Area: [tex]3.14*3^2=28.26 cm^2\\[/tex]
Circumference: [tex]2*3.14*3=18.84cm[/tex]
select the function that represents the simple interest formula
The function that represents the simple interest formula is A(n)=P+(n-1)i*P, where n is a positive integer. (Option D)
Simple interest refers to the method of calculating the amount of interest charged on a sum at a given rate and for a given period of time. It is given by the formula:
SI = Pin
Where SI is the interest amount, P is the principal amount, i is the interest rate, and n is the number of period.
So, for n-1 years, the simple interest is:
SI = P(n-1)*i
The total amount charged is given by
A(n) = P + SI
A(n) = P + (n-1)i*P
Note: The question is incomplete. The complete question probably is: Select the function that represents the simple interest formula. A. A(n)=(n-1)(P*i)^n, where n is any real number. B. A(n)=n+(P-1)i*P, where n is a positive integer. C. A(n)=P(1+i)^n-1, where n is any real number. D. A(n)=P+(n-1)i*P, where n is a positive integer
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A three-sided fence is to be built next to a straight section of river, which forms the fourth side of a
rectangular region. The enclosed area is to equal 128 m². Find the minimum perimeter and the
dimensions of the corresponding enclosure.
Answer:
perimeter: 32 mdimensions: 16 m parallel to the river; 8 m wideStep-by-step explanation:
You want the length of the minimum perimeter fence to enclose 3 sides of a rectangular area of 128 m² with one side of the enclosure provided by a river. You also want the enclosure dimensions.
PerimeterIf x represents the dimension of the enclosure parallel to the river, then the other dimension of the enclosure is found from ...
A = LW
128 = x·W
W = 128/x
There will be two sides of this length, so the perimeter is ...
P = L +2W = x +2(128/x)
P = x + 256/x
MinimumThis has an extreme value (minimum) where its derivative is zero:
dP/dx = 0 = 1 -256/x²
Solving for x gives ...
x² = 256
x = √256 = 16
and the perimeter is ...
P = 16 +256/16 = 32
The other dimension is 128/16 = 8.
The minimum perimeter is 32 meters; the enclosure is 16 by 8 meters.
__
Additional comment
This can be solved without using derivatives by working the reverse problem: the largest area for a given perimeter.
Using the same definition of x, the area in terms of perimeter is ...
A = x · (P -x)/2
This is a quadratic equation with a maximum halfway between its zeros at x=0 and x=P. So, the value of x for maximum area is x = P/2. That area is ...
A = (P/2)(P -P/2)/2 = (P/2)(P/4) = P²/8
Or, the minimum perimeter for a given area is ...
P = √(8A)
In this problem, that is ...
P = √(8·128) = √1024 = 32
The dimensions of the enclosure are (P/2)×(P/4) = 16×8.
Determine if the following represents a function.
1. n ={(-4,2),(0,9),(-4,8),(4,5),(-1,10)}
The given set is not a function.
We must keep in mind the following guidelines in order to determine whether the provided set of ordered pairs is a function or not:
1. We first determine the input or the x values.
2. Keep in mind that each x-value needs to be distinct.
A relation where there is both an input and an output is called a function. The same input cannot be used to generate distinct outcomes.
It is known that n = (-4,2), (0,9), (-4,8), (4,5), and (-1,10)
List each of the input values (x) in step one: -4, 0, -4, 4, -1
Every input value (x) has to be distinct: Observe how -4 repeats.
Therefore, the set is not a function.
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Question 4
The graph of f(x) is shown below.
What is the value of f(-3)?
(1) 6
2) 2
(3)-2
(4) -4
The value of the function instance, f (-3) as required to be determined according to the graph of f (x) as in the attached image is; -4.
What is the value of the function instance; f (-3)?It follows from the task content that the value of the function instance; f (-3) is to be determined according to the attached graph.
By observation; when a vertical line; x = -3 is drawn; it follows that the line passes through and intersects the lines; y = -1 and y = -4.
However, there's an open circle at; y = -1 which indicates that; -1 is not in the range of f (x).
Ultimately, the value of the function instance; f (-3) as required to be determined is; Choice 4; -4.
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what is 1 +1 x 30(200-125) + 999² ÷2000
what i got when i looked it up: 2750.0005
what i got when i did it 500.0005
Twice my hat size is 3 times my shoe size. If my hat size is 18 more than my shoe size, then the sum of my hat size and shoe size together is:
A) 36 B) 54 C) 90 D) 108
What is the least 3-digit odd sum of two prime numbers
A) 101 B) 103 C) 105 D) 107
What is the greatest possible product of the ones digits of 4 numbers
A) 9 B) 105 C) 945 D) 6561
Please give a detailed and simple explanation please!
Answer:
Q1. The sum of your hat size and shoe size is 54.
Q2. The correct answer is 101.
Q3. The correct answer is 6561.
Step-by-step explanation:
Q1. Let's call the size of your hat H and the size of your shoe S. You can set up the following equation based on the given information:
H = 2S
H = S + 18
Substituting the first equation into the second equation, we get:
2S = S + 18
S = 18
Then, substituting this value back into the first equation, we get:
H = 2S
H = 2 * 18
H = 36
The sum of your hat size and shoe size is S + H = 18 + 36 = 54.
Q2. The least 3-digit odd sum of two prime numbers is 101, which can be achieved by adding the two prime numbers 2 and 99. Both 2 and 99 are prime numbers, and their sum is 101, which is a 3-digit odd number.
Q3. The greatest possible product of the ones digits of 4 numbers is 6561, which can be achieved by choosing the numbers 9901, 9911, 9921, and 9931. The ones digits of these numbers are 1, 1, 1, and 1, respectively, and their product is 6561.
Choose all the options that cannot be part of the net of a cube
Answer:
all of the above(ans)
For the functions f(t) = et and g(t) = e-6t, defined on 0 Le t Le infinity, compute f * g in two different ways: By directly evaluating the integral in the definition of f * g. (f * g) (t) = dw = By computing L-1 {F(s)G(s)} where F(s) = L{f(t)} and G(s) = L{g(t)}. (f * g)(t) = L-1 {F(s)G(s)} = L-1{ }
The value of the expression (f * g) by using two ways that is by direct integral and by Laplace transform is equal to (1/2)e^t/(1-t) - (1/2)e^t/(1+t) + C.
To compute the convolution of f(t) and g(t) by directly evaluating the integral in the definition of the convolution, we have:
(f * g)(t) = ∫f(w)g(t-w)dw
Substituting in the expressions for f(t) and g(t), we have:
(f * g)(t) = ∫e^w*e^(-6)(t-w)dw
This integral can be evaluated as follows:
(f * g)(t) = ∫e^(-5w)dw
(f * g)(t) = (-1/5)e^(-5w) + C
(f * g)(t) = (-1/5)e^(-5w) + C
To compute the convolution of f(t) and g(t) by computing the inverse Laplace transform of the product of the Laplace transforms of f(t) and g(t), we have:
F(s) = L{f(t)} = ∫f(t)e^(-st)dt = ∫e^t*e^(-st)dt = 1/(s-1)
G(s) = L{g(t)} = ∫g(t)e^(-st)dt = ∫e^(-6t)*e^(-st)dt = 1/(s+6)
Therefore,
F(s)G(s) = (1/(s-1))(1/(s+6)) = 1/(s^2-1)
To find the inverse Laplace transform of F(s)G(s), we use the following formula:
L^-1{F(s)G(s)} = ∫F(s)G(s)e^st ds
Substituting in the expression for F(s)G(s), we have:
L^-1{F(s)G(s)} = ∫(1/(s^2-1))e^st ds
This integral can be evaluated as follows:
L^-1{F(s)G(s)} = (1/2)e^st/(s-1) - (1/2)e^st/(s+1) + C
L^-1{F(s)G(s)} = (1/2)e^st/(s-1) - (1/2)e^st/(s+1) + C
Thus, the convolution of f(t) and g(t) can be computed either by directly evaluating the integral in the definition of the convolution or by computing the inverse Laplace transform of the product of the Laplace transforms of f(t) and g(t). In both cases, the result is:
(f * g)(t) = (1/2)e^t/(1-t) - (1/2)e^t/(1+t) + C
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What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.) A button hyperlink to the SALT program that reads: Use SALT. (a) a preliminary estimate for p is 0.27 (b) there is no preliminary estimate for p
a)Preliminary estimate for p = 0.27
[tex]n = \frac{0.27 (1 -0.27)}{(\frac{0.1}{1.96})^2 }[/tex] = 78.84
And rounded up we have that n = 79
b) No preliminary estimate for p
[tex]n = \frac{0.5(1 - 0.5)}{(\frac{0.1}{1.96} )^2}[/tex] = 96.04
And rounded up we have that n=97
A confidence interval is "a range of values that is likely to contain the population value with some degree of confidence. Often expressed as a %, the population mean falls between an upper and lower interval. ”.The error bars are the range of values above and below the sample statistic in the confidence interval.The normal distribution is "a probability distribution that is symmetric about the mean and indicates that data closer to the mean occur more frequently than data further away."The population proportion have the following distribution
p ~ [tex]N ( p , \sqrt{\frac{p(1 -p)}{n} }[/tex]
Solution to the problem
Part a) preliminary estimate for p :
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by α = 1 - 0.95 and α/2 = 0.025. And the critical value would be given by:
[tex]z_{\alpha /2} = - 1.96 , z_{1 - \alpha /2} = 1.96[/tex]
The margin of error for the proportion interval is given by this formula:
(a) [tex]ME = z_{\alpha /2} \sqrt{\frac{p (1-p)}{n} }[/tex] ----------------- (1)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b) [tex]n = \frac{p(1 -p)}{(\frac{ME}{2} )^2}[/tex] ---------------------- (2)
And replacing into equation (2) the values from part a we got:
[tex]n = \frac{0.27 (1 -0.27)}{(\frac{0.1}{1.96})^2 }[/tex] = 78.84
And rounded up we have that n = 79
Part b) no preliminary estimate
Since we don't have a prior estimation for p we can use . And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b) [tex]n = \frac{p(1 -p)}{(\frac{ME}{2} )^2}[/tex]
And replacing into equation (b) the values from part a we got:
[tex]n = \frac{0.5(1 -0.5)}{(\frac{0.1}{1.96})^2 }[/tex] = 96.04
And rounded up we have that n=97
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choose r for a qualification for a member of the house of representatives, s for a qualification for a senator, or b for both.
Qualifications for members of house of representatives and senate
r ;- Be a resident of the state from which they are elected, be at least 25 years old, and have been citizens for at least 7 years.
s ;- Be a resident of the State from which he or she is elected, at least 30 years old, and a citizen for at least 9 years.
Given,
The House of Representatives is the lower body of the United States Congress, and the United States Senate is its upper chamber. The United States' national bicameral legislature is made up of them all. Washington DC
Then,
Qualification for a member of the house of representatives, r ;-
Be a resident of the state from which they are elected, be at least 25 years old, and have been citizens for at least 7 years.
Qualification for a senator, s ;-
Be a resident of the State from which he or she is elected, at least 30 years old, and a citizen for at least 9 years.
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The differential treatment of individuals or groups without reference to behavior, qualifications, or other legal factors, resulting in a difference in outcome, is known as discrimination. Discrimination can occur based on various factors such as race, gender, age, religion, disability, or nationality.
There are different forms of discrimination, including: 1. Direct discrimination: This occurs when someone is treated less favorably because of a specific characteristic or attribute. For example, if an employer refuses to hire someone solely based on their gender, it would be considered direct discrimination. 2. Indirect discrimination: This happens when a seemingly neutral policy, criterion, or practice puts individuals with a particular characteristic at a disadvantage. For instance, if a job requires a height requirement that disproportionately affects a certain racial group, it would be considered indirect discrimination.
3. Systemic discrimination: This refers to discrimination that is built into the structures, policies, and practices of an organization or society. It may be unintentional but still leads to unequal outcomes. An example is when certain communities consistently receive lower funding for education compared to others, leading to systemic disadvantages for students in those areas.
Discrimination can have negative impacts on individuals and society as a whole, perpetuating inequality and hindering social progress. It is important to promote equality, fairness, and inclusivity to create a just and equitable society.
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The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows. Brand Bose Scullcandy Koss Phillips/O'Neill Denon JVC Price ($) 192 156 90 84 72 48 Score 78 78 60 60 42 a. Does the t test indicate a significant relationship between price and the overall score? The test t-conclusion at ?-.05 t1.68 (to 2 decimal places.)
Based on the given consume reports data, the t value is 2.228.
T - value:
In statistics, t - value measures the size of the difference relative to the variation in your sample data.
Given,
Here we have the tale with price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports.
Now, we need to find the t test indicate a significant relationship between price and the overall score.
While we looking into the question, the values in this one are,
n = 6
And table of 6 stereo headphone price and overall score are given.
Based on the given details we have calculated the frequency table and the table is attached below.
Based on the resulting table we have identified that the value of t is 2.228.
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Exxon sells its bonds at 108.375. The amount of premium or discount the bond is selling for is:
Multiple Choice
$83.75
$13.75
$13.25
$8.38
The amount premium on bond selling is $83.75. Option A is correct.
Given that,
Exxon sells its bonds at 108.375%. The amount of premium or discount the bond is selling for is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Face value of bonds = $1000
The selling price of bond = 1000 × 108.375%
=$1083.75
Premium on bonds = difference in the selling price - value of a bond
= 1083.75-1000
= $83.75.
Thus, the amount of the premium on bond selling is $83.75. Option A is correct.
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Solve 19 - 4x = 2x + 1
Answer: The answer is 3
Step-by-step explanation: I’m smart.
x= 3.
Step-by-step explanation:1. Write the expression.[tex]19 - 4x = 2x + 1[/tex]
2. Subtract 19 from both sides of the equation.[tex]19 - 4x-19 = 2x + 1-19\\ \\-4x=2x-18[/tex]
3. Subtract 2 from both sides of the equation.[tex]-4x-2x=2x-18-2x\\ \\-6x=-18[/tex]
4. Divide both sides by "-6".[tex]\frac{-6x}{-6} =\frac{-18}{-6} \\ \\x=3[/tex]
5. Verify the answer by substituting the calculated value of m into the original equation and simplifying.[tex]19 - 4(3) = 2(3) + 1\\ \\19-12=6+1\\ \\7=7[/tex]
That's correct. Therefore, x= 3 is the correct answer!
Ellon aeronautics desires an 8% ROI on all investment projects. Details of a proposed investment include the following:
Sales Revenues $30,000
Expenses 27,000
Investment Turnover 1.5
Hurdle rate is 55%.
Ellon aeronautics has an ROI of 8% based on revenues of $30,000. the expenses residual income is $27,000 and the investment turnover is 1.5. The hurdle rate is 55%.
Investment
Investment Mathematics provides an introductory analysis of investments from a quantitative viewpoint, drawing together many of the tools and techniques required by investment professionals.
Residual Income
Residual income is calculated as net income less a charge for the cost of capital. This is known as the equity charge and is calculated as the value of equity capital multiplied by the cost of equity or the required rate of return on equity. The formula is: Residual Income = Net Income - Equity Charge
The investment turnover using this formula
Investment turnover=Sales/invested capital
Investment turnover = ($27000 / $30,000) × 1.5
Investment turnover = 0.9 × 1.5
Investment turnover =1.35
The hurdle rate using this formula
Hurdle rate = ROI - Investment turnover
Hurdle rate = 8 - 1.35
Hurdle rate = 0.55 × 100
Hurdle rate = 55%
Therefore the hurdle rate is 55%.
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a newly discovered planet is found to have twice the radius and five times the mass of earth. if the acceleration of gravity at the surface of earth is g, the acceleration of gravity at the surface of the new planet is
g(planet)/g(earth) = 12.25/9.8 = 1.25 m/s²
Gravitational Force
The gravitational force is a force that attracts any two objects with mass. We call the gravitational force. It is given by, F=Gm1m2r2, direction of force will be always towards the other mass along the line joining the two bodies. It is attractive force in nature.
Gravity
The force of attraction by which terrestrial bodies tend to fall toward the center of the earth. heaviness or weight. gravitation in general.
The acceleration due to gravity of a planet with mass M and radius R is g as:
free-fall acceleration = 12.25 m/s²
Formula for free fall acceleration is given by the gravity equation;
g = Gm/r²
Where;
M is mass of the Earth
r is radius of the Earth
G is the gravitational constant
That equation applies to the earth.
For this new planet, that the mass = 5 × mass of earth
And radius = 2 × radius of earth.
Thus, free fall acceleration for this planet is;
g_ p = G(5m)/(2r)²
g_ p = (5/4)(Gm/r²)
Gravitational constant has a value of 6.674 × 10^(−11) N.m²/kg²
Mass of the earth = 5.972 × 10^(24) kg
Radius of the earth = 6378 km = 6378000
Thus
g_ p = (5/4)(6.674 × 10^(−11) × 5.972 × 10^(24))/(6378000²) = 12.25 m/s²
The acceleration of gravity at the surface of the new planet is
g(planet)/g(earth) = 12.25/9.8 = 1.25 m/s²
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What are the first six numbers of the Fibonacci sequence?; What is the value of Fibonacci 6?; What is the 63rd term of the Fibonacci sequence?; What is the 12th term of the Fibonacci sequence 1 1 2 3?
The solutions for all three questions regarding the Fibonacci sequence are given below.
The Fibonacci sequence can be defined as a set of integers that form a sequence that follows one rule ie., every number is the sum of the preceding two numbers. The first six numbers of the Fibonacci sequence are = 1, 1, 2, 3, 5, 8.
The 63rd term of the Fibonacci sequence is 4052739537881. The 12th number in this sequence is 144. This can be found out using the formula -
= [tex]F_{n-1}[/tex] + [tex]F_{n-2}[/tex]
Here, if we know the values of the preceding two numbers, we can easily find out the value of any number in the Fibonacci sequence.
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A pharmacy has determined that a healthy person should receive 70 units of
proteins, 100 units of carbohydrates and 20 units of fat daily. If the store carries
the six types of health food with their ingredients as shown in the table below,
what blend of foods satisfies the requirements at minimum cost to the
pharmacy? Make a mathematical model for the given problem.
Foods Protein units Carbohydrates
units
Fat units Cost per unit
A 20 50 4 2
B 30 30 9 3
C 40 20 11 5
D 40 25 10 6
E 45 50 9 8
F 30 20 10 8
optimal solution is arrived with value of variables as :
x1=0.9091,x2=1.8182,x3=0,x4=0,x5=0,x6=0
minimize cost:
z=2x₁+3x₂+5x₃+6x₄+8x₅+8x₆=2x
subject to:
20x₁+30x₂+40x₃+40x₄+45x₅+30x₆ ≥70 : amount of protein
50x₁+30x₂+20x₃+25x₄+50x₅+20x₆ ≥100 : amount of carbohydrate
4x₁+9x₂+11x₃+10x₄+9x₅+10x₆ ≥20 : amount of fat
where x₁, x₂, x₃, x₄, x₅, x₆ are units of 6 foods
solution using Simplex method:
After introducing artificial variables:
Min Z=2x₁+3x₂+5x₃+6x₄+8x₅+8x₆+0S₁+0S₂+0S₃+MA₁+MA₂+MA₃
subject to
20x₁+30x₂+40x₃+40x₄+45x₅+30x₆-S₁+A₁ ≥ 70
50x₁+30x₂+20x₃+25x₄+50x₅+20x₆-S₂+A₂≥ 100
4x₁+9x₂+11x₃+10x₄+9x₅+10x₆-S₃+A₃=20
and x₁,x₂,x₃,x₄,x₅,x₆,A₁,A₂,A₃≥0
Refer to the image for Z
Since all Zj-Cj≤0
Hence, optimal solution is arrived with value of variables as :
x1=0.9091,x2=1.8182,x3=0,x4=0,x5=0,x6=0
Min Z=7.2727
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Use analysis of variance rather than a t test whenever the null hypothesis makes a claim about:____
The use of analysis of variance rather than a t-test for the null hypothesis claims more than two populations.
Analysis of Variance (ANOVA) is a statistical component used to evaluate variances throughout the method (or average) of various groups. A variety of eventualities use to decide if there's any distinction among the method of various groups. Student's t-test is used to compare means between two His groups and ANOVA is used to compare means between three or more His groups. ANOVA first obtains the common t-test. A significant t-test for the ANOVA test indicates at least one pair for which the mean difference was statistically significant.
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How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
a) The line belongs to the plane.
b) The line does not belong to the plane.
How to verify if a line belongs or not to a plane?The equation of a line has the format given as follows:
[tex]\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}[/tex]
The equation of a plane has the format given as follows:
Ax + By + Cz + D = 0.
The line will belong to the plane if these two conditions are satisfied:
[tex]Ax_1 + By_1 + Cz_1 + D = 0[/tex]aA + bB + cC = 0.In standard format, the line for item a is given as follows:
[tex]\frac{x - 1}{4} = \frac{y + 2}{9.5} = \frac{z - 3}{1}[/tex]
Then the conditions are tested as follows:
3(1) - 2(-2) + 7(3) - 28 = 0.4 x 3 - 2 x 9.5 + 1 x 7 = 0.The two conditions are satisfied, hence the line belongs to the plane.
For item b, we have that:
(-2)(-6) + 1(8) - 5(-3) + 1 = 36.
First condition already not satisfied, hence the second does not need to be tested, meaning that the line does not belong to the plane.
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francisco makes garlic bread qith 1/6 pound of garlic and 2/5 pounds of butter. how much garlic and butter is on the bread?
Answer:17/30 lbs
Step-by-step explanation:
john is jogging on a straight jogging trail toward a flagpole at a speed of 500 ft/min. he is currentyl 1500 feet from the flagpole.
As per the unitary method, it take 3 minutes will it take John to reach the flagpole.
The term unitary method in math is defined as in which the value of one article is first obtained to find out the value of any required articles.
Here we have given that John is jogging on a straight jogging trail toward a flagpole at a speed of 500 ft/min. He is currently 1500 feet from the flagpole. And here we have to write an absolute value function that models John's distance from the flagpole after x minutes.
Here let us consider x be the time taken by John to reach the flagpole.
And here we know that
speed = 500 ft/min
height = 1500 feet
Then the absolute function for the given situation is written as,
=> f(x) = 500|x|
Apply the value of f(x) as 1500, then we get
=> 1500 = 500|x|
=> x = 3
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(3) construct a quadratic equation
For -1/3 and -2/3
Answer:
y = 9x² +9x +2
Step-by-step explanation:
You want a quadratic equation with roots -1/3 and -2/3.
FactorsWhen p is a root of a polynomial, x-p is a factor. That means your quadratic will have factors (x -(-1/3)) and (x -(-2/3)). If we want integer coefficients, we can multiply each of these by 3:
y = (3x+1)(3x+2)
y = 9x² +9x +2 . . . . . . the result of multiplying it out
What is the value of |โ32|?
The value of |-32| is 32.
|−32| is the absolute value or modulus of −32 . Absolute value or modulus of a real number is always positive i.e. without its sign (i.e. negative or positive) and in value is equal to just physical value of the number under consideration. So |−32|=32 .
Modulus
The meaning of MODULUS is the factor by which a logarithm of a number to one base is multiplied to obtain the logarithm of the number to a new base.
A modulus function is a function which gives the absolute value of a number or variable. It produces the magnitude of the number of variables.
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The function gives the cost, in dollars, to produce a particular product, where C(z) is the cost, in dollars. to produce units of the product. The function M defined by M (a)=C(+1) Cla) cives the marginal cost in dollars, to produce un number + 1 Which of the following gives the best estimate for the marginal cost in dollars, to produce the 57th unit of the product? CAT C C'(56) DC) - C(86)
The best estimate for the marginal cost in dollars, to produce the 57th unit of the product is C'(57) - C'(56). This is also known as the difference in cost between producing the 57th unit and the 56th unit, and is represented by the expression C'(57) - C'(56).
The marginal cost of producing a particular unit of a product is the cost of producing that unit minus the cost of producing the previous unit. So to find the marginal cost of producing the 57th unit of the product, you can subtract the cost of producing the 56th unit from the cost of producing the 57th unit.
This means that the best estimate for the marginal cost of producing the 57th unit of the product is given by:
M(57) = C(57) - C(56)
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If a and b are positive numbers, find the maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5.
The maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is 0 ≤ x ≤ 5 is 5^b.
What is the maximum value?Generally, To find the maximum value of a function on a given interval, it is generally helpful to find the critical points (points, where the derivative is equal to zero or the function, is undefined) and the endpoints of the interval, and then evaluate the function at these points to find the maximum value.
The d/dx f(x) is given by:
f'(x) = ax^(a-1)(5-x)^b - bx^a(5-x)^(b-1)
Setting this equal to zero and solving for x, we find that the critical points are x = 0, x = 5, and x = (5b)/(a+b).
We can then evaluate the function at these points to find the maximum value. At x = 0, f(x) = 0^a*(5-0)^b = 5^b.
At x = 5, f(x) = 5^a*(5-5)^b = 0.
At x = (5b)/(a+b),
f(x) = [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.
Since a and b are positive, the maximum value must occur at either x = 0 or
x = (5b)/(a+b).
To determine which of these points gives the larger value of f(x), we can compare the values of
5^b and [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.
The expression [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b is equal to [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b.
Since a and b are positive, [(5b)/(a+b)]^a and [(a+b-5b)/(a+b)]^b are both greater than or equal to 1, so the expression [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b is greater than or equal to 1.
Therefore, the maximum value of f(x) is 5^b, which occurs at x = 0.
Thus, the maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is 5^b.
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Complete the solution of the equation. Find the value of y whey x equals -5. -7x + 6y = -13
Answer:
4
Step-by-step explanation:
Because
Please help me I’m really confused.
Answer:
c=4
Step-by-step explanation:
all three angles of a triangle add up to be 180
we can add all of these angles and set it to 180 to find c
88+12c+11c=180
88+23c=180
-88 -88
23c=92
/23. /23
c=4
hopes this helps please mark brainliest
Evaluate The Integral.(Sec2(T) I + T(T2 +1)4 J + T6 Ln(T) K) Dt
The Integral [tex]\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)[/tex]
Given integral;
[tex]\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt[/tex]
By solving the above integral, we have;
⇒ [tex]\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt[/tex]
By applying the sum rule,
⇒ [tex]\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex]
[tex]=\int \sec ^2\left(t\right)idt+\int \:t\left(t^2+1\right)^4jdt+\int \:t^6\ln \left(t\right)kdt[/tex]
[tex]\int \sec ^2\left(t\right)idt=i\tan \left(t\right)[/tex]
[tex]\int \:t\left(t^2+1\right)^4jdt = \frac{j\left(t^2+1\right)^5}{10}[/tex]
[tex]\int \:t^6\ln \left(t\right)kdt = k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)[/tex]
⇒ [tex]i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)[/tex]
Therefore, the integral [tex]\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)[/tex]
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planning her retirement, Liza deposits some money at 4.5% interest, with twice as much deposited at 5%. Find the amount deposited at each rate if the total annual interest income is $2030.
The amount deposited at each rate is 7,700 if the total annual interest income is $2030
What is annual interest income?
The compensation received by an entity for lending its money or allowing another organization to utilize it is known as interest income. The amount that an investor's money invested in a project or venture earns is referred to as interest income on a bigger scale.
Here, we
Let x = the amount invested at 4.5%.
let y = the amount invested at 5.0%.
Total interest is $2030
Equation becomes:
.045*x + .05*y = 2030.....(1)
y = 2 x,
so we can replace y with 2x and your equation becomes:
.045*x + .05*2*x = 2030
factor out the x to get x * (.045 + .05*2) = 2030
simplify and combine like terms to get
.145 * x = 2030
solve for x to get x = 14,000
2x is therefore equal to 28,000.
she has 14,000 invested at 4.5% and
28,000 invested at 5%.
Now, put the value of x and y in equation (1), and we get
.045*14,000 + .05*28,000 = 7,700
Hence, the amount deposited at each rate is 7,700 if the total annual interest income is $2030.
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Help me please quick
Answer:
Step-by-step explanation:
1. 87.92
2. 9940/113
3. 88
