The five-number summary for the given data is as follows: Minimum = 40, First Quartile = 51.5, Median = 69, Third Quartile = 86, Maximum = 95.
To obtain the five-number summary, we consider the minimum, first quartile, median, third quartile, and maximum values of the dataset.
Minimum: The smallest value in the dataset is 40.
First Quartile: The first quartile (Q1) is the median of the lower half of the dataset. To find Q1, we arrange the data in ascending order: 40, 46, 50, 55, 58, 61, 64, 69, 74, 79, 85, 86, 90, 94, 95. Since there are 15 data points, the median is the 8th value (69), which becomes the first quartile.
Median: The median is the middle value of the dataset. In this case, since we have an odd number of data points, the median is the 8th value (69).
Third Quartile: The third quartile (Q3) is the median of the upper half of the dataset. Again, using the ordered data, we find Q3 as the median of the values above the median (69). This gives us the third quartile of 86.
Maximum: The largest value in the dataset is 95.
Thus, the five-number summary for the given data is Minimum = 40, Q1 = 51.5, Median = 69, Q3 = 86, and Maximum = 95.
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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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I AM GIVING BRAINLIEST TO WHOEVER ANSWERS, IF IT SAYS IT'S ALREADY ANSWERED, IT'S A LINK. PLEASE HELP ME :D
How many yards are equivalent to 38 feet? Show your work.
Answer:
12.6
Step-by-step explanation:
divide the length value by 3
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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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)
function project: a day of fun
Answer:
Yay fun day :DDDDDD
Step-by-step explanation:
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
plssssss helpppp !!
tysmmmm
I think that the answer would be two triangles.
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)
(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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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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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.
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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which of the following rational functions has a horizontal asymptote at y = 3 and vertical asymptotes at x = 4 and x = –3?
To have a horizontal asymptote at y = 3 and vertical asymptotes at x = 4 and x = -3, the rational function should have the following form:
f(x) = (a polynomial in x) / ((x - 4)(x + 3))
The polynomial in the numerator can have any degree, but it must be of lower degree than the denominator.
Therefore, among the given rational functions, the one that satisfies these conditions would be the one in the form:
f(x) = (a polynomial) / ((x - 4)(x + 3))
Please provide the specific options you have, and I can help you determine which of those options matches this form.
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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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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
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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Mark 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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Write in standard form
531800000
Answer:
5.318 * 10 to power of 8
Step-by-step explanation:
Answer:
5.318 × [tex]10^{8}[/tex]
Step-by-step explanation:
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:
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
(x_6)(x_5)+(x_5)(x_6)
Answer:
(X+6)(x-5) + (X-5)(X+6)
Answer:
[tex]2x ^{2} - 22x + 60[/tex]
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
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]
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
The diameter of a circle has endpoints at (0,11) and (-6,-1). Write the equation of the circle in standard form.
Answer:
(x - 3)^2 + (y - 6)^2 = 17
Step-by-step explanation:
The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.
(x - 3)^2 + (y - 6)^2 = 17
what is the positive solution to the equation 4x^{2}+12x=135
Answer:
9/2 = 4 1/2
Step-by-step explanation:
Please help me on this question if you would want brianleist!! Tank yah!! ^^
Answer:
x axis
Step-by-step explanation:
Change from rectangular to spherical coordinates. (Let rho ≥ 0, 0 ≤ θ ≤ 2π, and 0 ≤ φ ≤ π.) (a) (5,5√3, 10√3 ) (rho,θ,φ) = (___) (b) (0,−3,−3) (rho,θ,φ) = (___)
The spherical coordinates for the point (0, -3, -3) are (3√2, -π/2, π/4).
(a) To change from rectangular coordinates to spherical coordinates, we use the following formulas:
rho = √(x² + y² + z²)
theta = atan2(y, x)
phi = acos(z / rho)
Given the rectangular coordinates (5, 5√3, 10√3), we can substitute the values into the formulas to find the corresponding spherical coordinates:
rho = √((5)² + (5√3)² + (10√3)²)
= √(25 + 75 + 300)
= √(400)
= 20
theta = atan2(5√3, 5)
= atan(√3)
≈ 1.0472 radians
phi = acos((10√3) / 20)
= acos(√3 / 2)
= π/6 radians
Therefore, the spherical coordinates for the point (5, 5√3, 10√3) are (20, 1.0472, π/6).
(b) Given the rectangular coordinates (0, -3, -3), we can apply the formulas for spherical coordinates:
rho = √((0)² + (-3)² + (-3)²)
= √(0 + 9 + 9)
= √(18)
= 3√2
theta = atan2(-3, 0)
= -π/2 radians
phi = acos((-3) / (3√2))
= acos(-1/√2)
= π/4 radians
Hence, the spherical coordinates for the point (0, -3, -3) are (3√2, -π/2, π/4).
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