Answers
a. The critical points are (0,0), (0,k), (k,0), and (k,k).
b. x³ and y³ are always non-negative, it can see that this critical point is a local minimum.
c. The function has a local minimum for all k > 0
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
(a) To find the critical points of f(x, y) = x³ + y³ - 3xy, we need to find where the partial derivatives with respect to x and y are equal to zero:
∂f/∂x = 3x² - 3ky = 0
∂f/∂y = 3y² - 3kx = 0
Solving these equations simultaneously, we get:
x = y
3x² - 3kx = 0
Substituting the first equation into the second, we get:
3x² - 3kx = 0
3x(x - k) = 0
So x = 0 or x = k. Since x = y, we also have y = 0 or y = k.
Therefore, the critical points are:
(0,0), (0,k), (k,0), and (k,k).
To determine the nature of these critical points, we need to compute the second partial derivatives of f(x):
∂²f/∂y² = 6y
∂²f/∂x∂y = -3k
At the point (0,0), we have:
∂²f/∂x² = 0
∂²f/∂y² = 0
∂²f/∂x∂y = 0
So we cannot use the second derivative test to determine the nature of this point.
At the point (0,k), we have:
∂²f/∂x² = 0
∂²f/∂y² = 6k
∂²f/∂x∂y = -3k
The determinant of the Hessian matrix is:
∂²f/∂x² × ∂²f/∂y² - (∂²f/∂x∂y)² = 0 - (-3k)² = 9k² > 0
Since ∂²f/∂y² is positive, we have a local minimum at the point (0,k).
Similarly, we can show that the points (k,0) and (k,k) are also local minima when k > 0.
(b) When k = 0, the partial derivatives are:
∂f/∂x = 3x² = 0
∂f/∂y = 3y² = 0
So x = y = 0 is the only critical point.
The second partial derivatives are:
∂²f/∂x² = 6x = 0
∂²f/∂y² = 6y = 0
∂²f/∂x∂y = 0
So we cannot use the second derivative test to determine the nature of this point. However, since the function is symmetric about the x and y axes, and x³ and y³ are always non-negative, we can see that this critical point is a local minimum.
(c) To find the values of k for which f(x) has a local minimum or maximum, we need to consider the discriminant of the Hessian matrix at each critical point:
For the point (0,k):
∂²f/∂x² × ∂²f/∂y² - (∂²f/∂x∂y)² = 0 - (-3k)² = 9k² > 0
So function has a local minimum for all k > 0
Learn more about the function here:
brainly.com/question/12431044
#SPJ1
Related Questions
The area of each figure can be calculated using the given dimensions. Which of the
figures has an area formula that is a linear function?
Answers
The figure that has an area formula that is a linear function is the rectangle.
What is area?Area is the size or measurement of a two-dimensional space. It is usually expressed in square units such as feet, meters, or kilometers. Area is a fundamental concept in mathematics, and is used to measure the size of shapes and surfaces. Area is also used to calculate the amount of material or resources needed to cover a given space. In addition, it can be used to measure the cost or value of a piece of land.
The formula for the area of a rectangle is A=lw, where l is the length and w is the width. This formula is a linear equation because it is a product of two variables, where the relationship between the two variables is a constant. Thus, the area of a rectangle is a linear function of its dimensions.
To know more about area click-
https://brainly.com/question/28012687
#SPJ1
reduce 42/84 what is the answer
Answers
Answer:
1/2
Step-by-step explanation:
42/84=1/2
A square scarf has a side length of 34 yard on each side.
What is the area of the scarf?
Enter your answer in the boxes as a fraction in simplest form.
Answers
la surface de l'écharpe est de 1 1 56 cm² car la formule pour calculer l'air d'un carré est A= coté * coté soit coté²
donc : Aécharpe=34²=1156
Evaluate and match each expression on the left to it's value on the right, when x=6 and y=5?
12+x
Answers
[tex]12 + x = 12 + 6[/tex]
[tex]\implies 12 + x = 18[/tex]
Which of the following expressions is equivalent to 3^2x − 3?
Answers
Answer:
3(3x−1)
Step-by-step explanation:
'Paraphrasing'
Original: Scientists are quick to state that the presence of these organic molecules is not sufficient evidence for ancient life on Mars, as the molecules could have been formed by non-living processes.
A- Scientists cannot agree whether the discovery of organic material on Mars is proof that creatures lived on Mars or not in the past.
B- Scientists quickly say that the existence of these organic materials is not sufficient proof for ancient life on Mars, as the molecules could have been formed by other non-living methods.
C- Scientists claim life on Mars was not possible, and that natural processes are responsible for discovering any organic molecules.
D- Science experts are not strongly convinced that the discovery of organic materials on Mars is proof that living creatures existed before on Mars. It is possible the organic matter was created naturally due to different natural causes.
Answers
The presence of these organic elements, according to scientists, is insufficient evidence for the existence of ancient life on Mars since the molecules been created via other non-living processes. This assertion true.
What kinds of things are organic materials?Everything that includes carbon compounds produced by living things is considered to be organic matter. Lawn trimmings, leaves, twigs, branches, moss, algae, lichens, any animal parts, sewage, dust, insects, earthworms, and bacteria are just a few examples of what it includes.
Which three categories best describe organic materials?Carbohydrates, lipids, protein, and nucleic acids are the four main kinds of organic substances that are found in all living organisms.
To know more about organic materials visit:
https://brainly.com/question/1495095
#SPJ1
Can you help me with this problem??
Answers
a) The finance charge for the financing of the company airplane priced at $250,000 with 15% down payment is $66,308.
b) The monthly payments Vista's aircraft loan are $4,646.80.
How are the finance charge and monthly payments computed?The finance charge and the monthly payments can be determined using an online finance calculator as follows:
The finance charge represents the total interest and other fees that the financier charges for the loan.
The monthly payments are the periodic payments that must be made to settle the loan and compounded interest with the installment period of 60 months.
Company Airplane Price = $250,000
Down Payment = 15%
Loan Term = 60 months (5 years x 12)
Interest Rate = 11.25%
Results:
Monthly Payment (PMT): $4,646.80
House Price = $250,000
Down Payment = $37,500 ($250,000 X 15%)
Loan Amount = $212,500 ($250,000 - $37,500)
Total of 60 Mortgage Payments = $278,808
Total Interest (Finance Charge) = $66,308 ($278,808 - $212,500)
Learn more about the finance charge and monthly payments at https://brainly.com/question/30250781.
#SPJ1
Identify the part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0).
Answers
The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is given as follows:
5/6.
How to obtain the part-to-whole ratio?The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is obtained applying the proportions in the context of the problem.
We have that both the x-coordinate and the y-coordinate of A and B have a difference of 6 units.
We also have that both the x-coordinate and the y-coordinate of point P(3,1) have a difference of five units from the coordinates of the starting point of the segment A.
Then the ratio is given as follows:
5/6.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
When 16 is subtracted from the square of a number, the result is 6 times the number. Find the positive solution.
Answers
The positive solution is t = 8.
What are quadratic equations?A quadratic equation is a polynomial which has variables in which one has the highest power of 2.
Considering the question, let the unknown number be represented by t. So that;
16 is subtracted from the square of a number = t^2 - 16;
the result is 6 times the number = 6t
So that;
t^2 - 16 = 6t
t^2 - 6t - 16 = 0
t^2 + 2t - 8t - 16 = 0
(t^2 + 2t)(-8t - 16) = 0
t(t + 2)-8(t + 2)
So that
(t + 2)(t - 8) =0
t + 2 = 0 or t - 8 = 0
t = -2 or t = 8
Thus the positive solution is t = 8.
Learn more about quadratic equations at https://brainly.com/question/28038123
#SPJ1
A roll has 12 yardsof ribbon. Haley uses 6 feet of the ribbon for a swing project. How many feet of ribbon are left on the roll? Show your work?
Answers
Answer:
30 feet
First, we have to make sure that the numbers have the same units of measurementWe can see that the roll had 12 yards, and Haley used 6 feetThere are 3 feet in a yard6 feet would be equal to 2 yards because 6 is double the amount of 3 feet; and 2 is double the amount of 1Now, we have to subtract 2 from 12 12-2= 10Remember: The question is asking for feet, so we can multiply 10 by 3 to get the number of feet left10 x 3 = 30,
So, 30 feet of ribbon is left on the roll
So NL + y = 5. What would NL be?
Answers
NL would be 3.1 cm
What are similar triangles?
These are set of triangles which have some common relations on comparing their corresponding properties. But similarity of the triangles does not imply that they are congruent.
From triangle PQN, applying the trigonometric function. We have;
Tan θ = opposite/ adjacent
Tan 60 = 3.2/ y
1.7321 = 3.2/ y
y = 3.2/ 1.7321
= 1.8475
y = 1.9 cm
To determine the value of NL,
NL + y = 5
NL = 5 - y
= 5 - 1.9
= 3.1
NL = 3.1 cm
The value of NL would be 3.1 cm.
Learn more about similar triangles at https://brainly.com/question/26068068
#SPJ1
a highway has at least one rest stop every 25 miles. Write solve and graph an inequality to represent the number of rest stops in the first 200 miles of the highway.
Answers
In a linear equation, The number of rest stops in the first 200 miles would be 8 or more.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
25x > 200
25 25
x > 8
The number of rest stops in the first 200 miles would be 8 or more.
Learn more about linear equation
brainly.com/question/11897796
#SPJ1
Ricardo is half as likely to spin a 2 or 4 than an odd number
Answers
Based on the information provided, the statement "Ricardo is half as likely to spin a 2 or 4 than an odd number" is false.
Ricardo has a 2/27 chance of spinning either a 2 or a 4, and a 2/9 chance of spinning an odd number.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes, total number of outcomes
Let's start by assigning some variables to the probabilities of spinning each type of number. Let's say:
P(odd) is the probability of spinning an odd number
P(2 or 4) is the probability of spinning a 2 or a 4
According to the problem, we know that:
P(2 or 4) = 1/2 * P(odd)
We also know that the sum of the probabilities of spinning all possible numbers must equal 1. Since there are 5 odd numbers and 2 even numbers (2 and 4) on a standard six-sided die, we can write:
P(odd) + P(2 or 4) = 5/6 + 1/3 = 7/6
However, this equation doesn't make sense because the sum of probabilities should never exceed 1. This means that our assumption about P(2 or 4) being half as likely as P(odd) is incorrect.
To correct this, we can use the fact that P(odd) + P(even) = 1, where P(even) is the probability of spinning an even number (either 2 or 4). Since Ricardo is half as likely to spin a 2 or 4 than an odd number, we can write:
P(even) = 1/3 * P(odd)
Substituting this into the equation P(odd) + P(2 or 4) = 1, we get:
P(odd) + 1/2 * P(odd) = 1 - 1/3 * P(odd)
Simplifying this equation, we get:
3/2 * P(odd) = 1 - 1/3 * P(odd)
Multiplying both sides by 2/3, we get:
P(odd) = 2/9
Substituting this back into our equation for P(even), we get:
P(even) = 1/3 * P(odd) = 2/27
Therefore, Ricardo has a 2/27 chance of spinning either a 2 or a 4, and a 2/9 chance of spinning an odd number.
To learn more about Probability from given link.
https://brainly.com/question/11234923
#SPJ1
Complete Question:
Use the information from the spinner to determine if the statement is True or False.
Ricardo is half as likely to spin a 2 or 4 than an odd number.
Write in index form using negative powers 7/2 x × 2 x
Answers
Answer:
7withax2
Step-by-step explanation:
3x^2+42x+72 Student 1 Student 2 (X+2)(x+12). 3(x+2)(x+12) Which answer is the correct answer? What was wrong with that is incorrect? Explain what they did wrong. What important note can you make about factoring that you’ve learned from mistakes made on this problem?
Answers
Answer:
3(x + 12)(x + 2)
Step-by-step explanation:
Given
3x² + 42x + 72 ← factor out 3 from each term
= 3(x² + 14x + 24) ← factor the quadratic
Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term.
The factors are + 12 and + 2, since
12 × 2 = 24 and 12 + 2 = 14, thus
x² + 14x + 24 = (x + 12)(x + 2) and
3x² + 42x + 72
= 3(x + 12)(x + 2) ← in factored form
Find the measure of the three missing angles in the parallelogram below.
Answers
Answer:
[tex]x[/tex] = 67 , [tex]y[/tex] = 113 , [tex]z[/tex] = 67
Step-by-step explanation:
What we need to know:
A parallelogram has two pairs of equal angles
Opposite angles are equal
Angles in a quadrilateral add up to 360
1) Find out as many angles we can
We know that the opposite angles are equal, this means that y would be equal to 113
y = 1132) Find the remaining angles
We already know that two of our angles are 113, this means that our total is 226 for now. We have two angles left which are equal so to find them we have to subtract 226 by 360 then divide by 2
360 - 226 = 134134 ÷ 2 = 67[tex]x[/tex] = 67[tex]z[/tex] = 67Hope this helps, have a lovely day! :)
Answer:
x = 67
y = 113
z = 67
Step-by-step explanation:
The properties of a parallelogram are:
The opposite sides are equal and parallel.Opposite angles are congruent.Adjacent angles are supplementary (sum to 180°).Two angles are said to be adjacent when they share a common vertex.
Therefore, both angle x and angle z are adjacent to the angle that measures 113°.
Since adjacent angles in a parallelogram are supplementary:
⇒ x° + 113° = 180°
⇒ x° = 67°
⇒ x = 67
Similarly:
⇒ z° + 113° = 180°
⇒ z° = 67°
⇒ z = 67
As opposite angles in a parallelogram are equal:
⇒ y° = 113°
⇒ y = 113
The probability of a student taking a statistics class is 0.83, and the probability of a student taking a calculus class and a
statistics class is 0.66. What is the probability of a student taking a calculus class given that the student takes a statistics
class?
Round your answer to three decimal places.
Answers
Answer:
Step-by-step explanation:
We can use the conditional probability formula to find the probability of a student taking a calculus class given that the student takes a statistics class:
P(calculus | statistics) = P(calculus and statistics) / P(statistics)
We are given that P(statistics) = 0.83 and P(calculus and statistics) = 0.66.
Substituting the values we have:
P(calculus | statistics) = 0.66 / 0.83
Simplifying the fraction:
P(calculus | statistics) = 0.795
Therefore, the probability of a student taking a calculus class given that the student takes a statistics class is 0.795. Rounded to three decimal places, the answer is 0.795.
Use synthetic division to evaluate for the indicated x value.
x³ + x²-3x +9; ƒ (-4)
f(-4)=
Answers
The first step to calculate the indicated x value using synthetic division is to assemble the synthetic division table, which will be:
Column 1 | Column 2-4 | 11 -3 91 -3 9 -63 |The first number on the top line, 1, is the coefficient of the highest degree term in the polynomial. The remaining coefficients are written in order, with 0 placeholders for any missing terms. The divisor, -4, is written to the left of the table.
How to calculate synthetic division?We must reduce the first coefficient, which is 1. Then we multiply -4 by 1 to get -4 and write that in the next coefficient, which is 1. We add the two numbers to get -3 , which we write under the next coefficient , which is -3. We multiply -4 by -3 to get 12 and write that under the last coefficient, which is 9. We add the two numbers together to get -51, which is the remainder.Therefore, we find ƒ(-4) = -51.
Find out more about synthetic division on:
https://brainly.com/question/24662212
#SPJ1
Which of these cannot be an r2-value?
Answers
The value given that cannot be an r ² value is A. - 0.75.
What is the r ² value ?The r² value, also known as the coefficient of determination, is a statistical measure that represents the proportion of variance in the dependent variable that can be explained by the independent variable(s). It is a value between 0 and 1, with higher values indicating a better fit of the regression model to the data.
It is not possible for the r² value to be negative because it is the square of the correlation coefficient. - 0.75 cannot possibly be a value of r ² as a result.
Find out more on the coefficient of determination at https://brainly.com/question/17237825
#SPJ1
Five years have passed and Jamie Lee, 34, is considering taking the plunge--not only is she engaged to be married, but she is also deciding on whether to purchase a new home. Jamie Lee’s cupcake café is a success! It has been open for over a year now and has earned itself rave reviews in the local press and from its regular customers who just cannot get enough of her delicious varieties of cupcakes. One such customer, who stopped by on a whim in the café’s first week of business, is Ross. After a whirlwind courtship, Ross, a self-employed web designer, proposed, and Jamie Lee agreed to be his wife. The bungalow that Jamie Lee has been renting for the past five years is too small for the soon-to-be newlyweds, so Jamie Lee and Ross have purchased a brand new three-bedroom, 2 ½ bath home in a quiet neighborhood for $276,000. Use the provided information and the table below to calculate the affordable mortgage amount that would be suggested by a lending institution based on Jamie Lee and Ross’s income. You will need to make note of the purchase price (above) of their home for future questions. Use the following for Jamie Lee and Ross's calculations: 10% down payment $650 per month for estimated combined property taxes and insurance 5% interest rate for 30 years Refer to Exhibit 7-7 for current mortgage rates
Answers
Therefore , the solution of the given problem of interest comes out to be $882.75 monthly affordable mortgage amount recommended by a lending organisation .
What does interest actually mean?To determine simple interest, divide the sum by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a fraction of the principal amount.
Here,
We can use an internet mortgage calculator to determine the affordable monthly mortgage payment. With the provided data, we can determine the monthly mortgage payment to be $1,187.25 using a mortgage calculator.
Assume that Jamie Lee and Ross earn $8,000 per month in gross revenue.
Affordable debt amount
=> $1,837.25 ($8,000 x 0.43)
=> $2,720 - $1,837.25
is an affordable mortgage sum.
=> $882.75 is an affordable mortgage sum.
This indicates that the $882.75 monthly affordable mortgage amount recommended by a lending organisation based on Jamie Lee and Ross's income.
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
a candidate is contesting for both national and provincial seats.
(A)what is the probability that he'll win both seats.
(B)what is the probability he'll loose both seats.
(C)what is the probability he'll win one seat.
Answers
A. The probability that he'll win both seats is 0.48.
B. The probability he'll loose both seats is 0.52.
C. The probability he'll win one seat is 0.92.
What is probability?The probability of an event is calculated using the mathematical notion of probability. We can only use it to determine the likelihood that an event will occur. On a scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.
We are given that a candidate is contesting for both national and provincial seats.
Event A = Winning national seat
Event B = Winning provincial seat
A. The probability that he'll win both seats is
P(A) × P(B) = 0.8 × 0.6 = 0.48
B. The probability he'll loose both seats is
1 - 0.48 = 0.52
C. The probability he'll win one seat is
Probability = 0.8 + 0.6 - 0.48
Probability = 0.92
Hence, the required probabilities have been obtained.
Learn more about probability from the given link
https://brainly.com/question/24756209
#SPJ1
Question: a candidate is consisting for both national and provincial assembly seats. the probability that he will win the national seat is 0.8 and will win the provincial seat is 0.6. what is the probability that
a) he will win both seats
b) he will lose both the seats
c) he will win at least one seat
HELPPP! A yard plan includes a rectangular garden that is surrounded by bricks. In the drawing, the garden
is 7 inches by 4 inches. The length and width of the actual garden will be 35 times larger than the
length and width in the drawing.
(a) What is the perimeter of the drawing? Show your work.
(b) What is the perimeter of the actual garden? Show your work.
(c) What is the effect on the perimeter of the garden with the dimensions are multiplied by 35?
Show your work.
Answers
Josh wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Josh can pay $35 per month, plus $2 for each group class he attends. Alternately, he can get the second membership plan and pay $34 per month plus $3 per class. If Josh attends a certain number of classes in a month, the two membership plans end up costing the same total amount. What is that total amount? How many classes per month is that?
Answers
Therefore, if Josh attends 1 group class per month, both membership plans will cost him a total of $37 per month.
What makes up a number's fundamental unit?In mathematics, the first 10 integers are referred to as the fundamental numbers. From 0 to 9, these foundational numbers are listed. The 0 to 9 range of basic integers includes 0 through 1, 2, 3, 4, 5, 6, 7 and 8.
Let's start by defining some variables. Let:
x be the number of group classes Josh attends per monthT1 be the total cost of the first membership plan (which charges $35 per month, plus $2 for each class)T2 be the total cost of the second membership plan (which charges $34 per month, plus $3 for each class)We can write the equations for the total cost of each plan as:
T1 = 35 + 2x
T2 = 34 + 3x
Since we know that the two plans end up costing the same total amount when Josh attends a certain number of classes in a month, we can set T1 equal to T2 and solve for x:
35 + 2x = 34 + 3x
35 = 34 + x
1 = x
So if Josh attends 1 group class per month, the two membership plans will cost the same total amount. Let's substitute x = 1 into our equations for T1 and T2 to find out what that total amount is:
T1 = 35 + 2(1) = 37
T2 = 34 + 3(1) = 37
Therefore, if Josh attends 1 group class per month, both membership plans will cost him a total of $37 per month.
To know more about number visit:
https://brainly.com/question/17429689
#SPJ1
Write your own question that involves time conversion and ask someone to solve it.
Make sure you solve it too so you know if they get the correct answer!
Answers
Answer: If a movie starts at 2:45 PM and has a duration of 2 hours and 10 minutes, what time does it end?
To solve this, we need to add the duration of the movie to the start time and convert it back to the 12-hour clock format.
Adding 2 hours and 10 minutes to 2:45 PM, we get:
2:45 PM + 2 hours + 10 minutes = 4:55 PM
So, the movie ends at 4:55 PM.
Step-by-step explanation:
Assuming and y are both positive, write the following expression in simplest
radical form.
4xy³√ 27x^2y^5
Answers
Answer:
We can simplify the given expression using the rules of exponents and radicals:
4xy³√ 27x^2y^5
= 4xy * ³√(27x^2y^5) (since y and ³√(27) cannot be simplified further)
= 4xy * ³√(3^3 * x^2 * y^3 * y^2)
= 4xy * 3xy * ³√y^2
= 12x^2y^2 * ³√y^2
Therefore, the expression 4xy³√ 27x^2y^5 simplifies to 12x^2y^2 * ³√y^2.
Step-by-step explanation:
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate
T.
P = $2300, A = $2762, t = 6 months
The loan's simple interest is %.
***
Answers
Based on the information provided, it can be concluded the loan's simple interest is 4.01%.
What is the loan's simple interest?The simple interest is the difference between the future value of the loan and the loan amount.
Simple interest = future value - loan amount $2762 - $2300 = $462
The simple interest rate is a linear function of the loan amount, the interest rate, and the duration of the loan. The simple interest that is paid is the same each year for each period of the duration of the loan.
Simple interest = loan amount x time x interest rate
Interest rate = simple interest / (loan amount x time) = 462 ÷ (6/12 x 2300) = 0.401= 4.01%
To learn more about simple interest, please check: https://brainly.com/question/27328409
#SPJ1
Find the minimum sample size n needed to estimate μ for the given values of c, σ, and E.
c = 0.95, σ = 9.1, E = 1
Answers
Answer:
The formula to calculate the minimum sample size required to estimate the population mean is given as:
n = (z^2 * σ^2) / E^2
Where,
z = the z-value for the given confidence level, which is 1.96 for c = 0.95
σ = the population standard deviation
E = the maximum error of estimate, also known as the margin of error
Plugging in the values, we get:
n = (1.96^2 * 9.1^2) / 1^2
n = 301.63
Rounding up to the nearest whole number, the minimum sample size required is 302.
Therefore, a sample size of at least 302 is needed to estimate the population mean with a 95% confidence level, assuming a population standard deviation of 9.1 and a maximum error of estimate of 1.
Step-by-step explanation:
Algebra l
Find an exponential model for the data.
ANSWER THIS: The exponential model for the data is y=___
Answers
The exponential model for the data is y=0.646(1.087)ˣ.
What is the exponential function?Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
From the table we have, (8, 1.26), (10, 1.49)
We know that, the general form of exponential model is y=abˣ.
Here, substitute (8, 1.26) in y=abˣ, we get
1.26=ab⁸ -------(i)
a=1.26/b⁸
Here, substitute (10, 1.49) in y=abˣ, we get
1.49=ab¹⁰ -------(ii)
a=1.49/b¹⁰
1.26/b⁸ = 1.49/b¹⁰
1.26=1.49/b²
b²=1.49/1.26
b=1.087
Substitute b=1.087 in equation (i), we get
1.26=a(1.087)⁸
1.26=a(1.95)
a=1.26/1.95
a=0.646
So, the equation is y=0.646(1.087)ˣ
Therefore, the exponential model for the data is y=0.646(1.087)ˣ.
Learn more about the exponential function here:
brainly.com/question/11487261.
#SPJ1
40. Social Security Numbers
A Social Security number is used to identify each resident of the United States uniquely. The number is of the form xxx-xx-xxxx, where each x is a digit
from 0 to 9.
(a) How many Social Security numbers can be formed?
(b) What is the probability of correctly guessing the Social
Security number of the president of the United States?
Answers
There are 10⁹(1 billion) possible Social Security numbers that can be formed. The probability of correctly guessing the Social Security number of the president of the United States is practically zero. This is because there are so many possible combinations, and it is highly unlikely that anyone would guess the correct number.
What is number?Number is a mathematical object used to count, measure, and label. It is used to express amounts, or magnitude of a quantity. Numbers are used in almost every field of life, such as science, engineering, economics, finance, and many other areas. Numbers are used in a wide range of contexts and are essential to modern life. They are used to communicate information, to measure time, and to represent values. Furthermore, numbers are used to represent abstract ideas, such as the probability of an event occurring. Numbers are also used to create patterns, which are essential to understanding complex systems. Without numbers, it would be impossible to measure anything, make estimates, or draw conclusions.
(a) There are a total of 10^9 (1 billion) possible Social Security numbers. This is calculated by multiplying the 10 possible digits (0-9) for each of the nine positions in the number, which gives 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10⁹.
(b) The probability of correctly guessing the Social Security number of the president of the United States is 1 in 10⁹. This is because there are a total of 10^9 possible Social Security numbers, and the president's number is only one of those.
To know more about number click-
https://brainly.com/question/24644930
#SPJ1
Describe an activity for Grade R to teach Subtraction that will accommodate each type of learning modality
Answers
Grade R learners can be best taught using hands-on experience, thus use physical beads or objects to practically teach subtraction.
How should learners in grade R be taught?A manipulatives-based project can be a fantastic method to teach subtraction to grade R students, who frequently learn best via hands-on experiences. This activity can be modified to accommodate students who learn better visually, aurally, or kinesthetically.
The activity that can be used to teach grade R learners to subtract is by using physical objects, and asking them to count the initial number.
Remove some items and recount them.
The objects removed will denote the subtraction.
Learn more about learning modality here:
https://brainly.com/question/18646515
#SPJ1