1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marianna [84]
3 years ago
10

If C(x) = 4x^2 - 3, find the following (a) C(0) (b) C (-1) (c) C (-2) (d) C (-3/2)

Mathematics
1 answer:
NeTakaya3 years ago
3 0

Step-by-step explanation:

C(x)=4x^2-3\\\\C(0),\ C(-1),\ C(-2),\ C\left(-\dfrac{3}{2}\right)\\\\\text{Substitute each value}\ \left\{0, -1, -2, -\frac{3}{2}\right\}\ \text{instead}\ C(x):\\\\C(0)=4(0^2)-3=4(0)-3=0-3=-3\\\\C(-1)=4(-1)^2-3=4(1)-3=4-3=1\\\\C(-2)=4(-2)^2-3=4(4)-3=16-3=13\\\\C\left(-\dfrac{3}{2}\right)=4\left(-\dfrac{3}{2}\right)^2-3=4\left(\dfrac{9}{4}\right)-3=9-3=6

You might be interested in
Select the correct answer.
tino4ka555 [31]

Answer:

A . The inequality sign always opens up to the larger number.

Step-by-step explanation:

4 0
3 years ago
A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average
marysya [2.9K]

Answer:

a) player’s expected payoff is $ 240

b) probability the player loses $1000 or more is 0.1788

c)  probability the player wins is 0.3557

d) probability of going broke is 0.0594

Step-by-step explanation:

Given:

Since there are 60 hands per hour and the player plays for four hours then the sample size is:

n = 60 * 4 = 240

The player’s strategy provides a probability of .49 of winning on any one hand so the probability of success is:

p = 0.49

a)

Solution:

Expected payoff is basically the expected mean

Since the bet is $50 so $50 is gained when the player wins a hand and $50 is lost when the player loses a hand. So

Expected loss =  μ

                        = ∑ x P(x)

                        = 50 * P(win) - 50 * P(lose)

                        = 50 * P(win) + (-50) * (1 - P(win))

                         = 50 * 0.49 - 50 * (1 - 0.49)

                        = 24.5 - 50 ( 0.51 )

                        = 24.5 - 25.5

                        = -1

Since n=240 and expected loss is $1 per hand then the expected loss in four hours is:

240 * 1 = $ 240

b)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 110.5 - 117.6 / √117.6(1-0.49)

  = −7.1/√117.6(0.51)

  = −7.1/√59.976

  = −7.1/7.744417

  =−0.916789

Here the player loses 1000 or more when he loses at least 130 of 240 hands so the wins is 240-130 = 110

Using normal probability table:

P(X≤110) = P(X<110.5)

             = P(Z<-0.916)

             = 0.1788

c)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 120.5 - 117.6 / √117.6(1-0.49)

  = 2.9/√117.6(0.51)

  = 2.9/√59.976

  = 2.9/7.744417

  =0.374463

Here the player wins when he wins at least 120 of 240 hands

Using normal probability table:

P(X>120) = P(X>120.5)

              = P(Z>0.3744)  

             =  1 - P(Z<0.3744)

             = 1 - 0.6443

             = 0.3557

d)

Player goes broke when he loses $1500

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 105.5 - 117.6 / √117.6(1-0.49)

  = -12.1/√117.6(0.51)

  = -12.1/√59.976

  = -12.1/7.744417

  =−1.562416

Here the player loses 1500 or more when he loses at least 135 of 240 hands so the wins is 240-135 = 105

Using normal probability table:

P(X≤105) = P(X<105.5)

             = P(Z<-1.562)

             = 0.0594

7 0
3 years ago
Jacob and Ashley run an animal shelter that houses only cats and dogs. they have 37 adult animals 21 cats and 16 dogs. A group o
Bond [772]
The most likely number of cats = 21/37 x 8 = 4.54 ≈ 5 cats
The most likely number of dogs = 16/37 x 8 = 3.46 ≈ 3 dogs

The probability of that arrangement happening = 1/8^2 = 1/64 = 0.00156
3 0
3 years ago
Why are standardized units of measure important to scientists?
iris [78.8K]
Why are standardized units of measure important to scientists?

5 0
3 years ago
What’s this answer ????
slega [8]
Divide by 6 on both sides to have the variable by itself. the answer is 8.
4 0
3 years ago
Other questions:
  • A 20-foot length of wire is to be cut into 2 pieces, so that the longer piece is two feet longer than two times the shorter piec
    11·1 answer
  • A local band is holding a concert. The price of a ticket to the concert is $15. The band must sell enough tickets to cover at le
    15·2 answers
  • Write two linear expressions that have a sum of 3x-8
    12·2 answers
  • Find the length of the third side. If necessary, round to the nearest tenth.<br> 15<br> 9
    7·1 answer
  • Graph the inequality on the axes below.
    12·1 answer
  • 4x + 5y = 10
    15·1 answer
  • The longest side of a triangle is 8 more units than the shortest side. The third side is 4 times the length of the shortest side
    8·1 answer
  • Which inequality is true?
    9·1 answer
  • David rents DVDs from a company that charges a $7.00 monthly fee and $1.50 for each DVD rental. He ends up paying $20.50 for the
    11·1 answer
  • Simplify. Divide the radicals.<br><br> √80<br> √20
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!