Kevin has an equal number of dimes, nickel and quarters in his piggy bank. He randomly picks a coin, replaces it, and picks another coin. What is the probability that the sum of the two coins is at least 30cents?
Answers
Answer:
5/9
Step-by-step explanation:
Related Questions
If a boat depreciates in value according to the simple interest formula y=20000(.92)^2 find the rate of decay write a percentage
Answers
Answer:
Y=16928
Step-by-step explanation:
A student wants to study the ages of women who apply for marriage licenses in his county. He selects a random sample of 94 marriage licenses issued in the last year in the county and makes a 95% confidence interval for the mean age at which women marry. The 95% confidence interval is (23.6, 27.3).Interpret the 95% confidence interval calculated by the student.
Answers
Answer:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
For this case the confidence interval obtained is: (23.6 ; 27.3)
And the best interpretation would be:
We have 95% of confidence that the true mean os ages of women who apply for marriage licenses in his county is between 23.6 and 27.3
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n=94 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
For this case the confidence interval obtained is: (23.6 ; 27.3)
And the best interpretation would be:
We have 95% of confidence that the true mean os ages of women who apply for marriage licenses in his county is between 23.6 and 27.3
mags wants to know what is the hottest hairstyle trend is in her town. Which is the best group to survey
A.Get a list of salons in her town and use a deck of cards to pick 5 of them to visit. Survey all hairstylists that work in each salon.
B.Get a list of salons in her town and circle the 5 salons that are close to her house. Survey all the hairstylists that work at each salon
C.Go to all the salons where Luna and her friends go. Survey all the hair stylists that work at each salon
D. Ask her clients that are celebrities which salons they go to. Survey all the hair stylists that work at each salon
Answers
Answer: A
Step-by-step explanation:
The best group to survey is option A. A.Get a list of salons in her town and use a deck of cards to pick 5 of them to visit. Survey all hairstylists that work in each salon.
What is the survey?Surveys represent the list of questions that should be focused on for extracting particular data from the people. It could be conducted via the phone, mail, internet, malls, etc.
Since mags want to know the hottest hairstyle trend so here he should get the list of towns and then use the deck of cards so that she should pick 5 for visiting them. Therefore, the correct option is a.
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What is 3+3×3-3+3 equal to
Answers
Answer:
12
Step-by-step explanation:
Use pemdas. You do multiplication first.
3×3=9
3+9-3+3
Now add
3+9=12
Subtract:
12-3=9
Add:
9+3=12
Answer:
Your answer should be 18
Step-by-step explanation:
3 + 3 = 6
6 × 3 = 18
18 - 3 = 15
15 + 3 = 18
In a histogram, are the lengths of the rectangles proportional to the width of the bars?
Answers
Answer:
No
Step-by-step explanation:
In different scenarios, the data will be different. However, sometimes, it's impossible to draw a histogram with equal widths, so in order to maintain clarity and fairness, the area of the bars should actually be proportional to the frequency, which is usually the y-axis of the graph or height of the bars.
Hope this helps!
Answer:
No
Step-by-step explanation:
Length is the frequency density which is obtained by:
Frequency/width
Height is not proportional to width.
Frequency is proportional to the area of the rectangle
summarize the difference between theoretical and experimental probability
Answers
Answer:
Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out
Step-by-step explanation:
The average number of shirts sold in the beach shop was 285 on Saturday in the
summer. As the temperature went lower, the average number of shirts decreased to 114
every Saturday. What was the percentage decrease of in the average number of shirts
sold in the shop?
Answers
Answer:
Decreased by 60%
Step-by-step explanation:
First take the difference to the original amount to the new amount to find the change. 285 - 114 = 171
171/285 = .6
Multiply that by 100 to get it's percent.
The amount of shirts sold decreased by 60%
Final answer:
The percentage decrease in the average number of shirts sold in the shop from 285 to 114 shirts is 60%.
Explanation:
The percentage decrease in the average number of shirts sold at the beach shop can be calculated using the following formula: Percentage decrease = ((Original Average - New Average) / Original Average) × 100. The original average is 285 shirts, and the new average is 114 shirts after the temperature decrease.
So, the calculation would be: ((285 - 114) / 285) × 100 = (171 / 285) × 100 = 0.6 × 100 = 60%.
Therefore, the percentage decrease in the average number of shirts sold in the shop is 60%.
a soccer ball is kicked toward the goal
Answers
Answer:yes
Step-by-step explanation:
The product of two consecutive odd integers is 1 less than twice their sum. Find the integers.
Answers
Two consecutive odd integers are [tex]2k+1[/tex] and [tex]2k+3[/tex], for some integer [tex]k[/tex].
Their product is [tex](2k+1)(2k+3)=4k^2+8k+3[/tex].
Twice their sum is [tex]2(2k+1+2k+3)=2(4k+4)=8k+8[/tex]
Since the product is 1 less than twice the sum, we have
[tex]\underbrace{4k^2+8k+3}_{\text{the product}}=\underbrace{8k+8}_{\text{twice the sum}}-1[/tex]
So, we have
[tex]4k^2-4=0 \iff 4k^2=4 \iff k^2=1 \iff k=\pm 1[/tex]
If [tex]k=1[/tex], the integers are 3 and 5
If [tex]k=-1[/tex], the integers are -1 and 1.
In both cases, in fact, we have:
3*5 = 15, which is one less than 2(3+5)=2*8=16(-1)*1=-1, which is one less than 2(-1+1)=0A consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level. They plan to test the hypothesis using a significance level of 0.05 and a sample size of n = 100 cars. It is believed that the population standard deviation is 3 mpg. Based upon this information, if the "true" population mean is 32.0 mpg, what is the probability that the test will lead the consumer group to "accept" the claimed mileage for this car? Question 36 options: About 0.9545 Approximately 0.0455 About 0.45 None of the above
Answers
Answer:
Probability that the test will lead the consumer group to "accept" the claimed mileage for this car is 0.00043.
Step-by-step explanation:
We are given that a consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level.
It is believed that the population standard deviation is 3 mpg. Based upon this information, the "true" population mean is 32.0 mpg.
Let [tex]\bar X[/tex] = sample mean highway miles per gallon
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = true population mean = 32.0 mpg
[tex]\sigma[/tex] = population standard deviation = 3 mpg
n = sample of cars = 100
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that a mean highway miles per gallon of at least 33 actually meets this level is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 33)
P([tex]\bar X[/tex] [tex]\geq[/tex] 33) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{33-32}{\frac{3}{\sqrt{100} } }[/tex] ) = P(Z [tex]\geq[/tex] 3.33) = 1 - P(Z < 3.33)
= 1 - 0.99957 = 0.00043
The above probability is calculated by looking at the value of x = 3.33 in the z table which has an area of 0.7673.
Therefore, the probability that the test will lead the consumer group to "accept" the claimed mileage for this car is 0.00043.
A deck of cards contains 52 cards.two decks are put together and divided amount eight players.how many cards does each person get
Answers
Answer:
each person gets 13 cards
Step-by-step explanation:
if each deck contains 52 cards and two of them are put together then it would be 52x2=104 divided by 8=13
When two decks of 52 cards each are combined and divided among eight players, each player receives 13 cards.
If two decks of 52 cards are combined, there would be a total of 104 cards (52 cards per deck × 2 decks). To find out how many cards each person gets when these are divided among eight players, we divide the total number of cards by the number of players:
Calculate the total number of cards: 52 cards/deck imes 2 decks = 104 cards.
Divide this number by the number of players: 104 cards / 8 players = 13 cards/player.
So, each person would receive 13 cards.
Suppose that a hypothesis test is conducted. 12 out of 100 subjects have the necessary qualities. The null hypothesis is that the proportion of the subjects who have the necessary qualities is equal to 0.2, while the alternative hypothesis is that this proportion is less than 0.2. The p-value is 0.023. Using a 5% significance level, state the conclusion to the hypothesis test in context. A : The p-value is less than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2. B : The p-value is less than the significance level, so we do not reject the null hypothesis. We cannot conclude anything about the proportion of the subjects who have the necessary qualities. C : The p-value is less than the significance level, so we do not reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is equal to 0.2. D : The p-value is more than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2. E : The p-value is more than the significance level, so we do not reject the null hypothesis. We cannot conclude anything about the proportion of the subjects who have the necessary qualities.
Answers
Answer:
Option A
The p-value is less than the significance level of 0.05 chosen and so we reject the null hypothesis H0 and can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.
Step-by-step explanation:
Normally, in hypothesis testing, the level of statistical significance is often expressed as the so-called p-value. We use p-values to make conclusions in significance testing. More specifically, we compare the p-value to a significance level "α" to make conclusions about our hypotheses.
If the p-value is lower than the significance level we chose, then we reject the null hypotheses H0 in favor of the alternative hypothesis Ha. However, if the p-value is greater than or equal to the significance level, then we fail to reject the null hypothesis H0
though this doesn't mean we accept H0 automatically.
Now, applying this to our question;
The p-value is 0.023 while the significance level is 0.05.
Thus,p-value is less than the significance level of 0.05 chosen and so we reject the null hypothesis H0 and can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.
The only option that is correct is option A.
Answer: A: The p-value is less than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.
Step-by-step explanation:
Here, p value = 0.023
significance level = 0.05
As p value < 0.05
Lauren simplified the expression (m Superscript negative 7 Baseline) Superscript negative 5 as shown. (m Superscript negative 7 Baseline) Superscript negative 5 = m Superscript negative 7 + (negative 5) Baseline = m Superscript negative 12 Baseline = StartFraction 1 Over m Superscript 12 Baseline EndFraction Which statement explains Lauren’s error? She should have subtracted the exponents instead of adding them. She should have multiplied the exponents instead of adding them. She should have found –2, not negative 12, as the exponent when she added. She should have written m Superscript negative 12 as m Superscript 12.
Answers
Answer:
She should have multiplied the exponents instead of adding them.
Step-by-step explanation:
Lauren simplified the expression (m Superscript negative 7 Baseline) Superscript negative 5 as shown.
(m⁻⁷)⁻⁵(m Superscript negative 7 Baseline) Superscript negative 5 = m Superscript negative 7 + (negative 5) Baseline = m Superscript negative 12 Baseline = StartFraction 1 Over m Superscript 12 Baseline EndFraction
(m⁻⁷)⁻⁵ = m⁻⁷⁺⁽⁻⁵⁾ = m⁻¹² = 1/m¹²Correct solution:
(nᵃ)ᵇ = nᵃᵇ required property, power of the power is the product of the powers(m⁻⁷)⁻⁵ = m⁽⁻⁷⁾⁽⁻⁵⁾ = m³⁵Correct answer option describing the error made:
She should have multiplied the exponents instead of adding them.
Answer:
B
Step-by-step explanation:
Tom swims a 1/2 mile every 1/4 hour. How far will he swim in one hour?
Answers
Answer:
2 mlies per hour
Step-by-step explanation:
She miles 1/2 mile every 15 minutes or 1/4 hours so
1/2*4=2 miles per hour
Answer:
2 miles
Step-by-step explanation:
if he swims 1/2 a mile in a 1/4 of an hour (15 minutes) then you will divide an hour by 4 to see how many times he swam. you should get 4 1/4 hours and then you will multiply 1/2 by 4.
in a nut shell you multiply 1/2 by 4 because he swam over the time of an hour.
Find the smallest perimeter and the dimensions for a rectangle with an area of 36 in squared. The smallest perimeter for a rectangle with an area of 36 in squared is nothing in. (Simplify your answer.) The dimensions of this rectangle are nothing in. (Simplify your answers. Use a comma to separate answers.)
Answers
Final answer:
The smallest perimeter for a rectangle with an area of 36 square inches is 24 inches, and the dimensions that achieve this are those of a square, specifically 6 inches by 6 inches.
Explanation:
The smallest perimeter of a rectangle with an area of 36 square inches is achieved when the rectangle is a square because the sides are equal, and a square minimizes the perimeter for a given area. The formula for the area of a square is area = side², so if we have an area of 36 square inches, the side length of the square is √36, which equals 6 inches. Using this side length, we can calculate the perimeter of the square, which is perimeter = 4 × side, giving us a perimeter of 6 inches × 4, which is 24 inches.
The smallest perimeter we can have is 24 inches, and the dimensions of the rectangle (in this case, a square) that give us this smallest perimeter are 6 inches by 6 inches.
The expression 5(2)^t Gives the number of leaves in a plant as a function of the number of weeks since it was planted. What does gives the number of leaves in a plant as a function of the number of weeks since it was planted. What does 2 Represent in this expression
Answers
Answer:
2 is the scale factor
100% increase/growth
Step-by-step explanation:
y = a × (b^t)
b is scale factor
b = 2 means 200% of tte previous value
100% growth
Answer:
its c The number of leaves is multiplied by 2 each week.
Step-by-step explanation:
because i just did it
Find B
............
Answers
Given:
In ΔABC, AB = 5 unit, BC = 2 unit and ∠C = 90°
To find the The value of ∠B.
Formula
By Trigonometric Ratio we know,
[tex]cos \ \theta=\frac{adj}{hyp}[/tex]
Let us take ∠B = θ
With respect to θ, BC is the adjacent side and AB is the hypotenuse.
So,
[tex]cos \ \theta=\frac{BC}{AB}[/tex]
[tex]cos \ B=\frac{2}{5}[/tex]
[tex]B=cos^{-1} (\frac{2}{5} )[/tex]
[tex]B = 66.42^{\circ}[/tex]
Hence, the value of ∠B is 66.42°.
hi what is 9times 30 divided by 9
Answers
Answer:
30
Step-by-step explanation:
9x30= 270
270/9= 30
The result of 9 times 30 divided by 9 is 30.
Evaluating a mathematical expression
To evaluate an expression in mathematics, means to find the value of the final answer after performing suitable arithmetic manipulations.
The operations required could be any combination involving addition, subtraction, multiplication, division etc.
From the information given in the question, we need to multiply 9 by 30 first,
9 * 30 = 270
Next, we divide the result by 9
270/9 = 30
The result is 30.
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a nutrition major at wright state was studying the relationship between carbohydrates (x) and calories (y). for example, a serving of a particular brand of wheat pasta yielded 42 carbohydrates and 210 calories. after collecting x and y data on many kinds of foods, the student determined the slope of the regression line to be 4.0 and the y intercept to be 3.0. if a new food is tested, and the number of carbohydrates (x) is 100, what would be the predicted calories (y’)?
Answers
Answer:
The predicted calories would be 403 calories.
Step-by-step explanation:
We have a linear regression model relating y: calories with x: carbohydrates, which has a slope of 4.0 and a y-intercept of 3.0.
Then, the model equation is:
[tex]y=4.0x+3.0[/tex]
With these model we can predict the calories values for any amount of carbohydrates, within the interval within which this model is valid.
If a new food is tested, and the number of carbohydrates (x) is 100, the predicted value will be:
[tex]y(100)=4.0(100)+3.0=400+3=403[/tex]
The predicted calories would be 403 calories.
Concert ticket sales of £21,000 are split in the ratio of 2 : 5 between the venue and the band.
How much money does the venue make from the ticket sales?
Answers
Answer:
Step-by-step explanation:
£21000/7=3000
I got seven by adding 2 and 5
3000 times 2=6000
3000 times 5 = 15000
6000:15000
6000 for the venue
15000 for the band
The amount of money the venue makes from the ticket sales is £6000.
How much does the venue make?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The amount the venue makes = 2/7 x 21000 = £6000
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M plus the product of 6 and n
Answers
Answer:
6n + M
Step-by-step explanation:
6 * n = 6n, 6n + M would be the answer
The expression is M +6n.
What is Algebra?
Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
given statement:
M plus the product of 6 and n
So, first product of 6 and n
=6n
Now, M is added to the result
=M +6n
Hence, the expression is M + 6n
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How do you round up to the nearest hundreth
Answers
Answer:
the second digit from the decimal, round it based on the the thousandth if above 5 round it to the next number 4 and below round it to the same number
Step-by-step explanation:
say for example 10.246 this would round to 10.25
another example is 10.244 this would round to 10.24
Amanda wants to sell her old car. she will open a classified ad in the Sacramento Bee. the newspaper charges $42 for the first two lines and $11 dollars each additional line. she buys a three week ad that has four lines. What is Amanda's cost?
Answers
A mechanic had 4 and one half gallons of motor oil at the start of the day. At the end of the day, only 5 pints remained.
How many pints of motor oil did the mechanic use during the day?
Answers
Answer:
Step-by-step explanation:
I believe that it's 19pints I've had a problem with this question also but I believe I have the answer HOPE THIS HELPS
Final answer:
The mechanic used 31 pints of motor oil during the day.
Explanation:
Question: The mechanic started with 4 and one-half gallons of motor oil and ended the day with 5 pints remaining. How many pints of motor oil did the mechanic use during the day?
Step-by-step explanation:
Convert 4 and one-half gallons to pints: 4.5 gallons x 8 pints/gallon = 36 pints.
Subtract the remaining 5 pints from the initial 36 pints: 36 pints - 5 pints = 31 pints.
Therefore, the mechanic used 31 pints of motor oil during the day.
Suppose that a recent poll found that 49% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 250 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor. The mean of X is nothing. (Round to the nearest whole number as needed.) The standard deviation of X is nothing. (Round to the nearest tenth as needed.)
Answers
Answer:
The mean of X is 122.5 and the standard deviation is 7.9.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they believe that the overall state of moral values is poor, or they do not believe this. The probability of an adult believing this is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem, we have that:
[tex]n = 250, p = 0.49[/tex]
So
[tex]E(X) = np = 250*0.49 = 122.5[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.49*0.51} = 7.9[/tex]
The mean of X is 122.5 and the standard deviation is 7.9.
When rounded to the nearest 100 I am the smallest whole number that becomes 5,000 what number am I
Answers
Step-by-step explanation:
Let the number to be identified be represented as x
Given, when rounded to the nearest 100 I am the smallest whole number that becomes 5,000
Therefore, the number is above 4000 and it is a whole number.
When rounded to the nearest 100, I am the smallest whole number that becomes 5,000
The smallest whole number must be 4950 when ronded to 100,it becomes 5000.
The number is 4950
Name the property that justifies the statement. 17 = 17
Answers
Step-by-step explanation:
I think when you will multiply 17 by 1 the answer is 17 so 17 = 17
Test-preparation organizations like Kaplan, Princeton Review, etc. often advertise their services by claiming that students gain an average of 100 or more points on the Scholastic Achievement Test (SAT). Do you think that taking one of those classes would give a test taker 100 extra points?
Answers
Answer:
High school students and their parents are often bombarded with SAT test prep applications as they get closer to the college application process. Exam preparation offers arrive in the mail; they are sent home by schools, and they are not cheap. (The Princeton Review "Ultimate Classroom" course costs $ 1,199 in New York City.) When students take these courses and do not see their scores improve, parents may wonder if their children have studied enough or if they have wasted their money.
Step-by-step explanation:
Previous year, the NACAC released a report concluding that exam preparation courses have minimal impact on improving SAT scores: approximately 10-20 points on average in math and 5-10 points on critical reading. The Association for college administration report also noted that this evidence is "contrary to claims made by many test preparation providers of large increases of 100 points or more on the SAT."
Kathleen Steinberg, a College Board spokeswoman, says that, on average, students who take the SAT twice only "increase their scores by about 30 points."
He further disclose that "The College Panel does not indorse taking the SAT more than twice, as there is no evidence to indicate that taking the test more than twice increases grade performance."
Parents might also be surprised at the actual average SAT scores: 501 in critical reading, 515 in math, and 493 in writing, according to Steinberg. (The highest score you can get in any section is 800).
Kaplan claimed that The Princeton Review's claims for score breaks were based on comparing the results of Princeton Review's "diagnostic" tests with the students' self-reported scores on the actual SAT tests, as opposed to SAT scores previous and after.
Final answer:
Test-preparation organizations like Kaplan, Princeton Review, etc. often claim that students gain an average of 100 or more points on the SAT after taking their classes. While it is possible for some students to achieve a significant score improvement after taking these classes, it is important to note that the average improvement may not be 100 points for every student.
Explanation:
Test-preparation organizations like Kaplan, Princeton Review, etc. often claim that students gain an average of 100 or more points on the SAT after taking their classes. While it is possible for some students to achieve a significant score improvement after taking these classes, it is important to note that the average improvement may not be 100 points for every student.
The effectiveness of these classes depends on various factors, such as the student's starting score, their commitment and effort in the class, and their ability to apply the strategies they learn. Some students may experience a smaller improvement, while others may see a larger gain.
It's recommended for students to research and read reviews before choosing a test-preparation organization to ensure they are selecting a reputable program that aligns with their learning style and goals.
Rewrite f(x) =x+1/x-1 in the form f(x)= a/x-h +k
Answers
Answer:
f(x) = 2/(x -1) +1
Step-by-step explanation:
[tex]f(x)=\dfrac{x+1}{x-1}=\dfrac{(x-1)+2}{x-1}=\dfrac{x-1}{x-1}+\dfrac{2}{x-1}\\\\\boxed{f(x)=\dfrac{2}{x-1}+1}[/tex]
Angle BCD is a circumscribed angle of circle A. Angle BCA measures 40°.
Circle A is shown. Line segments B A and D A are radii. Tangents B C and D C intersect at point C outside of the circle. A line is drawn to connect points A and C. Angle B C A is 40 degrees.
What is the measure of minor arc BD?
40°
50°
80°
100°
Answers
Answer:
D. 100
Step-by-step explanation:
correct on edu2020
Based on the calculations, the measure of minor arc BD is equal to 100°.
Given the following data:
Angle BCA = 40°.What is a line segment?A line segment can be defined as a part of a line that is bounded by two (2) distinct points and has a fixed length.
Based on the information given, we can deduce the following:
Angle BAD = 2(BCA)
Angle BAD = [tex]2\times 40[/tex]
Angle BAD = 80°.
Also, angle ABC and ADC both have a measure of 90 degrees because angle BCD is a circumscribed angle.
Note: The sum of the interior angles in a quadrilateral is equal to 360°.
[tex]ABC + ADC + BAD + BCD = 360\\\\90+90+ BAD + BCD = 360\\\\180+ BAD + BCD = 360\\\\BAD + BCD = 360-180\\\\BAD + BCD = 180[/tex]
For the minor arc BD:
[tex]BCD =180-BAD\\\\BCD =180-80[/tex]
Angle BCD = 100°.
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