¡Hola! 0.1 (también escrito como 0.10) como fracción es 1/10 or \(\frac{1}{10}\). ¡Espero que esto te ayude! Buena suerte y que tengas un gran día / noche. ❤️✨
USING TOOLS The table shows the numbers y (in thousands) of people in a city who regularly use sharable
electric scooters x weeks after the scooters are introduced.
Time, x Number of users, y
1, 1.5
4, 2.2
6, 2.4
10, 3.9
12, 5.5
15, 6.8
20, 12.3
24, 16.4
25, 17.6
1. Write function that models the data
2. Use the model to predict the number of users after 32 weeks
From the data given, we have that:
1. The linear regression equation is given by:y = 0.69684x - 1.43675.
2. 21 users during the 32th week.
How to find the equation of best fit using a calculator?To find the equation, we need to insert the points (x,y), given in a scatter plot or in a table, in the calculator. We also have to identify the type of data that models the situation, such as linear, quadratic or exponential.
For this problem, the data is increasing somewhat linearly, hence linear regression is used.
The points of the function, from the table, are given as follows:
(1, 1.5), (4, 2.2), (6, 2.4), (10, 3.9), (12, 5.5), (15, 6.8), (20, 12.3), (24, 16.4), (25, 17.6).
Hence the the linear equation that models the data is:
y = 0.69684x - 1.43675
The value during the 32th week is found when x = 32, hence:
y = 0.69684(32) - 1.43675 = 21 (rounded up, as the first decimal digit is greater than 0.5).
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The wholesale price for a pillow is $3. 50. A certain department store marks up the wholesale price by 90%. Find the price of the pillow in the department store.
Round your answer to the nearest cent, as necessary.
3.5 * 1.9 = answer
3.5 * 1.9 = 6.65
$6.65 is new price
I need help asap thank you..
Step-by-step explanation:
the angle TSW is the total angle and is 73°.
from that total angle, we have one part : angle 1 = 36°.
as angle TSW = angle 1 + angle 2
we have
73 = 36 + angle 2
angle 2 = 73 - 36 = 37°
A triangle has an angle that measures 68º.
Which of these can be the measures of the
other two angles?
A. 112° and 90°
B. 84° and 42°
C. 54° and 58°
D. 28° and 152°
Answer: B
Step-by-step explanation:
Dont trust me
Lauren owns 28 acres of land which she rents to a rancher for $3603 per acre per year. Her property taxes are $942 per acre per year. How much profit does she make on the land each year?
a) $99,942
b) $127,260
c) $101,826
d) $74,508
Answer:
B)$127,260
Step-by-step explanation:
28 x 3603= 100884
942 x 28=26376
100884 + 26376= B) $127260
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
Answer:
1.
the distance is 6 units
Explanation: you can just count the squares cince the line is straight and even if you use the Distance Formula... you'll get the same answer.
2.
A to B = 6 units
B to C = 4 units
C to D = 3 units
So...
6+4+3 = 13 units
3.
The distance between A to D is = 5 units
You can find the answer by using the Distance Formula.
Two trains leave towns 1016 kilometers apart at the same time and travel toward each other. One train travels 10 km/ h faster than the other. If they meet in 4 hours, what is the rate of each train?
Using the given information, we can set the following system of equations:
\(\begin{gathered} 4r_1+4r_2=1016, \\ r_2=r_1+10, \end{gathered}\)where r₁, and r₂ are the rates of the trains.
Substituting the second equation in the first one, we get:
\(4r_1+4(r_1+10)=1016.\)Solving for r₁, we get:
\(\begin{gathered} 4r_1+4r_1+40=1016, \\ 8r_1+40=1016, \\ 8r_1=1016-40, \\ 8r_1=976, \\ r_1=\frac{976}{8}, \\ r_1=122. \end{gathered}\)Therefore:
\(r_2=122+10=132.\)Answer: \(\begin{gathered} 122\text{ km/h,} \\ 132\text{ km/h.} \end{gathered}\)During a Team scavenger hunt event, the average number of steps taken was 1800. Calculate the distance traveled using 10,000 steps = 5 miles. Using a time of 27 minutes to complete the event, calculate your average speed.
Answer:
The average speed was of 2 miles per hour.
Step-by-step explanation:
Average speed:
Average speed is distance divided by time.
Distance:
Solved by proportions, using rule of three.
1800 steps - x miles
10,000 steps - 5 miles
\(10000x = 5(1800)\)
\(x = \frac{9000}{10000}\)
\(x = 0.9\)
Distance of 0.9 miles.
Using a time of 27 minutes to complete the event, calculate your average speed.
Distance of 0.9 miles in 27/60 of an hour. So
\(d = \frac{0.9}{\frac{27}{60}} = \frac{60(0.9)}{27} = 2\)
The average speed was of 2 miles per hour.
If ST = p + 31, RU = 6p + 14, and VW = 4p + 53, what is the value of p?
Answer:
If we subtract 14 from both sides of the equation for RU, we get 6p = RU - 14, or 6p = RU - 14. We can then substitute this expression for 6p into the equation for ST to get:
ST = p + 31
ST = (RU - 14) + 31
Expanding RU, we get:
ST = RU - 14 + 31
ST = RU + 17
Since RU = 6p + 14, we can substitute this expression into the above equation to solve for p:
ST = 6p + 14 + 17
ST = 6p + 31
Finally, we can subtract 31 from both sides of the equation to find p:
ST - 31 = 6p + 31 - 31
ST - 31 = 6p
ST - 31 = 6p
p = (ST - 31) / 6
So, to find the value of p, we need to know the value of ST.
Anything helps! Thank you :).
The measure of <BDC is 68 degree.
What are parallel Lines?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.First, Interior of ( 2y+ 34) = 180 - (2y + 34)
= 146- 2y
Now, using Corresponding Angle
74 = 146 - 2y
2y= 72
y= 72 / 2
y= 36
Second, Using Linear Pair
-7x+ 12 + (-8x+ 48)= 180
-7x + 12 - 8x + 48 = 180
-15x + 60 = 180
-15x = 120
x= -8
So, <BDC = -7x+ 12 = 56+ 12 = 68 degree
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NEED HELP ASAP!! WILL MARK BRAINLIEST IF ITS RIGHT!!
Answer:
A'(3,5), B'(6,10), C'(8,8)
Answer:
a'(3,5) b'(6,10) c'(8,8)
All u do is replace the x and y values with the points and just add by 1 and 3
Dana is making bean soup. The recipe she has makes 10 servings and uses
3/4
of a pound of beans. How many total pounds of beans does she need to make 5 servings of soup?
She has
1/16
of a pound of beans in one container and
1/4
of a pound of beans in another container. How many more pounds of beans does Dana need to make the 5 servings of soup? Show your work or explain your answer.
Which statement proves that this angle pair is the Corresponding Angles Theorem.
Criteria Laval
Answer:
its jess
here is ur ans
first option is your answer
• ANGLE 2 AND ANGLE 6 ARE CONGRUENT BECAUSE THEY ARE CORRESPONDING ANGLES.
There are 32 chickens and 12 sheep on a farm. The ratio of sheep to horses is 4:1. Write a ratio expressing the relationship between the chicken and the sheep. Then explain what that ratio means. Determine the number of horses on the farm.
This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:
\(12 * 0.25 = 3\)
What is ratio?Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.
For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.
The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.
To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:
\(chickens : sheep = 32 : 12\)
We can simplify this ratio by dividing both sides by 4:
\(chickens: sheep = 8: 3\)
This means that for every 8 chickens on the farm, there are 3 sheep.
To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:
\(sheep : horses = 4 : 1\)
We can simplify this ratio by dividing both sides by 4:
\(sheep : horses = 1 : 0.25\)
This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:
\(12 * 0.25 = 3\)
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Mrs. Chu's famous peanut butter cookies call for 1 cup of peanut butter for every 1/2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?
Answer:
she should use 2 cups of peanut butter
Step-by-step explanation:
to know the answer to that
use this equation (pb is peanut butter &o is oil)
1cup of pb=1/2 cup of o
?=1 cup of o
1×1÷1/2= 1×1×2/1=2co cups of pb
Help pls I rlly need help it’s important
Answer:
2. 112
3. 78
5. 672
7. 149.8
9. 17.5
10. 19360
11. 64 000
13. 29
14. 350240
15. 386
16. 224
17. 0.9071847
Step-by-step explanation:
In New York the mean salary for high school teachers in 2017 was 97010 with a standard deviation of 9540. Only Alaska’s mean salary was higher. Assume new York’s state salaries follow a normal distribution. (A) what percent of new York’s high school teachers earn between 83,000 and 88,000? (B) what percent of New York teachers earn between 88,000 and 103,000?
(C) what percent of new York’s state high school teachers earn less than 73,000?
a. 20.31% of New York's high school teachers earn between 83,000 and 88,000
b. 18.49% of New York teachers earn between 88,000 and 103,000
c. 1.19% of New York’s state high school teachers earn less than 73,000
Given,
The salary for high school teachers in 2017 = 97010
Standard deviation = 9540
Consider salaries as normal distribution.
Here,
Mean, μ = 97010, Standard deviation, σ = 9540
a. Percentage of New York's high school teachers earn between 83,000 and 88,000
The proportion is the p-value of Z when X = 88,000 subtracted by the p-value of Z when X = 83,000.
That is,
X = 88,000
Z = (X - μ) / σ = (88,000 - 97010) / 9540 = -9010/9540 = -0.944
The p value of z score - 0.944 is 0.3452
Next,
X = 83,000
Z = (X - μ) / σ = (83,000 - 97010) / 9540 = -14010/9540 = -1.468
The p value of z score - 1.468 is 0.1421
Then,
0.3452 - 0.1421 = 0.2031 = 20.31%
That is,
20.31% of New York's high school teachers earn between 83,000 and 88,000
b. Percentage of New York teachers earn between 88,000 and 103,000
The proportion is the p-value of Z when X = 103,000 subtracted by the p-value of Z when X = 88,000
X = 103,000
Z = (X - μ) / σ = (103,000 - 97010) / 9540 = 5990/9540 = 0.6279
The p value of z score 0.6279 is 0.5301
Next,
X = 88,000
Z = (X - μ) / σ = (88,000 - 97010) / 9540 = -9010/9540 = -0.944
The p value of z score - 0.944 is 0.3452
Then,
0.5301 - 0.3452 = 0.1849 = 18.49%
That is,
18.49% of New York teachers earn between 88,000 and 103,000
c. Percentage of new York’s state high school teachers earn less than 73,000
The proportion is the p-value of Z when X = 73000
X = 73,000
Z = (X - μ) / σ = (73,000 - 97010) / 9540 = -24010/9540 = -2.516
The p value of z score - 2.516 is 0.0119
That is,
1.19% of New York’s state high school teachers earn less than 73,000
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Ramesh dan syarika ans. Ramesh takes a medical and health insurance policy with a deductible of RM1 500 per year and co-insurance of 20% of covered medical expenses. Ramesh went to the hospital for the first time for knee treatment and the medical cost was RM700, the medical cost for the second and third treatments was RM2 000 and RM1 700 respectively. The three treatments were in the same year. How much medical expenses should be borne by Ramesh and the insurance company?
Ramesh will bear a total medical expense of RM1,760, and the insurance company will cover RM2,900.
1. Ramesh's deductible is RM1,500 per year. This means that he is responsible for paying the first RM1,500 of medical expenses before the insurance coverage kicks in.
2. For the first treatment, the medical cost was RM700. Since this amount is less than the deductible, Ramesh will have to pay the entire RM700 out of pocket.
3. For the second treatment, the medical cost was RM2,000. Since Ramesh has already met his deductible with the first treatment, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the remaining RM500 (RM2,000 - RM1,500), which amounts to RM100. The insurance company will cover the remaining 80% of RM500, which amounts to RM400.
4. For the third treatment, the medical cost was RM1,700. Again, since Ramesh has already met his deductible, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the entire cost, which amounts to RM340 (20% of RM1,700). The insurance company will cover the remaining 80% of RM1,700, which amounts to RM1,360.
5. To calculate the total medical expenses borne by Ramesh, we add up the amounts he is responsible for in each treatment: RM700 + RM100 + RM340 = RM1,140.
6. The total medical expenses covered by the insurance company can be calculated by adding up the amounts they pay in each treatment: RM400 + RM1,360 = RM1,760.
7. Finally, to find the overall amount borne by Ramesh and the insurance company, we sum up the individual expenses: Ramesh's expenses + insurance company's expenses = RM1,140 + RM1,760 = RM2,900.
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The expression 45h +225 represents the total cost in dollars of
renting a large party tent from a local rental store for h hours. Jamal's
parents are willing to spend between $500 and $750 for the tent.
Part A. Write an inequality to represent the possible lengths of time
the tent can be rented.
Part B. Using your inequality in Part A, what is one possible length of
time the tent could be rented? Give your answer in number of hours.
Part A Write an inequality to represent the possible lengths of time
the tent can be rented
\(6.11\leq h\leq 11.66\)
Part B. Using your inequality in Part A, what is one possible length of
time the tent could be rented
\(6hr 6min\leq h\leq 11hr39min\)
The definition of a linear inequality
The inequality symbol is used to compare two mathematical expressions in what are referred to as linear inequalities. The expression could be both numerical and algebraic, or it could just be one.
What does a linear inequality in mathematics look like?
What Is an Example of Linear Inequality? An example is the linear inequality x - 5 > 3x - 10. The LHS is obviously greater than the RHS because the greater than symbol is being utilized in this inequality. After being resolved, the inequality appears as follows: 2x 5 x (5/2).
Given That
45h+225 is total cost in dollars for renting tent and parents are willing to spend between $500 and $750 for the tent.
Part A
\(500\leq 45h+225\leq 750\\500-225\leq 45h+225-225\leq 750-225\\275\leq 45h\leq 525\\\frac{275}{45} \leq h\leq \frac{525}{45} \\6.11\leq h\leq 11.66\)
Part B
\(6.11hr\leq h\leq 11.66hr\)
6.11 hr = 366 minute approx.
11.66 hr = 699 minute approx.
\(6hr 6min\leq h\leq 11hr39min\)
Hence this is the answer
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Question 2
10 pts
There are 120 girls and 80 boys in the sixth grade at a middle school. Of these, 9 girls and 3
boys write left-handed. What percentage of the sixth graders at this middle school write left-
handed?
Simplifying
Column
(optional)
Part
12
?
Total
200
100%
495
8%
6%
20%
Is 604,892 divisible by 4?
Answer:
yes it is 604892÷4=151,223
right now need answer now ok please do not do wrong
Answer: -7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
The present ages of Ramesh and his elder brother are in the ratio 5 : 7. After four years, the
ratio of their ages will be 3 : 4. Find their present ages
In the word problem, The present ages of Ramesh and his elder brother are 20 years and 28 years.
What is word problem ?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided expression are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here let us take present age of Ramesh and His elder brother are 5x and 7x.
Now After 4 years their ages will be 3:4. Then,
=> \(\frac{5x+4}{7x+4}=\frac{3}{4}\)
=> 20x+16=21x+12
=> 21x-20x=16-12
=> x= 4
Then Present age of Ramesh = 5*4=20 years.
Present age of his elder brother = 7*4=28 years.
Hence The present ages of Ramesh and his elder brother are 20 years and 28 years.
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You buy 3 gallons of milk at $2.48/gallon, 2 gallons of
ice cream at $1.49/gallon, and 4 lbs of strawberries at
$0.58/1b. What is your total cost?
(1 point)
O$9.51
O$12.74
0$4.55
O$10.67
The total cost is $12.74
In this question, we have been given the cost of 1 gallon of milk, 1 gallon of ice-cream and 1 1b of strawberry.
1 gallon of milk costs $2.48,
1 gallon of ice-cream costs $1.49
and 1b of strawberry costs $0.58
You buy 3 gallons of milk, 2 gallons of ice cream, and 4 lbs of strawberries.
So by unitary method total cost would be,
(3 * 2.48) + (2 * 1.49) + (4 * 0.58) = $12.74
Therefore, the total cost is $12.74
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The population of a town is predicted to grow according to the following model:
P = 15e0.012r
where P represents the number of people in thousands and t is the number of years since 2020. Find
the predicted population in the year 2030. Round your answer to nearest person
O 16,912 people
O 16,913 people
O 16 people
O 17 people
The predicted population in the year 2030 is 10 people
How to determine the predicted population in the year 2030From the question, we have the following parameters that can be used in our computation:
Population function, P(t)= 15е⁻⁰.⁰¹²⁺
Also from the question, we have
The variable t represents the number of years since 2020
This means that the value of t in 2030 is
t = 2030 - 2020
t = 10
So, we have
P(10)= 15е⁻⁰.⁰¹² ˣ ¹⁰
Evaluate the above products
P(10)= 15е⁻⁰.¹²
Evaluate the exponents
P(10)= 13.30
Approximate the above expression
P(10) = 13
This means that the number of people is 13
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a + 2(a - 5) = 320i need the answer
What are the like terms in the expression 6x + 9 – 4x – y - 8
Answer:
6x and -4x
9 and -8
Step-by-step explanation:
As you can see, both of the numbers at the top have a variable x. Both of the numbers at the bottom have no variable. These are two pairs of like terms because they either have the same variable or no variable at all.
What is the M.A.D. (mean absolute deviation) of the following data set?
8 9 9 7 8 6 9 8
The mean absolute deviation is 0.75
How to determine the mean absolute deviationTo calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set
From the information given, we have that the data set is;
8 9 9 7 8 6 9 8
Let's calculate the mean, we get;
Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8
Mean = 64 / 8
Divide the values
Mean = 8
Let's determine the absolute difference, we get;
Absolute differences=
|8 - 8| = 0
|9 - 8| = 1
|9 - 8| = 1
|7 - 8| = 1
|8 - 8| = 0
|6 - 8| = 2
|9 - 8| = 1
|8 - 8| = 0
Find the mean of the absolute differences:
Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8
Absolute difference = 6 / 8 = 0.75
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Find the absolute maximum and minimum values of the function on the described domain. When checking for extrema on any boundaries, you may choose whether you want to use a parametrization or Lagrange Multipliers; some problems might be easiest when using a combination. (a) f(x,y)=x 2 ây 2 â2xyâ2x, on the triangular region whose vertices are (1,0),(0,1), and (â1,0). (b) g(x,y)=x+xyâ2y 2, on the domain yâ¥0,y⤠x, xâ¤1. (c) h(x,y)=e xy, on the disk (2x) 2+y 2â¤1 tâ If you use your answers to part (a) and part (b) to justify why this is a maximum, you don't have to do the second rivative test. (d) f(x,y)=xy, on the part of the curve 2x 3+y 3=16 which is in the first quadrant (including endpoints). (e) g(x,y)=x 2+3y, on the line segment from (â2,2) to (2,â2). (f) h(x,y,z)=x+2y+3z, on the unit sphere.
(a) The Absolute minimum value is -3/2 and maximum value is 3.
(b) We have global minima at x = 4/9 and global minimum value at x = −4/27.
(c) Global maximum value of function is 2.72 and minimum value of function is 0.37.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Four main categories may be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element. The graph is a function if any vertical line created may cross it at no more than one point. The graph is not a function if there is any location where a vertical line may cross it at two or more points.
Here,
a) Given function as:
f(x,y)=x2-y2-2xy-2x
The triangular region described by the vertices (1,0),(0,1) and (-1,0) can be described by the straight lines :
a) Straight line joining (1,0) and (0,1) i.e y= 1-x
b) Straight line joining (0,1) and (-1,0) i.e y= 1+x
c) Straight line joining (-1,0) and (1,0) i.e the x axis where y=0
When y=0, we have, x^2-2x
Now, df/dx=0 for maxima / minima
2x-2=0
X=1
Also, d^(2)f/dx^(2)=2>0 and df/dx<0 for x<1
So, we have minimum value = 12−2×1=−1
and maximum value = (−1)2−2×−1=3
When y=1+x, we have ,
f(x,y)=x^2−(1+x)^2−2x(1+x)−2x
df/dx=2x−2(1+x)−2x−2(1+x)−2
=−6−4x<0, for x>−3/2
Hence f(x,y) is always decreasing function in the interval x=[-1,0] , with minimum
=f(0,1)
=02−12−2×0×1−2×0
=−1
Maximum value = f(-1,0)
=(−1)2−02−2×−1×0−2×−1
=1−0+2
=3
When y= 1-x, we have,
f(x,y)=x^2−(1−x)^2−2x(1−x)−2x
df/dx=2x+2(1−x)+2x−2(1−x)−2
=4x−2>0,for x>1/2
Hence at x=1/2,we have df/dx=0 which is global minima point since
d2(f)/dx2=4>0
So, minimum value for y = 1- x
=f(1/2,1/2)
=1/22−1/22−2×1/2×1/2−2×1/2
=−1/2−1=−3/2
Maximum value in the interval [ 0 1] shall be
=max(f(0,1).f(1,0))
=max(−1,−1)=−1
So, considering all points on this triangle , we have absolute maximum
= max(f(x,y) for y=0, f(x,y) for y=1+x, f(x,y) for y=1-x)
=max(3,3,−1)
=3
Absolute minimum considering all points on the triangle
= min(f(x,y) for y=0, f(x,y) for y=1+x, f(x,y) for y=1-x)
=min(−1,−1,−1.5)
=−3/2
b) Given g(x,y)=x+xy−2y2
When y=x0.5, we have,
g(x,y)=x+x^1.5−2x
=x^1.5−x
For the domain x = [0 , 1], we have ,
dg/dx=1.5×x^0.5−1=0
x=4/9
d^2(g)/d^x2=0.75x0.5>0 for x=4/9
Hence, we have global minima at x = 4/9 and global minimum value
=(4/9)1.5−49
=8/27−4/9
=−4/27
Global maximum = max(g(0,0),g(1,1))
=max(0,0)
=0
(a) The Absolute minimum value is -3/2 and maximum value is 3.
(b) We have global minima at x = 4/9 and global minimum value at x = −4/27.
(c) Global maximum value of function is 2.72 and minimum value of function is 0.37.
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How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answer:
no solutions
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.