The probability of getting a total of 8 when two dice are rolled is 0.139.
Probability is a number that expresses the likelihood or chance that a specific event will take place. Probabilities can be represented by proportions on a 0–1 scale.
A single die will have six sides with the numbers: 1, 2, 3, 4, 5, and 6. Each of these events is equally likely to occur if the dice are rolled fairly. So the probability of getting any side of the number is 1/6. Therefore, the probability of getting 1 in dice is 1/6, 2 is 1/6, and so on.
Therefore, the total possible outcomes are the multiplication of the total possible outcomes on dice 1 and dice 2, which is 36.
This possible outcome of rolling two dice is given by,
[tex]\left\{\begin{array}{ccccccc}(1, 1)&(1, 2)& (1, 3)&(1, 4)&(1, 5)&(1, 6)\\(2, 1)&(2, 2)&(2, 3)&(2, 4)&(2, 5)&(2, 6)\\(3, 1)&(3, 2)&(3, 3)&(3, 4)&(3, 5)&(3, 6)\\(4, 1)&(4, 2)&(4, 3)&(4, 4)&(4, 5)&(4, 6)\\(5, 1)&(5, 2)&(5, 3)&(5, 4)&(5, 5)&(5, 6)\\(6, 1)&(6, 2)&(6, 3)&(6, 4)&(6, 5)&(6, 6)\end{array}\right\}[/tex]
The probability of getting a total of 8 from both dice is given by, (2, 6) (3, 5) (4, 4) (5, 3) (6, 2). So the number of favorable outcomes is 5 and the total outcome is 36. The probability is P(getting a total of 8 from both dices)=5/36= 0.139.
The answer is 0.139.
The complete question is -
Consider rolling dice and getting a total of 8. Find the probability of two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places).
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Noelia has 144 role-playing cards. She and
her friends buy another set that costs $27,
and Noelia pays $9. They evenly split the
cost and the 72 cards in the set. How many
cards does Noelia have after she buys part
of the set with her friends?
Noelia has 216 cards after buying part of the set with her friends.
What is addition?Combining items and counting them as a single, large group is done through addition.
Given that, Noelia has 144 role-playing cards.
Now, she bought 72 cards more, therefore, the number of cards Noelia has is:
144 + 72
= 216
Hence, Noelia has 216 cards after buying part of the set with her friends.
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multiply 144 times 27 which is 3,888
3888
- 9
-----------
3,879 3,879
- 72
--------------
3,807
suppose i want to represent the following set of words using a phone lattice: {cattle, battle, cattles,battles}. what is the minimum number of states that i require?
⇒We can represent this phone lattice in two minimum number of ways and states to represent it.
What is phone lattice?
A state diagram, or directed network in which each node stands for a state of a system, is what is known as a phone lattice. Each edge of a phone lattice has exactly one letter. A word is represented by each route from the start node to the final/end node.
The minimum no. Of states in using a phone lattice to the given requirement is two.
We can represent this phone lattice in two minimum number of ways and states to represent it.
A dual lattice may be defined as the inclusion on the extents. We represent a lattice using a Hasse diagram of the given partial ordering on all the maximal rectangles, transitivity and reflexivity arcs that are omitted. Concepts in the given system are often known as elements of this lattice.
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Maleia is tracking her running training program. The table gives her 5K run time at the end of each month.
Month Time (minutes)
1 47
2 43
3 39
4 36
5 35
6 33
What is the equation for the line of best fit where x represents the month and y represents the time?
y = −2.78x + 33.6
y = −2.78x + 48.5
y = 2.78x + 33.6
y = 2.78x + 48.5
The required regression equation is y = -2.78x + 48.5 for the line of best fit where x represents the month and y represents the time.
The table is given in the question.
As per the given table, the required solution would be as:
Let x represents the month and y represents the time
[tex]\bar{x}[/tex] = (1+2+3+4+5+6)/6 = 21/6 = 3.5
[tex]\bar{y}[/tex] = (47+43+39+36+35+33)/6 = 233/6 = 38.83
Sum of x = 21
Sum of y = 233
Mean x = 3.5
Mean y = 38.8333
Sum of squares (SSX) = 17.5
Sum of products (SP) = -48.5
Regression Equation = y = bx + a
b = SP/SSX = -48.5/17.5 = -2.77143
a = MY - bMX = 38.83 - (-2.77×3.5) = 48.53333
y = -2.78x + 48.5
Thus, the required regression equation is y = -2.78x + 48.5 for the line of best fit.
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Answer:
y = -2.78x + 48.5
Step-by-step explanation:
I just took the test like 2 seconds ago...
why should we use non-parametric tests? choose the one false answer. group of answer choices because they are more powerful than parametric tests because when you have quantitative data but assumptions of normality are not met because when you are only using ordered data because when there is no linearity
Option B. Because when you have quantitative data, but assumptions of normality are not met. This is because, unlike parametric tests, non-parametric tests do not make assumptions about the data's underlying distribution.
Why should we use non-parametric tests? Option B. Because when you have quantitative data, but assumptions of normality are not met.Non-parametric tests are often used when dealing with data that is not normally distributed, as they allow for a more accurate analysis of such data. They can also be used when a linearity of the data cannot be assumed and when dealing with ordinal data. Non-parametric tests are more powerful than parametric tests, which makes them a good choice when a more precise analysis is needed.
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dr. chidi anagonye studied how self-esteem (high versus low) and success on a school project (passed/succeeded or failed) influences whether students attribute the cause of the outcome to themselves or others. high scores on the dependent variable mean they attribute the outcome to themselves and low scores mean they attributed the outcome to others. below are his results. look at the graph below and select the statement that is most true about the graph:
As per dr. Chidi Anagonye, self esteem and success on school project results in low distinctiveness.
What is all about the attribution theory?The focus of attribution theory is on how people make sense of events and how this influences their perceptions and actions. Heider (1958) was the first to suggest a psychological theory of attribution, but Wener and his colleagues (e.g., Jones et al., 1972; Wener, 1974, 1986) created a theoretical framework that has grown to be a significant research paradigm in social psychology. Attribution theory assumes that people try to figure out why people do what they do, i.e., attribute causes to behavior. If someone is trying to figure out why someone else did something, they could assign one or many reasons to that action. An attribution is based on a three-stage process: (1) the person must notice or watch the activity, (2) the person must think that the behavior was done purposefully.
Education, legislation, clinical psychology, and the field of mental health have all seen extensive use of Wener's thesis. Achievement and one's self-concept are closely related. Causal attributions control how we feel about success and failure, according to Wener (1980). For example, one is unlikely to feel satisfaction in achievement or competence while obtaining a 'A' from a professor who only delivers that grade, or when defeating a tennis opponent who always loses... An 'A' from a teacher who gives few high grades, on the other hand, or a victory over a highly rated tennis player after a lot of practice has a big impact. Higher self-esteem students and students who perform well academically have a tendency to credit success to internal, stable, uncontrolled causes.
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Write an inequality that represents the graph below. Please help
Answer: x≥3
Step-by-step explanation:
3) you roll a die 48 times with the following results. number 1 2 3 4 5 6 frequency 2 14 2 12 3 15 use a significance level of 0.05 to test the claim that the die is fair. use the p-value method. (a) set up the null hypothesis and alternative hypothesis and indicate the claim. (b) calculate the test statistic. be sure to set up the equation. round to three decimal places.
The claim to be indicated is that there is enough evidence to reject the null hypothesis and the test statistic would be 21.75
What do you understand by Hypothesis testing?A type of statistical inference called hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution. The parameter or distribution is initially assumed in a preliminary manner. The null hypothesis is also known as H0, because it is the default assumption. Then, the opposite of what the null hypothesis claims is characterized as an alternative hypothesis (designated Ha). Using sample data, the hypothesis-testing technique determines whether or not H0 may be rejected. If H0 is rejected, the statistical inference is that the alternative hypothesis Ha is correct.
How to solve?
If the die is fair, the probability of getting any of the six numbers is equal (1/6).
The test statistic (TS) is given as:
TS=∑(Oi−Ei)2Ei∼χ2n−1
TS=(4−8)^2/8+(13−8)^2/8+…(2−8)^2/8
TS=21.75
In conclusion, the die is unfair.
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Yesterday, Ralph took a math test and a history test. The sum of his scores was 170. He scored
10 points higher on his math test than on his history test. What score did Ralph receive on
his math and history tests?
Answer:ralph got an 90 on his math test and a 80 on his history test
Step-by-step explanation:
so i divided 170 and that = to 85 so i took the two 5 from the two 80 and added it to the 80 for math
8 baskets ?
16 movies = ————
?
How many movies will fit into 24
baskets?
Answer:
48 movies
Step-by-step explanation:
8/16=1/2
24/48=1/2
There are two buildings beside each other that are 47 feet and 31 feet high. The buildings are 12 feet apart. What is the distance between the rooftops of the buildings?.
By using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.
What is the Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
So, draw a figure of the 2 buildings as follows:
(Refer to the image attached below)
Now, we know that we can get the distance between the rooftops using the Pythagorean theorem.
Pythagorean theorem: c² = a² + b²
Now, insert the values and calculate as follows:
c² = a² + b²
c² = 12² + 16²
c² = 144 + 256
c² = 400
c = √400
c = 20ft
Therefore, by using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.
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OM
C2022
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Question 14
II Pause
Use this situation to answer the problem
A river in one part of the Rocky Mountains has a flow rate of 250 cubic meters of
water per second. The flow of the water can be modeled mathematically with the
function, w(t) = 250t, where w(t) represents the volume of the water in cubic
meters, at time t, in seconds.
zoom
Iluminate Education, Inc.
Type here to search
ii
C
Find the number of cubic feet of water that have flowed down the river in 5 minutes
58°F Clear
2648625 cubic feet of water that have flowed down the river in 5 minutes
How to find the number of cubic feet of water that have flowed down the river in 5 minutes?Given that:
The flow of the water can be modeled mathematically with the
function, w(t) = 250t, where w(t) represents the volume of the water in cubic meters, at time t, in seconds.
In order to find the number of cubic feet of water that have flowed down the river in 5 minutes. We'll first convert the time t = 5 minutes into seconds and then substitute it into the function. That is:
t = 5 minutes = 5 × 60 = 300 seconds
w(t) = 250t
w(300) = 250 × 300
w(300) = 75000 cubic meters
To convert to cubic feet multiply by 35.315:
w(300) = 75000 × 35.315 = 2648625 cubic feet
Therefore, the number of cubic feet of water that have flowed down the river in 5 minutes is 2648625 cubic feet
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the combined average weight of an okapi and a llama is 450450450 kilograms. the average weight of 333 llamas is 190190190 kilograms more than the average weight of one okapi. on average, how much does an okapi weigh, and how much does a llama weigh? on average, an okapi weighs kilograms and a llama weighs kilograms.
Answer:
Okapi weighs 290, and llama weighs 160.
jogger runs around a circular track of radius 70 ft. let (x,y) be her coordinates, where the origin is the center of the track. when the jogger's coordinates are (42, 56), her x-coordinate is changing at a rate of 18 ft/s. find dy/dt.
The derivative dy/dt when the x coordinate's rate of change 18 feet is 13.5 feet.
Given,
The radius of the circular track in which the jogger runs = 70 feet
The coordinates of the jogger = (42, 56)
The rate of change in x coordinate = 18 feet/sec
Let (x,y) be the coordinates
We have to find dy/dt;
Then we know x,y satisfies the equation of the circle as
x² + y² = 70²
Let us differentiate this implicit function with respect to t
2x dx/dt + 2y dy/dt = 0
At this point, dx/dt 18 and x = 42. y = 56
Substitute to have
2 × 42 × 18 + 2 × 56 dy/dt = 0
1512 + 112 dy/dt = 0
dy/dt = 1512/112
dy/dt = 13.5 feet
Therefore,
The derivative dy/dt here is 13.5 feet
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help guys this was from a while back so i don’t remember
Answer: x = 3
Step-by-step explanation: both expressions are equal to each other because the angles are opposite of each other, so you would set the expressions equal to each other and solve from there.
set equations = to each other: 6x - 7 = 4x - 1
add 7 to the other side: 6x = 4x + 6
subtract 4x to the other side: 2x = 6
divide both sides by 2: x = 3
Which is the equation of the line, in point-slope form, with a slope of 5 that passes through (1, −3)?
A. y = 5x − 3
B. y = −5x + 1
C. y + 3 = 5(x − 1)
D. y − 3 = 5(x + 1)
Answer: The correct answer is C. y + 3 = 5(x − 1)
Step-by-step explanation:
Change the equation into slope-intercept form
y + 3 = 5(x − 1)
y = 5x - 8
Using the slope-intercept form of y = mx + b, m = slope, and b = the y-intercept.
Therefore, y = 5x - 8 has a slope of 5 and a y-intercept of -8
When we graph the slope from y = -8, it passes through (1, -3)
Find the 4th term in the expansion of (a+b)^{10} in simplest form.
a researcher designs a study where participants are randomly assigned to one of the two groups--one is run at night and one is run during the day. each participant in each group is then measured twice, under two different conditions, red and blue. this is best described as a(n) design.
The correct answer is Independent groups design.
Given that,
Participants in a study are randomly allocated to one of two groups; one group is run at night, while the other is run during the day. Then, each member of each group is measured twice under the red and blue conditions, respectively.
Independent groups design.
Independent measures style, conjointly called between groups is an experimental style wherever completely different participants are employed in every condition of the experimental variable. This suggests that every condition of the experiment includes a distinct cluster of participants.
Therefore, the correct answer is Independent groups design.
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This is a Linear equation.
Based on the slope (-8) of the linear equation, the amount Austin pays each week, which is $8.
What is a Linear Equation?A linear equation can be defined as y = mx + b, which shows the relationship between variable x and variable y, where we have the following:
Slope value = m = change in y / change in x [this is also the unit rate]
Y-intercept of initial value = b.
Given that the table represents a linear equation, find the slope or unit rate of the linear equation, which represents the amount Austin pays every week.
Slope (m) = change in L / change in t
Using two pairs of values from the table, (2, 24) and (4, 8):
Slope (m) = change in L / change in t = (24 - 8) / (2 - 4) = 16/-2
Slope (m) = -8
This implies that, Austin pays $8 every week.
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A researcher is concerned about the level of knowledge possessed by university students regarding United States history. Students completed a high school senior level standardized U.S. history exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. Compute the appropriate test for the data provided below.
Education Business/Management Behavioral/Social Science Fine Arts
62 72 42 80
81 49 52 57
75 63 31 87
58 68 80 64
67 39 22 28
48 79 71 29
26 40 68 62
36 15 76 45
Source SS df MS F
Between 63.25 3 21.0833333333 .04
Within 12298.25 28 439.2232143 Total 12361.5 31 What is your computed answer? F = .04 (3,28), not significant
What would be the null hypothesis in this study? There will be no difference in history test scores between students with different academic major.
What would be the alternate hypothesis? There will be a difference somewhere in history scores between the four groups with different academic major.
What probability level did you choose and why? p = .05 There is little risk involved if either a Type I or a Type II major is made.
What were your degrees of freedom? 3, 28
Is there a significant difference between the four testing conditions? No significant differences were found between the four groups in terms of performance on a U.S. history exam.
Interpret your answer. Students regardless of academic major performed equally (in this case poorly) on a high school senior standardized U.S. history exam.
If you have made an error, would it be a Type I or a Type II error? Explain your answer. If I have made an error, it would be a Type II error. There really is a difference in history knowledge between academic major but somehow I failed to demonstrate that with this study.
On solving the provided question, significant difference between the four testing conditions is α = 0.10
What does the term "alternative hypothesis" mean?An alternative hypothesis is one in which the researchers predict a difference (or an effect) between two or more variables, indicating that the observed pattern of the data is not the result of chance.
Null hypothesis: : μ1 ≥ μ2, There is no significant difference in history test scores between students with different academic major
Alternative Hypothesis: Ha : μ1 < μ2. Exam outcomes in history are substantially more varied among students with different academic specialties.
Determine the significance level. α = 0.10
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Which best describes the location of A', the image of A
after a dilation by a factor of 1/2 with center at C?
c²
A' will be closer to A than to C
O A' will be half way between C and A
O A' will be closer to C than to A
C will be the midpoint of the line
connecting A and A'
'A
Answer:
1/c2
Step-by-step explanation:
college officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. how many randomly selected students must be surveyed in order to be 9898% confident that the sample percentage has a margin of error of 1.51.5 percentage points? (a) assume that there is no available information that could be used as an estimate of p^p^.
3206 students are randomly chosen since there is no knowledge of the sample fraction.
Explain the term Margin of Error?When determining the confidence interval, the margin of error is crucial. The critical z value,the sample size, and proportion can all be used to determine the margin of error in the case of proportion.The following can be used to represent the formula for calculating the margin of error for a single proportion:
ME = z√p(1 - p)/n
In order to be 91% certain that the sampling percentage seems to have an error margin of 1.5 percentage points, the number of randomly chosen students that must be surveyed is equal to;
0.015 = 1.6954×√0.5(1 - 0.5)/n
0.015/1.6954 = √0.5(0.5)/n
On further solving,
n = 3205.128
n ≈ 3206
As a result, 3206 students are randomly chosen since there is no knowledge of the sample fraction.
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The correct question is-
College officials want to estimate the percentage of students who carry a gun, knife, or other such weapons. How many randomly selected students must be surveyed in order to be 91% confident that the sample percentage has a margin of error of 1.5 percentage points?
a) Assume that there is no available information that could be used as an estimate of p.
If X be a random variable taking values x1,x2,x3,….,x???? with probabilities P1,P2,P3,…..P????, respectively. Then, Var (x) is equal to …….. .
Using the probabilities the variance of x represented by Var(x) is equal to var(X) = E(X²) – [E(X)]² , where E(x) represents the expected value of x.
Given the probabilities of the random variable given by x₁ , x₂ , x₃ ,... has the probabilities of P₁ , P₂ , P₃ ...
We know that Variance is given by the formula:
[tex]Var(x) = \sigma^2=\sum_{i=1} ^n (x_i-\mu)^2px_i)\\\\=\sum_{i=1} ^n(x_i^2-2x_i+\mu^2)\\\\=E(x^2)-[E(x^2)][/tex]
We know that expected value is denoted by E(x) .
Hence the variance is denoted by var(X) = E(X²) – [E(X)]² .
In probability theory and statistics, variance is the predicted squared deviation of a random variable from its population mean or sample mean.
The scattering, or how far apart from the mean a bunch of data are from one another, is measured by variance. A few ideas that involve variance are descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.
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I don’t understand need help asap please. Complete the square to determine the minimum or maximum value of the function defined by the expression a^2-2a-8 show work
Answer:
(a-1)^2-9
Step-by-step explanation:
First you divide the coefficient of a by 2, which is 1. Now, do this: [tex](a-1)^2-8[/tex] where the -1 is half the coefficient of a. What this does is get the first two terms: a^2 and 2a, but we have an extra + 1(expanding this out gives [tex]a^2 -2a + 1[/tex]. So we have to subtract 1 to cancel it out. This gives [tex](a-1)^2-9[/tex], because -8-1=9. We can check this by expanding it out, and seeing if it equals our previous equation. Expanding this out gives [tex]a^2-2a+1-9[/tex], which is equal to our originial equation.
a survey, 29 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $35.9 and standard deviation of $9.5. estimate how much a typical parent would spend on their child's birthday gift (use a 98% confidence level). give your answers to 3 decimal places. express your answer in the format of ¯ x ± e. $ ± $
Using test statistic z, Typical parent would spend on their child's birthday gift is between $30.927 and $40.873.
In the given question we have to estimate how much a typical parent would spend on their child's birthday gift using a 98% confidence level.
Given in the question
Number of sample (n) = 29
Sample mean (X) = 35.9
Sample standard deviation (S) = 9.5
We need to calculate 98% confidence interval which can be calculated as
CI = X± [tex]t_{\alpha/2}[/tex] * S/√n
Here confidence level CI = 0.98
Level of significance (\alpha) = 1-0.98=0.02
α/2 = 0.01
Degree of freedom (df) = n-1 = 29-1 = 28
from t table we found [tex]t_{\alpha/2}[/tex] = 2.821
So 98% confidence interval is
CI = 35.9 ± 2.821* 9.5/√29
CI = 35.9± 2.821* 9.5/5.39
CI = 35.9± 2.821*1.763
CI = 35.9± 4.973
CI = (35.9-4.973, 35.9+4.973)
CI = (30.927, 40.873)
30.927 < μ < 40.873
So, Typical parent would spend on their child's birthday gift is between $30.927 and $40.873.
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a farmer needs to enclose three sides of a garden with a fence (the fourth side is a river). the farmer has 47 meters of fence and wants the garden to have an area of 266 sq-meters. what should the dimensions of the garden be?
The dimensions of the garden would be length = 28 meters and width = 9.5 meters
A database of research funds called Dimensions connects funding to articles, clinical trials, and patents as well as other outcomes. Dimensions is a division of the technology firm Digital Science, which has its global headquarters in London, United Kingdom.
Let the width be = w
Let the length be = L
enclose three side ( 2w+L) = 47 meter
L = 47-2w
Area of field = w*L
Area = w(47 - 2w)
266 = 47w - 2w²
2w² - 47w + 266 = 0
Solving this, we get
w = 14 or w = 9.5
The width should be less than the length so w = 9.5
Length = 47 - 2(9.5)
= 47 - 19
= 28 meters.
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PLEASE HELP!!!! HURRY!!!!
I think it might be all them but the third one, if I'm wrong sorry.
Determine the value of "z" in the equation
z + (14 - 5i) = 9 + 2i
Answer:
z = − 5 + 7i
Step-by-step explanation:
z + 14 - 5i = 9 + 2i
Subtract 14 from both sides.
z - 5i = 9 + 2i -14
Subtract 14 from 9 to get -5.
z - 5i = -5 +2i
Add 5i to both sides.
z = -5 + 2i + 5i
Combine real and imaginary parts.
z = -5 + (2+5)i
Add 2 to 5.
z = -5 + 7i
Hope this helps!
Answer:
7i - 5
Step-by-step explanation:
z + (14 - 5i) = 9 + 2i
=> z + 14 - 5i = 9 + 2i
=> z = 9 + 2i + 5i - 14
=> z = 7i - 5
hello everyone one last time, I just want to say I've been here before and thank you all for support :3 and to finish out with a question...what is the liklihood of pulling a red marble out of a bag of 8 blue marbles and 3 red marbles.
Answer: 27.3 %
Step-by-step explanation:
There are 8 blue and 3 red marbles in the bad so total is 11 marbles
We just need to take 3 divided by 11, then timed 100 and will get the percent of 27.27, or I round up to 27.3%
Is this function linear or nonlinear? y=1x responses linear linear nonlinear
Answer: Nonlinear.
Step-by-step explanation:
the perpendicular bisector of side AB of triangle ABC intersects side AB at point D and BC at point E. If angle CAB = 82 degrees and angle C = 68 degrees, what is angle CAE
After finding the value of the angle CAE will be equal to 22°.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the information provided in the question,
The perpendicular bisector of side AB of ABC intersects side AB at point D and BC at point E in the ABC equation. Also, m∠CAB = 82° and m∠C = 68°.
Join A and E.
In Δ ABC
∠A+∠B+∠C = 180° (Angle sum property of triangle.)
82°+∠B+68° = 180°
∠B = 180°-150°
∠B =30°
In Δ ADE and Δ BDE
AD=B D(DE shown is a perpendicular bisector.)
∠ADE =∠BDE = 90°
DE is common.
Δ ADE ≅ Δ EDB (By using the property SAS)
∠DEB=∠D A E [By using the property CPCT] (1)
In Δ DBE
∠EDB + ∠DBE+∠BED = 180°
90° +30°+∠BED = 180°
∠BED = 180°-120°
∠BED = 60°
So, ∠BAE=∠BED=60° (By using equation 1)
∠CAE=∠CAB - ∠BAE
∠CAE = 82°-60°
∠CAE = 22°.
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