Answers
Answer:
FGH DEJ .................
Related Questions
Find the missing side length of
the triangle.
Answers
Answer:
50 units
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Trigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
Step 1: Define
a = 48
b = 14
c = ?
Step 2: Solve for c
Substitute in variables [Pythagorean Theorem]: 48² + 14² = c²Evaluate exponents: 2304 + 196 = c²Add: 2500 = c²[Equality Property] Square root both sides: 50 = cRewrite: c = 50In a two-digit number, the units digit is 5 more than the tens digit. The number is 6 less than 4 times the sum of the digits. Find the number.
Answers
Answer:
Tens digit, x = 3
Unit digit, y = 8
Number = 38
Step-by-step explanation:
Let the 2 digit number = xy
y = x + 5 - - - (1)
10x + y = 4(x + y) - 6
10x + x + 5 = 4(x + x + 5) - 6
11x + 5 = 4(2x + 5) - 6
11x + 5 = 8x + 20 - 6
11x + 5 = 8x + 14
11x - 8x = 14 - 5
3x = 9
x = 9/3
x = 3
From (1)
y = x + 5
y = 3 + 5
y = 8
which of the following rational functions has a horizontal asymptote at y = 3 and vertical asymptotes at x = 4 and x = –3?
Answers
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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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)?
Answers
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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(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.
Answers
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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Find the surface area of a cylinder with a height of 4 yd and a base radius of 3 yd.
Answers
Answer:
131.95yd squared
Step-by-step explanation:
A=2πrh+ 2 r(2)=2*π*3*4+2*π*3(2)~131.94689yd(2)
Joe's lunch at a restaurant cost $18.00 without tax he leaves the server a tip of 14% of the cost of lunch without tax what is the total cost of lunch including tip without tax
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Ok. So 14% of 18.00 can be figured out without a calculator. 18.00 / 10 = 1.80 = 10%.
(18.00 / 100) x 4 = 0.72
1.80 + 0.72 = $2.52 is the tip.
$18 + $2.52 = $20.52
⭐ Answered by Foxzy0⭐
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⭐ If you have questions, leave a comment, I'm happy to help! ⭐
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) = (___)
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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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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?
Answers
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.
plssssss helpppp !!
tysmmmm
Answers
I think that the answer would be two triangles.
What is the perimeter of abcd ?
Answers
Answer:
38
Step-by-step explanation:
(10*2)+(9*2)
What value of x makes this proportion true? x/6=36/24 O A. 8 O B. 9 O C. 18 O D. 7
Answers
Answer:
B. 9
Step-by-step explanation:
Proportions are just like fractions and to figure them out sometimes you can use simplification in different forms.
[tex]\frac{x}{6}[/tex] = [tex]\frac{36}{24}[/tex]
Now to get to 6, 24 had to be divided by 4...in proportions and fractions usually, the top and bottom are both simplified or proportioned to the same number or scale
36 ÷ 4 = 9
Check your answer by inserting it there to see if it works
9*4 = 36 6*4 = 24
Answer:
[tex]\boxed {\boxed {\sf B. \ 9}}[/tex]
Step-by-step explanation:
We are given this proportion:
[tex]\frac {x}{6}=\frac{36}{24}[/tex]
We want to solve for x, so we must isolate the variable using inverse operations.
It is being divided by 6. The inverse of division is multiplication, so we multiply both sides of the proportion by 6.
[tex]6*\frac {x}{6}=\frac{36}{24}*6[/tex]
[tex]x=\frac{36}{24}*6[/tex]
[tex]x=1.5*6 \\x=9[/tex]
Another way to solve is with cross multiplication. Multiply the first numerator by the second denominator, then the first denominator by the second numerator.
[tex]\frac { x}{6}=\frac{36}{24}[/tex]
[tex]24*x=6*36[/tex]
[tex]24x=216[/tex]
The variable is being multiplied by 24. The inverse of multiplication is division, so we divide both sides of the equation by 24.
[tex]24x/24=216/24\\x=9[/tex]
The value of x that makes this proportion true is 9.
I need help on this math problem fast with work shown and answer thx
Answers
Answer:
angle 1 = 124
angle 2 = 56
angle 3 = 124
angle 4 = 56
Step-by-step explanation:
This problem is a bit like a puzzle. To make notation easier I'm going to do this:
angle 1 = a
angle 2 = b
angle 3 = c
angle 4 = d
Now, let's start with what we know from the image.
All angles added together form a circle or 360 degrees
a + b + c + d = 360
In the same regard a + d = 180, and b + c = 180
Also,
a = c
and
b = d
It also tells us angle 4 is 25 degrees greater than one fourth of angle 1. Which is written as.
d = 1/4(a) + 25
If we look at all the equations we have, we can see that two of the equations have two of the same variables:
a + d = 180
and
d = 1/4(a) + 25
Using substitution we can take the second equation substitute it for d in the first equation giving us:
a + (1/4(a) + 25) = 180
Now we just solve for a
[tex]\frac{4}{4} a+ \frac{1}{4} a + 25 = 180\\\\\frac{5}{4}a + 25 = 180 \\\\(\frac{5}{4}a + 25) - 25 = (180) -25\\\\\frac{5}{4} a = 155\\\\\frac{5}{4} a * \frac{4}{5} = 155 * \frac{4}{5}\\\\a = 124[/tex]
Therefore a, or angle 1, is 124
Since a = c, then c, or angle 3, is also 124
Since a + d = 180 and a = 124 then
d = 180 -124
d = 56
So, d, or angle 4, is 56
And because b = d then b, or angle 2, is also 56
a = 124
b = 56
c = 124
d = 56
For extra measure, we can check our work by using the first equation
a + b + c + d = 360
124 + 56 + 124 + 56 = 360
Complete the table of values y = x2 + 4x - 6
Answers
Answer:
x=-2
Step-by-step explanation:
The price of calculator is increased from R150 to R174.What is the percentage increased
Answers
Answer:
16%
Step-by-step explanation:
(174-150)/150= 0.16
0.16*100 = 16%
please help!! i will give brainliest.
Answers
Answer:
3/10 inches apart
Step-by-step explanation:
total miles based on 2" equals 33 miles can be found by solving this proportion:
2/33 = 6/x
2x = 198
x = 99
99 miles divided by 11 rest stops means each stop is 9 miles apart
now use new ratio of 1" equals 30 miles
1/30 = x/9
30x = 9
x = 9/30 or 3/10 inches
Please help me solve these two questions
Answers
I hope the answer is helpful
The diameter of a circle has endpoints at (0,11) and (-6,-1). Write the equation of the circle in standard form.
Answers
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
match each hypotenuse with the leg that will create a right
triangle
Answers
Answer:
Where is the question so that I can help you with it
A zoo has 5 Emperor penguins. The Emperor penguins make up 30%, percent of all the penguins at the zoo. How many penguins live at the zoo
Answers
Answer:
50
Step-by-step explanation:
this can be solved by ratio 15/x = 30/100. Cross multiply and solve for x. The answer is 50.
I AM GIVING BRAINLIEST TO WHOEVER ANSWERS, IF IT SAYS IT'S ALREADY ANSWERED, IT'S A LINK. PLEASE HELP ME :D
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Probability 0.35 0.3 0.05 0.1 0.05 0.15 8 9 10 11 Find the expected value of the above random variable.
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The expected value of the given random variable is 8.3. This means that, on average, if we repeatedly sample from this random variable, we can expect the resulting values to be around 8.3.
To find the expected value of a random variable, you multiply each possible value by its corresponding probability and sum them up. In this case, we have a combination of probabilities and numerical values. Let's calculate the expected value:
Multiply each numerical value by its corresponding probability:
(0.35 * 8) + (0.3 * 9) + (0.05 * 10) + (0.1 * 11) + (0.05 * 11) + (0.15 * 11)
Perform the calculations:
2.8 + 2.7 + 0.5 + 1.1 + 0.55 + 1.65
Sum up the results:
8.3
Therefore, the expected value of the given random variable is 8.3. This means that, on average, if we repeatedly sample from this random variable, we can expect the resulting values to be around 8.3. The expected value provides a measure of central tendency for the random variable.
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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
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(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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Write in standard form
531800000
Answers
Answer:
5.318 * 10 to power of 8
Step-by-step explanation:
Answer:
5.318 × [tex]10^{8}[/tex]
Step-by-step explanation:
function project: a day of fun
Answers
Answer:
Yay fun day :DDDDDD
Step-by-step explanation:
How many yards are equivalent to 38 feet? Show your work.
Answers
Answer:
12.6
Step-by-step explanation:
divide the length value by 3
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?
Answers
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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what is the positive solution to the equation 4x^{2}+12x=135
Answers
Answer:
9/2 = 4 1/2
Step-by-step explanation:
Find all the missing elements
Round to the nearest tenth.
Answers
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)
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
Answers
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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