Complete Question
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.
Answer:
The sample size is [tex]n = 1537 \ gallons[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]MOE = 0.5[/tex]
The confidence level is [tex]C = 95[/tex]%
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is [tex]Z_{\frac{\alpha }{2} } = 1. 96[/tex]
The reason we are obtaining critical values of
[tex]\frac{\alpha }{2}[/tex]
instead of
[tex]\alpha[/tex]
is because
[tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval (
[tex]1-\alpha[/tex]
) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]
is just the area of one tail which what we required to calculate the sample size
Now the sample size is mathematically represented as
[tex]n = \frac{[Z_{\frac{\alpha }{2} }] ^2 * \sigma ^2}{MOE^2}[/tex]
substituting values
[tex]n = \frac{1.96^2 * 10 ^2}{0.5^2}[/tex]
[tex]n = 1537 \ gallons[/tex]
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
Answer:A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
Step-by-step explanation:
The cylinder is given by A = pi/4 the volume of the prism or π/4 x (4r²h) or π x r² x h
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Area circle is A = πr²
Area square with side s = s²
The side of the square is equal to the diameter of the circle
Area square = D²
A diameter of square is always twice the radius
Area square = (2r)² = 2²r² = 4r²
So , on simplifying , we get
Area circle/Area square = (πr²)/(4r²)
Area circle/Area square = π/4
Now , The volume Prism = Area Square x h
Volume Prism = 4r²h
Volume of Cylinder= Area Circle x h
Volume of Cylinder = π x r² x h
So , Volume Cylinder/Volume Prism = π x r² x h/4r² x h
Volume of Cylinder/Volume of Prism = π/4
Volume of Cylinder = π/4 x Volume Prism
And , The volume of Cylinder = π/4 x (4r²h)
Hence , the volume of cylinder is V = π/4 x (4r²h)
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The ratio of the legs of a trapezoid is 1:2, and the sum of the angles adjacent to the bigger base is 120°. Find the angle measures of the given trapezoid.
Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
mark wants to invest $10,000 for his daughter’s wedding. Some will go into a short term CD that pays 12% and the rest in a money market savings account that pays 5% interest. How much should he invest at Each rate if he wants to earn $1095.00 in interest in one year.
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
If ABC~DEF and the scale factor from ABC to DEF is 3/4, what is the length of DF?
Answer:
the length of DF = 3/4 AC
see below for explanation
Step-by-step explanation:
ABC is said to be approximately equal to DEF
The scale factor from ABC to DEF = 3/4
From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.
We can deduce from the question, ΔABC was dilated to form ΔDEF
In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.
In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :
AB, BC and AC
ΔDEF has 3 sides : DE, EF and DF
If AB corresponds to DE
BC corresponds to EF
AC corresponds to DF
Then:
length DE = scale factor × AB = 3/4 AB
length EF = scale factor × BC = 3/4 BC
length DF = scale factor × AC = 3/4 AC
Therefore, the length of DF = 3/4 AC
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. VIEW FILE ATTACHED
Answer: see below
Step-by-step explanation:
[tex]P(x)=\dfrac{2}{3x-1}\qquad \qquad Q(x)=\dfrac{6}{-3x+2}\\[/tex]
P(x) ÷ Q(x)
[tex]\dfrac{2}{3x-1}\div \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\times \dfrac{-3x+2}{6}\\\\\\=\large\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]
P(x) + Q(x)
[tex]\dfrac{2}{3x-1}+ \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)+ \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)+6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4+18x-6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{12x-2}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{2(6x-1)}{(3x-1)(-3x+2)}}[/tex]
P(x) - Q(x)
[tex]\dfrac{2}{3x-1}- \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)- \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)-6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4-18x+6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-24x+10}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{-2(12x-5)}{(3x-1)(-3x+2)}}[/tex]
P(x) · Q(x)
[tex]\dfrac{2}{3x-1}\times \dfrac{6}{-3x+2}\\\\\\=\large\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]
Use the minimum and maximum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 14, max = 121, 8 classes
Answer:
The class width is [tex]C_w \approx 13[/tex]
Step-by-step explanation:
From the question we are told that
The upper class limits is [tex]max = 121[/tex]
The lower class limits is [tex]min = 14[/tex]
The number of classes is [tex]n = 8 \ classes[/tex]
The class width is mathematically represented as
[tex]C_w = \frac{max - min}{n }[/tex]
substituting values
[tex]C_w = \frac{121 - 14}{8 }[/tex]
[tex]C_w = 13.38[/tex]
[tex]C_w \approx 13[/tex]
Since
The number of users on a website has grown exponentially since its launch. After 1 month, there were 120 users. After 4 months, there were 960 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Answer:
f(x) = 60(2)ˣ
Step-by-step explanation:
f(x) = a(b)ˣ
After one month:
120 = a(b)¹
After four months:
960 = a(b)⁴
Divide the second equation by the first:
8 = b³
b = 2
Plug into either equation and find a.
120 = a(2)¹
a = 60
Therefore, f(x) = 60(2)ˣ.
Which of the following points is a solution of the inequality y <-Ixl
You did not give any options but i will try to answer.
y < -lxl basically means that the value of y is less than the absolute value of x time - 1.
So if x = 2, then y is any number less than -2.
And if x is -3. then y is any number less than -3.
Happy to help!
Assume that IQ scores are normally distributed, with a standard deviation of 16 points and a mean of 100 points. If 60 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points
Answer:
The probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.67
Step-by-step explanation:
Please check attachment for complete solution and step by step explanation
Datguy323 is going to complain again. What's the variables for: [tex]x^2+y^2=29\\x+y=7[/tex]
y<4
Answer: :o I FINALLY MADE IT
(5, 2)
x = 5
y = 2
Step-by-step explanation:
First, I graphed both equations. They meet at the points (5,2) and (2,5). Because y < 5, the solution is (5, 2)
Hope it helps <3
Answer:
[tex]x=5\\y=2[/tex]
Step-by-step explanation:
[tex]x^2 +y^2 =29[/tex]
[tex]x+y=7[/tex]
Solve for x in the second equation.
[tex]x+y=7[/tex]
[tex]x+y-y=7-y[/tex]
[tex]x=7-y[/tex]
Plug in the value for x in the first equation and solve for y.
[tex](7-y)^2 +y^2 =29[/tex]
[tex]y^2-14y+49+y^2 =29[/tex]
[tex]2y^2-14y+20=0[/tex]
[tex]2(y-2)(y-5)=0[/tex]
[tex]2(y-2)=0\\y-2=0\\y=2[/tex]
[tex]y-5=0\\y=5[/tex]
[tex]y<4[/tex]
[tex]y=2[/tex]
[tex]y\neq 5[/tex]
Plug y as 2 in the second equation and solve for x.
[tex]x+y=7[/tex]
[tex]x=7-y[/tex]
[tex]x=7-2[/tex]
[tex]x=5[/tex]
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced?
Answer:
The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.
Ava is buying paint from Amazon. Ava needs 3⁄4 cup of blue paint for every 1 cup of white paint. Ava has 28 ounces of white paint. How much blue paint does he need?
Answer:
Blue paint=21 ounces
Step-by-step explanation:
3/4 cup=6 ounces
1 cup=8 ounces
3/4 cup of blue paint=6 ounces of blue paint
1 cup of white paint= 8 ounces of white paint
Ava has 28 ounces of white paint
Find the required blue paint
Let the required blue paint=x
Blue paint ratio white paint
6:8=x:28
6/8=x/28
Cross product
6(28)=x(8)
168=8x
x=168/8
x=21 ounces
Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.
Answer:
In 10 years she'll have approximately $21865.4 in her account.
Step-by-step explanation:
When an amount is compounded continuously its value over time is given by the following expression:
[tex]v(t) = v(0)*e^{rt}[/tex]
Applying data from the problem gives us:
[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]
In 10 years she'll have approximately $21865.4 in her account.
Answer:
21,865.43
previous answer left out the last digit
Step-by-step explanation:
Find the value of annuity if the periodic deposit is $250 at 5% compounded quarterly for 10 years
Answer:
The value of annuity is [tex]P_v = \$ 7929.9[/tex]
Step-by-step explanation:
From the question we are told that
The periodic payment is [tex]P = \$ 250[/tex]
The interest rate is [tex]r = 5\% = 0.05[/tex]
Frequency at which it occurs in a year is n = 4 (quarterly )
The number of years is [tex]t = 10 \ years[/tex]
The value of the annuity is mathematically represented as
[tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)
substituting values
[tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]
[tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]
[tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]
[tex]P_v = \$ 7929.9[/tex]
Con proceso por favor
Answer:se
Step-by-step explanation:
Please answer this correctly without making mistakes
Answer:
Step-by-step explanation:
2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.
A city's population is currently 50,000. If the population doubles every 70 years, what will the population be 280 years from now?
Answer:
200,000
Step-by-step explanation:
The current population: 50,000
Doubling time:70
Population after 280 years=?
280/70=4
50,000*4=200,000
Hope this helps ;) ❤❤❤
Answer: 800,000
Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.
Please help with 4d.
Answer:
(Hemingway, The Old Man and the Sea)(Orwell, 1984)Step-by-step explanation:
A short web search will turn up the authors of the given titles:
The Old Man and the Sea - Hemingway
Huckleberry Finn - Twain
Moby D.ick - Melville
1984 - Orwell
Crime and Punishment - Dostoevsky
What is the value of the rate of change when we put a glass of water at room temperature in the freezer for 15 minutes, what is its temperature at 5 minutes and then at 10 minutes
Answer:
Step-by-step explanation:
I do not understand your question very well but I think that the state of the glass of the water would be liquid and solid at the same time since the water would not freeze 100% and would be with small pieces of solid and some parts liquid, in terms of temperature, I think that at 5 minutes it would be 5 ° C and at 10 it would be 3-4 ° C the longer it is in the freezer the less its temperature will be
(All of that is my point of view)
Average temperature 30 °
So :
30 ÷ 15 = 2 °
30 ÷ 10 = 3 °
30 ÷ 5 = 6 °
What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
A restaurant gat an average of 14 calls in a 2 hr time period. What is the probability that at most 2 calls in 45 min period
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
In the equation, the value of a is:
Answer:
Please check if the answer is a = 4 or not
Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs
of which 2 are defective, Box 2 has 1 defective and 3 functional bulbs and Box 3
contains 3 defective and 4 functional bulbs. A box is selected at random and a bulb
drawn from it at random is found to be defective. Find the probability that the box
selected was Box 2.
Answer:
1/6
Step-by-step explanation:
As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.
The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2 divided by total number of defective bulbs.
P(defective in box 2)= N(defective in box 2)/N(defective total)
As we know there is only 1 defective lamp in box 2.
So N(defective in box 2)=1
Total number of defective bulbs is Box1- 2 defective bulbs, box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.
So N(defective total)=6
So P(defective in box 2)=1/6
In the diagram of RST, which term describes point U?
A.
Circumcenter
B.
Centroid
C.
Incenter
D.
Orthocenter
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.
Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.
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Simplify the expression.(4+2i)-(1-i)
ANSWER :
6i - (1-i)
Step - by - step explanation:
( 4 + 2i ) - ( 1 - i )
( 4 + 2 × i) - ( 1 - i )
( 6× i ) - ( 1 - i )
= 6i- (1-i)
Hope this helps and pls mark as brainliest :)
A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds will be donated to a local alcohol information center. Admission is $6.00 for adults and $3.00 for students. However, this situation has two constraints: The theater can hold no more than 240 people and for every two adults, there must be at least one student. How many adults and students should attend to raise the maximum amount of money?
Answer:
160 adults and 80 students
Step-by-step explanation:
With the information from the exercise we have the following system of equations:
Let x = number of students; y = number of adults
I want to maximize the following:
z = 3 * x + 6 * y
But with the following constraints
x + y = 240
y / 2 <= x
As the value is higher for adults, it is best to sell as much as possible for adults.
So let's solve the system of equations like this:
y / 2 + y = 240
3/2 * y = 240
y = 240 * 2/3
y = 160
Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.
A rectangle is to be inscribed in a right triangle having sides of length 6 in, 8 in, and 10 in. Find the dimensions of the rectangle with greatest area assuming the rectangle is positioned as in Figure 1. Figure1
Answer: width = 2.4 in, length = 5
Step-by-step explanation:
The max area of a right triangle is half the area of the original triangle.
Area of the triangle = (6 x 8)/2 = 24
--> area of rectangle = 24 ÷ 2 = 12
Next, let's find the dimensions.
The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.
length = 10 ÷ 2 = 5
Use the area formula to find the width:
A = length x width
12 = 5 w
12/5 = w
2.4 = w
The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.
Let the length and width of the rectangle be x and y.
Then Area of the rectangle = xy
Now, from the triangle we can conclude that
[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]
Put the value of y in Area we get
[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]
Differentiating it w.r.t x we get
[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]
Put A'(x)=0 for maximum /minimum value
[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]
Now, [tex]A''(3)=-\frac{8}{3} <0[/tex]
Therefore the area of the rectangle is maximum for x=3 inch
Now,
[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]
Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.
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Answer:
(28/33+28 ) *100
Step-by-step explanation:
(28/33+28 ) *100
(28/61)*100
Answer:
it's 2
Step-by-step explanation:
I did it before