in the final event of a track meet, 6 runners run a 100 meter dash. A) How many possible arrangements are there for the medal winners (gold, silver and bronze)? B) state whether it is a combination or permutation
Answer:
120 possible arrangements.
It is a permutation
Step-by-step explanation:
Imagine that you are going to give the gold medal to any of the 6 runners. There would be 6 possibilities; now, imagine that you are going to give the gold and the silver medals random in the same way: you could give the gold medal to a person and you would have 5 possibilities to give the silver medal (you can't give both medals to the same person). So, note that for each possibility to give the gold medal there would be 5 possibilities to give the silver one.
Analogously, if you give the three medals random and supposing that you have already given the gold one, for each possibility to give the silver medal you would have 4 possibilities to give the bronze one. That is the reason for the calculation to be a multiplication:
N= Total number possibilities:
[tex]N=6*5*4=120[/tex]
This also can be seen as a permutation. A permutation is a reorganization of elements where the order matters. In this case, it is not just relevant who are the winners (who receive the medal), but their order. A combination just helps us to make groups without taking in mind the order, but the permutation does consider that.
The permutation can be learnt by the formula:
[tex]N=\frac{p!}{(p-n)!}[/tex]
where p is the total ef elements and n is the amount of elements of each subgroup that I want to built. In this case, our population 'p'=6, and we want to organize them in groups of 3 (n=3) where it is important for us the order:
[tex]N=\frac{6!}{(6-3)!}=6*5*4=120[/tex]
subtract one- fifth from seven times w
What is the ratio of the two values and what new value do they produce? 4m in 2 min
Answer:
2:1
Step-by-step explanation:
The ratio is 2:1 and the new value can also be 8/4= 2/1
Consider a game in which player 1 moves first. the set of actions available to player 1 is a1={a,b,c}. after observing the choice of player 1, player 2 moves. the set of actions available to player 2 is a2={a,b,c,d}. at how many information sets does player 2 move?
The slope of a vertical line is zero. true or false
The solution is False
The slope of a vertical line is given by the equation Slope m = undefined
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the line be represented as A
Now , the line A is a vertical line
So , the equation of line will be represented as y = mx + c
where m is the slope of the line
And , Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
The slope of a vertical line is infinite or undefined as it has no y-intercept
Because , the change is x is 0
So , the denominator of the fraction is 0 and division by 0 is undefined
Slope m = ( y₂ - y₁ ) / 0
Hence , the slope m is undefined
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Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the paraboloid z = 7x2 + y2 and the parabolic cylinder y = 3x2
Final answer:
The vector function r(t) representing the curve of intersection of the surfaces z = 7x² + y² and y = 3x² is r(t) = it + 3t²j + (7t² + 9t´)k.
Explanation:
Finding a Vector Function for a Curve of Intersection
To find the vector function r(t) that represents the curve of intersection of the surfaces z = 7x² + y² and y = 3x², we can parameterize the variables using a suitable parameter, commonly denoted as t. We can set x = t, which imminently provides y as y = 3t² by substituting t into the equation of the parabolic cylinder. Then, substituting both x and y into the equation of the paraboloid gives us z = 7t² + (3t²)² = 7t² + 9t´. Therefore, the vector function is:
r(t) = it + j3t² + k(7t² + 9t´).
This function r(t) represents all points (x, y, z) on the curve where the two surfaces intersect. Since the curve lies on both surfaces simultaneously, z must be equal for both equations when x and y from the curve are substituted into them.
Which set of numbers does 8 2/3 belong to
How do you rename 5400
805 tens in standard form
find the coefficient of x^6 in the binomial expression of (2x+3)^9
Which expression is equivalent to 3(8 + 7)? 24 + 7 24 + 21 11 + 10 11 + 7
There are 36 girls and 40 boys at a summer camp. The campers will be divided into equal-sized groups. Each group will have the same number of girls and the same number of boys. What is the greatest number of groups that can be formed?
Knowing that this number, the Golden Ratio, is present not just in mathematics, but may also be present within your own brain and body (at the atomic or subatomic level), what do you think it means? Is this number evidence of a grand design, a massive freak coincidence or something else?
The Golden Ratio is a mathematical relationship that exists in art, shapes, nature and the human body. The golden ratio can be present in your body, from the length of your arms and legs when compared to your torso. Fingers is another example because the length of our fingers, each section from the tip of the base to the wrist is larger than the preceding.
The measurement of the human navel to the floor and to the top of the head to the navel is also the Golden ratio. Plastic surgeons and dental surgeons use it to reconstruct the human face. It also appears in everything around us like in the nature and science. It appears on in flower petals because it is believed that each petal is placed to so that each petal gets the best exposure to sunlight. Dolphins, starfish, sea urchins and honeybees also exhibit the proportion like humans. DNA molecules measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral, these two number are successive numbers. I think that the Golden Ratio is just a freak coincidence that happened.
On Saturday, a local hamburger shop sold a combined total of 273 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Final answer:
To determine the number of hamburgers sold on Saturday, we used the given total of 273 burgers and the relationship that cheeseburgers were twice as numerous as hamburgers. By setting up an equation and solving for the number of hamburgers, we found that 91 hamburgers were sold.
Explanation:
The question asks us to determine how many hamburgers were sold on Saturday given that the total number of hamburgers and cheeseburgers sold was 273, and the number of cheeseburgers was two times the number of hamburgers. Let's denote the number of hamburgers as H and the number of cheeseburgers as C. The problem states that C = 2H. The total number of burgers sold was H + C = 273. Substituting C with 2H, we get H + 2H = 273.
Solving for H, we combine like terms to get 3H = 273, and then we divide both sides by 3 to find H = 273 / 3. Therefore, H = 91. So, 91 hamburgers were sold on Saturday.
Nate rides his bike to school every day. From his home he rides 2.5 miles north, and then six miles west. If a straight line is drawn from Nate's house to the school, find the distance between these two locations.
use Pythagorean Theorem
2.5^2 + 6^2 = x^2
6.25 +36 = 42.25
x= sqrt(42.25) = 6.5 miles
The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse
last year, Carmen opened an investment account with $7400. At the end of the year, the amount in the account had decrease buy 26.5%. How much is this decrease in dollars? How much money was in her account at the end of the year?
The decrease in Carmen's account was $1961, which is 26.5% of her original investment of $7400. Hence, by subtracting this decrease from the original investment, we find that Carmen had $5439 left at the end of the year.
Explanation:The decrease in Carmen's account over the year is 26.5% of the original investment of $7400. In mathematical terms, we can calculate this value by multiplying the original investment by the percentage decrease, using the formula: Decrease = Original Amount * Percentage Decrease.
In Carmen's case, this would be $7400 * 0.265 (converted from 26.5%). Upon calculating, we find that the decrease is $1961.
Now, to find how much money Carmen had at the end of the year, we subtract this decrease from the original amount invested. Again, using the formula: Final Amount = Original Amount - Decrease, we plug in the numbers to get $7400 - $1961, which equals $5439. This is how much Carmen had left in her account at the end of the year after the decrease.
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Felicia invested money at an interest rate of 4%. After six months, she had earned $90.00 interest. How much money did Felicia invest?
Answer:
the answer is 4500 i got it right
Step-by-step explanation:
What are the solutions to the quadratic equation (5y + 6)2 = 24? y = and y = y = and y = y = and y = y = and y =
For this case we have the following quadratic expression:
[tex] (5y + 6) ^ 2 = 24
[/tex]
From here, we must clear the value of y.
For this, we follow the following steps:
1) We clear the square term:
[tex] (5y + 6) =+/-\sqrt{24} [/tex]
[tex] (5y + 6) =+/-2\sqrt{6} [/tex]
2) Pass the value of 6 by subtracting:
[tex] 5y =-6+/-2\sqrt{6} [/tex]
3) Pass the value of 5 to divide:
[tex] y =\frac{-6+/-2\sqrt{6} }{5} [/tex]
Answer:
The solutions to the quadratic equation are:
[tex] y =\frac{-6+2\sqrt{6} }{5} [/tex]
[tex] y =\frac{-6-2\sqrt{6} }{5} [/tex]
Henry recorded the number of miles he biked each day for a week. His miles were 25, 40, 35, 25, 40, 60, and 75. Enter the data into the statistics calculator. What is the standard deviation of the miles Henry biked to the nearest tenth?
The standard deviation of the miles Henry biked to the nearest tenth is 17.1. The standard deviation is calculated following the steps below.
Calculation of standard deviationFirst calculate the mean of the numbers that where given which is = 25 + 40 + 35 + 25 + 40 + 60+ 75/7
= 300/7
= 42.9
Then for each number, subtract the Mean and square the result.
(25 - 42.9)² = −17.9² = 320.41
(40-42.9)² = -2.9²= 8.42
(35-42.9)² = -7.9² = 62.41
(25-42.9)² = −17.9² = 320.41
(40-42.9)² = -2.9²= 8.42
(60-42.9)² = 17.1²= 292.41
(75-42.9)² = 32.1²= 1030.41
Then work out the mean of those squared differences. That is,
320.41+ 8.42+62.41+320.41+8.42+292.41+1030.41/7
= 2042.89/7
= 291.8
Take the square root of 291.8 which is,
√291.8 = 17.08215443
= 17.1 to the nearest tenth.
Therefore, the standard deviation of the miles Henry biked to the nearest tenth is = 17.1
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Answer:
17.1
Step-by-step explanation:
got it right
In mathematics, the distance between one point (a) and another point (b), each with coordinates (x,y), can be computed by taking the differences of their x coordinates and their y coordinates and then squaring those differences. the squares are added and the square root of the resulting sum is taken and... voila! the distance. given two variables, p1 and p2 that are of type point -- a structured type with two fields, x and y, both of type double-- write an expression whose value is the distance between the two points represented by p1 and p
The distance between two points can be found using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2).
Explanation:The distance between two points can be found using the formula sqrt((x2 - x1)^2 + (y2 - y1)^2). To find the distance between the two points represented by p1 and p2, we substitute the x and y coordinates of p1 and p2 into the formula:
distance = sqrt((p2.x - p1.x)^2 + (p2.y - p1.y)^2).
The sun produces 3.9 x 10^33 ergs of radiant energy per second. how many ergs of radiant energy does the sun produce in 3.25 x 10^3 seconds?
Answer:
1.2675 x 10^37
Step-by-step explanation:
you would have to first multiply 3.9 x 3.25 =12.675. It is not in scientific notation so you would have to change the decimal 1.2675 x 10^37
The ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]
The rate of energy is given as:
[tex]Rate = 3.9 * 10^{33}\[/tex] radiant energy per second
The time is given as:
[tex]Time = 3.25 * 10^3[/tex] seconds
The amount of radiant energy produced in this time is:
[tex]Energy = Rate * Time[/tex]
So, we have:
[tex]Energy = 3.9 * 10^{33} * 3.25 * 10^3[/tex]
Multiply
[tex]Energy = 12.675* 10^{36}[/tex]
Rewrite as:
[tex]Energy = 1.2675* 10^{37}[/tex]
Approximate
[tex]Energy = 1.3* 10^{37}[/tex]
Hence, the ergs of radiant energy produced is: [tex]1.3* 10^{37}[/tex]
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in 2000 you weighed 175 pounds. in 2001 you weighed 62 pounds, and in 2002 you weighed 154 pounds. how many pounds did you lose from 2000 to 2002.
The vertex form of the equation of a parabola is y = (x - 4)2 + 22. What is the standard form of the equation?
The equation in standard form is y = x^2 - 8x + 38
How to write the equation in standard form?The vertex form of the equation is given as':
y = (x - 4)^2 + 22
Expand the equation
y = x^2 - 8x + 16 + 22
Evaluate the sum
y = x^2 - 8x + 38
Hence, the equation in standard form is y = x^2 - 8x + 38
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What is the derivative of this function?
Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.
Answer:
Joint variation.
Step-by-step explanation:
There are four types of variation,
Direct variation : When a variable varies directly as another variable,
Example : y varies directly with x ⇒ y = kx,
Where, k is the constant of variation,
Inverse variation : When a variable varies inversely as another variable,
Example : y varies inversely with x ⇒ [tex]y=k\frac{1}{x}[/tex]
Joint variation : When a variable varies directly with two or more than two variables,
Example : y varies directly with both x and z ⇒ y = kxz
Combined variation : When a variable varies both directly and indirectly as another variables,
Example : y varies directly with x and inversely with z ⇒ [tex]y=k\frac{x}{z}[/tex]
Now, here the given expression,
y = 4mt,
Where, y, m and t are variables and 4 is the constant of variation,
⇒ y varies directly as both m and t,
⇒ y = 4mt is an example of joint variation.
A radio telescope has a parabolic surface, as shown below.
If the telescope is 1 m deep and 12 m wide, how far is the focus from the vertex? (5 points)
For a parabolic dish, the focus is at a depth equal to one-fourth of the square of the width of the dish's aperture. Given the width as 12m, the focus of the radio telescope is 36m from the vertex.
Explanation:For a parabolic dish like a radio telescope, the focus (or focal point) is located at the depth equal to one-fourth of the square of the width (i.e., one-fourth of the square of the diameter) of the dish's aperture.
Given the width (diameter) of the dish is 12 meters, we square it to get 144. Quarter of this value is 36 m. So, the focus is 36 m from the vertex of the parabola represented by the dish's surface.
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What is next number after 2 7 8 3 12 9
1. Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
2. Divide all terms in the equation by a.
3. Subtract the constant (the term without an x) from both sides.
4. Add a constant (in terms of a and b) that will complete the square.
5. Take the square root of both sides of the equation.
6. Solve for x.
We are given that:
a x^2 + b x + c = 0
Divide all terms with c/ a:
x^2 + (b / a) x + (c / a) = 0
Subtract c from both sides:
x^2 + (b / a) x + (c / a) – c / a = 0 – c / a
x^2 + (b / a) x = - c / a
Add a constant k to complete the square:
where k = ((b / a) / 2)^2 = (b /2a)^2
x^2 + (b / a) x + k = - c / a + k
x^2 + (b / a) x + (b/2a)^2 = - c / a + (b /2a)^2
So the perfect square trinomial is:
(x + b/2a)^2 = - c / a + (b /2a)^2
Taking the square root of both sides:
x + b/2a = sqrt [- c / a + (b /2a)^2]
x = sqrt [(-c/a) + (b /2a)^2] – (b/2a)
Answer:
My equation is 3x^2 + 12x + 24 = 0. When I divide all of the terms by 3, the equation becomes x^2 + 4x + 8 = 0. When I subtract both sides by the constant, 8, the equation is x^2 + 4x = -8. When I add a constant to create the perfect square, the equation now becomes x^2 + 12x + 36 = 28. Finally, the equation simplified equals (x + 6)= the square root of 28.
Step-by-step explanation:
Without using a trigonometric ratio, find the distance from the ship to the buoy, B. Round the distance to the nearest tenth of a mile.