The point P where the function f(x, y, z) = xºy$z reaches the maximum value for x, y, z > 0 on the unit sphere is (1/√3, 1/√3, 1/√3).
To find the point P where the function f(x, y, z) = [tex]x^y^z[/tex] reaches the maximum value for x, y, z > 0 on the unit sphere, we can use Lagrange multipliers.
Let g(x, y, z) = x² + y² + z² - 1 be the equation of the unit sphere. We want to maximize f(x, y, z) subject to the constraint g(x, y, z) = 0.
Using Lagrange multipliers, we set up the system of equations
∂f/∂x = λ∂g/∂x
∂f/∂y = λ∂g/∂y
∂f/∂z = λ∂g/∂z
g(x, y, z) = 0
Taking partial derivatives, we get
[tex]y^z * x^{y-1}[/tex]= 2λx
[tex]x^z * y^{z-1}[/tex] = 2λy
[tex]x^y * z^{y-1}[/tex]* ln(z) = 2λz
Simplifying these equations and dividing them by each other, we get:
y ln(x)/x = x ln(y)/y
y ln(z)/z = z ln(y)/y
x ln(z)/z = z ln(x)/x
From the first equation, we get:
y ln(x) = x ln(y)
Taking the exponential of both sides, we get
[tex]x^y[/tex] = yˣ
Similarly, from the second equation, we get
[tex]y^z[/tex] = [tex]z^y[/tex]
And from the third equation, we get
[tex]x^z[/tex] = zˣ
These equations suggest that x, y, and z should all be equal to each other. To confirm this, we can take the logarithm of both sides of x^y = yˣ to get:
y ln(x) = x ln(y)
ln(x)/x = ln(y)/y
This function has a maximum at x = y, which implies that x = y = z. Furthermore, since we are looking for a point on the unit sphere, we have x² + y² + z² = 1, which gives us:
x = y = z = 1/√3
Therefore, the point P is given by (1/√3, 1/√3, 1/√3).
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30 POINTS
WHAT PRODUCTS ARE DEFINED FOR THESE MATRICES
The products that are defined are given as follows:
LP, LQ.
The products that are not defined are given as follows:
NM, QM.
When we can multiply matrices?The multiplication of two matrices is possible when the number of columns of the first matrix is equals to the number of rows of the second matrix.
The dimensions of each matrix are given as follows:
L = 2 x 2.M = 4 x 2.N = 1 x 4.P = 2 x 2.Q = 2 x 1.Hence the defined products are:
LP, LQ.
The non-defined products are:
NM, QM.
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if we select one at random, what is the probablitlity it is red or orange
Therefore, the probability of selecting a red or orange item at random depends on the total number of items and the number of red and orange items and can be calculated by dividing the total number of red and orange items by the total number of items.
The probability of selecting a red or orange item at random depends on the total number of items and the number of red and orange items. Let's say there are 10 items in total and 4 of them are red, while 2 are orange. The probability of selecting a red or orange item would be 6/10 or 0.6. This means that there is a 60% chance of selecting either a red or orange item. In conclusion, the probability of selecting a red or orange item at random depends on the total number of items and the number of red and orange items and can be calculated by dividing the total number of red and orange items by the total number of items.
Therefore, the probability of selecting a red or orange item at random depends on the total number of items and the number of red and orange items and can be calculated by dividing the total number of red and orange items by the total number of items.
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The cards are well shuffled and you randomly draw one card. a. How many elements are there in the sample space? b. Find the probability of drawing a green card.
Therefore, the probability of drawing a green card is 0.0769 or 7.69%.
a. To determine the number of elements in the sample space, we need to know the number of cards in the deck and the possible outcomes for each card. Let's assume that the deck contains 52 cards with four different suits (clubs, diamonds, hearts, spades) and 13 cards in each suit (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king).
The possible outcomes for each card are the suit and the rank. Therefore, there are 4 possible outcomes for the suit and 13 possible outcomes for the rank. Using the multiplication principle, we can determine the number of elements in the sample space by multiplying the number of possible outcomes for the suit by the number of possible outcomes for the rank:
Number of elements in the sample space = 4 x 13 = 52
Therefore, there are 52 elements in the sample space.
b. To find the probability of drawing a green card, we need to know how many green cards there are in the deck and how many cards there are in total. Let's assume that there are 4 different colors of cards in the deck: red, blue, yellow, and green. We also assume that there are 13 cards of each color in the deck.
Therefore, there are 4 green cards in the deck. The probability of drawing a green card can be calculated by dividing the number of green cards by the total number of cards in the deck:
Probability of drawing a green card = number of green cards / total number of cards
Probability of drawing a green card = 4 / 52
Probability of drawing a green card = 0.0769 or 7.69%
Therefore, the probability of drawing a green card is 0.0769 or 7.69%.
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Judah asked 200 students if they play basketball 60 said yes 140 said no, determine the percent of students who played basketball
Answer:
Out of the 200 students Judah asked, 60 said yes when asked if they play basketball while 140 said no. To determine the percentage of students who played basketball, we can divide the number of students who said yes by the total number of students and then multiply by 100.
So, the percentage of students who played basketball is (60/200) x 100 = 30%.
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use the ratio test to determine whether the series is convergent or divergent. [infinity] (−5)n n2 n = 1
The series ∑(-5)^n/(n^2) is convergent.
The ratio test is a method for determining whether an infinite series converges or diverges. It involves taking the limit of the absolute value of the ratio of successive terms:
lim n→∞ |an+1/an|
If this limit is less than 1, then the series converges. If it is greater than 1, then the series diverges. If it is exactly equal to 1, then the test is inconclusive and another method must be used.
For the series ∑(-5)^n/(n^2), we have:
|a(n+1)/an| = |-5|^(n+1)/(n+1)^2 * n^2/(-5)^n
Simplifying this expression gives:
|a(n+1)/an| = (25(n^2))/((n+1)^2)
Taking the limit as n approaches infinity gives:
lim n→∞ |a(n+1)/an| = 25
Since the limit is greater than 1, the series diverges by the ratio test.
Therefore, we conclude that the series ∑(-5)^n/(n^2) is convergent.
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What is the annual yield of 15%
compounded monthly? (round to 4
decimal places and write your answer
as a %)
[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 15\%\to \frac{15}{100}\dotfill &0.15\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12 \end{cases} \\\\\\ \left(1+\frac{0.15}{12}\right)^{12}-1\implies 1.0125^{12}-1\approx 0.1608\hspace{5em}\stackrel{ 0.1608 ~~ \times ~~ 100 }{\approx \text{\LARGE 16.08\%}}[/tex]
Your teacher states that your model will meet the state regulations. Clearly show that your teacher s correct including calculations and explanations. Pls help me im stuck :)
The length of the hypotenuse is approximately 50.16.
For the slope of the given triangle,
In general slope = Δy(horizontal)/Δx(verticle)
The slope = 4/50 = 1/12.5
This slope is under state regulation since it falls between the standard ratio.
As we can see in the given right angle triangle that is made in the given model,
the base is 50 and the height is 4, so for the hypotenuse,
Let's label the hypotenuse as 'c.'
We have:
[tex]y^2 = 50^2 + 4^2\\\\y^2 = 2500 + 16\\\\y^2 = 2516[/tex]
To find the value of 'y,' we take the square root of both sides:
y ≈ √(2516)
y ≈ 50.16
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a simple random sample of 64 concert tickets were drawn from a normal population. the mean and standard deviation of the sample were $120 and $25 respectivlly. estimate the population mean
95% confidence that the population means lies between $110.25 ($120 - $9.75) and $129.75 ($120 + $9.75).
To estimate the population mean, we can use the sample mean as an unbiased estimate. Therefore, the estimated population mean is also $120. However, to calculate the margin of error for this estimate, we can use the formula:
The margin of error = (z-score) x (standard deviation / square root of sample size)
Since the population is assumed to be normal, we can use the z-distribution. For a 95% confidence level, the z-score is 1.96. Substituting the given values, we get:
Margin of error = 1.96 x (25 / √64) = 9.75
Therefore, we can say with 95% confidence that the population mean lies between $110.25 ($120 - $9.75) and $129.75 ($120 + $9.75).
It's important to note that this is only an estimate and the true population mean could still be outside of this range. However, with a 95% confidence level, we can be fairly certain that our estimate is accurate within this range.
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in compound time signatures the top number represents the number of beats per measure. select one: true false
True. In compound time signatures, the top number represents the number of beats per measure. Compound time signatures are typically used for music that has a more complex rhythmic structure, and they are characterized by the subdivision of each beat into three equal parts (known as triplets).
The most common compound time signatures are 6/8, 9/8, and 12/8, with each representing six, nine, and twelve beats per measure respectively.
In 6/8 time, for example, there are two beats per measure, each of which is subdivided into three equal parts. This results in a feeling of two larger beats, each consisting of three smaller beats. In 9/8 time, there are three beats per measure, each of which is subdivided into three equal parts. This results in a feeling of three larger beats, each consisting of three smaller beats. Similarly, in 12/8 time, there are four beats per measure, each of which is subdivided into three equal parts, resulting in a feeling of four larger beats, each consisting of three smaller beats.
Overall, the top number in a compound time signature represents the number of larger beats per measure, while the bottom number represents the duration of each beat (usually an eighth note).
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Mike’s fitness center charges $30 per month for a membership. All-day fitness club charges $22 a month plus an $80 starting fee. Write an equation that represents Mike’s fitness center charges
The equation that represents Mike's fitness center charges is C = 30, where C is the cost of a membership in dollars.
This equation indicates that the cost of a membership at Mike's fitness center is a fixed amount of $30 per month, regardless of the number of visits or services used by the member.
This pricing model is commonly used in the fitness industry and provides a simple and straightforward option for those who only need access to basic facilities and equipment. However, for those who require additional services or amenities, such as personal training or specialized classes, a different pricing model may be more appropriate
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The equation that represents Mike's fitness center charges is C = 30, where C is the cost of a membership in dollars.
This equation indicates that the cost of a membership at Mike's fitness center is a fixed amount of $30 per month, regardless of the number of visits or services used by the member.
This pricing model is commonly used in the fitness industry and provides a simple and straightforward option for those who only need access to basic facilities and equipment. However, for those who require additional services or amenities, such as personal training or specialized classes, a different pricing model may be more appropriate
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Surface area: How much canvas is needed to make an a-frame tent that is 4 ft high with a rectangular floor 6 ft wide and 9 ft long?
Answer:
Step-by-step explanation:
To calculate the surface area of an A-frame tent with a rectangular floor, you need to find the area of each of its three faces: the front, the back, and the roof.Assuming that the A-frame tent has a symmetrical design, the front and the back will be identical triangles with a base of 6 feet and a height of 4 feet. To find the area of one of these triangles, you can use the formula for the area of a triangle: A = 1/2 * base * height. Therefore, the area of one of the triangular faces is:A_front/back = 1/2 * 6 ft * 4 ft = 12 ft²The roof of the A-frame tent is also a triangle, but with a base of 9 feet and a height that is half of the tent's height (since the tent is symmetrical). So, the height of the roof triangle is 2 feet, and its area is:A_roof = 1/2 * 9 ft * 2 ft = 9 ft²To find the total surface area of the tent, you simply need to add up the areas of the three faces:Total surface area = 2 * A_front/back + A_roof
= 2 * 12 ft² + 9 ft²
= 33 ft²Therefore, you would need at least 33 square feet of canvas to make the A-frame tent described.
In Nkubu High School cach lesson in Junior Secondary and Senior Secondary classes last 30minutes and 40minutes respectively. The first time the bells ring at the same time, the children go out for tea break. If the lessons for the whole school starts at 8.00am. a) At what time does tea break start. 1
Tea break in Nkubu High School starts at 10:00am, which is two hours after the start of the school day. The first time the bells ring at the same time for Junior Secondary and Senior Secondary classes is the signal for tea break.
For Junior Secondary (JS) classes, each lesson lasts for 30 minutes. Therefore, if the school starts at 8:00am, the first lesson for JS will end at:
8:00am + 0:30hrs = 8:30am
For Senior Secondary (SS) classes, each lesson lasts for 40 minutes. Therefore, if the school starts at 8:00am, the first lesson for SS will end at:
8:00am + 0:40hrs = 8:40am
Since the first time the bells ring at the same time, the children go out for tea break, the tea break will start at the earliest common multiple of 30 and 40, which is 120.
Therefore, tea break will start 120 minutes after 8:00am, which is:
8:00am + 2:00hrs = 10:00am
So, tea break will start at 10:00am.
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Statistics software can be used to find the five-number summary of a data set. Here is an example of MINITAB's descriptive statistics summary for a variable stored in column 1 (C1) of MINITAB's worksheet. (a) Use the MINITAB output to calculate the interquartile range. (b) Are there any outliers in this set of data?
The five-number summary, as shown in the MINITAB output, includes the minimum value, Q1 (the first quartile), the median (Q2), Q3 (the third quartile), and the maximum value.
To calculate the interquartile range (IQR), we need to find the difference between Q3 and Q1. In this case, Q1 is 6 and Q3 is 11, so the IQR is 5.
To determine if there are any outliers in the data set, we can use the rule that any data points that are more than 1.5 times the IQR below Q1 or above Q3 are considered outliers. In this case, the lower limit would be 6 - (1.5 x 5) = -1.5 and the upper limit would be 11 + (1.5 x 5) = 18.5. Looking at the data in column 1, we can see that there are no values that fall outside of these limits, so there are no outliers in this set of data.
Using statistics software to calculate the five-number summary, IQR, and identify outliers is a quick and efficient way to analyze data. This information can provide valuable insights into the distribution of the data and help identify any potential issues or trends that need to be addressed.
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what is the probability the child will catch 10 or more balls?
The probability that the child will catch 10 or more balls in 20 attempts, assuming a 0.2 probability of catching a ball on any single attempt, is very small, approximately 0.00014.
The probability that the child will catch 10 or more balls can be calculated using the binomial distribution.
Let X be the number of balls caught by the child in a total of 20 attempts. The probability of catching a ball on any single attempt is p = 0.2, assuming that each attempt is independent of the others.
The probability of catching exactly k balls in 20 attempts is given by the binomial distribution formula:
P(X = k) = (20 choose k) * p^k * (1-p)^(20-k)
where (20 choose k) is the binomial coefficient, which is equal to 20!/(k!(20-k)!).
The probability of catching 10 or more balls can be calculated as the sum of the probabilities of catching 10, 11, 12, ..., 20 balls:
P(X ≥ 10) = P(X = 10) + P(X = 11) + ... + P(X = 20)
Using a calculator or computer software, this probability can be found to be approximately 0.00014 (rounded to five decimal places).
Therefore, the probability that the child will catch 10 or more balls in 20 attempts, assuming a 0.2 probability of catching a ball on any single attempt, is very small, approximately 0.00014.
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Complete the table to find the standard deviation of jamies rebounds. x= 6 8 8 8 9 10 11 12 13 15 (SOLVED EVERYTHING just need the last sum at the bottom!!)
According to the information, we can infer that the sum of the squared deviations from the mean is 88.
How to identify the standard deviation of the Jamie's rebunds?To find the standard deviation of Jamie's rebounds, we need to calculate the sum of the squared deviations from the mean. In this case, we have to calculate the mean of the data set with the following procedure:
Mean = (6 + 8 + 8 + 8 + 9 + 10 + 11 + 12 + 13 + 15) / 10Mean = 100 / 10Mean = 10Also, we have to calculate the deviation of each value from the mean. We subtract the mean from each value:
Deviation = x - MeanUsing the given data set, the deviations from the mean are:
(6 - 10), (8 - 10), (8 - 10), (8 - 10), (9 - 10), (10 - 10), (11 - 10), (12 - 10), (13 - 10), (15 - 10)-4, -2, -2, -2, -1, 0, 1, 2, 3, 5Also, we have to comsider the squared deviations:
16, 4, 4, 4, 1, 0, 1, 4, 9, 25To conclude this procedure we sum up the squared deviations to find the sum of the squared deviations from the mean:
Sum of Squared Deviations = 16 + 4 + 4 + 4 + 1 + 0 + 1 + 4 + 9 + 25Sum of Squared Deviations = 88Learn more about mean in: https://brainly.com/question/31101410
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what statistical test should i take if i am interested in studying if college major is related to living location preference
If you are interested in studying whether college major is related to living location preference, the appropriate statistical test to use is the chi-square test. This is because both the college major and living location preference are categorical variables, and the chi-square test is used to analyze the association between two categorical variables.
To perform the chi-square test, you will need to create a contingency table that displays the frequency of individuals in each combination of college major and living location preference. You can then calculate the expected frequencies under the null hypothesis of independence, which assumes that there is no association between the two variables.
The chi-square test statistic is calculated by comparing the observed frequencies to the expected frequencies, and it measures the degree of association between the two variables. If the chi-square test statistic is large enough, it indicates that there is a significant relationship between college major and living location preference.
Overall, the chi-square test is a powerful statistical tool for analyzing the relationship between categorical variables, and it can provide valuable insights into the factors that influence living location preference among college students.
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find the area of the triangle t with sides u = <3,3,3>, v = <6,0,6> and u-v. (the area of a triangle is half the area of the corresponding parallelogram)
The area of the triangle T with sides u = ⟨3, 3, 3⟩, v = ⟨6, 0, 6⟩, and u-v is 9√3 square units.
Determine the area of the triangle?To find the area of the triangle T, we first calculate the cross product of vectors u and v, denoted as u × v. The magnitude of the cross product gives us the area of the corresponding parallelogram, and dividing it by 2 gives us the area of the triangle.
Calculating the cross product:
u × v = |i j k|
|3 3 3|
|6 0 6|
Expanding the determinant:
u × v = (36 - 30)i - (36 - 36)j + (30 - 36)k
= 18i - 0j - 18k
= 18(1, 0, -1)
The magnitude of the cross product:
|u × v| = |18(1, 0, -1)|
= 18|1, 0, -1|
= 18√(1² + 0² + (-1)²)
= 18√2
= 18√3 square units.
Therefore, the area of triangle T is half the area of the parallelogram, which is (1/2)(18√3) = 9√3 square units.
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Ms. Guzman orders 6,370 marbles. Each package contains 182 marbles. How many packages does Ms. Guzman order? Record your answer on the grid. Then fill in the bubbles.
The solution is:
Cash received on account =$ 6381.63
Explanation:
The payment terms 3/10, n/30 implies that if Guzman Housewares pays within the next 10 days of purchase, it will receive a discount of 3% of the net invoice amount and that the latest date for the settlement of bill is within the next 30 days of purchase.
The latest payment date to qualify for discount is May 27th i.e ( May 12 + 10) but the payment was made by May 20th , so this qualifies Guzman Housewares for the discount.
The net amount of cash received by Blue Company is computed as follows:
Net sales = Gross sales - Returns inwards ( Sales returns)
= 6,897 - 318 =$6,579
Cash received on account = Net sales - discount
= =$6,579 - (3%×6,579) = $6,381.63
Cash received on account =$ 6381.63
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complete question:
Q 8.21: On May 12, 2017, Hudson Merchandise sold merchandise on account to Guzman Housewares for $6,897, terms 3/10, n/30. If Guzman returns merchandise with a sale price of $318 on May 15, 2017, what amount will Hudson record in their Cash account if Guzman pays in full on May 20, 2017
what is educational inequality and how is it measured? why is it important to measure the degree of educational inequality in a country? explain your answer
Educational inequality can be measured in different ways, including by looking at enrollment rates, completion rates, standardized test scores, and educational attainment levels.
Educational inequality refers to the unequal distribution of educational opportunities and resources among different groups of people within a society or country. This can manifest in various forms, including unequal access to education, disparities in educational outcomes, and differences in educational quality.
Educational inequality can be measured in different ways, including by looking at enrollment rates, completion rates, standardized test scores, and educational attainment levels. Other factors such as socio-economic status, race, ethnicity, and gender can also be used to analyze educational inequality.
Measuring the degree of educational inequality in a country is important for several reasons. First, it helps identify disparities in access to education and highlights groups that may be marginalized or disadvantaged. Second, it can provide insights into the effectiveness of educational policies and programs aimed at reducing inequality. Finally, reducing educational inequality is crucial for promoting social mobility, reducing poverty, and achieving economic growth and development.
In summary, educational inequality is a significant issue that can have far-reaching consequences for individuals and societies. Measuring and addressing educational inequality is important for promoting equity, social justice, and sustainable development.
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please help find the gradient PLEASE HELPPPPPP
The gradient of the line, which is also the slope of the line is calculated as: m = -2.
How to Find the Gradient of a Line?The gradient of a line is the same as the slope of a line. It is calculated using the same slope formula which can be expressed as:
Gradient of a line (m) = change in y / change in x = rise/run = y2 - y1 / x2 - x1.
To calculate the gradient of the line, choose any two points on the graph:
(0, 5) = (x1, y1)
(3, -1) = (x2, y2)
Plug in the values into the formula:
Gradient of the line = (-1 - 5) / (3 - 0)
Gradient = -6/3 = -2.
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What is the end behavior of the function f of x equals negative 2 times the cube root of x?
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞.
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
The end behavior of the function f(x) = -2∛x can be determined by looking at the highest degree term in the function, which is ∛x. Since the cube root of a negative number is also negative, as x approaches negative infinity, f(x) approaches negative infinity as well. Similarly, as x approaches positive infinity, f(x) approaches positive infinity. Therefore, the correct answer is:
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
Help me find the Area!!
The area that was cut out is 457cm²
How to determine the area
The formula for calculating the area of a semi-circle is expressed as;
A = 1/2 πr²
Given that the diameters = 2 radius
Radius = 20/2 = 10cm
Substitute the values
Area = 1/2 × 3.14 × 10²
Find the square and substitute
Area = 157 cm²
Area of the triangle = 1/2 × b × h
Such that 'b' is the base and 'h' is the height
Substitute the values
Area = 1/2 × 20 × 30
Multiply the values
Area = 300cm²
Area cut out = 300 + 157 = 457cm²
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You select a marble without looking and then put it back. If you do this 12 times, what is the best prediction possible for the number of times you will pick a blue marble?
3 marbles total: 2 blue 1 green
The best guess for how many times you will choose a blue marble out of 12 trials is 8 times.
The likelihood of choosing a blue marble on each trial stays constant over the course of the 12 trials if there are 3 marbles total—2 blue and 1 green—and you choose one without looking.
The likelihood of selecting a blue marble on any given trial is 2/3, or 2 out of 3.
You may multiply the likelihood of selecting a blue marble on each trial by the number of trials to determine how many times you will choose a blue marble over the course of 12 trials:
E = Probability of blue marble * Number of trials
E = (2/3) * 12
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Review the graph of function j(x).
A line goes from the open circle to closed circle (6, 5). What is Limit of j (x) as x approaches 3? 3 4 5 6
Note that given the above graph, the limit of j (x) as x approaches 3 is 4.
Why is this so?A line begins at an open circle (2, 6) on a coordinate plane and falls via (-2, 2), according to the query. (3, 6) is a full circle. A curve travels from a solid circle (2, 3) to an open circle (3, 4). A line (6, 5) connects the open and closed circles.
The graph shows that the function j(x) has a limit of 4 as the value of x approaches 3.
A graph is a diagram or graphical representation that organizes the portrayal of facts or values.
Note that the points on a graph are typically used to depict the relationships between two or more things.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image..
What is the quotient of
5.688
×
1
0
9
5.688×10
9
and
7.9
×
1
0
2
7.9×10
2
expressed in scientific notation?
Answer:
4.49352×10¹²
Step-by-step explanation:
You want the product of 5.688×10⁹ and 7.9×10² expressed in scientific notation.
CalculatorGenerally, we use a calculator to simplify multiplication of such numbers. We can ask that same calculator to display the results in scientific notation. The number of significant digits in the product will be the sum of the numbers of significant digits in the given coefficients: 4 + 2 = 6.
5.688×10⁹ · 7.9×10² = 4.49352×10¹²
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Additional comments
A spreadsheet also gives you the option of displaying the number in scientific notation.
Note that many calculators use an "E" notation for entering the exponent of numbers in scientific notation. The key used for entering the exponent may be labeled EEX or EE or EXP. Some also use that same E notation for displaying the result.
The number of significant digits in the product that are of interest depends on the application. We have given the result of straight multiplication of these numbers. In a measurement or physics application, the result should be rounded to 2 significant digits, the number of digits in the least-precise factor. For general engineering application, you may want to round to about 4 significant digits, as more precision than that is often unneeded. If this is a value that will be added or subtracted with another, you probably want to keep the full precision available.
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The distribution of weights of female college cross country runners is approximately normal width mean 122 pounds and standard deviation 8 pounds. Which of the following is closest to the percent of the runners who’s way between 114 pounds in 138 pounds 
The percentag.e of female college runners between 114 - 138 pounds is 82%
What % of runners weigh 114 - 138 pounds?Given that X is normally distributed with mean μ = 122 pounds and standard deviation σ = 8 pounds.
We want to find [tex]P(114 < X < 138)[/tex]
To get this, we will standardize X first:
[tex]P(114 < X < 138) = P((114 - 122)/8 < (X - 122)/8 < (138 - 122)/8)[/tex]
= P(-1 < Z < 2)
Using standard normal table, we find that probability of Z falling between -1 and 2 is:
= 0.8186
That means:
[tex]P(114 < X < 138)[/tex] = 0.8186
[tex]P(114 < X < 138)[/tex] = 81.86%
[tex]P(114 < X < 138)[/tex] = 82%
Missing options:
(A)18% (B) 32% (C) 68% (D) 82% (E)95%
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sophie is a bargain shopper. she collects coupons, then every saturday she plans her route to take advantage of as many sales as possible. sophie is a(n)
Based on the information we can infer that Sophie is a Savvy Shopper.
That she is a Savvy Shopper?A "savvy shopper" is an informal term used to refer to a person who is an expert in finding and taking advantage of the best deals and promotions when shopping. Another outstanding characteristic of these people is that they plan their purchases in advance and take advantage of promotions and discounts.
According to the above, we can infer that if Sophie is a bargain shopper who collects coupons and plans her route to take advantage of sales. She is a savvy shopper.
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Rain Simpson, Alsen, and Eden (Technometrics 1975) reported the results of trials in which clouds were seeded and the amount of rainfall recorded. The authors reported on 26 seeded and 26 unseeded clouds in order of the amount of rainfall, largest amount first. Here are two possible tests to study the question of whether cloud seeding works. Which test is appropriate for these data? Explain your choice. Using the test you select, state your conclusion.
Paired t-Test of m(1 - 2) Mean of Paired Differences = -277. 39615 t-Statistic = -3. 641 w/25 df P = 0. 0012 2-Sample t-Test of m1 - m2 Difference Between Means = -277. 4 t-Statistic = -1. 998 w/33 df P = 0. 0538
a) Which of these tests is appropriate for these data? Explain. Clearly state the the assumption needed to justify the answer
b) Using the test you selected, state your conclusion. Include assessment of the strength of evidence
a) The paired t-test is appropriate for these data as it compares the difference in the amount of rainfall between seeded and unseeded clouds.
The assumption needed to justify this is the test is that the differences between the paired observations are normally distributed.
b) Based on the paired t-test, with a t-statistic of -3.641 and a p-value of 0.0012, there is strong evidence to reject the null of hypothesis that there is no difference in the amount of rainfall between seeded and unseeded clouds.
Therefore, we can conclude that cloud seeding has a significant effect on the amount of rainfall.
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In circle X, m∠YXZ=135∘ and the area of the shaded sector =3/2pi. Find the length of XY
The length of XY in the shaded sector that has an area of 3/2pi is calculated as: XY = 2 units.
What is the Area of a Shaded Sector?The area of a shaded sector = ∅/360 * πr², where r is the radius and ∅ is the central angle.
Given the following:
m<YXZ (∅) = 135 degrees
Area of the shaded sector = 3/2π
Radius (r) = XY = ?
Substitute the values:
3/2π = 135/360 * πr²
Solve for r (XY):
1.5π = 0.375 * πr²
Divide both sides by 0.375π:
1.5π/0.375π = r²
4 = r²
r = 2
XY = 2 units
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After how many seconds, rounded to the nearest hundredth, did the ball hit the ground?
The ball hits the ground after a time of 3.05 seconds.
How to model the situation?The quadratic function giving the ball's height after t seconds is given as follows:
h(t) = -16.1t² + 150.
(In which -16.1 is the gravity's effect, while 150 is the initial height).
The ball hits the ground when the height function has a numeric value of zero, that is:
h(t) = 0.
Hence the time is obtained solving the equation, isolating the variable t, as follows:
-16.1t² + 150 = 0
16.1t² = 150
t² = 150/16.1
[tex]t = \sqrt{\frac{150}{16.1}}[/tex]
t = 3.05 seconds.
Missing InformationThe complete problem is:
The quadratic function h(t)=-16.1t^2 + 150 models a balls height, in feet, over time, in seconds, after it is dropped from a 15 story building. After how many seconds, rounded to the nearest hundredth, did the ball hit the ground?
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