The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.6321.
Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1.
The exponential probability distribution with a mean of 12 seconds is given by
f(x) = (1/12) × e^(-x/12)
where x represents the time between arrivals of vehicles.
To find the probability that the arrival time between vehicles is 12 seconds or less, we need to integrate the probability density function from 0 to 12
P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] f(x)dx
= [tex]\int\limits^{12}_0[/tex] (1/12) × e^(-x/12) dx
= [(-e^(-x/12))]_[0,12]
= (-e^(-12/12)) - (-e^(0/12))
= 1 - e^(-1)
≈ 0.6321
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The given question is incomplete, the complete question is:
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. What is the probability that the arrival time between vehicles is 12 seconds or less?
What three regular polygons have special triangles formed by their radius and apothem and what are the special triangles?
The regular triangle, regular hexagon, and regular dodecagon have special triangles formed by their radius and apothem, which are congruent right triangles with legs equal to half the length of one side and hypotenuse equal to the radius or apothem, and are 30-60-90 triangles.
Regular polygons with three special triangles formed by their radius and apothem are,
Regular triangle
The radius and apothem of an equilateral triangle are equal. Therefore, the special triangles formed by the radius and apothem are congruent right triangles with legs equal to half the length of one side of the equilateral triangle and hypotenuse equal to the radius or apothem. In other words, the special triangles are 30-60-90 triangles.
Regular hexagon
The radius of a regular hexagon is equal to the length of one side, and the apothem is equal to the height of an equilateral triangle with side length equal to the length of one side of the hexagon.
Regular dodecagon
The radius of a regular dodecagon is equal to the length of one side multiplied by the square root of 2 plus the square root of 2 times the square root of 3. The apothem is equal to the height of an isosceles triangle with base equal to one side of the dodecagon and legs equal to the radius of the dodecagon.
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For the hexagon, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the longer leg.
The three regular polygons that have special triangles formed by their radius and apothem are the triangle, square, and hexagon.
For the triangle, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the shorter leg.
For the square, the special triangle formed by its radius and apothem is a 45-45-90 right triangle, where the radius is the hypotenuse and the apothem is one of the legs.
For the hexagon, the special triangle formed by its radius and apothem is a 30-60-90 right triangle, where the radius is the hypotenuse and the apothem is the longer leg.
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you have a cake that is 16 inches by 18 inches.you want each piece to be exactly the same size.how many people can u serve equal sized piece of cake
The number of people are 72.
What is HCF?Highest Common Factor is the full name for HCF in mathematics.
According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.
What is LCM?Least Common Multiple is the full name for LCM in mathematics.
LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.
We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.
Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.
We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:
288 / x² = (16*18) / x² = 288 / x²
Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.
As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.
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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.
What is area?A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.
To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.
The total area of the cake is:
16 inches x 18 inches = 288 square inches
To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:
√(288 square inches) ≈ 16.97 inches
Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:
Each piece of cake will be approximately 16 inches by 16 inches.
To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:
288 square inches ÷ (16 inches x 16 inches) = 18
Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.
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How can i do parallelogram shown below has an area of
15
1515 units
2
2
The height of given parallelogram is 5 units.
Given that, the parallelogram shown below has an area of 15 units.
The base is 3 units.
We know that, the area of a parallelogram is Area = Base × Height
Here, Area = 3×Height
15 = 3×Height
Height = 15/3
Height = 5 units
Therefore, the height of given parallelogram is 5 units.
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"Your question is incomplete, probably the complete question/missing part is:"
The parallelogram shown below has an area of 15 units. Find the missing height.
The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a
mean diameter of 22 mm and a standard deviation of 2. 5 mm. After they are picked and washed, tomatoes with a
diameter of at most 15 mm or at least 30 mm are rejected and not sold. What proportion of such tomatoes are
rejected?
Find the z-table here.
O 0. 0033
O 0. 0201
O 0. 9799
O 0. 9967
The proportion of cherry tomatoes that are rejected based on their diameter is 0.0033. (option a).
To use the CDF, we need to standardize the diameter values using the z-score formula:
z = (x - μ) / σ
where z is the z-score, x is the diameter value, μ is the mean diameter, and σ is the standard deviation.
For tomatoes with a diameter of at most 15 mm, we have:
z = (15 - 22) / 2.5 = -2.8
For tomatoes with a diameter of at least 30 mm, we have:
z = (30 - 22) / 2.5 = 3.2
Next, we use the z-table to find the area under the Normal distribution curve that corresponds to these z-scores. For a z-score of -2.8, the area is 0.0026. For a z-score of 3.2, the area is 0.9993.
Finally, we add these two areas together to get the total proportion of rejected tomatoes:
proportion = 0.0026 + (1 - 0.9993) = 0.0033
Hence the correct option is (a).
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The sales department at a certain company consists of two people, the manufacturing department consists of six people, and the accounting department consists of four people. Three people will be selected at random from these people and will be given gift certificates to a local restaurant. Determine the probability that two of those selected will be from the manufacturing department and one will be from the accounting department. Assume that the selection is done without replacement.
The probability that two of those selected will be from the manufacturing department and one will be from the accounting department is approximately 0.409.
To solve the problem, we first need to find the total number of ways to select 3 people out of the 12 people in the company, which is given by the combination formula:
C(12,3) = 12! / (3! * (12-3)!) = 220
Next, we need to find the number of ways to select 2 people from the manufacturing department and 1 person from the accounting department. We can do this by using the combination formula again:
C(6,2) * C(4,1) = (6! / (2! * (6-2)!)) * (4! / (1! * (4-1)!)) = 90
Finally, we can find the probability by dividing the number of desired outcomes by the total number of possible outcomes:
P(2 manufacturing, 1 accounting) = 90 / 220 ≈ 0.409
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PLEASE HELP ME! I’m not sure how to do this :(
The distance from Earth to Mercury is approximately 5.7 x 107 miles, which is less than the fuel capacity of Spigot to travel 125% of the distance from Earth to Mars. Therefore, Spigot has enough fuel to travel from Earth to Mercury and return to Earth before refueling. The correct option is D.
What is distance?Distance refers to the amount of space between two points, objects, or locations. It is typically measured in units such as meters, kilometers, miles, feet, or yards. Distance can be measured in a straight line or along a curved path, depending on the context.
Distance is often used in conjunction with time to calculate speed and velocity. For example, the distance traveled by a car in a certain amount of time can be used to calculate its speed.
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How could you mathematically prove that the elevation on ramp B is steeper than ramp A? (without using logic)
Elevation on ramp B is more steep than ramp A.
What is elevation?"Elevation" typically refers to the height of a location above sea level. It is often used in geography and topography to describe the height of a mountain or the altitude of a city or other location. Elevation is usually measured in feet or meters, and it can have a significant impact on climate, weather patterns, and other environmental factors.
What is steep?"Steep" can have a few different meanings depending on the context. It can refer to a steep slope or incline, such as a steep hill or mountain. It can also mean a high price or cost, as in "the price is too steep for me." Additionally, "steep" can refer to the act of soaking something in hot water in order to extract flavor, as in steeping a tea bag in hot water.
For RampA:
tanα=36/30
tanα=1.2
For Ramp B:
tanβ=36/20
tanβ=1.8
Therefore for Ramp B angle is more than Ramp A and incase of tangent function value of angle increases with the angle measures.
So β>α.
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Please help me.
Giving 40 points
a) i) The pressure on the ground by snowshoe hare is 0.07 N/cm².
ii) The pressure on the ground by European hare is 0.15 N/cm².
b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet.
a) The pressure on the ground can be calculated by dividing the force on the ground due to weight by the total surface area of the feet.
i) For the snowshoe hare, the pressure on the ground is:
Pressure = Force on ground / Total surface area of feet
Pressure = 14 N / 200 cm²
Pressure = 0.07 N/cm²
ii) For the European hare, the pressure on the ground is:
Pressure = Force on ground / Total surface area of feet
Pressure = 38 N / 250 cm²
Pressure = 0.15 N/cm²
b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet than the European hare and exerts less pressure on the ground. This allows the snowshoe hare to move more easily over the snow without sinking.
Additionally, the snowshoe hare has fur on the soles of its feet, which provides additional insulation against the cold snow. These adaptations help the snowshoe hare survive in its snowy environment by allowing it to move and find food more easily.
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Which is more, 7 yards or 19 feet?
According to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.
What is multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product.
According to the given information:To compare 7 yards and 19 feet, we need to convert them to the same unit. Since 1 yard is equal to 3 feet, we can convert yards to feet by multiplying by 3, and we can convert feet to yards by dividing by 3.
In the first answer, we converted 7 yards to feet by multiplying by 3, which gave us 21 feet. Then we compared 21 feet to 19 feet, and found that 21 feet is greater than 19 feet. Therefore, we concluded that 7 yards is more than 19 feet.
In the second answer, we converted 19 feet to yards by dividing by 3, which gave us approximately 6.33 yards (rounded to two decimal places). Then we compared 7 yards to 6.33 yards, and found that 7 yards is greater than 6.33 yards. Therefore, we concluded that 7 yards is more than 19 feet.
Therefore, according to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.
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Please help with functions!
The linear equation have the following results: f(- 2) = 0, f(0) = 2, f(1) = 3.
How to evaluate a linear equation
In this problem we find a linear equation that must be evaluated at x = - 2, x = 0 and x = 1. Linear equations are expressions of the form:
y = m · x + b
Where:
m - Slopex - Independent variable.b - Intercepty - Dependent variable.Now we proceed to evaluate the function, the results are described:
x = - 2
f(- 2) = - 2 + 2
f(- 2) = 0
x = 0
f(0) = 0 + 2
f(0) = 2
x = 1
f(1) = 1 + 2
f(1) = 3
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3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors. (True or False)
Given statement "3-4 If you know the rise and run of a fable roof, you can calculate the rake length and area using slope factors." is true. Because the rise and run of a gable roof allows you to calculate the slope factor, which can then be used to calculate the rake length and area of the roof.
If you know the rise and run of a gable roof, you can calculate the rake length and area using slope factors. The slope factor is a ratio that relates the length of the roof to the height of the roof.
The slope factor is calculated by dividing the rise of the roof by the run of the roof. Once you have the slope factor, you can use it to calculate the rake length and area of the roof.
The rake length is the length of the diagonal edge of the roof, and it can be calculated by multiplying the slope factor by the run of the roof.
For example, if the run of the roof is 10 feet and the slope factor is 0.5 (which corresponds to a 6:12 pitch), then the rake length would be 5 feet (0.5 x 10).
The area of the roof can be calculated by multiplying the rake length by the width of the roof.
For example, if the width of the roof is 20 feet and the rake length is 5 feet, then the area of the roof would be 100 square feet.
Statment is true.
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Marcellus and Anika are playing a video game where they earn 35 stars for each level they pass. Which equation represents the total number of stars earned, y, for passing x levels?
The equation represents the total number of stars is y = 35x
Which equation represents the total number of starsThe equation that represents the total number of stars earned, y, for passing x levels would be:
y = 35x
where y represents the total number of stars earned, and x represents the number of levels passed.
For example, if Marcellus and Anika passed 10 levels, they would earn:
y = 35(10) = 350 stars
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2. A carnival game uses a fair spinner with 16 sections. There are 2 white sections, 4 red sections, and 10 blue sections on the spinner. Part A Find the probability of each event. Express your answer as a fraction in simplest form. P(blue) = = P(green) = P(red) =
The probability of landing on a blue section on the spinner is 10/16, which simplifies to 5/8.
The probability of landing on a green section is 0/16, which simplifies to 0.
The probability of landing on a red section is 4/16, which simplifies to 1/4.
What is probability?The probability of any event occurring is calculated by finding the total number of possible outcomes that would result in that event occurring, and then dividing that number by the total number of possible outcomes.
In this case, the total number of possible outcomes is 16, since there are 16 sections on the spinner.
The total number of outcomes that would result in a blue section being chosen is 10, since there are 10 blue sections on the spinner.
Dividing 10 by 16 gives us the probability of landing on a blue section, which is 5/8.
The same process is used to calculate the probabilities for green and red sections, with the only difference being that the number of sections for each color is different.
Since there are no green sections, the probability of landing on a green section is 0.
There are 4 red sections, so the probability of landing on a red section is 4/16, which simplifies to 1/4.
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The National Junior Honor Society made $238at their cake sale. They sold circular Shaped cakes for $7 and heart shaped cakes for $5. If they Sold twice as many heart cakes as circular ones. how many heart cakes did they sell?
The number of heart cakes that were sold at the cake sale was 28
According to the question,
Cost of circular-shaped cake = $7
Cost of heart shaped cake = $5
Total sale = $238
Let the number of circular cakes shaped be x
Since the number of heart cakes was sold twice as many as the circular cake, the number of heart cakes will be 2x
Cost of x circular-shaped cake = $7 * x
Cost of 2x heart shaped cake = $5 * 2x
Total sale = Cost of x circular cake + Cost of 2x heart cake
Thus, we get the following equation,
238 = 7x + 10x
238 = 17x
x = 14
Thus, the number of heart cakes sold was 2x that is 28.
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Henry is saving up to buy a new jacket. He already has $95 and can save an additional $5 per week using money from his after school job. How much total money would Henry have after 10 weeks of saving? Also, write an expression that represents the amount of money Henry would have saved in w weeks
An expression that represents the amount of money Henry would have saved in w weeks is $95 + ($5 x w)
Henry already has $95, and he can save an additional $5 per week. So after one week of saving, Henry would have a total of $100 ($95 + $5). After two weeks, he would have $105 ($100 + $5), and so on.
To find out how much total money Henry would have after 10 weeks of saving, we can use the same method. After 10 weeks, Henry would have saved a total of $145 ($95 + ($5 x 10)). So, Henry would have a total of $145 after 10 weeks of saving.
Now, let's talk about an expression that represents the amount of money Henry would have saved in w weeks. We can use the formula:
Total amount saved = $95 + ($5 x w)
This formula takes into account the $95 that Henry already has, and the additional $5 he can save each week. The "w" in the formula represents the number of weeks Henry has been saving for. By plugging in different values of "w", we can determine how much money Henry would have saved at different points in time.
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Determine whether the triangles are similar. If so, write a similarity statement. Explain ur reasoning.
Answer:
Both 2B and 2A are not similar.
Step-by-step explanation:
----------------------------------------
Let me be helpful!
Let's start with 2B. It is easier to understand the subject that way.
->for a triangle to be similar, it's angles and sides must be the same.
-2B's triangle shows that line TW got scaled by x2.2 (22/10)
-Line ZW got scaled by 1.18
-2b are not similar.
Now on it 2A!
- line JK got scaled by 0.75
- Line JL got scaled by 0.5
-they are not similar
Let me know if I am incorrect!
-A friendly 8th grader :)
3-9 On a 1500 square foot gable roof, there will be approximately 11% waste. (True or False)
Given statement: On a 1500 square foot gable roof, there will be approximately 11% waste.
The given statement is False.
The statement provides information on the amount of waste but does not provide sufficient information to determine the total area of roofing material required for the gable roof.
Therefore, it is impossible to determine whether the waste percentage is accurate or not.
The statement "On a 1500 square foot gable roof, there will be approximately 11% waste" can be either True or False depending on the specific roofing materials and project details.
However, it's not uncommon for roofing projects to have waste percentages in that range (around 10-15%), especially for complex designs or when using materials like shingles.
Keep in mind that waste factors may vary depending on the type of roof, materials used, and installation methods. Always consult with a professional to get accurate waste estimates for your specific project.
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Whats a product with 2 consecutive digits
The two consecutive digits whose product is 132 are equals to 11 and 12.
Product of two consecutive digits = 132
Let us consider that the two consecutive digits are y and y+1.
Then we can write the expression as,
⇒y × ( y + 1 ) = 132
Expanding the left side of the expression, we get,
⇒ y² + y = 132
Rearranging the values and solving for y, we get,
⇒ y² + y - 132 = 0
Factorize this quadratic equation to get the value of y we have,
⇒ y² + 12y - 11y - 132 = 0
⇒ y( y + 12 ) -11 ( y + 12 ) = 0
⇒ ( y + 12)(y - 11) = 0
This implies,
The two possible values of y are -12 and 11.
However, choose the positive value of y .
Since we are dealing with digits.
Thus, y = 11, and the consecutive digits are 11 and 12.
Therefore, the two consecutive digits are 11 and 12, and their product is indeed 132.
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The given question is incomplete, I answer the question in general according to my knowledge:
The product of two consecutive digit is equal to 132 . What are the numbers?
Use inverse operations to solve each of the following quadratic equations. Put each of your responses in the simplest radical form possible.
The given quadratic equations by solving using inverse operations gives,
(a) x = ±2√2, (b) x = ±3√2 + 5, (c) x = ±4√2, (d) x = ±√90 - 2 and (e) x = 4 ±3√3.
Given are some quadratic equations.
We have to solve this using the inverse operations.
Inverse operations are operations which undo the operation which is done to the equation.
(a) 1/2 x² - 4 = 0
Adding both sides by 4,
1/2 x² = 4
Multiplying both sides by 2,
x² = 8
Taking the square root on both sides,
x = ±√8 = ±2√2
(b) (x - 5)² = 18
Taking the square root on both sides,
x - 5 = ±√18
x - 5 = ±3√2
Adding 5 on both sides,
x = ±3√2 + 5
(c) 2x² + 7 = 71
Subtracting by 7 on both sides,
2x² = 64
Dividing by 2 on both sides,
x² = 32
Taking the square root on both sides,
x = ±4√2
(d) 5 (x + 2)² + 37 = 487
Subtracting by 37 on both sides,
5 (x + 2)² = 450
Dividing by 5 on both sides,
(x + 2)² = 90
Taking the square root on both sides,
x + 2 = ±√90
Subtracting by 2 on both sides,
x = ±√90 - 2
(e) (x - 4)² /3 + 8 = 17
Subtracting by 8 on both sides,
(x - 4)² /3 = 9
Multiplying both sides by 3,
(x - 4)² = 27
Taking the square root on both sides,
x - 4 = ±3√3
Adding both sides by 4,
x = 4 ±3√3
Hence the values are found.
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Let f be the function given by f(x)=2x3+3x2+1. What is the absolute maximum value of f on the closed interval [â3,1] ?
The absolute maximum value of f(x)=2x³ +3x² +1 on the closed interval [-3, 1] is 6, which occurs at x=1.
To find the absolute maximum value of the function f(x) on the closed interval [-3, 1], we need to evaluate the function at the endpoints of the interval and at any critical points in the interior of the interval.
First, we evaluate the function at the endpoints of the interval
f(-3) = 2(-3)³ + 3(-3)² + 1 = -17
f(1) = 2(1)³ + 3(1)² + 1 = 6
Next, we find the critical points of the function f(x) by taking its derivative and setting it equal to zero
f'(x) = 6x² + 6x
6x(x+1) = 0
x = 0 or x = -1
Now we evaluate the function at these critical points
f(0) = 1
f(-1) = 2(-1)³ + 3(-1)² + 1 = 2
Therefore, the absolute maximum value of f(x) on the closed interval [-3, 1] is 6, which occurs at x=1.
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The given question is incomplete, the complete question is:
Let f be the function given by f(x)=2x³ +3x² +1. What is the absolute maximum value of f on the closed interval [-3,1] ?
4.a) Increase £75 by 5%
Please help me and explain this to me.
Answer:
£78.75
Step-by-step explanation:
An easy way step but longer way to do this is
10% of 75 is 7.5 ((75/10= 7.5))
divide by 2 on both sides
5% = 3.75
then just add it, its increasing 75 by 5%
so 75 + 3.75 = 78.75
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The area of the figure is 160.6 unit²
How to find the area of the figure?
Since the figure is composed of a parallelogram and one semicircle, the area will be:
Area of figure = area of parallelogram + area of semicircle
Area of figure = bh + 1/2πr²
where b = 10, h = 6 and r = 8
Area of figure = (10*6) + (1/2 * 22/7 * 8²)
Area of figure = 60 + 100.6
Area of figure = 160.6 unit²
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a cathedral ceiling shown in the figure below is 8 feet high at the west wall of a room. as you go from the west wall toward the east wall, the ceiling slants upward. three feet from the west wall, the ceiling is 10.5 feet high. exercise (a) what is the slope of the ceiling? step 1 the slope is the rise over the run. when we move 3 feet east from the west wall the run is incorrect: your answer is incorrect. feet. the corresponding rise is the difference in ceiling heights. rise
The slope of the cathedral ceiling is 0.83.
To calculate the slope of the cathedral ceiling, we need to find the rise over the run. The rise is the difference in ceiling heights between the two points. The run is the horizontal distance between the two points.
From the problem statement, we know that the ceiling is 8 feet high at the west wall and 10.5 feet high three feet from the west wall. So the rise is:
rise = 10.5 - 8 = 2.5 feet
The run is the horizontal distance between the two points, which is:
run = 3 feet
Now we can calculate the slope:
slope = rise/run = 2.5/3 = 0.83
Therefore, the slope of the cathedral ceiling is 0.83.
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Need help completing this
Answer:
a) What is her GROSS pay for a week? 1,400
b) What is her GROSS pay for a year? 67,200
c) What are her TOTAL DEDUCTIONS for a week? 351.39
d) What is her NET pay for a week? 1,048.61
e) What is her NET pay for a year? 50,333.28
f) What does she pay in Income Tax per YEAR? 13,535.52
g) What does she pay in CPP contributions per YEAR? 2,537.28
h) What does she pay in El contributions per YEAR? 793.92
i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%
Step-by-step explanation:
GROSS
without tax or other contributions having been deductedNET
Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.There are 4 weeks in a month, 52 weeks in a year.
a) What is her GROSS pay for a week? 1,400
The amount of money she makes per hour × the amount of hours she works per week35 × 401,400b) What is her GROSS pay for a year? 67,200
The amount of money she earns in a month × 12(The amount of money she makes per week × 4) × 12(1,400 × 4) × 125600 × 1267,200c) What are her TOTAL DEDUCTIONS for a week? 351.39
Income Tax + CPP + El281.99 + 52.86 + 16.54334.85 + 16.54351.39d) What is her NET pay for a week? 1,048.61
Her gross pay for a week - Her total deductions for a week1,400 - 351.391,048.61e) What is her NET pay for a year? 50,333.28
Her gross pay for a year - Her total deductions for a yearHer gross pay for a year - ([Her total deductions for a week × 4] × 12)Her gross pay for a year - ([351.39 × 4] × 12)67,200 - ([351.39 × 4] × 12)67,200 - (1,405.56 × 12)67,200 - 16,866.7250,333.28f) What does she pay in Income Tax per YEAR? 13,535.52
Income tax per month × 12(Income tax per week × 4) × 12(281.99 × 4) × 121,127.96 × 1213,535.52g) What does she pay in CPP contributions per YEAR? 2,537.28
CPP per month × 12(CPP per week × 4) × 12(52.86 × 4) × 12211.44 × 122,537.28h) What does she pay in El contributions per YEAR? 793.92
El per month × 12(El per week × 4) × 12(16.54 × 4) × 1266.16 × 12793.92i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%
(Her yearly Income Tax ÷ Her yearly Gross Pay) × 100(13,535.52 ÷ 67,200) × 1000.20142... × 10020.142...% or 20.14%If x = 4 units , y = 6 units, and h =5 units, and the area of the rhombus shown above using decomposition
The total area of the rectangle and the two right-angled triangles is 50 square units.
What is meant by area?
Area refers to the measurement of the size or extent of a two-dimensional surface or shape. It is usually expressed in square units, such as square meters or square feet.
What is meant by a rectangle?
A rectangle is a four-sided polygon with two pairs of parallel sides and four right angles. The opposite sides of a rectangle are equal in length, and the area can be calculated as length x width.
According to the given information
Area of rectangle = h * x
Area of one right-angled triangle = (1/2) * h * y
Total area of two right-angled triangles = 2 * (1/2) * h * y = h * y
Adding the area of the rectangle and the area of the triangles, we get the total area:
Total area = Area of rectangle + Total area of two right-angled triangles
Substituting the given values, we get:
Total area = (5 * 4) + (5 * 6)
Total area = 20 + 30
Total area = 50 square units
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A certain sine function has a midline at y=3.
Which function rule could model this situation?
The function rule that could model this situation is f(x)=sin(x)+3. The correct answer is (c).
Understanding sine functionThe sine function is a mathematical function that describes a periodic oscillation. It is one of the basic trigonometric functions, along with cosine, tangent, cotangent, secant, and cosecant.
Let us relate this to our given question.
The midline of a sine function is the horizontal line that the graph oscillates around.
In this case, the midline is y=3, which means that the sine function oscillates between y=3+1=4 and y=3-1=2.
The function rule that could model this situation is c. f(x)=sin(x)+3, because adding 3 to the sine function shifts the midline up to y=3, and the sine function oscillates between y=4 and y=2.
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100.0
How long would it take the bowling ball to fall 150 feet? (Estimate your answer to one
decimal place. Hint: Use the equation d = 16t².)
It would take the bowling ball approximately 3.1 seconds to fall 150 feet.
What is distance?
Distance is the total movement of an object, regardless of direction. We can define distance as how much ground an object has covered, regardless of its starting or ending point.
Distance is defined as the size or amount of displacement between two positions. Note that the distance between two locations is not the same as the distance between them. The distance traveled is the total length of the path traveled between two positions.
Here given equation,
d = 16t², where t is the time in seconds and d is the distance in feet and distance is 150 feet.
We want to find the value of t.
Now,
[tex]d = 16 {t}^{2} \\ {t}^{2} = \frac{d}{16} \\ {t}^{2} = \frac{150}{16} \\ t = \sqrt{( \frac{150}{16}) } \\ t = \sqrt{9.375} \\ t = 3.0619[/tex]
So, t = 3.1 (rounded to one decimal place)
Therefore, it would take the bowling ball approximately 3.1 seconds to fall 150 feet.
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Correct question is "How long would it take the bowling ball to fall 150 feet where equation of distance is d = 16t² ?(Estimate your answer to one decimal place). "
3-6 You can determine the slope of a roof using a flat board, a bubble level and a ruler,or a sight card can be used. (True or False)
Given statement "3-6 You can determine the slope of a roof using a flat board, a bubble level and a ruler,or a sight card can be used." is true. Because flat board, a bubble level and a ruler,or a sight card methods are commonly used to determine the slope of a roof, and both are effective.
Determining the slope of a roof is an important task for many construction and roofing projects.
One method to determine the slope of a roof is to use a flat board, a bubble level, and a ruler.
First, place the flat board horizontally on the roof surface, and use the bubble level to make sure it is level.
Then, measure the distance between the bottom of the board and the roof surface at the point where the board intersects with the roof using the ruler. This distance is the rise.
Next, measure the distance from the point where the board intersects with the roof to the end of the board using the ruler. This distance is the run. Finally, divide the rise by the run to get the slope.
Another method to determine the slope of a roof is to use a sight card. A sight card is a specially designed tool that can help to measure the angle of a slope or pitch. The sight card is held at the bottom of the roof and lined up with a known vertical or horizontal line, such as the edge of a building.
Statement is true.
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Mr. Liaw has two cylindrical travel mugs that he likes to take on his drive to work. His stainless steel mug has a height of 8.5 inches and a radius of 1.5 inches. What is the volume of the stainless steel mug?
Use ≈3.14 and round your answer to the nearest whole number
Mr. Liaw's ceramic mug has the same volume, but a radius of 2 inches. What is the height of the ceramic mug?
Use ≈3.14 and round your answer to the nearest whole number
Therefore , the solution of the given problem of volume comes out to be ceramic mug has a 5 inch height.
What does volume actually mean?A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.
Here,
The following formula determines a cylinder's volume:
=> V = π * r² * h
where r is the cylinder's radius and h is its height, and is roughly equivalent to 3.14.
For the mug made of stainless steel:
1.5 inches is the radius (r).
Height in inches (h) is 8.5
With these values entered into the formula, we obtain:
=> V = 3.14 * (1.5)² * 8.5
=> V ≈ 3.14 * 2.25 * 8.5
=> V ≈ 60.14
The stainless steel mug has a 60 cubic inch volume, rounded to the nearest whole number.
Regarding the mug:
Radius (r) equals two inches
Given that it has the same volume as the stainless steel mug, its volume (V) is equal to 60 cubic inches.
=> 60 = 3.14 * (2)²* h
=> h = 60 / (3.14 * 4)
=> h ≈ 4.77
The ceramic mug has a 5 inch height.
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In this polygon, all angles are right angles.
What is the area of the polygon? Show your work.
The area of the polygon is solved to be 1044 squared cm
How to find the are of the c]polygonThe area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas
Section 1 has dimensions:
length * width = 46 * 14 = 644
section 2 has dimensions:
length = 46 - 21 = 25
width = 30 - 14 = 16
Area = 25 * 16 = 400
Area of the composite figure
section 1 + section 2
= 644 + 400
= 1044 squared cm
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