To achieve a mean of 78 with four scores, the fourth score must be 90.
We need to consider the current mean, the number of tests, and the desired mean in order to find the fourth score needed to achieve a mean of 78
Let's assume the three test scores are x1, x2, and x3.
We know that the mean of these three scores is 74. So we can assume that
The sum of these numbers is 74 or
(x1 + x2 + x3)/3 = 74
Let's denote it as x4 ,to find the fourth score we will use the formula to calculate the mean:
(x1 + x2 + x3 + x4)/4 = 78
To solve for x4, we can rewrite it as:
x1 + x2 + x3 + x4 = 78 * 4
Now, we can substitute the value of the mean of the first three scores into the equation:
(x1 + x2 + x3) + x4 = 312
we know that,
(x1 + x2 + x3) = 3 * 74
or,
3 * 74 + x4 = 312
Simplifying this, we get:
222 + x4 = 312
Subtracting 222 from both sides:
x4 = 312 - 222
x4 = 90
Therefore, to achieve a mean of 78 with four scores, the fourth score must be 90.
Learn more about mean in mathematical expressions:
https://brainly.com/question/14532771
i think x is 10 but what do i write for the reason
thanks
Answer:
Step-by-step explanation:
Due to isosceles triangle , ∠ABC = ∠ACB = 7x
∠ACB + ∠ACD = 180 ( Linear pair I think )
7x + 110 = 180
7x = 70
x = 10°
a) Work out the area of the whole rectangle shown below. b) Use your answer to part a) to help you work out the area of the dotted, purple triangle. 4 cm 7 cm
a) Area of rectangle = 28 cm²
b) Area of triangle = 14 cm²
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Length of rectangle = 4 cm
Width of rectangle = 7 cm
Since, WE know that;
Area of rectangle = Lenght x Width
Hence, We get;
Area of rectangle = 4 x 7
Area of rectangle = 28 cm²
And, By figure,
Heigh of triangle = 4 cm
Base of triangle = 7 cm
Hence,
Area of triangle = 1/2 x 4 x 7
Area of triangle = 14 cm²
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ1
Draw the following shapes on geoboard paper. Find the area of each shape by partitioning it into sub-shapes and finding the areas of the sub-shapes. Remember to label your answers.
Draw the following shapes on geoboard paper. Surround each triangle with a rectangle so that the vertices of the triangle are on the exterior of the rectangle. Think about how you can use rectangles to determine the areas of right triangles that are inside the rectangles.
Answer:
I apologize, I am not able to provide visual drawings or diagrams. However, I can still provide a step-by-step guide to solve the problem.
To find the area of each shape, we need to use rectangles to determine the areas of right triangles that are inside the rectangles. Here are the steps:
1. Draw the given shape on geoboard paper.
2. Surround each triangle with a rectangle so that the vertices of the triangle are on the exterior of the rectangle.
3. Identify the right triangles that are inside the rectangles.
4. Use the formula for the area of a triangle, which is A = (base x height) / 2, to find the area of each right triangle.
5. Use the formula for the area of a rectangle, which is A = length x width, to find the area of each rectangle.
6. Add up the areas of the triangles and rectangles to find the total area of the shape.
Remember to label your answers with the correct units (square units).
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
The correct answer is:
(A) enlargement
Brennan knew his parents had set up their will some years ago. Neither he nor his sister, Maureen, had ever discussed the will with their parents. When both parents passed away, they met with the family lawyer about the will. What they found was that the money their parents had been giving them over the last few years was a gift and part of their estate planning. The gifts reduced the size of the estate to ensure the value of the estate upon their passing would be under the tax-free limit.
Their parents had not really talked with Brennan or Maureen about how the “gift” money they had been receiving would affect their final inheritance. As they listened to
the estate lawyer give them details of their inheritance, they were shocked to learn there was less than what they had thought.
1. Discuss your thoughts on how Brennan’s and Maureen’s parents handled the informationin the will prior to their passing. Should the parents have explained more clearly about the “gift” money and how it affected their inheritance?
2. What responsibility did Brennan and Maureen have to discuss the will with their parents?
3. What experience do you have with a family member’s will? How would you approach
the topic of writing a will with a family member?
1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.
2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.
3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.
1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.
2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.
3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.
To know more about financial advisor based topics here
https://brainly.com/question/29767702
#SPJ1
Mrs horwitz is wrapping a present in a rectangular prism box for mr roberts. the dimensions of the gift are 13 in by 8 in by 11 in. how much wrapping paper does she need. should mrs horwitz find the volume or surface area to figure out how much wrapping paper she needs. based on your answer above, find the solution. show all your work
Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.
We have,
To figure out how much wrapping paper Mrs. Horwitz needs, she should find the surface area of the rectangular prism box.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Given dimensions:
Length (l) = 13 in
Width (w) = 8 in
Height (h) = 11 in
Plugging these values into the formula, we get:
Surface Area = 2(13)(8) + 2(13)(11) + 2(8)(11)
Surface Area = 208 + 286 + 176
Surface Area = 670 in²
Therefore,
Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.
Learn more about Prism here:
https://brainly.com/question/12649592
#SPJ1
Numbers 1 to 20 are placed in a bag. Without replacing the first number, what is the probability that the first number drawn will be odd and the second number be even?
Answer:
5/19 or 26.3%---------------------------
There are total 20 numbers and half of them odd and half of them even.
Without replacement, the probability of an odd and then even number is:
P(odd then even) = P(odd) * P(even)P(odd then even) = 10/20 * 10/(20 - 1)P(odd then even) =1/2 * 10/19P(odd then even) = 5/19 or 26.3%What are the values of the trigonometric ratios for this triangle?
Drag the answers into the boxes.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
sinθ
cosθ
tanθ
543435434553
A right triangle. The hypotenuse is labeled as 5. The legs are labeled as 3 and 4. The angle opposite the side labeled 3 is theta.
The trigonometric ratios are expressed as;
sin θ = 3/5
cos θ = 4/5
tan θ = 3/4
How to determine the valueTo determine the trigonometric ratios, we need to know the six identities.
These trigonometric identities are listed thus;
sinetangentcosinecotangentcosecantsecantFrom the information given, we have that;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
We have that;
The hypotenuse is labeled as 5.
The adjacent leg is 4
The angle opposite the side labeled 3 is theta
Now, substitute the value to determine the ratios for each identity, we have that;
sin θ = 3/5
cos θ = 4/5
tan θ = 3/4
Learn more about trigonometric identities at: https://brainly.com/question/7331447
#SPJ1
Consider the quadrilateral above. It undergoes the following sequence of transformations:
Answer: (-2, -1)
Step-by-step explanation:
Ok since we just have to find A", let's transform only point A.
Point A=(-1, 5).
Now let's translate it: (-1+3, 5-4). Point A' = (2, 1).
Now, we have to do a 180° rotation. The formula is (-x, -y).
Point A'' = (-2, -1)
PLEASE HELP ASAP! For show and tell, Sophie brought 28 trading cards to class. During the day, Sophie got 54 more from her friends. How many trading cards does Sophie have now?
Answer:
84
Step-by-step explanation:
28+54=84
Answer:84
Step-by-step explanation:
Hi! So to start/set up the problem, since Sophie brought 28 cards, that is how many she has so, so far we only have, 28+_=_.
The next step is to add 54 cards since she added that many. Now we have 28+54=_.
The last step is to calculate. 28+54=84.
please help me solve this
The minor arcs of the circle C are given as follows:
Arc LM.Arc MN.Arc NP.Arc PL.How to classify the arcs of a circle?The arcs of a circle can be classified as minor arcs or major arcs, depending on their angle measures, as follows:
Minor arcs: angle measure less than 180º.Major arcs: angle measure greater than 180º.The entire circumference of the circle is of 360º, hence we have that segment LN, connecting two points on the circumference of the circle through the center, represents the diameter of the circle, with an arc length of 180º.
Hence the minor arcs are all the arcs that are smaller than LN, given as follows:
Arc LM.Arc MN.Arc NP.Arc PL.More can be learned about the arcs of a circle at https://brainly.com/question/30894646
#SPJ1
(a) Find the multiples of 2 greater than 40 and less than 80 in such a way that the sum of their digits is 8. (b) Find the multiples of 5 more thane 106 and less than 200 in such a way that the sum of their digits is 12.
Answer:
(a) 44 (4 + 4 = 8), 62 (6 + 2 = 8)
(b) 165 (1 + 6 + 5 = 12)
Alex tested three brands of batteries to learn which would last the longest in a flashlight. He placed two brand “A” batteries in a flashing, turned the flashlight on, and measured the time and the light shined. He repeated the experiment with battery brands “B” and “C” using the same flashlight. He recorded the data on the bar graph below.
Which of these is an accurate conclusion that Alex can make about the batteries he tested?
A. Brand “C batteries lasted twice as long as brand “A” batteries.
B. Brand “C” batteries listed three times longer than brand “B” batteries
C. The light was twice as bright with brand “A” batteries than with brand “B” batteries.
D. The light shined three times farther with brand “C” batteries than with brand “B” batteries.
The correct statement regarding the bar graph is given as follows:
D. The light shined three times farther with brand “C” batteries than with brand “B” batteries.
What does a bar graph show?A bar graph shows the output considering a given input.
Hence the bar graph in this problem shows the average lifetime for each battery type, given as follows:
Brand A: 270 minutes.Brand B: 120 minutes.Brand C: 360 minutes.Brand C has triple the length of Brand B, hence the correct statement is given by option D.
More can be learned about bar graphs at brainly.com/question/28535024
#SPJ1
Let E be the event where the sum of two rolled dice is greater than 3
. List the outcomes in Ec
The number of possible outcomes that Event E has is 33.
The 36 possible conclusions when rolling two dice is given in the image.
Now, we need to find the event where the sum of two rolled dice is greater than 3
Then, from the outcomes given above we can write those pair whose sum is greater than 3 as
1 + 3=4
1 + 4= 5
1+ 5 = 6
1 + 6 = 7
2+ 2 = 4
2 + 3 = 5
2 + 4 =6
2 + 5 = 7
2 + 6 = 8
3 +3=6
3 + 4 = 7
3 + 5 =8
3 + 6 =9
4 + 3 =7
4 + 4=8
4 + 5 = 9
5+ 5 = 10
5 + 6= 11
6 + 6 = 12
So, there are 33 outcomes whose sum is greater than 3.
The picture related sum greater than 3 is attached below.
Learn more about Outcome of probability here:
https://brainly.com/question/30661698
#SPJ1
Finding the angle when given the right angle and two sides. Please show explanation. Thank you.
The measure of angle A in the right triangle is 75.52°
What is the measure of angle A?The figure in the image is a right triangle.
Measure of angle A = ?
Adjacent to angle A = 2
Hypotenuse = 8
To solve for the measure of angle A, we use the trigonometric ratio.
Note: cosine = adjacent / hypotensue
Hence:
cos( A) = adjacent / hypotensue
cos( A ) = 2/8
cos( A ) = 1/4
Take the cos inverse
A = cos⁻¹( 1/4 )
A = 75.52°
Therefore, the measure of the angle is 75.52 degree.
Learn more about trigonometric ratio here: brainly.com/question/28016662
#SPJ1
Side panel MF Open course index Open block drawer Learnership Pre-Assessment and Evaluation v1 Figure Classification Assessment  QUIZ Figure Classification Assessment Back Time left 0:59:33 Question 1 Not yet answered Not graded Flag question Question text This test consists of several different items. Each item of the test appears in a separate question. The form of an item - item 25, say, is as follows:  You will notice that there are six boxes: 1 box in the first row 2 boxes in the second row, and 3 boxes in the third row In the top left-hand corner of each box, there is a letter labelling each box. For example, the letter ‚"A" labels the box in the first row. The number, which appears to the left of the box ‚"A" is the number of the item. In this example, it is item 25. Every item of the test will have this form, with each box containing a drawing of shapes or patterns. The following is an example of an item:  You must group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. In the example - item 25 - drawings A, B and F belong together because they are shaded the same way, and drawing C, D and E belong together because their shadings are the same. Now turn to your answer sheet and look at it carefully. At the top of the page is 2 rows of 6 boxes. The first row of the boxes refers to the item "Example (i)" and the second row of the boxes refer to the item "Example (ii)." Below these two rows are 24 rows of 6 boxes. Each row refers to a particular item of the test. The number which appears to the left of each row of boxes refers to the item number in the test. Each row of 6 boxes is divided into 2 groups of 3 boxes. The first box of each row contains the letter "A". In the following two empty boxes, you insert the letters of the two drawings which belongs to the same group as that to which drawing A belongs. In the second group of 3 empty boxes you must insert the letters of the other 3 drawings which belong together. Here is another example of an item - item 26.  In this item, drawings A, D and E belong together because their outlines consist of single lines. Drawings B, C and F belong together because their outlines consist of double lines. The answer to this practice item should be filled in as follows:  Please note the following: 1. It is NOT correct to find a reason for grouping together 3 drawings of an item, and assume that the other 3 drawings belong together. For example, when solving item 26 (Previous page), it would be incorrect to group together drawings A, E and F on the basis that each of these is a 4-sided figure, and drawings B, C and D on the basis that they do not have 4 sides. You must be able to find something common to the 3 drawings of each group. 2. A drawing may NOT belong to both groups. For example, the response-  would be incorrect since the drawing "D" is common to both groups. Select one: a. Continue b. Ask for assistance Clear my choice Question 2 Not yet answered Not graded Flag question Question text You must now do two example items on your own. These examples are on the next two pages. Please fill in the answers to the two examples in the first two rows of the answer sheet. These two rows are labelled “Example (i)" and “Example (ii)". Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. Hint: Type the answer as one word e.g. ABC  Answeris the first group. Answeris the second group.
The solution is: the dimensions of the flag in inches is:
40 inches by 55 inches.
The flag is rectangular in nature and the formula for calculating the perimeter of a rectangle is P = 2(L+W) where;
L is the length of the flag
W is the width of the flag
From the diagram, L = y and W = 11y/8
Since the perimeter = 190 inches, we will substitute the given parameters into the formula and firs calculate the value of y.
190 = 2(y+11y/8)
190 = 2y + 11y/4
multiply through by 4
760 = 8y+11y
760 = 19y
y = 760/19
y = 40
The length of the flag is 40 inches and the Width of the flag is 11(40)/8 = 55inches.
Hence, the dimensions of the flag in inches is 40 inches by 55 inches.
Learn more about perimeter here:
brainly.com/question/397857
#SPJ1
complete question:
Item 15 Question 1 Write and solve an equation to answer the question. The perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag? Equation: =190 y= Question 2 Label the dimensions of the flag in inches.
Answer:
Step-by-step explanation:
Can someone please answer and provide an explanation for these problems?
The measure of the arc or angle indicated are:
(9). m∠KLN = 55°, (10). m∠LMN = 40°, (11). arc RT = 61°, (12). arc PR = 240°, (13). arc EG = 150° and (14). arc ? = 225°
How to calculate for the measure of the arc and angle indicated(9). m∠KLN = 1/2(arc NK - arc MK) {secant tangent angle}
m∠KLN = 1/2(160 - 50)
m∠KLN = 110/2
m∠KLN = 55°
(10). m∠LMN = 1/2(140 - 60)
m∠LMN = 80/2
m∠LMN = 40°
(11). 60° = 1/2(181 - arc RT)
120° = 181 - arc RT {cross multiplication}
arc RT = 181 - 120
arc RT = 61°
(12). Angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference.
arc PR = 2(120)
arc PR = 240°
(13). arc EG = 2(75)
arc EG = 150°
(14). m∠TUV = 180 - arc TV {angle between two tangents}
arc TV = 180 - 45
arc TV = 135°
the larger arc ? = 360° - 135°
arc ? = 225°.
Therefore, the measure of the arc or angle indicated are:
(9). m∠KLN = 55°, (10). m∠LMN = 40°, (11). arc RT = 61°, (12). arc PR = 240°, (13). arc EG = 150° and (14). arc ? = 225°
Read more about arc and angle here:https://brainly.com/question/29545060
#SPJ1
help please ambree!!
Answer:
130 blackberries
Step-by-step explanation:
[tex]\displaystyle 600\biggr(\frac{78^\circ}{360^\circ}\biggr)=130[/tex]
Evaluate: 0.36×4.2_0.008÷25.5
The value of the expression 0.36 × 4.2 - 0.008 ÷ 25.5 is approximately 1.5116863.
To evaluate the expression 0.36 × 4.2 - 0.008 ÷ 25.5, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, let's simplify the division: 0.008 ÷ 25.5 = 0.0003137 (rounded to six decimal places).
Now, we can substitute the simplified division back into the expression: 0.36 × 4.2 - 0.0003137.
Next, we perform the multiplication: 0.36 × 4.2 = 1.512.
Finally, we subtract the result of the multiplication from the simplified division: 1.512 - 0.0003137 = 1.5116863 (rounded to seven decimal places).
To learn more about the PEMDAS;
https://brainly.com/question/36185
#SPJ1
Find the missing probability.
P(B)=1/4P(AandB)=3/25P(A|B)=?
The missing probability is P(A|B) is 12/25 if P(B) is 1/4P and (A and B) is 3/25P.
P(B) = 1/4
P(A and B) = 3/25
The conditional probability is used to find the P(A|B):
P(A|B) = P(A and B) / P(B)
Conditional probability is defined as the number of possible outcomes from a given event based on the previous outcomes of the events.
By substituting the given values in the given probability, we get:
P(A|B) = (3/25) / (1/4)
Divide the fraction and multiply it with its reciprocal:
P(A|B) = (3/25) * (4/1)
P(A|B) = 12/25
Therefore, we can conclude that the missing probability is P(A|B) is 12/25.
To learn more about Probability
https://brainly.com/question/30034780
#SPJ1
The complete question is:
Find the missing probability.
P(B)=1/4P
(AandB)=3/25P
P(A|B)=?
WHICH STATEMENT ABOUT A QUADRILATERAL IS TRUE
A quadrilateral is a polygon with four sides. All trapezoids have two pairs of parallel sides. Option (a) is correct.
Understanding the Properties of QuadrilateralA quadrilateral is a polygon with four sides, and there are several properties and characteristics that can be true about a quadrilateral. Some possible true statements about a quadrilateral include:
1. A quadrilateral has four angles.
2. A quadrilateral has four vertices.
3. The sum of the interior angles of a quadrilateral is always 360 degrees.
4. A quadrilateral can have sides of different lengths.
5. A quadrilateral can have parallel sides.
Compare each of the properties above to the given options.
Options:
a) All trapezoids have two pairs of parallel sides.
b) Only some rectangles have four right angles.
c) All squares are rectangles.
d) Some rhombuses are trapezoids.
We can conclude that option (a) is correct because it correspond to the property 5 of a quadrilateral.
Learn more about quadrilateral here:
https://brainly.com/question/23935806
#SPJ1
Find the length of side x to the nearest tenth.
Answer: x=6.6
Step-by-step explanation:
The is a 30-60-90 triangle, which means it falls into the special right triangles category
That means that the hypotenuse (x) is the smaller leg (sqrt11) multiplied by 2.
Sqrt11 times 2 is 6.6332495807108
Rounded to the nearest tenth would turn out to be 6.6
ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
Lindsey estimated the amount of liquid in a container to be 5 oz. The actual amount of liquid was 4 oz.
What is the percent error?
A: 10%
B: 15%
C: 20%
D: 25%
Answer:
and c 20
Step-by-step explanation:
20 percent of t is 1
5 -1 =4
Toheebah ran round the playground 12 times. the playground is 240m by 160m.What distance did she cover?
Toheebah covered a distance of 9600 meters by running around the playground 12 times.To
How to determine 160m.What distance did she cover?The perimeter of a rectangle can be calculated by adding the lengths of all four sides. In this case, the playground has dimensions of 240 meters by 160 meters, so the perimeter is:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (240m + 160m)
Perimeter = 2 * 400m
Perimeter = 800m
Therefore, the perimeter of the playground is 800 meters.
To find the distance Toheebah covered by running around the playground 12 times, we multiply the perimeter by 12:
Distance covered = Perimeter * Number of laps
Distance covered = 800m * 12
Distance covered = 9600m
So, Toheebah covered a distance of 9600 meters by running around the playground 12 times.
Learn more about distance at https://brainly.com/question/26550516
#SPJ9
Out of 200 students in a senior class, 10 students are varsity athletes and on the honor roll. There are 70 seniors who are varsity athletes and 68 seniors who are on the honor roll. What is the probability that a randomly selected senior is a varsity athlete or on the honor roll? Write your answer as a fraction in simplest form or as a decimal.
Answer: We can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are two events.
In this case, we want to find the probability that a randomly selected senior is a varsity athlete or on the honor roll. We can define the events as follows:
A = the event that a senior is a varsity athlete
B = the event that a senior is on the honor roll
From the problem statement, we know:
P(A and B) = 10/200 = 1/20
P(A) = 70/200 = 7/20
P(B) = 68/200 = 17/50
Plugging these values into the formula:
P(A or B) = P(A) + P(B) - P(A and B)
= 7/20 + 17/50 - 1/20
= 21/50
Therefore, the probability that a randomly selected senior is a varsity athlete or on the honor roll is 21/50.
Number 6 look at the image
It would take Arron 3 hours to travel 18 miles upstream (against the river)
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operations.
Speed is the ratio of total distance to total time taken.
Arron boat has a speed of 9 mph in still water and the speed of the river is 3 mph. Since he is travelling upstream, we subtract both speed:
He needs to travel 18 miles upstream at time t, hence:
(9 mph - 3 mph) = 18 miles / t
6t = 18
t = 3 hours
It would take Arron 3 hours
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Solve each of the following graphically method method
A. Max Z = 10x1 + 20x2
Subject to
5x1+ 3x2 ≤ 30
3x1+ 6x2 ≤ 36
2x1+ 5x2 ≤ 20
x1 ≥ 0 , x2 ≥
Answer:
Step-by-step explanation:
To solve the given linear programming problem graphically, we'll plot the feasible region determined by the given constraints and then identify the optimal solution by maximizing the objective function Z = 10x1 + 20x2.
Step 1: Plotting the Constraints
We'll start by plotting the equations representing each constraint.
Constraint 1: 5x1 + 3x2 ≤ 30
To plot this constraint, we'll first find the points on the line 5x1 + 3x2 = 30. We can do this by setting x1 to 0 and solving for x2, then setting x2 to 0 and solving for x1.
Setting x1 = 0, we get: 3x2 = 30
x2 = 10
So, one point is (0, 10).
Setting x2 = 0, we get: 5x1 = 30
x1 = 6
So, another point is (6, 0).
Plotting these two points and drawing a line passing through them, we get a boundary line for the first constraint.
Constraint 2: 3x1 + 6x2 ≤ 36
Similarly, we find two points on the line 3x1 + 6x2 = 36.
Setting x1 = 0, we get: 6x2 = 36
x2 = 6
So, one point is (0, 6).
Setting x2 = 0, we get: 3x1 = 36
x1 = 12
So, another point is (12, 0).
Plotting these points and drawing a line passing through them, we get a boundary line for the second constraint.
Constraint 3: 2x1 + 5x2 ≤ 20
Again, we find two points on the line 2x1 + 5x2 = 20.
Setting x1 = 0, we get: 5x2 = 20
x2 = 4
So, one point is (0, 4).
Setting x2 = 0, we get: 2x1 = 20
x1 = 10
So, another point is (10, 0).
Plotting these points and drawing a line passing through them, we get a boundary line for the third constraint.
Step 2: Finding the Feasible Region
Now, we shade the region of the graph that satisfies all the constraints. The feasible region is the intersection of the shaded regions determined by each constraint.
Step 3: Maximizing the Objective Function
To maximize the objective function Z = 10x1 + 20x2, we look for the highest possible value within the feasible region. The optimal solution will be at one of the corner points of the feasible region.
We calculate the coordinates of each corner point formed by the intersection of the constraint lines and evaluate Z = 10x1 + 20x2 at each of these points. The corner point with the highest Z value will be the optimal solution.
By evaluating Z at each corner point, we can determine the optimal solution and its corresponding values of x1 and x2.
Note: Without specific numerical values for the corner points, I am unable to provide the exact coordinates and the optimal solution for this problem. However, by following the steps outlined above and evaluating the objective function at each corner point, you can identify the optimal solution for the given linear programming problem.
Hi. First of all, please give me 5 stars. There is the response:
To solve this problem graphically, we first plot the lines corresponding to the constraints, and then find the feasible region by shading the region that satisfies all constraints. Finally, we evaluate the objective function at each corner point of the feasible region to find the optimal solution.
The constraints can be rewritten in slope-intercept form as follows:
5x1 + 3x2 ≤ 30 => x2 ≤ (-5/3)x1 + 10
3x1 + 6x2 ≤ 36 => x2 ≤ (-1/2)x1 + 6
2x1 + 5x2 ≤ 20 => x2 ≤ (-2/5)x1 + 4
We plot these lines on a graph:
```
| / 5x1 + 3x2 = 30
6 +-------/------------
| / 3x1 + 6x2 = 36
| /
4 +----/--------------
| / 2x1 + 5x2 = 20
| /
2 +-/----------------
| /
|/
+------------------
0 2 4 6 8
```
Next, we shade the feasible region:
```
| /
6 +-------/-----RR-----
| / -----RR-----
| / -----RR-----
4 +----/-----RRR------
| / --RRRRRR------
| / -RRRRR--------
2 +-/----RRRR----------
| / R--------------
|/ R--------------
+------------------
0 2 4 6 8
```
The feasible region is the shaded area. There are 4 corner points: (0, 4), (4, 2), (6, 0), and (8/7, 26/21).
Finally, we evaluate the objective function at each corner point:
- (0, 4): Z = 10(0) + 20(4) = 80
- (4, 2): Z = 10(4) + 20(2) = 80
- (6, 0): Z = 10(6) + 20(0) = 60
- (8/7, 26/21): Z = 10(8/7) + 20(26/21) = 170/7
The optimal solution is (8/7, 26/21) with a maximum value of 170/7.
need help fast just answer
Step-by-step explanation:
The volume of a pyramid is 1/3 bh
First step is to find the base
The area of a triangle is 1/2 bh
We have both b and h of the base triangle
Area of base = 16.5 cm^2
Now we can sub. that in with the volume formula
1/3 16.5 x 9
1/3 x 148.5
49.49999999999995
Venessa bought 80 apples for 4$.out of these apples 25 precent were rotten and had to be thrown away Vanessa sold the remaining apples at 6 cents per apple. What is the profit or loss percentage
The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.
Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.
Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.
Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.
For more question on profit
https://brainly.com/question/1446002
#SPJ8
How do I covert 45 degrees to a radian
Step-by-step explanation:
There are pi radians in 180 degrees
you want 1/4 of 180 degrees (45/180 = 1/4)
so this would be 1/4 pi radians or pi / 4 radians
45 * pi / 180 = pi/4