the polyatomic charge of the sulfate ion is -2.
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The complete question goes thus:
Match the polyatomic ions with their appropriate charge(s)
Charges:
G1 → +1
G2 → +2
G3 → +3
G4 → -3
G5 → -2
G6 → -1
G7 → 0
Poly ahmic ions:
(OH- (hydroxide)
CO₃²- (Carbonate)
So₄²⁻ (Sulphate)
NH₄⁺ (Ammonium)
NO₃⁻ (Nitrate).
Select ALL the correct answers.
Identify the two tables which represent quadratic relationships.
Answers
The selected all the correct answers are table 5 and table 6.
We are given that;
The tables of 4 options
Now,
If the first differences are not constant, but the second differences are constant, then the relationship is quadratic.
we can check each table and see which ones have constant second differences. Here are the results:
Table First Differences Second Differences Quadratic?
1 2, 2, 2 0, 0 No
2 -2, -4, -8 -2, -4 No
3 1, 1, 1 0, 0 No
4 -2, 0, 0 2, 0 No
5 1, 2, 4 1, 2 Yes
6 -8, 0, 8 8, 8 Yes
Therefore, by quadratic equation the answer will be table 5 and table 6.
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The Following Data Were Obtained From A Repeated-Measures Research Study. What Is The Value Of MD For These Data?Subject 1st 2nd#1 10 15#2 4 8#3 7 5#4 6
​The following data were obtained from a repeated-measures research study. What is the value of MD for these data?
Subject 1st 2nd
#1 10 15
#2 4 8
#3 7 5
#4 6 11
Group of answer choices
​4
​3. 5
3
4. 5
Answers
The value of MD (mean difference) for the given repeated-measures research study data can be calculated by subtracting the scores of the first condition from the scores of the second condition for each subject, then calculating the mean of those differences.
The mean difference (MD) for the given data can be calculated as follows:
MD = ((15-10) + (8-4) + (5-7) + (11-6))/4
MD = (5 + 4 - 2 + 5)/4
MD = 3
Therefore, the value of MD for the given data is 3.
In a repeated-measures research study, the same group of subjects is measured on the same variable multiple times. MD represents the average difference between the scores of the same group of subjects on the same variable across two different conditions or time points.
To calculate MD, we need to subtract the scores of the first condition from the scores of the second condition for each subject, and then calculate the mean of those differences. In this case, the mean difference is 3, indicating that there is an average increase of 3 units from the first to the second condition. MD is a useful statistic in repeated-measures studies, as it provides information about the magnitude and direction of the change in the variable being measured.
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what are the benefits and costs to a nation that participates in international trade? do the benefits outweigh the costs or do the costs outweigh the benefits?
Answers
Participating in international trade can have both benefits and costs for a nation. One of the main benefits of international trade is the potential for increased economic growth and development.
By engaging in trade, countries can access larger markets for their goods and services, which can lead to increased sales and profits for businesses. This, in turn, can lead to increased investment and job creation, as well as increased tax revenues for the government.
Another benefit of international trade is the potential for increased consumer choice and lower prices for consumers.
By importing goods from other countries, consumers can access a wider variety of products than would be available domestically, and competition from foreign producers can help to drive down prices.
However, there are also costs associated with international trade. One potential cost is the risk of job losses in industries that face competition from imports.
When businesses in other countries can produce goods more efficiently or at lower cost than domestic producers, this can lead to job losses and a decline in certain industries.
Another potential cost of international trade is the risk of economic instability.
If a country becomes heavily dependent on exports to one or a few countries, a decline in demand from those countries can have a major impact on the economy.
Overall, the benefits and costs of international trade depend on a variety of factors, including the specific industries involved, the level of competition, and the economic policies of the countries involved.
While international trade can provide opportunities for economic growth and development, it is important to consider and manage the potential risks and costs.
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a glass jar contain 1 red 3 green 2 blue and 4 yellow marbles.if single marble is chosen at random from the jar what is the probability that it is yellow or green?
Answers
The probability that a single marble chosen at random from the jar is yellow or green is 7/10, or 0.7.
The probability that a single marble chosen at random from the jar is yellow or green can be found by adding the probability of choosing a yellow marble to the probability of choosing a green marble.
There are a total of 1 + 3 + 2 + 4 = 10 marbles in the jar. The probability of choosing a yellow marble is 4/10 = 2/5, and the probability of choosing a green marble is 3/10. Therefore, the probability of choosing a yellow or green marble is:
P(yellow or green) = P(yellow) + P(green) = 4/10 + 3/10 = 7/10
So the probability that a single marble chosen at random from the jar is yellow or green is 7/10, or 0.7.
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please help me find the measure of the arc or angle indicate
Answers
Answer:
∠U = 65°
Step-by-step explanation:
You want the measure of external angle U formed by two tangents that intersect a circle creating major arc TV of 245°.
External angleThe measure of the external angle is half the difference of the two arcs of the circle that the secants (tangents) intercept.
The major arc is shown as 245°. The minor arc TV completes the circle, so is 360° -245°.
Half the difference is ...
(245° -(360°-245°))/2 = 245° -180° = 65°
Angle U is 65°.
__
Additional comment
You will notice the angle formed by the tangents is 180° less than the measure of the major arc. (It is also equal to the supplement of the minor arc.)
A tangent is a special case of a secant, where the two points of intersection with the circle merge to a single point. The relations applicable to secants also apply to tangents.
A cylindrical container closed at both ends has a radius of 7cm and height of 6cm what is the total surface area of the container and what is the volume of the container
Answers
The total surface area of the cylinder 572 cm²is and it's volume is 924cm³
What is a cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.
The total surface area of a cylinder is expressed as ;
SA = 2πr( r+h)
r is the radius and h is the height.
radius = 7cm
height = 6cm
SA = 2 × 3.14 × 7( 7+6)
= 44 × 13
= 572 cm²
The volume of a cylinder is expressed as
V = πr²h
= 3.14 × 7² × 6
= 154 × 6
= 924 cm²
Therefore the surface area and volume of the cylinder are 572cm² and 924cm²
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what would be the value of the autonomous expenditure multiplier if all taxes are autonomous
Answers
The value of the autonomous expenditure multiplier would be equal to 1 divided by (1 minus the tax multiplier).
The value of the autonomous expenditure multiplier would depend on the size of the tax multiplier.
The tax multiplier is the inverse of the marginal propensity to consume (MPC) from taxes, which is the portion of each dollar of taxes that households and businesses will spend.
If all taxes are autonomous, this means that taxes are not influenced by changes in income or other economic factors, and will remain constant.
In this case, the tax multiplier would be equal to the MPC from taxes.
The autonomous expenditure multiplier is calculated by dividing 1 by the marginal propensity to save (MPS), which is the portion of each dollar of income that households and businesses will save.
Since the MPC and MPS always add up to 1, we can use the tax multiplier to calculate the MPS from taxes as 1 minus the tax multiplier.
Therefore, the value of the autonomous expenditure multiplier would be equal to 1 divided by (1 minus the tax multiplier).
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a boat leaves port and follows a course of n77°e at 9 knots for 3 hr and 20 min. then, the boat changes to a new course ofs27°eat12knotsfor4hr. howfar is the boat from port?
Answers
If a boat leaves port and follows a course of n77°e at 9 knots for 3 hr and 20 min. then, the boat changes to a new course ofs27°east 12knots for 4hr then the boat is approximately 67.9 nautical miles from the port.
To solve the problem, we can use the law of cosines to find the distance from the boat to the port.
Let A be the position of the boat after the first leg of the trip and B be the position after the second leg. Let x be the distance from A to B. Then, we have:
cos(77°) = (distance from port to A) / x
cos(27°) = (distance from port to B) / x
We can solve for the distances from the port to A and B using the given course and speed information:
(distance from port to A) = 9 knots x 3.33 hours = 29.97 nautical miles
(distance from port to B) = 12 knots x 4 hours = 48 nautical miles
Substituting into the law of cosines, we get:
x^2 = (29.97)^2 + (48)^2 - 2(29.97)(48)cos(130°)
Solving for x gives:
x ≈ 67.9 nautical miles
Therefore, the boat is approximately 67.9 nautical miles from the port.
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Mathematics for the practical man explaining simply and quickly all the elements of algebra, geometry, trigonometry, logarithms, coördinate geometry, calculus
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"Mathematics for the Practical Man" is a book that aims to provide a simplified and quick explanation of various mathematical concepts such as algebra, geometry, trigonometry, logarithms, coordinate geometry, and calculus.
The book is targeted towards individuals who may not have a strong background in mathematics, but need to understand these concepts for practical purposes.
The book is divided into chapters that cover each topic in depth, providing clear explanations and examples for the reader to follow. The language used in the book is simple and easy to understand, without sacrificing the accuracy and rigour of the mathematical concepts being taught. Overall, "Mathematics for the Practical Man" is a useful resource for anyone who needs to quickly and easily learn or refresh their knowledge of key mathematical concepts.
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HELP PLEASE
{3x + y = 9
{y = 3x + 6
Topic: Solving Systems by Elimination
Answers
6x = 3
3/6 = 0.5 x
1.5+ 6 = y= 7.5
ANSWERS:
X = 0.5
Y=7.5
(ROTATE !!!!!!!) help plssss i’ll give a lot of points for being quick
Answers
Answer:
(a) - [tex]V_{tank}\approx 2010.6 \ yd^3[/tex]
(b) - [tex]Total= 1005 \ \text{fish}[/tex]
Step-by-step explanation:
Given the cylindrical fish tank with a diameter of 16 yards and a height of 10 yards. We are asked to answer the following.
(a) - How much water can the tank hold, in other words what is the tank's volume?
(b) - Given that a specific kind of fish requires 2 yd³ of water per fish, find the total amount of fish that can occupy the tank.
Part (a):
Given:
[tex]d=16 \ yd\\h=10 \ yd[/tex]
Find:
[tex]V_{tank}= \ ?? \ yd^3[/tex]
For part (a) the question is essentially asking what the volume of the tank is, the tank is a cylinder. We can use the following formula to find the volume of a cylinder.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Volume of a Cylinder:}}\\\\V=\pi r^2h\end{array}\right}[/tex]
(1) Find the radius of the tank given that the diameter is 10 yards
[tex]r=\frac{d}{2}\\\\ \Longrightarrow r=\frac{(16 \ yd)}{2} \\\\\therefore \boxed{r=8 \ yd}[/tex]
(2) - Compute the volume of the tank using the formula from above and the value of the radius we just found.
[tex]V_{tank}=\pi r^2h\\\\\Longrightarrow V_{tank}=\pi (8 \ yd)^2(10 \ yd)\\\\ \Longrightarrow V_{tank}=\pi (64 \ yd^2)(10 \ yd)\\\\\Longrightarrow V_{tank}=640\pi\\\\\therefore \boxed{\boxed{V_{tank}\approx 2010.6 \ yd^3}}[/tex]
Thus, the volume of the tank is found.
Part (b):
Given:
[tex]V_{tank}=2010.6 \ yd^3\\V_{1 \ fish}= 2 \ yd^3[/tex]
Find:
[tex]\text{Total}= \ ?? \ \text{fish}[/tex]
To find the total amount of fish that can fit in the tank, simply divide the total volume of the tank by the volume one fish requires.
[tex]Total=\frac{V_{tank}}{V_{1 \ fish}} \\\\\Longrightarrow Total=\frac{2010.6 \ yd^3}{2 \ yd^3}\\\\\therefore \boxed{\boxed{Total= 1005 \ fish}}[/tex]
Thus, the tank can hold 1005 fish.
You want to buy a new car. You can afford payments of $300 per month and can borrow the money at an interest rate of 3.8% compounded monthly for 5 years. Round appropriately. How much are you able to borrow? $ How much interest would you pay for the amount you are able to borrow?
Answers
You would pay approximately $1630.19 in interest for the amount you are able to borrow.
To calculate the amount you are able to borrow, we can use the formula for the present value of an annuity:
P = PMT ((1 - (1 + r)⁻ⁿ) / r)
Where:
P is the principal amount (the amount you are able to borrow)
PMT is the monthly payment you can afford ($300)
r is the monthly interest rate (3.8% divided by 100, then divided by 12)
n is the number of months (5 years multiplied by 12)
Let's calculate the amount you are able to borrow:
r = 3.8% / 100 / 12 = 0.0031667 (rounded to 7 decimal places)
n = 5 years x 12 = 60 months
P = $300 x ((1 - (1 + 0.0031667)⁻⁶⁰) / 0.0031667)
P ≈ $16369.81
Therefore, you are able to borrow approximately $16369.81.
To calculate the interest you would pay for the amount you are able to borrow, we can subtract the principal amount from the total amount paid over the 5-year period. The total amount paid can be calculated as:
Total Amount Paid = Monthly Payment x Number of Months
Total Amount Paid = $300 x 60 = $18,000
Interest Paid = Total Amount Paid - Principal Amount
Interest Paid = $18,000 - $16369.81 ≈ $1630.19
Therefore, you would pay approximately $1630.19 in interest for the amount you are able to borrow.
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Lashonda drove 495 miles in 9 hours.
At the same rate, how many miles would she drive in 13 hours?
Answers
Answer:
715 miles
Step-by-step explanation:
We Know
Lashonda drove 495 miles in 9 hours.
495 / 9 = 55 miles per hour
At the same rate, how many miles would she drive in 13 hours?
We Take
55 x 13 = 715 miles
So, she drives 715 miles in 13 hours.
[tex]\begin{array}{ccll} miles&hours\\ \cline{1-2} 495 & 9\\ m& 13 \end{array} \implies \cfrac{495}{m}~~=~~\cfrac{9}{13} \\\\\\ (495)(13)=9m\implies \cfrac{(495)(13)}{9}=m\implies 715=m[/tex]
The radius of a circle is
35
centimeters. Find the area of the circle. Use
22/7
as an approximation for π.
Answers
[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=35 \end{cases}\implies A=\pi 35^2\implies A=\cfrac{22}{7}\cdot 35^2\implies A=3850[/tex]
Probability that a random selected student is a senior or a student who drives to school?
Answers
65% is the probability that a randomly selected student is a senior or a student who drives to school.
First, let's calculate the probability of a student being a senior. We can do this by dividing the number of seniors by the total number of students:
Probability of being a senior = Number of seniors / Total number of students
Probability of being a senior = 25 / 100
Probability of being a senior = 0.25
Next, let's calculate the probability of a student driving to school. Again, we divide the number of students who drive by the total number of students:
Probability of driving to school = Number of students who drive / Total number of students
Probability of driving to school = (2 + 13 + 25) / 100
Probability of driving to school = 40 / 100
Probability of driving to school = 0.4
To find the probability of a student being a senior or driving to school (the union of these two events), we add their probabilities:
P(Senior U Drive to school) = P(Senior) + P(Drive to school)
P(Senior U Drive to school) = 0.25 + 0.4
P(Senior U Drive to school) = 0.65
Therefore, the probability that a randomly selected student is a senior or a student who drives to school is 0.65, or 65%.
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In past years, the proportion of engineering students at the local college who did not own a calculator was 0.15. Angelina believes the proportion of current population of engineering students who do not own a calculator is lower. She randomly selects 55 students and finds that 6 of them do not own a calculator. She uses a significance level of alpha equals 0.05 and calculates a p-value of 0.198. What null and alternative hypothesis did Angelina use for this test, and what conclusion can she make?
Answers
The hypotheses of the research is:
Null Hypothesis: H₀: p = 0.15
Alternative Hypothesis: Hₐ: p < 0.15
The conclusion is;
Angela fails to reject the null hypothesis because the p-value is greater than the significance value.
How to find the null and alternative hypothesis?Null and alternative hypotheses are basically methods used in statistical hypothesis testing. The null hypothesis of a test is one that always predicts no effect or no relationship existing between variables. Meanwhile, the alternative hypothesis states the research prediction of an effect or relationship.
We are told that the proportion of engineering students at the local college who did not own a calculator was 0.15.
Now, Angelina believes the proportion of current population of engineering students who do not own a calculator is lower.
Thus, the hypotheses is defined as:
Null Hypothesis: H₀: p = 0.15
Alternative Hypothesis: Hₐ: p < 0.15
Now, the p-value is greater than the significance value and as such we fail to reject the null hypothesis
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for a two-tailed test, if 2.36 is in the rejection region and the test statistic is -3.11, and the null hypothesis is true, do we have a correct decision? give an explanation for your answer.
Answers
If the test statistic is -3.11, it means that the observed data is 3.11 standard deviations below the mean of the null distribution.
Since 2.36 is in the rejection region, it means that the critical value for the test is greater than 2.36 in absolute value. This implies that the null hypothesis would be rejected if the test statistic is either less than the negative critical value or greater than the positive critical value.
However, since the test statistic of -3.11 is smaller than the negative critical value, we would fail to reject the null hypothesis. This means that we would conclude that there is not enough evidence to support the alternative hypothesis and we accept the null hypothesis. Therefore, we would have made an incorrect decision if we rejected the null hypothesis based on the given information.
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Three white balls and three black balls are distributed in two urns in such a way that each contain three balls. We say that the system is in state i, i=0,1,2,3, if the first urn contains i white balls. At each step, we draw one ball from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Letdenote the state of the system after the nth step. Explain whyis a Markov chain and calculate its transition probability matrix.
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The process described above satisfies the Markov property because the future state of the system only depends on the current state, and not on any previous states. The transition probability matrix is P =[tex]\left[\begin{array}{cccc}0&1&0&0\\1/2&0&1/2&0\\0&1/2&0&1/2\\0&0&1&0\end{array}\right][/tex]
In other words, given the current state, the probability distribution of the next state depends only on the current state and not on any previous history.
Let Xn denote the state of the system after the nth step, where Xn = i means that the first urn contains i white balls and 3-i black balls. Since each step involves drawing one ball from each urn and switching them, the number of white balls in the first urn can only change by one after each step. Thus, the only possible transitions are:
If Xn = 0, then the next state Xn+1 can only be 1, with probability 1, since there is only one white ball in the first urn.
If Xn = 1, then the next state Xn+1 can be either 0 or 2, each with probability 1/2, since there are two white balls in the first urn and each ball is equally likely to be drawn.
If Xn = 2, then the next state Xn+1 can be either 1 or 3, each with probability 1/2, since there are two black balls in the first urn and each ball is equally likely to be drawn.
If Xn = 3, then the next state Xn+1 can only be 2, with probability 1, since there is only one black ball in the first urn.
Therefore, the transition probability matrix is:
P =[tex]\left[\begin{array}{cccc}0&1&0&0\\1/2&0&1/2&0\\0&1/2&0&1/2\\0&0&1&0\end{array}\right][/tex]
where Pij is the probability of transitioning from state i to state j. For example, P12 = 1/2 means that the probability of transitioning from state 1 (one white ball in the first urn) to state 2 (two white balls in the first urn) is 1/2.
Correct Question :
Three white balls and three black balls are distributed in two urns in such a way that each contain three balls. We say that the system is in state i, i=0,1,2,3, if the first urn contains i white balls. At each step, we draw one ball from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xn denote the state of the system after the nth step. Explain why Xn = 0, 1, 2, ......... is a Markov chain and calculate its transition probability matrix.
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When plotting marginal and average cost curves, the cost curve always crosses the cost curve at its Select one: a. average fixed; marginal; minimum b. marginal; average variable; maximum c marginal; average total; minimum d. average variable; marginal; maximum
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The correct answer is c. marginal; average total; minimum. When plotting marginal and average cost curves, the marginal cost curve intersects the average total cost curve at its minimum point.
This is because the average total cost curve is U-shaped, with a downward-sloping portion at low levels of output and an upward-sloping portion at high levels of output. The marginal cost curve intersects the average total cost curve at the point where the upward-sloping portion of the average total cost curve starts, which is also the point where the average total cost curve is at its minimum. At this point, the marginal cost is equal to the average total cost.
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- The midpoint of CD is M(-1,7) and one endpoint of CD is D(4, 5). What are
the coordinates of C?
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Answer:
(-6,9)
Step-by-step explanation:
We can use the midpoint formula to find the coordinates of C. The midpoint formula states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is:
((x1 + x2)/2, (y1 + y2)/2)
In this case, we know that the midpoint of CD is M(-1, 7) and one endpoint of CD is D(4, 5). Let C = (x, y) be the coordinates of the other endpoint of CD. Then we can use the midpoint formula to set up two equations:
(x + 4)/2 = -1
(y + 5)/2 = 7
Solving for x and y, we get:
x + 4 = -2
y + 5 = 14
x = -6
y = 9
Therefore, the coordinates of C are (-6, 9).
a manufacturer of batteries would like to insure that their defective rate is less than 5%. in order to be sure that their batteries meet this quality control standard, the supervisor randomly samples 100 batteries and finds that 4 are defective. is there significant statistical evidence that the manufacturer is meeting their quality control standards?? find the p-value rounded to 4 decimal places.
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Since the p-value (0.1021) is greater than the significance level (0.05), we fail to reject the null hypothesis.
What is null hypothesis?The null hypothesis is a type of hypothesis that describes the population parameter and is used to examine the validity of experimental results.
To test whether the manufacturer's defective rate is less than 5%, we can use a one-tailed hypothesis test with a significance level of 0.05.
Let p be the true proportion of defective batteries in the population. The null hypothesis is that p >= 0.05, and the alternative hypothesis is that p < 0.05.
We can use the normal approximation to the binomial distribution, since n = 100 and p₀ = 0.05 > 10. The test statistic is:
z = (x - np₀) / √(np₀(1-p₀))
where x is the number of defective batteries in the sample, n is the sample size, and p₀ is the hypothesized proportion under the null hypothesis.
Plugging in the values, we get:
z = (4 - 100*0.05) / √(100*0.05*0.95) = -1.2649
The p-value for this test is the probability of getting a test statistic as extreme as -1.2649 or less, assuming the null hypothesis is true. From a standard normal distribution table, the probability of getting a z-score of -1.2649 or less is 0.1021.
Since the p-value (0.1021) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the manufacturer is not meeting their quality control standards.
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