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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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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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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What is the product? assume x greater-than-or-equal-to 0 (startroot 3 x endroot startroot 5 endroot) (startroot 15 x endroot 2 startroot 30 endroot) 3 x startroot 5 endroot 3 startroot 165 x endroot 10 startroot 6 endroot 3 x startroot 5 endroot 6 startroot 10 x endroot 5 startroot 3 x endroot 10 startroot 6 endroot 3 x startroot 5 endroot 10 startroot 6 endroot startroot 3 x endroot 5 startroot 3 x endroot 10 startroot 6 endroot
The product of the given expression is 2,916,000,000x³√(9,900x²).
The given expression contains several terms with roots and variables. To simplify and find the product, we'll first multiply the terms with similar roots and variables. The expression is:
√(3x)√5 √(15x)√2 √(30) 3x√5 3√(165x) √10 √6 3x√5 √6 √(10x) √5 √(3x) √10 √6 3x√5 √10 √6 √(3x) √5 √(3x) √10 √6
We can group terms with the same roots and variables together:
(√(3x))⁴ (3x)³ (√5)⁴ (√10)³ (√6)³ √15x √2 √30 √165x
Now, we can simplify each group:
81x³ * 625 * 1000 * 216 * √(2 * 15x * 30 * 165x)
Combine the constants and variables under the root:
81x³ * 625 * 1000 * 216 * √(9,900x²)
Calculate the product of the constants:
13,500,000 * 216 = 2,916,000,000
So, the final simplified expression is:
2,916,000,000x³√(9,900x²)
In summary, the product of the given expression is 2,916,000,000x³√(9,900x²).
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find the area of a joined rectangle
1st rectangle has 6cm length and 4cn width
2nd rectangle has 7cm length and 3cm width
apparently the answer to this question is 33cm² but I don't know how they got it
To find the area of the joined rectangle, you need to add the areas of both rectangles and subtract the area of the overlap.
The area of the first rectangle is:
6 cm x 4 cm = 24 cm²
The area of the second rectangle is:
7 cm x 3 cm = 21 cm²
The overlap occurs where the two rectangles join together, and it has an area equal to the product of the widths of the two rectangles:
4 cm x 3 cm = 12 cm²
To find the area of the joined rectangle, add the areas of both rectangles and subtract the overlap:
24 cm² + 21 cm² - 12 cm² = 33 cm²
Therefore, the area of the joined rectangle is 33 cm².
the process standard deviation is ounces, and the process control is set at plus or minus standard deviations. units with weights less than or greater than ounces will be classified as defects. what is the probability of a defect (to 4 decimals)?
The probability of a defect in the manufacturing process, assuming that the weight of the products follows a normal distribution, is 0.1587 to four decimal places.
To calculate the probability of a defect, we first need to calculate the z-score of the weight that would classify the product as a defect. The z-score is a measure of how many standard deviations a value is from the mean. In this case, the z-score is -1 or 1, depending on whether the weight is less than one standard deviation below the mean or greater than one standard deviation above the mean.
Once we have calculated the z-score, we can use a standard normal distribution table or a calculator to find the probability of a product being classified as a defect. If the z-score is -1, the probability of a product being classified as a defect is 0.1587. If the z-score is 1, the probability of a product being classified as a defect is also 0.1587.
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I Need help with this problem
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
What is the value of the x-coordinate of point A?
a) sin (pi/6)
b) cos (pi/6)
c) sin (pi/3)
d) cos (pi/3)
e) sin (2pi/3)
f) cos (2pi/3)
Without a diagram or additional information, it is impossible to determine the value of the x-coordinate of point A.
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How many pieces of 10 5/6 inch bar can be cut from a stock 29 foot bar
20 pieces of 10 5/6 inch bar can be cut from a stock 29 foot bar.
To calculate the number of pieces of 10 5/6 inch bar that can be cut from a 29 foot bar, we need to first convert the measurements to a common unit. One foot is equal to 12 inches, so 29 feet equals 348 inches.
Next, we need to determine how many 10 5/6 inch bars can be cut from the 348-inch stock bar. To do this, we can use division. First, we need to convert the mixed number 10 5/6 to an improper fraction by multiplying the whole number by the denominator and adding the numerator. This gives us 125/6 inches.
Now, we can divide the length of the stock bar (348 inches) by the length of one 10 5/6 inch bar (125/6 inches). This gives us:
348 / (125/6) = 20.736
Since we cannot cut a partial bar, we need to round down to the nearest whole number. Therefore, we can cut 20 pieces of 10 5/6 inch bar from a 29 foot stock bar.
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Camden and violet are reading the same book. at the beginning of the month, camden was on page 18 and violet was on page 39. camden will read 11 pages per day and violet will read 8 pages per day. let c represent the page of the book that camden is on at the end of t days into the month. write an equation for each situation, in terms of t. and determine whether camden or violet is farther along in 2 days.
For Camden the equation is c = 18 + 11t and for Violet the equation is v = 39 + 8t. After 2 days, Camden will be on page 40 and Violet will be on page 55.
Let's represent the situation with two equations, one for Camden (c) and one for Violet (v), using the given information and the variable t for the number of days.
Camden:
At the beginning of the month, Camden was on page 18 and will read 11 pages per day. So, his equation will be:
c = 18 + 11t
Violet:
At the beginning of the month, Violet was on page 39 and will read 8 pages per day. So, her equation will be:
v = 39 + 8t
Now, we need to determine who is farther along in the book after 2 days. To do this, we will substitute t = 2 into both equations.
Camden's equation (c):
c = 18 + 11(2)
c = 18 + 22
c = 40
Violet's equation (v):
v = 39 + 8(2)
v = 39 + 16
v = 55
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Ying Yu bought a rectangular box to display her doll collection. She decided
to exchange the box for a similar one that had five times its dimensions.
How does the volume of the larger rectangular box compare to the volume
of the smaller box?
The volume of the larger rectangular box is 125 times the volume of the smaller box.
To compare the volume of the larger rectangular box to the smaller box, we need to consider how the dimensions have changed.
Since the larger box has dimensions 5 times those of the smaller box, let's represent the dimensions of the smaller box as length (L), width (W), and height (H). Therefore, the dimensions of the larger box would be 5L, 5W, and 5H.
Now, let's calculate the volume of both boxes:
1. Volume of the smaller box: V_small = L * W * H
2. Volume of the larger box: V_large = (5L) * (5W) * (5H)
To find the ratio of the larger box's volume to the smaller box's volume, we can divide the volumes:
V_large / V_small = ((5L)*(5W)*(5H)) / (L * W * H)
Notice that L, W, and H can be canceled out:
(5 * 5 * 5) = 125
So, the volume of the larger rectangular box is 125 times the volume of the smaller box.
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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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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.)
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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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 quotient of 1x10^-2 and 8x10^-2
Answer:
The first one is - 5 and the other is - 40
from the following quadratic function , g(x)= -4(x+2)^2-3 identify the difference between its parent function f(x)=x^2
Thus, through the steps of horizontal translation, dilation and at last vertical translation, the new quadratic function , g(x)= -4(x+2)²-3 from the parent function f(x)=x².
Explain about the parent function:The simplest function which nonetheless complies with a particular type of function's definition is a parent function. For instance, y = x would be the parent function when considering the linear functions that make a family of functions. The most basic linear function is this one.
In addition, by applying various transformations to the graph of the parent function, all of the functions in a family of functions can also be derived from it. Vertical shifts, extending or compressing both horizontally and vertically, reflecting and over x or y axes, and horizontal shifts are some of these transformations.Given parent function: f(x)=x²
new quadratic function , g(x)= -4(x+2)²-3
there is the translation of 2 units to right such that 2 is added to x.Now, there is dilation with the scale factor of -4.At last the function is shifted 3 units downThus, through the steps of horizontal translation, dilation and at last vertical translation, the new quadratic function , g(x)= -4(x+2)²-3 from the parent function f(x)=x².
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Complete question:
from the following quadratic function , g(x)= -4(x+2)²-3 .identify the difference between its parent function f(x)=x² and g(x).
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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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?
"Consider the following function: f(x,y)=y^5 ln(−2x^4+3y^5) find fx and fy"
From the function f(x,y)=y⁵ ln(−2x⁴+3y⁵). The value of fx = -10x³y⁵ / (-2x⁴ + 3y⁵) and
fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]
To find fx, we differentiate f(x,y) with respect to x, treating y as a constant:
fx = d/dx [y⁵ ln(-2x⁴ + 3y⁵)]
Using the chain rule and the derivative of ln u = 1/u, we have:
fx = y⁵ * 1/(-2x⁴ + 3y⁵) * d/dx [-2x⁴ + 3y⁵]
Simplifying and applying the power rule of differentiation, we get:
fx = -10x³y⁵ / (-2x⁴ + 3y⁵)
Similarly, to find fy, we differentiate f(x,y) with respect to y, treating x as a constant:
fy = d/dy [y⁵ ln(-2x⁴ + 3y⁵)]
Using the chain rule and the derivative of ln u = 1/u, we have:
fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]
Applying the power rule of differentiation and simplifying, we get:
fy = 15y⁴ ln(-2x⁴ + 3y⁵)
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Determine whether Rohe Theorem can be applied to on the dood inter - 2x-) -1.31 WS
A. Yes, Rolle's Theorem can be applied B. No, because is not continuous on the closed intervals
The Rohe Theorem can be applied to on the dood inter - 2x-) -1.31 WS. No, because it is not continuous on the closed intervals.
To determine whether Rolle's Theorem can be applied to the given function (ignoring typos and irrelevant parts), we need to consider the requirements for Rolle's Theorem: the function must be continuous on a closed interval and differentiable on an open interval within that closed interval.
Your answer: B. No, because the function is not continuous on the closed intervals. This is due to the presence of irrelevant parts in the given function, which makes it impossible to determine its continuity and differentiability. Therefore, Rolle's Theorem cannot be applied in this case.
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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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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?
Consider the function f(x) = 1/z on the interval (5,9). (A) Find the average or mean slope of the function on this interval, Average Slope =?
(B) By the Mean Value Theorem, we know there exists a c in the open interval (5,9) such that f'(c) is equal to this mean slope. Find all values of c that work and list them separated by commas) in the box below
Therefore, the only value of c that works is 6√5.
(A) To find the average slope of the function f(x) = 1/x on the interval (5, 9), we use the formula:
Average Slope = (f(9) - f(5)) / (9 - 5)
Plugging in the values, we get:
Average Slope = (1/5 - 1/9) / 4 = -1/180
Therefore, the average slope of the function on the interval (5, 9) is -1/180.
(B) By the Mean Value Theorem, we know there exists a c in the open interval (5, 9) such that f'(c) is equal to this mean slope.
The derivative of f(x) = 1/x is f'(x) = -1/x^2.
Setting f'(c) = -1/180, we get:
-1/c^2 = -1/180
Solving for c, we get:
c = ±6√5
Since c must be in the open interval (5, 9), the only value that works is:
c = 6√5
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The base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively, with a possible error in measurement of as much as 0.1 cm in each dimension. Use differentials to estimate the maximum error in the calculated volume of the cone. (Hint: V = 1/3 πr²h)
The estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.
How to estimate the maximum error in the calculated volume of the cone?Let V = (1/3)πr²h be the volume of the cone, where r and h are the base radius and height of the cone, respectively.
Let dr and dh be the possible errors in the measurements of r and h, respectively.
Then, the actual dimensions of the cone are (r+dr) cm and (h+dh) cm, respectively.
The differential of V is given by:
dV = (∂V/∂r)dr + (∂V/∂h)dh
We have:
∂V/∂r = (2/3)πrh and ∂V/∂h = (1/3)πr²
Substituting the given values, we get:
∂V/∂r = (2/3)π(10 cm)(25 cm) = 500π/3
∂V/∂h = (1/3)π(10 cm)² = 100π/3
Substituting into the differential equation, we get:
dV = (500π/3)dr + (100π/3)dh
Using the given maximum error of 0.1 cm for both r and h, we have:
|dr| ≤ 0.1 cm and |dh| ≤ 0.1 cm
Therefore, the maximum possible error in V is given by:
|dV| = |(500π/3)(0.1 cm) + (100π/3)(0.1 cm)|
|dV| = 50π/3 + 10π/3
|dV| = 60π/3
|dV| = 20π cm³
Therefore, the estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.
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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
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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For the line y=2/5x+9, what will be the angle this line makes with the x-axis?
Answer:
21.8014 degrees (to 4 decimal places)
Step-by-step explanation:
The equation y=2/5x+9 forms a certain angle with the x-axis. Note that all lines parallel to y=2/5x+9 also form the same angle with the x-axis, due to Corresponding Angles (the fact that the original line has a y-intercept of 9 is irrelevant). Therefore, we could simplify this problem slightly by considering the angle that y=2/5x (a y-intercept of 0) forms with the x-axis.
To find the angle that this line makes with the x-axis, we'll need the vertex (the origin -- let's call this point "B"), and one point on each of two rays from the vertex (Let Ray #1 be the ray from the origin directly to the right; and let Ray #2 be the ray from the origin extending into Quadrant I -- up and to the right, along the equation y=2/5x).
One point on Ray #1 is (5,0) -- it is on the positive x-axis. Call this point "A"
One point on Ray #2 is (5,2) -- inputting "5" for x, the result for y is "2" Call this point "C"
y = 2/5 * (5) = 2To find the angle (Angle ABC), observe that the three points form a right triangle (the angle CAB is a right angle because the two lines are perpendicular).
To solve for [tex]\angle ABC[/tex], recall the definition of the tangent function:
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
The Opposite side, side AC, is just the height (or the y-value) of point C. So, opposite = 2.
The Adjacent side, side BA, is just the x-coordinate of point A (and also point C). So adjacent = 5.
Substituting these known values into the tangent function, we get the following:
[tex]tan(m\angle ABC)=\dfrac{2}{5}[/tex]
To solve for the measure of angle ABC, we need to apply the inverse tangent function (also known as arctangent).
[tex]arctan(tan(m\angle ABC)=arctan(\dfrac{2}{5})[/tex]
The left side simplifies because they are inverse functions:[tex]m\angle ABC=arctan(\dfrac{2}{5})[/tex]
Calculating the right side of the equation (rounding to 4 decimal places):
[tex]m\angle ABC \approx 21.8014^{o}[/tex]
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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