Based on simultaneous equations, the number of children and adults who swam at the public pool that hot summer's day is as follows:
Children = 296Adults = 374.What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently.
Simultaneous equations are also referred to as a system of equations because the equations are solved at the same time.
The total number of people who used the public swimming pool = 670
The unit price for children = $1.25
The unit price for adults = $2.00
The total amount collected that day = $1,118
Let the number of children who swam at the public pool that day = x
Let the number of adults who swam at the pool that day = y
Equations:x + y = 670 ... Equation 1
1.25x + 2y = 1,118 ... Equation 2
Multiply Equation 1 by 2:
2x + 2y = 1,340 Equation 3
Subtract Equation 2 from Equation 3:
2x + 2y = 1,340
-
1.25x + 2y = 1,118
0.75x = 222
x = 296
y = 670 - 296
= 374
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Deriving the Law of Cosines
Try it
Follow these steps to derive the law of cosines.
✓ 1. The relationship between the side lengths in AABD is
C2 = x2 +hby the Pythagorean theorem M
✓ 2. The relationship between the side lengths in ACBD is
Q2 = (b - x)2 +hby the Pythagorean theorem
V 3. The equation e? = (6 – x)2 + h? is expanded y to become
22 = 62 - 2x + x2 +h?
a
h
✓ 4. Using the equation from step 1, the equation
22 = 62 - 2bx +32+ hbecomes a = 62 - 2bx + 2
by substitution
A
х
D
b-x
С
Correct! You have completed this exercise.
b
1) The relationship between the side lengths in ΔABD is c² = x² + h² by the Pythagorean Theorem.
2) . The relationship between the side lengths in Δ CBD is a² = (b-x)² + h² by the Pythagorean Theorem.
3) The expanded equation is e² = x² -12x + 36 + h²
4) the expanded equation is a² = b²-x²+32
According to the Pythagorean theorem, the square of the hypotenuse (c) of a right triangle equals the sum of the squares of the other two sides (a² + b²).
So
1) The relationship between the side lengths in ΔABD is c² = x² + h² by the Pythagorean Theorem.
2) The relationship between the side lengths in Δ CBD is a² = (b-x)² + h² by the Pythagorean Theorem.
3) The equation is e² = (6 - x)² + h² when expanded
e² = 36 - 12x + x² + h²
or
e² = x² -12x + 36 + h²
4) Using this equation, we can solve for h² by subtracting (b-x)² from both sides:
a² - (b-x)² = h²
Now we can substitute this expression for h² into the equation given in step 3
2² = 6² - 2bx + (a² - (b-x)²)
Simplifying this equation, we get:
4 = 36 - 2bx + a² - (b-x)²
Expanding the square term, we get:
4 = 36 - 2bx + a² - (b² - 2bx + x²)
Simplifying further, we get:
4 = 36 - b² + x² + a²
Rearranging, we get:
a² = b² - x² + 32
So the equation expanded is a² = b² - x² + 32.
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Full Question:
For 1 and 2, see attached image.
3) The equation e²= (6 – x)² + h² is expanded y to become ?
4) Using the equation from step 1, the equation
2² = 6² - 2bx +32+ h becomes a = 62 - 2bx + 2
by substitution
22 = 62 - 2x + x2 +h?
2. How many checks must a customer write per month before the new plan is cheaper than the old plan? and new plan? 3. What formula/equations can be formed to find the cost for any number of checks for the old cheaper for a customer who writes 10 checks per month? 1. Compute the cost of 10 checks under the old plan and under the new plan. Which plan is check will cost 8 cents. The bank claims the new plan will save the customer money. Plus 15 cents for each check announces that it will change its monthly fee to $3 and that each Problem #3 A bank that has been charging a monthly service fee of $2 for checking accounts
The old plan is cheaper for a customer who writes 10 checks per month.
To determine how many checks a customer must write per month before the new plan is cheaper than the old plan, we need to set up an equation to compare the two plans. Let x be the number of checks written per month. The cost of the old plan is given by:
C_old = 0.08x + 2
The cost of the new plan is given by:
C_new = 3 + 0.15x
To find out when the new plan becomes cheaper, we need to set the two costs equal to each other and solve for x:
0.08x + 2 = 3 + 0.15x
0.07x = 1
x ≈ 14.29
Therefore, a customer would need to write 15 checks per month for the new plan to be cheaper than the old plan.
For a customer who writes 10 checks per month, the cost of the old plan is:
C_old = 0.08(10) + 2 = 2.80
The cost of the new plan is:
C_new = 3 + 0.15(10) = 4.50
Therefore, the old plan is cheaper for a customer who writes 10 checks per month.
The formula for the cost of any number of checks for the old plan is:
C_old = 0.08x + 2
where x is the number of checks written per month
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You ask your best friend to lend you Rs.300 to buy your favorite toy she says she can lend you the money. Only if you give her an extra three rupees for every three months the past before you return it.
Your best friend is charging you an annual interest rate of 4% for lending you ₹300 for nine months with a quarterly interest rate of 1%.
What is rate of interest?The amount a lender charges a borrower for the use of assets, such as money, consumer goods, or physical assets, is known as an interest rate. It is a fraction of the loan's principal, which is the amount borrowed to cover the cost of the purchase or the deposit made with a bank or other financial institution.
If your best friend is charging you an extra ₹3 for every three months that pass before you return the money, then after nine months, you will owe her an extra ₹9 in addition to the original ₹300.
So the total amount you must pay her if you return the ₹300 after nine months would be ₹309.
To calculate the annual rate of interest she is charging you, we can use the formula:
Annual Interest Rate = (Total Interest / Principal) x (12 / Number of Months)
Where the Principal is the original amount borrowed (₹300), the Total Interest is the extra amount you owe her (₹9), and the Number of Months is the time period for which you borrowed the money (9 months).
Plugging in the values, we get:
Annual Interest Rate = (9 / 300) x (12 / 9) = 0.04 or 4%
So, your best friend is charging you an annual interest rate of 4% for lending you ₹300 for nine months with a quarterly interest rate of 1%.
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The complete question is:
You ask your best friend to lend you ₹300 to buy your favourite toy. She says she can lend you the money only if you give her an extra ₹3 for every three months that pass before you return it. What is the total amount you must pay her if you return it after nine months? What is the annual rate of interest she is charging you?
please help im stressing
To multiply these fractions, we can simplify each fraction first:
64e^2/5e * 3e/8e = (8*8*e*e)/(5*e) * (3*e)/(2*2*2*e)
Next, we can cancel out common factors between the numerators and denominators:
= (8*8*1*1)/(5*1) * (1*1)/(2*2*2*1)
= 64/5 * 1/8
= 8.
Answer:
24e^2/5e my answer needs to be 20+characters sooooooooooo
7 NEXT QUESTION e = READ NEXT SECTION G # O ASK FOR HELP 2 e By what percentage did the median earnings of college degreed exceed that of high school degreed for 1973 for men (to the nearest tenth)? 2 3 TURN IT IN
The percentage by which the median earnings of college degree exceed that of high school degreed for 1973 for men is 17.9%
Why is this so?College: Women= 4400
H.School: Women = 3300
Solving we have
The base number is the high school women.
The difference is 4400 - 3300 = 1100
So the % = (1100/3300) * 100% = 33.3%
1973
The base number is again high school 5600
Difference: 6600 - 5600 = 1000
% = (1000/5600) * 100% = 17.9
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See the aattached image.
multiply the polynomials
To multiply the polynomials (1-2t)(5t+t^2), we can use the distributive property and multiply each term in the first polynomial by each term in the second polynomial:
(1-2t)(5t+t^2) = 1(5t+t^2) - 2t(5t+t^2)
Multiplying the first term by each term in the second polynomial, we get:
5t + t^2
Multiplying the second term by each term in the second polynomial, we get:
-10t^2 - 2t^3
Combining like terms, we get:
-2t^3 - 10t^2 + 5t
Therefore, the answer is D. -2t^3 - 9t^2 + 5t.
The drama club is selling tickets to their play to raise money for the ticket sells for $9. The auditorium can hold no more than 110 people. The drama club must make a minimum of $720 from show's expenses. Each student ticket sells for $4 and each adult ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine two possible solutions.
A system of inequalities to model this situation is 4x + 9y ≥ 720 and x + y ≤ 110.
The two possible solutions are (80, 40) and (100, 20).
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the number of student tickets sold and the number of adult tickets sold respectively, and then translate the word problem into a linear equation as follows:
Let the variable x represent number of student tickets sold.Let the variable y represent number of adult tickets sold.Since each student ticket was sold for $4 and each adult ticket sales to cover the show's costs sells for $9 in order to make a minimum of $720 from show's expenses, a linear equation which can be used to model the situation is given by;
4x + 9y ≥ 720
Additionally, the auditorium can hold no more than 110 people;
x + y ≤ 110
Next, we would use an online graphing calculator to plot the above system of linear equations in order to determine its solution as shown in the graph attached below.
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Find the quotient of 1x10^-2 and 8x10^-2
Answer:
The first one is - 5 and the other is - 40
Shawn wrote down the activities for his day on Saturday. In which situation will his activity result in a final value of zero?
1 point
A. Shawn places four quarters in a jar of quarters which contains four quarters.
B. In the morning, Shawn added six hard candies to a jar which contained four hard candies. By the end of the day he ate ten candies from this jar.
C. Shawn starts out on the ground and then climbs ten feet on a ladder.
D. Shawn travels east ten feet and then travels south ten feet
The situation in which Shawn's activity will result in a final value of zero is Shawn travels east ten feet and then travels south ten feet. The correct option is D.
This is because when Shawn travels east ten feet, he moves horizontally to the right of his starting point. When he travels south ten feet after that, he moves vertically downwards from his previous position, cancelling out the horizontal movement he made earlier.
The displacement caused by Shawn's movement in the east direction is equal in magnitude but opposite in direction to the displacement caused by his movement in the south direction.
The net displacement of Shawn's movement is zero, and he ends up back at his starting point. Options A, B, and C do not involve any movements that result in a net displacement of zero.
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Pls help, answer both of the questions with explanation.
Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)
The area of the triangle is (a-6, b-12) square units 6 sq unit.
What is the triangle?A triangle is described as a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.
This means that the sum of the interior angles of a triangle is equal to 180°
Now that we have the points they make a 3-4-5 triangle.
The two legs are 3 and 4, so the hypotenuse has to be 5.
We could also use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5
We then calculate the area
Area =1/2 b*h
Area = 1/2(3*4)
Area = 6 sq unit
The area of the triangle is (a-6, b-12) square units 6 sq unit.
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If x=2, y=4,m=-1 and n=3, find the value of x^m+n * y^n-m/x^m-n * y^n+m
Answer:
1024
Step-by-step explanation:
I hope everything I wrote is clear, I really need to sharpen my pencil oof
2. 7.G.1.2 Look at each set of conditions. Do the conditions given describe a unique triangle or many different triangles? Select Unique or Many for each description by placing a check or X in the appropriate box. Conditions Unique Many Side lengths 3 cm, 6 cm, 7 cm Angle measures 30°, 60°, 90° Angle measures 35º, 35°, 110° Side lengths 5 cm, 5 cm, 5 cm Side lengths 3 in and 4 in with an included 95° angle
The Unique or Many for each description by placing a check or X in the appropriate box is given below.
We are given that;
Measurements= 30°, 60°, 90°
Side lengths 5 cm, 5 cm, 5 cm Side lengths 3 in and 4.
Now,
If three angle measures are given, and they add up to 180 degrees, then there are infinitely many similar triangles with those angle measures, but they differ in size. This is called the AAA (angle-angle-angle) similarity criterion.
If two angles and a non-included side are given, then there may be zero, one, or two possible triangles with those measurements, depending on the length of the side and the position of the angles. This is called the AAS (angle-angle-side) or SSA (side-side-angle) criterion.
Using criteria, we can fill in the table as follows:
Conditions | Unique | Many Side lengths 3 cm, 6 cm, 7 cm | ✓ | Angle measures 30°, 60°, 90° | | ✓ Angle measures 35º, 35°, 110° | | ✓ Side lengths 5 cm, 5 cm, 5 cm | ✓ | Side lengths 3 in and 4 in with an included 95° angle | ✓ |
Therefore, by the angle the answer will be given.
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Solve x∕3 < 5 Question 12 options: A) x < 15 B) x ≥ 15 C) x ≤ 15 D) x > 15
Answer:
A) x < 15
Step-by-step explanation:
You want the solution to x/3 < 5.
InequalityThe steps to solving an inequality are basically identical to the steps for solving an equation. There are a couple of differences:
the direction of the inequality symbol must be respectedmultiplication/division by negative numbers reverses the inequality symbol1-stepIf this were and equation, it would be a "one-step" equation. That step is to multiply both sides by the inverse of the coefficient of x.
The coefficient of x is 1/3. Its inverse is 3. Multiplying both sides by 3, we have ...
3(x/3) < 3(5)
x < 15 . . . . . . . . . simplify
Note that 3 is a positive number, so we leave the inequality symbol pointing the same direction.
__
Additional comment
We can swap the sides of an equation based on the symmetric property of equality:
a = b ⇔ b = a
When we swap the sides of an inequality, we need to preserve the relationship between them. (This is the meaning of "respect the direction of the inequality symbol".)
a < b ⇔ b > a
Besides multiplying and dividing by a negative number, there are other operations that affect the order of values.
-2 < 1 ⇔ 2 > -1 . . . . . multiply by -12 < 3 ⇔ 1/2 > 1/3 . . . . . take the reciprocal (same signs)a < b ⇔ cot⁻¹(a) > cot⁻¹(b) . . . . use function having negative slopeNote that the 1/x function is another one that has negative slope, which is why it reverses the ordering for values with the same sign. (It has no effect on ordering of values with opposite signs.)
The diameter of a circle is 6 kilometers. What is the circle's circumference?
Use 3.14 for л.
Answer:
18.84 kilometers
Step-by-step explanation:
Formula for circumference: C=2πr
1) find radius
r = d / 2
In this case the diameter is 6 so:
r = 6 / 2
r = 3
2. Plug in your values in the formula:
C = 2 (3.14) (3)
3. Solve (multiply)
C = 2 x 3.14 x 3
C = 18.84
So your answer is 18.84 kilometers, and rounded its 19 kilometers.
Hope this helps :D
callum says 300cm2 is the same as 3m2 because there are 100cm in 1m so you divide by 100 callums method is wrong explain why
Answer:
Callum’s method is incorrect because he is confusing the conversion of linear units with the conversion of square units. There are indeed 100 cm in 1 m, but when converting square units, you need to square the conversion factor. So 1 m² is equal to (100 cm)² or 10,000 cm². Therefore, 300 cm² is equal to 0.03 m², not 3 m².
Step-by-step explanation:
Answer:
The answer is wrong because the 3m is still squared if you divided it by 100 then it should only be 3m not 3m^2.
Step-by-step explanation:
I am not 100% sure this is correct so please dont get mad at me.
Find the theoretical probability of the event when rolling a 12-sided die.
P(less than 9)
P(less than 9) =
The theoretical probability of rolling less than 9 on a 12-sided die is 0.6667 or approximately 67%.
How we find the theoretical probability?To find the theoretical probability of rolling less than 9 on a 12-sided die, we need to count the number of outcomes that satisfy this condition and divide by the total number of possible outcomes.
There are 8 outcomes that satisfy this condition, namely 1, 2, 3, 4, 5, 6, 7, and 8. The total number of possible outcomes is 12, since the die has 12 sides. Therefore, the theoretical probability of rolling less than 9 on a 12-sided die is:
P(less than 9) = Number of outcomes that satisfy the condition / Total number of possible outcomes
= 8 / 12
= 2 / 3
= 0.6667
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Gina put all the boxes weighing less than 1/2 pound into a small box she puts all the boxes by more than 1/2 pound into a large box how many pounds heavier are the blocks in a large box than pounds in a small box
Weight difference between the large box and the small box is [tex](1/2)*(w2 - w1)[/tex] pounds.
How to find weight difference?Let's assume that Gina has n boxes in total, and let x be the weight of each box in pounds. We can then express the weight of the boxes that weigh less than [tex]1/2[/tex] pound as [tex](1/2)*w1[/tex], where [tex]w1[/tex] is the number of boxes that weigh less than [tex]1/2[/tex] pound. Similarly, we can express the weight of the boxes that weigh more than 1/2 pound as [tex](1/2)*w2[/tex], where [tex]w2[/tex] is the number of boxes that weigh more than [tex]1/2[/tex] pound.
Since Gina puts all the boxes weighing less than [tex]1/2[/tex] pound into a small box, the weight of the small box will be the sum of the weights of all the boxes that weigh less than [tex]1/2[/tex] pound, which is [tex](1/2)*w1[/tex].
Similarly, since Gina puts all the boxes weighing more than [tex]1/2[/tex] pound into a large box, the weight of the large box will be the sum of the weights of all the boxes that weigh more than [tex]1/2[/tex] pound, which is [tex](1/2)*w2[/tex].
The weight difference between the large box and the small box will be:
[tex](1/2)*w2 - (1/2)*w1[/tex]
Simplifying this expression, we get:
[tex](1/2)*(w2 - w1)[/tex]
Therefore, the weight difference between the large box and the small box is [tex](1/2)*(w2 - w1)[/tex] pounds.
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Jewelers consider weight, cut grade, color, and clarity when pricing diamonds. In researching jewelry prices, Sandra makes the following statements based on her observations. Which of the statements are statements of causation? Select all that apply.
A. A particular diamond costs $264.
B. A darker color decreases a diamond's clarity.
C. Higher clarity drives up the price of a diamond.
D. Heavier diamonds tend to be sold at higher prices.
E. There appears to be a relationship between color and price.
F. Diamonds with lower cut grades seem to sell at lower prices
Statements C and D are statements of causation, while statements A, B, E, and F are not.
Causation refers to the relationship between cause and effect, where a change in one variable causes a change in another variable. Statements of causation imply a cause-and-effect relationship between two variables.
Based on the given statements, the statements of causation are C and D. Statement C implies that higher clarity causes an increase in the price of a diamond, and statement D implies that a higher weight causes an increase in the price of a diamond.
Statements A, B, E, and F are not statements of causation. Statement A only provides information about the cost of a particular diamond and does not explain the reason behind the cost. Statement B suggests a relationship between color and clarity, but it does not imply a cause-and-effect relationship.
Statement E also suggests a relationship between color and price, but it does not imply causation. Statement F only suggests an observation about the relationship between cut grade and price, but it does not imply causation.
In summary, statements C and D are statements of causation, while statements A, B, E, and F are not.
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A mailer for posters is a triangular prism as shown below. Find the surface area of the mailer.
HINT: You should draw each face on a piece a paper and find all the areas, and then add them together. Remember there are 3 rectangles and 2 triangles in this figure.
Total Surface Area =
Therefore, the surface area of the mailer is approximately 229.3 square inches.
What is total surface area?Total surface area refers to the sum of the areas of all the faces or surfaces of a three-dimensional object. It includes the area of all the faces including the bases, top and sides.
Here,
To find the total surface area of the mailer, we need to find the area of all the faces and then add them up.
First, let's find the area of the rectangular faces. The length of the mailer is 18 inches and the height is 4 inches, so the area of each rectangular face is:
Area of rectangle = length x height
= 18 x 4
= 72 square inches
Since there are 3 rectangular faces, the total area of the rectangular faces is:
Total area of rectangular faces = 3 x 72
= 216 square inches
Next, let's find the area of the triangular faces. The triangular side is 4.7 inches and the base is 5 inches. To find the area of a triangle, we use the formula:
Area of triangle = (1/2) x base x height
where base is the length of the triangle's base and height is the perpendicular distance from the base to the opposite vertex.
To find the height of the triangle, we can use the Pythagorean theorem since we know the length of the triangular side and the height of the mailer. The Pythagorean theorem states that:
c² = a² + b²
where c is the hypotenuse (the triangular side), and a and b are the other two sides (the height of the mailer and the height of the triangle).
Solving for b, we get:
b = √(c² - a²)
= √(4.7² - 4²)
= 2.66 inches
Now we can find the area of each triangular face:
Area of triangle = (1/2) x base x height
= (1/2) x 5 x 2.66
= 6.65 square inches
Since there are 2 triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 2 x 6.65
= 13.3 square inches
Finally, we add up the areas of all the faces to get the total surface area:
Total surface area = area of rectangular faces + area of triangular faces
= 216 + 13.3
= 229.3 square inches (rounded to one decimal place)
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Ribbon is sold at $7 for 3 metres at the factory and $2.50 per metre at the store. How much money is saved when 15 metres of ribbon is bought at the factory rather than at the store?
The cost of 15 meters of ribbon at the factory is:
15 meters / 3 meters per $7 = 5 times $7 = $35
The cost of 15 meters of ribbon at the store is:
15 meters x $2.50 per meter = $37.50
Therefore, the amount saved by buying 15 meters of ribbon at the factory rather than at the store is:
$37.50 - $35 = $2.50
Help me now pretty please
Help asap will give 100 points and brainiest
what is the mean absolute deviation for doctor a’s data set on corrective lenses? what is the mean absolute deviation for doctor b’s data set on corrective lenses? write a sentence comparing the variation of the two data sets using their mean absolute deviations.
In statistical analysis, the mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean of the data set. For Doctor A's data set on corrective lenses, the MAD is calculated as 0.42, while for Doctor B's data set, it is calculated as 0.38.
This shows that Doctor B's data set has a slightly smaller variation compared to Doctor A's data set.
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(1 point) Evaluate the double integral I = s do xy dA where D is the triangular region with vertices (0,0),(1,0), (0,6).
To evaluate the double integral I = ∬D xy dA, where D is the triangular region with vertices (0,0),(1,0), (0,6), we need to set up the limits of integration for x and y.
Since D is a triangular region, we can integrate over the two sides that meet at the origin and then integrate over the third side. Let's integrate over the sides that form the right angle at (0,0).
For the side along the x-axis, y = 0 to y = 6x.
For the side along the y-axis, x = 0 to x = 1.
Thus, the double integral becomes:
I = ∫0^1 ∫0⁶x xy dy dx
Evaluating the inner integral with respect to y, we get:
I = ∫0^1 [x(y²/2)]0⁶x dx
Simplifying and evaluating the outer integral with respect to x, we get:
I = ∫0^1 18x⁴ dx
I = 18/5
Therefore, the value of the double integral I = ∬D xy dA over the triangular region with vertices (0,0),(1,0), (0,6) is 18/5.
To evaluate the double integral I = ∬_D xy dA for the triangular region D with vertices (0,0), (1,0), and (0,6), we first need to set up the limits of integration.
The base of the triangle lies on the x-axis, from x = 0 to x = 1. The height of the triangle lies on the y-axis, from y = 0 to the line y = 6(1-x), since the slope of the hypotenuse is -6 and passes through (1,0).
Now we can set up the integral:
I = ∬_D xy dA = ∫_(0 to 1) ∫_(0 to 6(1-x)) xy dy dx
Let's first integrate with respect to y:
∫_(0 to 6(1-x)) xy dy = [x(y²)/2]_(0 to 6(1-x)) = 18x(1-x)²
Next, integrate with respect to x:
I = ∫_(0 to 1) 18x(1-x)² dx
Using integration by substitution or expanding and integrating term by term, we get:
I = 2
So, the value of the double integral is 2.
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Tanya made this graph that represents the total cost for each of the three locations. Depending on the number of students that attend. Which function represents the cost of the restaurant 
The functions that represents the cost are
(a) y = 8800, (b) y = 1900 + 4/7x and (c) y = 4800, x ≤ 150; y = 1200 + 24x x > 150
Identifying the function that represents the costFrom the question, we have the following parameters that can be used in our computation:
The graph
The function (a) is a horizontal line that passes through y = 8800
So, the function is
y = 8800
The function (b) is a linear function that passes through
(0, 1900) and (175, 2000)
So, the function is
y = 1900 + 4/7x
The function c is a piecewise function with the following properties
Horizontal line of y = 4800 uptill x = 150Linear function of (150, 4800) and (200, 6000)So, the function is
y = 4800, x ≤ 150
y = 1200 + 24x x > 150
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Mr. Jones has $410,000 in a retirement account that earns 3. 85% simple interest each year. Find the amount of interest earned by this investment if it is in there for 5 years
The amount of interest earned by Mr. Jones's retirement account over 5 years is $79,025.
Mr. Jones has invested $410,000 in a retirement account that earns 3.85% simple interest per year. Simple interest is calculated by multiplying the principal amount by the annual interest rate and the time period in years.
In this case, the time period is 5 years. Using the formula for simple interest, we can calculate the amount of interest earned on this investment as:
I = P * r * t = $410,000 * 0.0385 * 5 = $79,025
Therefore, the amount of interest earned by Mr. Jones's retirement account over 5 years is $79,025. This means that the total value of his retirement account after 5 years would be $489,025 ($410,000 + $79,025).
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Determine the intervals on which the given function is concave up or concave down and find the points of inflection. S(x) = (x - 10)(1 - x) (Use symbolic notation and fractions where needed. Give your answer in three decimal numbers
There are no points of inflection.
To determine the intervals on which the function S(x) = (x - 10)(1 - x) is concave up or down and find the points of inflection, we need to find the second derivative and analyze its sign.
First, find the first derivative, S'(x):
S'(x) = (x - 10)(-1) + (1 - x)(1) = -x + 10 - 1 + x = 9
Next, find the second derivative, S''(x):
S''(x) = d(S'(x))/dx = d(9)/dx = 0
Since the second derivative S''(x) is constant and equal to 0, there is no concavity, and the function is neither concave up nor concave down. There are no points of inflection.
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show that tan(15 ) = 2 - rt3
By using trigonometry,
we have shown that tan(15°) = 2 - √3.
what is the trignometry?One of the most significant areas of mathematics, trigonometry has a wide range of applications. T
he study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."
Hence, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.
Angles in trigonometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently employed in computations.
We can use the half-angle formula for tangent to show that:
tan(15°) = tan(30°/2) = (1 - cos(30°)) / sin(30°)
We know that cos(30°) = √3/2 and sin(30°) = 1/2, so we can substitute those values in:
tan(15°) = (1 - √3/2) / 1/2
Simplifying the denominator and multiplying by the reciprocal:
tan(15°) = 2(1 - √3/2)
Simplifying the expression:
tan(15°) = 2 - √3
Therefore, we have shown that tan(15°) = 2 - √3.
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A boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 5 , before they draw closer. They measure the angle of elevation a second time from point
B at some later time to be 18∘ Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
If boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water, the distance from point A to point B is approximately 973 feet.
To find the distance from point A to point B, we can use trigonometry and the fact that the angles of elevation from both points are known.
Let x be the distance from point A to the lighthouse, and y be the distance from point B to the lighthouse. We can set up two equations using tangent function:
tan(5) = 119/x
tan(18) = 119/y
We can solve for x and y by isolating them in each equation:
x = 119/tan(5) ≈ 1343.44 feet
y = 119/tan(18) ≈ 370.79 feet
Therefore, the distance from point A to point B is approximately 1343.44 - 370.79 = 972.65 feet.
We rounded the final answer to the nearest foot, which is 973 feet.
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7. At Burger Heaven a double contains 2 meat patties and 6 pickles, whereas a
triple contains 3 meat patties and 3 pickles. Near closing time one day, only
24 meat patties and 48 pickles are available. If a double burger sells for
$1. 20 and a triple burger sells for $1. 50, then how many of each should be
made to maximize the total revenue?
(4. 6 5pts)
a) Write your constraints (1pt)
At Burger Heaven, to maximize the total revenue from selling double burgers containing 2 meat patties and 6 pickles, you need to consider the following constraints:
1. Ingredient availability: Ensure that there are enough meat patties and pickles in stock to meet the demand for double burgers.
2. Production capacity: The kitchen staff must be able to efficiently prepare and assemble the double burgers without compromising on quality.
3. Pricing strategy: Set a competitive price for the double burger to attract customers and generate optimal revenue.
4. Demand forecasting: Accurately predict customer demand for the double burger to prevent overstocking or understocking of ingredients, which can impact revenue.
To maximize total revenue at Burger Heaven, follow these steps:
a) Analyze the availability of meat patties and pickles to determine how many double burgers can be made with the current inventory.
b) Evaluate the production capacity of the kitchen staff to ensure that they can efficiently prepare and assemble the double burgers.
c) Research the market to set a competitive price for the double burger, considering the costs of ingredients, labor, and other expenses.
d) Forecast customer demand for the double burger to ensure optimal inventory levels and to meet customer expectations.
By addressing these constraints and following the steps above, Burger Heaven can successfully maximize its total revenue from selling double burgers with 2 meat patties and 6 pickles.
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