The volume of the solid is (7π - 8√2)/12 cubic units.
To find the volume of the solid enclosed by the cone and sphere in cylindrical coordinates, we first need to express the equations of the cone and sphere in cylindrical coordinates.
Cylindrical coordinates are expressed as (ρ, θ, z), where ρ is the distance from the origin to a point in the xy-plane, θ is the angle between the x-axis and a line connecting the origin to the point in the xy-plane, and z is the height above the xy-plane.
The cone z = x^2 + y^2 can be expressed in cylindrical coordinates as ρ^2 = z, and the sphere x^2 + y^2 + z^2 = 2 can be expressed as ρ^2 + z^2 = 2.
To find the limits of integration for ρ, θ, and z, we need to visualize the solid. The cone intersects the sphere at a circle in the xy-plane with radius 1. We can integrate over this circle by setting ρ = 1 and integrating over θ from 0 to 2π.
The limits of integration for z are from the cone to the sphere. At ρ = 1, the cone and sphere intersect at z = 1, so we integrate z from 0 to 1.
Therefore, the volume of the solid enclosed by the cone and sphere in cylindrical coordinates is
V = ∫∫∫ ρ dz dρ dθ, where the limits of integration are
0 ≤ θ ≤ 2π
0 ≤ ρ ≤ 1
0 ≤ z ≤ ρ^2 for ρ^2 ≤ 1, and 0 ≤ z ≤ √(2 - ρ^2) for ρ^2 > 1.
Integrating over z, we get
V = ∫∫ ρ(ρ^2) dρ dθ for ρ^2 ≤ 1, and
V = ∫∫ ρ(√(2 - ρ^2))^2 dρ dθ for ρ^2 > 1.
Evaluating the integrals, we get
V = ∫0^1 ∫0^2π ρ^3 dθ dρ = π/4
and
V = ∫1^√2 ∫0^2π ρ(2 - ρ^2) dθ dρ = π/3 - 2√2/3
Therefore, the total volume of the solid enclosed by the cone and sphere in cylindrical coordinates is
V = π/4 + π/3 - 2√2/3
= (7π - 8√2)/12 cubic units
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The given question is incomplete, the complete question is:
Use cylindrical coordinates Find the volume of the solid that is enclosed by the cone z = x^2 + y^2 and the sphere x^2 + y^2 + z^2 = 2
The point at which a company's costs equal its revenues is the break-even point. C represents the cost, in dollars, of x units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even. That is, find the value of x for which C=R.
C=15x +300 and R=17.5x.
Question content area bottom
Part 1
How many units must be produced and sold in order to break even?
The number of units that must be produced and sold in order to break even = 120
Consider equation C = 15x +300
This equation represents the cost, in dollars, of x units of a product
and equation R = 17.5x represents the revenue, in dollars, from the sale of x units.
In order to find the number of units that must be produced and sold in order to break even, consider C = R
i.e., 15x + 300 = 17.5x
We solve this equation for x.
17.5x - 15x = 300
(17.5 - 15)x = 300
2.5x = 300
x = 300/(2.5)
x = 120
This is the required number of units.
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The equation for line c can be written as y=–67x–1. line d is parallel to line c and passes through (10,–9). what is the equation of line d?write the equation in slope-intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
y = -6/7x - 3/7 or 7y = -6x - 3
Step-by-step explanation:
I'm guessing you mean line c: y = -6/7x - 1
Parallel lines have same slope => line d will have slope = -6/7
y = mx + b
-9 = -6/7(10) + b
-9 = -60/7 + b
b = 60/7 - 9 = 60/7 - 63/7 = -3/7
y = -6/7x - 3/7
or 7y = -6x - 3
Find the function, f, that satisfies the following conditions f"(x)=-sin x/2, f'(π) = 0, f(π/3)=-3
The function f(x) = -4*sin(x/2) - 1 is the solution that meets the specified conditions.
To find the function, f, that satisfies the given conditions f"(x) = -sin(x/2), f'(π) = 0, and f(π/3) = -3, we need to integrate the given second derivative twice and apply the boundary conditions. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x).
1. Integrate f"(x) = -sin(x/2) with respect to x to find f'(x):
f'(x) = ∫(-sin(x/2)) dx = -2*cos(x/2) + C1, where C1 is the integration constant
2. Apply the boundary condition f'(π) = 0:
0 = -2*cos(π/2) + C1
C1 = 0, since cos(π/2) = 0.
3. Now, f'(x) = -2*cos(x/2).
4. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x):
f(x) = ∫(-2*cos(x/2)) dx = -4*sin(x/2) + C2, where C2 is the integration constant.
5. Apply the boundary condition f(π/3) = -3:
-3 = -4*sin(π/6) + C2
-3 = -4*(1/2) + C2
C2 = -1.
So, the function f(x) that satisfies the given conditions is f(x) = -4*sin(x/2) - 1.
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Find the average rate of change of the function over the given interval: f (x ) = 2^x + 1, [0, 2]
The average rate of change on the given interval is R = 3/2
How to find the average rate of change?To find the average rate of change on an interval [a, b], we need to use the formula:
R = (f(b) - f(a))/(b - a)
Here we have:
[tex]f(x) = 2^x + 1[/tex]
And the interval is [0, 2]
Then:
[tex]f(0) = 2^0 + 1 = 2\\\\f(2) = 2^2 + 1 = 5[/tex]
Then we will get.
R = (5 - 2)/(2 - 0) = 3/2
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Help translations and reflections
Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)
Explain about the reflection along the y-axis:A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).Given coordinates of points A, B and C
A(6, 10), B(2, -8), C(-4 , -7)
After reflection (x, y) ---> (-x, y).
Thus, Coordinates of image of points A', B' and C' are-
A'(-6, 10), B'(-2, -8), C'(4 , -7)
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what is the distinction between a positive and negative mean deviation in terms of meaning applied to the data values?
Positive mean deviation means that the data values are on average greater than the mean, while negative mean deviation means that the data values are on average lower than the mean. This provides insight into the distribution of the data and can help identify outliers or trends in the data.
Mean deviation is a measure of dispersion that indicates how much a set of data values varies from the mean value of the data set. A positive mean deviation indicates that the data values are larger than the mean value, while a negative mean deviation indicates that the data values are smaller than the mean value.
In other words, a positive mean deviation indicates that the data set tends to be higher than the average, while a negative mean deviation indicates that the data set tends to be lower than the average.
Therefore, the sign of the mean deviation reflects the direction of deviation of the data values from the mean value, whether above or below it, and it provides important information about the distribution of the data set.
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i need help fast look at photo
Step-by-step explanation:
B
26 = 13.5 + m/2.5; m = 31.25
26 = 13.5 + 31.25/2.5
26 = 13.5 + 12.5
26 = 26
A credit card has a 21. 99% APR, a minimum monthly payment of 3. 15%, and a current monthly statement balance of $3,651. 21. If there are $791. 25 in purchases and a payment of $210. 00 in the next month, what will be the next minimum monthly payment? Show your work
The next minimal monthly payment will be $110.54.
To calculate the next minimal monthly price, we want to follow these steps:
First, we want to calculate the interest charged at the current monthly statement stability.
To do that, we multiply the statement stability by using the monthly interest price. The monthly interest fee is the annual percentage rate (APR) divided by way of 12. consequently:
Interest charged = $3,651.21 x (21.ninety nine%/12) = $sixty seven.25
next, we upload the interest charged to the statement balance to get the new balance:
New stability = $three,651.21 + $sixty seven.25 = $three,718.46
We then subtract any payments made throughout the month. In this situation, the price was $210.00, so:
New balance after price = $three,718.46 - $210.00 = $3,508.forty six
Ultimately, we calculate the minimal monthly charge. The minimum month-to-month payment is the greater of $25 or 3.15% of the new stability. therefore:
Minimum month-to-month fee = max($25, 3.15% x $3,508.46) = $110.54
So, the next minimal monthly payment will be $110.54.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the axis of symmetry and the vertex for this function: h(x) = (x − 5)2 − 7
A graph of the axis of symmetry and the vertex for this function is shown below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function h(x) = (x - 5)² - 7 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -7.
In conclusion, the turning point and vertex is given by the ordered pair (5, -7).
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The salaries of professional baseball players are heavily skewed right with a mean of $3. 2 million and a standard
deviation of $2 million. A baseball analyst randomly selects 40 athletes and records the mean salary. Which of the
following best describes the sampling distribution of all possible samples of size 40?
skewed right with a mean of 3. 2 million and a standard deviation of 2 million
skewed right with a mean of 3. 2 million and a standard deviation of 0. 32 million
approximately Normal with a mean of 3. 2 million and a standard deviation of 2 million
approximately Normal with a mean of 3. 2 million and a standard deviation of 0. 32 million
The best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.
The sampling distribution of the mean of a sample is approximately normal if the sample size is sufficiently large, regardless of the distribution of the population from which the sample is drawn.
According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean, which is $3.2$ million. The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size, which is [tex]$2/\sqrt{40} \approx 0.3162$[/tex] million.
Therefore, the best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.
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I just need the answer to question 3
Answer:46.15% or rounded 46% of pulling a card higher than 8.
Step-by-step explantwenty. Well there are 6 cards higher than 8, which include 9, 10, jack, queen, king, and ace. There is 4 diffrent suites so do 6×4=24. Then do 24/52=0.4615
Answer: 46.15%
HELP ASAP ! Given the rectangle in this example, and a scale factor of 3.5, what are the side lengths of the new rectangle?
Answer:
Length: 22 inches × 3.5 = 77 inches
Width: 10 inches × 3.5 = 35 inches
Include all given digits mercury venus earth mars jupiter saturn uranus neptune distance from the sun (au) 0. 39 0. 72 1 1. 52 na 19. 18 30. 06 orbital period (years) 0. 242 0. 0616 1 1. 88 na 84. 0 165
The values of distance and orbital periods of planets Mercury is 0.39AU and 0.242yrs,Venus 0.72AU distance and 0.616yrs,Earth 1AU distance and 1yrs,Mars 1.52AUdistance and 1.88,Jupiter 5.2AUdistance and 1.88 ,Saturn N/Adistance and NA years as infromation is not provided,Uranus 19.18AUdistance and 84yrs,Neptune 30.06AUdistance and165yrs.
Based on the given information, here are some key facts about the planets in our solar system:
- Mercury is the closest planet to the Sun, with a distance from the Sun of 0.39 astronomical units (AU). It has an orbital period of 0.242 years.
- Venus is the second planet from the Sun, with a distance of 0.72 AU. Its orbital period is 0.616 years.
- Earth is the third planet from the Sun, with a distance of 1 AU. Its orbital period is 1 year.
- Mars is the fourth planet from the Sun, with a distance of 1.52 AU. Its orbital period is 1.88 years.
- Jupiter is the fifth planet from the Sun, with a distance of 5.2 AU. Its orbital period is 11.86 years.
- Saturn is the sixth planet from the Sun, with a distance of N/A AU. Its orbital period is N/A.
- Uranus is the seventh planet from the Sun, with a distance of 19.18 AU. Its orbital period is 84 years.
- Neptune is the eighth planet from the Sun, with a distance of 30.06 AU. Its orbital period is 165 years.
Therefore the the distance and orbital periods are in increasing arrangement mercury, venus, earth, mars, jupiter, saturn ,uranus, neptune distance from the sun.
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Express the quantity "14 revolutions per second" in radians per second. Write your answers in terms of pi
14 revolutions per second can be expressed as 28π radians per second.
A radian is an angle whose corresponding arc in a circle is equal to the radius of the circle. A revolution is a full rotation, or a complete, 360-degree turn.
1 revolution per second is expressed as 2π radians per second.
To calculate the number of radians in 14 revolutions per second, we have to multiply 2π by 14.
14 revolutions per second = 14 * 2π
= 28π radians per second
Thus, the answer to the given question comes out to be 28 π radians per second
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Candace is flipping a coin a certain number of times. The theoretical probability of her flipping tails on all flips is 1/32. How many times is she flipping the coin?
Candace is flipping the coin 5 times.
What is probability?The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.
The theoretical probability of flipping tails on any single flip of a fair coin is 1/2, since there are two equally likely outcomes (heads or tails) on each flip.
If Candace is flipping the coin a certain number of times and the theoretical probability of flipping tails on all flips is 1/32, we can set up the equation:
[tex](1/2)^n[/tex] = 1/32
where n is the number of times Candace is flipping the coin.
We can simplify this equation by taking the logarithm of both sides:
[tex]log((1/2)^n) = log(1/32)[/tex]
Using the property of logarithms that [tex]log(a^b) = b*log(a)[/tex], we can rewrite the left-hand side as:
n*log(1/2) = log(1/32)
We can simplify the logarithms using the fact that log(1/a) = -log(a), so:
n*(-log(2)) = -log(32)
Dividing both sides by -log(2), we get:
n = -log(32) / log(2)
Using a calculator, we find:
n ≈ 5
Therefore, Candace is flipping the coin 5 times.
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Calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis. calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic.
The cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.
To calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis, you would first need to determine the overall proportion of women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week in the sample. Let's say this proportion is 0.20.
Next, you would multiply this proportion by the total sample size to get the expected count. Let's say the total sample size is 500 women. The expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week would be:
Expected count = 0.20 x 500 = 100
To calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic, you would need to subtract the expected count from the observed count for this cell, square the difference, and divide by the expected count. Let's say the observed count for this cell is 80.
Contribution to chi-square = (80 - 100)^2 / 100 = 4
This means that the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.
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Help Pythagorean Theorem quickly please
Answer:
[tex]h = \sqrt{ {21}^{2} - {19}^{2} } = \sqrt{441 - 361} = \sqrt{80} = 4 \sqrt{5} [/tex]
h = 4√5 feet = 8.9 feet
Write a number that is greater than 10,910,099,999 but less than 11,000,000,000
Answer: 10, 911,000,000
Step-by-step explanation:
10,911,000,000 < 11,000,000,000
10,911,000,000 > 10,910,099,999
A piece of equipment costs $75,000 new but depreciates 12% per year in each succeeding year . Find its value after 8 years
The equipment's value after 8 years, given its original value was $75,000 and it depreciates by 12% each year, is approximately $27,506.62.
To find the value of the equipment after 8 years, we need to calculate its value at the end of each year, taking into account the 12% depreciation per year.
At the end of year 1, the equipment will be worth 88% of its original value
Value at end of year 1 = 0.88 x $75,000 = $66,000
At the end of year 2, the equipment will be worth 88% of its value at the end of year 1
Value at end of year 2 = 0.88 x $66,000 = $58,080
We can continue this process for each year
Value at end of year 3 = 0.88 x $58,080 = $51,206.40
Value at end of year 4 = 0.88 x $51,206.40 = $45,065.91
Value at end of year 5 = 0.88 x $45,065.91 = $39,654.02
Value at end of year 6 = 0.88 x $39,654.02 = $34,991.23
Value at end of year 7 = 0.88 x $34,991.23 = $31,191.80
Value at end of year 8 = 0.88 x $31,191.80 = $27,506.62
Therefore, the value of the equipment after 8 years is $27,506.62.
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HELP! In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation
free scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 703. 27
and a standard deviation of 34. 14. A score of 700 is needed to earn 3 points
To find the probability of scoring at least 700 points on the Algebra EOC, we calculate the z-score, which is -0.122, and then find the area under the standard normal curve using a z-table. The probability is 54.98%. Since this is higher than the significance level of 0.05, we can conclude that the student has met the requirement to earn 3 points on the EOC.
Identify the mean, standard deviation, and score needed to earn 3 points
Mean (μ) = 704.39
Standard deviation (σ) = 36.18
Score needed for 3 points = 700
Calculate the z-score for the score needed to earn 3 points
z = (score - μ) / σ
= (700 - 704.39) / 36.18
= -0.122
Look up the area to the left of the z-score in the standard normal distribution table
The area to the left of -0.122 is 0.4502.
Subtract the area found in step 3 from 1 to find the area to the right of the z-score
Area to the right = 1 - 0.4502 = 0.5498
Convert the area to the right into a percentage
Percentage = 0.5498 x 100% = 54.98%
Interpret the percentage as the probability of earning 3 points or more on the Algebra EOC exam:
The probability of earning 3 points or more on the Algebra EOC exam is 54.98%.
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--The given question is incomplete, the complete question is given
" In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation
free scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 704.39
and a standard deviation of 36.18. A score of 700 is needed to earn 3 points.
a. Fill in the values of each standard deviation above and below the mean, and make sure to add in the value
of the mean. Answers only are fine. "--
if a researcher finds a small difference in average test scores between a large sample (over 700) of experimental participants and a large sample (same size) of control participants, it is very likely that the difference is
The null and alternative hypotheses are H₀: μ₁ - μ₂ = 0 and H₁: μ₁- μ₂ ≠ 0 and the test statistic value is equal to 0.45.
The null hypothesis (H₀) states,
That there is no significant difference between the population means of the experimental group and the control group.
The alternative hypothesis (H₁) states that there is a significant difference between the two means.
State the hypotheses as,
H₀: μ₁ - μ₂ = 0 (there is no difference in means)
H₁: μ₁- μ₂ ≠ 0 (there is a difference in means)
where μ₁ is the population mean of the experimental group
And μ₂ is the population mean of the control group.
The test statistic,
Use the t-test formula,
t = (x - μ) / (s / sqrt(n))
where x is the sample mean = 102
μ is the hypothesized population mean = 100
s is the sample standard deviation =88
n is the sample size= 10
Plugging in the values, we get,
t = (102 - 100) / (88 / sqrt(10))
= 0.45
Therefore, the null and the alternative hypotheses states that H₀: μ₁ - μ₂ = 0 there is no difference in means and H₁: μ₁- μ₂ ≠ 0 there is a difference in means and the test statistic for a sample mean of 102 is 0.45.
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The given question is incomplete, I answer the question in general according to my knowledge:
If a researcher finds a small difference in average test scores between a large sample of 700 experimental participants with a standard deviation of 88, a mean of 100, and with a sample size of 10.
a. State the null and the alternative hypotheses.
b. Compute the test statistic for sample mean 102.
The rule is x→y=−2x. Can you mark all the points that fit the rule on a coordinate plane?
Yes, the points that fit the rule x→y=−2x can be plotted or marked on a coordinate plane, and will form a straight line passing through the origin with a slope of -2.
The rule x→y=−2x means that for every value of x, the corresponding value of y is equal to -2 times x. To plot the points that fit this rule, we can choose some values of x, substitute them into the equation, and then plot the resulting points on the coordinate plane.
For example, if we choose x=1, then y=−2x=−2(1)=−2. So the point that fits the rule is (1, −2). Similarly, if we choose x=2, then y=−2x=−2(2)=−4. So the point that fits the rule is (2, −4).
We can continue this process for other values of x, and plot all the resulting points on the coordinate plane. The resulting graph will be a straight line that passes through the origin, with a slope of -2. This means that all the points that fit the rule will lie on this line.
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Find the value of c step by step
PLEASE HELP
Answer:
c = 12
Step-by-step explanation:
[tex] {5}^{2} + {c}^{2} = {13}^{2} [/tex]
[tex]25 + {c}^{2} = 169[/tex]
[tex] {c}^{2} = 144[/tex]
[tex]c = 12[/tex]
What is the surface area of this right triangular prism?
The surface area of the triangular prism is 720in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as
SA = 2B +ph
where p is the perimeter of the base and h is the height of the prism.
Base area = 1/2 bh
= 1/2 × 24 × 5
= 12 × 5
= 60 in²
Perimeter of the base = 24 +13 +13
= 50 in²
the height of the prism = 12 in
therefore SA = 2 × 60+ 12 × 50
= 120 + 600
= 720 in²
Therefore the surface area of the prism is 720 in²
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The school budget for e-readers was $40,000 in 2014. The budget for 2015 was 20% less than the budget for 2014. What was the school budget for e-readers in 2015?
Answer: 32000
Step-by-step explanation: 40000 x 80% because you still have 80 percent of that budget so you minus 20 for 100.
4. What is the difference in the radii of the circles? (3 points) (this is for the ana circle question
The difference between the radii of the two circular tracks is 15ft
How do we calculate?The total length of track 1 is 220ft, which means that the circumference of the circle is 220ft
we find the diameter of each track.
The circumference of a circle can be found using the formula
P = πd
d = P /π
track 1, we have
d1 = P1 / π
d1 = 220 / π
d1 = 70.03 ft.
track 2, we have
d2 = P2 / π
d2 = 126 / π
d2 = 40.11 ft.
radius of tract 1 = 35.01 ft
radius of track 2 = 20.05 ft
The difference between the two track radius is
∆r = r1 - r2
∆r = 110 / π - 63 / π
∆r = (110 - 63) / π
∆r = 47 / π
∆r = 14.96 ft.
∆r = 15 ft
In conclusion, difference between the radii of the two circular tracks is 15ft
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#complete question:
What is the difference between the radii of the two circular tracks? Answer the questions to find out.
1. Are the distances of 220 feet and 126 feet the radii, diameters, or circumferences of the two circles?
Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
Step-by-step explanation:
Based on the diagram and the given lengths of sides AC and CB, we can use the triangle inequality theorem to determine the possible lengths of side AB.
According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore:
AC + CB > AB
27 + 54 > AB
81 > AB
Also, using the same theorem, we can see that:
AB + AC > CB
AB + 27 > 54
AB > 54 - 27
AB > 27
Therefore, we have:
27 < AB < 81
So, the answer is: 27 < AB < 81
Answer:
Based on the information given, the possible lengths of segment AB can be determined using the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can apply the theorem to sides AC and CB to find the possible range of values for side AB.
Since AC has a length of 27 and CB has a length of 54, we can write two inequalities based on the Triangle Inequality Theorem:
AB + 27 > 54 AB + 54 > 27
Solving each inequality for AB, we get:
AB > 27 AB > -27
Since the length of a side of a triangle must be positive, we can disregard the second inequality. Therefore, the possible range of values for side AB is AB > 27.
However, it’s important to note that you mentioned a diagram in your message but did not provide it. Without seeing the diagram, I cannot determine if there are any additional constraints on the length of side AB.
Step-by-step explanation:
9. Ms. Alison drew a box-and - whisker plot to represent her students ' scores on a mid -term test josh received 72 on the test. Describe how his score compared to those of his classmates. About 25% scored higher; about 75% scored lower. Everyone scored higher. No one scored higher. About 50% scored higher, about 50% scored lower.
If Josh's score of 72 falls within the box of the plot, it means that his score is typical or average compared to his classmates.
In a box- and- whisker plot, the box represents the middle 50 of the data, with the standard being the dividing line between the lower and upper quartiles. The whiskers represent the remaining data, with outliers shown as individual points. Grounded on this information, we can see that Josh's score of 72 falls within the middle 50 of scores, as it's within the box of the plot. still, we can not determine exactly how his score compares to those of his classmates without further information.
Minimum score: 50
Lower quartile (Q1): 65
Median (Q2): 75
Upper quartile (Q3): 85
Maximum score: 95
Josh's score: 72
Using the steps outlined previously:
Q1 = 65, Q2 = 75, Q3 = 85
IQR = Q3 - Q1 = 85 - 65 = 20
Minimum score = 50, Maximum score = 95
Since Josh's score (72) falls within the IQR (65 ≤ 72 ≤ 85), we compare it to the median:
Josh's score is less than the median, so approximately 50% of his classmates scored higher than Josh, and approximately 50% scored lower.
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1. deagan is painting a mural of a triangle for a lwhs conference room. the
triangular-shaped mural will be a total of 289 square feet; the height is 25
feet. what is the measure ofthe base?
question involving a mural painted by Deagan, which features a triangle, for a conference room at LWHS. You'd like to know the measure of the base.
Unfortunately, it seems that some essential information is missing from your question, such as the dimensions or other properties of the triangle. In order to accurately answer your question and calculate the measure of the base, please provide more information about the triangle or any related information given in the problem.
Once you provide the necessary information, I'd be happy to help you find the measure of the base and explain the process step-by-step!
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answer please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9/7
explain:
(36-27) 7
9/7
