Therefore, the area of the trapezoid is 60 cm².
What is trapezoid?A trapezoid is a four-sided polygon with two parallel sides (called bases) of different lengths, and two non-parallel sides (called legs). The legs of a trapezoid are usually not congruent and can be of different lengths. Trapezoids can have different shapes and sizes, but they always have at least one pair of parallel sides. The area of a trapezoid can be calculated using the formula:
[tex]Area = ((b_1 + b_2) * h) / 2,[/tex]
where b1 and b2 are the lengths of the parallel bases, h is the height or perpendicular distance between the two bases.
To calculate the area of a trapezoid, we use the formula:
[tex]Area = (b_1 + b_2) * h / 2[/tex]
where b1 and b2 are the lengths of the parallel sides of the trapezoid and h is the height (perpendicular distance) between the parallel sides.
In this case, we are not given which sides are the parallel sides and which one is the height, so we cannot directly apply the formula. However, we can make an educated guess based on the dimensions given.
Assuming that the two 8 cm sides are parallel, we can use the formula as follows:
[tex]Area = (b_1 + b_2) * h / 2[/tex]
[tex]Area = (8 cm + 16 cm) * 10 cm / 2[/tex]
[tex]Area = 120 cm^{2} / 2[/tex]
[tex]Area = 60 cm^{2}[/tex]
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What are two other ways to name <1?
Answer: <PFY and <YFP
Step-by-step explanation:
Answer:
<PFY and <YFP
Step-by-step explanation:
[EF] is the diameter of a circle of center O and of radius R. G is a of this circle, distinct from E and F. Prove that GEF is a right triangle.
Answer:
Step-by-step explanation:
Given : O is the centre of the circle with radius r. AB, CD and EF are the diameters of the circle. ∠OAF = ∠OCB = 60°.
To Find : What is the area of the shaded region?
Solution:
∠OAF = 60°
OA = OF = Radius
=> ΔOAF is Equilateral Triangle
∠OCB = 60°
OC = OB Radius
Hence ΔOCB is Equilateral Triangle
∠AOF = 60° , ∠BOC = 60°
=> ∠COF = 180° - 60° - 60° = 60° as AC is straight Line
∠DOE = ∠COF ( vertically opposite angle )
∠DOE = 60°
ΔODE is also an equilateral Triangle
Each sector has 60 ° angle
Area of shaded region = (60/360)πr² - (√3/4) r²
= r² (π/6 - √3/4)
= (r²/6) (π - 3√3/2)
Area of 3 shaded regions
= 3 (r²/6) (π - 3√3/2)
= (r²/2) (π - 3√3/2)
(r²/2) (π - 3√3/2) is the correct answer
boardwalk electronics manufactures 200,000 circuit boards per month. a random sample of 4,000 boards is inspected every week for seven characteristics. during a recent week, seven defects were found for one characteristic, and two defects each were found for the other six characteristics. if these inspections produced defect counts that were representative of the population, what are the dpmo's for the individual characteristics and what is the overall dpmo for the boards? do not round intermediate calculations. round your answers to the nearest whole number.
The overall DPMO for the boards would be 4750.
Boardwalk Electronics manufactures 200,000 circuit boards per month. A random sample of 4,000 boards is inspected every week for seven characteristics. During a recent week, seven defects were found for one characteristic, and two defects each were found for the other six characteristics. If these inspections produced defect counts that were representative of the population, the dpmo's for the individual characteristics and what is the overall dpmo for the boards would be as follows:To calculate the DPMO, the formula used is:DPMO = (Number of defects / Number of Opportunities) × 1,000,000For Characteristic
1:Number of defects = 7Number of opportunities = 4000DPMO = (7/4000) × 1,000,000= 1750For Characteristic 2:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 3:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 4:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 5:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 6:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 7:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500The overall DPMO for the boards would be the sum of the DPMO of all characteristics which would be 1750 + 500 + 500 + 500 + 500 + 500 + 500 = 4750.
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The point T(-4, -1) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, T?
Answer:
(1, -4)
Step-by-step explanation:
if you rotate from quadrant 3 to 4, x=-y and y=x
After the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).
What is image rotation?A rotation is a type of transformation which is a turn.A figure can be turned clockwise or counterclockwise on the coordinate plane.In both transformations the size and shape of the figure stays exactly the same.Given is the coordinate of point as (-4, - 1). It is rotated by 90° clockwise about the origin.
When we rotate a figure 90 degrees clockwise about the origin, then the new coordinates will be -
A(x, y) → A(y, - x)
Then, we can write the new coordinates according to the rule as -
P(-4, - 1) → P'(- 1, - 4)
Therefore, after the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).
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can somebody help me with a.) please
Answer:
y = -1/500x² +2/5x
Step-by-step explanation:
You want the equation for the path of a football that is thrown 200 m downfield and reaches a maximum height of 20 m.
Initial heightThe initial height is not given. The equation is much more easily written if we assume it is zero, or we assume the launch height is the same height at which the ball is caught.
PointsWe know the maximum height is reached halfway between the launch point and the final point of interest. Then we're required to write the equation of a parabola that passes through the points (0, 0), (100, 20), and (200, 0).
EquationSince we know the x-intercepts, we can write the equation as ...
y = ax(x -200)
Then all we have to do is find the value of 'a' so the equation has (100,20) as a solution.
20 = a(100)(100 -200) = -10000a
a = -1/500 . . . . . divide by -10000
The equation of the path of the football is ...
y = (-1/500)(x)(x -200)
y = -1/500x² +2/5x
__
Additional comment
When x=185, y = -1/500(185)(185 -200) = 15/500(185) = 5.55 . . . meters
The domain is [0, 200]; the range is [0, 20].
To achieve that distance and height, the football would need to be thrown at a speed in excess of 119 miles per hour. For comparison, the fastest baseball pitch ever thrown was 108.1 miles per hour.
the percentage of people who prefer dogs to cats is 78% for a given population. what is the standard error of the sampling distribution of sample proportions for samples of size n
The standard error of the sampling distribution of sample proportions for samples size
1) n = 35 ⇒ SE = 0.07
2) n = 100 ⇒ SE = 0.04
3) n = 250 ⇒ SE = 0.03
We know that the formula for thr standard error(SE) of the sample Proportion is:
SE = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
as the sample size increases, the standard error decreases.
Here, the percentage of people who prefer dogs to cats is 78%
so, p = 0.78
For samples of size n = 35,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{35} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{35} }[/tex]
SE = 0.07
For sample size n = 100,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{100} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{100} }[/tex]
SE = 0.041
For samples of size n = 250,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{250} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{250} }[/tex]
SE = 0.03
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The complete question is:
The percentage of people who prefer dogs to cats is 78% for a given population. What is the standard error of the sampling distribution of sample proportions for samples of size n=35, n=100, and n=250?
PLEASE HELP ME DUE MIDNIGHT !!!
Answer:
Column 1:
[tex]\pi/3[/tex] (given)
[tex]5\pi/4[/tex]
[tex]11\pi/6[/tex]
Column 2:
[tex]\sqrt{3}/2[/tex]
[tex]-\sqrt{2}/2[/tex] (given)
[tex]-1/2[/tex]
Column 3:
all given
Column 4:
[tex]\sqrt{3}[/tex]
[tex]1[/tex]
[tex]-\sqrt{3}/3[/tex] (given)
Step-by-step explanation:
Solved by using unit circle and inverse trig functions
Solve the inequality for u.
5u≤45
Simplify your answer as much as possible.
Answer:
u ≤ 9
Step-by-step explanation:
5u ≤ 45 ( divide both sides by 5 )
u ≤ 9
What is 14x15 and what is an art teacher ordered 26 sets for class there are 100 markers in each set how many in 26 sets?
Answer: 210
Step-by-step explanation:
The value of 14x15 is 210.
If an art teacher ordered 26 sets for class and there are 100 markers in each set, then the total number of markers is:
26 x 100 = 2600
Therefore, there would be 2600 markers in 26 sets.
The image of a composite figure is shown.
A four-sided shape with the bottom side labeled as 21.4 yards. The height is labeled 9 yards. A portion of the top side from the perpendicular to right vertex is labeled 2.2 yards. The portion of the top from the perpendicular to the left vertex is 19.2 yards.
50 POINTS PLEASE GET CORRECT
What is the area of the figure?
192.6 yd2
211.86 yd2
212.4 yd2
423.72 yd2
Answer:
area=192.6yards^2
Step-by-step explanation:
9×2.2=19.8÷2= 9.9 for area of one of the triangles
19.2×9=172.8 for area of the rectangle
21.4-19.2=2.2
2.2×9=19.8÷2=9.9
19.8+172.8=192.6
Answer: its a
Step-by-step explanation:
The straight line shown below passes through the points (3, 1) and (8, 36).
What is the gradient of this line?
Give your answer as an integer or as a fraction in its simplest form.
Answer:
the gradient of the line is 7.
Step-by-step explanation:
To find the gradient of the straight line that passes through the points (3,1) and (8,36), we use the formula:
Gradient = (change in y) / (change in x)
The change in y is the difference between the y-coordinates of the two points, which is:
36 - 1 = 35
The change in x is the difference between the x-coordinates of the two points, which is:
8 - 3 = 5
Therefore, the gradient of the straight line is:
Gradient = (change in y) / (change in x) = 35 / 5 = 7
So the gradient of the line is 7.
Solve the equation.
4π=w−6π
Answer: W=10pi
Step-by-step explanation:
Does anyone understand this?
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
Step-by-step explanation:
Statements 1, 2, 5 are all true
Compute the volume of the prism when d=1 when d=2 and when d=1/2
Answer: To compute the volume of a prism, we need to know the area of the base and the height of the prism. Assuming that the prism has a rectangular base, the formula for the volume of the prism is:
Volume = Area of Base × Height
Let's assume that the length and width of the rectangular base are both equal to 2d (since we don't have specific dimensions). The height of the prism is also equal to d, as given.
When d = 1:
The area of the base is 2d × 2d = 4 square units
The height is d = 1 unit
Therefore, the volume is:
Volume = Area of Base × Height = 4 × 1 = 4 cubic units
When d = 2:
The area of the base is 2d × 2d = 8 square units
The height is d = 2 units
Therefore, the volume is:
Volume = Area of Base × Height = 8 × 2 = 16 cubic units
When d = 1/2:
The area of the base is 2d × 2d = 1 square unit
The height is d = 1/2 unit
Therefore, the volume is:
Volume = Area of Base × Height = 1 × (1/2) = 1/2 cubic units
So, the volume of the prism is 4 cubic units when d=1, 16 cubic units when d=2, and 1/2 cubic units when d=1/2.
Step-by-step explanation:
7.) IF y = a√x² and if y=0.4 when x = 4; Find
a. y in terms of x
b. y if x=100
c. x when y=1.4
The equation y = a√x² is equal to y = 0.1√x² given that y = 0.4 when
x = 4. We also found that when x = 100, y = 10 and when y = 1.4, x = 14.
Given y = a√x² and y = 0.4 when x = 4.
a. To find y in terms of x, we substitute the given values into the equation y = a√x² as follows:
0.4 = a√4²
0.4 = 4a
Dividing both sides by 4, we get:
a = 0.1
Therefore, the equation becomes:
y = 0.1√x²
b. To find y when x = 100, we substitute x = 100 in the equation y = 0.1√x² as follows:
y = 0.1√10000
y = 10
Therefore, when x = 100, y = 10.
c. To find x when y = 1.4, we substitute y = 1.4 in the equation y = 0.1√x² as follows:
1.4 = 0.1√x²
Squaring both sides, we get:
1.96 = 0.01x²
Dividing both sides by 0.01, we get:
x² = 196
Taking the square root of both sides, we get:
x = ±14
Since x represents a distance, it cannot be negative. Therefore, x = 14.
Therefore, when y = 1.4, x = 14.
In conclusion, we found that the equation y = a√x² is equal to y = 0.1√x² given that y = 0.4 when x = 4. We also found that when x = 100, y = 10 and when y = 1.4, x = 14.
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Molly is filling bags of marbles. She makes each bag so that 3 out of every 8 marbles are blue. Which equation correctly compares the number of marbles she uses, x, to the number of blue marbles, y?
The equation that correctly compares the number of marbles used, x, to the number of blue marbles, y, is y = 3/8x.
To calculate the number of marbles used, x, and the number of blue marbles, y, Molly is making, the following equation can be used: y = 3/8x. This equation states that for every 8 marbles used, 3 of them will be blue. For example, if Molly uses 24 marbles, then 3/8x = 3/8(24) = 9. Therefore, 9 of the 24 marbles will be blue. To calculate the number of blue marbles for a different number of marbles used, x, the equation can be rearranged to solve for y. For example, if Molly uses 48 marbles, then the equation can be rearranged to y = 8/3x, and then 8/3(48) = 16. Therefore, 16 of the 48 marbles will be blue.
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The path of a cannon ball is modeled by the quadratic
f(x) = - 16x
2 + 120x + 10.
The graph in red and black show the same function.
What similarities and differences to do you see?
The only significant variation between the red and black graphs is the scales used for the x and y axes. The two graphs both display the same quadratic function.
What is math as a quadratic?x ax2 + bx + c = 0 is a quadratic equation, which is a second-degree polynomial problem in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given :
The quadratic function f(x) = -16x2 + 120x + 10 is depicted in both the red and black graphs, however, they are plotted at various scales. In comparison to the black graph, the red graph has a narrower range on both the x and y axes.
On both graphs, the parabola's vertex, or lowest point on the curve, is situated at x = 3.75 and y = 412.5.
This indicates that the cannonball's maximum height is 412.5 feet, and it does so at a horizontal distance of 3.75 feet from the cannon.
The only significant variation between the red and black graphs is the scales used for the x and y axes. The two graphs both display the same quadratic function.
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5% of what number is 29?
Answer:
1,45
Step-by-step explanation:
[tex] \frac{29 \times 5\%}{100\%} = 1.45[/tex]
lynne has \$8.00$8.00dollar sign, 8, point, 00 to spend on apples and oranges. apples cost \$0.65$0.65dollar sign, 0, point, 65 each, and oranges cost \$0.75$0.75dollar sign, 0, point, 75 each. if there is no tax on this purchase and she buys 555 apples, what is the maximum number of whole oranges she can buy?
Lynne can buy 5 apples and 6 oranges with her $8.00.
The first thing to do is determine how much money Lynne spends on the apples. Since she is buying 5 apples,
we can multiply the price of each apple ($0.65) by 5: $5 * 0.65 = $3.25
Therefore, Lynne has $8 - $3.25 = $4.75 to spend on oranges.
Now we need to determine the maximum number of whole oranges that she can buy with $4.75. We can do this by dividing $4.75 by the price of each orange ($0.75): $4.75 ÷ $0.75 = 6.33.
Since we can't buy a fraction of an orange, the maximum number of whole oranges Lynne can buy is 6. Therefore, Lynne can buy 5 apples and 6 oranges with her $8.00.
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...................................
Answer:
america
Step-by-step explanation:america!!
The data given cars a moter by graph representing Year s No. of produced below shows. shows the production of company Draw a line the data. 2013 2009 10,200/12, 400 11, 200|15, 100 18.000 2010 2011 2012
Answer:
To draw a line graph, you need to plot your data on the graph. For example, if you have the data for the number of cars produced in a year, you would plot the number of cars on the Y-axis and the year on the X-axis. Then, you would trace both lines to the point where they intersect and place a dot on the intersection. You would repeat this process for each year and then connect the dots with a line.
nitially 100 milligrams of a radioactive substance was present. after 6 hours the mass had decreased by 5%. if the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. (round your answer to one decimal place.)
If the rate of decay is proportional to the amount of the substance present at time t, then the amount remaining after 24 hours is 57.7 milligrams
Now we need to find the value of k. We know that the mass decreased by 5% after 6 hours, which means that the amount remaining is 95% of the initial amount. We can substitute these values into our formula and solve for k:
0.95 initial amount = initial amount x (1 - k x initial amount)⁶
Simplifying this equation, we get:
1 - [tex](0.95)^{(1/6)})[/tex] = k x initial amount
Solving for k, we get:
k = (1 - [tex](0.95)^{(1/6)})[/tex]) / initial amount
Now we can use this value of k to find the amount remaining after 24 hours:
Amount remaining = 100 x (1 - k x 100)²⁴
Plugging in the value of k, we get:
Amount remaining = 100 x (1 - (1 - [tex](0.95)^{(1/6)})[/tex] * 100)²⁴
Evaluating this expression, we get:
Amount remaining = 57.7 milligrams
Therefore, after 24 hours, there will be approximately 57.7 milligrams of the radioactive substance remaining.
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(T/F) a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint.
The statement " a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint" is true because shadow prices provide valuable information about the marginal value of resources and constraints in linear programming problems
A shadow price represents the marginal value of a resource or constraint in a linear programming problem. It indicates how much the optimal value of the objective function will increase if the right-hand side of a constraint is increased by one unit, while keeping all other constraints and variables fixed. The shadow price of a constraint is calculated by adding one unit to the right-hand side of the constraint and re-solving the linear programming problem.
The resulting increase in the objective function value is the shadow price of that constraint. Shadow prices are useful in making decisions about resource allocation, pricing, and capacity planning in a variety of industries such as manufacturing, transportation, and energy.
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A circular watch has a minute hand that is 2.5 cm long.
(a) What distance does the tip of the hand move through in 20 minutes?
(b)What area of the watch face is covered by the minute hand in 30 minutes? (Pi = 3.14)
Assuming that the clock is circular, the length of the minute hand is the radius.
The distance that the tip of the minute hand moves in a given time is the length of an arc along the circle.
If s is the length of arc, then s = rθ, where r is the radius and θ is the measure (in radians) of the central angle formed by the initial position and the final position of the minute hand (measured clockwise).
(a)
r = 2.5"
20 minutes is 1/3 of an hour.
Since there are 2π radians in 1 rotation of the minute hand (1 hour),
θ = (1/3)(2π) = 2π/3.
So, s = rθ = (2.5")(2π/3) = 10π/3 inches ≈ 5.24"
(b)
A = π x ^ 2 x 2
3.14 x 15 x 15 = 706.5
The area of the watch face is covered by the minute hand in 30 minutes is 706.5
hope you understood this question
A new cylindrical can with a diameter of 4 cm is being designed by a local company The surface area of the can is 130 square centimeters What is the height of the can? Estimate using 3 14 for x and
round to the nearest hundredth Apply the formula for surface area of a cylinder SA-28+ Ph
The height of the can is approximately 9.74 centimeter.
Define surface area of cylinderThe surface area of a cylinder is the total area of the curved and flat surfaces that make up the cylinder. It can be calculated using the formula:
SA = 2πr² + 2πrh
where r is the radius of the cylinder and h is its height.
In this case, we are given that the diameter of the can is 4 cm, which means the radius is 2 cm.
We are also given that the surface area is 130 square centimeters. Substituting these values into the formula, we get:
130 = 2π(2)² + 2π(2)h
Simplifying this equation, we get:
130 = 8π + 4πh
Subtracting 8π from both sides, we get:
122 = 4πh
Dividing both sides by 4π, we get:
h = 122/(4π) ≈ 9.74 cm (rounded to the nearest hundredth using 3.14 for π)
Therefore, the height of the can is approximately 9.74 cm.
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tan(sin^-1(-1))= _____________
Answer:
tan(sin^-1(-1)) is undefined.
The inverse sine function returns a value between -pi/2 and pi/2, and since sin(-pi/2) = -1, sin^-1(-1) = -pi/2. However, at -pi/2, the tangent function is undefined since it results in a vertical asymptote.
Write 39.76% as a decimal
Decimal form of number 39.76% is,
= 0.3976
We have to write,
A number 39.76% into a decimal form.
Now, We can write the number in decimal form as,
= 39.76%
= 39.76 / 100
= 0.3976
Therefore, Decimal form of number 39.76% is,
= 0.3976
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what number does not appear in the first 30 digits of pi? a) 1 b) 2 c) 3 d) 4 e) 0
Answer:
0
Step-by-step explanation:
100 points!!!
Express the function graphed on the axes below as a piecewise function
Answer: { (-1/2)x - 1, -2 ≤ x ≤ 4
Step-by-step explanation:
Let's start with the first line:
The line passes through two points: (-5, 8) and (-2, 2). The hollow circle at (-5, 8) indicates that this point is not included in the graph, while the closed circle at (-2, 2) indicates that this point is included.
We can find the slope of the line using the two points:
slope = (change in y) / (change in x) = (2 - 8) / (-2 - (-5)) = -6 / 3 = -2
Using point-slope form, we can write the equation of the line as:
y - 2 = -2(x - (-2))
Simplifying:
y - 2 = -2x - 4
y = -2x - 2
Next, let's consider the second line:
The line passes through two points: (-2, -2) and (4, -5). The hollow circle at (-2, -2) indicates that this point is not included in the graph, while the closed circle at (4, -5) indicates that this point is included.
We can find the slope of the line using the two points:
slope = (change in y) / (change in x) = (-5 - (-2)) / (4 - (-2)) = -3 / 6 = -1/2
Using point-slope form, we can write the equation of the line as:
y - (-2) = (-1/2)(x - (-2))
Simplifying:
y + 2 = (-1/2)x + 1
y = (-1/2)x - 1
Now we can write the piecewise function:
f(x) = { -2x - 2, -5 ≤ x < -2
{ (-1/2)x - 1, -2 ≤ x ≤ 4
This piecewise function represents the two lines graphed on the given axes, where the first line is defined for x values between -5 and -2 (inclusive on -2 but not on -5), and the second line is defined for x values between -2 and 4 (inclusive on both).