(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.
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
c) Given h(x,y)=exp(xy)
When (x/2)^{2}+y^{2}=1, we have
y=(1−x^{2}/4)^0.5
So, h(x,y) = [tex]\text{exp}\left(x(1-\frac{x^{2}}{4})^{0.5}\right)[/tex]
Now,dh/dx=[tex]\text{exp}\left(x(1-\frac{x^{2}}{4})^{0.5}\right) \times ((1-\frac{x^2}{4})^{0.5}+0.5x\times\frac{-x/2}{(1-x^2/4)^{0.5}}[/tex]
For maxima / minima , we mush have ,
dh/dx=0
[tex](1-\frac{x^2}{4})^{0.5}+0.5x\times\frac{-x/2}{(1-x^2/4)^{0.5}}[/tex]5=0
[tex](1-x^2/4)^{0.5}-0.25 \frac{x^2}{(1-x^2/4)^{0.5}}[/tex]=0
[tex]1-x^2/4-0.25x^2[/tex]=0
1−x^2/2=0
x = 1.41,−1.41
In the range [-1.41,1.41], we always have dh/dx>0
At x=20.5and x=−20.5, we have
y=(1−x2/4) 0.5
=(1−24)0.5
=120.5,−120.5
Global maximum value of function
=f(20.5,1/20.5)
=exp(1)
=2.72
Global minimum value of function
=f(20.5,−1/20.5)
=exp(−1)
=(0.37)
To learn more about Global maximum and minimum value link is here
brainly.com/question/29258664
#SPJ4
what is 309x317/9-4+7/8x3
[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Step-by-step explanation:1. Write the expression.[tex]\frac{(\frac{309*317}{9-4+7})}{8x3}[/tex]
3. Solve the main denomonator.[tex]\frac{(\frac{309*317}{9-4+7})}{24}[/tex]
4. Solve the secondary denominator.[tex]\frac{(\frac{309*317}{12})}{24}[/tex]
5. Solve the secondary numerator.[tex]\frac{(\frac{97953}{12})}{24}[/tex]
6. Solve the main numerator.[tex]\frac{(8162.75)}{24}[/tex]
7. Simplify the fraction.[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Find m/S
U
10x + 8
11x + 2
T
S
Q. Find the measure of the angle indicated in the following parallelogram.
The measure of the angle S is 112° in the following parallelogram.
What is parallelogram?
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of a polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. In a parallelogram, the opposing sides are of equal length, and the opposite angles are of equal size. A parallelogram has adjacent angles that add up to 180 degrees.
Given, ∠T= 11x + 2
∠V = 10x + 8
From the above definition, opposite angles are equal
So, ∠T = ∠V
or, 11x + 2 = 10x + 8
or, 11x - 10x = 8 - 2
or, x = 6
∠V= 10x + 8 = 10*6 + 8 = 68 degree
From the above definition, adjacent angles add up to 180 degrees
∠V + ∠S = 180°
or, 68° + ∠S =180°
or, ∠S = 180° - 68° = 112°
Hence, the measure of the angle S is 112°.
To learn more about parallelograms
https://brainly.com/question/20526916
#SPJ1
What is the product?
2•[-1]
[0]
Answer:
-2
Step-by-step explanation:
PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
The length of segment AY is 16.7 ft if the length of segment BC is 16.7 ft
How to determine the length of the side length AYFrom the question, we have the following parameters that can be used in our computation:
BC = 16.7 ft
The measures of the angles are not given
However, the marks on the side lengths imply that:
The points A, B and C divides the line segments XY, XZ and YZ into equal segmentsThe parallel segments are equal segmentsUsing the above as a guide, we have the following:
AY = BC
This is because these segments are parallel segments
Recall that parallel segments are equal segments
Substitute the known values in the above equation, so, we have the following representation
AY = 16.7
Hence, the length of AY is 16.7 ft
Read more about triangles at
brainly.com/question/14285697
#SPJ1
What value is a discontinuity of
x²+2x+3?
x²-x-12
Ox=-1
Ox = -2
Ox= -3
Ox= -4
Value is a discontinuity is undefined when [tex]x=-5[/tex] or [tex]x=3[/tex] The answer is then the third choice. [tex]\frac{x^2+7 x+1}{x^2+2 x-15}=\frac{x^2+7 x+1}{(x+5)(x-3)}[/tex]
What is discontinuity?
A discontinuous function is a graph function that is not linked to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first sort at x = a.
A zone within the earth where a sudden change in physical properties, such as the velocity of earthquake waves, occurs. Such a zone marks the boundary between the different layers of the earth, as between the core and mantleSee also Mohorovičić discontinuity.
In mathematics, functions, and applications, continuous functions are crucial. Not all functions, nevertheless, are continuous. A function is said to have a discontinuity at that point in its domain if it is not continuous elsewhere in its domain.
To learn more about discontinuity visit
https://brainly.com/question/28783981
#SPJ1
A graphing calculator is recommended.
Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.)
Weights of Student Lab Rats
Linda's rats Tuan's rats Javier's rats
46.3 49.8 53.3
42.3 42.7 43.1
44.1 41.8 40.2
48.7 48.9 47.7
40.8 46.5 51.5Enter an exact number as an integer, fraction, or decimal.
df(num) =
Enter an exact number as an integer, fraction, or decimal.
df(denom) =
State the distribution to use for the test.
A. F2, 12
B. F12, 2
C. F14, 2
D. F14, 12
E. F2, 14
What is the test statistic? (Round your answer to two decimal places.)
What is the p-value? (Round your answer to four decimal places.)
Explain what the p-value means for this problem.
A. If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
B. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.
C. If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
D. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =
(ii) Decision:
reject the null hypothesisdo not reject the null hypothesis
(iii) Reason for decision:
Since α < p-value, we do not reject the null hypothesis.
Since α > p-value, we reject the null hypothesis.
Since α < p-value, we reject the null hypothesis.
Since α > p-value, we do not reject the null hypothesis.
(iv) Conclusion:
There is sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
There is not sufficient evidence to conclude that there is a difference among the different nutritional formulas for rats with respect to weight gain.
The graph representation of the given distribution is attached below.
The term graph in math refers the visual representation of the collection of data that has the x and y coordinate values.
Here we have given that Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams and we need to find the graphical representation of the distribution.
Here by using the values in the foregoing ANOVA table are quickly produced by the calculator, including the test statistic and the p-value of the test calculator shows :
=> F=0.66853555
=> p = 0.530548
And the FACTOR df =2 and SS=23.212
=> MS = 11.606
Here the ERROR df = 12
=> SS=208.324
=> MS = 17.36
Here by using the f distribution for the test of three different means.
Then the value of the test statistic (F-value) is 0.668 and the p -value for the test is 0.5301
When we plot the graph for the distribution then we get he graph like the following.
To know more about Graph here.
https://brainly.com/question/17267403
#SPJ4
an application is using a two-dimensional list defined as follows: write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. write nested loops that get an integer value from the user for each element in the list, example: values
Complete Question :
An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.
Sum of rows : [ 6, 60, 600, 6000 ]
Sum of columns : [ 1111, 2222, 3333]
Sum of all elements : 6666
The nested loops are :
Enter a number at row 0, and column 0 : 1
Enter a number at row 0, and column 1 : 2
Enter a number at row 0, and column 2 : 3
Enter a number at row 1, and column 0 : 10
Enter a number at row 1, and column 1 : 20
Enter a number at row 1, and column 2 : 30
Enter a number at row 2, and column 0 : 100
Enter a number at row 2, and column 1 : 200
Enter a number at row 2, and column 2: 300
Enter a number at row 3, and column 0 : 1000
Enter a number at row 3, and column 1 : 2000
Enter a number at row 3, and column 2 : 3000
To read more about nested loops, visit https://brainly.com/question/29973787
#SPJ4
What will be the answer to this question
3x-4y=3
Step-by-step explanation:
3x - 3y=3 which means 3x=3+4y
3x/3=3/3+4y/3 devide both sides by 3 to find c
x=1+4/3y we solve x instead of y
3(1+4/3y)-4y=3 replace x instead of y
Any value of y makes the equation True.
Slope =____
2
3
{1}/{3}
Answer:
slope of the line =
y2 - y1 / x2 - x1
take the appropriate point namely:
(-1,-3) as (x1,y1)
(1,3) as (x2,y2)
(you can change the position whether {-1,-3) as {x2,y2} or {1,3} as {x1,y1})
3 - (-3) / 1 - (-1)
3 + 3 / 1 + 1
6 / 2
= 3
On December 31 of last year, Dog Corporation had an inventory of 550 units of its product, which cost $24 per unit to produce. During January, the company produced 950 units at a cost of $28 per unit. Assuming that Dog Corporation sold 900 units in January at a price of $35 per unit, what was the sales revenue, cost of goods sold and gross profit? (Assume FIFO inventory accounting.)
We got sales revenue= $31500, cost of goods sold =$8300 and gross profit =$23200
What is sales revenue?The income that someone earn from his product and services before the deduction of any charges or expenses.
What is cost of goods sold and gross profit?All direct and indirect cost needed to make a product such as raw materials, transportation cost and labor cost is called cost of goods sold.
The profit earns by a business organization after deducting all the costs associated with manufacturing and selling products.
we calculated gross profit by using the formula, Gross profit= sales revenue- cost of goods sold.
We calculate cost of goods sold by using the formula
beginning inventory + purchases during the period - ending inventory
= 550×24+950×28-900×35
costs of goods sold =$8300
given, number of units sold = 900
average sales price per unit= $35
Now sales revenue= 900 × $35
=$31500
Now gross profit= $31500-$8300
$23200
to know more about revenue, cost of goods sold and profit visit:
https://brainly.com/question/8645356
#SPJ1
11. A triangle has a base length of 3.9 cm and a height of 9 cm. Which dimensions could
be the measurements of a similar triangle?
The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm
How to Identify a similar triangle?Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.
Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.
Thus, this means that a similar triangle will have same ratio of side lengths. Thus;
If new height is h and new base is b, then we have;
9/h = 3.9/b
Thus,
h/b = 9/3.9
If we multiply the right side top and bottom by 2, then we have;
h/b = 18/7.8
18 and 7.8 cm could be similar dimensions.
Read more about Similar Triangles at; https://brainly.com/question/14285697
#SPJ1
Using your own words, explain why the APR does not compare loans for different lengths of time.
When comparing loans with different terms, it is important to consider not just the APR in order to get a more accurate picture of the total cost of borrowing and help you make a more informed decision about which loan is right for you
Why does APR not compare loans for different lengths of time?The annual percentage rate (APR) is a measure of the annual cost of borrowing, expressed as a percentage of the loan amount. It takes into account the interest rate, any fees or other charges associated with the loan, and the length of the loan.
However, because the APR takes into account the length of the loan, it is not an accurate way to compare loans with different loan terms. For example, a loan with a lower APR but a longer term will generally have a higher overall cost than a loan with a higher APR but a shorter term, even though the APR is lower.
Therefore, when comparing loans with different terms, it is important to consider not just the APR, but also the loan term and any fees or charges associated with the loan.
Learn more about annual percentage rate (APR) on:
https://brainly.com/question/24715857
#SPJ1
Which of the following statements about histograms is true?
a. A histogram is a summary of interval data.
b. A histogram is made of a series of intervals, called classes.
c. The classes in a histogram cover the complete range of observations.
d. All of these choices are true.
The correct statement about histograms is given as follows:
d. All of these choices are true.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
Each element is said in case that the histogram can represent element by element, but in the case of distribution with a wider range of possible output values, the histogram is divided into classes, and then the histogram shows the number of observations that were observed for each class, which cover the complete range of observations, meaning that the histogram is a summary of interval data.
The above paragraph, in case the histogram covers a wide range of data, means that all the statements in this problem are correct, and thus option d is correct.
More can be learned about histograms at https://brainly.com/question/25983327
#SPJ1
Graph the rational function Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X ?
The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.
Graph is attached.
As given in the question,
Given function is :
f(x) =6 /(- 2x +1)
f(x) = y
Degree of the numerator is zero
Degree of the denominator is 1.
Degree of denominator is greater than the degree of numerator.
Function represent the horizontal asymptotes for y =0
To get the vertical asymptotes equate denominator equals to zero
(- 2x +1) = 0
⇒2x = 1
⇒x = 1/2
Vertical asymptotes is given by x =1/2.
Graph is attached.
Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.
The above question is incomplete, the complete question is:
Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.
Learn more about asymptotes here
brainly.com/question/4084552
#SPJ4
A rock is thrown at 12 m/s at an angle of 60° above horizontal. (use g = 9.81 m/s2)
a. How high does the rock rise?
b. How long is it in the air if it falls to the same elevation at which it was thrown?
c. How far from the thrower does the rock land?
a) The maximum height of the rock is of: 5.50 metres.
b) The time that the rock was in the air is of: 2.12 seconds.
c) The distance which the rock landed is of: 12.72 meters.
How to model the height of the projectile?The height of the projectile is modeled using a quadratic function, as follows:
y = -4.905t² + v(0)sin(60)ºt + h(0).
The parameters are given as follows:
-4.905 is the acceleration of the gravity divided by 2.v(0) = 12 is the initial velocity.60º is the angle.h(0) = 0 is the initial height.Considering the values of these parameters, the function is given as follows:
y = -4.905t² + 10.39t.
The coefficients are given as follows:
a = -4.905, b = 10.39, c = 0.
The maximum height is obtained as the y-coordinate of the vertex, as follows:
Hmax = -(10.39² - 4(4.905)(0))/(4(-4.905)) = 5.50.
The rock hits the ground when:
y = 0.
Hence:
-4.905t² + 10.39t = 0
t(-4.905t + 10.39) = 0.
4.905t = 10.39
t = 10.39/4.905
t = 2.12 seconds.
The horizontal distance is given as follows:
x = v(0)cos(60º)t
Hence:
x = 12 x 0.5 x 2.12 = 12.72 meters.
More can be learned about quadratic functions at https://brainly.com/question/24737967
#SPJ1
Can anyone help me ASAP?
Answer:
Equation 1 - x + 4y = 12
Equation 2 - 2x + 4x = 16
Cost of 1 Cheeseburger - $4
Cost of 1 Taco - $2
Step-by-step explanation:
Cheeseburger(x) and Taco(y)
x + 4y = 12 and 2x + 4y = 16
x = - 4y + 12
2(- 4y + 12) + 4y = 16
- 8y + 24 + 4y = 16
- 4y = - 8
y = 2
x + 4(2) = 12
x + 8 = 12
x = 4
We are interested in determining the dielectric constant,Eof a new material our lab has developed. The new material was derived using a variation of existing methods, and you know the material should have a value of e~ 2.50. There was only a limited eoretically, amount of time for experiments and the following data was obtained after conducting only n-4 repetitions {2.749, 2.866, 2.420, 1.637) a) Letting Y be the random variable corresponding to the experimental value of the dielectric constant, report an estimate of y and a 95% CI using standard statistical methods. Show all your work. b) Now we will try a Bayesian approach. Use as previous knowledge, your theoretical value ofe along with a weighting factor of Ko-10 to determine a Bayesian estimate of μy. Provide a 95% Bayesian coverage interval. A good set of starting parameters for the variance are Vo-1 and ơ2-0.25. Show all your work and provide hardcopies of all code used. c) The true value for uy is 2.55. Comment on why the Bayesian method provided much better results compared to traditional methods.
a) The 95% confidence interval is (1.638, 3.236).
b) The 95% Bayesian coverage interval is (2.041, 2.889).
c) The Bayesian method provided much better results compared to traditional methods because it takes into account previous knowledge of the dielectric constant, rather than just relying on the experimental data.
a) To find an estimate of the dielectric constant y and a 95% confidence interval using standard statistical methods, we can use the sample mean and standard deviation of the experimental data.
The sample mean of the experimental data is:
(2.749 + 2.866 + 2.420 + 1.637)/4 = 2.437
The sample standard deviation of the experimental data is:
√(((2.749 - 2.437)² + (2.866 - 2.437)² + (2.420 - 2.437)² + (1.637 - 2.437)²)/(4 - 1)) = 0.399
To find the 95% confidence interval, we can use the t-distribution with n-4 degrees of freedom. The t-value for a 95% confidence interval with 4 degrees of freedom is 2.776.
The 95% confidence interval is then:
2.437 +/- (2.776 × 0.399) = (1.638, 3.236)
b) To find a Bayesian estimate of the dielectric constant using the previous knowledge of the theoretical value and a factor, we can use the following formula:
μ × y = (K × [tex]e[/tex] + n × y)/(K + n)
Using the given values, the Bayesian estimate of the dielectric constant is μy = (10 × 2.50 + 4 × 2.437)/(10 + 4) = 2.465
μ × y +/- (t × √(V/n + q))
Using the given values and the t-value for a 95% confidence interval with 4 degrees of freedom (2.776), the 95% Bayesian interval is:
2.465 +/- (2.776 × √(1/4 + 0.25)) = (2.041, 2.889)
c) The Bayesian method provided much better results compared to traditional methods because it takes into account previous knowledge of the dielectric constant, rather than just relying on the experimental data. By incorporating the theoretical value and a weighting factor, the Bayesian estimate of the dielectric constant is more accurate and has a narrower confidence interval compared to the estimate obtained using just the experimental data.
Learn more about the Bayesian Approach at
https://brainly.com/question/29111348?referrer=searchResults
#SPJ4
How do you graph this line using intercepts 9x - 10y = -90
Answer:
The intercepts are:
(0,9) and (-10,0)
Step-by-step explanation:
Plot the two intercepts and draw a line growing through both points. See below.
Given the points (1, -4) and (4, 5), construct two equations in point slope form using each of the points. Construct and upload the graph of the line. Show your work and upload your graph for your teacher to review.
The equation of line passes through the points (1, -4) and (4, 5) will be;
⇒ y = 3x - 7
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (1, -4) and (4, 5).
Now,
Since, The equation of line passes through the points (1, -4) and (4, 5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - (-4)) / (4 - 1)
m = 9 / 3
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - (-4)= 3 (x - 1)
⇒ y + 4 = 3x - 3
⇒ y = 3x - 3 - 4
⇒ y = 3x - 7
Therefore, The equation of line passes through the points (1, -4) and (4, 5) is given as;
⇒ y = 3x - 7
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ1
A reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours. If the tank originally contained 200 gallons of coolant, approximately how many gallons are in the tank after 8 hours?
The gallons after 8 hours will be 3400 gallons.
How to illustrate the expression?Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.
In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.
Therefore, the gallons after 8 hours will be:
= 200 + 400(8)
= 200 + 3200
= 3400 gallons.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Zareen has 24 minutes to work on her math homework, and each problem is taking her of a minute, on average, to complete. Which expression can be used to determine the number of math problems she will be able to complete in the time she has?
By using division, it can be concluded that
Number of math problem she can be able to complete within given time is [tex]24 \div \frac{2}{3}[/tex]
This is the required expression
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem on division
Zareen has 24 minutes to work on her math homework
Fraction of time taken to do each sum =[tex]\frac{2}{3}[/tex]
Number of math problem she can be able to complete within given time is
[tex]24 \div \frac{2}{3}[/tex]
To learn more about division, refer to the link-
https://brainly.com/question/25289437
#SPJ1
S.
5 Ester spends $40 to $50 at the
grocery store each week. She spends
about 20% of the amount on
vegetables and fruit. Which of the
following is a reasonable estimate of
the amount of money Ester will spend
on vegetables and fruit at the grocery
store the next 3 weeks?
The reasonable amount Ester will spend on vegetables is $27
How to determine the amount Ester spends?The amount is the value in $ which Ester will spend on vegetable and fruits in the grocery market. To determine the amount we have to determine the average of the current expenditure for the current period
The given parameters are
The range of values to spend
$40 to $50
Percentage of amount to spend = 20%
Number of weeks = 3
Average amount to be spend = (40+50)/2 = 90/2 = $45
(20/100)*45/1 = 9
In the next 3 weeks
In the nest 3 weeks Ester spends ($3*9)= $27
In conclusion, Ester spends $27 in the next three weeks
Learn more about Amount spending on https://brainly.com/question/12763762
#SPJ1
give an example of a finite group g and a positive integer n such that n divides |g| but no action of g (on any set) can have an orbit of size n. prove that your answer has this property.
he group g and the positive integer n = 3 satisfy the conditions given in the problem.
Let g be the 6th group isomorphic to the rotationally symmetric group of regular hexagons. Let n = 3.
Since |g| = 6, it is clear that n |g|. Split. However, the action of g on any set cannot have orbitals of magnitude 3. To see this, note that the order of each element of g is either 1, 2, or 3. If an element of g has degree 1, then its orbit under the action of g is the element itself with magnitude 1.
If the elements of g have degree 2, then the orbitals under the action of g have magnitude 2. If the elements of g have degree 3, then the orbitals under the action of g have magnitude 3. However, g only has order elements. Since it is of order 3 (that is, a rotation of 120 degrees), the effect of g cannot have an orbit of magnitude 3.
Hence, the group g and the positive integer n = 3 satisfy the conditions given in the problem.
Learn more about this on brainly.com/question/7201810
#SPJ4
A firm manufactures two products; the net profit on product 1 is Rupees 3 per
unit and Rupees 5 per unit on product 2. The manufacturing process is such that
each product has to be processed in two departments D1 and D2. Each unit of
product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit
of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2.
Machine time available per day is 860 minutes at D1 and 1200 minutes at D2.
How much of product 1 and 2 should be produced every day so that total profit
is maximum. Make the mathematical model for the given problem.
To answer this question we need to make use of Linear Programming
The solution is:
x = 170 units
y = 345 units
z(max) = 2235 rupees
To solve a linear programming problem, we need to formulate the model
The Objective Function
Let´s call x the number of product 1 manufactured
and y the number of product 2 manufactured
Then the Objective Function is:
z = 3× x + 5×y to be maximize
The set of constraints are:
D1 D2
( min. ) ( min. )
Product 1 (x) 1 3
Product 2 (y) 2 2
Availability 860 1200
First constraint:
Time available in D1: 860 minutes
1×x + 2×y ≤ 860
Second constraint:
Time available in D2: 1200 minutes
3×x + 2×y ≤ 1200
General constraint: x ≥ 0 ; y ≥ 0 integers ( we will assume only complete products at the end of the period no fractions )
Then the model is:
z = 3× x + 5×y to be maximize
Subject to:
1×x + 2×y ≤ 860
3×x + 2×y ≤ 1200
x ≥0 y ≥ 0 integers
With the help of Avtomat we get the solution:
x = 170 units
y = 345 units
z(max) = 2235 rupees
To learn more about Programming visit
https://brainly.com/question/11023419
#SPJ1
Write another division problem that has a quotient of 3 and a remainder of 28.
Division problem with quotient of 3 and a remainder of 28 are-
43 / 157 = 3, leaving a difference of 28.Three times 37 yields three, leaving a leftover of 28.Explain the term quotient of the division?The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient.In this example, the number being divided (15) is known as the dividend, as well as the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. Observe how 15 ÷ 3 = 5 is a correct equation even if you change the quotient and divisor. 15 ÷ 5 = 3.The given data is-
quotient=3remainder=28To estimate:
division problem?
43 / 157 = 3, leaving a difference of 28.Three times 37 yields three, leaving a leftover of 28.To know more about the quotient of the division, here
https://brainly.com/question/28867023
#SPJ1
exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.
Sample size: n = 13
Sample mean: x’ = 8.52 mps
Sample standard deviation: s = 0.78 mps
95% lower confidence bound for the true average proportional limit stress of all such joints
Level of Significance (α) = 1-95% = 5% = 0.05
α/2 = 0.025
So the value of t(α/2) = 1.8
The confidence interval = x’± t(α/2)*s/√n
Now putting the value:
The confidence interval = 8.41± (1.8)*(0.78)/√12
The confidence interval = 8.41± (1.8)*(0.226)
The confidence interval = 8.41± 0.4068
The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)
The confidence interval = (8.01, 8.82)
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
To learn more about confidence interval link is here
brainly.com/question/24131141
#SPJ4
The right question is:
A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.
Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
Graph the solution of the inequality on a number line.
2(x − 3) – 5x < x-2
Ο
Α.
OB.
OC
OD.
℗
-5 -4 -3 -2 -1 0 1 2
←
+1
-5 -4 -3 -2 -1 0 1
#2
0111
1
-5 -4 -3 -2 -1 0
2
3 4 5
3 4 5
3 4
+
5
4
110111
-5 -4 -3 -2 -1 0 1 2 3 4 5
Answer:
Choice D : x > - 1
Step-by-step explanation:
Left hand side (LHS) of the inequality can be siimplified
[tex]2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\[/tex]
Inequality becomes
[tex]-3x-6 < x-2[/tex]
Move x to the left side and -6 to the right side:
[tex]-3x - x < -2 + 6\\\\-4x < 4\\\\[/tex]
Multiply both sides by -1(the inequality sign changes to >)
[tex]4x > -4\\\\[/tex]
Divide both sides by 4:
[tex]x > -1[/tex]
The number line corresponding to this is the fourth choice
The Picture and Sound electronics store has hired Brennan to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. He turns the crank 15 times to lift a box 15 feet. He turns the crank 45 times to lift a box 45 feet.
In this relationship, x represents the number of times Brennan turns the crank to lift a box, and y represents the height the box has been lifted (in feet).
Graph two points for this relationship and the line passing through them.
The graph (created with MS Excel) of the height the box is lifted to the number of times Brennan turns the crank to lift the box which is the graph of the proportional relationship, y = x, is attached.
What is a proportional relationship?A proportional relationship is one in which one variable (the output variable) is a constant multiple of the another variable known as an input variable.
The number of times Brennan turns the crank = x
The height to which the box is lifted = y
The points on the graph are; (15, 15), and (45, 45)
The ratio of the y-values to the x-values is 15/15 = 45/45 = 1, which indicates that the relationship is a proportional relationship
A point on the graph of a proportional relationship is the point (0, 0), therefore, the points on the graph are; (0, 0), (15, 15), and (45, 45)
Please find attached the graph of the proportional relationship between the number of times Brennan turns the crank to the height to which the box is lifted created with MS Excel
The relationship between the variables x and y is; y = x
Learn more about proportional relationships here:
https://brainly.com/question/19752715
#SPJ1
Through C construct a parallel to AB.
Through A construct a parallel to BC.
Through B construct a parallel to AC.
Extend these lines to form a new triangle.
What relationship exists between the
two triangles?
A
C
B
Answer:
new triangle is similar to and 2 times the size of the original
Step-by-step explanation:
You want to construct a new triangle with the sides of the existing one being midsegments of the new one. Then you want to know the relationship between the triangles.
ConstructionThe attachment shows the described construction.
RelationshipThe sides of the original triangle are midsegments of the new triangle, so the new triangle is ...
scaled up by a factor of 2 (has 4 times the area)similar to the originalrotated 180° about the common centroid of the two trianglesA laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x) .
a. The blue line represents g(x) = 250,000csc(π30x).
b. g(5) = 25,000 km. This is the distance of the comet from Earth after 5 days.
c. The minimum distance between the comet and Earth is 250,000 km, which occurs when x = 0. This corresponds to the constant csc(π30x).
d. The equation has a vertical asymptote at x = 30/π.
Write the solution to following questions:a. Graph the value of x on the range [0,35].b. Analyze g(5) and explain the results.c. What is the shortest path the comet must take to reach Earth? When does this take place? What equation constant does this match up to?d. Find any vertical asymptotes and explain their significance.a. Graph g(x):
To graph g(x), we can plot several points on the interval [0,35] and then connect them to form a graph of the function. For example, we can plot the points (0,250,000), (5,50,000), (10,25,000), (15,16,667), (20,12,500), (25,10,000), (30,8,333) and (35,7,143). Connecting these points will give us a graph of the function g(x).
b. Evaluate g(5):
The value of g(5) can be found by plugging in x = 5 into the equation: g(5) = 250,000 csc(π30*5) = 50,000 km. This means that after 5 days, the comet will be 50,000 km away from Earth.
c. Minimum distance between the comet and Earth:
The minimum distance between the comet and Earth can be found by taking the derivative of the equation and setting it to 0.
d. Vertical Asymptotes:
The vertical asymptotes of g(x) occur at x = 0 and x = 30. This means that the comet approaches an infinitely large distance from Earth at x = 0 and x = 30.
To learn more about asymptotes refer to:
https://brainly.com/question/4138300
#SPJ1
