Five students and two teachers pose for a picture.in how many ways can they line up side by side for a picture. 2. In how many ways can they line up if they must have the teachers on both sides of the picture? 3.what is the probability that the two teachers occupy two of the three middle slots?

Answers

Answer 1
First, 5 students and 2 teachers is 7 different people. That means there are 7! Ways they can stand in a line. (7! Means 7x6x5x4x3x2x1)
That is 5040 ways.

Having the teachers on either side with the five students in the middle splits the question. There are 2 ways the teachers could stand (TA on left, TB on right or vice versa). There are 5! Ways to arrange the students in the middle. That is, 120. So combined, there are 2x120 ways to have them lined up with the teachers on either side. 240 ways.

Out of the 5040 ways for all of them to line up, one teacher will be in the middle 3 spaces 3/7 of the time. The second teacher will be on one of the remaining 2 central spaces 2/6 (1/3) of the time. 3/7x1/3 = 1/7. That means 1/7 or 14.29% of the time, the two teachers will occupy two of the three middle slots.

Related Questions

Find the equation of the line.
Use exact numbers.

Answers

Answer:

Y = 2x + 5

Step-by-step explanation:

2x is your slope and 5 is your y intercept.

The formula for this is: y = mx + b

please help i have to resit math final so bare with me


help me with this equation : x^2 - 7 = 0 IN QUADRATIC EQUATION

PS. 1st one to answer gets a brainly crown :)

Answers

I hope this is the correct answer

Prove That

cot 2A + tan 2A cot 2A-tan 2A = sec 4A​

Answers

Answer:

*Refer the graph

Step-by-step explanation:

Blue : y= cot 2A + tan 2A cot 2A-tan 2A

domain a ≠ kπ/4

Yellow : y= sec 4A

domain a ≠ π/8 + kπ/4

vertical intercept (0,1)

What is the domain of the following function ?

Answers

Answer:

{-6, 1, 5, 8}

Step-by-step explanation:

The domain is the set of x-coordinates or inputs.

{-6, 1, 5, 8}

Answer is A
-6, 1, 5, 8

Domain is always gonna be in the left side of the relation, while range is the right (7, -2.)

Which of the following are remote interior angles of _1? Check all that apply.
u A. 25
I B. 26
III C. 21
D. 24
E. 23
F. 22

Answers

Answer:

angle 3

angle 2

Step-by-step explanation:

Mathematically, from the angle sum theorem of triangles, the sum of two opposite interior angles of a triangle equals the exterior angle on the third side

Now, for angle 1, it is an exterior angle for angle 4

The two other opposite interior angles that would make angle 1 is simply angles 3 and 2

I need help with this, Im never good with these

Answers

Answer:

(a) basketball

(b) hat

(c) stuffed animal

explanation:

I'm not sure if got right but from what i see;

Chances from 1-23 you get a stuffed boi

Chances from 24-54 you get a hat (why)

Chances from 55-100 you get a basketball

Winner 5 got 90, which is between 55-100

Winner 6 got 35, which is between 24-54

winner 8 got a 7, which is between 1-23

Hope I didn't read it wrong

Find the angle between u = (8,-3) and v = (-3,8). Round to the nearest tenth of a degree.

Answers

Mark Brainliest please

Answer is 90 degrees

Taking a discount of 50% off followed by a discount of 50% off results in a total discount of_______. A. 25% B. 50% C. 75% D. 100%​

Answers

Answer:

A. 25%

Step-by-step explanation:

50% = 1/2

1/2 of 1/2 = 1/2 * 1/2=

1/4 = 25%

Answer:

100%-50%=50% so the answer is B

please help and dont get it wrong! thank you =)))

Answers

Answer:

tanong mo sa may mga nakaka alam niyan para walang mali, thanks

algebra help pls answer

Answers

Answer:

[tex]\frac{-1+1}{0-(-2)}=0[/tex]

[tex]ANSWER: A)~0[/tex]

------------------------------

HOPE IT HELPS

HAVE A GREAT DAY!!

Ten years from now, Abdul will be twice as old as his son pavel ten years ago, Abdul was seven times as old as pavel how old are Abdul and pavel now?

Answers

Answer:

Age of Pavel = y - 10

→ x - 7y = -60. Now, Calculating X. Hence, Present age of Abdul = 38.

Step-by-step explanation:

hope this is helpful.

What
Is the volume of this object

Answers

Answer:

100

Step-by-step explanation:

5x4=20

20x5=100

If you times the length by with: 5x4 you get 20. Then you multiply 20x5 then you get your volume: 100

Does every integer have a successor?

Answers

Answer:

Yes every integer has a successor and a predecessor

Step-by-step explanation:

What goes in the blanks? The measure of angle θ is 7π/4. The measure of its reference angle is _____°, and tan θ is ______?

Answers

Answer:

The measure of angle θ is 7π/4. The measure of its reference angle is 45°, and tan θ is -1.

Answered by GAUTHMATH

Se conoce que 6 jarras cuestan lo mismo que 5 cubiertos y que 3 cubiertos cuestan S/. 7.20, ¿Cuánto costarán 7 jarras? (2 PUNTOS)

Answers

Answer:

7 jarras costarán 14 $

Step-by-step explanation:

Si 3 cubiertos cuestan  7.20 $

1 cubierto cuesta     7.20/3  =  2.40 $

y 5 cubiertos cuestan    5* 2.40   =  12 $

que también cuestan 6 jarras  =  12 $

Luego 1 jarra cuesta  12/6  =  2  $

Por lo que 7 jarras costarán:  7 * 2  =  14 $

Below are the ages of the employees of a small gift shop in town. Describe the data using the five number summary.

17, 18, 19, 40, 42, 16, 33, 17, 33, 44, 19, 40, 37, 26, 25


helppppp pleaseeeee

Answers

median is 26

maximum is 44

minimum is 17

third quartile is 40

first quartile is 18    

should be correct but I'm not sure

The median is 26, the maximum value is 44. The minimum value is 17. The third quartile is 40 and first quartile is 18.

What are quartiles?

When we get data that can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each group approximately possessing 25% of the data.

The given data set is;

17, 18, 19, 40, 42, 16, 33, 17, 33, 44, 19, 40, 37, 26, 25

The data using the five-number summary.

The median is 26

The maximum value is 44

The minimum value is 17

The third quartile is 40

The first quartile is 18  

Learn more about quartiles here:

brainly.com/question/9260741

#SPJ2

a package is accidentally dropped from a helicopter from a height of 3,136ft. if the equation for height as a function of time is h(t) = -16t^2 + initial height where t is time in seconds and h(t) is height in feet, how many seconds will it take for the package to hit the ground?

Answers

Answer:

t = 14 seconds

Step-by-step explanation:

Given that,

A package is accidentally dropped from a helicopter from a height of 3,136ft.

The equation for height as a function of time is :

[tex]h(t) = -16t^2 + \text{initial height}[/tex]

So,

[tex]h(t) = -16t^2 +3,136[/tex]

When it hits the ground, h(t) = 0

So,

[tex]-16t^2 +3,136=0\\\\-16t^2=-3136\\\\t^2=\dfrac{3136}{16}\\\\t^2=196\\\\t=14\ s[/tex]

So, it will take 14 seconds for the package to hit the ground.

pls help me i’m so stuck

Answers

Answer:

Step-by-step explanation:

If a point (x, y) is reflected across y = -x, coordinates of the image point will be,

(x, y)→ (-y, -x)

Following this rule,

Vertices of the triangle will be,

(3, 1) → (-1, -3)

(3, -2) → (2, -3)

(6, -3) → (3, -6)

Therefore, image of the given triangle A will be,

(-1, -3), (2, -3) and (3, -6)

Find the missing side of the right triangle if two sides are 6, and 10

Answers

approx. 11.661… or 2 • sr of 35

Hope this helps!!

(If you have any questions, feel free to ask in the comments, If you found my answer helpful, please consider marking my answer brainliest, thanks!!)

Which product is negative?
(-3/8)(-5/7)(1/4)

(3/8)(-5/7)(-1/4)

(3/8)(5/7)(1/4)

(-3/8)(-5/7)(-1/4)

Answers

Answer:

[tex]( - \frac{ 3}{8} )( - \frac{5}{7} )( - \frac{1}{4} )[/tex]

Step-by-step explanation:

[tex]( - \frac{ 3}{8} )( - \frac{5}{7} )( - \frac{1}{4} )[/tex][tex] \frac{3}{8} \times \frac{5}{7} \times (- \frac{1}{4} )[/tex][tex] \frac{3 \times 5}{8 \times 7} ( - \frac{1}{4} )[/tex][tex] - \frac{15}{56 \times 4} [/tex][tex] - \frac{15}{224} [/tex]Hope it is helpful.....

Can someone help me with this math homework please!

Answers

Answer:

same after 3 years

because .............................

Answer:

The populations of orangutans will be same after 3 years

Step-by-step explanation:

Let the populations or orangutans is the same after n years

Decrease in population of oragnutans in the first study

=784-25n=784−25n

Decrease in population of oragnutans in the second study

=817-36n=817−36n

According to the question

784-25n=817-36n784−25n=817−36n

\implies 36n-25n=817-784⟹36n−25n=817−784

\implies 11n=33⟹11n=33

\implies 11n=33⟹11n=33

\implies n=\frac{33}{11}⟹n=

11

33

\implies n=3\text{ years}⟹n=3 years

Therefore, the populations of orangutans will be equal after 3 years

Hope this is helpful.

Solve the inequality 6 is greater or equal than m- 1

Answers

Answer:

7 ≥ m OR m ≤ 7

Step-by-step explanation:

You can actually solve this in two ways , either :

6 ≥ m - 1

6 + 1 ≥ m

7 ≥ m

OR

m -1 ≤ 6

m ≤ 6 + 1

m ≤ 7

Both are correct.

can someone help me to solve this question. the questions is about to calculate the value of x . please help me thankyou​

Answers

Answer:

180-(63+63)

=180-126

=54

180-(37+90)

180-127

53

180-(54+53)

=180-107

=73°

Answer:

Step-by-step explanation:

AC = AD So,  Δ ACD is as isosceles triangle.

∠ADC ≅∠ACD = 63°

In ΔACD ,

    63 + 63 + ∠DAC = 180   {Angle sum property of triangle}

            126 + ∠DAC = 180

                     ∠DAC = 180- 126

                     ∠DAC = 54°

In ΔABC,

90+ 37 + ∠CAB = 180

        127 + ∠CAB = 180

                 ∠CAB = 180 - 127

                 ∠CAB = 53

∠EAD + ∠DAC + ∠CAB = 180   {Straight line angles}

x + 54  + 53 = 180

        x + 107  = 180

                  x = 180 -107

x = 73°

     


Over what interval is the parabola below decreasing?

Answers

I think it’s the first answer choice

Please help! Awarding Brainly :)

Answers

Answer:

Step-by-step explanation:

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 8 to 5. If there were 4605 no votes, what was the total number of votes?

I need it by tonight for a pop quiz tomorrow

Answers

Answer:

Try to do it yourself, since you have a test tomorrow

Good luck

Step-by-step explanation:

5: 4605

13 (8+5):

[tex] \frac{4605}{5} \times 13 = [/tex]

=Your answer

if P = (1,6) find r90° (P)

Answers

Answer:

(-6,1) got you homie

Step-by-step explanation:

Find the length of CZ

A. 32
B. 45
C. 9
D. 1

Answers

Answer:

c

Step-by-step explanation:

just took it

Answer:

D. 1

Step-by-step explanation:

CA = 17

ZA = 16

CZ + ZA = CA

CZ + 16 = 17

CZ = 1

D. 1

The third National Health and Nutrition Examination Survey collected body fat percentage (BF%) and gender data from 13,601 subjects ages 20 to 80. The average BF% for the 6,580 men in the sample was 23.9, and this value was 35.0 for the 7,021 women. The standard error for the difference between the average men and women BF%s was 0.114. Do these data provide convincing evidence that men and women have different average BF%s. You may assume that the distribution of the point estimate is nearly norma

Answers

Answer:

Yes, the data provides convincing evidence that men and women have different average BF%s

Step-by-step explanation:

The given parameters are;

The number of the subjects ages 20 to 80 = 13,601

The body fat percentage, BF%, for the 6,580 men, [tex]\overline x_1[/tex] = 23.9

The body fat percentage, BF%, for the 7,021 women, [tex]\overline x_2[/tex] = 35.0

The standard error for the difference between the average men and women = 0.144

The null hypothesis, H₀; [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, Hₐ; [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

The test statistic = (35.0 - 23.9)/(0.114) = 97.368

Therefore, given that the z-test is larger than the critical-z, we reject the null hypothesis, H₀, therefore, there is convincing statistical evidence to suggest that men and women have different body average BF%

Meena has ₹600 in the form of notes of ₹10 and ₹20 denomination. Number of ₹10 notes is three times the number of ₹20 notes. Find the number of notes of each denomination.​

Answers

Answer:

Meena has twelve (12) ₹20 notes and thirty six (36) ₹10 notes

Step-by-step explanation:

The amount Meena has as notes in ₹10 and ₹20 denominations = ₹600

The number of ₹10 notes = 3 × The number of ₹20 notes

Let 'x' represent the number of ₹20 notes Meena has, we get;

The number of ₹10 notes = 3 × x

The total number of notes = x × 20 + 3·x × 10 = 50·x = ₹600

∴ 600/50 = 12

The number of the ₹20 notes, x = 12

The number of the ₹10 = 3 × x

∴ The number of the ₹10 = 3 × 12 = 36

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