To find the radius of the sphere passing through points A, B, C, and D in space, we can use the fact that the sphere will be the circumsphere of triangle ABC and triangle ABD.
Since BAC = BAD = CAD = 90, we know that triangle ABC and triangle ABD are both right triangles.
Using the Pythagorean theorem, we can find the length of BC and BD:
BC^2 = AB^2 + AC^2 = 6^2 + 6^2 = 72
BD^2 = AB^2 + AD^2 = 6^2 + 6^2 = 72
Since BC = BD, we know that triangle BCD is an isosceles triangle. Therefore, the altitude from vertex C to side BD will bisect BD, and the altitude from vertex B to side CD will bisect CD. Let E be the point where the altitudes intersect.
Now we can use the Pythagorean theorem again to find the length of CE:
CE^2 = BC^2 - BE^2 = 72 - (BD/2)^2 = 72 - 36 = 36
CE = 6
Since the sphere passes through point C, its center must be equidistant from points A, B, and D. Let O be the center of the sphere. Then we have:
OA = OB = OD
OA^2 = OC^2 + AC^2 = OC^2 + 36
OB^2 = OC^2 + BC^2 = OC^2 + 72
OD^2 = OC^2 + AD^2 = OC^2 + 36
Since OA = OB = OD, we can equate the expressions for OA^2, OB^2, and OD^2:
OC^2 + 36 = OC^2 + 72 = OC^2 + 36
72 = 2(OC^2 + 36)
OC^2 = 18
Therefore, the radius of the sphere is:
r = OC = sqrt(18) = 3sqrt(2)
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Please Help Quickly Hurry ASAP This is Geometry
What is the area of this figure?
___ units²
The calculated value of the area of this figure is 28 sq units
What is the area of this figure?From the question, we have the following parameters that can be used in our computation:
The composite figure
The area is the sum of the individual areas
The figure can be divided into two trapezoids
Using the above and the area formulas as a guide, we have the following:
Area = 1/2 * (3 + 5) * 2 + 1/2 * (3 + 7) * 4
Evaluate
Area = 28
Hence, the area is 28 sq units
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I need help please I'm stuck on this question
Answer:
84.3%
Step-by-step explanation:
Percentage of people completed the task under 40 s is(rounded) 84.3%
a caterer is competing for a company's business, the caterer selects a simple random sample of entrees, a simple random sample of sides, and a simple random sample of desserts for a tasting. the sample is a sample.
The sample is a three-stage cluster sample
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does the point (-3,3) lie inside, outside, or on the circle? the center of the circle is (-5,1) and the radius is 3. you must prove this ALGEBRAICALLY
yessss because as you can see the answer is what it is
According to a study on the effects of smoking by pregnant women on rates of asthma in their children, for expectant mothers who smoke 20 cigarettes per day, 22.7% of their children developed asthma by the age of two in the us. a biology professor at a university would like to test if the percentage is lower in another country. she randomly selects 335 women who only deliver one child and smoke 20 cigarettes per day during pregnancy in that country and finds that 68 of the children developed asthma by the age of two. in this hypothesis test.
In this hypothesis test, the test statistic, z = -0.9559 and the p-value = _________
Answer:
Step-by-step explanation:
The p-value in this hypothesis test is 0.3398.
To find the p-value for this hypothesis test, we will follow these steps:
1. Identify the null hypothesis (H0) and the alternative hypothesis (H1). In this case, H0: p = 0.227 (percentage of asthma in children is the same in both countries) and H1: p < 0.227 (percentage of asthma in children is lower in the other country).
2. Calculate the test statistic. In this case, the test statistic z is given as -0.9559.
3. Find the p-value associated with the test statistic. Since the alternative hypothesis is one-tailed (p < 0.227), we will look up the one-tailed p-value corresponding to the z-score -0.9559 in the standard normal (z) table or using a calculator.
Looking up the z-score in a table or using a calculator, we find that the p-value is approximately 0.1694.
So, in this hypothesis test, the test statistic, z = -0.9559 and the p-value = 0.1694.
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for a few weeks, a music producer kept track of newly released songs on a music streaming website. she recorded the music genre and number of times the song was played on its release date. 0-500 plays 501-1,000 plays country 7 7 rock 3 2 what is the probability that a randomly selected song had 501-1,000 plays given that the song was country?
So the probability that a randomly selected song had 501-1,000 plays given that the song was country is 7/12, or approximately 0.583.
To find the probability that a randomly selected song had 501-1,000 plays given that the song was country, we need to use conditional probability.
Using Bayes' theorem, we have:
P(B|A) = P(A|B) * P(B) / P(A)
We can find each of these probabilities from the given information:
P(A) = (7+3)/(7+3) = 1 (since all songs recorded were either country or rock)
P(B) = (7+2)/(7+3+2) = 9/12 (since 9 out of the 12 songs recorded had 501-1,000 plays)
P(A|B) = P(A and B) / P(B) = 7/9 (since out of the 9 songs with 501-1,000 plays, 7 were country)
Therefore,
P(B|A) = (7/9) * (9/12) / 1
P(B|A) = 7/12
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a bullet is shot from a rifle straight upward at a velocity of 1200 feet per second from a starting height of 5 feet. write an equation and find x intercept and vertex
Step-by-step explanation:
if you need to know the formula yourself, then this is actually physics and not just mathematics.
anyway, we assume this happens on the surface of Earth.
so, with Earth's gravity and such the formula for the height of the bullet at a certain time is
h(t) = -16t² + v0×t + staying height =
= -16t² + 1200t + 5
the x-intercept is the time, when the bullet falls back down and hits the ground. in other words. when it's height = 0.
0 = -16t² + 1200t + 5
a quadratic equation
ax² + bx + c = 0
has the genetic solution
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -16
b = 1200
c = 5
t = (-1200 ± sqrt(1200² - 4×-16×5))/(2×-16) =
= (-1200 ± sqrt(1,440,000 + 320))/-32 =
= (-1200 ± sqrt(1,440,320))/-32 =
= (-1200 ± sqrt(64×22505))/-32 =
= (-16×75 ± 8×sqrt(22505))/-32 =
= (75/2 ± 1/4 × sqrt(22505))
t1 = 75/2 + 1/4 × 150.0166657... = 75.00416644... seconds
t2 = 75/2 - 1/4 × 150.0166657... = -0.004166435... seconds
after about 75 seconds the bullet will hit the ground (x-intercept).
the t2 solution is the theoretical extension of the flight curve backwards in time (remember, the staying height is 5 ft, but using the shot graph and the corresponding accelerations the bullet would have started 0.004166435... seconds before the shot on the ground, and this is therefore also an x-intercept.
for the vertex (the max. height of the bullet) we need the zero of the first derivation (the extreme point of the function).
h'(t) = -32t + 1200 = 0
32t = 1200
t = 1200/32 = 37.5 seconds
so, after 37.5 seconds the bullet reaches is maximum height, which is
-16×37.5² + 1200×37.5 + 5 = 22,505 ft
so, the vertex is (37.5, 22505).
A factory makes 8000 tubs of ice cream, each tub contains 500 millilitres. How many litres of ice cream does the factory make?
Answer:
4,000 L (4 thousand)
Step-by-step explanation:
1 tub = 500 mL
2 tub = 1000 mL = 1 L
8000 tubs = 4,000,000 mL = 4,000 L
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Bill bought pounds of cheese
A cone is sliced in such a way that the plane cuts in a direction parallel to the base, what is the resulting cross section?
When a cone is sliced in a direction parallel to the base, the resulting cross section is a circle.
A plane parallel to the base will intersect the curved surface of the cone at the same distance from the vertex all the way around, creating a circular shape.
This type of cross section is called a parallel cross section, and it is one of three types of cross sections that can be made when slicing a cone (the others being perpendicular and oblique).
In practical terms, this means that if you were to slice a cone-shaped cake or piece of fruit parallel to the base, you would end up with circular slices. This type of slicing can also be useful in engineering and construction, as it can create cylindrical shapes that can be used as columns or supports.
In summary, when a cone is sliced parallel to the base, the resulting cross section is a circle, and this type of slicing can be useful in a variety of applications.
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when a test for steroids is given to soccer players, 93% of the players taking steroids test positive and 12% of the players not taking steroids test positive. suppose that 5% of soccer players take steroids. what is the probability that a soccer player who tests positive takes steroids? (enter the value of the probability in decimal format and round the final answer to three decimal places.)'
The probability that a soccer player who tests positive takes steroids is approximately 0.279 or 27.9%.
To solve this problem, we can use Bayes' theorem:
P(Steroids|Positive) = P(Positive|Steroids) * P(Steroids) / P(Positive)
where:
P(Steroids|Positive) = probability of taking steroids given a positive test result
P(Positive|Steroids) = probability of testing positive given that the player takes steroids (93%)
P(Steroids) = probability of a soccer player taking steroids (5%)
P(Positive) = overall probability of testing positive (calculated below)
To calculate P(Positive), we need to use the law of total probability:
P(Positive) = P(Positive|Steroids) * P(Steroids) + P(Positive|No Steroids) * P(No Steroids)
where:
P(Positive|No Steroids) = probability of testing positive given that the player does not take steroids (12%)
P(No Steroids) = probability of a soccer player not taking steroids (100% - 5% = 95%)
Plugging in the values, we get:
P(Positive) = 0.93 * 0.05 + 0.12 * 0.95 = 0.1165
Now we can calculate P(Steroids|Positive):
P(Steroids|Positive) = 0.93 * 0.05 / 0.1165 = 0.398
Therefore, the probability that a soccer player who tests positive takes steroids is 0.398 (rounded to three decimal places).
To find the probability that a soccer player who tests positive takes steroids, we can use Bayes' Theorem:
P(A|B) = (P(B|A) * P(A)) / P(B)
Here, let A be the event "player takes steroids" and B be the event "player tests positive."
We are given:
- P(B|A) = 0.93 (93% of players taking steroids test positive)
- P(A) = 0.05 (5% of soccer players take steroids)
- P(B|A') = 0.12 (12% of players not taking steroids test positive)
To find P(B), we can use the Law of Total Probability:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')
Since P(A') = 1 - P(A) = 1 - 0.05 = 0.95, we have:
P(B) = (0.93 * 0.05) + (0.12 * 0.95)
Now, we can use Bayes' Theorem to find P(A|B):
P(A|B) = (0.93 * 0.05) / ((0.93 * 0.05) + (0.12 * 0.95))
P(A|B) ≈ 0.279
Therefore, the probability that a soccer player who tests positive takes steroids is approximately 0.279 or 27.9%.
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Select the correct answer. Consider functions f and g. = -3x² + 4x + 4 * (-7x - 7) g(x) Which expression is equal to f(x) + g(x)? = O A. A. -10x² + 4x - 3 O B. -102² 3x + 4 O c. C. 4x² 3x + 4 O D. -3x² - 3x - 3
The expression that is equal to f(x) + g(x) is -3x² - 3x - 3
Which expression is equal to f(x) + g(x)?From the question, we have the following parameters that can be used in our computation:
f(x) = -3x² + 4x + 4
g(x) = -7x - 7
The expression that is equal to f(x) + g(x) is represented as
f(x) + g(x) = -3x² + 4x + 4 -7x - 7
When the like terms are evaluated, we have
f(x) + g(x) = -3x² - 3x - 3
Hence, the expression is f(x) + g(x) = -3x² - 3x - 3
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some data mining algorithms require that variables are standardized (sometimes called normalized) to zero mean and standard deviation of 1.0. what is the reason for this?
The reason why some data mining algorithms require that variables are standardized to zero mean and standard deviation of 1.0 is because it helps to normalize the data and make it more comparable across different variables.
Standardizing the data helps to remove the impact of the scale of the variables on the analysis, allowing for more accurate comparisons and correlations between variables. By doing this, it ensures that no one variable has an undue influence on the results of the analysis. Standard deviation is a statistical measure that is used to measure the amount of variability or dispersion in a dataset. When data is standardized, it allows for a more accurate assessment of the relationship between variables and can improve the accuracy of the analysis. Overall, standardizing variables is a crucial step in the data mining process, as it helps to ensure that the results of the analysis are reliable and accurate.
The reason some data mining algorithms require variables to be standardized (or normalized) to a zero mean and a standard deviation of 1.0 is to ensure consistent and comparable scales for all variables involved. Standardizing variables helps in improving the performance and accuracy of the algorithms.
When variables have different scales or units, it can be challenging for algorithms to interpret their relative importance accurately. By transforming variables to have a zero mean and a standard deviation of 1.0, the algorithms can more effectively process and analyze the data. This standardization process is particularly important for distance-based and gradient-based algorithms, where scale differences can significantly impact the results.
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c . main 2.7.1: sphere volume. given sphereradius, compute the volume of a sphere and assign spherevolume with the result. use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division. volume of sphere
sphere volume = (4.0 / 3.0) * 3.14159 * sphere radius ** 3
Here's a step-by-step explanation using the terms "radius", "volume", and "division":
1. Given the sphere's radius (sphere radius), we'll use the formula for calculating the volume of a sphere: V = (4.0 / 3.0) * π * r^3, where V is the sphere's volume and r is its radius.
2. Perform floating-point division by using (4.0 / 3.0) instead of (4 / 3). The floating-point division ensures a more accurate result since it retains decimal values.
3. Compute the sphere's volume (sphere volume) using the formula: sphere volume = (4.0 / 3.0) * π * (sphere radius)^3.
4. Assign the calculated value to the sphere volume.
By following these steps and using the given formula, you can calculate the volume of a sphere with the specified radius.
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Confidence Intervals Using the T-Distribution LEARNING OBJECTIVE: Calculate a confidence interval using the t-distribution. Morgan sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. Using a 90% confidence level, she also found that t = 1.660. confidence interval = t* s/n A 90% confidence interval calculates that the average number of hours of sleep for working college students is between _________ hours. Answer choices are rounded to the hundredths place. O a.) 6.15 and 6.85 O b.) 6.46 and 6.85 O c.) 6.08 and 6.92 O d.) 6.46 and 6.54
Rounded to the hundredth place, this gives us answer choice (D), which is the correct answer. So we can say with 90% confidence that the average number of hours of sleep for working college students is between 6.46 and 6.54 hours.
To calculate the confidence interval using the t-distribution, we use the formula:
Confidence interval = sample mean ± (t-score)*(standard error)
where the standard error is calculated as the standard deviation divided by the square root of the sample size, i.e.,
standard error = standard deviation / sqrt(sample size)
In this case, Morgan sampled 101 students and found an average of 6.5 hours of sleep with a standard deviation of 2.14. So the standard error is:
standard error = 2.14 / sqrt(101) = 0.213
The t-score for a 90% confidence level with 100 degrees of freedom (n-1) is 1.660, as given in the problem.
Therefore, the confidence interval is:
Confidence interval = 6.5 ± (1.660)*(0.213) = (6.46, 6.54).
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2
Select the correct answer from each drop-down menu.
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides.
The heights of the pyramids are the same.
The volume of pyramid A is
volume of pyramid B is
the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new
the volume of pyramid A.
The volume of pyramid A is twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.
How to calculate the volume of a pyramid?In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:
Volume = 1/3 × b × h
Where:
h represent the height of a pyramid.b represent the base area of a pyramid.Volume of pyramid A = (10 × 20 × h)/3 = 200h/3
Volume of pyramid B = (10 × 10 × h)/3 = 100h/3
Since the heights of the two (2) pyramids are equal, we would substitute them as follows;
Volume of pyramid A = (200 × 3 × Volume of pyramid B)/(100 × 3)
Volume of pyramid A = 2 × Volume B
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Complete Question;
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.
The volume of pyramid A is ____ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is ______the volume of pyramid A.
Why will there always be an upside down triangle? What is it about how the pattern is formed that makes this always true?
The reason that there always be an upside down triangle in the Sierpiński triangle is because of its recursive process or what we call the self-similar nature of all of its pattern.
What is the Sierpiński triangle about?The pattern of the Sierpiński triangle is seen as a product the result of repeatedly removing certain triangles from an original equilateral triangle. The process involves dividing an equilateral triangle into four smaller triangles by connecting their midpoints during each iteration.
Note that, afterwards the triangle located at the center is eliminated. This procedure is repeated endlessly, where every triangle that remains is split into four smaller triangles, and the middle one is extracted.
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Look at these details from a paragraph about the same topic:
Many people enjoy pies filled with peaches, apples, or blueberries.
Cobbler is a popular dessert of baked fruit topped with pieces of crust.
Sherbet, a cold treat made of fruit or fruit juice, is often enjoyed in the summer.
Choose the main idea that ties all the details together.
The main idea that ties all the details together is that there are various types of desserts that are made from fruit or fruit juice, and they are enjoyed by many people.
The paragraph is about different types of desserts that are made from fruit or fruit juice. The details in the paragraph mention three specific desserts: pies filled with peaches, apples, or blueberries; cobbler, which is a baked fruit dessert topped with pieces of a crust; and sherbet, which is a cold treat made of fruit or fruit juice that is often enjoyed in the summer.
Despite their differences in preparation and presentation, all of these desserts have one thing in common: they are made using fruit or fruit juice. The paragraph suggests that fruit-based desserts are popular among many people and can be enjoyed in a variety of forms.
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En el vestíbulo de entrada hay un mostrador para la venta de entradas, el arquitecto jefe le
plantea a uno de sus ayudantes que determine cuánto mide de ancho con las siguientes
condiciones: su valor en metros es un número tal que su potencia al cuadrado sumado a su
potencia a la cuarta dará 90. El mostrador tiene que medir de ancho:
The width of the counter is 3 meters or 9/3 meters as a fraction considering the condition that its value in meters is a number such that its power squared added to its power to the fourth will give 90.
Let's represent the width of the counter in meters as "x". As per the given condition, we can form the equation:
x² + [tex]x^4[/tex] = 90
Simplifying the equation, we get:
[tex]x^4[/tex] + x² - 90 = 0
Now, we can factor the equation as:
(x² - 9)(x² + 10) = 0
So, the possible values of "x" are:
x² = 9 or x² = -10
Since the width of the counter cannot be negative, we can ignore the second solution. Therefore, we have:
x² = 9
x = ±√9
x = ±3
Since the width of the counter cannot be negative, the only possible solution is:
x = 3
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The question is -
In the entrance hall, there is a counter for the sale of tickets, the chief architect will ask one of your assistants to determine how wide it is with the following conditions: its value in meters is a number such that its power squared added to its power to the fourth will give 90. Does the counter have to measure the width?
as a manager, when faced with ethical crises you shouldmultiple choice a. focus on issues most relevant to stockholders only. b. wait for the other party to make the first move. c. take the initiative to address the problem.d. cover up as much as possible.
As a manager, when faced with ethical crises in time, you should:
C. Take the initiative to address the problem.
As a manager, when faced with ethical crises in time, you should take the initiative to address the problem.
It is important to consider the impact on multiple stakeholders, including employees, customers, and the community. Ignoring the issue or attempting to cover it up can lead to further complications and damage to the company's reputation.
It is important to address the issue head-on and take appropriate actions to prevent similar situations from occurring in the future.
This approach ensures that you proactively identify and resolve ethical issues in a timely and responsible manner, rather than focusing only on stockholders, waiting for others to act, or attempting to cover up the situation.
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a theater is staging a series of 12 different plays. you wawnt to attend at least 3 of the plays. how many different combinations of plays can you attend?
You can attend 4,941 different combinations of plays at the theater.
To find the different combinations of plays that you can attend, we need to use the combination formula. Since you want to attend at least 3 plays, we can calculate the combinations for attending 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 plays.
For attending 3 plays, the number of combinations is 220.
For attending 4 plays, the number of combinations is 495.
For attending 5 plays, the number of combinations is 792.
For attending 6 plays, the number of combinations is 924.
For attending 7 plays, the number of combinations is 792.
For attending 8 plays, the number of combinations is 495.
For attending 9 plays, the number of combinations is 220.
For attending 10, 11, or 12 plays, there is only one combination each.
Therefore, the total number of different combinations of plays that you can attend is:
220 + 495 + 792 + 924 + 792 + 495 + 220 + 1 + 1 + 1 = 4,941
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if p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?
To solve this problem, we need to first find the prime factorization of each integer from 1 to 30. We can then count the number of times the prime factor 3 appears in each of these prime factorizations.
The prime factorization of 1 is 1, which does not contain the prime factor 3. The prime factorization of 2 is 2, which also does not contain the prime factor 3. The prime factorization of 3 is 3, which contains one factor of 3. Continuing in this way, we find that the prime factorization of each integer from 1 to 30 contains a certain number of factors of 3.
To find the greatest integer k for which 3k is a factor of p, we need to find the maximum value of k such that there are at least k factors of 3 in the prime factorization of p. We can do this by counting the number of factors of 3 in each prime factorization and finding the minimum value of these counts.
The prime factorization of p is:
p = 1 × 2 × 3 × ... × 30
To find the number of factors of 3 in this product, we can count the number of times the prime factor 3 appears in each of the factors being multiplied together. For example, the factor 9 contains two factors of 3, and the factor 27 contains three factors of 3.
Counting the number of factors of 3 in each factor from 1 to 30, we get:
1: 0 factors of 3
2: 0 factors of 3
3: 1 factor of 3
4: 0 factors of 3
5: 0 factors of 3
6: 1 factor of 3
7: 0 factors of 3
8: 0 factors of 3
9: 2 factors of 3
10: 1 factor of 3
11: 0 factors of 3
12: 1 factor of 3
13: 0 factors of 3
14: 0 factors of 3
15: 1 factor of 3
16: 0 factors of 3
17: 0 factors of 3
18: 2 factors of 3
19: 0 factors of 3
20: 0 factors of 3
21: 1 factor of 3
22: 0 factors of 3
23: 0 factors of 3
24: 1 factor of 3
25: 0 factors of 3
26: 0 factors of 3
27: 3 factors of 3
28: 0 factors of 3
29: 0 factors of 3
30: 1 factor of 3
The minimum number of factors of 3 among these integers is 1, which occurs for the factors 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. Therefore, the greatest integer k for which 3k is a factor of p is 10.
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In Exercises 17-22, determine which sets of vectors are orthonormal. If a set is only orthogonal, normalize the vectors to produce an orthonormal set.22 [ 1/√18] [ 1/√2 ] [ -2/3 ] [ 4/√18] [ 0 ] [ -2/3]1/√18 -1/√2 -2/3
The set of vectors {[1/√18], [1/√2], [-2/3]} and {[4/√18], [0], [-2/3]} is an orthonormal set.
To verify whether a set of vectors is orthonormal, we need to check two conditions: orthogonality and normalization. Orthogonality means that the dot product of any two distinct vectors in the set is zero. Normalization means that the magnitude or length of each vector is 1.
First, we check for orthogonality. The dot product of the first and second vectors is:
[1/√18] * [4/√18] + [1/√2] * [0] + [-2/3] * [-2/3] = 4/18 + 0 + 4/9 = 8/18
The dot product of the first and third vectors is:
[1/√18] * [1/√2] + [1/√2] * [(-2/3)] + [-2/3] * [(-1/√18)] = 1/√36 - 2/3√2 - 2/3√2 = 0
The dot product of the second and third vectors is:
[4/√18] * [1/√2] + [0] * [-2/3] + [-2/3] * [(-1/√18)] = 2/√36 + 2/√36 = 4/√36
Since the dot product of any two distinct vectors is not always zero, the set is not orthogonal. We need to normalize the vectors to produce an orthonormal set.
To normalize a vector, we divide it by its magnitude. The magnitude of a vector [a, b, c] is √(a^2 + b^2 + c^2). Thus, the normalized version of the first vector is:
[1/√18, 1/√2, -2/3] / √[(1/18) + (1/2) + (4/9)] = [1/√2, √(2/9), -2/√9]
The normalized version of the second vector is:
[4/√18, 0, -2/3] / √[(16/18) + 0 + (4/9)] = [2/√9, 0, -2/√9]
The normalized version of the third vector is:
[1/√18, -1/√2, -2/3] / √[(1/18) + (1/2) + (4/9)] = [1/√2, -√(2/9), -2/√9]
We can now check for orthogonality again:
The dot product of the first and second vectors is:
[1/√2] * [2/√9] + [√(2/9)] * [0] + [-2/√9] * [(-2/√9)] = 0
The dot product of the first and third vectors is:
[1/√2] * [1/√2] + [-√(2/9)] * [-2/√9] + [-2/√9] * [-2/√9] = 1/2 + 2/9 + 4/9 = 1
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Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3052.08
Step-by-step explanation:
v = 4/3[tex]\pi r^{3}[/tex]
v = [tex]\frac{4(3.14)9^{3} }{3}[/tex]
v = [tex]\frac{4(3.14)(729)}{3}[/tex]
v = [tex]\frac{9156.24}{3}[/tex]
v = 3052.08
Helping in the name of Jesus.
Answer:
The answer for Volume is 3052.08in³
Step-by-step explanation:
Volume of sphere=4/3pir³
V=4_3×3.14×9³
V=4/3×9×9×9×3.14
V=4×3×9×9×3.14
V=12×81×3.14
V=3052.08in³
The graph of the function y = 2x2 + bx + 8 is shown. What is the value of b? Enter your answer in the box. In the xy graph, the range of the x axis is minus three to five by increment of one. The range of the y axis is minus ten to six by increment of two. On x axis minus two, two, and four are labeled and on the y axis minus eight, minus four, and four are labeled. The curve is parabola open upwards. The vertex of the parabola is (3, -10), The parabola passes through the points (2, -8) and (4, -8). b =
The value of b in the given function is 4.
How to calculate the valueSince we know that the coefficient of the term is 2, we can plug in the values of a and b into the equation for the axis of symmetry.
We also know that the vertex of the parabola lies on the axis of symmetry, and we can see from the graph that the vertex is at the point.
Since x = -1 and y = 6, this will be;
6 = 2(-1)² + b(-1) + 8
b = 4
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y = 3x + 9; if x = 6
The hexagonal prism below has a height of 9 units and a volume of 216.9 units³. Find the area of one of its bases.
Answer:
24.1 square units
Step-by-step explanation:
You want the base area of a prism with height 9 units and volume 216.9 units³.
VolumeThe formula for the volume of a prism is ...
V = Bh
where B is the area of the base, and h is the height. Solving for the base area, we have ...
B = V/h = (216.9 u³)/(9 u) = 24.1 u²
The area of one of the bases is 24.1 square units.
What is true about sampling in statistics?
A. As the sample size increases, the variability increases
B. Sample parameters vary and are known
C. Sample Values are estimated from known population
Sample Values are estimated from known population is true about sampling in statistics.
In statistics, sampling refers to the process of selecting a subset of individuals or objects from a larger population. The sample is used to estimate or make inferences about the population from which it was drawn. Option A is false because as the sample size increases, the variability generally decreases as the sample better represents the population. Option B is false because sample statistics (such as the sample mean or sample standard deviation) vary from sample to sample and are estimated from the data in the sample. Option C is true because sample values (such as the sample mean or sample proportion) are estimated from the known population values, and this estimation process involves sampling error due to random variability in the sample.
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a check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had tvs, and 21% had both a tv and a refrigerator. what's the probability that a randomly selected dorm room has either a refrigerator or a tv (or both)? please enter your answer as a decimal, rounded to two places after the decimal point.
The probability that a randomly selected dorm room has either a refrigerator or a TV (or both) is 0.69, or 69% (rounded to two decimal places).
The probability of a aimlessly named dorm room having either a refrigerator or a television( or both) is0.69, as calculated from the given data. This implies that nearly 70 of the dorm apartments have at least one of these amenities. We can also interpret this as saying that having a television or a refrigerator is a fairly common circumstance in the dorm apartments on this particular council lot.
P(R) = 0.38 (38% had refrigerators)
P(T) = 0.52 (52% had TVs)
P(R and T) = 0.21 (21% had both a TV and a refrigerator)
Substituting these values into the equation, we get:
P(R or T) = 0.38 + 0.52 - 0.21
P(R or T) = 0.69
It's worth noting that having both a television and a refrigerator in a dorm room isn't as common, with only 21 of the apartments having both amenities. This could be due to a number of factors, similar as space constraints or particular preference. still, it's still important to fete that having both amenities can give fresh convenience and comfort to the scholars living in these apartments.
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Which is the equation in slope-intercept form of a line that contains points D and E?
The equation in slope-intercept form of a line that contains points D and E is y = x.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 2)/(4 - 2)
Slope (m) = 2/2
Slope (m) = 1.
At data point (2, 2) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 1(x - 2)
y = x - 2 + 2
y = x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.