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3 years ago

Write a recursive definition for the sequence 21,16,11,6

1 answer:

4 0

A recursive definition for the sequence shown above can be x = n-5.
21 - 5 = 16
16 - 5 = 11
11 - 5 = 6
and so on...

The number sequence has a difference of 5 in each of the values before and after them.

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A newborn baby has about 26000000000 cells an adult has about 1.9 ×10 to the third times as many cells as a newborn baby how man

KonstantinChe [14]

An adult has 37.2 trillion cells

5 0

3 years ago

Read 2 more answers

You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week

bonufazy [111]

Answer:

a) The demand function is

$q(p) = -4 p + 107$

b) The nightly revenue is

$R(p) = -4 p^2 + 107 p$

c) The profit function is

$P(p) = -4 p^2 + 133.75 p - 939$

d) The entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.

Step-by-step explanation:

a) Lets find the slope s of the demand:

$s = \frac{79-43}{7-16} = \frac{36}{-9} = -4$

Since the demand takes the value 79 in 7, then

$q(p) = -4 (p-7) + 79 = -4 p + 107$

b) The nightly revenue can be found by multiplying q by p

$R(p) = p*q(p) = p*( -4 p + 107) = -4 p^2 + 107 p$

c) The profit function is obtained from substracting the const function C(p) from the revenue function R(p)

$P(p) = R(p) - C(p) = p*q(p) = -4 p^2 + 107 p - (-26.75p + 939) = \\\\-4 p^2 + 133.75 p - 939$

d) Lets find out the zeros and positive interval of P. Since P is a quadratic function with negative main coefficient, then it should have a maximum at the vertex, and between the roots (if any), the function should be positive. Therefore, we just need to find the zeros of P

$r_1, r_2 = \frac{-133.75 \,^+_-\, \sqrt{133.75^2-4*(-4)*(-939)} }{-8} = \frac{-133.75 \,^+_-\, 53.526}{-8} \\r_1 = 10.03\\r_2 = 23.41$

Therefore, the entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.

7 0

3 years ago

Write the equation of a circle with the following pints in the picture using the completing the square method. Thanks

pantera1 [17]

So hmm notice the picture below

you have the center, and a point on the circle... all you need is the radius

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ -2}})\quad 
% (c,d)
&({{ 3}}\quad ,&{{ -4}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\leftarrow r$

then use that radius in the circle's equation

$\bf (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad center\ ({{ h}},{{ k}})\qquad
radius={{ r}}$

8 0

3 years ago

The probability of rolling a number less than 3 on a number cube 2/6. Jennifer rolls a number cube 60 times how many times shoul

Savatey [412]

Answer:

20 times

Step-by-step explanation:

Given the following :

Probability of rolling a number less than 3 on a number cube:

Required outcome = (1, 2)

Total possible outcomes = (1, 2, 3, 4, 5, 6)

Required outcome / Total possible outcomes

= 2 /6

= 1/3

Hence, if number cube is rolled 60 times, number of times a number less than 3 is expected :

(Probability of obtaining a number less than 3 in one roll × number of rolls)

= (1 / 3) × 60

= 60 / 3

= 20 times

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3 years ago

brianna bought a computer game for $36 with a coupon for %25 off, How much would it cost without the coupon

Butoxors [25]

The game would cost $45

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3 years ago