Answer:
We can solve the inequality by adding 4 to both sides:
2b - 4 + 4 ≥ 3 + 4
2b ≥ 7
b ≥ 7/2
The values in the replacement set that are greater than or equal to 7/2 are {3, 4, 5}. Therefore, the solution set is:
{3, 4, 5}
So the answer is B. {3, 4, 5}.
which of the following statements is true? a. the sum of the squared deviations from the arithmetic mean is always zero b. the sum of the deviations from the arithmetic mean is always zero c. the standard deviation is always less than the variance d. the distance between the first and third quartiles is twice the distance between the first quartile and the median e. the arithmetic mean is always less than the geometric mean if two data sets have the same range: a. the distances from the smallest to largest observations in both sets will be the same b. the smallest and the largest observations are the same in both sets c. both sets will have the same mean d. both sets will have the same interquartile range
2) how did taking data at several different inclined-plane angles affect your final results (specifically the uncertainties)
When taking data at different inclined plane angles, it will have an effect on the final results specifically the uncertainties because of gravitational force.
This is because as the angle of the plane increases, the gravitational force acting on the object decreases, while the force of friction increases.
Therefore, by taking data at different inclined-plane angles, the uncertainties in the results will be affected. The uncertainties will increase as the angle of the plane increases because it becomes more difficult to measure the gravitational force acting on the object. In order to minimize uncertainties, it is recommended to take measurements at several different angles and take an average of the results.
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Behaviors are executed when neurons from the ___ send instructions to muscles along a descending neural network called the ___, which decussates in the ____.
The corticospinal tracts carry information from the motor cortex, which is responsible for coordinating the movement of muscles, to the lower motor neurons. The extra-pyramidal tracts are made up of several types of neurons that play a role in modulating and fine-tuning the movement of muscles.
Neurons in the central nervous system (CNS) send instructions to muscles along a descending neural network called the descending motor pathways, which decussate in the medulla oblongata. This means that information from the brain travels down the spinal cord on both sides of the body, and crosses over to the opposite side at the medulla. The descending pathways start from the brainstem and motor cortex, and control the contraction of skeletal muscles, which are responsible for body movements.
The descending motor pathways are a series of neurons that connect the CNS to the muscles, transmitting the information required for voluntary body movements. Through the descending pathways, the brain can communicate with the muscles and control them. The pathways are divided into two parts, the corticospinal tracts and the extra-pyramidal tracts.
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if y = 2, then -3y(1-5)
[tex] \: [/tex]
Solution:-[tex] \rm{-3y( 1 - 5)}[/tex][tex] \: [/tex]
put the value of y = 2 in equation
[tex] \rm \: -3( 2 ) ( 1 - 5 )[/tex][tex] \: [/tex]
[tex] \rm \: -6 ( 1 - 5 )[/tex][tex] \: [/tex]
[tex] \rm \: -6 - 5[/tex][tex] \: [/tex]
[tex] \underline{ \rm{ \red{ \: \: -11 \: \: }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
after weeks of practice, mrs. carroll recalculated the free throw percentages of the team and found that the 3 players with the highest free throw percentage increased it by 4 points. if mrs. carroll recalculates the statistical measures, which of the measures would stay the same?
The measures such as overall team free throw percentage, the percentages of the other players, the median, the mean, and the shape of the distribution would remain the same.
The 3 players with the highest free throw percentage increased their percentage by 4 points, but all other statistical measures, such as overall team free throw percentage and the percentages of the other players, would stay the same.
The overall team free throw percentage is calculated by adding the percentages of all players and dividing the total by the number of players. Since the percentages of the other players remain the same, the overall team free throw percentage would remain unchanged.
Additionally, since only the 3 players with the highest percentages increased theirs, the median and mean of the free throw percentages would remain the same.
The increase in free throw percentage of the 3 players affects the free throw percentage distribution, but the shape of the distribution would remain the same.
That is, the distribution will still have the same range, but the 3 players with the highest free throw percentage would have a slightly higher percentage.
In conclusion, the only statistical measure that would change after Mrs. Carroll recalculates the free throw percentages of the team is the percentage of the 3 players with the highest free throw percentage, which would increase by 4 points.
All other measures, such as overall team free throw percentage, the percentages of the other players, the median, the mean, and the shape of the distribution would remain the same.
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Solve using equivalent ratios.
Wayne has a recipe on a 3-inch-by-5-inch index card that he wants to
enlarge to 15 inches long. How wide will the enlargement be?
The width of the enlargement will be 9 inches since the ratio of the length and width of the original recipe card is equal to the ratio of the length and width of the enlarged recipe card.
Since we want to enlarge the recipe on a 3-inch-by-5-inch index card to a length of 15 inches while maintaining the same proportions, we can use equivalent ratios to find the width of the enlargement.
Let x be the width of the enlargement in inches. Then, we can set up the following ratio:
3/5 = x/15
This ratio is formed by comparing the length and width of the original recipe card with the length and width of the enlarged recipe card.
To solve for x, we can cross-multiply and simplify:
3/5 = x/15
=> 3 * 15 = 5 * x
=> 45 = 5x
=> x = 9
Therefore, the width of the enlargement will be 9 inches.
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in designing an invertebrate biodiversity study of a stream, different areas within the study site need to be sampled. a major consideration is how many areas to sample, which will largely be determined by available resources (people, money, time). imagining two possible scenarios, one where only 5 areas within a stream site are sampled, and another where 50 are sampled, how would the taxa richness values of the two differ? if the number was increased to 500, how might it change? draw a simple graph (species/area curve), with total cumulative number of areas sampled on the x-axis and taxa richness on the y-axis, to illustrate the relationship between these variables.
a) The number of areas sampled within a stream site is directly proportional to the taxa richness values obtained.
b) If the number of areas sampled is increased to 500, the taxa richness values would be expected to increase even further, as more areas increase the likelihood of encountering rare and less frequently occurring species
The number of areas sampled within a stream site is directly proportional to the taxa richness values obtained. In general, the more areas sampled, the higher the number of taxa observed. Therefore, in the scenario where only 5 areas are sampled, the taxa richness values obtained would be lower than those obtained from 50 sampled areas.
Similarly, increasing the number to 500 would likely result in even higher taxa richness values. However, it is important to note that there is a point of diminishing returns where the number of additional areas sampled does not result in a significant increase in taxa richness values. Therefore, the number of areas to sample should be determined based on available resources and the goals of the study.
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The given question is incomplete, the complete question is:
In designing an invertebrate biodiversity study of a stream, different areas within the study site need to be sampled. A major consideration is how many areas to sample, which will largely be determined by available resources (people, money, time). Imagining two possible scenarios, one where only 5 areas within a stream site are sampled, and another where 50 are sampled, how would the taxa richness values of the two differ? If the number was increased to 500, how might it change?
does the confidence interval suggest that the difference, if any, observed in this sample will also generalize to the larger population?
In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.
What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.
A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.
A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.
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suppose that each party must select a speaker and a vice speaker. how many ways are there for the speaker and vice speaker to be selected in the demonstrators party?
There are n x (n-1) number of ways for the speaker and vice speaker to be selected in the demonstrator's party, where n is the number of members in the party.
For the demonstrator's party, the first position of the speaker can be filled by any of the n members. After the speaker is chosen, there are n-1 members left to select from for the position of vice speaker. Therefore, the total number of ways the speaker and vice speaker can be selected is n x (n-1).
For example, if the demonstrator's party has 4 members, there are 4 choices for the speaker position. After the speaker is chosen, there are 3 choices left for the position of vice speaker. So, the total number of ways to select a speaker and vice speaker in the party is 4 x 3 = 12.
This formula can be applied to any size of the party to determine the total number of possible ways to select a speaker and vice speaker.
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jeff had $20. he spent 38 of his money on lunch. how much money does jeff have left? a. $12.50 b. $7.50 c. $8.25 d. $16.75
Answer:
$12.50
Step-by-step explanation:
62% would be left,so
[tex]\frac{62}{100}[/tex] × $20
=$12.50
Solve for x.
2x^2-28x+98=0
X=
11 POINT’S
⇒First take out the highest common factor 2 form the quadratic equation and divide each and every term of that equation by that common factor.
⇒Factorise the equation and equate the factors of the equation to 0 and solve for the unknown variable x.
⇒Below are the steps on solving for the unknown variable.
[tex]2(x^{2} -14x+49)=0 \\\frac{2(x^{2} -14x+49)}{2} =\frac{0}{2} \\x^{2} -14x+49=0\\(x-7)(x-7)=0\\x-7=0\\x=7[/tex]
a 12 sided die is rolled. what is the probability that an even number or a number greater than 3 is rolled
The probability that an even number or a number greater than 3 is rolled on a 12-sided die is 0.833.
A 12-sided die has 12 equally likely outcomes, numbered from 1 to 12. To find the probability of rolling an even number or a number greater than 3, we need to count the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.
There are 6 even numbers on a 12-sided die, namely 2, 4, 6, 8, 10, and 12, and there are 9 numbers greater than 3, namely 4, 5, 6, 7, 8, 9, 10, 11, and 12. However, we need to be careful not to count the numbers that satisfy both conditions twice, namely 4, 6, 8, 10, and 12.
Therefore, the number of outcomes that satisfy the condition is 6 + 9 - 5 = 10. The probability of rolling an even number or a number greater than 3 is therefore 10/12, which simplifies to 5/6 or approximately 0.833.
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describe a dataset where defining a confidence interval would be important for testing validity of data. what do you want to know about the data? which population parameter (and test statistic) would you use? what confidence interval would you choose and why.
Defining a confidence interval is important in analyzing a dataset to test the validity of data. The choice of population parameter, test statistic, and confidence interval depends on the type of data being analyzed and the level of confidence required by the researcher.
When analyzing a dataset, it is important to determine the confidence interval to test the validity of the data. The confidence interval measures the precision of an estimate and indicates the range in which the population parameter is likely to exist.
There are several types of datasets where defining a confidence interval would be important for testing validity of data, some of them include;
1. Medical research: In medical research, researchers gather data to examine how a treatment plan affects a group of people. They can define a confidence interval to determine the range of possible outcomes. They use the test statistic to help them determine how significant the results are.
2. Business Data: When analyzing business data, defining a confidence interval is crucial to determine the success rate of a marketing campaign, sales data, or employee turnover. It allows the business to assess their performance and make data-driven decisions.
3. Political Polling: When conducting political polls, defining a confidence interval is necessary to determine the reliability of the data. It helps the pollsters to estimate the likely outcome of the election and the level of confidence that can be placed in the results.
When analyzing a dataset, it is essential to determine which population parameter and test statistic to use. The population parameter is the numerical value that describes the entire population. It can be the mean, proportion, variance, or standard deviation. The test statistic is used to determine if the population parameter is within the confidence interval, or if it lies outside the interval. The choice of population parameter and test statistic depends on the type of data being analyzed.
The confidence interval to choose depends on the level of confidence required by the researcher. The commonly used confidence intervals are 90%, 95%, and 99%. The level of confidence chosen by the researcher determines the size of the interval. The higher the confidence level, the wider the confidence interval. The researcher should choose a confidence interval that is wide enough to contain the population parameter, but not too wide to reduce the precision of the estimate.
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describe in words how to calculate the probability of two mece events from their odds using the ratio method.
To calculate the probability of two separate events using the ratio method, we must first understand the odds associated with each event. The odds are expressed as a ratio, with the first number representing the chances of success and the second number representing the chances of failure. For example, the odds of an event happening might be 3:2, which indicates that there is a 3/5 chance of success.
Once the odds for each event are known, we can calculate the probability of both events occurring by multiplying the odds of each event together. So, for example, if the odds of Event A are 3:2 and the odds of Event B are 4:5, the probability of both events occurring is 3/2 * 4/5 = 6/10. This means that there is a 6 in 10 chance of both events occurring.
To sum up, calculating the probability of two separate events using the ratio method is fairly simple. Just look at the odds associated with each event and multiply them together to get the probability of both events occurring.
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an open rectangular gutter is made by turning up the sides of a piece of metal 20 in wide. the area of the cross section of the gutter is 50 in^2 find the depth of the gutter
the graph of f(x) to answer the question.
f(x) 18
16-
(-10, 14)
10-
6
(-6, 1.2)
-14-12-10-8-6-4-2
(-5, -1)
(10, 14)
(8, 6.8)
6 8 10 12 14
(5, -1)
(0, -6)
©2018 StrongMind. Created using GeoGebra.
What is the output off when x = -6?
Enter your answer as the numerical value shown in the graph
The output of the graphed function when x = 6 is given as follows:
y = 1.2.
How to define a quadratic function according to it's vertex?The coordinates of the vertex are (h,k), meaning that:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.Considering a leading coefficient a, the quadratic function is given as follows:
y = a(x - h)² + k.
The vertex is the turning point of a quadratic equation, hence it's coordinates for this problem are given as follows:
(0, -6).
Meaning that the function is defined as follows:
y = ax² - 6.
When x = 5, y = -1, hence the leading coefficient a is obtained as follows:
-1 = 25a - 6
a = 0.2.
Hence the function is:
y = 0.2x² - 6.
Hence the output when x = -6 is given as follows:
y = 0.2(-6)² - 6
y = 1.2.
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Write an equation that describes the function.
4. Input, x Output, Y
0 0
1 4
2 8
3 12
Answer:
Y = 4x
Step-by-step explanation:
In this equation, x represents the input value, and Y represents the output value. Coefficient 4 illustrates the rate of change or slope of the function, indicating that for every unit increase in x, the value of Y increases by four units. When x is 0, Y is also 0, consistent with the given data. Similarly, when x is 1, 2, and 3, Y is 4, 8, and 12, respectively, matching the provided output values.
a bag contains 3 black ,4 red and 2 green balls if two balls are drawn at random what's the probability of getting exactly 2 balls
Answer:9 red
Step-by-step explanation:
what is the value of x ?
Answer: 98.5 if this is wrong im sry.
Step-by-step explanation:
Simon is making a frame for a photo that measures 6 inches by 8 inches. He wants the frame to be the same width all the way around and the total area of the frame and photo to be 120 square inches. Which quadratic equation represents the area of the picture and frame?
Answer: A
Step-by-step explanation:
how long will it take for $500 to amount to $850 at 10% simple interest? question 37 options: 7 years 5 years 3.5 years 10 years none of these
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 850\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years \end{cases} \\\\\\ 850 = 500[1+(0.1)(t)] \implies \cfrac{850}{500}=1+0.10t\implies \cfrac{17}{10}=1+0.10t \\\\\\ \cfrac{17}{10}-1=0.10t\implies \cfrac{7}{10}=0.10t\implies \cfrac{7}{(10)(0.10)}=t\implies 7=t[/tex]
two people start from the same point. one walks east at 9 mi/h and the other walks northeast at 8 mi/h. how fast is the distance between the people changing after 15 minutes? (round your answer to three decimal places.) mi/h
The distance between the two people is changing at a rate of 24.884 mi/h after 15 minutes.
We can use the Pythagorean theorem to determine the distance between the two people as a function of time. Let x be the distance traveled by the person walking east, and y be the distance traveled by the person walking northeast. Then, after 15 minutes (or 0.25 hours), we have:
x = (9 mi/h) * (0.25 h) = 2.25 mi
y = (8 mi/h) * (0.25 h) = 2 mi
The distance between the two people is given by:
[tex]d = sqrt(x^2 + y^2)[/tex]
Taking the derivative with respect to time t, we get:
[tex]d' = (2x dx/dt + 2y dy/dt) / (2sqrt(x^2 + y^2))[/tex]
Substituting the values we found earlier, we get:
[tex]d' = (2(2.25)(9) + 2(2)(8)) / (2sqrt((2.25)^2 + (2)^2))= 24.884 mi/h[/tex]
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the area of a square is 500. If its width is one-fifth as long as its length is 4 times long, what is the new area?
A.100
B.400
C.500
Option A, 100 is the new area.
Explanation:
Let's assume that the length of the square is x. Then, according to the problem, the width of the square is one-fifth as long as the length, which means the width is x/5. The area of the square is given as 500, which means:
x * x = 500
x^2 = 500
x = sqrt(500) = 10 * sqrt(5)
So, the length of the square is 10 * sqrt(5). Using this information, we can find the width:width = x/5 = (10 * sqrt(5))/5 = 2 * sqrt(5)
Now we can find the new area of the square by multiplying the new length and width:new area = (2 * sqrt(5)) * (10 * sqrt(5)) = 100
Therefore, the new area of the square is 100, which is option A.
sin 30° = 0.5 Using the equality above, copy and complete the following: sin-¹ (0.5) =
However, sin⁻¹ is defined to return an angle between -90° and 90°, so it returns the angle that is closest to 30° (which is 30° in this case).
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle.
Here,
If sin 30° = 0.5, then sin⁻¹(0.5) is the angle whose sine is 0.5. In other words, we are looking for the angle whose sine is 0.5. Since sin 30° = 0.5, we know that one possible answer is 30 degrees. However, there are other angles that also have a sine of 0.5. One way to find the other angles is to use the inverse sine function, denoted as sin⁻¹. This function takes a value between -1 and 1 as its input and returns an angle between -90° and 90° as its output. So, if we want to find sin⁻¹(0.5), we are asking: what angle has a sine of 0.5?
The answer is: sin⁻¹(0.5) = 30°.
Note that there are other angles that also have a sine of 0.5, such as 150°, 390°, etc.
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Complete question:
Using the equality above, copy and complete the following:
The value of sin⁻¹ (0.5) when sin 30° = 0.5.
A song costs 90p to download. How many songs can you get for 2pound?
we can download 2 songs for £2 if each song costs 90p. This calculation can be useful for budgeting and planning purchases, and it shows the importance of being mindful of the cost of individual items when making larger purchases.
To find out how many songs can be downloaded for £2, we need to divide £2 by the cost of each song.
We know that each song costs 90p, which is equivalent to £0.90. Therefore, we can set up the following equation:
£2 / £0.90 per song = x songs
To simplify the equation, we can first divide £2 by £0.90 to get the number of songs that can be downloaded:
£2 ÷ £0.90 = 2.22 (rounded to two decimal places)
So we can download 2.22 songs with £2. However, since we can't download a fraction of a song, we need to round down to the nearest whole number of songs.
Therefore, we can download 2 songs with £2 if each song costs 90p.
We can also verify this by multiplying the number of songs by the cost per song:
2 songs × 90p per song = £1.80
This means that we have spent £1.80 on two songs, leaving us with £0.20. We cannot afford another full song, so we cannot download a third song.
In conclusion, we can download 2 songs for £2 if each song costs 90p. This calculation can be useful for budgeting and planning purchases, and it shows the importance of being mindful of the cost of individual items when making larger purchases.
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6. A theme park guest takes an innertube into the wave pool. The innertube moves up and down in a way such that the height h of the innertube, in meters, above the floor of the pool can be modeled by the function h = asinbx + 3. When the wave pool is turned on, the innertube's height fluctuates between 2 meters and 4 meters, with an interval of 8 seconds between maximums. Based on the context of the problem, what are the values of a and b? = b a = 1 and 4 a = 1 and 8 = a = 2 and 4 = b a = 2 and 8
The values of a and b are a = 1 and b = π/4.
Explanation:
We know that the height of the innertube can be modeled by the function:
h = asinbx + 3
where h is the height in meters,
a is the amplitude of the wave,
b is the frequency of the wave in cycles per meter, and
3 is the average height of the wave.
We also know that the innertube's height fluctuates between 2 meters and 4 meters, so we can set up the following equation:
2 <= asinbx + 3 <= 4
Subtracting 3 from each term, we get:
-1 <= asinbx <= 1
Dividing by a, we get:
-1/a <= sinbx <= 1/a
Since the maximum value of sinbx is 1 and the minimum value is -1, we know that:
1/a >= 1 or -1/a <= -1
Simplifying, we get:
a <= 1 or a >= -1
However, a must be positive because it represents the amplitude of the wave. Therefore, we have:
a >= 1
Next, we can use the fact that the innertube reaches its maximum height every 8 seconds to find the value of b. Since the period of a sine function is given by:
period = 2π / b
and the period in this case is 8 seconds, we have:
8 = 2π / b
Solving for b, we get:
b = 2π / 8 = π / 4
Therefore, the values of a and b are:
a = 1 and b = π / 4
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if 10 friends are going to occupy 10 seats in shuttle on the way to the airport, how many different ways can they arrange themselves in the shuttle? provide your answer below:
If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.
Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.
Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800
Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.
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The triangle shown is rotated about line m.
A triangle with side lengths of 6 centimeters, 8 centimeters, and 10 centimeters is shown. The triangle is rotated about line m at the side with length 8 centimeters.
What is the approximate base area of the resulting three-dimensional figure?
Area of a circle: A = πr2
38 sq. cm
113 sq. cm
201 sq. cm
314 sq. cm
Answer:
Step-by-step explanation:
When the triangle is rotated about the side with a length of 8 cm, it forms a cone with a base radius equal to 4 cm and height equal to 6 cm.
Using the formula for the volume of a cone, V = 1/3 * πr^2h, where r is the radius and h is the height, we can find the volume of the resulting solid:
V = 1/3 * π * 4^2 * 6
V ≈ 100.53 cubic centimeters
To find the approximate base area, we need to calculate the area of the circle with a radius of 4 cm (the base of the cone):
A = πr^2
A ≈ 50.27 sq. cm
Therefore, the approximate base area of the resulting three-dimensional figure is about 50.27 sq. cm.
So, the closest option available in the given choices is 38 sq. cm, but the correct answer based on calculations is approximately 50.27 sq. cm.
Answer:
I just did the quiz. Look below.
Step-by-step explanation:
i need help on all of this
Answer: 1 1/12
Step-by-step explanation:
so you would subtract 2-1=1
Then you do 1/3-1/4=1/12
The answer would be 1 1/12
UR WELCOME
a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 139 like snickers, 184 like twix, 181 like reese's peanut butter cups, 129 like snickers and twix, 109 like twix and reese's peanut butter cups, 71 like snickers and reese's peanut butter cups, and 70 like all three kinds of chocolate candy. how many students like at most 2 kinds of these chocolate candies?
433 students like at most two types of these chocolate candies.
A survey of 500 high school students was conducted to determine their favorite chocolate candy.
139 students liked snickers, 184 liked Twix, 181 liked Reese's Peanut Butter Cups, 129 liked Snickers and Twix, 109 liked Twix and Reese's Peanut Butter Cups, 71 liked Snickers and Reese's Peanut Butter Cups, and 70 liked all three types of chocolate candy. So, how many students like at most two types of these chocolate candies?
Step-by-step explanation:
If you use the Principle of Inclusion-Exclusion, you can figure out how many students enjoy two or fewer candies. The PIE formula is as follows:
n(Snickers U Twix U Reese's) = n(Snickers) + n(Twix) + n(Reese's) - n(Snickers ∩ Twix) - n(Snickers ∩ Reese's) - n(Twix ∩ Reese's) + n(Snickers ∩ Twix ∩ Reese's)n(Snickers U Twix U Reese's)
= 139 + 184 + 181 - 129 - 109 - 71 + 70
n(Snickers U Twix U Reese's) = 503
Students who liked two or fewer types of candies can be found by subtracting the number of people who liked all three from the total number of individuals in the study who like any one candy.
503 - 70 = 433 students
Therefore, 433 students like at most two types of these chocolate candies.
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