The point (3, -3 - √3, 6√3) in spherical coordinates is (3√14, arccos(√42 / 7), arctan((-3 - √3) / 3)).
To convert the point (3, -3 - √3, 6√3) from rectangular coordinates to spherical coordinates, we need to calculate the radius (r), inclination (θ), and azimuth (φ).
The formulas to convert rectangular coordinates to spherical coordinates are as follows:
r = √(x² + y²+ z²)
θ = arccos(z / r)
φ = arctan(y / x)
Given the coordinates (3, -3 - √3, 6√3), we can calculate:
r = √(3² + (-3 - √3)² + (6√3²)
= √(9 + 9 + 108)
= √(126)
= 3√14
θ = arccos((6√3) / (3√14))
= arccos(2√3 / √14)
= arccos((2√3 * √14) / (14))
= arccos((2√42) / 14)
= arccos(√42 / 7)
φ = arctan((-3 - √3) / 3)
= arctan((-3 - √3) / 3)
The point (3, -3 - √3, 6√3) in spherical coordinates is (3√14, arccos(√42 / 7), arctan((-3 - √3) / 3)).
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Find the slope: numbers are: (1,-3) and (-5,-4)
[tex]\frac{-3 - (-4)}{1 - (-5)}[/tex]
= [tex]\frac{-3 + 4}{1 + 5}[/tex]
= 1/6
Answer: the slope is 1/6Mark can make 9 pancakes in 15 minutes, and Charlotte can make 42 pancakes in 45 minutes. Working together, how many minutes would it take to make 138 pancakes?
Answer:
60 mins
Step-by-step explanation:
15+45=60
The time needed to make 138 pancakes if both Mark and Charlotte work together is 227.142 minutes.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.
As it is given that Mark can make 9 pancakes in 15 minutes, therefore, the number of pancakes that Mark can make in one minute,
[tex]\text{Number of Pancake in one minute} = \dfrac{9}{15}[/tex]
Now, for Charlotte, it is given that he makes 42 pancakes in 45 minutes, therefore, the number of pancakes that Charlotte can make in one minute,
[tex]\text{Number of Pancake in one minute} = \dfrac{42}{45} = \dfrac{12}{15}[/tex]
Further, the total pancakes that can be made in one minute,
[tex]\text{Total Number of Pancake in one minute} = \dfrac{9}{15} +\dfrac{12}{15} = \dfrac{21}{15}[/tex]
As they both need to make 138 pancakes together, therefore, the time they need is,
[tex]\rm Time\ Needed = \dfrac{\text{Total number of pancakes}}{\text{Total number of pancakes in one minute}}[/tex]
[tex]\rm Time\ Needed = \dfrac{138}{\frac{21}{15}} = \dfrac{138\times 15}{21} = 227.142[/tex]
Hence, the time needed to make 138 pancakes if both Mark and Charlotte work together is 227.142 minutes.
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1. The angle of depression from the top of the
school to the base of the flag pole in front of
the school is 50°. If the flag pole is 35 feet from
the base of the school, find the height of the
school.
Answer:
41.7feet
Step-by-step explanation:
From the question we are given the following
angle of depression = 50°
Distance of the pole from the base of the feet = 35feet (Adjacent)
Required
height of the school (opposite)
Using the SOH CAH TOA identity
Tan theta = opp/adj
Tan 50 = H/35
H = 35tan 50
H = 35(1.1918)
H = 41.7feet
Hence the height of the school is 41.7feet
(Fermat's Theorem, 5pt) Calculate 2^2873686243768478237864767208 mod 101 using Fermat's little theorem (that is, without computer, and without repeated squaring). Explain how you did it. Hint: 101 is prime.
To calculate[tex]2^2873686243768478237864767208[/tex] mod 101 using Fermat's little theorem, we can simplify the exponent by taking it modulo 100, since 100 is the Euler's totient function value of 101. Therefore,[tex]2^2873686243768478237864767208[/tex] mod 101 is equal to 57.
Fermat's little theorem states that if p is a prime number and a is any integer not divisible by p, then a^(p-1) ≡ 1 (mod p). In this case, p = 101, and we need to find[tex]2^2873686243768478237864767208[/tex]mod 101.
First, we simplify the exponent by taking it modulo 100, since 100 is the Euler's totient function value of 101. The exponent 2873686243768478237864767208 is congruent to 8 modulo 100. So, we need to calculate 2^8 mod 101. Applying Fermat's little theorem, we know that 2^(101-1) ≡ 1 (mod 101), since 101 is prime. Therefore, 2^100 ≡ 1 (mod 101).
We can express [tex]2^8[/tex] in terms of 2^100 as [tex](2^100)^0.08[/tex]. Simplifying this, we get [tex](2^100)^0.08 ≡ 1^0.08[/tex]≡ 1 (mod 101).
Thus, we conclude that[tex]2^8[/tex] ≡ 1 (mod 101), and therefore 2^2873686243768478237864767208 ≡ [tex]2^8[/tex] (mod 101).
Finally, evaluating [tex]2^8[/tex] mod 101, we find that [tex]2^8[/tex] ≡ 57 (mod 101).
Therefore,[tex]2^2873686243768478237864767208[/tex] mod 101 is equal to 57.
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How many yards are equivalent to 38 feet? Show your work.
Answer:
12.6
Step-by-step explanation:
divide the length value by 3
What is the fraction that is equal to 0.534
Answer:
267/500
Step-by-step explanation:
0.534 = 534 / 1000
Simplify to 267/500
Step-by-step explanation:
537/1000
this is the correct answer
Let M = {x +1, x2 – 2,3x}. Which of the following statements is true about M? M spans P3 O the above is true M spans P2 O the above is true O None of the mentioned
The correct statement is : M spans P2.
The set M = {[tex]x+1, x^2-2, 3x[/tex]} consists of three polynomials in the variable x.
To determine whether M spans P3 or P2, we need to consider the highest degree of the polynomials in M.
The highest degree of the polynomials in M is 2 (from [tex]x^2-2[/tex]), which means that M can span at most the space of polynomials of degree 2 or less, i.e., P2.
To check whether M spans P2 or not, we need to see if any polynomial of degree 2 or less can be expressed as a linear combination of the polynomials in M.
We can write any polynomial of degree 2 or less as [tex]ax^2 + bx + c[/tex], where a, b, and c are constants.
To express this polynomial as a linear combination of the polynomials in M, we need to solve the system of equations:
[tex]a(x^2-2) + b(x+1) + c(3x) = ax^2 + bx + c[/tex]
This can be written as:
[tex]ax^2 + (-2a+b+3c)x + (b+c) = ax^2 + bx + c[/tex]
Equating the coefficients of [tex]x^2, x,[/tex] and the constant term, we get:
[tex]a = a,\\-2a+b+3c = b,\\b+c = c.[/tex]
The first equation is always true, and the other two equations simplify to:
[tex]-2a+3c = 0,\\b = 0.[/tex]
Solving for a, b, and c, we get:
[tex]a = 3c/2,\\b = 0,\\c = c.[/tex]
Therefore, any polynomial of degree 2 or less can be expressed as a linear combination of the polynomials in M. This means that M spans P2.
However, M cannot span P3, because P3 includes polynomials of degree 3, which cannot be expressed as a linear combination of the polynomials in M (since the highest degree polynomial in M is [tex]x^2[/tex]).
Therefore, the correct statement is: M spans P2.
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A 12-sided solid has faces numbered 1 to 12. The table shows the results of rolling the solid 200 times. Find the experimental probability of rolling a number less than 3 .
Answer:
The experimental probability of rolling anumber less than 3 is 3/20
Step-by-step explanation:
16+14=30
30/200
=3/20
Answer:
7/50
Step-by-step explanation:
Find the cost of cat food for a 29-day supply, a 30-day supply, and a 31-day supply
Answer:
not a complete question..
Step-by-step explanation:
A hockey tournament consists of 16 teams. In the first round, every team is randomly assigned to one of 8 games (2 teams per game). Suppose exactly 3 of the teams are from Alberta. What is the probability all 3 Alberta teams are randomly assigned to different games (call this event A)?
Given that a hockey tournament consists of 16 teams. In the first round, every team is randomly assigned to one of 8 games (2 teams per game). We are supposed to find the probability that all three Alberta teams are randomly assigned to different games. Let A be the event of assigning all three Alberta teams to different games.
Then the number of ways to select 3 teams from 16 teams is $\ dbinom {16}{3}$, the number of ways to assign 3 teams to different games is $8\times7\times6$, and the number of ways to assign the remaining 13 teams to games is $(13!) / (2^6\times6!)$.The probability of event A is given by;$$
P(A) = \frac{\text{number of ways to assign 3 teams from Alberta to different games}}{\text{number of ways to assign all teams to games}} = \frac{8\times7\times6 \times (13!) / (2^6\times6!)}{\dbinom{16}{3} \times (14!) / (2^7\times7!)}
$$Simplifying the above expression,$$
P(A) = \frac{8\times7\times6 \times 13! \times 2}{\dbinom{16}{3} \times 14!} = \frac{8\times7\times6 \times 2}{\dbinom {16}{3}} = \frac{336}{560} = \frac{3}{5}
Therefore, the probability that all three Alberta teams are randomly assigned to different games is $\frac{3}{5}$.
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Last translation I need help with I promise-
The types of transformation in this problem is given as follows:
Vertical and horizontal translation.
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a. -> horizontal translation.Right a units: x -> x + a. -> horizontal translation.Up a units: y -> y + a. -> vertical translation.Down a units: y -> y - a. -> vertical translation.The translations for this problem are given as follows:
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In macroeconomics, the economy can best be understood through the use of
money.
models.
pricing.
debates.
Answer:
models
Step-by-step explanation:
Answer: B.) Models
Edge
a cookie factory uses 1/6 pf a barrel pf oatmeal in each batch of cookies, the factory used 1 1/3 barrels of oatmeal yesterday. how many batches of cookies did the factory make?
Answer:
5 batches
Step-by-step explanation:
1/6 oatmeal can make 1 batch, so 5/6 makes 5 batches
1) Which of the following can cause OLS estimators to be biased? Which of the following do not cause the usual OLS t statistics to be invalid (that is, to have t distributions under H0)? (6 points)
Omitting an important independent variable
Multicollinearity
Heteroskedasticity
Including irrelevant variable
The error term non-normally distributed
The following can cause OLS estimators to be biased: Omitting an important independent variable.
Multicollinearity. Heteroskedasticity, Including an irrelevant variable.
The following does not cause the usual OLS t statistics to be invalid (that is, to have t distributions under H0): The error term non-normally distributed
OLS (ordinary least squares) estimates are typically unbiased when calculated.
However, the following problems may cause OLS estimates to be biased:
Omitting an important independent variable: When an important independent variable is omitted from the regression equation, the OLS estimate of the effect of one variable on the dependent variable is biased.
In particular, the estimate of the effect of the variable that is omitted is influenced by the remaining variables' presence in the equation.
Multicollinearity: When the independent variables in a multiple regression model are strongly related, multicollinearity exists.
When there is multicollinearity in a model, the estimated slope coefficients are frequently biased, making them difficult to interpret.
In this scenario, small changes in the data may cause substantial changes in the estimated coefficients.
As a result, the usual tests of hypothesis may fail to produce reliable inferences.
Heteroskedasticity: In the population, heteroskedasticity exists when the variance of the error term is not constant across observations.
Heteroskedasticity can induce OLS estimates' variance to be biased, even if the estimates are unbiased themselves.
When there is heteroskedasticity, the OLS estimates are no longer BLUE (best linear unbiased estimator).
Including irrelevant variable: When an irrelevant variable is included in a regression equation, the OLS estimates of the other variables' effects are biased, and the estimates' standard errors are larger than necessary.
The error term non-normally distributed: When the error term in a regression equation is non-normally distributed, the distribution of the OLS estimates is also non-normal.
However, this does not affect the distribution of the t statistics under H0.
The reason for this is that, even if the error term is non-normally distributed, the sample mean converges to the population mean, according to the central limit theorem.
Furthermore, the standard error of the mean is unaffected by the distribution of the error term, as long as the sample size is large enough.
As a result, the t statistics can be trusted to be asymptotically normally distributed under H0.
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use mathmatecial induction to prove that for each non negative odd integer n: 24 / (2²³1 +1+1) (n²₁)
Mathematical induction can be used to prove that for every non-negative odd integer n, the expression [tex]24 / (2^{(3n+1)}+1+1) * (n^2+1)[/tex] holds true.
To prove the statement using mathematical induction, we need to follow two steps: the base case and the induction step.
First, we verify if the statement holds true for the base case, which is typically the smallest value of n. In this case, let's consider n = 0. Plugging in n = 0 into the expression, we get [tex]24 / (2^{(3*0+1)}+1+1) * (0^2+1)[/tex]. Simplifying, we have 24 / (2+1+1) * 1, which equals 24 / 4 * 1, resulting in 6. Therefore, the statement holds true for n = 0.
Next, we assume that the statement is true for some arbitrary odd integer k, and we will prove that it holds true for k+2. Assume that [tex]24 / (2^{(3k+1)}+1+1) * (k^2+1)[/tex] holds true.
Now, we substitute k+2 into the expression and aim to show that it holds true for k+2 as well. We have [tex]24 / (2^{(3(k+2)+1)}+1+1) * ((k+2)^2+1)[/tex]. Simplifying the expression, we get [tex]24 / (2^{(3k+7)}+1+1) * (k^2 + 4k + 5)[/tex].
We can manipulate the equation further to demonstrate that it is equal to the assumed expression for k. By performing algebraic manipulations and simplifications, we can equate the expressions and conclude that the statement holds true for k+2.
Since we have verified the base case and shown that the statement holds true for k+2 when it holds true for k, we can conclude that the statement is true for every non-negative odd integer n.
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function project: a day of fun
Answer:
Yay fun day :DDDDDD
Step-by-step explanation:
Please help me on this question if you would want brianleist!! Tank yah!! ^^
Answer:
x axis
Step-by-step explanation:
If you flip two coins, what is the probability that both will be heads?
Answer:
1/2 x 1/2 = 1/4
Step-by-step explanation:
P(H,H) = 1/2 x 1/2 = 1/4
P(T,T) = 1/2 x 1/2 = 1/4
P(H,T) = 1/2 x 1/2 = 1/4
P(T,H) = 1/2 x 1/2 = 1/4
Which expression is equivalent to 10(−45x+3)−2x?
−8x+3
−10x+3
−10x+30
−30x+30
Answer:
-10x+30
Step-by-step explanation:
just got it right on edg 2021 :)
None of these are correct
(x_6)(x_5)+(x_5)(x_6)
Answer:
(X+6)(x-5) + (X-5)(X+6)
Answer:
[tex]2x ^{2} - 22x + 60[/tex]
Please please please help me with this pleasseee!!!
[tex]\Large\boxed{\tt Answer:~A:~y=-3x+5}[/tex]
All we have to do in order to find the equation that is equivalent to 6x + 2y = 10 is to solve for y.
Step 1: Keep y on one side of the equation and move the rest to the other.
[tex]\tt 6x + 2y = 10\\2y = -6x + 10[/tex]
Step 2: Divide all terms by 2 to isolate y.
[tex]\tt 2y \div 2=y\\-6x \div 2 = -3x\\10 \div 2 =5\\\\y=-3x+5[/tex]
Consider an election with 129 votes.
(a) If there are 4 candidates, what is the smallest number of votes that a plurality candidate could have? Explain your answer.
(b) If there are 8 candidates, what is the smallest number of votes that a plurality candidate could have? Explain your answer
(a) If there are 4 candidate, the smallest number of votes that a plurality candidate could have is 33.
(b) If there are 8 candidate, the smallest number of votes that a plurality candidate could have is 17.
What is the smallest number of votes obtained?The smallest number of votes that a plurality candidate could have is calculated as follows;
(a) If there are 4 candidate, the number of votes for each candidate;
= 129 / 4
= 32.25
The least number of votes for the plurality candidate = 33
(b) If there are 8 candidate, the number of votes for each candidate;
= 129 / 8
= 16.125
The least number of votes for the plurality candidate = 17
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Find all the missing elements
Round to the nearest tenth.
Answer:
B = 48.7°
C = 61.3°
b = 12
Step-by-step explanation:
Given:
A = 70°
a = 15
c = 14
Required:
B, C, and b
Solution:
✔️Using the law of sines, let's find C:
Sin C/c = Sin A/a
Plug in the values
Sin C/14 = Sin 70/15
Cross multiply
Sin C × 15 = Sin 70 × 14
Divide both sides by 15
Sin C = (Sin 70 × 14)/15
Sin C = 0.8770
C = Sin^{-1}(0.8770)
C = 61.282566° = 61.3° (nearest tenth)
✔️Find B:
B = 180 - (70 + 61.3) (sum of triangle)
B = 48.7°
✔️Find b using the law of sines:
b/sinB = a/sinA
Plug in the values
b/sin 48.7 = 15/sin 70
Cross multiply
b*sin 70 = 15*sin 48.7
Divide both sides by sin 48.7
b = (15*sin 48.7)/sin 70
b = 11.9921789
b = 12.0 (nearest tenth)
Read the story.
Nolan reads his little sister one of her two favorite books each night before bed. This month, she has chosen the mermaid book 3 times for every 2 times she has chosen the princess book.
Pick the diagram that models the ratio in the story.
If Nolan has read his sister a book before bed 20 times this month, how many times has he read the mermaid book?
Answer:The diagram that models the ratio in the story is:
Mermaid book: Princess book = 3:2
To find out how many times Nolan has read the mermaid book, we can set up the following proportion:
3/2 = x/20
Cross-multiplying, we get:
2x = 3 * 20
2x = 60
Dividing both sides by 2, we find:
x = 60/2
x = 30
Therefore, Nolan has read the mermaid book 30 times this month.
what is the volume of the right triangle prism shown
Answer:
42cm3
Step-by-step explanation:
v = 0.5× b × h × l
= 0.5 × 4 × 3 × 7
= 42cm3
A person borrows a certain amount of money. He has to pay the debt in equal installments once every month, for 10 years. The first installment was paid on 2016-01-01. Find the date on which he has to pay the final installment.
Answer: January 1, 2025
Step-by-step explanation:
The debt is due to be paid back in 10 years.
If the first payment was in 2016, the last payment should therefore be:
= 2016 + 9 years
= 2025
We used 9 years because 2016 was the first year of payment so the remaining years would be 9 years.
As the first payment was on January 1, 2016, the last payment would have to be on the same date in 2025 which is:
= January 1, 2025
Which of the following factors does not affect the mortgage payment? No A. Interest rates
B. The down payment
C. The borrower's credit score
D. The neighborhood the home is located in
Answer:
The neighborhood the home is located in
The factors which does not affect the mortgage payment is the neighborhood the home is located in.
The correct option is D.
We are aware of this;
A mortgage is a loan when the borrower's property is used as security. The mortgage payment is determined by the cost of the property, the interest rate, the down payment, the length of the loan, taxes, and various insurances like homeowners insurance, among other factors.
Hence, It's not depend on ''The neighborhood the home is located in.''
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What is the perimeter of abcd ?
Answer:
38
Step-by-step explanation:
(10*2)+(9*2)
Find the surface area of a cylinder with a height of 4 yd and a base radius of 3 yd.
Answer:
131.95yd squared
Step-by-step explanation:
A=2πrh+ 2 r(2)=2*π*3*4+2*π*3(2)~131.94689yd(2)
What is a volume of this composite solid?
Shape a = 6 x 4 x 3 = 72
Shape b = 4 x 4 x 4 = 64
72 + 64 = 136
A
Answer:
A
Step-by-step explanation: