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seropon [69]
2 years ago
5

Six friends, four boys and two girls, went to a movie theater. They wanted to sit in a way so no girl sits on either first or la

st chair. How many such arrangements are possible?
Mathematics
1 answer:
mel-nik [20]2 years ago
8 0

Answer:

120 ways

Step-by-step explanation:

Since no girl wil sit either first or last

Hence, in all irrespective whether boy or girl = (6 - 1)! = 5! = 5 X 4 X 3 X 2 = 120

∴ Number of arrangements = 120 ways

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The line 3y+x=25 is a normal to the curve y=x2-5x+k.find the value of constant k.
ladessa [460]

Answer:

k = 11.

Step-by-step explanation:

y = x^2 - 5x + k

dy/dx = 2x - 5 = the slope of the tangent to the curve

The slope of the normal = -1/(2x - 5)

The line  3y + x =25 is normal to the curve so finding its slope:

3y = 25 - x

y = -1/3 x + 25/3 <------- Slope is -1/3

So at the point of intersection with the curve, if the line is normal to the curve:

-1/3 = -1 / (2x - 5)

2x - 5 = 3  giving x = 4.

Substituting for x in y = x^2 - 5x + k:

When x = 4, y =  (4)^2 - 5*4 + k  

y = 16 - 20 + k

so y = k - 4.

From the equation y = -1/3 x + 25/3,  at x = 4

y = (-1/3)*4 + 25/3 = 21/3 = 7.

So y = k - 4 = 7

k = 7 + 4 = 11.

6 0
2 years ago
What are the coordinates of the image of vertex R -3,4 after a reflection across the y-axis? (–4, 3) (4, –3) (–3, –4) (3, 4)
Feliz [49]
The coordinate of the image after being reflected is R(3,4).

When dealing with reflection of a line or shape or a figure in the coordinate plane, especially if it is reflected across the y- axis, you just have to give the opposite of the given (original) x- coordinate in order to give a symmetric figure.
7 0
2 years ago
Read 2 more answers
What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5? 20 pts.
fgiga [73]

ANSWER

a_n = 11 - 3n

EXPLANATION

The explicit rule for an arithmetic sequence is given by:

a_n = a_1 + d(n - 1)

It was given that:

a_1 = 8

and

a_2 = 3

The common difference is

d = 5 - 8 =  - 3

We plug in the values into the explicit formula to get,

a_n = 8+  - 3(n - 1)

Expand to get,

a_n = 8 - 3n  + 3

The explicit rule is

a_n = 11 - 3n

6 0
2 years ago
A pond had 60 fish. 27 were carp and the rest were tench. 10 fish were added. The probability that a fish picked at random is a
ivanzaharov [21]

Answer: 2

<u>Explanation:</u>

A pond had 60 fish but 10 were added so now the pond has 70 fish.

The probability of choosing a carp is 1/2 so \frac{1}{2} (70) = 35 are now carp.  

There were 27 carp and now there are 35 carp so 8 carp were added.

10 fish were added and 8 of them were carp so 2 of them were tench.

6 0
2 years ago
Select the correct answer. Tanya distributes pencils to students in her class for an upcoming test. The number of pencils she ha
aliina [53]

Answer:

D.

Step-by-step explanation:

p=3s

p=3(16)

p=48 pencils

8 0
2 years ago
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