Mathematics High School

Eight two-person teams are participating in a three-legged race. Find the number of orders in which all 8 teams can finish the race.

Answers

Answer 1
Each team needs two people for a 3-legged race.
Therefore, the number of orders (combinations) of 2 people at a time from 8 is
₈C₂ = 8!/(2!6!)
      = (8*7*6!)/(2*6!)
      = (8*7)/2
      = 56/2
      = 28

Answer: 28
Answer 2

Answer:

thx for points man

Step-by-step explanation:

Related Questions

On a 10-item test, three students in professor hsin's advanced chemistry seminar received scores of 2, 5, and 8, respectively. for this distribution of test scores, the standard deviation is equal to the square root of

Answers

The standard deviation is 5 because (2+5+8)/3=5. So the equal square root is square root of 25

f(x) = Square root of x plus eight.; g(x) = 8x - 12 Find f(g(x))

Answers

Final answer:

To find f(g(x)), substitute g(x) into f(x) and simplify the expression to get the final answer. The final answer to the question would be as f(g(x)) = 8x⁴ - 32x³ + 32x² + 3

Explanation:

To find the value of f(g(x)) the following steps to be followed where the value of f(x) be substituted in g(x).

f(x) = 2x² + 3; g(x) = −2x² + 4x

Find f(g(x)) by substituting g(x) into f(x): f(g(x)) = 2(-2x² + 4x)² + 3

Simplify the expression: f(g(x)) = 2(4x⁴ - 16x³ + 16x²) + 3

Final answer after expansion: f(g(x)) = 8x⁴ - 32x³ + 32x² + 3

what is the value of x to the nearest tenth

Answers

12.0 is the value of x to the nearest tenth
I think it is 12 because the approximate diameter is 24 and to x is the radius. To find the radius, you take the diameter and divide by two.

The last step in a proof contains the

Answers

The last step in a proof contains the conclusion.
hope this helps:)
The answer is "Conclusion". Feel free to ask more if needed.

The probability that an american industry will locate in shanghai, china, is 0.7, the probability that it will locate in beijing, china, is 0.4, and the probability that it will locate in either shanghai or beijing or both is 0.8. what is the probability that the industry will locate

Answers

The answer to this equation is 0.5

-8-(3x+6)=4-x

Wow I'm dumb lol

Answers

hello: 
solve for x : 
-8-(3x+6)=4-x
-8 -3x-6 =4-x
-3x+x = 8+6+4
-2x =18
x = 18/-2
x= -9

The average grade mark received on 4 tests was 94. if he drops his lowest grade of 85, what will his new average be

Answers

After dropping his lowest marks of 85 the new average test mark is 97.

Given, average test score of 4 tests is 94.

Average concept:

Average = sum of all the observations / total number of observations.

Average of 4 test marks = 94

94 = Sum of all the marks obtained in 4 tests / 4

Sum of all the marks obtained in 4 tests = 94 × 4

Sum of all the marks obtained in 4 tests = 376

Now the lowest marks of 85 are removed,

Remaining sum of 3 test marks = 376  - 85

Remaining sum of 3 test marks = 291

New average of 3 tests:

Average of 3 test marks = 291/3

Average of 3 test marks  = 97

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At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]

Answers

he rides for 7 min and waits in line for 20 min, if he was to wait in line for 60 min then he would ride for 21 min, if you divide 20/60 then you'll get 3. Multiply the 7 with that 3 and you'll get "21".

Answer:

21

Step-by-step explanation:

Alice wants to buy some paper towels. She has two options. She can either buy a package of four rolls or she can buy one roll now and buy another when she runs out. Which of these options is better? Give reasons for your answer.

Answers

buying 4 rolls. If she buys 4 rolls, whenever she used up one roll she already has 3 to replace it. If she buys one roll and then one later, when she uses up the one roll she will have to go buy more

Answer:

Correct Answer: Alice should buy the package of four paper towels because buying in bulk means she gets each roll of towels for less money.

Step-by-step explanation:

For the function f(x) = –5x, which ordered pair will be a point on the graph of the function?
A.
(–5, 1)
B.
(2, 10)
C.
(15, –3)
D.
(0, 0)

Answers

f(x) = –5x
when x = 0, f(x) = –5(0) = 0

answer is D.
(0, 0)

Answer:

0,0 i think.. not sure so dont get mad at me

Step-by-step explanation:

What value should go in the empty box to complete the calculation for finding the product of 62.834 × 0.45?

Answers

I assume your empty box is the product lol:)

So the product is: 28.2753. No tricks, better to use calculator, but you can do by hand too, not that hard.
28.2753  its the answer just use google calculator it's easy to use

(NEED HELP!!!)Which of the following lines is perpendicular to y= 3x + 2?

A. y=3x -1/2

B. y=-1/3x+6

C. y=1/3x+2

D. y=3x+1/2

Answers

The correct answer is:  [B]:  " y = (-⅓)x  + 6 " .
____________________________________________________________

Answer:

[tex]y=\frac{-1}{3}x+6[/tex]

Step-by-step explanation:

We have to find the equation of the line from the options given which is perpendicular to the line y=3x+2.

In order to do so we must know that , the product of the slope of the two perpendicular lines is always -1

Hence

if the slope of line A is "m" and the line B which is perpendicular to A, will have [tex]-\frac{1}{m}\\[/tex]

Also , in the slope intercept form of any equation the coefficient of x is our slope. Hence the slope of y=3x+2., is 3

Hence the slope of any line perpendicular to this will be [tex]\frac{-1}{3}[/tex]

as the product of two slopes is -1

Hence in the given options only c options has the line whose slope is  [tex]\frac{-1}{3}[/tex]

Two way Frequency table question

Answers

Answer: choice A

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Work Shown:

P(TV) = (number who watch tv)/(number total)
P(TV) = 30/100
P(TV) = 0.30

P(Girl) = (number of girls)/(number total)
P(Girl) = 55/100
P(Girl) = 0.55

P(TV)*P(Girl) = 0.30*0.55 = 0.165 which rounds to 0.17
We'll use this value later. So let's call this M = 0.17

Look in the "girl" row and "tv" column. The value 17 is here.
This is out of 100 people total, so
P(TV and Girl) = 17/100 = 0.17
Call this value N = 0.17

Because M = N = 0.17 approximately, this means that the two variables "TV" and "Girl" are approximately independent

So the equation P(TV and Girl) = P(TV)*P(Girl) is approximately true in this example.

This points to choice A being the answer.

You're 35 years old now, and you want to purchase life insurance which will cover your spouse for your lost income in the event of your death. You want this policy to last until what would be your normal retirement age of 65. Based on the given information, what is the best policy to buy?

Answers

a 30 year term policy .

30 year term policy beacause until you retire you want to be insured.

salas little brother is learning to talk. he has a vocabulary of 30 words. each week his vocabulary grows by about 6%. at this rate how many words will he know 5 weeks from now

Answers

30 * (1+0.06)^5=

30* 1.338225578 = 40.146

 he will know 40 words in 5 weeks

True or false? in order to inscribe a circle in a triangle, the circle's center must be placed at the circumcenter of the triangle

Answers

Answer:

False.

Step-by-step explanation:

A inscribe circle in a triangle means to draw the biggest circle possible inside such triangle. To do that perfectly, we first have to find the incenter of the circle, which is the intersection of all three internal bisector of the triangle, that point is the center of the inscribed circle.

Therefore, the statement is false.

In addition, a circumcenter allow to perfectly draw a circumscribed circle, which is outside the triangle, which is not the case here.

An image showing the inscribed circle is attached.

Answer:

false

Step-by-step explanation:

angle LMP and angle PMN are complementary. Find the value of x.

A. 22.5
B. 7.5
C. 15
D. 30

Answers

complimentary angles add up to 90 degrees

2x + 4x = 90
6x = 90
x = 90/6
x = 15 <==
The answer is C because if you multiply 15 * 4 and 15 * 2 it will sum to 90

Who can help me with that one please ? Thanks!

Answers

∠APB is an inscribed angle  
The measure of the intercepted arc is twice that of the inscribed angle ⇒
arc AB = 2 * ∠APB = 2 * 108 = 216°

The original price of a couch is $650. It is on sale for $546. What is the percent change in the price off the couch?

Answers

%change=100(final-initial)/initial

%change=100(546-650)/650

%change= -16%

So 16% was taken off of the original price.

In the diagram below, line segment bc is an altitude of triangle abd. What is the length of line age meant cd? If necessary, round your answer to two decimal places, PLEASE HELP ME IM REALLY STUCK

Answers

check the picture below.

running a perpendicular line like so from the right-angle, makes three similar triangles, the large, containing the smaller ones, and a medium and a small one.  Now, using proportions, you can just  use there, the medium and smalle to get "x".

a lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. Describe what is being measured in this experiment and what variable is being manipulated?

Answers

The goal of any experiment is to test the hypothesis by adjusting the independent variables so you can see the trend of the dependent variable that you want to investigate. The independent variables are parameters that you manipulate. In this experiment, that would be the time of day. You have two independent variables: night and day. The speed of the mice is the parameter that you will measure. Once you do these set-up, you can conclude in the end the effect of the time of day on the speed of the mice. 

y=4x -1 and 12x=3y+7

Answers

You didn't really ask a question, so I'm assuming you want to know if there are any solutions to BOTH equations.

Use the first equation to substitute 4x - 1 for y in the second equation:

12x = 3(4x - 1)+7
12x = 12x - 3 + 7
12x = 12x +4
0 = 4

The last equation is FALSE, indicating the system of two equations has no solution.

Sec^-1(-square root 2)

Answers

[tex]\bf \textit{let's say that, is an angle }\theta\quad so\qquad sec^{-1}(-\sqrt{2})=\theta \\\\\\ \textit{this means}\qquad sec(\theta )=-\sqrt{2}\quad but\quad sec(\theta)=\cfrac{1}{cos(\theta)}\qquad then \\\\\\ \cfrac{1}{cos(\theta)}=-\sqrt{2}\implies \cfrac{1}{-\sqrt{2}}=cos(\theta ) \\\\\\ \textit{now, if we rationalize the denominator, we get }-\cfrac{\sqrt{2}}{2} \\\\\\ -\cfrac{\sqrt{2}}{2}=cos(\theta )\implies cos^{-1}\left( -\frac{\sqrt{2}}{2} \right)=cos^{-1} [cos(\theta )][/tex]

[tex]\bf cos^{-1}\left( -\frac{\sqrt{2}}{2} \right)=\measuredangle \theta \implies \measuredangle \theta = \begin{cases} \frac{3\pi }{4}\\ \frac{5\pi }{4} \end{cases}[/tex]

Two numbers have a sum of 30 and a product of 209. what is the positive difference between them?

Answers

y + x = 30
xy = 209
y = 30 -x
x(30-x) = 209
30x - x^2 = 209
x^2 - 30x + 209 = 0
x = 19
y = 11

the difference is 19-11 = 8


The numbers are 11 and 19.

Given to us,Sum of the two numbers = 30,Product of the two numbers = 209,

Assumption

Let's assume that the first number be a and the second is b.

equation 1,

a + b = 30

equation 2,

ab = 209

Therefore, in equation 1,

[tex]a\times b = 209\\b= \dfrac{209}{a}[/tex]

substitute the value of b in equation 1,

[tex]a+b=30\\\\a+\dfrac{209}{a}=30\\\\\dfrac{a^2+209}{a} =30\\\\a^2 +209 = 30a\\a^2-30a +209 = 0[/tex]

[tex]a^2 -30a+209= 0\\a^2 -19a-11a+209= 0\\a(a-19)-11(a-19)=0\\(a-11)(a-19)=0[/tex]

Substituting the factor against 0,

[tex](a-11) = 0\\a = 11\\\\(a-19)=0\\a = 19[/tex]

Therefore, the numbers are 11 and 19.

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What is the work done by moving in the force field f~ (x, y) = h2x 3 + 1, 2y 4 i along the parabola y = x 2 from (−1, 1) to (1, 1)?

a.compute directly

b.use the theorem?

Answers

The force field seems to be

[tex]\mathbf f(x,y)=\langle2x^3+1,2y^4\rangle[/tex]

(though it's not entirely clear whether that's it...)

The parabolic path can be parameterized by

[tex]\mathbf r(t)=\langle t,t^2\rangle[/tex]

where [tex]-1\le t\le1[/tex]. Then the work done by the field along the path is

[tex]\displaystyle\int_C\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{t=-1}^{t=1}\langle2t^3+1,2t^8\rangle\cdot\langle1,2t\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_{-1}^1(2t^3+1+4t^9)\,\mathrm dt[/tex]
[tex]=2[/tex]

Not sure what theorem is being referred to in part (b). Perhaps you mean the gradient theorem? In which case you would need to show that there's a scalar function [tex]f(x,y)[/tex] such that [tex]\nabla f(x,y)=\mathbf f(x,y)[/tex]. We have

[tex]\nabla f(x,y)=\left\langle\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y}\right\rangle=\left\langle2x^3+1,2y^4\right\rangle[/tex]

from which we have

[tex]\dfrac{\partial f}{\partial x}=2x^3+1\implies f(x,y)=\displaystyle\int(2x^3+1)\,\mathrm dx[/tex]
[tex]\implies f(x,y)=\dfrac12x^4+x+g(y)[/tex]

[tex]\implies\dfrac{\partial f}{\partial y}=g'(y)=2y^4[/tex]
[tex]\implies g(y)=\dfrac25y^5+C[/tex]

[tex]\implies f(x,y)=\dfrac12x^4+x+\dfrac25y^5+C[/tex]

We have a candidate for a potential function, so we apply the gradient theorem, which asserts that the value of the line integral is path independent and can be determined by evaluating the potential function at the endpoints of the path. We then have

[tex]\displaystyle\int_C\mathbf f(x,y)\cdot\mathrm d\mathbf r=f(1,1)-f(-1,1)[/tex]
[tex]=\dfrac{19}{10}-\left(-\dfrac1{10}\right)[/tex]
[tex]=2[/tex]

as expected.

In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.

Find a quadratic model for the data in the table. Type your answer below. Show your work.


Answers

You have to solve 3 equations pretty much simultaneously here using the x and y values in the general form of the quadratic equation [tex]y=a x^{2} +bx+c[/tex]
Start with the first values of x=0 and y=5.1 to solve for c:
[tex]5.1=a(0) ^{2} +b(0)+c[/tex] so c = 5.1
Next use the second x and y values along with the value of c in the next equation:
[tex]3.03=a(1) ^{2} +b(1)+5.1[/tex] gives you
-2.07 = a + b.  Solve this for a:
a = -2.07 - b
Finally use the third set of numbers with the c value AND the subbed value for a:
[tex]1.17=a(3) ^{2} +b(3)+5.1[/tex]
1.17 = 9(-2.07 - b)+ 3b + 5.1 which simplifies to:
1.17 = -18.63 - 9b + 3b + 5.1 which further simplifies to:
14.7 = -6b and b = -2.45
Now you have c and b, let's find a using one of the simplified equations:
-2.07 = a + b
-2.07 = a - 2.45
a = .38
So here's your equation:
[tex]y=.38 x^{2} -2.45x+5.1[/tex]

A normal curve is ___________ about the mean. consequently, 50% of the total area under a normal distribution curve lies on the left side of the mean, and 50% lies on the right side of the mean.

Answers

In statistics, when you gather data points for the same test, you construct a distribution graph. For example, you make a statistics based on the score of a class for a 145-item test. You graph it based on frequency such as, 10 students got 50 points and so and so forth. When that test have a few outliers and have more or less the same score, you form a normal distribution graph. It is more commonly known as the Gaussian Bell Curve. An example would be shown in the picture.

A normal distribution curve is symmetric about the mean. As a result, the area under the curve on the left side of the mean would be equal to the area under the curve on the right side of the mean. So, each would constitute 50%.

If the sum of 7 and 9 is more than 12 add 3; if less, subtract 2. the correct answer is

Answers

The sum of 7 and 9 is:

7 + 9 = 16

The sum which is 16 is greater than 12. Therefore we add 3 to the sum:

16 + 3 = 19

Therefore the correct answer to this problem is 19.

The average of six numbers is 4. a seventh number is added and the new average is 5. what is the seventh number?

Answers

the average of 6 numbers is 4....
t/6 = 4.....t = 24 (the total of the 6 numbers)

(24 + x) / 7 = 5
24 + x = 35
x = 35 - 24
x = 11 <== ur 7th number

According to the question, the seventh number is 11.

Use the concept of average defined as:

Average, also known as the mean, is a statistical measure that represents the central value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total count of numbers.

To find the seventh number,

If the average of six numbers is 4, then the total sum of those six numbers would be 6 multiplied by 4, which is 24.

Assume the seventh number is 'x'.

If the new average (after adding the seventh number) is 5, then the total sum of all seven numbers would be 7 multiplied by 5, which is 35.

To find the seventh number 'x',

Subtract the sum of the initial six numbers (24) from the sum of all seven numbers (35).

This gives us 35 - 24 = 11.

Hence,

The seventh number is 11.

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Raina makes eight dollars for each hour of work. Write an equation to represent her total pay p after working h hours

Answers

p=8h is the equation which shows the total pay is 8 times the number of hours worked.
P= 8h

P is her total pay
h is the amount of hours so if she works one hour she makes 8x 1
2 hours 8x2 and so on
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The first method, then, of getting fire for use was to light sticks of wood at a flame kindled by natureby a volcano, perhaps, or by a stroke of lightning. These firebrands were carried to the home and used in kindling the fires there. The fire secured in this way was carefully guarded and was kept burning as long as possible. But the flame, however faithfully watched, would sometimes be extinguished. A sudden gust of wind or a sudden shower would put it out. Then a new firebrand would have to be secured, and this often meant a long journey and a deal of trouble.In 1827, John Walker, a druggist in a small English town, tipped a splint with sulphur, chlorate of potash, and sulphid of antimony, and rubbed it on sandpaper, and it burst into flame. The druggist had discovered the first friction-chemical match, the kind we use to-day. It is called friction-chemical because it is made by mixing certain chemicals together and rubbing them. 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