For (a), 105 can be written as the product of two fractions, one of which is equal to 1. The expression would be:
105 = (105/1) × (1/1)
This expression can be simplified to:
105 = 105
For (b), the expression can be written as the product of two fractions, one of which is equal to 1. The expression would be:
5/2 = (5/2) × (1/1)
This expression can be simplified to:
5/2
For (c), the expression can be written as the product of two fractions, one of which is equal to 1. The expression would be:
18 = (18/1) × (1/1)
This expression can be simplified to:
18 = 18
Corey is ready to begin the process of producing his final animation. Unfortunately,
his computer does not have the power to render the final scene, so he outsources
the render to a computer that will execute the function. What method allows him to
do this?
(1 point)
O image sequences
Obatch render
O net rendering
O multi-passing
Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network.
Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network. This technique allows a user to take advantage of the computing power of multiple computers to render a scene. To do this, the user would divide the scene into several parts, assigning each part to a different computer. The computers would then render each part of the scene independently, and then the results are combined into a single image. This process can significantly reduce the time required to render a scene, as the workload is distributed over multiple computers. For example, if it would normally take a single computer 10 minutes to render a scene, net rendering could reduce that time to 2 minutes.
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a man allow 12% discount in a computer having marked price RS 32000. If he make Rs.1160 profit on it , Find the cost price of computer
Answer:
CP of computer = 27000 rs.
Step-by-step explanation:
D% = Dis/MP*100
12*32000/100 = Dis Dis = 3840 rs.We know, Dis = MP-SP
32000 - 3840 = SP28160 = SPGiven Profit= 1160 rs.
SP-CP = 1160CP = 28160-1160 = 27000So,CP = 27000 rs.
B=6,c=7.5 what is A in Pythagorean therom
Answer: 4.5
Step-by-step explanation:
A^2 +B^2 =C^2
A^2 + 6^2 =7.5^2
A^2 + 36= 56.25
A^2= 20.25
A= square root of 20.25
A= 4.5
A granola bar weighs 0.84 ounces. There are 8 bars in a box. What is the
total weight of the granola bars using the correct number of significant digits
it's not 6.72 i need the answer with significant digits
The total weight of the granola bars in the box is 6.7 ounces.
How to find the total weight of the granola barsTo calculate the total weight of the granola bars with the correct number of significant digits, we need to multiply the weight of a single bar by the number of bars in the box.
Given parameters:
Weight of a single bar = 0.84 ouncesNumber of bars in the box = 8Total weight of the granola bars
= Weight of a single bar x Number of bars in the box
= 0.84 ounces x 8
= 6.72 ounces
Since the weight of a single bar is given with two significant digits, and we have multiplied it by a whole number, the answer should be reported with two significant digits.
so we can say that, the total weight of the granola bars is 6.7 ounces.
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Assume a jar has five red marbles and four black marbles. Draw out two marbles with and without replacement. Find the requested probabilities. (Enter the probabilities as fractions.)
(a) P(two red marbles)
with replacement without replacement (b) P(two black marbles)
with replacement without replacement (c) P(one red and one black marble)
with replacement without replacement (d) P(red on the first draw and black on the second draw)
with replacement without replacement
The probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement
(a) P(two red marbles) with replacement:The probability of drawing a red marble from a jar with five red marbles and four black marbles is 5/9, as there are five red marbles and nine total marbles. As a result, the probability of selecting two red marbles in a row with replacement is:P(two red marbles with replacement) = (5/9) × (5/9) = 25/81without replacement:When the first marble is removed, there are now only eight marbles remaining in the jar. Because there are only four black marbles in the jar, the probability of drawing a red marble is now 5/8. Therefore, the probability of selecting two red marbles in a row without replacement is:P(two red marbles without replacement) = (5/9) × (5/8) = 25/72(b) P(two black marbles)with replacement:For the first draw, there are four black marbles in the jar and a total of nine marbles. Therefore, the probability of drawing a black marble on the first draw is 4/9. Since the first marble was not removed, there are now eight marbles in the jar, including three black ones, and there are a total of nine marbles. Therefore, the probability of selecting another black marble is 3/9 or 1/3.
The probability of drawing two black marbles in a row with replacement is:P(two black marbles with replacement) = (4/9) × (1/3) = 4/27without replacement:Since the first marble was removed, there are only eight marbles in the jar, and there are four black ones. Therefore, the probability of selecting a black marble is 4/8 or 1/2. When the first black marble is removed, there are only seven marbles left, including three black ones. Therefore, the probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement is:P(two black marbles without replacement) = (4/9) × (3/7) = 12/63(c) P(one red and one black marble)with replacement:When one red and one black marble are selected with replacement, there are nine marbles in the jar for each draw. The probability of selecting one red and one black marble in a row is:P(one red and one black marble with replacement) = 2 × (5/9) × (4/9) = 40/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2.
As a result, the probability of drawing one red and one black marble without replacement is:P(one red and one black marble without replacement) = (5/9) × (4/8) + (4/9) × (5/8) = 20/36 + 20/36 = 10/18 = 5/9(d) P(red on the first draw and black on the second draw)with replacement:There are nine marbles in the jar for each draw. The probability of selecting a red marble first is 5/9. When the red marble is returned to the jar, there are still nine marbles in the jar, but now there are only four black marbles. The probability of selecting a black marble on the second draw is 4/9. As a result, the probability of drawing a red marble first and a black marble second with replacement is:P(red on the first draw and black on the second draw with replacement) = (5/9) × (4/9) = 20/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2. As a result, the probability of drawing a red marble first and a black marble second without replacement is:P(red on the first draw and black on the second draw without replacement) = (5/9) × (4/8) = 5/18
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In tests of significance about an unknown parameter of some population, which of the following is considered strong evidence against the null hypothesis?
A. The value of an estimate of the unknown parameter based on a simple random sample from the population is not equal to zero.
B. The value of an estimate of the unknown parameter lies within 2 units of the sample value.
C. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very consistent with the null hypothesis
D. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true.
In tests of significance about an unknown parameter of some population, "We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true" is considered strong evidence against the null hypothesis. The correct answer is Option (D).
We apply the principle of hypothesis testing to test a population's claims in inferential statistics. The null hypothesis (H₀) is always a statement about the population parameter that we believe to be true. However, we use the sample data to decide whether the null hypothesis is true or not. When we perform the hypothesis testing, we must consider the level of significance, the sample size, and the nature of the test.
The value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true is considered strong evidence against the null hypothesis. In other words, if the value of the test statistic is greater than the critical value, we can reject the null hypothesis. Consequently, we will have sufficient evidence to support the alternative hypothesis.
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The mean height of 15 pupils is 159 cm. One of these pupils is 148 cm and leaves the group. Determine the new mean height of the group. Give your answer correct to 1 decimal place.
Using the mean formula we know that the new mean height of 14 people is 159.7 cm.
What is mean?A mean in math is the average of a data set, calculated by adding all numbers together and then dividing the total of the numbers by the number of numbers.
For illustration, with the dataset containing: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.
The mean height given is 159 cm.
Let, x1, x2, x3 ..... x15 be the height of 15 people.
x1+x2+x3 ..... x15/15 = 159
x1+x2+x3 ..... x15 = 159 * 15 = 2385 cm ...(1)
Let, x1 = 148 cm, who leaves the group.
148+x2+x3 ..... x15 = 2385 cm
x2+x3 ..... x15 = 2237 cm
Now, we have 14 people.
New mean = x2+x3 ..... x15/14
= 2237/14
= 159.7 cm
Therefore, using the mean formula we know that the new mean height of 14 people is 159.7 cm.
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Find the compound interest and the total amount after eight years if the interest is compounded every two years.
Principal = ₹10,000
Rate of interest = 20%
Total amount = (find)
Total interest = (find)
After 8 years, the total amount is ₹38,416 and the compound interest is ₹28,416.
What is the total amount and compound interest earned on ₹10,000 invested at 20% interest compounded every 2 years for 8 years?
To find the compound interest and the total amounts after eight year with interest compounded every two years, we'll use the compound interest formula:
Total Amount (A) = P(1 + r/n)¹/²(nt)
Where:
P = Principal = ₹10,000
r = Rate of interest = 20% = 0.2
n = Number of times the interest is compounded in a year (every 2 years, so n = 1/2)
t = Time in years = 8 years
Convert the interest rate to a decimal by dividing by 100:
20% ÷ 100 = 0.2
A = ₹10,000x (1 + 0.2¹/²)(1/2 x 8)
Calculate the expression inside the parentheses:
1 + 0.2/(1/2) = 1.4
Calculate the exponent (1/2x 8):
1/2x 8 = 4
Calculate the total amount:
A = ₹10,000 x (1.4)^4
A = ₹10,000 x3.8416
A = ₹38,416
Step 6: Calculate the compound interest:
Total interest = Total amount - Principal
Total interest = ₹38,416 - ₹10,000
Total interest = ₹28,416
So, after eight years, the total amount is ₹38,416 and the compound interest is ₹28,416.
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Create a Dataset Give a positive integer less than 100 as the last data value in each of the following datasets so that the resulting dataset satisfies the given condition (a) The mean of the numbers is substantially less than the median 51,52,53,54 (b) The mean of the numbers is substantially more than the median 2,3,4,5, (c) The mean and the median are equal. 2,3,4,5
(a) Dataset with mean substantially less than median:
9, 10, 11, 12, 90
The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.
(b) Dataset with mean substantially more than median:
98, 99, 100, 101, 200
The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.
(c) Dataset with mean equal to median:
2, 3, 4, 4, 5
The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.
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Simplify.
Remove all perfect squares from inside the square root. Assume x is positive.
20x8 =
The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.
What is the simplified form of the given expression?It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.
On this note, since the given expression is; √20x⁸.
We have that; = √ (4 × 5 × x⁸)
Therefore, since 4 and x⁸ are perfect squares; it follows that we have;
= 2x⁴ √5.
Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.
Complete question; The correct expression is; √20x⁸.
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Simplify the expression 3(x+2)+5x and find the value of x=2
Answer:
12.
Step-by-step explanation:
Given: 3(x + 2) + 5x
Put in x:
3(2 + 2) + (5 x 2)
(3 x 4) + 10
12 + 10
= 12.
Help me with this question please
Answer:
x= 2√ 7
Step-by-step explanation:
We can solve it with applying the sin of 30°
Sin 30° = opposite leg / hypotenuse
Sin 30° = √ 7 / x
Being x unknown.
Now, being 30° a notable angle, we know that its sin is 1/2.
Sin 30° = 1/2
Replacing,
Sin 30° = √ 7 / x. (we clear x)
1/2 = √ 7 / x
x/2 = √ 7
x= 2√ 7
Please help me answer!
As a result, the percentage of adults who selected math is different from the percentage of kids who did.
what is percentage ?As a number out of 100, a percentage is a method to express a proportion or a fraction. It is symbolized by the number %. If there are 25 boys in a class of 100 pupils, for instance, then there are 25% of boys in the class. It is a helpful method to compare quantities and to express changes in values over time.
given
120 80
Total 200
Women Overall Party A Party B
70 60
Overall 130
Therefore, there are 130 ladies in the group.
b) The chart indicates that 70 women plan to support Party A.
Thus, the percentage of adults who selected English was 40% of 48, which is equal to 0.4 times 48 and 19.2 when rounded to the closest whole number.
b) Reeshma is not accurate. The percentage of adults who selected math is 35%, while for children it is 40%, according to the pie chart.
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The complete question is:- complete the two-way table, which shows the voting intentions of a group of men and women. a How many women are in the group?
Men
Party A Party B 120
Total 200
Women 130
Total 380
b How many women intend to vote for Party A?
2 A group of 48 adults are asked what their favourite subject was at school. They can choose from
maths, English and science.
A group of 32 school children are asked the
same question.
can someone help me asap pls.
Answer:
[tex](x + 4)(2x - 5) = 0[/tex]
explanation:
[tex]x \times 2x = 2 {x}^{2} [/tex]
[tex]( - 5 \times x) + (4 \times 2x) = 3x[/tex]
[tex] (- 5) \times 4 = - 20[/tex]
The number of employees for a certain company has been decreasing each year by 5%. If the company cumently has 860 employees and this rate continues, find the number of employees in 10 years
The number of employees in 10 years will be approximately
(Round to the nearest whole number as needed)
Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.
What is exponential decay equation?The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.
Exponential decay equation is one of the two exponential functions. The other is the exponential growth equation.
The annual decrease in the number of employees = 5%
The current number of employees in the company = 860
The expected time = 10 years.
The exponential decay equation is as follows, y = 860 x 0.95^10.
y = 860 x 0.95^10 = 515
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Find the area of the figure.
Answer:
A = 32 ft²
Step-by-step explanation:
the area (A ) of a square is calculated as
A = s² ( s is the side length )
the diagonal divides the square into 2 right triangles
using Pythagoras' identity on the lower right triangle with hypotenuse 8 and sides s , then
s² + s² = 8²
2s² = 64 ( divide both sides by 2 )
s² = 32
Then
A = s² = 32 ft²
My question is,
"The midpoint between x and 27 is -3. Find x."
25 points if you get this correct.
Answer:
The number x that is midway between x and 27, and has a midpoint of -3, is -33
midpoint = (x + 27) / 2
We also know that the midpoint is equal to -3, so we can set these two expressions equal to each other and solve for x:
-3 = (x + 27) / 2
Multiplying both sides by 2 gives:
-6 = x + 27
Subtracting 27 from both sides gives:
x = -33
If the block suppported by the pulley system has a weight of 20N what is the input force(effort) on the rope?(Assume the pulley system is frictionless ).
Answer: The input force (effort) on the rope is 20 N.
Step-by-step explanation:
In a frictionless pulley system, the tension in the rope is constant throughout. Therefore, the force applied to the rope on one side of the pulley system is equal to the force exerted on the other side of the system.
In this problem, we know that the weight of the block is 20 N. This means that there is a force of 20 N acting downwards on one side of the pulley system.
Since the pulley system is frictionless, the tension in the rope is also 20 N. Therefore, the force applied to the rope on the other side of the pulley system (i.e., the input force or effort) must also be 20 N in order to balance the weight of the block.
So the input force (effort) on the rope is also 20 N.
Find the height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000cm²
The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.
The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh
where r --> radius of cylinder
h --> height of cylinder
π --> math special constant
We have an open cylinder with the following dimensions,
Radius of cylinder, r = 8 cm
Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr
=> h = A/2π
=> h = 1000/2 ( 3.14)
=> h = 1000/6.28
=> h = 159.24
Hence, required value of height is 159.24 cm.
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let be the linear transformation given by let be the basis of given by and let be the basis of given by find the coordinate matrix of relative to the ordered bases and . HW6.7. Coordinate matrix for differentiation Let L :P2P be the linear transformation given by L(p(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t). Let E = (C1, C2, C3) be the basis of P2 given by el(t) = 1, ez(t) = t, ez(t) = ť. and let F = (f1, 82, 83, fa) be the basis of P3 given by fi(t) = 1, fz(t) = t, fz(t) = {2, fa(t) = {'. Find the coordinate matrix LFE of L relative to the ordered bases & and F. LFE = Save & Grade 2 tries left Save only
The coordinate matrix LFE of L relative to the ordered bases E and F is
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex].
Since here L is a linear transformation from a vector space of dimension 3 to a vector space of dimension 4, the coordinate matrix of L relative to the given ordered bases must be a (4×3) matrix,
Linear transformation is given by,
L(P(t)) = 5p"(t) + 1p' (t) + 3p(t) + 3tp(t)
The given basis is IP² is E = (C1, C2, C3) where, e1(t) = 1, e2(t) = t, e3(t) = t².
Also the given basis of IP³ is (f1, f2, f3, f4) where, f1(t) = 1, f2(t) = t, f3(t) = t², f4(t) = t³.
Now to find the coordinate matrix,
Now,
L(e1(t)) = 5.0 + 1.0 + 3.1 + 3t.1
= 3 + 3t
= 3f1(t) + 3f2(t) + 0.f3(t) + 0.f4(t)
L(e2(t)) = 5.0 + 1.1 + 3.t + 3t.t
= 1 + 3t + 3t²
L(e3(t)) = 5.2 + 1.2t + 3.t² + 3t.t²
= 10 + 2t + 3t² + 3t³
Now writing the coefficients as a column vector we get,
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex]
The coordinate matrix LFE of L relative to the ordered bases E and F is
[tex]\left(\begin{array}{ccc}3&1&10\\3&3&2\\0&3&3\\0&0&3\end{array}\right)[/tex].
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Write a quadratic function in standard form to represent the data in the table.
Ordered pairs arranged in a table. From left to right the pairs are: 2, 3, and 4, 1, and 6, 3, and 8, 9, and 10, 19.
y = x2 − x +
If the sum of two numbers is 10 and the product of the numbers is 15, then find the following:
(a) The difference of numbers.
(b) Sum of cube of the numbers.
Answer:
the numbers are
[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]
Step-by-step explanation:
then there difference is
square root of 10 + 5 -(- square root of 10 +5)
=
[tex]2 \sqrt{10} [/tex]
and the cube of there sum is 15^3 = 15* 15* 15
= 3375
the graph of the sales of a new product at a candy store, where x is time in months and y is number sold in hundreds, goes through the points (4, 2) and (6, 8). what is the rate of change, in candies sold per month?
The rate of change in candies sold per month is 3 hundred candies.
What is the Rate of change?The momentum of a variable is conveyed by the rate of change, which is used for expressing the percentage change in value over a particular amount of time.
To find the rate of change in candies sold per month, it is necessary to find the slope of the line connecting the two points.
The slope formula is given by: Δ[tex]\frac{y}{x}[/tex][tex]\frac{y2-y1}{x2-x1}[/tex]
Using the coordinates of the points, [tex]\frac{8-2}{6-4} =\frac{6}{2} =3[/tex]
The slope is 3. This means that for every month, the store sells 300 more candies.
Therefore, the rate of change, in candies sold per month is 300.
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Sunflower canola oil is a cooking oil sold in south african supermarkets a 750ml bottle cost R28 and a 2litre bottle cost R63 evaluate which option will be the most cost effective option
A 2-liter container costs R0.032 per milliliter, which is less than a 750-milliliter bottle, which costs R0.037 per milliliter.
A milliliter is it an ML?a volumetric measurement using the metric system. One litre is equivalent to 1,000 milliliters. Additionally known as cc, mL, and cubic centimetre.
To evaluate which option is the most cost-effective, we need to calculate the cost per milliliter of each bottle of cooking oil.
For the 750ml bottle, the cost per milliliter is:
R28 / 750ml = R0.037 per ml
For the 2-liter bottle, the cost per milliliter is:
R63 / 2000ml = R0.032 per ml
Therefore, the 2-liter bottle is the more cost-effective option, as it has a lower cost per milliliter than the 750ml bottle. The cost per milliliter of the 2-liter bottle is R0.032, which is cheaper than the cost per milliliter of the 750ml bottle, which is R0.037.
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how can i slove this??
Answer:
[tex]5x {}^{3} - x + 5x + 2[/tex]
Step-by-step explanation:
Greetings!!!
So to find the sum of (f+g)(x) just simply add these two functions
f(x)+g(x)3x²+5x-2+(5x³-4x²+4)Add like terms together
5x³-x²+5x+2If you have any questions tag it on comments
Hope it helps!!!
I need help with this question
Answer: the answer is c I think
use the newton-raphson method to find an approximate value of 3√7 . use the method until successive approximations obtained by calculator are identical. an appropriate function to use for the approximation would be f (x) = A x^2 + B x^3 + C x + D where A= B= C= D=
If c1 = 2, then c2 = ___
2√3= ____
use the equations 10,16,22,28
rule to determine the 10th term and the general term?
Answer:
Below in bold.
Step-by-step explanation:
10,16,22,28
16-10 = 6, 22-16 = 6 and 28-22 = 6
This is an arithmetic sequence with first term a1 = 10 and common difference d = 6
General (nth) term = a1 + d(n - 1)
10th term = 10 + 6(9 -1)
= 10 + 48
= 58.
Find the trigonometric ratios and the measures of the angles or the unknown lengths of these right tiangles, Round off angles to the nearest whole degree, trigonometric values to four decimal places, and lengths of sides to two decimal places.)
The value of x= 10.2.
What is trignometric ratios?This is the boundary or contour length of a 2D geometric shape.
Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
Hence, The value of x= 10.2.
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Jose and his children went into a grocery store where they sell apples for $2.25 each and mangos for $1.25 each. Jose has $20 to spend and must buy at least 9 apples and mangos altogether. Also, he must buy at least 3 apples and at most 9 mangos. If � x represents the number of apples purchased and � y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer: $15.25
Step-by-step explanation:
Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:
2.25x + 1.25y ≤ 20 (Jose has $20 to spend)
x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)
x ≥ 3 (Jose must buy at least 3 apples)
y ≤ 9 (Jose can buy at most 9 mangos)
To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.
First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:
When x = 0, we have 1.25y = 20, so y = 16.
When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).
Plotting these intercepts and connecting them with a line, we get:
| *
16 | *
|
| /
| /
|/
0 *--------*
0 8.89
Next, we graph the line x + y = 9 by finding its intercepts:
When x = 0, we have y = 9.
When y = 0, we have x = 9.
Plotting these intercepts and connecting them with a line, we get:
|
9 | *
|
| /
| /
|/
0 *--------*
0 9
Finally, we shade the feasible region by considering the remaining constraints:
x ≥ 3: This means we shade to the right of the line x = 3.
y ≤ 9: This means we shade below the line y = 9.
Shading these regions and finding their intersection, we get:
| *
16 | * |
| |
| / |
| / |
|/ |
9 *--------*---
| | /
| |/
| *
0 *--------*
3 8.89
The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.
To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.
