To calculate the perimeter, add the lengths of sides AB, BC, and AC. The area can be found using Heron's formula. To find the angles, use the law of cosines.
1. **Perimeter and area of triangle ABC**
To find the perimeter and area of triangle ABC, we need to use the given information about its sides and angles.
Let's assume that side AB has a length of "a", side BC has a length of "b", and side AC has a length of "c". The given angles are angle A, angle B, and angle C.
The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter P of triangle ABC is given by: P = a + b + c.
To find the area of triangle ABC, we can use Heron's formula, which states that the area A of a triangle with side lengths "a", "b", and "c" is given by: A = √(s(s - a)(s - b)(s - c)), where s is the semi-perimeter of the triangle, given by: s = (a + b + c) / 2.
Once we have calculated the area, we can use the law of cosines to find the measures of the angles. The law of cosines states that for a triangle with side lengths "a", "b", and "c", and opposite angles A, B, and C, the following relationships hold:
cos(A) = (b^2 + c^2 - a^2) / (2bc)
cos(B) = (a^2 + c^2 - b^2) / (2ac)
cos(C) = (a^2 + b^2 - c^2) / (2ab)
Using these formulas, we can calculate the measures of the angles A, B, and C.
To find the exact values of the perimeter, area, and angles, we would need the specific lengths of the sides and the measures of the angles. Please provide those values, and I can assist you with the calculations.
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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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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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Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. His Revenue is given by the function R - $62p, where Cis the total cost
per month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. How many pets must he groom each month
to break even?
Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. The monthly cost function for Jordan's pet-grooming company is C - $12p+ $2100.
His Revenue is given by the function R - $62p, where C is the total costper month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. We need to find out how many pets must he groom each month to break even.Let's set revenue equal to costs, and solve for p.R = C62p = 12p + 2100p = (12p + 2100) / 62p = 0.1935p ≈ 19.35 petsJordan must groom approximately 19.35 pets each month to break even. The nearest whole number is 19.
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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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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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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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Reflect the triangle across the y-axis, and then translate the image 5 units down. The final image is the same as which of the following transformations? Translate 5 units down, and then reflect over the x-axis. Translate 5 units down, and then reflect over the y-axis. Rotate 180° about the origin. Reflect over the x-axis, and then translate 5 units left.
The final image obtained after reflecting the triangle across the y-axis and translating it 5 units down is equivalent to reflecting the original triangle over the x-axis and then translating it 5 units down.
When we reflect the triangle across the y-axis, each point's x-coordinate is negated while the y-coordinate remains unchanged. This reflection essentially flips the triangle horizontally.
After reflecting the triangle, we then translate it 5 units down. This translation involves shifting each point of the triangle downward by 5 units along the y-axis.
Now let's consider the second transformation: reflecting the original triangle over the x-axis and then translating it 5 units down.
Reflecting the triangle over the x-axis means that each point's y-coordinate is negated while the x-coordinate remains unchanged. This reflection flips the triangle vertically.
After reflecting the triangle, we translate it 5 units down, which involves shifting each point of the triangle downward by 5 units along the y-axis.
By comparing the two sequences of transformations, we can see that they result in the same final image. First, we horizontally flip the triangle and then shift it downward, which is equivalent to first vertically flipping the triangle and then shifting it downward.
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Answer:
B. Translate 5 units down, and then reflect over the y-axis.
Step-by-step explanation:
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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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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A scooter rental store charges a $4 rental fee plus $1. 50 for each hour a scooter is rented. What are the slope and y- intercept that represent this situation
Answer:
y = 1.5x + 4
The slope is 1.5, and the y-intercept is 4.
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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Nicholas scoops a few gumballs into his bag. When he weighs it, he finds that he scooped 0.76 pounds.
Nicholas scooped a few gumballs into his bag and found that it weighed 0.76 pounds.
Nicholas's bag of gumballs weighs 0.76 pounds. This weight includes the combined mass of the gumballs and the bag itself. The weight measurement indicates the force exerted by the bag due to the gravitational pull of the Earth. To determine the weight of just the gumballs, Nicholas would need to subtract the weight of the bag from the total weight.
To find the weight of the bag, Nicholas could use a scale or balance to measure an empty bag of the same type. Once he knows the weight of the empty bag, he can subtract that weight from the total weight of the bag with the gumballs. The result will give him the weight of the gumballs alone.
It's important to note that the weight of the gumballs may vary depending on their size, density, and the material of the bag. Different types of gumballs may have different weights. To get an accurate measurement, Nicholas should use a precise weighing instrument and account for any external factors that could affect the weight, such as moisture or contaminants.
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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.
One link in a chain was made from a cylinder that has a radius of 2. 5 cm and a height of 22 cm. How much plastic coating would be needed to coat the surface of the chain link? Use
3 14 for TT
O2512 cm
O 314 cm?
O 345 4 cm
O 471 cm
The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.
A cylinder's surface area is the overall area or region that the shape's surface covers. A cylinder's total surface area comprises both the area of the curved surface and the area of the two flat surfaces since there are two flat surfaces and one curved surface.
The formula for a particular cylinder's total surface area is as follows:
TSA = 2πr (h + r)
Given that;
One link in a chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm.
Hence, The plastic coating would be needed to coat the surface of the chain is,
2 × 3.14 × 2.5 × 22
= 345.4 cm²
So, The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.
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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:
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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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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An 85kg man stands on a scale inside an elevator. What is the weight in Newtons that the scale reads when the elevator is
a. at rest?
b. moving upward at a constant speed of 5m/s?
c. moving downward at a constant speed of 8m/s?
d. moving with an upward acceleration of 3 m/s2
e. moving with a downward acceleration of 4 m/s2
The weight in Newtons that the scale reads when the elevator is in different scenarios can be calculated using the formula W = mg, where W = weight, m= mass, and g = the acceleration due to gravity.
a. When the elevator is at rest, there is no acceleration, so the weight will be equal to the gravitational force acting on the person. The weight can be calculated as W = mg, where m is the mass of the person (85 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, the weight is W = 85 kg * 9.8 m/s^2.
b. the weight will remain the same as the gravitational force, which is calculated using the formula W = mg. c. The acceleration is still zero, and the weight will be the same as the gravitational force, calculated using the formula W = mg.
d. We need to consider the net force acting on the person. The net force will be the sum of the gravitational force and the force due to the acceleration. The weight can be calculated as W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the upward acceleration (3 m/s^2).
e. We calculate the weight similarly to case d. The weight is W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the downward acceleration (-4 m/s^2) since it acts in the opposite direction.
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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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Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related. The cost of each minute is constant.
A. What is the cost, c, ofa call of m minutes duration?
B. How long can you talk on the phone if you have $12 to spend?
The cost of a call of m minutes duration, given the cost of the calls would be c = 0. 05 + 0. 99m
If you have $ 12 to spend, the time you can spend is 10.15 minutes.
How to find the cost per minute ?The cost per minute would be :
= Difference between 5 and 10 minute call / Number of minutes
= ( 10. 86 - 5. 91 ) / 5
= $ 0.99
The cost per minute is therefore:
= 0. 99 x number of minutes
= 0. 99m
The initial cost is :
= 5 - 0. 99 x 5
= $ 0. 05
The number of minutes with $12 is:
= ( 12 - 0.05 ) / 0. 99
= 12. 1 minutes
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Steve determines that sides DK and BC are congruent. He also measures
Therefore, the measure of the angle BDK is 62.5°.
Given: Steve determines that sides DK and BC are congruent. Therefore, DK ≅ BC.
He also measures the angle DBK to be 55°. Therefore, ∠DBK = 55°.
To find the measure of the angle BDK, we can use the fact that the sum of the angles in a triangle is 180°.
∠BDK = 180° - ∠DBK - ∠BKD
Since DK ≅ BC, ∠BDK = ∠BCD.
∴ ∠BDK = ∠BCD = (125° - ∠BCD)
Simplifying the equation, we get:
2∠BCD = 125°
∠BCD = 62.5°
Therefore, the measure of the angle BDK is 62.5°.
Hence, option D is correct.
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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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30% of the members of a tennis club are pensioners. 36 members are pensioners
a) how many members there in total ?
b) how many members are not pensioners
Answer
there's 120 members in total
84 not pensioners
Explaination
36÷30% = 120
70% are not pensioners
so 70% × 120 = 84
or you could minus the pensioners from the total 120-36=84
Write log12 in four different ways. Name each you use and explain your process
The logarithm base 12 can be expressed as log12 or in exponential form as 12^x = y, where x is the exponent and y is the result.
The logarithm function is the inverse of exponentiation. It represents the exponent to which a given base (in this case, 12) must be raised to obtain a certain value. There are four different ways to express log12:
Logarithmic form: log12(y) - This notation indicates that the logarithm base 12 is being applied to a value y.
Exponential form: 12^x = y - In this form, the base 12 is raised to an exponent x to produce a value y.
Fractional exponent form: y^(1/12) - The fractional exponent represents the root of y with a base of 12. It is equivalent to log12(y).
Common logarithm form: log(y) / log(12) - If the logarithm base 12 function is not directly available, we can use the common logarithm (base 10) or any other logarithmic base and apply the change of base formula. The result is the logarithm of y divided by the logarithm of 12.
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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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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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(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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find the side of the triangle if two of its sides are equal the third side is 1 1/3 cm longer than the others and its perimeter is 5 2/5cm
The lengths of the sides of the triangle are approximately:
The two equal sides: 61/45 cm
The third side: 1089/405 cm
Let's assume that the two equal sides of the triangle are represented by "x" cm each. According to the given information, the third side is 1 1/3 cm longer than the other two sides.
So, the length of the third side can be represented as "x + 1 1/3" cm.
The perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 5 2/5 cm.
Using this information, we can write the equation:
2x + (x + 1 1/3) = 5 2/5
To solve this equation, let's convert the mixed number 1 1/3 to an improper fraction.
1 1/3 = (3× 1 + 1) / 3 = 4/3
Substituting the value, we have:
2x + (x + 4/3) = 5 2/5
To simplify the equation, let's convert the mixed number 5 2/5 to an improper fraction.
5 2/5 = (5 ×5 + 2) / 5 = 27/5
Now, the equation becomes:
2x + (x + 4/3) = 27/5
Combining like terms, we have:
3x + 4/3 = 27/5
To eliminate the fractions, let's multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 15:
15 × (3x + 4/3) = 15 ×(27/5)
45x + 20 = 81
Subtracting 20 from both sides:
45x = 61
Dividing both sides by 45:
x = 61/45
So, the value of x is 61/45 cm. This represents the length of the two equal sides of the triangle.
Now, to find the length of the third side, we substitute x back into the expression:
x + 1 1/3 = (61/45) + 4/3
To add these fractions, we need to find a common denominator. The LCM of 45 and 3 is 45:
[(61/45) × (3/3)] + (4/3) = (183/135) + (4/3)
Now, we can add the fractions:
(183/135) + (4/3) = (549/405) + (540/405) = 1089/405
So, the length of the third side is 1089/405 cm.
Therefore, the lengths of the sides of the triangle are approximately:
The two equal sides: 61/45 cm
The third side: 1089/405 cm
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