Answer:
Step-by-step explanation:
There are four numbers in the sample space that are less than 4: -3, -2, -1, and 0. Of these, three are less than 2: -3, -2, and -1. Therefore, the probability P(the number is less than 2 | the number is less than 4) is 3/4.
To evaluate 4!, we perform the multiplication 4 x 3 x 2 x 1, which equals 24.
To evaluate 6!, we perform the multiplication 6 x 5 x 4 x 3 x 2 x 1, which equals 720.
To evaluate 5!/3!, we first calculate 5! (which is equal to 5 x 4 x 3 x 2 x 1, or 120) and then divide by 3! (which is equal to 3 x 2 x 1, or 6). Therefore, 5!/3! = 120/6 = 20.
a study was conducted to evaluate the stress level of senior business students at a particular college. forty students were selected at random from the senior business class, and their stress level was monitored by attaching an electrode to the frontalis muscle (forehead). for the forty students, the mean emg (electromyogram) activity was found to be 35.8 microvolts. in addition, the standard deviation of the emg readings was found to be 2.5 microvolts. what would be the 99% confidence interval on the true mean emg activity for all seniors in the class? (you should be using statistical software such as statcrunch.) group of answer choices [34.7296, 36.8704] [34.7296, 36.7804] [34.7456, 36.0566] [34.9672, 36.7840]
The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]
To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula
CI = X ± Zα/2 (σ/√n)
where
X = sample mean = 35.8
Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.
σ = sample standard deviation = 2.5
n = sample size = 40
Substituting these values into the formula, we get
CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].
Therefore, the correct option is (a) [34.7296, 36.8704]
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which of the following is the most likely to call up mental images of specific sights, sounds, tastes, or smells?
This connection makes smells particularly powerful in triggering memories and emotions.
The sense of smell is the most likely to call up mental images of specific sights, sounds, tastes, or smells. This is because the olfactory system, which is responsible for the sense of smell, is closely linked to the brain's limbic system, which is involved in emotions and memory. This connection makes smells particularly powerful in triggering memories and emotions.
The olfactory system, which is responsible for the sense of smell, is unique in its connection to the brain's limbic system, which is involved in processing emotions and memory. When we smell something, the odor molecules enter our nose and are processed by specialized sensory neurons in the olfactory epithelium. These neurons then send signals to the olfactory bulb, which is located in the brain and is the first site of olfactory processing.
From there, the olfactory information is sent to several brain regions, including the amygdala and hippocampus, which are both part of the limbic system. The amygdala is involved in processing emotions and is responsible for generating feelings of pleasure, disgust, or fear in response to smells. The hippocampus, on the other hand, is involved in forming new memories and is responsible for encoding information about the context in which a smell is experienced.
The strong connection between the olfactory system and the limbic system makes smells particularly powerful in triggering memories and emotions. For example, the scent of freshly baked bread may evoke memories of childhood mornings spent in the kitchen with a loved one, while the smell of a certain perfume may remind you of someone special. Additionally, certain smells may elicit strong emotional responses, such as the smell of smoke triggering feelings of panic and fear in someone who has experienced a fire.
Overall, the sense of smell is closely linked to our emotional and memory centers, making it a powerful tool for triggering mental images of specific sights, sounds, tastes, or smells.
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10 points question at position 1 samples of rejuvenated mitochondria are mutated (defective) with a probability 0.15. find the probability that at most one sample is mutated in 10 samples
The probability that at most one sample is mutated in 10 samples is 0.746.
To calculate this probability, we use the binomial distribution formula.
The binomial distribution formula is used to calculate the probability of a certain number of successes (in this case, samples that are mutated) in a certain number of trials (10 samples). We need to find the probability of 1 success or fewer in 10 trials.
This is equal to P(x<=1) = 1 - P(x>1), where x is the number of successes.
For this calculation, we need the following parameters: n = 10 (number of trials), p = 0.15 (probability of a single sample being mutated), and x = 1 (number of successes). So, P(x<=1) = 1 - P(x>1) = 1 - P(x = 2) - P(x = 3) - P(x = 4) - P(x = 5) - P(x = 6) - P(x = 7) - P(x = 8) - P(x = 9) - P(x = 10).
The probability of at most one sample being mutated in 10 samples is calculated by adding the individual probabilities of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 samples being mutated, which equals 0.746.
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replace each * with a digit that makes the solution of the equation a whole number and find all the possibilities. 10x+11=144*
The * must be replaced by a digit of 1, hence the solution to the equation is given as follows:
x = 143.
What is the rule for divisibility by 10?A number is divisible by 10 if and only if its last digit is 0. This is because 10 is a multiple of 5 and 2, which are the prime factors of 10. Therefore, a number is divisible by 10 if it can be divided evenly by both 5 and 2.
For this problem, the equation is given as follows:
10x + 11 = 144*
Hence, when * = 1, we have that:
10x + 11 = 1441
10x = 1430.
Then the solution for the equation is obtained as follows:
x = 1430/10
x = 143.
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Shade in the region represented by the inequalities.
The length οf the hypοtenuse AC is 10 units.
What is graph?In mathematics, a graph is a visual representatiοn οf data οr infοrmatiοn that cοnsists οf pοints, called vertices οr nοdes, and lines, called edges οr arcs, that cοnnect them.
Graphs are οften used tο represent relatiοnships between οbjects, events, οr quantities.
They can be used tο mοdel and sοlve prοblems in variοus fields, such as cοmputer science, engineering, ecοnοmics, and sοcial sciences. There are many types οf graphs, including bar graphs, line graphs, scatter plοts, pie charts, and netwοrk graphs, amοng οthers. Each type οf graph is suited fοr visualizing different types οf data οr relatiοnships.
Based οn the given diagram, we can use the Pythagοrean theοrem tο find the length οf the hypοtenuse AC οf the right triangle ABC:
[tex]AC^2 = AB^2 + BC^2[/tex]
Substituting the given side lengths, we get:
[tex]AC^2 = 6^2 + 8^2[/tex]
[tex]AC^2 = 36 + 64[/tex]
[tex]AC^2 = 100[/tex]
Taking the square rοοt οf bοth sides, we get:
AC = 10
Therefοre, the length οf the hypοtenuse AC is 10 units.
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explain how you know which type of feed the zookeeper will run out of first
Answer:
well since there is no math, the first feed that runs out, will be the animal that they have the most of, or the bigger animals. meaning lemurs for multiple or large meaning elephant, or your mother
Step-by-step explanation:
no offense, it's just faster to drive around the world than trying to print a picture of your mom
a waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 20 yd^3 of debris. find the dimensions of the dumpster that will minimize its surface area.
The width of the dumpster that minimizes its surface area is approximately 1.71 yards, and the length is approximately 3.42 yards.
The length of the rectangular dumpster is equal to two times its width, or 2x, if x is its width. The dumpster's height is not specified, however it is not necessary for this issue.
We need to determine the dumpster's size to reduce the amount of surface area it has. The following sources provide the rectangular dumpster's surface area:
A = lw + lh + lw
where w stands for width, l for length, and h for height.
Given that the container must hold [tex]20 yd3[/tex] of waste, we can use the formula for the volume of a rectangular solid to create the following sentence:
[tex]V = lwh = (2x) (x)\\h = 2x^2 h = 20\\h = 10/x^2[/tex]
Inputting this expression for h into the surface area A formula yields the following results:
[tex]A = 2lw + 2lh + 2wh = 2(x)(2x) + 2(x)(10/x) + 2(2x)(10/x) = 4(x)(2x) + 40(x)[/tex]
We can take the derivative of A with respect to x, set it equal to zero, and solve for x to determine the dimensions that minimise A:
[tex]dA/dx = 8x - 40/x^2 = 0\\8x = 40/x^2\\x^3 = 5\\x = (5)^(1/3)\\[/tex]
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Can someone help me?!??
Answer:
4,320
Step-by-step explanation:
answer is 4,320
9x2x3x8x2x5
Answer:
66 km²
Step-by-step explanation:
To solve this, you should find the area of the rectangle as if it were complete and then subtract the area of the missing section.
Step one: Finding the area of the big rectangle
A = length x width
A = 9 x 8
A = 72 km²
Step two: Find the area of the smaller rectangle
A = 2 x 3 = 6 km²
Step three: Subtract the area of the small rectangle from the area of the big rectangle
72 - 6 = 66
g when is welch's t-test used to compare two population means, and what distributional assumptions are needed?
In the following question, Welch's t-test is used to compare the means of two populations with unequal variances. It is a variation of the standard Student's t-test, which is used when the variances are assumed to be equal.
Welch's t-test is generally used when the sample sizes are small and the variances are significantly different.
The distributional assumptions that are needed for Welch's t-test include:
Normality - The data from each population must be normally distributed, although this assumption is not always strictly required for the test to be valid.
Equal variances - The variances of the two populations must be equal. In practice, this assumption is often difficult to satisfy, particularly when the sample sizes are small. Welch's t-test does not require the assumption of equal variances.
Independence - The samples from each population must be independent of each other. This means that the observations in one sample should not be related to the observations in the other sample.
Welch's t-test is a parametric test, which means that it is based on assumptions about the underlying distribution of the data. If the distributional assumptions are not met, then the test may not be valid. In such cases, non-parametric tests may be used instead, such as the Wilcoxon rank-sum test.
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I need help the answer that was put is incorrect I need the right answer
Answer:
Step-by-step explanation: Its 6x, you add the 6 + 1 then keep the x.
about 4% of the population has a particular genetic mutation. 1000 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 1000.
The standard deviation for the number of people with the genetic mutation in a group of 1000 individuals is approximately 4.89.
To find the standard deviation for the number of people with a particular genetic mutation in a group of 1000 individuals, we first need to understand the concept of binomial distribution.
Binomial distribution is a statistical probability distribution that represents the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).
In this case, the probability of success (having the genetic mutation) is 0.04, and the probability of failure (not having the mutation) is 0.96. Thus, we can model the number of people with the mutation in a group of 1000 individuals using a binomial distribution with n = 1000 and p = 0.04.
The formula for the standard deviation of a binomial distribution is:
σ = √(np(1-p))
Where σ is the standard deviation, n is the number of trials, and p is the probability of success. Plugging in the values, we get:
σ = √(1000 x 0.04 x 0.96) = 4.89
In other words, we can expect that the number of people with the genetic mutation in a group of 1000 individuals will vary around the mean of 40 (1000 x 0.04) by about 4.89, with about 68% of the observations falling within one standard deviation of the mean.
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Which equation matches the hanger diagram?
Equations are collections of two or more statements with equal signs.
I must locate the solution that the hanger diagram matches. [tex]3x=4[/tex] is the equation that fits the hanger diagram. Thus, option C is correct.
What is a hanger diagram?The hanger shows a total weight of 7 units on one side that is balanced with 3 equal, unknown weights and a 1-unit weight on the other.
Two or more expressions containing equal signs are called equations. I need to find the equation that corresponds to the hanger diagram. The hanger model is a visual representation of the equation.
Both sides must have the same weight to keep the hanger balanced. Like scales and barbells. There are 3 x on the left side of the hanger and 4 x on the right side.
So [tex]3x=4[/tex] is an equation that satisfies the given trailer diagram.
So option C is correct. [tex]3x=4[/tex] is the equation that fits the hanger diagram.
From the diagram we have,
Left=x+x+x
Right [tex]=1+1+1+1[/tex]
This gives
Left=[tex]3x[/tex]
Right [tex]=4[/tex]
Therefore, the equation [tex]3x =4[/tex]
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suppose that the value of a stock varies each day from $8.82 to $16.17 with a uniform distribution. find the third quartile, i.e., 75% of all days the stock is below what value?
The third quartile is $10.6575, which means that 75% of all days the stock is below this value.
The range of the stock price is from $8.82 to $16.17, and the distribution is uniform, which means that the probability of the stock price being any value between the minimum and maximum is the same.
To find the third quartile, we need to find the value x such that 75% of the observations are less than or equal to x, and 25% of the observations are greater than or equal to x.
Since the distribution is uniform, we can find x by finding the value that separates the bottom 25% of the distribution from the top 75% of the distribution.
The bottom 25% of the distribution spans from $8.82 to some value x. Since the distribution is uniform, we can find x by setting the probability of the stock price being less than or equal to x to 0.25, which gives:
(x - 8.82) / (16.17 - 8.82) = 0.25
Solving for x, we get:
x - 8.82 = 0.25 * (16.17 - 8.82)
x - 8.82 = 1.8375
x = 10.6575
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There are 36 students in the school choir. The ratio of girls to boys in the choir is
5:4. Two girls are absent from practice on Monday. What is the ratio of girls to
boys at choir practice on Monday?
A 3:4
C 9:8
B 5:2
D 10:7
Answer:
C 9:8
Step-by-step explanation:
total students = 36
5+4=9
5:4 = 20:16
20-2=18
ratio for monday = 18:16
=9:8
Ali and ben and clare each played a game
clares score was seven times alis score
ben score was half of alis score
write down the ratio of alis score to bens score to clares score
give your answer in its simplest form
The ratio of Ali's score to Ben's score to Clare's score in its simplest form is 1 : 3.5 : 7
Given data:
Claire's score = 7 * Ali's score
Ben's score = 0.5 * Claire's score
How to solve for the ratio of Ali's score to Ben's score to Clare's score
let Ali's score = x
let Ben's score = y
let Claire's score = z
z = 7 * x = 7x
z = 7x
y = 0.5 * z = 1/2 * z = z / 2
plugging the value of z gives
y = 7x / 2
writing the ratios in terms of x gives
Ali : Ben : Claire
x : y : z
x : 7x/2 : 7x
Reducing the terms by dividing through by x
1 : 7/2 : 7
OR
1 : 3.5 : 7
clearing the fraction gives
2 : 7 : 14
Therefore, the ratio of Ali's score to Ben's score to Clare's score in its simplest form is 1 : 3.5 : 7
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you spin the spinner once.
what is p(less than 4)?
write your answer as a fraction or whole number
The equation used to obtain the probability of a number less than 4 on the spinner is given as follows:
P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes for this problem are given as follows:
Desired: number of regions with numbers that are less than 4.Total: total number of regions.Hence the probability is calculated as follows:
P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.
Missing InformationThe problem asks for the probability of spinning a number less than 4 on the spinner.
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Last year, 89 musicians attended a jazz camp, and 15 of them were bassists. What is the experimental probability that the first musician to sign up will be a bassist?
There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
What is experimental probability?Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability
According to question:The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.
Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:
Experimental probability = Number of bassists / Total number of musicians
Experimental probability = 15 / 89
Experimental probability = 0.1685 or approximately 16.85%
As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.
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Give a counterexample
for the following
conjecture: "an odd number plus another odd
number will always be divisible by 4".
13.
5 and 25
Step-by-step explanation:A single counterexample to any conjecture that states that something will always be true immediately disproves the statement.
Conjecture
Conjecture is a statement or conclusion that is offered with little to no proof. The conclusion given in the question has no mathematical proof to support the idea; thus, it is conjecture. Conjecture is often easy to disprove.
Counterexamples are examples that follow the conditions of a statement (or conjecture) but do not meet the same conclusion. The conditions of the conjecture given are "an odd number plus another odd number". So, a counterexample must also meet these conditions. The conclusion of the conjecture is that this sum " will always be divisible by 4". Thus, the counterexample should not be divisible by 4.
Counterexample
At first, the conjecture may seem to be true because of pairs like 13+15 or 21+23. However, because the conjecture includes the word "always", it only takes one counterexample to completely disprove the statement.
I know that 30 is not divisible by 4, so I can find 2 odd numbers that sum to 30. I pair I chose was 5+25, but there are other possibilities like 13+17 or 1+29. No matter which you choose, it's clear that the conjecture is not true.
helppppp!! For #19-20, solve for x. Simplify all radicals.
The diameter of a softball is 3.8 inches. Estimate the volume within the softball. Round answers to the nearest
whole number and leave in the answer.
a. Volume: 73
b. Volume: 14
c. Volume: 9
d. Volume: 58
The volume of the ball is 9π (optionC)
What is volume of a sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center.
The ball takes the shape of the sphere. The volume of a sphere is therefore calculated as ;
V = 4/3 πr³
r = d/2 = 3.8/2 = 1.9
V = 4/3 × π × 1.9³
V = 27.44 π/3
V = 9π ( nearest whole number)
therefore the volume of the ball is 9π (nearest whole number)
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Answer for x=
Please
Answer:
53°
Step-by-step explanation:
it’s vertical, verticals are always identical, I think
Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. If she spends 3x-7 dollars on rent, how much does she spend on electricity? Use pencil and paper. For which
value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you found the value(s)
She spends
(Simplify your answer.)
dollars on electricity.
The values of x is [tex]x < 39.5[/tex].
Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]
Spending of shopkeeper on rent [tex]= 3x-7[/tex]
So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]
Given that amount the shopkeeper spends on electricity less than 100.
So suitable inequality,
[tex]2x+21 < 100[/tex]
[tex]2x < 100-21[/tex]
[tex]2x < 79[/tex]
[tex]x < 39.5[/tex]
All the values of [tex]x < 39.5[/tex].
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the measures of two acute angles of a right triangle differ by 22 degrees. find the measure of each angle.
Answer:
In a right triangle, one of the angles measures 90 degrees, and the other two angles are acute angles that add up to 90 degrees. Let's call the measures of the two acute angles x and y.
We know that x and y differ by 22 degrees. So we can set up an equation:
x - y = 22
We also know that x + y = 90, since the two acute angles add up to 90 degrees.
Now we can solve this system of equations for x and y. One way to do this is to add the two equations together, which eliminates y:
x - y + x + y = 22 + 90
2x = 112
x = 56
Now we can substitute x = 56 into one of the equations to find y:
x + y = 90
56 + y = 90
y = 34
Therefore, the measures of the two acute angles of the right triangle are 56 degrees and 34 degrees.
8x 2 + [ 3x3-8] = with explanation pls and its due in six minutes
Answer: 16x+3x^3−8
Please mark me brainliest :)
People of different ages were asked the question "Do you listen to audiobooks?” The bar chart displays the percentage of "yes” responses in each age group.
The percentage of people aged 55-64 who answered “yes” was slightly lower (50%), followed by people aged 65-74 (45%) and people over 75 (43%).
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol “%” and is used to compare values or express change. It can be used to compare two or more numbers, to show how much one number is a percentage of another, or to indicate the rate of change. In mathematics, percentages are often used to compare the size of one number to the size of another number.
The bar chart shows that the percentage of people who responded “yes” to listening to audiobooks increases with age. Only 18% of people aged 18-24 said they listen to audiobooks, while 30% of people aged 25-34 and 44% of people aged 35-44 responded positively. The percentage continues to increase with age, with the highest percentage of people aged 45-54 saying they listen to audiobooks (54%).
The percentage of people aged 55-64 who answered “yes” was slightly lower (50%), followed by people aged 65-74 (45%) and people over 75 (43%).
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No, since the ratios do not constitute a whole. Option(a) is the required response to the posed query.
What is a bar chart and pie chart?A collection of categorical data can be summarised using a bar chart, and continuous data can be made categorical using auto-binning. The bar chart uses several bars to show data, with each bar denoting a distinct category.
A pie chart, also known as a circle chart, is a visual representation of the various values of a given variable or a way to summarise a collection of nominal data. This kind of chart consists of a circle with numerous parts. A specific group is represented by each segment. A pie chart is useful for organising and displaying data by proportion of the total.
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The rest of the question is,
Would it be appropriate to display the data with a pie chart?
a). No, because the proportions are not parts of a whole.
b). No, because the data categories are too broad.
c). Yes, because the data are grouped into categories.
d). Yes, because the data can be represented by a relative frequency compared to the whole.
Help I don’t have a clue ?
Answer: Yes
Step-by-step explanation:
Because she tested it more times, her results should (in theory) be more accurate, due to more tests leading to the results being more diverse. The results indicate that one side of the coin (the tails side) is more likely to land down, which leads the head side up.
A hot air balloon is rising at a constant rate of 10 meters per second, while blowing east at a rate of 3 meters per second. The balloon travels on a diagonal path, and its position after 1 second is shown. How far does the balloon travel after 10 seconds?
Answer:130 meters
Step-by-step explanation:
it travels up 10 meters and over 3 meters per second. so that means it travels 13 meters per second. then you do 13 x 10 and get 130 meters
Answer:
3,000 meters.
Step-by-step explanation:
What you should first do is set up a diagram to demonstrate the velocity of the balloon and wind.
After having that set up, you can use the pythagorean theorem to find the hypotenuse of the triangle made after 10 seconds.
3²*10²=√900 (for one second)
√900 = ±30 m traveled in one second
30²×100²=√9,000,000
√9,000,000 = ±3,000 m
what would happen if 300 people were sampled instead of 200, and the confidence level remained the same?
If 300 people were sampled instead of 200, and the confidence level remained the same, it would produce a more accurate result.
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 your university, you could survey a sample of 100 students. In statistics, sampling allows you to test a hypothesis about the characteristics of a population.
This is because a larger sample size allows for a better representation of the population, providing a more accurate result. Additionally, with a larger sample size, the confidence interval of the sample would be narrower, indicating a higher level of confidence in the accuracy of the result.
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Pls help! It's my homework.
a) The radius of the circle is r = 18 cm, b) angle AOC is a right angle, which is π/2 radians, c) the area of the shaded region is 125.66 cm², d) the perimeter of the shaded region is 57.85 cm.
Describe Circle?A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are at a constant distance from a given point in the plane, called the center of the circle. The distance between the center of the circle and any point on the circle is called the radius of the circle. Alternatively, the diameter of a circle is the distance across the circle passing through the center, and it is twice the length of the radius.
A circle has several important properties, including:
Circumference: The circumference of a circle is the distance around its outer edge. It is calculated using the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.
Area: The area of a circle is the amount of space inside its boundary. It is calculated using the formula A = πr², where π (pi) is the mathematical constant approximately equal to 3.14 and r is the radius of the circle.
a) To find the radius r, we can use the Pythagorean theorem to solve for the length of segment OP, which is the height of the rectangle:
OP² + AP² = OA²
OP² + 6² = r²
OP² = r² - 6²
We can also use the fact that AC is a diameter of the circle to find the length of segment OC:
AC = 2r
36 = 2r
r = 18
Substituting this value into the equation for OP² gives:
OP² = 18² - 6²
OP² = 300
OP = 10√3
Therefore, the radius of the circle is r = 18 cm.
b) Angle AOC is a central angle of the circle that intercepts segment AC. Since AC is a diameter, angle AOC is a right angle, which is π/2 radians.
c) The shaded region is the difference between the area of segment ABC and the area of triangle AOC. The area of segment ABC is equal to the area of sector AOC minus the area of triangle AOC. The area of sector AOC is:
(1/2) r² angle AOC
Substituting r = 18 cm and angle AOC = π/2 radians gives:
(1/2) (18)² (π/2) = 81π
The area of triangle AOC is:
(1/2) OA OC sin AOC
Substituting OA = OC = r = 18 cm and AOC = π/2 radians gives:
(1/2) (18)(18) sin(π/2) = 162
Therefore, the area of the shaded region is:
81π - 162 ≈ 125.66 cm²
d) The perimeter of the shaded region is the sum of the lengths of segments AB, BC, and the arc of the circle between A and C. To find the length of the arc, we can use the formula for the length of an arc of a circle:
length of arc = radius x central angle
Substituting r = 18 cm and angle AOC = π/2 radians gives:
length of arc = 18 x (π/2) = 9π
Therefore, the perimeter of the shaded region is:
AB + BC + length of arc = 36 + 2(6) + 9π ≈ 57.85 cm.
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The box plot shows the population of several states (in millions). Is the range or the IQR a better measure of variation for these data? Why?
In conclusion, we can say that the IQR is a better measure of variation for these data because it is less affected by outliers and gives a more accurate picture of the spread of the data.
The given box plot illustrates the population of several states (in millions).
The range and the interquartile range (IQR) are both the measures of variation that explain the variation within a set of data, but there are some variations between these two measures.
Let's discuss the differences between these two measures.
Range:
The range is defined as the difference between the highest and lowest values of a data set.
The range is useful for describing the overall spread of the data, which is particularly useful when dealing with very small datasets.
This measure is sensitive to the extreme values, such as outliers.
Because of this, the range of the population of several states can be used to identify the minimum and maximum value for the population of several states.
IQR:
The interquartile range (IQR) is the difference between the 75th and 25th percentiles, also known as the first and third quartiles, in a data set.
The IQR is a better measure of variation than the range because it is less sensitive to extreme values or outliers.
As a result, the IQR is a more robust measure of the spread of the data.
Therefore, it is better to use the IQR for the population of several states since it gives a more accurate picture of the spread of the data.
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