Your friend swims on the school team.
In his first four races, his times are 24.7, 23.5, 25.6, and 27.2 seconds.
Which time listed for his next race would make the range larger?
CLEAR CHECK
23.2 seconds
25.0 seconds
26.1 seconds
27.2 seconds
Answers
The time listed for his next race that would make the range larger is 23.2 seconds.
To make the range larger, your friend's next race time should be farther away from the previous race times. Therefore, the time listed for his next race that would make the range larger is 23.2 seconds.
In the given scenario, the range refers to the difference between the fastest and slowest times. Currently, the range is 27.2 - 23.5 = 3.7 seconds. If your friend's next race time is 23.2 seconds, which is faster than his current fastest time of 23.5 seconds, the new range would become 27.2 - 23.2 = 4 seconds. This results in a larger range compared to the initial range of 3.7 seconds.
On the other hand, if your friend's next race time is 25.0 seconds, it falls within the existing range and does not affect the range size. Similarly, if the next race time is 26.1 seconds or 27.2 seconds (the same as his previous slowest time), the range remains unchanged. Therefore, selecting a time outside the existing range, such as 23.2 seconds, would make the range larger.
Learn more about range here
https://brainly.com/question/30389189
#SPJ11
Which time listed for his next race would make the range larger?
Related Questions
Need help with lcm (Least common multiple)
Answers
Answer:
sure can help you shoot the question
Step-by-step explanation:
You can find the least common multiple of 2 numbers by using prime factorisation to find its index notation.
Example:
6=2×3
9=3^2
So to find the LCM of these to find the LCM of these numbers, you need to take the number with the higher index notation and the remaing factor and multiply them.
Example:
LCM(6,9)=2×3^2
=18
Let W
be a subspace of Rn
spanned by n
non-zero orthogonal vectors. Show that W=Rn
.
Answers
W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.
To show that W=Rn, we need to show that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W.
Let v be any vector in Rn. Since the n non-zero orthogonal vectors span W, we can write v as a linear combination of them:
v = c1v1 + c2v2 + ... + cnvn
where c1, c2, ..., cn are scalars, and v1, v2, ..., vn are the n non-zero orthogonal vectors that span W.
To show that v is in W, we need to show that v is orthogonal to all vectors in W except itself. Since the n non-zero orthogonal vectors are linearly independent, any linear combination of them that is orthogonal to v must be the zero vector.
Therefore, if w is any vector in W that is not equal to v, we have:
= = c1 + c2 + ... + cn = 0
since v is orthogonal to all the non-zero orthogonal vectors. This means that v is orthogonal to all vectors in W except itself.
Therefore, since v is in W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.
Know more about Non-zero orthogonal vectors here:
https://brainly.com/question/30264840
#SPJ11
Could I please get assistance with this question. Create a mini cricket/rugby clinic explanation where you teach learners about cricket/rugby while incorporating Mathematics or English literacy. Your explanation should be informative and insightful.
Answers
Introduce the sport of cricket/rugby and explain its history and rules.
Use cricket/rugby as a context for teaching Mathematics or English literacy. For example:
Mathematics: You can use cricket/rugby statistics to teach learners about probability, percentages, and data analysis. For instance, you can ask learners to calculate the batting average of a cricket player or the conversion rate of a rugby team. You can also ask learners to solve word problems related to cricket/rugby, such as "If a cricket team scores 240 runs in 50 overs, what is their run rate per over?"
English literacy: You can use cricket/rugby as a context for teaching learners about reading comprehension, writing, and vocabulary. For instance, you can ask learners to read a cricket/rugby article and summarize it in their own words. You can also ask learners to write a persuasive essay on why cricket/rugby is the best sport. Additionally, you can teach learners cricket/rugby-specific vocabulary, such as "wicket," "boundary," "try," and "conversion."
Use cricket/rugby drills and exercises to reinforce the Mathematics or English literacy concepts you have taught. For example:
Mathematics: You can ask learners to measure the distance between the wickets or the length of the cricket pitch using a tape measure. You can also ask learners to count the number of runs scored in a cricket match or the number of tries scored in a rugby match.
English literacy: You can ask learners to write a cricket/rugby-themed story or poem using the vocabulary they have learned. You can also ask learners to read a cricket/rugby rulebook and explain the rules in their own words.
Overall, incorporating Mathematics or English literacy into a cricket/rugby clinic can make the learning experience more engaging and meaningful for learners. By using cricket/rugby as a context for teaching these subjects, learners can see the real-world applications of what they are learning and develop a deeper understanding of the concepts.
Evaluate the indefinite integral. Use a capital " C " for any constant term. ∫(3ex+4x5−x34+1)dx= TIP Enter your answer as an expression. Example: 3x∧2+1,x/5,(a+b)/c Be sure your variables match those in the question
Answers
The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.
∫3e^x dx = 3∫e^x dx = 3e^x + C₁
∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂
∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃
∫1 dx = x + C₄
Now, we can combine these results to obtain the final answer:
∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C
Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:
∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C
where C is the constant of integration.
Learn more about integration here:brainly.com/question/32510822
#SPJ11
Please please please help asapp
question: in the movie lincoln lincoln says "euclid's first common notion is this: things which are equal to the same things are equal to each other. that's a rule of mathematical reasoning and it's true because it works - has done
and always will do. in his book euclid says this is self-evident. you see there it is even in that 2000 year old book of mechanical law it is the self-evident truth that things which are equal to the same things are equal to each other."
explain how this common notion is an example of a postulate or a theorem
Answers
The statement made by Lincoln in the movie "Lincoln" refers to a mathematical principle known as Euclid's first common notion. This notion can be seen as an example of both a postulate and a theorem.
In the statement, Lincoln says, "Things which are equal to the same things are equal to each other." This is a fundamental idea in mathematics that is often referred to as the transitive property of equality. The transitive property states that if a = b and b = c, then a = c. In other words, if two things are both equal to a third thing, then they must be equal to each other.
In terms of Euclid's first common notion being a postulate, a postulate is a statement that is accepted without proof. It is a basic assumption or starting point from which other mathematical truths can be derived. Euclid's first common notion is considered a postulate because it is not proven or derived from any other statements or principles. It is simply accepted as true. So, in summary, Euclid's first common notion, as stated by Lincoln in the movie, can be seen as both a postulate and a theorem. It serves as a fundamental assumption in mathematics, and it can also be proven using other accepted principles.
To know more about mathematical visit :
https://brainly.com/question/27235369
#SPJ11
2x + 11 = 25
Solve x
I need the working out.
Answers
So x= 7.
Step-by-step explanation:
No problem,
The first steps we take is we will subtract 11 from the equation and subtract it from the total so it is easier for us.
Its one of the basic rules of Algebra.
2x + 11 = 25
2x + 11 - 11 = 25 -11 (We subtracted from both sides.)
2x = 14 (Now we are going to divide.)
2x / 2 = x
14 / 2 = 7
Now if we put this equation together we get x = 7.
Hope this helps.
Comment down if you have any questions
If z = x² - xy + 4y2 and (x, y) changes from (1, -1) to (0.96, -0.95), compare the values of Az and dz. dz = -0.56 X Az = -0.57 X
Answers
To compare the values of Az and dz, we first need to calculate the change in z and the change in x and y. Thus, the comparison of the values of Az and dz are as follows: Az = -0.0088 (= -0.57)dz = -0.88 (= -0.56)Therefore, we can observe that dz = -0.56 x Az = -0.57 x.
Change in z (Δz) can be calculated by subtracting the initial value of z from the final value of z:
Δz = z(final) - z(initial)
Given that z = x² - xy + 4y², we can substitute the initial and final values of (x, y) into the equation to find z(initial) and z(final).
For the initial point (1, -1):
z(initial) = (1)² - (1)(-1) + 4(-1)²
= 1 + 1 + 4
= 6
For the final point (0.96, -0.95):
z(final) = (0.96)² - (0.96)(-0.95) + 4(-0.95)²
= 0.9216 + 0.912 + 3.616
= 5.4496
Therefore, the change in z (Δz) is:
Δz = z(final) - z(initial)
= 5.4496 - 6
= -0.5504
Now, let's calculate the change in x and y:
Δx = x(final) - x(initial) = 0.96 - 1 = -0.04
Δy = y(final) - y(initial) = -0.95 - (-1) = 0.05
Finally, we can calculate dz and Az:
dz = Δz = -0.5504
Az = -0.56 × Δx + -0.57 × Δy = -0.56 * (-0.04) + -0.57 × (0.05) = 0.0224 - 0.0285 = -0.0061
Comparing the values of Az and dz, we have:
Az = -0.0061
dz = -0.5504
Thus, the comparison of the values of Az and dz are as follows:Az = -0.0088 (≈ -0.57)dz = -0.88 (≈ -0.56)Therefore, we can observe that dz = -0.56 x Az = -0.57 x.
To know more about value
https://brainly.com/question/843074
#SPJ11
from a collection of 50 store customers, 3 are to be chosen to receive a special gift. how many groups of 3 customers are possible?
Answers
The combination of number of ways of groups of 3 customers are 19600 .
What is permutation and combination?
Combination and permutation are two alternative strategies to divide up a collection of elements into subsets in mathematics. The components of the subset may be arranged in any order when combined.The subset's components are listed in a permutation in a certain order.The number of store customer is N = 50
The number of customer that receive a special gift is r = 3
The expression for the number of possible ways to choose 3 customers is
= ⁿCr
= ⁵⁰C₃
= 50 * 49 * 48/3 * 2 * 1
= 19600
Thus, the number of ways of groups of 3 customers are 19600.
Learn more about Combination and permutation
brainly.com/question/28720645
#SPJ4
335cm rounding off to the
nearest
Answers
Answer:
nearest what?
Step-by-step explanation:
nearest tens's=340
nearest hundred's=300
how to work out 15% of £24
Answers
Answer:
3.6.
Step-by-step explanation:
15% = 15/100 = 0.15
so the answer is 0.15 * 24
= 3.6
Answer:
3.60
Step-by-step explanation:
Note:
Of = Multiply
15% can also be written as .15 as decimal
Solve:
.15 × 24 = 3.60
Or we can solve like this:
\(\frac{24}{x}=\frac{100\%}{15\%}\)
\(\frac{x}{24}=\frac{15}{100}\)
\(\Rightarrow x=3.6\)
Therefore, 15% of £24 is 3.60
~Lenvy~
Find the median and mean of the data set below:
11,48,6,25,31
Answers
Answer:
mean 24.2
median 25
Step-by-step explanation:
6 11 25 31 48
The distance from Capital City to Little Village is 660 miles. From Capital City to Mytown is 310 miles, from Mytown to Yourtown is 200 miles, and from Yourtown to Little Village is 150 miles. How far is it from Mytown to Little Village
Answers
The distance from Mytown to Little Village is 350 miles.
The distance from Capital City to Little Village is 660 miles.
The distance from Capital City to Mytown is 310 miles,
The distance from Mytown to Yourtown is 200 miles,
and from Yourtown to Little Village is 150 miles.
Assuming all the places are collinear,
The distance from Mytown to Little Village is
200 + 150 = 350 miles
Hence, The Mytown is 350 miles far from the Little Village
Learn more about distance here https://brainly.com/question/17273444
#SPJ4
PLEASE HELP FOR ALGEBRA TEST write an equation that contains the coordinates (0,-1) and (3,7)
Answers
Answer:
The answer is y=8/3x-1
Step-by-step explanation:
7-(-1)/3-0
=8/3
y-y=m(x-x¹)
y-7=8/3(x-3)
y-7=8/3x-8
+7 +7
y=8/3x-1
In rectangle ABCD, AD=200, and diagonal AC=90, what is the perimeter of ABCD
Answers
Answer:Length = 200
Breadth=90
perimeter of rectangle
\( = 2(l + b) \\ = 2(200 \times 90) \\ = 2 \times 18000 \\ = 63000\)
Hope it helped
PLS mark BRAINLIEST
What are all values of x for which the function f defined by f(x) = (x2 - 3)e-x is increasing?.
Answers
The function f is increasing for x > 3/2.
To determine the values of x for which the function f is increasing, we need to find the critical points of f, which are the values of x where the function changes from increasing to decreasing or vice versa.
The first step is to find the derivative of f:
f'(x) = (2x - 3)e-x
Next, we need to find the critical points by setting f'(x) = 0 and solving for x:
(2x - 3)e-x = 0
2x - 3 = 0
x = 3/2
This is the only critical point of f. To determine the behavior of f near this critical point, we need to find the second derivative of f:
f''(x) = (2 - 3e-x)
For x < 3/2, f''(x) < 0, which means f is concave down and f'(x) is decreasing. This means that f is decreasing for x < 3/2.
For x > 3/2, f''(x) > 0, which means f is concave up and f'(x) is increasing. This means that f is increasing for x > 3/2.
You can learn more about function f at
https://brainly.com/question/25638609
#SPJ4
hurry the ratio of girls to boys in the middle school band is 4 to 5 whick of these show the possible numbers of the girls and boys in band
A 45 girls,54 boys
B 12 girls 20 boys
C 36 girls 45 boys
D 50 girls 40 boys
Answers
Answer:
C.) 36 girls 45 boys
Step-by-step explanation:
4 is divisible by 36 and 5 is divisible by 45 so C
A recipe uses 3 cups of milk to make 12 servings. if the same amount of milk is used for each serving, how many servings can be made from three gallons?
Answers
Answer:
16 cups are in a gallon, meaning we are working with 48 cups. 1 cup of milk works for 4 servings.
Therefore 48 * 4 = 192 servings.
A recipe uses 3 cups of milk to make 12 servings. if the same amount of milk is used for each serving,192 servings can be made from three gallons.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, A recipe uses 3 cups of milk to make 12 servings and the same amount of milk is used for each serving,
As we know,16 cups are in a gallon,
1 gallons = 16 cups
3 gallons = 3 × 16 cups
3 gallons = 48 cups
If 1 cup of milk works for 4 servings,
The number of servings that can be made from three gallons will be,
=48 × 4
= 192 servings.
Thus, a recipe uses 3 cups of milk to make 12 servings. if the same amount of milk is used for each serving,192 servings can be made from three gallons.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ5
consider a pi controller and the following feedback process what are the roots of the characteristic equation
Answers
The characteristic equation of a closed-loop control system with a proportional-integral (PI) controller is given by:
s^2 + (k_i/k_p)s + (1/k_p) = 0
where k_p is the proportional gain and k_i is the integral gain of the PI controller. To find the roots of the characteristic equation, we can use the quadratic formula:
s = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. Therefore, the roots of the characteristic equation depend on the values of k_p and k_i, which in turn depend on the specific feedback process being controlled.
Know more about closed-loop control system here:
https://brainly.com/question/30896173
#SPJ11
The 1st term of an arithmetic sequence in 8 and the 21st term is 108
Answers
Given the 1st term as 8 and the 21st term as 108, the 7th term of the arithmetic sequence needs to be found.
In an arithmetic sequence, the difference between consecutive terms remains constant. To find the 7th term, we can use the formula for the nth term of an arithmetic sequence: nth term = a + (n - 1) * d, where "a" is the 1st term and "d" is the common difference.
Substituting the given values, we have: 7th term = 8 + (7 - 1) * d.
We still need to find the common difference, which can be calculated using the formula: common difference = (21st term - 1st term) / (21 - 1). With the given information, the common difference is (108 - 8) / 20 = 5. Plugging this into the formula, we get: 7th term = 8 + (7 - 1) * 5 = 8 + 6 * 5 = 8 + 30 = 38.
Therefore, the 7th term of the arithmetic sequence is 38.
Learn more about Arithmetic sequence click here :brainly.com/question/6561461
#SPJ11
Question is - The 1st term of an arithmetic sequence in 8 and the 21st term is 108. Find the 7th term .
What is the measure of angle x? A 58°B. 38°C 42° D. 28°
Answers
Answer:
B. 38°
Explanation:
From the given figure, angles x and 142 degrees are on a straight line.
The sum of angles on a straight line is 180 degrees, therefore:
\(x+142\degree=180\degree\)Next, we solve the equation for x:
\(\begin{gathered} x=180\degree-142\degree \\ x=38\degree \end{gathered}\)The correct choice is B.
Answer: i don't care
Step-by-step explanation: I am doing it for the points
sry for not knowing the answer
Find the MEAN, VARIANCE, STANDARD DEVIATION, and COEFFICIENT OF VARIATION for the following SAMPLE of the number of severe car accidents in 1-90 from 2015 to 2020. (YOU MUST SHOW YOUR WORK!!!)
256, 189, 172, 220, 320, 192
Answers
The Mean, Variance, Standard Deviation, and Coefficient of Variation for the given sample of the number of severe car accidents in 1-90 from 2015 to 2020 are:
Mean = 224.833
Variance = 1956.0667
Standard Deviation (SD) = 108.319
Coefficient of Variation (CV) = 48.163%
From the question above, Given data is: 256, 189, 172, 220, 320, 192
Mean, variance, standard deviation and coefficient of variation for the given sample of the number of severe car accidents in 1-90 from 2015 to 2020 are given below:
The mean of data is equal to the sum of all data points divided by the total number of data points.
N = 6
Sum of data = 256 + 189 + 172 + 220 + 320 + 192 = 1349 ∴ Mean = 1349 / 6= 224.833
Calculation of Variance: The variance of data is the average of the squared differences from the mean.
Variance is calculated by dividing the sum of squared deviations by N-1, where N is the number of data points and then find the average.
Calculation of standard deviation: The standard deviation of data is the square root of the variance.SD = √11736.4 = 108.319
Coefficient of variation (CV): The coefficient of variation (CV) is a normalized measure of the dispersion of the data points. It is the ratio of the standard deviation to the mean.
CV is used to analyze and compare data of different sizes.
So, CV = (SD / Mean) × 100%CV = (108.319 / 224.833) × 100%= 48.163%∴
Learn more about standard deviation at
https://brainly.com/question/1505056
#SPJ11
square root of 44,100 by division
Answers
210 IS THE POSSIBLE ANSWER
John had $55. He spent $3 per day for nine days. Then he was given $12 to divide equally between himself and his two cousins. John used the following expression to calculate the amount of money he had after splitting the money with his cousins.
55 – 3 • 9 + 12 ÷ 3
Based on this expression, what is the amount of money John had remaining?
A.$160
B.$32
C.$24
D.$20
Answers
fifteen is what percent of 5
Answers
Answer:
300%
Step-by-step explanation:
You want to know what percentage 15 is of 5.
PercentA ratio or fraction is converted to a percentage by multiplying by 100%.
\(\dfrac{15}{5}\times100\% = \boxed{300\%}\)
15 is 300% of 5.
Which relation is a function?
Answers
Only table 2 is a function since it is a one to one mapping
What is a function?A function is a one-to-one mapping of an equation.
Since we have four expressions to determine if they are functions, we notice that
Expressions 1, 3 and 4 have more than one y value for the same value of x. so, they are one to many mappings and thus not functions.Also, we notice that table 2 has only one value of y for one value of x and thus one to one mappins and thus a functionSo, only table 2 is a function
Learn more about functions here:
https://brainly.com/question/10439235
#SPJ1
The square root of 20 is between which two integers
Answers
Answer:
The square root of 20 is 4.4
Step-by-step explanation:
The two integers show the square of 20 is between 4 and 5.
Given that,
There is a square root of 20.And, there are two integers.Based on the above information, the calculation is as follows:
16<20<25
16 represents the square of 4.
And, 25 represents the square of 5.
Therefore we can conclude that the two integers show the square of 20 is between 4 and 5.
Learn more: brainly.com/question/15276410
You are planning on purchasing a new car and have your eye on a specific model. You know that new car prices are projected to increase at a rate of 5% per year for the next few years.
Find the cost of the car 2 years from now if the current price is $25,000. Write the equation that represents the projected cost C and provide a solution for the problem.
a.
C = 25,000 (1.05) squared
$27,562.50
c.
C = StartFraction 25,000 (2) Over 1.05 EndFraction
$47,619.05
b.
C = 25,000 (1.05) (2)
$52,500
d.
C = 25,000 (2) Superscript 1.05
$51,763.25
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
A
Step-by-step explanation:
Cost of the car in "n" years=25000*(1+0.05)^n
Cost of the car in 2 years=25000*(1+0.05)^2=25000*(1.05)^2=27562.5
PLEASE HELP!
Stephanie is running a 5K race. She wants to keep track of her time and her distance throughout the race. Identify the independent and dependent variable.
A. The independent variable is the length of the race. The dependent variable is the time.
B. The independent variable is the time. The dependent variable is the distance of the race.
C. The independent variable is the time. The dependent variable is Stephanie's distance.
D. The independent variable is Stephanie's distance. The dependent variable is the time.
Answers
Answer:
A
Step-by-step explanation:
It mentions she is running a 5K race. That means the distance of the race is fixed and will not change. That means :
Length of the race is the independent variable and the dependent variable is time.
Answer:
The correct answer is letter A
4. Show that the matrix [XX-X'Z(ZZ)-¹Z'X). where both the x & matrix X and the x matrix Z. have full column rank and m2, is positive definite. Discuss the implications of this result in econometrics.
Answers
To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.
Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:
A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'. The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric. Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v
Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.
When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.
To learn more about eigenvalues click here: brainly.com/question/29861415
#SPJ11
The 130 juniors at Smithers High School are taking a class trip. Three buses will be taking the students and
chaperones to their destination, and each bus can hold up to 45 people. The first bus will be filled to capacity,
followed by the second and third buses. The function f(x) describes the total number of people on the first
bus, where x
is the number of minutes spent loading the bus.
If the first bus is boarded at a rate of 15 people per minute, what is the domain of the function?
Answers
If the first bus is boarded at a rate of 15 people per minute, the domain of the function is; (15 ≤ x ≤ 45)
How to solve Inequality word problems?We are told that;
Total number of Juniors at Smithers High School that are taking a class trip = 130
Number of buses taking each student to their destination = 3 buses
Capacity of each bus = 45 people
Now, if the function f(x) describes the total number of people on the first
bus, where x is the number of minutes spent loading the bus.
Then since the maximum number of people on the first bus is 45, then it means that the domain of the function is;
(15 ≤ x ≤ 45)
Read more about Inequality Word Problems at; https://brainly.com/question/25275758
#SPJ1