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Lana71 [14]
3 years ago
9

There are four students and a lecturer for a photography session. Determine the number of ways the people can be arranged such t

hat the lecturer stands in the middle.
Mathematics
1 answer:
steposvetlana [31]3 years ago
5 0

Answer:

24 ways

Step-by-step explanation:

Given that

Number of students = 4

Lecturer have to stand in the middle position.

We have five places in which middle place is for lecturer,now we have four places and we have to arrange four students on that four places.So there will 4! ways to arrange those students.

4!= 4 x 3 x 2 x 1

4! =24

So we have 24 ways to arrange 4 students and one lecturer .

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Please show work! Factor sin^2Θ + sin^2Θ cos^2Θ
ivanzaharov [21]

Factorization of sin²θ + sin²θ cos²θ gives us; 2sin²θ - sin⁴θ

<h3>How to simplify Trigonometric Functions?</h3>

We want to simplify;

sin²θ + sin²θ cos²θ

Let us factorize out sin²θ to get;

sin²θ(1 + cos²θ)

Now, we know that cos²θ = 1 - sin²θ

Thus;

sin²θ(1 + cos²θ) = sin²θ(1 + 1 - sin²θ)

⇒ sin²θ(2 - sin²θ)

⇒ 2sin²θ - sin⁴θ

Read more about Trigonometric functions at; brainly.com/question/6904750

#SPJ1

5 0
2 years ago
You expect to receive $10,000 at graduation in two years. You plan on investing it at 11% until you have $75,000. How long will
stich3 [128]

Answer:

about 19.31 years

Step-by-step explanation:

10000( {1.11}^{x} ) = 75000

{1.11}^{x}  = 7.5

x ln(1.11)  =  ln(7.5)

x =  \frac{ ln(7.5) }{ ln(1.11) }  = 19.31

4 0
2 years ago
6. Solve P = C + rC for r.
slavikrds [6]

Answer:

r=c2pi ok

Step-by-step explanation:

that the answer

4 0
3 years ago
Read 2 more answers
Forrest is texting while driving along the freeway at 70 miles per hour. How many feetdoes the car travel during the 3-second in
MakcuM [25]

Answer:

d = 308ft

Therefore, the car travelled 308ft in 3sec

Step-by-step explanation:

Given;

Speed v = 70miles/hour

converting the speed to ft/sec. We have

v = 70miles/hour × 5280ft/mile × 1/3600sec/hour

v = 102.67ft/sec

Time = 3 sec

To determine the distance travelled in 3sec

distance = speed × time

d = 102.67 × 3

d = 308ft

Therefore, the car travelled 308ft in 3sec

8 0
3 years ago
Which statement correctly compares the constants of variation for the graph and the equation below?
Lynna [10]

Answer:

  The equation has a greater constant of variation

Step-by-step explanation:

The graph is of a line through point (0, 0) can be represented by the equation ...

   y = kx

Using the given values for x and y, we see that ...

  3 = k·1

  k = 3 . . . . . the constant of variation for the graph

__

The given fraction can be rewritten as ...

  y = (10/3)x = (3 1/3)x

In this form, the constant of variation is 3 1/3, greater than that of the graph.

4 0
3 years ago
Read 2 more answers
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