Change the triple integral to spherical coordinates: MS 62+y2+z2yžov Where Q is bounded by the upper hemisphere : x2 + y2 +22 = 100. .10 ,* 1.*pºsing dpdøde $5*1pºsinø dpdøde 5655*p? sing dpdøde *** .2 10 ? 0 T 10 p3 sino dpdøde
Answers
To change the triple integral to spherical coordinates, we consider the integral of the function MS = 62 + y^2 + z^2 in the region Q, which is bounded by the upper hemisphere x^2 + y^2 + z^2 = 100. The integral can be expressed in spherical coordinates as ∫∫∫ Q (62 + ρ^2 sin^2φ) ρ^2 sinφ dρ dφ dθ.
In spherical coordinates, the triple integral is expressed as ∫∫∫ Q f(x, y, z) dV = ∫∫∫ Q f(ρ sinφ cosθ, ρ sinφ sinθ, ρ cosφ) ρ^2 sinφ dρ dφ dθ, where ρ is the radial distance, φ is the polar angle, and θ is the azimuthal angle.
In this case, the function f(x, y, z) = 62 + y^2 + z^2 can be rewritten in spherical coordinates as f(ρ sinφ cosθ, ρ sinφ sinθ, ρ cosφ) = 62 + (ρ sinφ sinθ)^2 + (ρ cosφ)^2 = 62 + ρ^2 sin^2φ.
The region Q is bounded by the upper hemisphere x^2 + y^2 + z^2 = 100. In spherical coordinates, this equation becomes ρ^2 = 100. Therefore, the limits of integration for ρ are 0 to 10, for φ are 0 to π/2 (since it represents the upper hemisphere), and for θ are 0 to 2π (covering a full circle).
Putting it all together, the integral in spherical coordinates is ∫∫∫ Q (62 + ρ^2 sin^2φ) ρ^2 sinφ dρ dφ dθ, where ρ ranges from 0 to 10, φ ranges from 0 to π/2, and θ ranges from 0 to 2π.
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Related Questions
B = 54°, b=15, c=
c = ? (Round answers to
the nearest hundredth.)
Answers
Answer:
18.54
Step-by-step explanation:
sine is opposite/hypotenuse, and you have opposite (b=15), so use that
sin(54) = 15/c
c = 15/sin54
then use calculator
c = 18.54
Equations, graphs, Slopes and y-intercepts : application
Answers
Answer:
the answer to the graph is y=-4x-3
Answer:
y = -4x - 3
Step-by-step explanation:
The given line has :-
slope = -4y-intercept = (0, -3)Substituting in slope-intercept form
y = mx + by = -4x - 3someone pls help
asap
ty :)
Answers
Answer:
56%
Step-by-step explanation:
We know that there are 6 groups of 6 and 4 groups of 5.
6x6 = 36
4x5 = 20
Add them up. 36 + 20 = 56.
Add the percent sign for 56%.
Answer:
56%
Step-by-step explanation:
a random sample of 200 voters in a town is selected, and 114 are found to support annexation suit. find the 96% confidence interval for the fraction of the voting population favoring the suit.
Answers
The 96% confidence interval for the fraction of the voting population favoring the suit is 0.498< p< 0.642.
Here we have to find the confidence interval.
Given
Sample, n = 200 voters
Let x represent those that support the annexation suit.
x = 114
First, we have to calculate the probability of supporting the annexation suit.
Let p represent the probability of supporting the annexation suit.
p = x/n
p = 114/200
p = 0.57
From elementary probability;
p + q = 1 where q represents the probability of failure.
In this case, q represent the probability of not supporting the annexation suit
Substitute 0.57 for p
0.57 + q = 1
q = 1 - 0.57
q = 0.43
To find the 96% confidence interval for the fraction of the voting population favoring the suit;
The confidence interval is bounded by the following;
^p - z(α/2) √(pq/n) < p < ^p + z(α/2) √(pq/n)
At this point, we have values for p,q, and n.
Next is to solve z(α/2)
First, we'll find the value of α/2 using
C.I = 100%(1 - α) where C.I = 96%
96% = 100%(1 - α)
1 - α = 96%
1 - α = 0.96
α = 1 - 0.96
α = 0.04
So,
α/2 = 0.04/2
α/2 = 0.02
So, z(α/2) = z(0.02)
Using a normal probability table
z0.02 = 2.055 --- This is the closest value which leaves an area of 0.02 to the right and 0.98 to the left
Recalling our formula to solve 96% interval;
^p - z(α/2) √(pq/n) < p < ^p + z(α/2) √(pq/n)
By substitution, we have
0.57 - 2.055 * √(0.57*0.43/200) < p < 0.57 + 2.055 * √(0.57*0.43/200)
0.57 - 0.071939677073920 < p < 0.57 + 0.071939677073920
0.498060322926079 < p < 0.641939677073920 ---- Approximate
0.498 < p < 0.642
Therefore the confidence interval is 0.498<p<0.642.
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Pls help asappp solve for x
Answers
Answer:
65
Step-by-step explanation:
If you need explanation please tell me.
A recent study focused on the method of payment used by college students for their cell phone bills. Of the 1,220 students surveyed, 600 stated that their parents pay their cell phone bills. Use a 0.01 significance level to test the claim that the majority of college students' cell phone bills are paid by their parents.
Identify the null and alternative hypotheses for this scenario.
Test the claim that the majority of college students' cell phone bills are paid by their parents.
Answers
The significance level of 0.01 indicates that we want to use a 1% level of significance to evaluate the evidence against the null hypothesis.
The null and alternative hypotheses for testing the claim that the majority of college students' cell phone bills are paid by their parents can be stated as follows:
Null hypothesis (H0): The majority of college students' cell phone bills are not paid by their parents.
Alternative hypothesis (Ha): The majority of college students' cell phone bills are paid by their parents.
In this scenario, the null hypothesis assumes that the proportion of college students whose parents pay their cell phone bills is less than 50% (not a majority), while the alternative hypothesis suggests that the proportion is greater than or equal to 50% (a majority). The significance level of 0.01 indicates that we want to use a 1% level of significance to evaluate the evidence against the null hypothesis.
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A turtle travels 5/12 mile in 1/3 hour and a snail travels 1/8 mile in 3/4 hour. Which animal is faster?
Answers
Answer:
1/6 or 4/24 either one is correct
Step-by-step explanation:
Since the velocity of turtle is more than the Snail. Turtle is faster.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations. The distance formula is,
Distance = speed × time
It is given that, A turtle travels 5/12 mile in 1/3 hour and a snail travels 1/8 mile in 3/4 hour.
The distance travelled by the turtle,
d₁=v₁×t₁
5/12= v₁ × 1/3
v₁=15/12
v₁=1.25 miles / hour
The distance travelled by the snail ,
d₂=v₂×t₂
1/8=v₂ × 3/4
v₂=1/6 miles / hour
v₂= 0.16 miles / hour
v₁>v₂
Thus, the velocity of turtle is more than the Snail. Turtle is faster.
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what is the mean for the population of scores shown in the frequency distribution table? x f 5 1 4 2 3 3 2 4 1 2
Answers
The mean for the population of scores shown in the frequency distribution table x f 5 1 4 2 3 3 2 4 1 2 is 2.67. This means that the population's average score is 2.67.
The formula for calculating the mean (sometimes known as the average) of a population of scores is:
(sum of all scores) / mean (total number of scores)
We must first obtain the total of all scores in order to compute the mean of the population of scores indicated in the frequency distribution table. To do this, we multiply each score by its frequency (f) and then sum the results. For example, the product of 5 and 1 (the frequency) for the score 5 is 5. The product of 4 and 2 (the frequency) with the score 4 is 8. We repeat this process for all scores, then add up all the products to get the total score.
The sum of all scores is then divided by the entire number of scores, yielding the sum of all frequencies.
The mean is determined using the data from the frequency distribution table as follows:
(5 * 1 + 4 * 2 + 3 * 3 + 2 * 4 + 1 * 2) / (1 + 2 + 3 + 4 + 2) = (5 + 8 + 9 + 8 + 2) / 12 = 32 / 12 = 2.67
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Imagine you have five total nieces and nephews and their ages are 4, 10, 8, 9, and 5. What is the average age of your nieces and nephews? What is their median age?
Answers
Answer:
The mean is 7.2 and the median ( average) is 8
Step-by-step explanation:
4 + 10 + 8 + 9 + 5 = 36 / 5
The mean is 7.2 and the median ( average) is 8
Answer:
7.2 is the average.
8 is the median.
Step-by-step explanation:
Average = Sum/count
36/5 = 7.2
To find the median, you can take away numbers one by one on each side of the numerical order until you get down to the last number(s) in the middle. 8 is the middle number.
explain what is wrong with the following statement.
"Last year we had 80 students attend a concert. This year we have a 50% increase or a total of 160 students attend."
Answers
Answer:
If you had 80 students attend a concert and the next year you had 160 students attend, that is a 100% increase but if it increased by 50%, there would be 120 students attend. So the wrong part is the '50%'
use the unique factorization theorem to write the following integers in standard factored form. (a) 504 (b) 819 (c) 5,445
Answers
Using the Unique factorization theorem for the following integers the standard factored form of 504 is 2³ x 3²x 7 , for 819 is 3² ×7×13 and for 5,445 is 3²×5×7².
The Unique Factorization Theorem states that any positive integer can be written as a product of prime numbers in a unique way. To write each of the integers in standard factored form.
Using this theorem, we can factorize any positive integer into its prime factors. Here are the steps to factorize a number:
Find the smallest prime factor of the number. Divide the number by this prime factor, and repeat step 1 with the result. Continue this process until the result is 1.The prime factors obtained in this process can then be multiplied together to obtain the standard factored form of the original number . Therefore,
)504 = 2³ x 3² x 7)819 = 3² ×7×13)5,445 =3²×5×7²To learn more about 'Unique Factorization Theorem':
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jaimie ran 3 1/2 on monday.She ran half as far on teusday as she did on monday.How far did jaimie run in all on monday and teusday?
Answers
Answer: 5 1/4
Step-by-step explanation:
hope this helps!
An ice-cube tray of negligible mass contains 12 g of ice at −10 ∘
C.C ice
=2.05 kJ/(kgK),C w
=4.18 kJ/(kgK),C stcam
= 2.02 kJ/(kgK),L f
=333.5 kJ/kg (latent heat of fusion), L v
=2257 kJ/kg (latent heat of vaporization). (a) How much heat is required to convert all of the ice into 12 g of liquid water at 0 ∘
C ? (b) How much heat is required to convert the 12 g of liquid water at 0 ∘
C to 12 g of steam at 110 ∘
C ? An insulated beaker with negligible mass contains 0.25 kg of water at 75 ∘
C. (a) How many kilograms of ice at a temperature of −20 ∘
C must be dropped into the water to make the final temperature of the system 30 ∘
C ? (b) How much heat will be lost by the 0.25 kg of water when the system reaches 30 ∘
C ?
Answers
(a) The amount of heat required to convert all of the ice into 12 g of liquid water at 0 ∘C is 39.3 kJ, the heat capacity of ice is 2.05 kJ/(kgK), so the heat required to raise the temperature of the ice from −10 ∘C to 0 ∘C is 12 × 2.05 × 10 = 24.6 kJ.
The latent heat of fusion for ice is 333.5 kJ/kg, so the heat required to melt the ice is 12 × 333.5 = 399.2 kJ.
In total, the heat required to convert all of the ice into 12 g of liquid water at 0 ∘C is 24.6 + 399.2 = 423.8 kJ.
(b) The amount of heat required to convert the 12 g of liquid water at 0 ∘C to 12 g of steam at 110 ∘C is 2542.4 kJ.
The heat capacity of liquid water is 4.18 kJ/(kgK), so the heat required to raise the temperature of the water from 0 ∘C to 100 ∘C is 12 × 4.18 × 100 = 491.2 kJ.
The latent heat of vaporization for water is 2257 kJ/kg, so the heat required to vaporize the water is 12 × 2257 = 2708.4 kJ.
In total, the heat required to convert the 12 g of liquid water at 0 ∘C to 12 g of steam at 110 ∘C is 491.2 + 2708.4 = 3199.6 kJ.
(a) The amount of ice that must be dropped into the water to make the final temperature of the system 30 ∘C is 0.06 kg.
The heat capacity of water is 4.18 kJ/(kgK), so the heat lost by the water is 0.25 × 4.18 × (75 - 30) = 37.5 kJ.
The latent heat of fusion for ice is 333.5 kJ/kg, so the heat gained by the ice is 0.06 × 333.5 = 20.01 kJ.
In order for the heat lost by the water to equal the heat gained by the ice, the mass of the ice must be 37.5 / 20.01 = 0.187 kg.
(b) The amount of heat lost by the 0.25 kg of water when the system reaches 30 ∘C is 21.875 kJ.
The heat capacity of water is 4.18 kJ/(kgK), so the heat lost by the water is 0.25 × 4.18 × (30 - 20) = 21.875 kJ.
In this case, the heat lost by the water is greater than the heat gained by the ice, so the final temperature of the system will be 30 ∘C.
The amount of heat required to change the state of a substance is equal to the mass of the substance times the latent heat of fusion or vaporization. The heat capacity of a substance is the amount of heat required to raise the temperature of the substance by 1 degree.
In the first part of the problem, we need to calculate the amount of heat required to convert all of the ice into 12 g of liquid water at 0 ∘C.
The heat required to raise the temperature of the ice from −10 ∘C to 0 ∘C is calculated using the heat capacity of ice. The latent heat of fusion for ice is then used to calculate the heat required to melt the ice.
In the second part of the problem, we need to calculate the amount of heat required to convert the 12 g of liquid water at 0 ∘C to 12 g of steam at 110 ∘C. The heat required to raise the temperature of the water from 0 ∘C to 100 ∘C is calculated.
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Rearrange the equation so b is the independent variable.
4a + b = -52
Answers
Answer:
The answer is a = -13 - 1/4b
Step-by-step explanation:
Look at attachment:
Hope this helps! :)
if i take business stream , in the future should i take one science subject?
Answers
Answer:
take more
Step-by-step explanation:
What is f(3) if f(x) = - 4x+1 ?
A.-44
B.-11
C. 1/2
D. 13
Please help me! :/
Answers
Answer:
Here is the equation:
f(x)=4x+1f(x)=4x+1
You need to find f(3). To do that, substitute all the x's with 3:
f(x)=4x+1 \rightarrow f(3)=4\times3 + 1f(x)=4x+1→f(3)=4×3+1
The first thing you need to do is multiply 4 by 3. Multiply:
4 \times 3 = 124×3=12
Here is your new equation:
f(3)=12+1f(3)=12+1
To get your answer, you need to add 12 and 1. Add:
12+1 = 1312+1=13
That means:
\bf f(3)=13f(3)=13
Step-by-step explanation:
13 is the ans
mithali buys a t.v at 12,000 and sells it at a profit of 20% how much money she gets? reduce the fraction of cp and sp to the lowest form
Answers
Answer:
14,400
Step-by-step explanation:
Hope this helpfull..but if it's not,im so sorry
Parallel to y=−3x−2, through (-3, -3)
Answers
Answer:
Use the formula y-y1=m(x-x1) <---memorize this. The m here is the slope.
Step-by-step explanation:
The equation is in y=mx+b form
Remember mx=slope and b=y-intercept
The question wants you to find the equation that is Parallel to y=-3x-2 and passes through (-3,-3)=(x1,y1)
Parallel=same slope -3x
So now all that's left is to plug into the equation.
y-(-3)=-3(x-(-3))
y+3=-3(x+3) ----> positive - a negative = positive so x-(-x)=x+x
y+3=-3x-9 ----> distribute like terms(subtract 3 from 3 and 3 from -9)
y=-3x-12 - This is your answer, you can check by graphing it.
Could i get Brainlest? thx :)
5.09 quiz: isosceles and equilateral triangles what is the value for x?
Answers
The measure of [x] in the triangle will be 61°.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a triangle as shown in the image attached.
The given triangle is a isosceles triangle. So, we can write -
[x] + [x] + 58 = 180
2x + 58 = 180
2x = 122
x = 61
Therefore, the measure of [x] in the triangle will be 61°.
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Latoya needs to make a total of deliveries this week. So far she has completed of them. What percentage of her total deliveries has Latoya completed?
Answers
Answer: 35%
Step-by-step explanation:
You did not give the numbers. Let me help out by giving some figures and explain with that.
Latoya needs to make a total of 60 deliveries this week. So far she has completed 21 of them. What percentage of her total deliveries has Latoya completed?
To solve this, we divide 21 by 60 and then multiply by 100. This will be:
= (21 / 60) × 100
= 7/20 × 100
= 35%
The distance between the point (-3,4) and the point of origin
Answers
Answer:
5
Step-by-step explanation:
1) origin point is (0;0);
2) the required distance is:
\(d=\sqrt{(-3-0)^2+(4-0)^2} =5.\)
4.) A store is having a sale in which all items are marked 30% off.
4a.) Which equation represents the selling price, s, in dollars, of an item originally
priced p dollars after a markdown of 30%?
a.) s=0.3p
b.) s=0.7p
c.) p=0.35
d.) p=0.75
Answers
Answer:
0.70p
Step-by-step explanation:
"30% off" means paying only 70% of the original sales price (subtracting 30% from 100% yields 70%). Next, find the decimal equivalent of 70%:
It is 0.70. Finally, multiply the price p by 0.70: 0.70p (Answer b)
Answer:
d
Step-by-step explanation:
what are the pair of solutions?
Please help‼️ domain and range‼️
Answers
The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively
Calculating the domain and range of the graph?From the question, we have the following parameters that can be used in our computation:
The graph
The above graph is an exponential function
The rule of an function is that
The domain is the set of all real values
In this case, the domain is (-∝, ∝)
For the range, we have
Range = (0, ∝)
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A culture of bacteria has an initial population of 37000 bacteria and doubles every 2 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 7 hours, to the nearest whole number?
Answers
the population of bacteria in the culture after 7 hours is approximately 418470
To find the population of bacteria after 7 hours, we can use the formula you provided:
\(P_t = P_0 * 2^{t/d\)
Given:
P₀ = 37000 (initial population)
t = 7 (time in hours)
d = 2 (doubling time)
Plugging in the values, we get:
P₇ = 37000 * 2⁽⁷/²⁾
Now let's calculate the population:
P₇ = 37000 * \(2^{3.5\)
To calculate \(2^{3.5\), we can use the property that \(a^{b/2} = \sqrt{(a^b)\). So:
P₇ = 37000 * √(2⁷)
P₇ ≈ 37000 * √(128)
P₇ ≈ 37000 * 11.31
P₇ ≈ 418470
Therefore, the population of bacteria in the culture after 7 hours is approximately 418470 (to the nearest whole number).
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Help,anyone can help me do quetion
Answers
Answer:
B2--> the answer is 121 degrees.This is because due to alternate interior angles, the triangle
Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point (1,70) she made on her graph. After day 4, Lin reaches page 190, which does not match the point (4,160) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.Sketch a line showing Lin's original plan on the axes. Click on the graph and select edit to complete the graph. Once done, hit save and close to see your completed graph. What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
Answers
No. of pages read on day of planning are represented by vertical intercept.
The difference between vertical intercept of original plan and line drawn by Lin is 10 unit.
What is slope-intercept form of line?The slope intercept form equation for a straight line with a slope, 'm', and 'c' as the y-intercept can be given as:
y = mx + c.
Given,
No. of pages Lin read on day of planning = 30
No. of pages she plans to read everyday = 40
If total pages are y for x days then,
y = 40x + 30
which is the original plan of Lin.
comparing it with slope-intercept form of line
y = mx + c
slope m = 40
vertical intercept of original plan c = 30 unit
slope m represents the no. of pages read everyday.
vertical intercept represents the no. of pages read on day of planning.
vertical intercept c' of line drawn by Lin = 40 unit
Comparing intercept of original plan to line drawn by Lin
= |c - c'|
= |30 - 40|
= 10 unit
Hence, the vertical intercept represents the no. of pages read on day of planning.
There is 10 unit difference between vertical intercept of original plan and line drawn by Lin.
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For each of the following relations, decide if it is reflexive, symmetric, and or transitive.
Prove your answers.
(a) Ri is the relation on R given by Ri = {(z,y) ERx R: |x-y <1}.
(b) Let A be a set with at least two elements. Let R be the relation on A given by
(c) Rs is the relation on Z given by R3 = {(z,y) ⬠Zà Z: xy > 0).
(d) R, is the relation on Z given by R, = {(2, y) ⬠Zx Z: 3|(à + 2y)}. (e) Rs is the relation on Z given by Rs = {(x,y) ⬠Zx Z: there exists k ⬠N such that
elyk and yak).
Answers
In this question, we were given five relations and asked to determine if they are reflexive, symmetric, and/or transitive.
(a) The relation Ri on R is reflexive, symmetric, and transitive.
(b) The relation R on A is not reflexive, not symmetric, and transitive.
(c) The relation Rs on Z is not reflexive, not symmetric, and transitive.
(d) The relation R, on Z is not reflexive, not symmetric, and not transitive.
(e) The relation Rs on Z is reflexive, not symmetric, and transitive.
What is reflexive relation?A reflexive connection is a relationship between items of a set A in which each element is related to itself. As the name implies, the image of each element of the set is its own reflection. In set theory, a reflexive relation is an essential concept.
(a) Ri is reflexive, symmetric, and transitive.
- Reflexive: For any x ∈ R, (x, x) ∈ Ri since |x - x| = 0 < 1.
- Symmetric: For any (x, y) ∈ Ri, we have |x - y| < 1, which implies |y - x| < 1. Therefore, (y, x) ∈ Ri.
- Transitive: For any (x, y), (y, z) ∈ Ri, we have |x - y| < 1 and |y - z| < 1. Adding these inequalities, we get |x - z| < 2, which implies (x, z) ∈ Ri.
(b) R is not reflexive, symmetric, or transitive.
- Not reflexive: For any x ∈ A, (x, x) ∉ R since x - x = 0 is not a positive integer.
- Not symmetric: For any distinct x, y ∈ A, if (x, y) ∈ R, then x - y = 1, which implies y - x = -1 is not a positive integer. Therefore, (y, x) ∉ R.
- Not transitive: Let A = {1, 2, 3} and R = {(1, 2), (2, 3)}. Then (1, 3) is not in R since 3 - 1 = 2 is not a positive integer.
(c) R3 is not reflexive, symmetric, or transitive.
- Not reflexive: For any x ∈ Z, (x, x) ∉ R3 since x * x = x^2 is not greater than 0.
- Symmetric: For any (x, y) ∈ R3, we have xy > 0, which implies yx > 0. Therefore, (y, x) ∈ R3.
- Not transitive: Let x = -1, y = 2, and z = -1. Then (x, y) ∈ R3 and (y, z) ∈ R3, but (x, z) = (-1, -1) ∉ R3 since xz = 1 is not greater than 0.
(d) R, is not reflexive, symmetric, or transitive.
- Not reflexive: For any y ∈ Z, (y, y) ∉ R, since 3 does not divide y + 2y = 3y.
- Not symmetric: For y = 1 and z = 2, we have (2, 1) ∉ R, but (1, 2) ∈ R since 3 divides 1 + 4 = 5.
- Not transitive: Let x = 2, y = 1, and z = 5. Then (x, y) ∈ R, (y, z) ∈ R, but (x, z) = (2, 5) ∉ R since 3 does not divide 2 + 10 = 12.
(e) Rs is the relation on Z given by Rs = {(x,y) ⬠Zx Z: there exists k ⬠N such that elyk and yak).
- Reflexive: This relation is not reflexive because (1, 1) ∉ Rs as there does not exist k such that 1 x k = 1.
- Symmetric: This relation is not symmetric because, for example, (1, 2) ∈ Rs but (2, 1) ∉ Rs since there does not exist k such that 2 x k = 1.
- Transitive: This relation is not transitive. For example, let x = 1, y = 2, and z = 4. Then (x, y) ∈ Rs and (y, z) ∈ Rs, but (x, z) ∉ Rs since there does not exist k such that 1 x k = 4.
In short, in this question, we were given five relations and asked to determine if they are reflexive, symmetric, and/or transitive.
(a) The relation Ri on R is reflexive, symmetric, and transitive.
(b) The relation R on A is not reflexive, not symmetric, and transitive.
(c) The relation Rs on Z is not reflexive, not symmetric, and transitive.
(d) The relation R, on Z is not reflexive, not symmetric, and not transitive.
(e) The relation Rs on Z is reflexive, not symmetric, and transitive.
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The number of reviews for each of the local restaurants is counted. The results are normally distributed with a mean of 25 and a standard deviation of 4.
What percentage of restaurants have between 20 and 25 reviews?
10.6%
50.0%
16.0%
39.4%
Answers
Using the normal distribution, it is found that 39.4% of restaurants have between 20 and 25 reviews.
Normal Probability DistributionIn a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by \(\mu = 25, \sigma = 4\).
The proportion of restaurants that have between 20 and 25 reviews is the p-value of Z when X = 25 subtracted by the p-value of Z when X = 20, hence:
X = 25:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{25 - 25}{4}\)
Z = 0.
Z = 0 has a p-value of 0.5.
X = 20:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{20 - 25}{4}\)
Z = -1.25.
Z = -1.25 has a p-value of 0.106.
0.5 - 0.105 = 0.394 = 39.4%.
Hence, 39.4% of restaurants have between 20 and 25 reviews.
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What are the first five terms in the recursive sequence defined by the following?
a1 = 150
an = 0.85a n-1
1. 150, 127.5, 108.375, 92.11875, 78.3009375
2. 150, 22.5, 3.375, 0.50625, 0.0759375
Answers
The answer of the given question based on the recursive sequence is , the first option (1) is one of the correct answers.
What is Sequence?A sequence is an ordered list of numbers, usually defined recursively or by an explicit formula. Each number in a sequence is called a term, and the position of a term in the sequence is called its index. Sequences can be finite, meaning they have a specific number of terms, or infinite, meaning they continue without end.
The recursive sequence is defined by:
a1 = 150
an = 0.85an-1
To find first five terms of sequence, we can use recursive formula:
a1 = 150
a2 = 0.85a1 = 0.85(150) = 127.5
a3 = 0.85a2 = 0.85(127.5) = 108.375
a4 = 0.85a3 = 0.85(108.375) = 92.11875
a5 = 0.85a4 = 0.85(92.11875) = 78.3009375
Therefore, the first five terms of the sequence are 150, 127.5, 108.375, 92.11875, and 78.3009375.
So, the first option is one of the correct answers.
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evaluate
Evaluate-8÷2+12×9-4×6
Answers
Answer:
Step-by-step explanation:
Use PEDMAS {Parenthesis ; Exponent ; Division ; Multiplication ; Addition; Subtraction }
8÷2 + 12*9 - 4*6 = 4 + 12*9 - 4*6 {Division}
= 4 + 108 - 24 {Multiplication}
= 112 - 24 {Additon}
= 88
Answer: 88
Step-by-step explanation:
Evaluate using PEMDAS.
P = Parenthesis; There are no parenthesis in this expression
E = Exponents; There are no exponents in this expression
M = Multiplication; 12 x 9 = 108, 4 x 6 = 24
D = Division; 8/2 = 4
A = Addition; 4 + (12 x 9) = 112
S = Subtraction; (4 + (12 x 9)) - (4 x 6)
112 - 24 = 88