The given statement to this question is true
What is an optimal solution?
An acceptable solution where the objective function reaches its highest (or minimum) value, such as the most profit or the lowest cost, is referred to as an optimal solution. When there are no other practical solutions with superior objective function values, the solution is said to be globally optimal.
Here, we have
The global optimum point may be superior to nearby points, but the local optimum point is the true optimal solution to a nonlinear programming problem.
Because when own linear model is solved this solution is merely local optimum.
The solver should consider that other local optimum Amy does not exist with better object values. The globally optimal solution is one where there are no feasible solutions with a better objective function.
However many nonlinear problems are non-convex and are likely to have multiple locally optimal solutions. The local optimum point is the true optimal solution for the nonlinear programming model.
Hence, the given statement to this question is true.
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Mickey earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3. 8% compounded annually. What will be his balance after 4 years rounded to the nearest cent?.
The balance after 4 years is $551.42. Here we use the formula of compound interest to calculate the total amount or balance after 4 years.
Define compound interest.Compound interest is the interest calculated based on the initial principal and sum of the interests calculated over the previous time periods.
Formula for calculating the compound interest is:
A = P( 1 + [tex]\frac{r}{n}[/tex])^nt
Here A is the final amount accumulated
P is the Principal = $475
r is the interest rate = 3.8%
n is the number of times compounded in a year(here it is compounded annually) so n = 1.
t is the given time period = 4
Therefore
A = 475(1 + 3.8%)⁴
= 475(1.038)⁴
= 551.42$
Therefore total balance after 4 years is $ 551.42
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What is the slope of the line that passes through 1/4 and 1 − 3 )?
The Slope of the line that passes through the points (1, 4) and (1, -3) is Undefined.
If we are provided with two points (x₁, y₁) and (x₂, y₂) then the formula of finding the slope between these points is expressed as
m = (y₂ - y₁)/(x₂ - x₁)
where m is the slope between the points, y₂ - y₁ is difference between the y coordinates and x₂ - x₁ is the difference between the x coordinates.
Now the points are (1, 4) and (1, -3), so the difference between the coordinates is expressed as
y₂ - y₁ = -3 - 4
y₂ - y₁ = -7
x₂ - x₁ = 1 -1
x₂ - x₁ = 0
Now the slope will be
m = -7/0
Since, we have zero in the denominator and any number divided by zero is undefined so the slope is undefined.
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Complete Question:
What is the slope of the line that passes through (1, 4) and (1, -3)?
How do you determine the end behavior of the graph of a polynomial function?
We can determine the end behavior of the graph of a polynomial function if we look at the x-right axis's end (as x approaches +) and left end (as x approaches ), respectively.
Given,
End behavior of polynomial function;
A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity. The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
Here,
The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f. In other words, if we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ), the end behavior of a function represents the trend of the graph.
That is,
If we examine the ends of the x-right and left axes (as x approaches +) in turn, we can ascertain the end behavior of the graph of a polynomial function.
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This is the Fraction Operations Please solve all these:
1. 3/8 + 2/3= ?
2. 3 1/4 - 1 1/8=?
3. 2 1/2 divided by 2= ?
Please explain how you got it. Thanks!
The required simplified solution of the given numerals is 1. 25/24, 2. -7/8, and 3. 5/4.
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.
here,
1.
3/8 + 2/3 = 9 + 16 / 24
= 25 / 24
2.
3 1/4 - 1 1/8 = 1/4 - 9 / 8
= -7/8
3.
[2 + 1 /2] / 2 = [5 / 2] / 2 = 5 / 4
Thus, the mandated simplified solution of the assigned numerals is 1. 25/24, 2. -7/8, and 3. 5/4.
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the paired values of the consumer price index (cpi) and the cost of a slic of pizza are listed in the table. assume a 0.01 significance level. determine the correlation coefficient and find the critical values.
r = 0.985; critical values = ±0.917
r = 0.985; critical values = ±0.811
r = 0.872; critical values = ±0.811
r = 0.872; critical values = ±0.917
The correct option regarding the correlation coefficient and the critical values for the the paired values of the consumer price index (cpi) and the cost of a slice of pizza is given as follows:
r = 0.985; critical values = ±0.917.
How to obtain the correlation coefficient and the critical value?The correlation coefficient for a data-set is obtained inserting the points of the data-set into a correlation coefficient calculator.
For this problem, the points are given as follows:
(30.2, 0.15), (48.3, 0.35), (112.3, 1), (162.2, 1.25), (191.9, 1.75), (197.8, 2.00).
Inserting these points into a calculator, the numeric value of the coefficient is given as follows:
r = 0.9852.
Then the critical value is also used a calculator for the r-distribution, with these following parameters:
r = 0.9852.Sample size of 6.Using the calculator, the critical value is of:
r = ±0.917.
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What is another word of split?
Another word for the word split is given by many other words like crack, to divide, tear, to break apart, bisect it into parts and so.
Explanation:
Another word of the given word split is given by:
Different words represents the meaning of the word split.Crack , separating, Tear, fragment , cleave are few words representing the another word of the given word splitting.Meaning or the another used instead of word split in two is given by dividing it into two equal parts, break one part into two equal parts.Bisecting a diagram or a line segment into parts is also done by splitting.Separation is also consider as another word for splitting which basically divides one species( living or non living ) from another.For example split number 24 is equal to 3 × 2 × 2 × 2.Therefore, the another word used for the given word split is given by crack , cleave, tear, divide it into two equal parts.
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6 cm 6 cm 6 cm Find the surface area of the cube. Surface Area = [?] cm2
Answer: 216 cm^2
Step-by-step explanation:
The equation finds the area of the cube is
6 * S^2
6 (6^2) = 216 cm^2
a rectangular box with a volume of 480 cubic feet is to be constructed with a square base on top. the cost per square ft for the bottom is 30 cents, for the top is 20 cents, and for the sides is 5 cents. determine the dimensions of the box to be minimize cost. what is the length of one side of the base of the box?
So, when the box has a square base with 4.8 feet on each side and a height of 40.41 feet, then cost will be at its lowest.
What in mathematics is a base?When referring to a specific mathematical item that serves as a building block, the word "basis" in mathematics is employed. The notions of a number system in which numbers are represented by digits and a numerical system in which logarithms were defined are the ones that are most frequently utilized.
V=x2×y931=x2y=93x2
Given that the square foot price for the bottom is 15 cents, the top is 10 cents, and the sides are 1.5 cents
Therefore, total cost
C=15x2+10x2+(1.5xy)
C=25x2+6xyC(x)=2x2+6x×931x2C(x)=25x2+5586x
Upon separating it from x, we obtain,
C′(x)=50x−5586x2
We obtain 50x5586x2=0x3=5586 when equating with zero.
50x=4.8ft
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twenty-five engine mounts are sampled each day and found to have an average width of 2 inches, with a standard deviation of 0.1 inches. what are the control limits that include 90% of the sample means?
The control limits that include 90% of the sample means be,
(24.9671 , 25.0329).
Given, twenty-five engine mounts are sampled each day and found to have an average width of 2 inches, with a standard deviation of 0.1 inches.
we have to find the confidence interval under confidence of 90%.
As, Mean = 2 and Standard Deviation = 0.1
Subtract 1 from your sample size. 25 – 1 = 24. This gives you degrees of freedom.
Subtract the confidence level from 1, then divide by two.
(1 – 0.9) / 2 = 0.05
For 24 degrees of freedom (df) and α = 0.05, the result is 1.645.
Divide your sample standard deviation by the square root of your sample size.
0.1 / √(25) = 0.02
Now, 0.02 × 1.645 = 0.0329
The lower end of the range
25 – 0.0329 = 24.9671
The upper end of the range
25 + 0.0329 = 25.0329
Hence, the confidence interval be, (24.9671 , 25.0329)
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Which statements are true about the functions y sin (c), y D sin (c) and y sin(2), y sin (z), y = sin (c), y = sin (2) and y = The graphs of y The domains of y = The amplitudes of y The periodela v Both y sin (2) and y on that interval. decreasing cos (x), and y tan (z)? cos (z) do not have midlines. cos (2), and y = tan (2) are all real numbers. cos(x), and y tan (z) are 1. cos (2) are 27, and the period of y – tan (I) is T. cos (x) is tan (x) are increasing on the interval (0,), and y
The true statements regarding the trigonometric functions are given as follows:
The periods of y = sin(x) and y = cos(x) are of 2π, while the period of y = tan(x) is of π.Both y = sin(x) and y = tan(x) are increasing on the interval (0, π/2), while y = cos(x) is decreasing on the same interval.What are the correct statements?The three trigonometric functions are defined as follows:
y = sin(x).y = cos(x).y = tan(x).The statements are described as follows:
Statement 1 is false, as tan(x) = sin(x)/cos(x), hence the tangent function is not defined when cos(x) = 0 at x = kπ/2, k = ± 1, ±3, ..., and it's domain is not all real values.Statement 2 is false, as the tangent function does not have an amplitude, as close to the vertical asymptotes it assumes values close to infinity.Statement 3 is false, as the sine function and the cosine function have a midline.The remaining statements are true.
Missing InformationThe statements are given by the image shown at the end of the answer.
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a couple plans to have three children. find the probability of having all boys. find the probability of having two boys or two girls.
the find the probability of having two boys or two girls will be 50%
What is probability ?
The probability formula can be used to calculate the likelihood of an event by simply dividing the favorable number of possibilities by the total number of options. The likelihood of an occurrence might vary from 0 to 1 because the favourable number of outcomes can never be greater than all possible outcomes.
For two genders and three children, there are a total of 2³=8 potential combinations.
There are (GGG, GGB, BGG, GBG) = 4 pairs where at least two of the children are female.
As a result, there is a 4/8 = 1/2 chance that the family of three children will include at least two girls.
Hence the find the probability of having two boys or two girls will be 50%.
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Determine which equation is false, based on the solution set S:{2}.
7 = 6p − 5
4t = 8
3(3c + 1) = 21
5m + 8 = 16
pls help ill give 45 points
Answer:
[tex]5m+8=16[/tex]
Step-by-step explanation:
[tex]5m+8=16 \\ \\ 5m=8 \\ \\ m=1.6 \neq 2[/tex]
PLEASEE HURRYYY
Given mn, find the value of x.
Answer:
(6x+3)
(7x-19)
Answer:x=+22
Step-by-step explanation:We move all terms to the left:
6x+3-(7x-19)=0
We get rid of parentheses
6x-7x+19+3=0
We add all the numbers together, and all the variables
-1x+22=0
We move all terms containing x to the left, all other terms to the right
-x=-22
x=-22/-1
x=+22
ia began filling the bathtub at a constant rate.
She then turned off the water for a while and some of the water drained out of the bathtub.
Tia turned the water back on at the same rate as before until the bathtub was full.
Which graph best represents Tia filling the bathtub?
The graph that represents the given situation is graph (A). (Refer to the graph attached below)
What is a graph?The set of ordered pairs is the graph of a function f in mathematics, where these pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical case when x and f(x) are real numbers.
To create a graph is to make a diagram that shows the relationship between two or more things.
So, we know that:
The bathtub is filling at a constant rate.
When the tap was closed, the water drained out.
Then again, the tap was open for the water to come out at a constant rate.
So, the correct graph that resembles these lines is a graph (A).
Therefore, the graph that represents the given situation is a graph (A). (Refer to the graph attached below)
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Simplify 5(k + 4) - 2k
If elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?.
The required probability that she'll use a cab exactly one time is 4/9.
What is the probability ?probability is a part of math that arrangements with figuring out the probability of the event of an occasion.
According to question:Elizabeth lives in San Francisco and works in Mountain View.
In the first part of the day she has 3 transportation choices (bus, cab, train) to work, and at night she has similar 3 options for her outing home.
All transportation (bus, cab, train) are comparably liable to be chosen, and 1 of them should be chosen in the first part of the day and night, so we get:
P (bus) = P (taxi) = P (train) = 1/3.
We additionally have P(no taxi in night) = P(no taxi at morning) = 2/3
Presently, P(using taxi precisely once) = P(cab at morning and no taxi at night) + P(no taxi at morning and taxi at night)
= P(cab, no taxi) + P(no taxi, taxi)
= 1/3 × 2/3 + 2/3 × 1/3
= 2/9 + 2/9
= 4/9
Consequently, the probability that Elizabeth utilizes a taxi just once is 4/9.
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Landon made plain cookies and raisin cookies in the ratio of 2:3
He then made 6 more raisin cookies and the ratio changed to 1:3.
How many cookies did Landon make in all?
Step-by-step explanation:
x = number pain cookies
y = number raisin cookies
x/y = 2/3
x/(y+6) = 1/3
x = (y + 6)/3
x = 2y/3
therefore,
x = x = (y + 6)/3 = 2y/3
y + 6 = 2y
6 = y
x = 2y/3 = 2×6/3 = 2×2 = 4
so, he made originally 4 + 6 cookies, and then he made 6 more raisin cookies, so, he made 4 + 6 + 6 = 16 cookies.
What are the four values that would complete the function table?
The required f(x) values are 5, 1 , -1 , -3
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
f(x)= -2x+1
Substitute the values for x and find the value of f(x)
For x= -2:
f(x)= -2(-2)+1
= 5
For x= 0:
f(x)= -2(0)+1
= 1
For x= 1:
f(x)= -2(1)+1
= -1
For x= -2:
f(x)= -2(2)+1
= -3
The required f(x) values are 5, 1 , -1 , -3
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In geometry, we have rules, definitions, postulates, theorem, etc. that help with problem-solving, deductive reasoning, spatial, reasoning, and relationships of shapes and solids just to name a few. Please explain in a minimum of five sentences has a Bible provides a similar guide to living a Christian life.
Answer:
Just as geometry has rules, definitions, postulates, and theorems that help with problem-solving and understanding the relationships of shapes and solids, the Bible provides a similar guide for living a Christian life. The Bible contains a set of principles and teachings that serve as a foundation for Christian beliefs and values. These principles and teachings help Christians to understand the nature of God and their relationship with him, as well as the principles for living a moral and virtuous life.
In the same way that geometry relies on deductive reasoning to draw conclusions and make predictions, Christians use their knowledge of the Bible to make decisions and navigate the challenges of daily life. The Bible provides guidance on a wide range of topics, including relationships, work, ethics, and personal growth, helping Christians to make wise choices and avoid pitfalls.
Additionally, just as geometry helps us to understand the spatial relationships of objects, the Bible helps us to understand our place in the world and our relationship with others. The Bible teaches us about the importance of love, compassion, and forgiveness, and helps us to see the value and worth of every human being.
Overall, the Bible serves as a guide for living a Christian life, providing principles, teachings, and guidance that help us to understand God, ourselves, and our relationships with others.
Step-by-step explanation:
Answer:
yes...........s..s.s..s..s..,...
Use substitution to solve the system of equations.
y = 5x + 1
4x + y = 10
Answer:
(1, 6 )
Step-by-step explanation:
y = 5x + 1 → (1)
4x + y = 10 → (2)
substitute y = 5x + 1 into (2)
4x + 5x + 1 = 10
9x + 1 = 10 ( subtract 1 from both sides )
9x = 9 ( divide both sides by 9 )
x = 1
substitute x = 1 into (1)
y = 5(1) + 1 = 5 + 1 = 6
solution is (1, 6 )
Answer: x = 1, y = 6
Step-by-step explanation:
y = 5x + 1
4x + y = 10
substitute y into the second equation
4x + 5x + 1 = 10
9x + 1 = 10
9x = 10 - 1
9x = 9
x = 9/9
x = 1
Now you have the x value substitute it in one of the equations above to get the y value
y = 5(1) + 1
y = 5 + 1
y = 6
so your x value is 1 and your y value is 6
8. Determine the perimeter of Parallelogram STUV.
Round to the nearest hundredth, if necessary.
The answer to this Question Based on Perimeter is 8.72
What is Perimeter?
Perimeter is total length of boundary of any closed figure
Solution:
to calculate perimeter of this first we need to calculate the lengths of all sides
BY pythagoras theorem we can see that SV = sqrt(4^2 + 1^2)
SV = sqrt(17)
By similar procedure other lengths we can calculate as
UV = sqrt(5)
UT = sqrt(17)
ST = sqrt(5)
Hence perimeter will be sum of all these that is 2sqrt(5) + 2sqrt(17)
2(2.24) + 2(4.12)
4.48 + 4.24
8.72 will be perimeter
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After adding a tip, the total lunch cost was $32. 24. What percentage tip did they give? write your answer to the nearest percentage.
Answer:
what was the original cost of the lunch before they added the tip?
two boxes of Apples the sum of their weight is 54 kilograms the first has 12kg more than the second so the number of kilograms in the second box is....... kg.
Answer:
The weight of the second box is 42 kilograms, since 54 - 12 = <<54-12=42>>42.
Solve 4x + 3 = 9 for x using the change of base formula log base b of y equals log y over log b.
The value of x for a given expression 4x + 3 = 9 is equal to -1.415.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 4x + 3 = 9. The value of x will be calculated as,
log(4)⁹= x + 3
log9 / log4 = x + 3
0.95424425 / 0.6020599 = x + 3
1.584962725 -3 = x + 3 - 3
x = -1.415037275
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? A, B, C, D? PLEASE HELP 10 POINTS. I HAVE 10 MINUTES
Answer:
A
Step-by-step explanation:
A polynomial function can be written as (x - 1)(x - 4)(x + 7). What are the x-intercepts of the graph of this function?
(1,0), (4,0), (7,0)
(-1.0), (-4, 0), (-7.0)
(1.0) (4 0) (-7, 0)
(-1,0), (-4, 0), (7.0)
Answer:
the 4th option is correct
Step-by-step explanation:
thank you
752 dividido por 16 cuanto da? ayudenme pliss
47
Cuando dividas 752 por 16 obtendrias 47.
A line passes through the point (-6, 8) and has a slope of 4.
Write an equation in point-slope form for this line.
Step-by-step explanation:
Slope-Point form : (y-y1) = m(x-x1)
So,
The equation is 4x -y +32 = 0
In march 2015, the public policy institute of california (ppic) surveyed 7525 likely voters living in california. Ppic researchers find that 68 out of 200 central valley residents approve of the california legislature and that 156 out of 300 bay area residents approve of the california legislature. Ppic is interested in the difference between the proportion of central valley and bay area residents who approve of the california legislature. Ppic researchers calculate that the standard error for the proportion of central valley residents who approve of the california legislature minus bay area residents who approve of the california legislature is about 0. 44. Find the 95% confidence interval to estimate the difference between the proportion of central valley and bay area residents who approve of the california legislature. Responses
The null hypothesis get rejected comparing the 95% confidence interval to the proportion of the given central valley residents and bay area residents .
As given in the question,
Total number of voters in California = 7525
x₁ = Number of voters of central valley residents approved California legislature
= 68
n₁ = Total number of voters of central valley residents
= 200
x₂ = Number of voters of bay area residents approved California legislature
= 156
n₂= Total number of voters of bay area residents
= 300
p₁ = proportion of voters of central valley
p₂= proportion of voters of bay area
p₁ = x₁/ n₁
= 68/200
= 0.34
p₂ = x₂/n₂
= 156/300
= 0.52
Standard error = √p₁(1 -p₁) / n₁ + p₂( 1- p₂)/n₂
= √0.34(1-0.34) / 200 + 0.52(1-0.52)/ 300
= √0.001122 + 0.000832
= 0.044
[tex]p_{w}[/tex] = (68 + 156 )/ (200 + 300)
= 0.448
[tex]q_{w} = 1- p_{w}[/tex]
= 1 - 0.448
= 0.552
null hypothesis p₁ - p₂ = 0
z = ( 0.52 - 0.34 ) - 0/ √(0.448)(0.552)( 1/200 + 1/300)
= 4
Tabular value for confidence interval 95% = 1.96
4 > 1.96
We reject the null hypothesis.
Therefore, the difference of proportion of central valley residents and the bay area residents rejection of null hypothesis as per given 95% confidence interval.
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To start her old lawn mower, rita has to pull a cord and hope for some luck. On any particular pull, the mower has a 20% chance of starting. What is the probability that it takes her more than 6 pulls to start the mower?.
The probability that it takes her more than 6 pulls to start the mower is 0.262144. The result is obtained by the formula of binomial distribution.
What is the formula of binomial distribution?The formula of binomial distribution is
[tex]P(X = x) = C_{n,x}.p^{x}. (1 - p) ^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x! (n-x)!}[/tex]
Where
x = number of successesn = number of trialsp = probability of a success on a single trialRita has to pull a cord to start her old lawn mower. If the probability of success is 20%, what is the probability that it takes her more than 6 pulls to start the mower?
We have:
p = 20% = 0.2n = 6Using the formula of binomial distribution,
[tex]P(X = 1) = C_{6,1}.(0.2)^{1}. (0.8) ^{5} = 0.393216[/tex]
[tex]P(X = 2) = C_{6,2}.(0.2)^{2}. (0.8) ^{4} = 0.24576[/tex]
[tex]P(X = 3) = C_{6,3}.(0.2)^{3}. (0.8) ^{3} = 0.08192[/tex]
[tex]P(X = 4) = C_{6,4}.(0.2)^{4}. (0.8) ^{2} = 0.01536[/tex]
[tex]P(X = 5) = C_{6,5}.(0.2)^{5}. (0.8) ^{1} = 0.001536[/tex]
[tex]P(X = 6) = C_{6,6}.(0.2)^{6}. (0.8) ^{0} = 0.000064[/tex]
The probability that it takes more than 6 pulls,
P(X > 6) = 1 - P(X ≤ 6)
P(X > 6) = 1 - [P(X = 1)+P(X = 2)+P(X = 3)+P(X = 4)+P(X = 5)+P(X = 6)]
P(X > 6) = 1 - (0.393216 + 0.24576 + 0.08192 + 0.01536 + 0.001536 + 0.00064)
P(X > 6) = 1 - 0.737856
P(X > 6) = 0.262144
Hence, the probability to take more than 6 pulls to start the old lawn mower is 0.262144.
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