Find the measurements (the length L and the width W) of an inscribed rectangle under the line with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answers
The question is incomplete. Here is the complete question.
Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -[tex]\frac{3}{4}[/tex]x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answer: L = 1; W = 9/4; A = 2.25;
Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:
A = x.y
A = x(-[tex]\frac{3}{4}.x + 3[/tex])
A = -[tex]\frac{3}{4}.x^{2} + 3x[/tex]
To maximize, we have to differentiate the equation:
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{d}{dx}[/tex](-[tex]\frac{3}{4}.x^{2} + 3x[/tex])
[tex]\frac{dA}{dx}[/tex] = -3x + 3
The critical point is:
[tex]\frac{dA}{dx}[/tex] = 0
-3x + 3 = 0
x = 1
Substituing:
y = -[tex]\frac{3}{4}[/tex]x + 3
y = -[tex]\frac{3}{4}[/tex].1 + 3
y = 9/4
So, the measurements are x = L = 1 and y = W = 9/4
The maximum area is:
A = 1 . 9/4
A = 9/4
A = 2.25
Related Questions
Consider the original parallelogram and its reduction.
A parallelogram with side length 18 millimeters. A parallelogram with side length 3 millimeters.
Figures not drawn to scale.
What is the scale factor?
One-sixth
One-third
3
6
Answers
Answer:
The answer is 1/6.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
OPTION A
Before reporting the results of the survival analysis, the investigators compared baseline characteristics of the 38 people who withdrew from the study before its end to those who had complete follow up. this was done for which of the following reason?a. To test whether randomization was successful
b. To check for changes in prognosis over time
c. To check whether those who remained in the study represent the total study population
d. To determine whether the outcome of those who remained in the study is the same as the outcome of the underlying population
e. To check for confounders in the exposed and nonexposed groups
Answers
Answer:
the answer is D.
Step-by-step explanation:
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.
(a) The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects. If required, round your answer to four decimal places.
(b) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10.15 ounces being classified as defects. If required, round your answer to four decimal places.
(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
Answers
Answer:
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}[/tex] to four decimal places.
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}[/tex] to four decimal places.
Step-by-step explanation:
a)
Assuming X to be the random variable which replace the amount of defectives and follows standard normal distribution whose mean (μ) is 10 ounces and standard deviation (σ) is 0.15
The values of the random variable differ from mean by ± 1 \such that the values are either greater than (10+ 0.15) or less than (10-0.15)
= 10.15 or 9.85.
The probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:
[tex]P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.15}< \dfrac{X-10}{0.15}< \dfrac{10.15-10}{0.15})[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- \phi (1) - \phi (-1)[/tex]
Using the Excel Formula ( = NORMDIST (1) ) to calculate for the value of z =1 and -1 ;we have: 0.841345 and 0.158655 respectively
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- (0.841345-0.158655)[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) =0.31731[/tex]
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}[/tex] to four decimal places.
b) Through process design improvements, the process standard deviation can be reduced to 0.05.
The probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:
[tex]P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.05}< \dfrac{X-10}{0.05}< \dfrac{10.15-10}{0.05})[/tex]
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- \phi (3) - \phi (-3)[/tex]
Using the Excel Formula ( = NORMDIST (3) ) to calculate for the value of z =3 and -3 ;we have: 0.99865 and 0.00135 respectively
[tex]P(X < 9.85 \ or \ X> 10.15) = 1- (0.99865-0.00135)[/tex]
[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}[/tex] to four decimal places.
(c) What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?
The main advantage of reducing the process variation is that the chance of getting the defecting item will be reduced as we can see from the reduction which takes place from a to b from above.
Multiply 6.4 x 108 by 3.1 x 10-5 and leave the
answer in standard form.
Answers
Answer:
hope this.helps you
if the degree of the monomial 3x^2y^az^a is 10 then what is a
Answers
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
i did it on edge
A study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95. Which of the following statements are correct?MARK ALL THAT ARE TRUE.There are four correct answers. You must mark them all to get credit.A. The interval was produced by a technique that captures mu 95% of the time. B. 95% of all college students work between 4.63 and 12.63 hours a week. C. 95% of all samples will have x-bar between 4.63 and 12.63. D. The probability that mu is between 4.63 and 12.63 is .95. E. 95% of samples will produce intervals that contain mu. F. The probability that mu is included in a 95% CI is 0.95. G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.
Answers
Answer:
Step-by-step explanation:
Confidence coefficient is also the confidence level. A confidence coefficient of 0.95 is the same as a confidence level of 95%.
Confidence level is used to express how confident we are that the population mean lies within the calculated confidence interval. It expresses the possibility of getting the same result if tests are repeated. Since the study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95, then the true statement is
G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.
If you go out to eat with 3 friends and your meal was $72.50, there is a 6.75% sales tax and you should tip the waiter 15%. How much should each person pay?
1)Tax $???
2)Total meal cost $???
3)Tip $???
4)Total cost of meal with tip $???
5)Price per person $???
Answers
Answer:
5 CAUSE ITS PER PERSON
Find the gradient of the line 2y=-6x+1 =
Answers
Answer:
A line in form of y = ax + b has the gradient a.
2y = -6x + 1
<=> y = -3x + 1/2
=> The gradient of this line: g = -3
Hope this helps!
:)
The slope represents the gradient of the line. Then the gradient of the line will be - 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
2y = - 6x + 1
Convert the equation into a slope-intercept form. Then we have
2y = - 6x + 1
y = - 3x + 1/3
The slope represents the gradient of the line. Then the gradient of the line will be - 3.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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17. El precio de los terrenos en Lima es proporcional al área e inversamente proporcional a su distancia con respecto al centro de la ciudad. Un empresario desea adquirir un terreno de 1200 m2 para instalar una pequeña planta procesadora que este localizada a una distancia máxima de 40 Km del centro de la ciudad. Si se sabe que un terreno de 900 m2 a 45 Km del centro de la ciudad cuesta S/ 250 000, ¿cuánto deberá pagar como mínimo dicho empresario para adquirir el terreno con las condiciones dadas?
Answers
Answer:
375000
Step-by-step explanation:
We have that in this case the following proportion would be fulfilled:
Price * Distance / area
Now, we have that for a distance of 45 km and an area of 900 m ^ 2 the price is 250,000, now for a distance of 40 km but with an area of 1,200 m ^ 2, how would the price be, we replace:
250000 * 45/900 = P * 40/1200
12500 * 1200/40 = P
P = 375000
Which means that for these conditions the price is 375000.
All equilateral triangles are also isosceles triangles.
Answers
Answer:
True
Step-by-step explanation:
Isosceles triangles are a subset of equilateral triangles
Equilateral have all three sides the same while isosceles have at least 2 sides the same
Equilateral have all three angles equal while isosceles have at least 2 angles equal
Answer:
Yes
Step-by-step explanation:
An equilateral triangle is one where all three sides are of equal length. (3)
An isosceles triangle has at least two sides of equal length. (2)
But, if it's the other way around than no
Factorize 225-49
[tex] {x}^{2} [/tex]
Answers
[tex]225-49x^2[/tex]
[tex]-49x^2+225[/tex]
[tex]=(7x+15)(-7x+15)[/tex]
Answer:
(15+7x)(15-7x)
Step-by-step explanation:
225-49 x² = 15² - (7x)² = (15+7x)(15-7x)
c^2 = a^2 + b^2 - 2ab cos C make cos C the subject of the formula
Answers
Answer:
[tex]\frac{c^{2}-a^{2}-b^{2} }{-2ab}[/tex]=cos C
Step-by-step explanation:
Start with the parts that are more loosely attached to the cos C: the a² and the b², they are only attached with addition, which can be easily undone by subtracting from both sides. That gives you c²-a²-b²=-2abC
Next, since you want to isolate cosC, you will want to divide by everything attached to the cosC by multiplication: (c²-a²-b²)÷(-2ab)=cosC. Then you can neaten it up and put it in fraction form: [tex]\frac{c^{2}-a^{2}-b^{2} }{-2ab}[/tex]=cos C
x/x+1-1/x-1+2x/x^2-1
Answers
Answer:
Input:
x/x + 1 - 1/x - 1 + 2×x/x^2 - 1
Result:
1/x
Evaluate the numerical expression.
9 × [(25 − 6) − (6 + 5)]
Answers
Answer:
72
Step-by-step explanation:
9 * (19 - 11)
= 9 * 8 = 72
POSSIBLE POINTS
A toy box contains 12 colored toys and 12 white toys. If you pick out 3 toys at random, what is the probability that they will all be white?
Answers
Answer:
12white
12 coloured
12-12=0
Identify J rounded to the nearest tenth. Please Explain!
Answers
Answer:
121.1
Step-by-step explanation:
By law of sines, (sin <I)/i = (sin <J)/j. Plugging in the values we know, we get sin 72deg / 206 = sin 34deg / j. When we solve for k, we get that it is about 121.122. Rounded to the nearest tenth, we get that j is 121.1.
Anybody know how to do this, it's about angles.
Answers
Step-by-step explanation:
45°+90°+60°+X°=360° (being complete angle)
or,195°+X°=360°
or,X°=360°-195°
or,X°=165°
Therefore,valueof X is 165°.
Answer:
165
Step-by-step explanation:
The sum of angles at a point is always 360 degrees and you know all the angles apart from x. so 360-90-45-60=165.
Better notation would be 360 = x+45+60+90 and then you have to find out what x is by rearangin the equation.
Please Someone help do not understand it ASAP
Answers
Answer:
1a) 90 = 2y + 2(2x) 1b) 45 - 2x = y
Step-by-step explanation:
1a) 90 = 2y + 2(2x)
1b) 90 = 2y + 2(2x) Use the equation from above and multiply
90 = 2y + 4x
-4x - 4x Subtract 4x from both sides
90 - 4x = 2y Divide both sides by 2
45 - 2x = y
evaluate (243/32)^-2/5*2^
-2
Answers
Answer:
1/9
Step-by-step explanation:
(243/32)^-2/5*2^ -2 = (3/2)^(5*-2/5) * 1/4 = (3/2)^-2 * 1/4 = 4/9 * 1/4 = 1/9
The difference between an ostrich's speed and a chicken's speed
is 31 miles per hour. An ostrich can run at a speed of 40 miles
per hour. Use mental math or the guess, check, and revise strategy
to solve the equation 40 – c= 31 to find c, the speed a chicken
can run.
Answers
Answer:
9 miles an hour
Step-by-step explanation:
9
Evaluate cos0 if sin0= 5/3
Answers
Answer:
cos0 = 4/3
Step-by-step explanation:
If sin0 = 5/3 then cos0 = 4/3
Sin is opposite/hypotenuse or 5/3.
Cos is adjacent/hypotenuse or 4/3
I found 4 because of Pythagorean Theorem on the triangle, which is known as a 345 triangle.
A quick quiz consists of a multiple-choice question with 3 possible answers followed by a multiple-choice question with 5 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol. prob = %
Answers
Answer:
Step-by-step explanation:
I assume that there is only one right answer in each multiple-choice question
If so:
P=(1/3)*(1/5)
P=1/15
P=0.06666666666
P≈0.067
P≈6.7%
These prisms have different shapes as end faces
Answers
Triangle (3 sides) 5 9 6
Rectangle (4 sides) 6 12 8
Pentagon (5 sides) 7 15 10
Hexagon (6 sides) 8 18 12
b) 300 edges and 200 vertices
(a) The complete table describes a number of faces, edges, and vertices shown below.
(b) There are 300 edges and 200 vertices in a prism with a 100-sided end face
In the given figure one is a triangular prism and the lower one is a pentagonal prism. With the help of the figure, we have to calculate the complete table and the number of edges and vertices a prism with a 100-sided end face has.
(a)
The complete table is given as:
Triangle (3 sides) 5 9 6
Rectangle (4 sides) 6 12 8
Pentagon (5 sides) 7 15 10
Hexagon (6 sides) 8 18 12
(b)
The number of vertices in a prism is determined by the number of vertices on its base polygon. Therefore, there are 300 edges and 200 vertices in a prism with a 100-sided end face.
Learn more about polygons here:
https://brainly.com/question/34047098
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A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 95% confidence if
(a) he uses a previous estimate of 32%?
(b) he does not use any prior estimates?
Answers
Answer:
a) [tex]n=\frac{0.32(1-0.32)}{(\frac{0.03}{1.96})^2}=928.81[/tex]
And rounded up we have that n=929
b) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
Part a
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
For a confidence of 95% we have that the significance is [tex]\alpha=0.05[/tex] and the critical value would be:
[tex] z = 1.96[/tex]
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.32(1-0.32)}{(\frac{0.03}{1.96})^2}=928.81[/tex]
And rounded up we have that n=929
Part b
For this case since we don't have prior info we can use as estimator for the true proportion the value [tex]\hat p=0.5[/tex] and replacing we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
What is the amplitude ? How do I find it? do I add -3.8 to 3.8 then divide? Thank you in advance
Answers
Answer:
7.6subtract the midline from the peak valueStep-by-step explanation:
The amplitude is the difference between the peak value (3.8) and the midline (-3.8). You find it by subtracting the midline from the peak:
amplitude = 3.8 -(-3.8)
amplitude = 7.6
j/k-0.02k when j=25 and k=5
Answers
Answer: 4.98
Step-by-step explanation:fractions are dividing so if j=25 and k=5 the division problem would be 25 divided by 5 then u would subtract 0.02 to get 4.98
Twelve books cost £51.60. How many books would I get for £193.50?
Answers
Answer:
45 books
Step-by-step explanation:
12=51.60
how about 193.50
193.50 x 12=2322 / 51.60=45 books
Solution,
Books Price
12 51.60
X(suppose) 193.50
In case of Direct proportion,
12/X=51.60/193.50
or,51.60x=2322( cross multiplication)
or,X=2322/51.60
X=45
Hope it helps
Good luck on your assignment
Give the numerical value of the parameter p in the following binomial distribution scenario.
The probability of winning an arcade game is 0.632 and the probability of losing is 0.368. If you play the arcade game 10 times, we want to know the probability of winning no more than 8 times.
Consider winning as a success in the binomial distribution. Do not include p= in your answer.
Answers
Answer:0.9306
Step-by-step explanation:
Given
Probability of winning [tex]p=0.632[/tex]
Probability of losing [tex]q=0.368[/tex]
Such that [tex]p+q=1[/tex]
Applying binomioal distribution for n=10 trials
Probability of winning no more than 8 time=P
[tex]P(r\leq 8)+P(r>8)=1[/tex]
[tex]P(r\leq 8)=1-P(r>8)[/tex]
[tex]P(r\leq 8)=1-^{10}C_9(p)^9(q)-^{10}C_{10}(p)^{10}(q)^0[/tex]
[tex]P(r\leq 8)=1-^{10}C_9(0.632)^9(0.368)-^{10}C_{10}(0.632)^{10}(0.368)^0[/tex]
[tex]P=P(r\leq 8)=0.9306[/tex]
What is 5 square root28 plus square root 63 in simplest radical form
Answers
Answer:
13√7
Step-by-step explanation:
[tex]5\sqrt{28} +\sqrt{63} =5\sqrt{2^2\cdot 7}+\sqrt{3^2\cdot 7}\\\\=5\cdot 2\sqrt{7}+3\sqrt{7}=(10+3)\sqrt{7}\\\\=\boxed{13\sqrt{7}}[/tex]
A dead body was found within a closed room of a house where the temperature was a constant 65° F. At the time of discovery the core temperature of the body was determined to be 80° F. One hour later a second measurement showed that the core temperature of the body was 75° F. Assume that the time of death corresponds to t = 0 and that the core temperature at that time was 98.6° F. Determine how many hours elapsed before the body was found. [Hint: Let t1 > 0 denote the time that the body was discovered.] (Round your answer to one decimal place.) hr Need Help? Read It Talk to a Tutor
Answers
Answer: 0.7 hours has elapsed before the body was found
Step-by-step explanation:
Please see the attachments below