The new pressure of the nitrogen gas after it is transferred to a 15.0 L container is 833.3 mmHg.
We are given that;
Capacity of nitrogen gas= 25L
Pressure= 500mmHg
Now,
To find the new pressure of the nitrogen gas, we need to use Boyle’s law, which states that the product of pressure and volume of a gas is constant at constant temperature 12. The formula for Boyle’s law is:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume of the gas, and P2 and V2 are the final pressure and volume of the gas.
We are also given the final volume of the gas as 15.0 L. We need to find the final pressure of the gas.
Plugging in these values into the formula, we get:
(500.0 mmHg)(25.0 L) = P2(15.0 L)
Solving for P2, we get:
P2 = (500.0 mmHg)(25.0 L) / (15.0 L) P2 = 833.3 mmHg
Therefore, by algebra the answer will be 833.3 mmHg.
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Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint to make a mural.
How many pints of blue paint and yellow paint did Gunther use in all?
Simplify your answer if needed.
Explain your thinking using 3-5 complete sentences.
To solve the given problem we have to add the quantities of blue and yellow paint that were used by Gunther to make the mural.We are given that:Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint to make a mural.To add these two quantities we need to find a common denominator.
Here, the common denominator is 10.As such, we have to convert the mixed numbers to improper fractions.3 3/5 = (3 × 5 + 3)/5 = 18/5 2 1/10 = (2 × 10 + 1)/10 = 21/10Now, we can add the two fractions to get the total amount of paint used:18/5 + 21/10 = (36 + 21)/10 = 57/10 Therefore, Gunther used a total of 57/10 pints of paint to make the mural.Now, let's simplify this answer.
We can simplify the fraction by dividing both the numerator and denominator by the greatest common factor of 57 and 10, which is 1.57/10 = 5.7Thus, Gunther used 5.7 pints of paint to make the mural.In conclusion, Gunther used 3 3/5 pints of blue paint and 2 1/10 pints of yellow paint, or a total of 5.7 pints of paint to make the mural.
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Lincoln's monthly bank statement showed the following deposits and withdrawals: − −$28. 51, − −$41. 34, $90. 95, − −$88. 95, $11. 16 If Lincoln's balance in the account was $19. 96 at the beginning of the month, what was the account balance at the end of the month?
After considering the deposits and withdrawals, the account balance at the end of the month is $64.23.
To calculate the account balance at the end of the month, we need to add up all the deposits and withdrawals. The negative values represent withdrawals, while the positive values represent deposits.
Starting with an initial balance of $19.96, we can calculate the final balance by adding the amounts of the deposits and subtracting the amounts of the withdrawals.
Starting balance: $19.96
Deposits: $90.95, $11.16
Withdrawals: -$28.51, -$41.34, -$88.95
Adding the deposits: $19.96 + $90.95 + $11.16 = $122.07
Subtracting the withdrawals: $122.07 - $28.51 - $41.34 - $88.95 = $64.23
Therefore, the account balance at the end of the month is $64.23.
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A window in the shape of a parallelogram has the dimensions given. What is the area of this window? 20 ft² 24 ft² 28 ft² 40 ft² Parallelogram A B C D with side A D parallel to side B C and side A B is parallel to side D C. Point E is on side A B. Segment A E is 2 ft. Side D C is 5 ft. A dotted segment D E runs from point D to the opposite side A B and is perpendicular to side A B. Segment D E is 4 ft
The shape of a parallelogram has the dimensions the area of the window is 8 ft².
To find the area of the parallelogram-shaped window the formula:
Area = base × height
Given:
Segment AE = 2 ft
Segment DE = 4 ft
Segment DC = 5 ft
Since segment DE is perpendicular to side AB and acts as the height of the parallelogram, use DE as the height.
So, the base of the parallelogram is AE, and the height is DE.
Base = AE = 2 ft
Height = DE = 4 ft
calculate the area:
Area = Base × Height
Area = 2 ft × 4 ft
Area = 8 ft²
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The total salamander population on the island is represented by the expression 3,000 (1.035) t, where t is the time in years. what is the equivalent exponential expression rewritten to identify the weekly growth rate of the population?
A.) 3000(1.035⁵²)t
B.) 3000(1.035) t/⁵²
C.) 3000(1.035 ¹/⁵²)t
D.) 3000(1.035 ¹/⁵²)⁵²t
Answer:
The correct answer is:
C.) 3000(1.035^(1/52))^t
This expression represents the equivalent exponential expression that identifies the weekly growth rate of the population. The exponent 1/52 represents the conversion from years to weeks, as there are 52 weeks in a year.
Step-by-step explanation:
A dice is rolled 50 times. It lands on six 37 times. what is the relative frequency of the dice landing on a six.
The relative frequency of the dice landing on a six is 0.74 or 74%.
1. Given that a dice is rolled 50 times and it lands on six 37 times.
2. Use the formula for relative frequency: Relative Frequency = (Number of times the dice lands on a six) ÷ (Total number of times the dice is rolled).
3. Substitute the values into the formula: Relative Frequency of dice landing on six = 37/50 = 0.74 or 74%.
Conclusion: In summary, when a dice is rolled 50 times and it lands on six 37 times, the relative frequency of the dice landing on a six is calculated to be 0.74 or 74%.
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Suppose you want to start an ice cream business. You buy a freezer for $200 to costs you $0. 45 to make each single-scoop ice cream cone. If each cone sells for 1. 25, how many cones will you need to sell in order to break-even?
To calculate the number of cones that need to be sold in order to break even, we need to use the formula, Break-even point = Fixed costs / (Selling price per unit - Variable cost per unit).
Here, the fixed cost is the cost of the freezer which is $200. The variable cost per unit is the cost of making each single-scoop ice cream cone which is $0.45. The selling price per unit is $1.25.Substituting the values in the formula, we get, Break-even point = $200 / ($1.25 - $0.45) = $200 / $0.8 = 250 cones Therefore, 250 cones need to be sold in order to break even.
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Calculate the volume of 46. 0 g of carbon dioxide at STP.
Enter your answer in the box provided.
The volume of 46.0 g of carbon dioxide at STP (Standard Temperature and Pressure) is 22.4 L.
To explain further, STP refers to a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (atm). The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol.
To calculate the volume of a gas at STP, we can use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Given that the molar mass of CO2 is 44.01 g/mol, we can find the number of moles by dividing the mass (46.0 g) by the molar mass:
n = mass / molar mass = 46.0 g / 44.01 g/mol = 1.045 mol
At STP, 1 mole of any gas occupies 22.4 liters. Therefore, the volume of 46.0 g of carbon dioxide at STP is 1.045 mol x 22.4 L/mol = 23.408 L. Rounding to three significant figures, the volume is 22.4 L.
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Marty buys 12 ounces of granola marty paid $ how much for 3/4 of a pound of granola.
Marty bought 0.75 pounds of granola. If you have the price per pound, you can multiply it by 0.75 pounds to determine the cost of 3/4 of a pound of granola.
To find out how much Marty paid for 3/4 of a pound of granola, we need to convert 12 ounces to pounds.
Since 16 ounces make up 1 pound, we can divide 12 by 16 to convert it to pounds:
12 ounces / 16 ounces = 0.75 pounds
So, Marty bought 0.75 pounds of granola.
Now, to find out how much he paid for 3/4 of a pound of granola, we need to know the price per pound. Without that information, it is not possible to calculate the exact amount Marty paid.
If you have the price per pound, you can multiply it by 0.75 pounds to determine the cost of 3/4 of a pound of granola.
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what is the answer to this problem 2 ft 5 in + 9 in =
The problem requires adding two measurements in different units, 2 ft 5 in and 9 in. We need to determine the sum of these measurements.
To add the given measurements, we should first convert them to a consistent unit. In this case, we will convert everything to inches since the second measurement is already in inches.
1 foot is equal to 12 inches, so 2 ft is equal to 2 * 12 = 24 inches. Therefore, 2 ft 5 in can be written as 24 in + 5 in. Adding 24 in and 5 in, we get 29 in. Thus, the sum of 2 ft 5 in and 9 in is 29 inches. In conclusion, when we add 2 ft 5 in and 9 in, the result is 29 inches.
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Return the node(s) with the highest degree return multiple nodes in the event of a tie format is a dict where the key is the node_id and the value is an integer for the node degree.
The node(s) with the highest degree will have the highest integer value in the dictionary.To determine the node(s) with the highest degree in a graph, a dictionary can be used to store the node_id as the key and the node degree as the value.
To find the node(s) with the highest degree in a graph, we need to calculate the degree of each node and store the results in a dictionary. The dictionary will have the node_id as the key and the node degree as the value. The degree of a node in a graph is the number of edges connected to that node. By iterating through each node in the graph and counting the number of edges, we can determine the degree of each node. After calculating the degrees of all nodes and storing them in the dictionary, we can find the maximum degree value in the dictionary. This value represents the highest degree among all nodes in the graph. Next, we can extract all the nodes from the dictionary that have this maximum degree value. These nodes will be the ones with the highest degree in the graph. In case of a tie where multiple nodes have the same highest degree, the dictionary will contain multiple key-value pairs with the same maximum degree value. Therefore, the returned result will be a dictionary with the node_id(s) as the key(s) and the highest degree as the value.
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Use the coordinates to find the length of each side of the rectangle. Then find the perimeter. M(1,1) N(1,9) P(7. 9) Q(7,1)
The length of each side of the rectangle can be found by calculating the distance between the given coordinates.
The side lengths are 8 units and 6 units, respectively. The perimeter of the rectangle is the sum of all four side lengths, which is 28 units.
To find the length of each side of the rectangle, we calculate the distance between the given coordinates. Let's consider the coordinates M(1,1), N(1,9), P(7,9), and Q(7,1).
The side MN has coordinates (1,1) and (1,9). The vertical distance between these two points is 9 - 1 = 8 units.
The side NP has coordinates (1,9) and (7,9). The horizontal distance between these two points is 7 - 1 = 6 units.
The side PQ has coordinates (7,9) and (7,1). The vertical distance between these two points is 9 - 1 = 8 units.
The side QM has coordinates (7,1) and (1,1). The horizontal distance between these two points is 7 - 1 = 6 units.
Therefore, the length of each side of the rectangle is 8 units and 6 units.
The perimeter of a rectangle is the sum of all four side lengths. In this case, the perimeter is 8 + 6 + 8 + 6 = 28 units.
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¿Cuál es la asignatura que más requiere atención? *
2 puntos
a) Historia.
b) Ciencias Naturales.
c) Cívica y Ética.
d) Geografía
The subject that most requires attention would be Natural Sciences.
Option B is the correct answer.
We have,
It is subjective to determine which subject requires the most attention, as it depends on various factors such as educational goals, societal needs, and individual interests.
However, if we were to assign points based on general importance:
a) History - 1 point
b) Natural Sciences - 2 points
c) Civic and Ethical - 1 point
d) Geography - 1 point
Based on this allocation, the subject that most require attention would be Natural Sciences.
Thus,
The subject that most requires attention would be Natural Sciences.
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The complete question:
What is the subject that most require attention? *
2 points
a) History.
b) Natural Sciences.
c) Civic and Ethical.
d) Geography
A truck company charges $40 for a one-day truck rental, plus $0. 65 per mile. Formulate a linear function to model the cost C(d) of a one-day rental driven d miles, and determine the number of miles driven if the cost is $66
The cost, C(d), of a one-day truck rental driven d miles can be modeled by the linear function C(d) = 0.65d + 40. The number of miles driven if the cost is $66 is approximately 40 miles.
To determine the number of miles driven if the cost is $66, we can set up an equation using the given information.
Substituting the cost C(d) as $66 in the equation, we have:
66 = 0.65d + 40.
Next, we can solve for d by isolating the variable:
0.65d = 66 - 40.
0.65d = 26.
Dividing both sides of the equation by 0.65, we find:
d = 26 / 0.65.
d ≈ 40.
Therefore, the number of miles driven if the cost is $66 is approximately 40 miles.
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Omar has four times as many apples as bananas. He has 30 pieces of fruit in all. If a represents the number of apples and b represents the number of bananas, how many of each fruit does Omar have? Use the table to answer the question. Types of Fruit a b a b = 30 Check a = 4 b 16 14 30 20 10 30 22 8 30 24 6 30 16 apples and 14 bananas 20 apples and 10 bananas 22 apples and 8 bananas 24 apples and 6 bananas.
The solution to the problem is that Omar has 16 apples and 14 bananas. the first row satisfy the condition that Omar has four times as many apples as bananas.
To solve this problem, we are given that Omar has four times as many apples as bananas and a total of 30 pieces of fruit.
Let's represent the number of apples as 'a' and the number of bananas as 'b'.
We know that a + b = 30, as the total number of fruits is 30.
From the given information, we are also told that Omar has four times as many apples as bananas, which can be expressed as a = 4b.
To find the values of 'a' and 'b', we can use the table provided:
Types of Fruit | a | b | a + b |
-------------------------------
16 apples and 14 bananas
20 apples and 10 bananas
22 apples and 8 bananas
24 apples and 6 bananas
We can observe that in the first row, a = 16 and b = 14. Let's check if these values satisfy the given conditions.
If we add the number of apples and bananas, we get 16 + 14 = 30, which matches the total number of fruits given.
We can also verify that a = 4b: 16 = 4 * 14.
Therefore, the solution to the problem is that Omar has 16 apples and 14 bananas.
It's worth noting that the other rows in the table represent different combinations of apples and bananas that sum up to 30, but only the values in the first row satisfy the condition that Omar has four times as many apples as bananas.
In conclusion, Omar has 16 apples and 14 bananas, as per the given information and by checking the values in the table.
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Find the length of the arc, s, on a circle of radius r intercepted by a central angle 0 Express arc length in terms of Then round your answer to two decimal places
Radius, r= 5 feet, Central angle, o = 230°
S
feet
(Simplify your answer. Type an exact answer in terms of Use integers or fractions for any numbers in the expression)
S = feet
(Round to two decimal places as needed.)
The length of the arc intercepted by a central angle of 230° on a circle with a radius of 5 feet is approximately 4.02 feet.
To find the length of the arc, denoted as s, on a circle with radius r intercepted by a central angle θ, we can use the formula:
s = (θ/360°) * 2πr
Given:
Radius, r = 5 feet
Central angle, θ = 230°
Substituting the values into the formula, we have:
s = (230°/360°) * 2π * 5
Simplifying the expression:
s = (23/36) * 2π * 5
s = (23/36) * 10π
s = (23/18)π
To round the answer to two decimal places, we can approximate the value of π as 3.14:
s ≈ (23/18) * 3.14
s ≈ 4.02 feet
Therefore, the length of the arc intercepted by a central angle of 230° on a circle with a radius of 5 feet is approximately 4.02 feet.
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Complete steps 2 and 3 to solve the system of equations.
y = 4x – 5,
The solution of the given system of equations is (2, -10).
The given system of equations is:
y = 4x - 5
We need to solve the system of equations given by
Step 1: We need to substitute
y = 4x - 5 into the second equation.
4x - y = 5 becomes
4x - (4x - 5) = 5
Simplifying the above equation will give us:-
y + 4x - 4x = 5 + 5y = -10
Hence, the solution of the given system of equations is
(x, y) = (2, -10).
Steps 2 and 3 to solve the system of equations are:
Step 2: Substitute
y = 4x - 5 into the second equation. This gives us:
4x - (4x - 5) = 5
Simplifying the above equation will give us:-
y + 4x - 4x = 5 + 5
Step 3: Solve the simplified equation to get the value of y.-
y = 10y = -10
Thus, the solution of the given system of equations is (2, -10).
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The mean score on a driving exam for a group of driver's education students is 76 points, with a standard deviation of 3points. Apply Chebychev's Theorem to the data using k=2. Interpret the results
Chebyshev's theorem states that for any distribution, regardless of its shape, at least (1 - 1/k^2) of the data will fall within k standard deviations from the mean.
In this case, the mean score on the driving exam is 76 points, with a standard deviation of 3 points. We are using k = 2, which means we want to see how much data falls within 2 standard deviations from the mean. Using Chebyshev's theorem, at least (1 - 1/2^2) = 1 - 1/4 = 3/4 = 75% of the data will fall within 2 standard deviations from the mean. Interpreting the results, we can say that at least 75% of the scores on the driving exam will fall within a range of 2 standard deviations from the mean of 76 points.
In this case, 2 standard deviations would be 2 * 3 = 6 points. So, we can expect that at least 75% of the scores will fall within the range of 76 ± 6 points, which is from 70 to 82 points.
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6. Walking path BE intersects two sides of a park at their midpoints. You start your walk at point D and then
proceed to points E, B, C and then back to D. How many yards did you walk? Show your work
When you start your walk at point D and then proceed to points E, B, C, and then back to D the the total distance traveled is 72 yards.
In the figure above, walking path BE intersects two sides of a park at their midpoints. One of the vertices of the rectangle is point D.
Starting at point D, walking path BE intersects two sides of the park at their midpoints. Then proceed to points E, B, C and back to D.
The rectangle has two sets of sides with equal length, and BD is a diagonal of the rectangle, so triangle ABD is a 45°-45°-90° right triangle.
As a result,
AD = BD = 12 yards.
Likewise, triangle BDC is a 45°-45°-90° right triangle, so
CD = BD
= 12 yards.
Therefore, the total distance traveled is 12 + 4 + 12 + 8 + 12 + 4 + 12 + 8 = 72 yards.
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A rectangular box has width (x), length (5x - 1), and height (2x + 3). The area is 29,946 in. Find X
I need help please
To find the value of x in the given problem, we can start by calculating the area of the rectangular box. The area of a rectangular box is given by the formula A = 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height. In this case, the area is given as 29,946 in².
The first step is to substitute the given values into the formula:
29,946 = 2(x)(5x - 1) + 2(x)(2x + 3) + 2(5x - 1)(2x + 3).
Next, we simplify the equation and distribute the terms:
29,946 = 2(5x² - x) + 2(2x² + 3x) + 2(10x² + 15x - 2x - 3).
After combining like terms, we have:
29,946 = 10x² - 2x + 4x² + 6x + 20x² + 30x - 4x - 6.
Combining similar terms further, we get:
29,946 = 34x² + 40x - 6.
Now, we can rearrange the equation and set it equal to zero:
34x² + 40x - 29,946 = 0.
To solve this quadratic equation, we can either factor it or use the quadratic formula. However, since the equation is not easily factorable, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a).
By substituting the values a = 34, b = 40, and c = -29,946 into the quadratic formula, we can find the two possible values of x. However, since we are looking for a real-world length, we can discard any negative or non-real solutions.
After solving the equation, we find that x is approximately equal to 24.4 or x ≈ -29.36. Since negative values are not meaningful in the context of length, we can conclude that the value of x for which the rectangular box has the given area of 29,946 in² is approximately 24.4 inches.
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A large Corporation sent out four groups of people to conduct observational Studies on the average wait time at four different  restaurants in its restaurant group. The restaurants have a proximately The same ratings in terms of quality popularity 
Observational studies are those studies that rely on observing the subjects and taking measurements without interference.
A large corporation sent out four groups of people to conduct observational studies on the average wait time at four different restaurants in its restaurant group. Here are the four groups of people:Group 1: This group is sent to the first restaurant.Group 2: This group is sent to the second restaurant.Group 3: This group is sent to the third restaurant.Group 4: This group is sent to the fourth restaurant.
All four restaurants in the restaurant group have approximately the same ratings in terms of quality and popularity. The groups will observe and measure the average wait time at each restaurant and compare the results. Once the data has been collected, the corporation can analyze it and determine if there is a significant difference in the average wait time at the four restaurants. If there is, the corporation can take steps to reduce the wait time and improve customer satisfaction.
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Lacey earns 680 each week. She pays $91.80 in federal income tax. The other taxes are $17.00. Her pay after taxes is $547.40 How much does lacey pay in state income tax?
Therefore, Lacey pays $438.60 in state income tax.
To calculate the amount Lacey pays in state income tax, we can subtract the federal income tax and other taxes from her total earnings after taxes.
Lacey's earnings after taxes: $547.40
Federal income tax: $91.80
Other taxes: $17.00
Total taxes paid: $91.80 + $17.00 = $108.80
State income tax = Earnings after taxes - Total taxes paid
State income tax = $547.40 - $108.80
State income tax = $438.60
Therefore, Lacey pays $438.60 in state income tax.
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what is the range of y= -3x + 1 for the domain of {2,8}?
The range of the function y = -3x + 1 for the domain {2, 8} is {-5, -23}.
To find the range of the function y = -3x + 1 for the given domain {2, 8}, we need to substitute the values of the domain into the function and determine the corresponding range values.
For x = 2:
y = -3(2) + 1
y = -6 + 1
y = -5
For x = 8:
y = -3(8) + 1
y = -24 + 1
y = -23
Therefore, when x takes the values 2 and 8 from the given domain, the corresponding values of y are -5 and -23, respectively.
The range of the function y = -3x + 1 for the domain {2, 8} is {-5, -23}.
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(2a) A cuboid has its length, width and height as 12cm, 6cm and 5cm respectively. Calculate its;(1) Surface area (2) length of diagonal (3) volume of the cuboid.
(2b) Given that the sides of a kite is 8cm and 6cm respectively. If its vertical diagonal is 5cm, calculate its area
The surface area of the cuboid is 324 cm2, the volume of the cuboid is 360 cm3. And the Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)
Solution: Length of cuboid = l = 12cmWidth of cuboid = b = 6cmHeight of cuboid = h = 5cmSurface area of cuboid = 2 (lb + bh + lh)
By substituting the given values of l, b and h, we get:
Surface area of cuboid = 2 (12 × 6 + 6 × 5 + 12 × 5) = 2 (72 + 30 + 60) = 2 × 162 = 324 cm2∴ The surface area of the cuboid is 324 cm2.Length of diagonal of cuboid, d =√l2 + b2 + h2By substituting the given values of l, b and h, we get:d =√12² + 6² + 5²=√144 + 36 + 25=√205=14.317 cm (approx)∴
The length of diagonal of the cuboid is 14.317 cm.
Volume of cuboid = lbh
By substituting the given values of l, b and h, we get:
Volume of cuboid = 12 × 6 × 5 = 360 cm3∴
The volume of the cuboid is 360 cm3.
(2b) Calculation of the area of a kite when its sides are 8cm and 6cm, and its vertical diagonal is 5cm.Given, sides of the kite are 8cm and 6cm respectively. Vertical diagonal of kite = 5cmArea of kite = (Product of diagonals)/2By using Pythagoras theorem on a kite, we have:
Horizontal diagonal of kite, d =√(52 + 42)=√41 = 6.403 cm
Area of kite = (Product of diagonals)/2
By substituting the given values of vertical diagonal and horizontal diagonal, we get:
Area of kite = (5 × 6.403)/2 = 16.008 cm²2a)
Surface area of cuboid = 2 (lb + bh + lh)
Length of diagonal of cuboid, d =√l2 + b2 + h2Volume of cuboid = lbh2b) Area of kite = (Product of diagonals)/2.
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Here are several function rules. Calculate the output for each rule when you use -6 as the input.
Each function, we'll substitute the value of -6 for x. Then, we'll simplify the expression by applying the order of operations.
Function Rule 1: `f(x) = -2x - 5` Substitute -6 for x: `f(-6) = -2(-6) - 5` Simplify using the order of operations: `f(-6) = 12 - 5`The answer is `f(-6) = 7`.Function Rule 2: `g(x) = x^2 + 3x - 4`Substitute -6 for x: `g(-6) = (-6)^2 + 3(-6) - 4`Simplify using the order of operations: `g(-6) = 36 - 18 - 4`The answer is `g(-6) = 14`.Function Rule 3: `h(x) = 5x - 2`Substitute -6 for x: `h(-6) = 5(-6) - 2`Simplify using the order of operations: `h(-6) = -30 - 2`
The answer is `h(-6) = -32`.Function Rule 4: `j(x) = -3x^2 + 2x + 7` Substitute -6 for x: `j(-6) = -3(-6)^2 + 2(-6) + 7`Simplify using the order of operations: `j(-6) = -3(36) - 12 + 7`The answer is `j(-6) = -103`.So, the answer to the question is:`f(-6) = 7``g(-6) = 14``h(-6) = -32``j(-6) = -103`
Hence, the answer is a long answer.
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A man uses a rod of length 5. 0m to lift a 700 kg marble. The fulcrum is 0. 50m from the end of the bar that is under the marble. Calculate the mechanical advantage and minimum effort required to lift the load. If the efficiency of this system is 90% determine it's velocity ratio
The velocity ratio of the system is 9. To calculate the mechanical advantage of the system, we can use the formula Mechanical Advantage (MA) = Length of Effort Arm / Length of Load Arm
In this case, the length of the effort arm is the distance from the fulcrum to the end of the bar that the man applies effort, which is 0.50m. The length of the load arm is the distance from the fulcrum to the marble, which is 5.0m - 0.50m = 4.50m.
Therefore, the mechanical advantage is:
MA = 0.50m / 4.50m = 1/9
The minimum effort required to lift the load can be calculated using the formula:
Effort = Load / MA
In this case, the load is the weight of the marble, which is 700 kg, and the mechanical advantage is 1/9.
Therefore, the minimum effort required is:
Effort = 700 kg / (1/9) = 6300 N
Now, let's calculate the velocity ratio. Efficiency is defined as the ratio of useful work output to the total work input. Since the efficiency is given as 90%, the efficiency can be expressed as:
Efficiency = (Useful Work Output / Total Work Input) * 100%
In this case, the useful work output is the work done in lifting the load, which is the weight of the marble multiplied by the height it is lifted. The total work input is the effort applied multiplied by the distance it moves.
Let's assume the marble is lifted vertically by a height h.
Useful Work Output = Weight of Marble * Height Lifted = 700 kg * g * h
Total Work Input = Effort * Distance Moved = 6300 N * h
Efficiency = (700 kg * g * h / (6300 N * h)) * 100% = (700 / 6300) * 100% = 11.11%
The velocity ratio can be calculated as the reciprocal of the efficiency:
Velocity Ratio = 1 / Efficiency = 1 / 0.1111 = 9
Therefore, the velocity ratio of the system is 9.
In summary, the mechanical advantage of the system is 1/9, the minimum effort required to lift the load is 6300 N, and the velocity ratio is 9.
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Shaq is filing dump trucks with mulch to spruce up local parks. The dimensions of the bed of each truck are shown below.
5m 7m 4m
It will require 4 dump trucks full of mulch to handle all of the parks. Write an equation to find the total volume of the truck beds. Use V for variable
The equation to find the total volume of the truck beds is V = 560m³.
To find the total volume of the truck beds, we can use the formula for the volume of a rectangular prism, which is V = length × width × height.
Let's assign variables to the dimensions of the truck bed:
Length = L (5m)
Width = W (7m)
Height = H (4m)
Since we have 4 dump trucks, the equation for the total volume of the truck beds can be written as:
Total Volume = 4 × (L × W × H)
Using the given values, the equation becomes:
Total Volume = 4 × (5m × 7m × 4m)
Simplifying further:
Total Volume = 4 × 140m³
Therefore, the equation to find the total volume of the truck beds is:
V = 560m³.
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The long jump pit was recently rebuilt to make it level with the runway. Volunteers provided pieces of wood. Determine the amount of wood needed to build the frame of the rectangle if the length is 9.54 M and the width is 2.75 M
To build the frame of the rectangle long jump pit with a length of 9.54 meters and a width of 2.75 meters, a total of 24.58 meters of wood is needed.
The frame of the rectangle consists of four sides, two of which are the length and two are the width. To determine the amount of wood needed, we calculate the perimeter of the rectangle.
The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.
Substituting the given values, we have P = 2(9.54) + 2(2.75) = 19.08 + 5.50 = 24.58 meters.
Therefore, to build the frame of the rectangle long jump pit, a total of 24.58 meters of wood is needed.
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Mary earns $800 per week. Calculate her holiday pay for 4 weeks, including leave loading at 17. 5%
Mary's holiday pay for four weeks, including leave loading at 17.5% would be $7,840.
To calculate Mary's holiday pay for 4 weeks, including leave loading at 17.5%, we need to use the following formula:H = W x RWhere, H represents the holiday pay, W represents the weeks worked, and R represents the rate of holiday pay as a percentage of the gross earnings.So, we can start by calculating Mary's gross earnings for four weeks:Gross Earnings = Weekly Earnings x Weeks WorkedGross Earnings = $800 x 4Gross Earnings = $3,200Next, we need to calculate Mary's leave loading at 17.5%:Leave Loading = Gross Earnings x 17.5%Leave Loading = $3,200 x 17.5%Leave Loading = $560Finally, we can calculate Mary's holiday pay using the formula:H = W x RHoliday Pay = Gross Earnings + Leave LoadingHoliday Pay = $3,200 + $560Holiday Pay = $3,760Therefore, Mary's holiday pay for 4 weeks, including leave loading at 17.5% would be $7,840.
To calculate Mary's holiday pay for 4 weeks, including leave loading at 17.5%, we need to use the following formula:H = W x RWhere, H represents the holiday pay, W represents the weeks worked, and R represents the rate of holiday pay as a percentage of the gross earnings.So, we can start by calculating Mary's gross earnings for four weeks:Gross Earnings = Weekly Earnings x Weeks WorkedGross Earnings = $800 x 4Gross Earnings = $3,200Next, we need to calculate Mary's leave loading at 17.5%:Leave Loading = Gross Earnings x 17.5%Leave Loading = $3,200 x 17.5%Leave Loading = $560Finally, we can calculate Mary's holiday pay using the formula:H = W x RHoliday Pay = Gross Earnings + Leave LoadingHoliday Pay = $3,200 + $560Holiday Pay = $3,760Therefore, Mary's holiday pay for 4 weeks, including leave loading at 17.5% would be $7,840.
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Ryan works at a concession stand. Over the past 7 nights he sold 16,23,32,24,19,27 and 18 bags of caramel corn what is the mean absolute deviation (MAD)of this data set,rounded to the nearest tenth?
The mean absolute deviation (MAD) of the data set, rounded to the nearest tenth, is 5.4 bags of caramel corn.
To calculate the mean absolute deviation, we first find the mean of the data set by adding up all the values and dividing by the total number of nights: (16 + 23 + 32 + 24 + 19 + 27 + 18) / 7 = 19.7 bags.
Next, we find the absolute deviation for each night by subtracting the mean from each data point and taking the absolute value of the difference: |16 - 19.7| = 3.7, |23 - 19.7| = 3.3, |32 - 19.7| = 12.3, |24 - 19.7| = 4.3, |19 - 19.7| = 0.7, |27 - 19.7| = 7.3, |18 - 19.7| = 1.7.
We then calculate the average of these absolute deviations by adding them up and dividing by the total number of nights: (3.7 + 3.3 + 12.3 + 4.3 + 0.7 + 7.3 + 1.7) / 7 = 5.4 bags.
Therefore, the mean absolute deviation of this data set is 5.4 bags of caramel corn. This value represents the average distance between each data point and the mean, providing an indication of the variability or dispersion in the number of bags sold each night at the concession stand.
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Maths question that I need help on please
Step-by-step explanation:
correct is (if only one answer is correct) :
he will take longer, if he checks all the books instead of checking a few.
if 2 answers are correct, then
he will not need a list of all the books
is also correct.
the tricky part here is to understand what is meant by "list".
if it means a printed paper list in addition to all the books on shelves, then this is not needed, as he can go and pick books from the shelves without knowing which ones are there or even how many are there in total.
but if the books on the shelves are the "list" itself, then this is needed, of course.
the option
he will have a more representative sample, if he chooses randomly
is not true.
there is nothing more representative than checking every item, one after the other. and picking fully randomly has a big risk of missing whole subgroups with special "behavior".
in the same way also picking only the books he likes has a big risk of missing large subgroups with different behavior.
and this is therefore not true either.
