The triple integral ∫∫∫ (x+8y)dV where E is bounded by the parabolic cylinder is 512,604.17.
The triple integral is ∫∫∫(x+8y)dV.
Curves from the question are:
y = 7x², z = 2x, y = 35x, z = 0
Then, 7x² = 35x
Divide by x on both side, we get
7x = 35
Divide by 7 on both side, we get
x = 5
And z = 2x or z = 0. So
2x = 0
x = 0
Now the limits are:
x = 0 to x = 5
y = 7x² to y = 35x
z = 0 to z = 2x
Now the integral is
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}\int_{0}^{2x}(x+8y)dzdydx[/tex]
Now first integrate with respect to z
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(x+8y)[z]_{0}^{2x}dydx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(x+8y)[2x-0]dydx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(2x^2+16xy)dydx[/tex]
Now integrate with respect to y
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(y)_{7x^{2}}^{35x}+16x(\frac{y^2}{2})_{7x^{2}}^{35x}\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(35x - 7x^2)+16x(\frac{1225x^2}{2}-\frac{49x^4}{2})\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(35x - 7x^2)+8x(1225x^2-49x^4)\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[70x^3 - 14x^4+9800x^3-392x^5\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\left[\frac{70x^4}{4} - \frac{14x^5}{5}+\frac{9800x^4}{4}-\frac{392x^6}{6}\right]_{0}^{5}[/tex]
∫∫∫(x+8y)dV = [tex]\left[\frac{70(5)^4}{4} - \frac{14(5)^5}{5}+\frac{9800(5)^4}{4}-\frac{392(5)^6}{6}\right]-\left[\frac{70(0)^4}{4} - \frac{14(0)^5}{5}+\frac{9800(5)^4}{4}-\frac{392(5)^6}{6}\right][/tex]
∫∫∫(x+8y)dV = [10937.5 - 8750 + 1531250 - 1020833.33]-0
∫∫∫(x+8y)dV = 512,604.17
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The complete question is:
Evaluate the triple integral ∫∫∫(x+8y)dV where E is bounded by the parabolic cylinder.
y = 7x² and the planes
z = 2x, y = 35x, and
z = 0
A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.4 inch and a height of 2.2 inches. How many total square inches of gift wrap will the makeup artist need to wrap 3 lipsticks? Leave the answer in terms of π.
2.08π square inches
6.24π square inches
8.32π square inches
19.59π square inches
The makeup artist will need approximately 7.296π square inches of gift wrap to wrap 3 lipsticks. Rounded to two decimal places, the answer is 19.59π square inches.
How to calculate how many total square inches of gift wrap will the makeup artist need to wrap 3 lipsticksThe formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder.
For one lipstick, the surface area is:
SA = 2π(0.4)² + 2π(0.4)(2.2)
SA = 1.024π + 1.408π
SA = 2.432π square inches
To wrap 3 lipsticks, the total surface area would be:
SA = 3(2.432π)
SA = 7.296π square inches
Therefore, the makeup artist will need approximately 7.296π square inches of gift wrap to wrap 3 lipsticks. Rounded to two decimal places, the answer is 19.59π square inches.
So the correct option is: 19.59π square inches.
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IClicker Question 16
Suppose that a random sample of 100 smokers
reveals that the average weight gain after quitting
smoking was 20 pounds with a standard deviation of 6
pounds.
The value of xis
A. 6.
B. 20.
C. 100.
D. 6/V100 = 0. 6.
The value of x, which is the sample mean and represents the average weight gain after quitting smoking, is 20. Therefore, the correct option is B.
Given that the random sample of 100 smokers reveals an average weight gain of 20 pounds after quitting smoking and a standard deviation of 6 pounds, the value of x is determined as follows.
1. Random sample of 100 smokers (n = 100)
2. Average weight gain after quitting smoking is 20 pounds (mean, x' = 20)
3. Standard deviation is 6 pounds (σ = 6)
Option A (6) is incorrect because it does not relate to the given information.
Option C (100) is also incorrect because it refers to the sample size, which is not relevant to finding the value of x.
Option D (6/√100 = 0.6) is incorrect because it calculates the standard error of the mean, which is not what the question is asking for.
Therefore, the correct answer is option B: 20, which is the sample mean and represents the average weight gain after quitting smoking.
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Use the digits -9 to 9 to complete the puzzle below. Try all the combinations. But as you begin doing that, you will realize that, in some cases, you are looking for factor combinations with a particular sum or difference. You will see that some numbers must be greater than a particular value in order to produce the product you are looking for. (Hint: Consider a negative imaginary number in the second set of parentheses.) Show your work to confirm your solution.
The correct equation is,
⇒ (5 - 6i) (2 + 4i)
Let us assume that;
⇒ (a + bi) (c + di)
⇒ ac + adi + bci + bdi²
⇒ (ac − bd) + (ad + bc)i
Matching coefficients:
30 < ac − bd < 80
ad + bc = 0
Hence, We need to pick four integers between -9 and 9 such that these two equations are satisfied. One possible combination is:
a = 8, b = -4, c = 6, d = 3
The number would be:
ac − bd = (8)(6) − (-4)(3) = 60
Puzzle 2
Using the result from Puzzle 1:
ac − bd = 34
ad + bc = 8
Like before, it makes sense to assume b is negative. With some trial and error, one possible answer is:
a = 5, b = -6, c = 2, d = 4
Thus, The correct equation is,
⇒ (5 - 6i) (2 + 4i)
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ignore the 94 don’t really understand this problem pls help (giving brainliest)
Answer:
measure of angle GHJ = 1/2 the measure of arc GJ = (1/2)(86°) = 43°
measure of angle JIG = 1/2 the measure of arc GJ = (1/2)(86°) = 43°
Hector parked his SUV in long-term parking while he traveled to China. What does the slope of the line represent? A Hector's parking fees decreased by $30 each week. B Parking cost a flat fee of $30. Parking cost $30 per day. Hector got a $30 discount to park his SUV.
The slope of the line represent Parking cost $30 per day. The correct answer is C.
The slope of a line represents the rate of change between two variables. In this case, the line represents the relationship between Hector's parking fees and the number of days he parked his SUV.
The unit of the slope of the ine represents
Cost/ number of days = 30 $/day
The fact that the slope is negative (-$30) means that for each additional day Hector parked his SUV, his parking fees decreased by $30. This indicates that the parking fee is a function of the number of days parked, and it costs $30 per day. The correct option is C.
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--The given question is incomplete, the complete question is given
" Hector parked his SUV in long-term parking while he traveled to China. What does the slope of the line represent?
A Hector's parking fees decreased by $30 each week.
B Parking cost a flat fee of $30.
C Parking cost $30 per day.
D Hector got a $30 discount to park his SUV. "--
can someone help please ? GIVING BRAINLIST TO ANYONE WHO ANSWERS!!
Answer: 2.46
Step-by-step explanation:
Since you are compounding interest annually, your formula is:
[tex]A=P(1+r)^{t}[/tex]
P=principal, what you start with =97000
r= rate of increase, changed to decimal
t=years increased = 16
A= what you end up= 143000
Plug it all in:
[tex]A=P(1+r)^{t}[/tex]
[tex]143000=97000(1+r)^{16}[/tex] >divide both sides by 97000
1.474 = [tex](1+r)^{16}[/tex] > take the 16th root of both sides or ^(1/16)
1.0246 = 1+r >subtract 1 from both sides
r=.0246 >change to percent by moving decimal over 2
Rate = 2.46%
Besides the 3 discontinuities (infinite, removable and jump) name 3 scenarios in which the derivative does not exist. Draw a sketch of the situation.
The function may still be continuous.
The lack of differentiability only implies that the function is not smooth at that point.
How to find that either the derivative exists or not?Here are three scenarios in which the derivative of a function may not exist, along with a sketch of each situation:
Corner: A function may not be differentiable at a corner, where the graph abruptly changes direction.
At a corner, the left and right-hand limits of the derivative do not match. Here is a sketch of the situation:
/
/
/
/
/
---------------/----------------
Cusp: A function may not be differentiable at a cusp, where the graph has a sharp point.
At a cusp, the left and right-hand limits of the derivative approach different values. Here is a sketch of the situation:
/
/
/
/
/
------/--------
\
\
\
\
\
Vertical tangent: A function may not be differentiable at a vertical tangent, where the graph has a vertical line tangent to the curve.
At a vertical tangent, the derivative is either infinite or undefined. Here is a sketch of the situation:
|
|
------|-------
|
|
Note that in all three of these situations, the function may still be continuous.
The lack of differentiability only implies that the function is not smooth at that point.
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f(x) = ln √(4x+5)/√(7x-4) f(x) = _____
The function can be expressed in terms of natural logarithms as f(x) = (1/2) ln (4x+5) - (1/2) ln (7x-4).
The function is, f(x) = ln √(4x+5)/√(7x-4)
First, note that we can simplify the expression inside the natural logarithm by applying the rules of radicals:
√(4x+5)/√(7x-4) = (4x+5)^(1/2) / (7x-4)^(1/2)
Now, we can apply the rule for the logarithm of a quotient, which states that:
ln (a/b) = ln a - ln b
Using this rule, we can rewrite the given function as:
f(x) = ln [(4x+5)^(1/2) / (7x-4)^(1/2)]
= ln (4x+5)^(1/2) - ln (7x-4)^(1/2)
Next, we can apply the rule for the logarithm of a power, which states that:
ln a^n = n ln a
Using this rule, we can simplify the logarithms in the expression above:
f(x) = (1/2) ln (4x+5) - (1/2) ln (7x-4).
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Directions: Write an equation for the circle shown on the graph in standard form. 15.
Answer: x(squared) + (y + 2)(squared) = 36
Step-by-step explanation:
The center of the circle is at (0 , -2), so we will eliminate the x value by just writing x(squared), and then we will write the y value as (y + 2)(squared) because the standard form for a circle is
(x - h)(squared) + (y + 2)(squared) = r(squared)
And if we count from the center to the top point of the circle, the number would be 6, so we would square 6 which would be 36.
Antawn Jamison lanza tiros libres. Anotar o fallar los tiros libres no cambia la probabilidad de que anote en el siguiente tiro, y él anota 73\%73%73, percent de sus tiros libres. ¿Cuál es la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres?
la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres es del 7.33%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
La probabilidad de que anote un tiro libre es del 73%, lo que significa que la probabilidad de que falle es del 27%.
La probabilidad de que anote sus próximos 9 tiros libres es:
0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 = 0.0733
Por lo tanto, la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres es del 7.33%.
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The diameter of a spherical ballon shrinks to one-half of it’s original size. Describe how the surface area and volume of the balloon change.
Answer:
when the diameter of a spherical balloon shrinks to one-half of its original size, the surface area of the balloon will decrease to one-fourth of its original size, while the volume will decrease to one-eighth of its original size.
Step-by-step explanation:
When the diameter of a spherical balloon shrinks to one-half of its original size, it means the new diameter is half of the original diameter.
Let's assume the original diameter of the balloon was "d," then the new diameter will be "d/2."
Surface Area:
The surface area of a sphere is given by the formula 4πr², where "r" is the radius of the sphere. Since the diameter of the sphere is halved, the radius will also be halved. Therefore, the new surface area (SA') of the balloon will be:
SA' = 4π (d/4)² = πd²/4
Thus, the new surface area of the balloon will be one-fourth (1/4) of the original surface area.
Volume:
The volume of a sphere is given by the formula (4/3)πr³. Again, since the diameter of the sphere is halved, the radius will also be halved. Therefore, the new volume (V') of the balloon will be:
V' = (4/3)π (d/4)³ = πd³/24
Thus, the new volume of the balloon will be one-eighth (1/8) of the original volume.
7. Eugene earns $2,700 monthly. He is going to be receiving a 3. 5% raise. With this new roise, he
believes he will earn more than $2,800 a month. Is Eugene correct in his thinking? Why or why
nol? Justifying your reasoning,
Summarize today's lesson:
Car Mr V Model 2017
Answer: Regarding "Car Mr V Model 2017," I'm not sure what you're asking. Can you please provide more context or a clear question?
Step-by-step explanation:
To determine if Eugene's thinking is correct, we need to calculate his new monthly salary with the 3.5% raise.
3.5% of $2,700 is (3.5/100) x $2,700 = $94.50
Eugene's new monthly salary is $2,700 + $94.50 = $2,794.50
So, Eugene's thinking is not correct. His new monthly salary with the 3.5% raise is $2,794.50, which is still less than $2,800.
Today's lesson was not provided in your question. Please provide a topic or question for me to provide a summary of today's lesson.
Regarding "Car Mr V Model 2017," I'm not sure what you're asking. Can you please provide more context or a clear question?
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A famer planted 154 tomato plants. 46 of the plants died. He replanted the plants in rows, with each row containing 9 plants. Which equation can be used to find p the number of rows the farmer planted
The equation we can use to find the number of rows the farmer planted is 108 = 9p.
To find the remaining number of plants, we subtract 46 from 154:
154 - 46 = 108 tomato plants
Now, the farmer replants the remaining plants in rows with 9 plants in each row. To find the number of rows (p), we can use the following equation:
108 = 9p
This equation represents the total number of remaining tomato plants (108) being divided into rows with 9 plants each, resulting in the number of rows (p).
Simplifying this equation will give us the value of p, which is:
p = 12
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Divide.
Simplify your answer as much as possible.
The polynomial expression becomes -20vz⁶ + 36v⁴z⁵ + 24v⁶ z⁶
How did we arrive at the above?In order to divide, first collect the like terms and then perform the operation. So, we have:
(-20vz⁶ + 32v⁴z⁵ +24v⁶ z⁶) + (4v⁴ z⁵) = -20vz⁶ + (32v⁴z⁵ +4v⁴ z⁵) + 24v⁶ z⁶
Simplifying the expression in parentheses, we get:
32v⁴z⁵ +4v⁴ z⁵ = 36v⁴z⁵
So, the expression becomes:
-20vz⁶ + 36v⁴z⁵ + 24v⁶ z⁶
This expression cannot be simplified any further.
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The following table gives the number of registered pleasure boats (in tens of thousands) and the number of manatee deaths caused by boats in florida for each year from 1991 to 2014. boats 'ten thousands) 68 manatee deaths 68 53 67 38 39 7 l 79 1 83 90 68
It appears that the relationship between the number of registered pleasure boats and manatee deaths fluctuates over the years. While there is no clear trend, it is important to consider the possible effects of increased boat registration on manatee populations.
The table you provided shows the number of registered pleasure boats (in tens of thousands) and the number of manatee deaths caused by boats in Florida from 1991 to 2014.
When the number of registered pleasure boats increases, there could be a higher likelihood of boat-related manatee deaths. As more boats are present in the water, manatees may face increased risks from boat strikes, which can lead to injuries or fatalities. Additionally, more boats may lead to habitat destruction, indirectly affecting manatee populations.
It is crucial for boat owners to follow safe boating practices to protect manatees and their habitats. Some measures to reduce manatee deaths include obeying speed limits in designated manatee zones, wearing polarized sunglasses to increase visibility, and being cautious in shallow areas where manatees might be feeding or resting.
In conclusion, the relationship between the number of registered pleasure boats and manatee deaths in Florida is complex and fluctuating. However, it is essential for boat owners to be aware of the potential risks and take necessary precautions to protect these gentle marine mammals.
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pls
show work NEATLY and make sure it is correct thank you
Question 1 < > Sketch the region enclosed by y = e, y = ez, and 2 = 1. Find the area of the region. Submit Question
The region enclosed by y = e and y = ez has an intersection point at (1, e), and the area of the region is infinite.
How to find the area of a region enclosed by curves using integration?To sketch the region enclosed by y = e, y = ez, and 2 = 1, and find the area of the region, follow these steps:
1. Analyze the given equations:
- y = e (a horizontal line with a constant value e ≈ 2.718)
- y = ez (an exponential curve)
- 2 = 1 (this equation is false and does not provide any relevant information for sketching the region)
2. Since the equation 2 = 1 is irrelevant, we'll focus on the two remaining equations.
3. Find the intersection points between y = e and y = ez:
Set y = e equal to y = ez and solve for x:
e = ex
Divide both sides by e:
1 = x
4. Sketch the region:
- Plot the horizontal line y = e
- Plot the exponential curve y = ez
- Mark the intersection point (1, e)
5. Determine the area of the region:
The region enclosed by the two given equations is unbounded, meaning that it extends infinitely in both the positive and negative x-directions. As a result, the area of the region is infinite.
In summary, the region enclosed by y = e and y = ez has an intersection point at (1, e), and the area of the region is infinite.
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75°(4x+7)° find x
(2x+10)°
(2x-10)° FIND X
The value of x using the assumptions of angle are 17 and 22.5
Finding the value of xFrom the question, we have the following parameters that can be used in our computation:
Angles: 75° and (4x + 7)°
Angles: (2x+10)° and (2x - 10)°
Assume 75° and (4x + 7)° are congruent angles, we have
4x + 7 = 75
So, we have
4x = 68
Divide by 4
x = 17
Assume (2x+10)° and (2x - 10)° are complementary angles, we have
2x + 10 + 2x - 10 = 90
So, we have
4x = 90
Divide by 4
x = 22.5
Hence, the values of x are 17 and 22.5
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Put the quadratic
y=2x^2-4x+2
into the quadratic formula
enter the number that belongs in the green box.
The quadratic formula for solving quadratic equations of the form ax^2 + bx + c = 0 is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
To put the quadratic equation y = 2x^2 - 4x + 2 into this formula, we need to identify the values of a, b, and c.
In this case, we have a = 2, b = -4, and c = 2. Substituting these values into the quadratic formula, we get:
x = (-(-4) ± sqrt((-4)^2 - 4(2)(2))) / (2 * 2)
x = (4 ± sqrt(16 - 16)) / 4
x = (4 ± 0) / 4
Simplifying this expression, we get:
x = 1 or x = 1/2
Therefore, the solutions to the quadratic equation y = 2x^2 - 4x + 2 are x = 1 and x = 1/2.
To explain this solution in more detail, we first need to understand the quadratic formula and how it can be used to solve quadratic equations. The quadratic formula is a formula that provides the solutions to any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.
In this case, we were given a specific quadratic equation, y = 2x^2 - 4x + 2, and we needed to find its solutions. To do this, we identified the values of a, b, and c and substituted them into the quadratic formula. We then simplified the expression to obtain the solutions, which were x = 1 and x = 1/2.
It is important to be able to use the quadratic formula to solve quadratic equations because many real-world problems can be modeled using quadratic equations. By being able to solve these equations, we can find important information such as the roots, or solutions, of the equation, which can help us make predictions and solve problems.
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Let f(x, y) = 1 - xy + y2 Compute fx(-2, 1) and fy(-2,1), and interpret these partial derivatives geometrically."
For the function f(x, y) = 1 - xy + y²= -y = -1, fy(-2,1) = 2y - x = 3.
When y is stationary, the rate of change of f with respect to x is determined by the partial derivative fx. Meanwhile, fy measures the rate of change of f in relation to y while holding x constant.
At the point (-2,1), the fx partial derivative symbolizes the incline of the level curve tangent line that follows the x-direction in relation to f. Its counterpart fy denotes the incline of the level curve tangent line that follows the y-direction regarding f at (-2,1).
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Complete answer - Let f(x, y) = 1 - xy + y² Compute fx(-2, 1) and fy(-2,1), and interpret these partial derivatives geometrically."
emma deposits $90 into a bank that pays 4% simple interest per year. calculate the value in dollars) of her deposit after 3 years? write the correct answer.
10.80
The value of Emma's deposit after 3 years, including simple interest, is $90 + $10.80 = $100.80.
Simple Interest = Principal x Rate x Time
In this case, the Principal is $90 (the initial deposit), the Rate is 4% (0.04 as a decimal), and the Time is 3 years.
Step 1: Calculate the simple interest.
Simple Interest = $90 x 0.04 x 3
Simple Interest = $10.80
Step 2: Add the simple interest to the initial deposit.
Total Value = Principal + Simple Interest
Total Value = $90 + $10.80
Total Value = $100.80
So, the value of Emma's deposit after 3 years is $100.80.
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Karissa wants to use the data to determine which brand is most absorbent. Based on the data collected at the beginning of the contest, enter the approximate number of paper towels needed to clean each square foot of the spill. Enter the number of Brand A paper towels needed per square foot in the first box. Enter the number of Brand B paper towels needed per square foot in the second box. Enter the number of Brand C paper towels needed per square foot in the third box
Answer:
Step-by-step explanation:
In the figure, is tangent to the circle at point U. Use the figure to answer the question.
Hint: See Lesson 3. 09: Tangents to Circles 2 > Learn > A Closer Look: Describe Secant and Tangent Segment Relationships > Slide 4 of 8. 4 points.
Suppose RS=8 in. And ST=4 in. Find the length of to the nearest tenth. Show your work.
1 point for the formula, 1 point for showing your steps, 1 point for the correct answer, and 1 point for correct units.
If you do not have an answer please dont comment
The length of UX (the length of a tangent segment to a circle) is approximately 4.9 inches.
To find the length of UX, we can use the formula for the length of a tangent segment to a circle:
Length of tangent segment = √(radius² - distance from center²)
In this case, we don't know the radius or the distance from the center, but we can use the fact that RU is perpendicular to UT to find them:
RU = RS + ST = 8 + 4 = 12 in.
UT = radius = RU/2 = 12/2 = 6 in.
Now we can plug these values into the formula:
Length of tangent segment = √(6² - 4²) ≈ 4.9 in.
Therefore, the length of UX is approximately 4.9 inches.
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how many favorable outcomes will there be for spinning the same color twice?
The number of favorable outcomes for spinning the same color twice will depend on the number of colors on the spinner.
If there are only two colors on the spinner, such as red and blue, then there will be only one favorable outcome, which is spinning either red or blue twice.
If there are more than two colors on the spinner, the number of favorable outcomes will depend on the number of times each color appears on the spinner.
For example, if there are four colors on the spinner, and each color appears equally, then there will be four favorable outcomes: spinning red twice, spinning blue twice, spinning green twice, or spinning yellow twice.
In general, if there are n colors on the spinner and each color appears with equal probability, then the number of favorable outcomes for spinning the same color twice will be n.
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PLEASE I NEED HELP I WILL MARK BRAINLEIST!!!!!!!!!!!!!
The table displays data collected, in meters, from a track meet.
three fourths 3 1 8
5 one fourth three fifths seven halves
What is the median of the data collected?
3.5
3
2
1
Answer:
2
Step-by-step explanation:
The median of a data set is the middle value when the data is arranged in order of size.
If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.The given table of data is:
[tex]\begin{array}{|c|c|c|c|}\cline{1-4}\vphantom{\dfrac12}\frac{3}{4}&3&1&8\\\cline{1-4}\vphantom{\dfrac12}5&\frac{1}{4}&\frac{3}{5}&\frac{7}{2}\\\cline{1-4}\end{array}[/tex]
Arrange the data in order of size:
[tex]\dfrac{1}{4},\;\dfrac{3}{5},\;\dfrac{3}{4},\;1,\;3,\;\dfrac{7}{2},\;5,\;8[/tex]
As there are 8 data values, the median is the average of the two middle values.
The two middle values are 1 and 3.
The average of 1 and 3 is 2:
[tex]\dfrac{1+3}{2}=\dfrac{4}{2}=2[/tex]
Therefore, the median of the given data is 2.
Find the measure of ZB b 60⁰
Answer: b = 30°
Step-by-step explanation:
The little square represents a 90-degree angle.
90° - 60° = b
30° = b
b = 30°
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The true triangle statement regarding the diagram are:
1. m∠5 + m∠6 = 180° ________Linear Pair
2. ∠ 2+ ∠ 3 = ∠ 6________Exterior angle Property of Triangle
3. m∠2 + m∠3 + m∠5 = 180°________Triangle Sum Property
What is the angle measurement?From the question, Δ ABC with Exterior angles as ∠ 1 , ∠ 4 ,and ∠ 6
Note that the Exterior angle Property of Triangle state that An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Hence: For Exterior ∠ 1 :
∠ 1 = ∠ 5 + ∠ 3 ________Exterior angle Property of Triangle
Also,
For Exterior ∠ 4:
∠ 4 = ∠ 5 + ∠ 2 ________Exterior angle Property of Triangle
Also,
In regards to Exterior ∠ 6:
∠ 6 = ∠ 2 + ∠ 3 ________ Exterior angle Property of Triangle
Using Triangle Sum Property, it state that In a triangle sum of the measures of angles is equal to 180° Hence: m∠2 + m∠3 + m∠5 = 180° ________Triangle Sum Property
The Linear Pair will be: The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Therefore, m∠5 + m∠6 = 180° ________Linear Pair
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See full question below
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 =
m∠6 m∠2 + m∠3 + m∠5 = 180°
Find the value of x.
If necessary, round your answer to the nearest tenth.
O is the center of the circle.
The figure is not drawn to scale. Hint: Draw in the radius for both chords.
Remember radii are equal in the same circle.
FG I OP, RS 1 o.
FG = 25, RS = 28, OP = 19
R
P
19
S
The value of x is 26.5, found using the property of intersecting chords in a circle and the Pythagorean theorem.
How to find the value of x in a circle with intersecting chords?To find the value of x, we can use the property that states that if two chords intersect in a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.
In this case, we can draw radii from O to points P and S, and label their lengths as 19. Then, we can label the segments of chords FG and RS as follows:
Let a = FG and b = GP
Let c = RS and d = SP
Since OP is a radius of the circle, we know that a + b = 19. Similarly, since OS is a radius of the circle, we know that c + d = 19.
Using the property mentioned above, we can write:
a * b = c * d
Substituting the given values, we get:
25 * (19 - b) = 28 * (19 - d)
Expanding and simplifying, we get:
475 - 25b = 532 - 28d
Substituting a + b = 19 and c + d = 19, we get:
b = 19 - a and d = 19 - c
Substituting these values, we get:
25a - 25(19 - a) = 28c - 28(19 - c)
Simplifying, we get:
53a - 475 = 28c - 532
Rearranging, we get:
53a - 28c = -57
We also know that a + c = 25 + 28 = 53.
We can solve these two equations simultaneously to find the values of a and c:
a = 13.8
c = 39.2
Therefore, the length of the segment RS is 39.2, and the length of the segment RP19S is 58.2.
Using the Pythagorean theorem, we can find the length of the segment OP:
(OP)²= (RP19S)² - (19)²
(OP)² = (58.2)² - (19)²
(OP)² = 3136.24
OP = 56
Finally, we can find x using the fact that the chords FG and RS are parallel:
x = (1/2) * (FG + RS)
x = (1/2) * (25 + 28)
x = 26.5 (rounded to the nearest tenth)
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one year ago, jay was 140 cm tall. He is 5% taller now than he was then. How tall is Jay now?
Answer:
Recall 5%=.05 as a decimal. Then multiply 140(.05)=7 to get how many centimeters he grew. Add 140+7=147 to get his current height.
As part of an exercise regimen, the probability of a person running outside is 0.45, the probability of a person joining a gym is 0.40, and the probability of a person both running outside and joining a gym is 0.25. what is the probability that a person either runs or joins a gym?
The probability that a person either runs outside or joins a gym is 0.60 or 60%.
To find the probability that a person either runs outside or joins a gym, you can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where A is the event of running outside, B is the event of joining a gym, and "and" represents the intersection of both events.
Given:
P(running outside) = 0.45
P(joining a gym) = 0.40
P(both running outside and joining a gym) = 0.25
Plug these values into the formula:
P(either runs or joins a gym) = 0.45 + 0.40 - 0.25
Calculate the result:
P(either runs or joins a gym) = 0.60
Therefore, the 60% of person either runs outside or joins a gym
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March 1, 2020, Dorchester Company's beginning work in process inventory had 6,000 units. This is its only production department. Beginning WIP units were 50% complete as to conversion costs. Dorchester introduces direct materials at the beginning of the production process. During March, all beginning WIP was completed and an additional 24,500 units were started and completed. Dorchester also started but did not complete 6,500 units. These units remained in ending WIP inventory and were 50% complete as to conversion costs. Dorchester uses the weighted-average method. Use this information to determine for March 2020 the equivalent units of production for conversion costs. Round to whole number (no cents)
For March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.
To determine the equivalent units of production for conversion costs in March 2020 for Dorchester Company, we need to follow these steps:
Calculate the equivalent units for the beginning work in process inventory:
Beginning WIP units = 6,000
Completion percentage for conversion costs = 50%
Equivalent units for beginning WIP = 6,000 * 50% = 3,000
Calculate the equivalent units for the units started and completed during March:
Units started and completed = 24,500
Completion percentage for conversion costs = 100%
Equivalent units for started and completed units = 24,500 * 100% = 24,500
Calculate the equivalent units for the ending work in process inventory: Ending WIP units = 6,500
Completion percentage for conversion costs = 50%
Equivalent units for ending WIP = 6,500 * 50% = 3,250
Sum up the equivalent units from steps 1, 2, and 3:
Total equivalent units for conversion costs = 3,000 (beginning WIP) + 24,500 (started and completed units) + 3,250 (ending WIP) = 30,750
So, for March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.
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