The probability that X has a value smaller than 7.5 is approximately 0.1056.
To find the probability that X is smaller than 7.5, we have to standardize the variable using the z-score formula:
z = (x - μ) /σ
here,
x = value of probability,
μ = mean of the distribution, and
σ= standard deviation.
Now, we get,
z = (7.5 - 10) / 2 = -1.25
Now, we have to find the probability that Z (the standardized variable) is less than -1.25.
From a standard normal distribution table, we get that the probability of Z being less than -1.25 is 0.1056.
Therefore, the probability that X has a value smaller than 7.5 is approximately 0.1056.
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The probability that X has a value smaller than 7.5 is approximately 0.1056. This means that in a large number of trials, we would expect X to be smaller than 7.5 about 10.56% of the time.
To answer this question, we need to use the properties of the normal distribution. We know that X is normally distributed with mean 10 and standard deviation 2. We want to find the probability that X has a value smaller than 7.5.
We can use the standard normal distribution to solve this problem. To do this, we first need to standardize the value of 7.5. We do this by subtracting the mean from 7.5 and dividing by the standard deviation:
Z = (7.5 - 10) / 2 = -1.25
Now we can use a standard normal distribution table or calculator to find the probability that Z is less than -1.25. This probability is approximately 0.1056.
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The mean cost of a five pound bag of shrimp is 5050 dollars with a standard deviation of 66 dollars. If a sample of 4040 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 51.351.3 dollars
The probability that the sample mean would be less than $51.3 when a sample of 40 bags is randomly selected is 55.71%.
To solve this problem, we can use the Central Limit Theorem (CLT), which states that the sample mean of a sufficiently large sample size drawn from any population with a finite mean and variance will be approximately normally distributed.
The first step is to calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the mean. The SEM can be calculated using the formula:
[tex]SEM = \frac{\sigma}{\sqrt{n}}[/tex]
where σ is the population standard deviation, and n is the sample size.
Substituting the values, we get:
[tex]SEM = \frac{66}{\sqrt{40}} = 10.45[/tex]
Next, we need to calculate the z-score corresponding to the sample mean of $51.3:
[tex]z = \frac{51.3 - 50}{10.45} = 0.1435[/tex]
Using a standard normal distribution table, we find that the area to the left of z = 0.1435 is 0.5571. This means that the probability of obtaining a sample mean of $51.3 or less from a sample of 40 bags is 0.5571 or 55.71%. It is important to note that this result is based on the assumption that the population is normally distributed. Additionally, the CLT only holds for sufficiently large sample sizes (typically n > 30).
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First use the digits in the box to create the targest possible number.then use the same digits to create the smallest possible number.
Then find the difference between the two numbers.
The difference between the largest and smallest numbers is 7173.
To create the largest possible number, we can arrange the digits in decreasing order:
8531
To create the smallest possible number, we can arrange the digits in increasing order:
1358
The difference between the largest and smallest numbers is:
8531 - 1358 = 7173
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Cici bought strawberries at a farmers' market, flour and sugar at the grocery store, and milk at a dairy, then returned home to bake strawberry pies. What logistical function did she perform in collecting all of these ingredients
Cici performed the logistical function of procurement by collecting all the necessary ingredients from different sources such as the farmers' market, grocery store, and dairy. This involved planning and coordinating the sourcing and transportation of the items to ensure they were available for her to use in baking the strawberry pies.
Hi! Cici performed the logistical function of procurement in collecting all of these ingredients. Procurement is the process of finding, acquiring, and transporting goods and services. In this case, Cici procured strawberries from a farmers' market, flour and sugar from the grocery store, and milk from a dairy. By visiting these different locations, she ensured she had all the necessary ingredients to bake her strawberry pies at home.
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Question 7
Does the point (-2, -10) lie on the line
y = 3x - 3?
The point (-2, -10) does not lie on the line y = 3x - 3.
How to check if a point lies on a line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of line in the question:
y = 3x - 3
To check if the point (-2, -10) lies on the line y = 3x - 3, we need to substitute the values of x and y into the equation and see if it is true.
y = 3x - 3
Plug in x = -2 and y = -10
-10 = 3(-2) - 3
Simplify
-10 = -6 - 3
-10 = -9
But we know that -10 ≠ -9, hence, this is not a true statement.
Therefore, the point does not lie on the line.
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In computing a seasonal index, specific seasonals were tabulated for each month. The averages over time for the twelve months were obtained and summed. If the mean seasonal factor for June was 96.9, and the sum for all twelve months is 1195, the adjusted seasonal index for June is
If the mean seasonal factor for June was 96.9, and the sum for all twelve months is 1195, the adjusted seasonal index for June is 8.11
To calculate the adjusted seasonal index for June, we need to divide the mean seasonal factor for June by the sum of the seasonal factors for all twelve months and then multiply the result by 100.
Adjusted seasonal index for June = (Mean seasonal factor for June / Sum of seasonal factors for all twelve months) × 100
Adjusted seasonal index for June = (96.9 / 1195) × 100 ≈ 8.11
The adjusted seasonal index for June is approximately 8.11.
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31001-1-9
22. An integer is quartered, and the result is squared. To this five is added to create a sum
that equals nine. Write an equation and solve to determine the possible values of the
integer.
Step-by-step explanation:
x = integer now 'quarter it'
1/4 x Now square it
(1/4x)^2 add five
(1/4x)^2 + 5 = 9 solve for x
(1/4 x)^2 ) = 4
1/16 x^2 = 4
x^2 = 64
x = ± 8
If eating oatmeal reduces her running time by one minute, how many days would she have to run the experiment for her to have a power of 95%
The actual duration of the experiment may vary depending on various factors, such as dropout rates, compliance, and unexpected events.
To determine the number of days needed for the experiment to have a power of 95%, we need to have some additional information about the experiment, such as the sample size, effect size, significance level, and variability in the data.
Assuming that the experiment involves comparing the running time of a group of participants who eat oatmeal with a group of participants who do not eat oatmeal, we can estimate the sample size, effect size, and variability based on previous studies or pilot data.
Let's say that the effect size is 1 minute, the standard deviation of the running time is 5 minutes, and the significance level is 0.05 (i.e., alpha = 0.05). The power of the experiment can be calculated using a power analysis tool, such as G*Power or R.
Using G*Power with a one-tailed t-test, we can calculate the required sample size to achieve a power of 0.95, given the effect size, alpha, and standard deviation. Assuming equal sample sizes in the two groups, we get a required sample size of about 64 participants per group.
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The time it takes me to wash the dishes on a randomly selected night is uniformly distributed between 8 minutes and 18 minutes. a) State the random variable in the context of this problem. Orv X - a randomly selected night rv X - the time it takes me to wash dishes on a randomly selected night Orv X = washing dishes OrvX - a uniform distribution b) Compute the height of the uniform distribution. Leave your answer as a fraction. c) What is the probability that washing dishes tonight will take me between 9 and 15 minutes? Give your answer as a fraction. Give your answer accurate to three decimal places. d) What is the probability that washing dishes tonight will take exactly 9 minutes?
The time it takes to wash dishes on a randomly selected night. The height is 1/10. The probability is 3/5 or 0.600. The probability of an exact value (like exactly 9 minutes) is always 0.
a) The random variable (rv) X in this context represents the time it takes to wash dishes on a randomly selected night.
b) The height of the uniform distribution can be calculated as the reciprocal of the range of the distribution. In this case, the range is (18 - 8) = 10 minutes. Therefore, the height is 1/10.
c) To find the probability that washing dishes tonight will take between 9 and 15 minutes, we need to calculate the area under the uniform distribution curve within this interval. Since it's a uniform distribution, the area can be calculated as the product of the height and the length of the interval. The length of the interval is (15 - 9) = 6 minutes. So, the probability is (1/10) * 6 = 3/5 or 0.600 (accurate to three decimal places).
d) In a continuous uniform distribution, the probability of an exact value (like exactly 9 minutes) is always 0, as there are infinite possible values within the range of the distribution.
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A bored college student on top of a 6-story tall building drops a water balloon on his friends directly below. In one second it falls one story down from the top. In one more second it will be:
Therefore, the water balloon will be on the fourth story in one more second.
The acceleration due to gravity is approximately 9.8 m/s^2. Since the water balloon falls one story down (which is approximately 6 meters) in one second, we can calculate its initial velocity using the equation: d = 1/2at^2. Plugging in the values, we get: 6 = 1/2(9.8)t^2, which simplifies to t = sqrt(1.2245) ≈ 1.11 seconds. Therefore, in one more second, the water balloon will have fallen another story down, i.e., it will be on the fourth story.
The water balloon dropped by the bored college student falls one story down from the top in one second. To calculate how long it will take for it to fall another story down, we can use the equation: d = 1/2at^2, where d is the distance, a is the acceleration due to gravity, and t is time. Plugging in the values, we get t = sqrt(1.2245) ≈ 1.11 seconds.
Therefore, the water balloon will be on the fourth story in one more second.
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Helppp will mark brainliest
I never en studied this stuff
Answer:
Step-by-step explanation:
All the digits of a number are different, the first digit is not zero, and the sum of the digit is 36. There are such numbers. What is the value of
The value of the number is 97432.
Let us denote the number by ABCDE, where A is the first digit, B is the second digit, and so on. Since the first digit is not zero, A can only take on values from 1 to 9.
The sum of the digits is given as 36, so we have:
A + B + C + D + E = 36
Since all the digits are different, we have 9 choices for the first digit (A), 9 choices for the second digit (since one digit has been used up), 8 choices for the third digit, and so on. Therefore, the total number of such numbers is:
9 x 9 x 8 x 7 x 6 = 27,648
To find the value of the number, we can simply list out all the possible combinations of the digits, keeping in mind that the first digit cannot be zero. One such number is:
97432
So the value of the number is 97432.
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the average lifespan of a set of tires is 38,000 miles, with a standard deviation of 1500 miles. What is the probability that the lifespan of a set of tires will be between 32,00 miles and 44,00 miles
The probability that the lifespan of a set of tires will be between 32,000 and 44,000 miles is approximately 0.99994 or 99.994%.
To solve this problem, we'll use the concepts of normal distribution, z-scores, and the z-table.
Calculate the z-scores for the given mileage values.
To calculate the z-score, use the formula: z = (X - μ) / σ
For 32,000 miles:
z1 = (32,000 - 38,000) / 1,500 = -6,000 / 1,500 = -4
For 44,000 miles:
z2 = (44,000 - 38,000) / 1,500 = 6,000 / 1,500 = 4
Look up the z-scores in the z-table and find the corresponding probabilities.
For z1 = -4, the z-table gives a probability of approximately 0.00003 (essentially 0).
For z2 = 4, the z-table gives a probability of approximately 0.99997.
Calculate the probability of the lifespan being between 32,000 and 44,000 miles.
Subtract the probability of z1 from the probability of z2:
P(32,000 < X < 44,000) = P(z2) - P(z1) = 0.99997 - 0.00003 = 0.99994.
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Charcoal drawings were discovered on walls and ceilings in a cave in a certain city. Determine the approximate age of the drawings, if it was found that 71% of C-14 in a piece of charcoal found in the cave had decayed through radioactivity. (Round your answer to one decimal place.)
Charcoal drawings found on walls and ceilings in a cave are significant archaeological findings as they provide insights into ancient human culture and art. The age of these drawings can be determined by analyzing the amount of C-14 remaining in a piece of charcoal found in the cave. C-14 is a radioactive isotope that decays at a constant rate over time.
If it was found that 71% of C-14 in a piece of charcoal had decayed through radioactivity, it means that only 29% of the original C-14 remains. Based on the half-life of C-14, which is 5,700 years, we can estimate the age of the charcoal to be approximately 17,100 years old (3 x 5,700 years).
Therefore, the approximate age of the charcoal drawings found in the cave is 17,100 years old. This age provides valuable information about the timeline of human civilization and helps us understand the development of art and culture during that time period. These drawings also offer a glimpse into the lives and beliefs of ancient people who created them, making them important historical artifacts.
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Calculate the %CW for a sample of 1040 steel that has an original diameter of 12 mm and a final diameter of 10 mm. (Enter your answer as a %, but without the % sign.)
The % Cold Work for the sample of 1040 steel is approximately 30.54%.
To calculate the % Cold Work (% C W) for a sample of 1040 steel with an original diameter of 12 mm and a final diameter of 10 mm, we will use the following formula:
%CW = [(A o - A f) / A o] x 100
Where:
%CW = Percentage of Cold Work
A o = Original area of the sample
A f = Final area of the sample
Since the cross-sectional area of a cylindrical sample is given by A = π(d/2)^2, we will calculate the original and final areas using the given diameters:
A o = π(12 mm / 2)^2
= π(6 mm)^2
= 113.097 mm²
A f = π(10 mm / 2)^2
= π(5 mm)^2
= 78.54 mm²
Now, we can calculate the % CW:
%CW = [(113.097 mm² - 78.54 mm²) / 113.097 mm²] x 100
%CW = [34.557 mm² / 113.097 mm²] x 100
%CW ≈ 30.54
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Solve for x. Type your answer as a number, without "x=", in the blank.
The value of x, for the angle subtended by the arc is derived to be equal to 19.
What is angle subtended by an arc at the centerThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. The arc measure and the angle it subtends at the center of the circle are directly proportional.
so;
262 = 2(6x + 17)
131 = 6x + 17 {divide through by 2}
6x = 131 - 17 {collect like terms}
6x = 114
x = 114/6
x = 19
Therefore, the value of x, for the angle subtended by the arc is derived to be equal to 19.
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Which system of equations is satisfied by the solution shown in the graph? A coordinate plane linear graph on inequalities in which a line intersects Y-axis at 6 and another line intersects y-axis at 10. Both lines intersect X-axis at minus 2 and Y-axis at 8. A. x + 2y = 6 and x − y = 10 B. x + y = 6 and x − 2y = 10 C. x + 2y = 10 and x − y = 6 D. x + y = 6 and x − y = -10 Reset Next
System of equations that is satisfied by the solution is C) x + 2y = 10 and x − y = 6.
The solution shown in the graph satisfies the equations x + 2y = 10 and x − y = 6, which means the answer is C. To see why, note that both lines intersect the y-axis at different points, so their equations cannot be of the form x + ay = b for the same values of a and b.
However, both lines intersect the point (-2, 8), so they must satisfy the equations x + 2y = 10 and x − y = 6. These equations can be solved simultaneously to find the unique solution (x, y) = (2, 4).
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The data set Beer Large, which can be found in StatCrunch Shared Data Sets, gives the Alcohol, Carbohydrates and Calories for different brands of beer. The explanatory variable is X = Alcohol and the response variable is Y = Calories. When testing the test statistic has a value of _______. (1decimal place)
Thus, the higher the test statistic, the stronger the evidence against the "null hypothesis" (i.e., no relationship between Alcohol and Calories).
To calculate the test statistic for the relationship between Alcohol (X) and Calories (Y) in the Beer Large data set, you'll need to perform a linear regression analysis.
1. Access the Beer Large data set in StatCrunch and load it into the platform.
2. Select 'Stat' > 'Regression' > 'Simple Linear' from the menu.
3. Choose 'Alcohol' as the explanatory variable (X) and 'Calories' as the response variable (Y).
4. Click 'Compute' to run the linear regression analysis.
The output will provide you with the test statistic value (rounded to 1 decimal place) for the relationship between Alcohol and Calories.
This value is important when assessing the significance of the relationship between the two variables, as it helps you determine if the relationship is statistically significant or not.
Remember, the higher the test statistic, the stronger the evidence against the null hypothesis (i.e., no relationship between Alcohol and Calories).
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A block of metal was heated and reached a temperature of 99 degrees Fahrenheit. The material then cooled at a rate of -1.4 degrees Fahrenheit per minute. Determine whether it took less than 10 minutes, 10-15 minutes, or more than 15 minutes for the block to reach the specified temperature. The temperatures are as followed:
(90 degrees Fahrenheit, 85 degrees Fahrenheit. 80 degrees Fahrenheit, 75 degrees Fahrenheit)
It would take less than 10 minutes for the block of metal to reach the specified temperatures.
To solve this problem, we need to calculate the time it took for the block of metal to cool from 99 degrees Fahrenheit to the specified temperatures.
For the first temperature of 90 degrees Fahrenheit, it would take 9 minutes for the block of metal to cool from 99 degrees Fahrenheit to 90 degrees Fahrenheit, since 9 x -1.4 = -12.6, and 99 - (-12.6) = 90.4.
For the second temperature of 85 degrees Fahrenheit, it would take 14 minutes for the block of metal to cool from 99 degrees Fahrenheit to 85 degrees Fahrenheit, since 14 x -1.4 = -19.6, and 99 - (-19.6) = 85.4.
For the third temperature of 80 degrees Fahrenheit, it would take 19 minutes for the block of metal to cool from 99 degrees Fahrenheit to 80 degrees Fahrenheit, since 19 x -1.4 = -26.6, and 99 - (-26.6) = 80.4.
For the fourth temperature of 75 degrees Fahrenheit, it would take 24 minutes for the block of metal to cool from 99 degrees Fahrenheit to 75 degrees Fahrenheit, since 24 x -1.4 = -33.6, and 99 - (-33.6) = 75.4.
Therefore, it would take less than 10 minutes for the block of metal to reach the specified temperatures.
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Find the probability that a randomly selected fertilized chicken egg takes between 19 and 21 days to hatch.
Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.
The probability that a randomly selected fertilized chicken egg takes between 19 and 21 days to hatch depends on several factors such as the breed of the chicken, temperature, and humidity. However, on average, most chicken eggs take around 21 days to hatch. Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.
The probability that a randomly selected fertilized chicken egg takes between 19 and 21 days to hatch depends on several factors such as the breed of the chicken, temperature, and humidity. However, on average, most chicken eggs take around 21 days to hatch.
Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.
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In a well-constrained problem space a. there are relatively a small number of states b. subgoal decomposition is not required c. the solution is always straightforward d. all of the states an operators are known
In a well-constrained problem space:
a. There are relatively a small number of states.
b. Subgoal decomposition is not required.
c. The solution is not always straightforward.
d. All of the states and operators are known.
A well-constrained problem space refers to a problem-solving environment that has clear boundaries and limitations, with well-defined rules, goals, and constraints. In such a space, there are typically a limited number of possible states or configurations that the system can be in, and the problem solver has access to all of the relevant information about the problem and its solution.
However, while a well-constrained problem space may have a relatively small number of states, it does not necessarily mean that the solution is always straightforward or that subgoal decomposition is not required. In fact, in some cases, even a well-constrained problem space can be complex and require considerable effort to solve. Nevertheless, having all of the states and operators known can help simplify the problem-solving process and enable more efficient and effective problem solving.
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how many 4 permutations of the positive integers not exceeding 100 contain three consecutive integers in the correct order where consecutive means in the usual order of the integers and where
There are 28,434 4-permutations of the positive integers not exceeding 100 that contain three consecutive integers in the correct order.
We want to find the number of 4-permutations containing three consecutive integers in the correct order.
Let's break this down step-by-step.
Identify the possible sets of consecutive integers:
Since we are looking for sets of three consecutive integers not exceeding 100, the highest possible set is (98, 99, 100). Therefore, we have a total of 98 sets (from 1-2-3 to 98-99-100).
Determine the number of ways to arrange each set within a 4-permutation:
Each set of consecutive integers can appear at the beginning, in the middle, or at the end of the permutation. So, there are 3 different positions for each set.
Calculate the remaining integer's options:
For each of the 3 positions, we have 97 options for the remaining integer since it must be different from the three consecutive integers in the set.
Multiply the number of sets, positions, and remaining integer options: 98 sets * 3 positions * 97 remaining integer options = 28,434 possible 4-permutations.
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In Exercises 11-28, find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) 12. f(x) = 14. g(x) = 1+2x2 16. g(t) = 2t-1 11. f(x) =- x + 2 13. (x) t+1 f(x) = x+2 h(x) =x3-3x2 + x + 1 5 23 g(t) = 2 + (1-2)2 fx)
The horizontal and vertical asymptotes of the function are given below.
We have,
The function f(x) has no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator (both are 2), and the leading coefficients of both are the same.
The vertical asymptotes are given by setting the denominator equal to zero and solving for x.
In this case, 2x² - 1 = 0, which gives x = ±√(1/2).
Therefore, the vertical asymptotes are x = √(1/2) and x = -√(1/2).
The function g(x) has no horizontal asymptote because the degree of the numerator is greater than the degree of the denominator (2 > 0).
The vertical asymptote is at x = 0 because the denominator is equal to zero when x = 0.
The function g(t) has no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator (1), and the leading coefficients of both are the same.
The function has no vertical asymptotes because the denominator is never equal to zero.
The function f(x) has no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator (1), and the leading coefficients of both are the same.
The function has no vertical asymptotes because the denominator is never equal to zero.
The function f(x) has no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator (1), and the leading coefficients of both are the same.
The function has a vertical asymptote at x = -1 because the denominator is equal to zero when x = -1.
The function h(x) has no horizontal asymptote because the degree of the numerator is greater than the degree of the denominator (3 > 2).
The function has no vertical asymptotes because the denominator is never equal to zero.
The function g(t) has a horizontal asymptote at y = 2 because as t approaches infinity, the expression (1 - 2)^2 approaches zero, so the function approaches 2.
The function has no vertical asymptotes because the denominator is never equal to zero.
Thus,
The horizontal and vertical asymptotes of the function are given above
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Answer for bonus points!!
By completing squares we will get:
y = (x - 5)^2 - 16
Then the minimum of the quadratic is at y = -16.
How to complete squares?Remember the perfect square trinomial:
(a + b)^2 = a^2 + 2ab + b^2
Here we have the quadratic:
y = x^2 - 10x + 9
We can rewrite that to get:
y = x^2 - 2*5*x + 9
Add and subtract 5^2 in both sides:
y + 5^2 = x^2 - 2*5*x + 5^2 + 9
Now we can complete squares:
y + 25 = (x - 5)^2 + 9
y = (x - 5)^2 + 9 - 25
y = (x - 5)^2 - 16
Then the vertex is at the point (5, -16), and thus the minimum is y = -16.
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Answer:
[tex](5, -16)[/tex]
Step-by-step explanation:
1.) [tex]y=x^2[/tex] [tex]-10x+9[/tex]
2.) [tex]y=x^2[/tex] [tex]-10x+25+9-25[/tex]
3.) [tex]y=x^2-10x+25 -16[/tex]
4.) [tex]y=(x-5)^2-16[/tex]
Therefore, the minimum point Is [tex](5, -16)[/tex]
. What is the smallest number of seats in a large auditorium that must be occupied in order to be certain that at least three people in attendance have the same first and last initials
The smallest number of seats that must be occupied in order to be certain that at least three people in attendance have the same first and last initials is 677. The answer to this question requires a bit of mathematical reasoning.
If we assume that there are 26 letters in the alphabet (one for each initial), and that each person in attendance has a unique first and last initial, then the maximum number of people that can be in the auditorium without any two people having the same initials is 52 (since there are 26 possible first initials and 26 possible last initials).
However, we are looking for the smallest number of seats that must be occupied in order to guarantee that at least three people have the same initials. To solve this, we can use a formula called the pigeonhole principle, which states that if n items are placed into m containers, and n is greater than m, then there must be at least one container with more than one item.
In this case, the "items" are the people in attendance, and the "containers" are the possible combinations of first and last initials. We know that there are 26 possible first initials and 26 possible last initials, which gives us a total of 26 x 26 = 676 possible combinations.
Using the pigeonhole principle, we can determine that if we have 677 people in the auditorium, there must be at least three people with the same first and last initials. Therefore, the smallest number of seats that must be occupied in order to be certain that at least three people in attendance have the same first and last initials is 677.
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The population N(t) (in millions) of a country t years after 1980 may be approximated by the formula N(t) = 217e0.0102t.When will the population be twice what it was in 1980? (Round your answer to one decimal place.)
The population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.
To find out when the population will be twice what it was in 1980, we need to set up an equation and solve for t.
Let's first determine the population in 1980:
N(0) = 217e0.0102(0) = 217
So, the population in 1980 was 217 million.
Now, we want to find out when the population will be twice that amount:
2(217) = 434
We can set up an equation:
434 = 217e0.0102t
Divide both sides by 217:
2 = e0.0102t
Take the natural logarithm of both sides:
ln(2) = 0.0102t
Solve for t:
t = ln(2)/0.0102
t ≈ 67.8
Therefore, the population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.
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Used Newton's divided differences to find the polynomial of lowest degree that passes through the points (-2,-9),(-1,-1),(1,-9),(3,-9)(-2,-9),(-1,-1),(1,-9),(3,-9) and (4.9)(4.9). Be sure to include the Newton divided difference diagram
We can add the remaining terms of the polynomial: f(x) = 8(x+2) + 2(x+2)(x+1) - 4(x+2)(x+1)(x-1) - 1(x+2)(x+1)(x-1)(x-3) + 0.0416667(x+2)(x+1)(x-1)(x-3)(x-4.9). This is the polynomial of lowest degree (4) that passes through the given points.
To use Newton's divided differences to find the polynomial of lowest degree that passes through the given points, we first need to construct a divided difference table. The table will show the differences between the y-values of the given points, and then the differences between those differences, and so on until we have a single value.
Here is the divided difference table:
|-2 -9 | -1 -1 | 1 -9 | 3 -9 | 4.9
---------------------------------------
|-9 | 8 | -16 | 0 |
| |-0.5 | 2 | |
| | 0.25 | | |
| |-0.125 | | |
| | 0.0416667| | |
The first column lists the x-values of the given points, and the second column lists the corresponding y-values. The remaining columns show the divided differences. For example, the entry in row 2, column 2 (-0.5) is the divided difference between the y-values -9 and -1.
Now we can use the divided differences to construct the polynomial of lowest degree that passes through the points. We start with the first divided difference in the second column, which is 8. This gives us the linear term of the polynomial:
f(x) = 8(x+2) + ...
Next, we use the second divided difference in the third column, which is 2. This gives us the quadratic term of the polynomial:
f(x) = 8(x+2) + 2(x+2)(x+1) + ...
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Suppose an experiment consists of rolling 9 regular six-sided dice. How many outcomes are there for this experiment
There are 10,077,696 possible outcomes when rolling 9 regular six-sided dice in this experiment.
You are rolling 9 regular six-sided dice. To determine the total number of outcomes for this experiment, you will use the concept of permutations in combinatorics. Since each die has 6 sides with distinct numbers (1 to 6), each die has 6 possible outcomes.
To find the total number of outcomes for all 9 dice combined, you simply multiply the possible outcomes for each die together. This is because the outcomes of each die roll are independent events, and the overall outcome depends on the combination of all 9 dice. So, you'll calculate the outcomes as follows:
Number of outcomes = (Outcomes for Die 1) x (Outcomes for Die 2) x ... x (Outcomes for Die 9)
Since there are 6 possible outcomes for each die, the equation becomes:
Number of outcomes = 6^9
By calculating 6 raised to the power of 9, you'll get:
Number of outcomes = 10,077,696
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The error of rejecting a true null hypothesis is always negligible in hypothesis testing. a Type I error. a Type II error. never committed in hypothesis testing.
The correct option is A, The error of rejecting a true null hypothesis is known as a Type I error in hypothesis testing.
A hypothesis is an educated guess or a tentative explanation for a phenomenon that can be tested through empirical research. It is a statement that provides a proposed explanation for a phenomenon based on limited evidence or observations. The goal of a hypothesis is to provide a framework for empirical testing, and to determine whether the data collected supports or disproves the hypothesis.
In science, a hypothesis is a crucial part of the scientific method. It helps scientists to define and clarify their research questions, to design experiments or studies, and to make predictions about the outcomes. A hypothesis should be testable, falsifiable, and based on previous research or observations.
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In wiring eight houses, the electricians install 68, 87, 57, 74, 49, 101, 99 and 56 outlets. Find the total number of outlets that must be roughed in.
The requreid electricians must rough in a total of 591 outlets for the eight houses.
To find the total number of outlets, we need to add up the number of outlets for each house:
Total outlets = 68 + 87 + 57 + 74 + 49 + 101 + 99 + 56
Total outlets = 591
Therefore, the electricians must rough in a total of 591 outlets for the eight houses.
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Consider the following passage: "Researchers wanted to know whether 3-D movies cause motion sickness or headaches in a significant number of people who watch them. In ten major cities, at randomly selected movie theaters that were showing 3-D movies, they interviewed people after viewings. Of the 893 people they spoke to, 268 people, or about 30%, reported experiencing some discomfort, motion sickness, or headache during the movie. On those grounds, they concluded that 30% of the people who see 3-D movies experience some physical discomfort from them." What is the sample in this argument? Question 1 options: People interviewed in the 10 city survey who watched a 3-D movie 30 893 Experiencing physical discomfort from watching 3-D movies All people who watch 3-D movies
The sample in this argument is "People interviewed in the 10 city survey who watched a 3-D movie".
This is because the researchers selected a random sample of people who watched 3-D movies in the ten major cities, and then interviewed them about their experience of physical discomfort. The 893 people who were interviewed constitute the sample, and their responses were used to draw conclusions about the broader population of people who watch 3-D movies.
Therefore, the sample is a subset of the population of all people who watch 3-D movies, and the researchers used this sample to make inferences about the larger population. The sample in this argument is the people interviewed in the 10 city survey who watched a 3-D movie.
The researchers conducted their study by interviewing a total of 893 individuals across ten major cities at randomly selected movie theaters showing 3-D movies. This sample was used to draw conclusions about the broader population of people who watch 3-D movies and their experiences with physical discomfort, motion sickness, or headaches.
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