Given the exponential function f(x)=50•2^x determine the rate of change over the interval (1,4)

A nationwide survey of college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking. I

Whitepunk [10]

Answer:

a) P(X≥6) = 0.9614

b) P(7≤ X ≤9) = 0.628

c) P(X≤5) = 0.0386

Step-by-step explanation:

This can be solved using the binomial distribution formula:

P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

Where p = probability of success

q = probability of failure = 1-p

n = number of trials

x = number of successful trials

We have p = 70% = 0.7

n = 12

a) Find the probability that the number who disapprove of smoking pot daily is no less than 6 i.e. P(X≥6). This can be calculated as:

P(X≥6) = 1 - P(X<6)

= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [¹²C₀ (0.7)⁰(0.3)¹² + ¹²C₁ (0.7)¹(0.3)¹¹ + ¹²C₂ (0.7)²(0.3)¹⁰ + ¹²C₃ (0.7)³(0.3)⁹ + ¹²C₄ (0.7)⁴(0.3)⁸ + ¹²C₅ (0.7)⁵(0.3)⁷]

= 1 - (0.000000531 + 0.0000148 + 0.0001909 + 0.00148 + 0.00779 + 0.02911)

= 1 - 0.0386

P(X≥6) = 0.9614

b) P(7≤ X ≤9) = P(X=7) + P(X=8) + P(X=9)

= ¹²C₇ (0.7)⁷(0.3)¹²⁻⁷ + ¹²C₈ (0.7)⁸(0.3)¹²⁻⁸ + ¹²C₉ (0.7)⁹(0.3)¹²⁻⁹

= 0.158 + 0.231 + 0.239

P(7≤ X ≤9) = 0.628

c) P(X≤5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

= ¹²C₀ (0.7)⁰(0.3)¹² + ¹²C₁ (0.7)¹(0.3)¹¹ + ¹²C₂ (0.7)²(0.3)¹⁰ + ¹²C₃ (0.7)³(0.3)⁹ + ¹²C₄ (0.7)⁴(0.3)⁸ + ¹²C₅ (0.7)⁵(0.3)⁷

P(X≤5) = 0.0386

4 0

3 years ago

Solve this system of equations. <br><br> 12x − 18y = 27 <br> 4x − 6y = 10

Marrrta [24]

Answer:

no solution

Step-by-step explanation:

12x − 18y = 27

4x − 6y = 10

Multiply the second equation by -3 so we can eliminate x

-3(4x − 6y) = 10*-3

-12x +18y = -30

Add the first equation to this new equation

12x − 18y = 27

-12x +18y = -30

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

0 = -3

This is not a true equation, so there is no solution

8 0

3 years ago

On the planet of Mercury, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas,

erastova [34]

Answer:

a

The distribution of X is normal

b

$P(X < 1.4) = 0.12654$

c

$P(X > 3.5) = 0.36051$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 3 \ hours$

The standard deviation is $\sigma = 1.4 \ hours$

Generally given from the question that the amount of time spent alone by the population size is normally distributed then then the distribution of X (i.e the amount of time spent by the sample size (the one Mercurian)) will be normally distributed

Generally the probability that the child spend less than one hour in a day is mathematically represented as

$P(X < 1.4) = P(\frac{X - \mu}{\sigma} < \frac{1.4 - \mu}{\sigma} )$

Here $\frac{X - \mu}{\sigma } = Z (The\ standardized\ value\ of\ X)$

So

$P(X < 1.4) = P(Z < \frac{1.4 - 3.0}{1.4} )$

$P(X < 1.4) = P(Z < -1.1429 )$

From the z-table the value of

$P(Z < -1.1429 )=0.12654$

So $P(X < 1.4) = 0.12654$

Generally the percentage of children that spends over 3.5 hours unsupervised is mathematically represented as

$P(X > 3.5) = P(\frac{X - \mu}{\sigma} > \frac{3.5 - \mu}{\sigma} )$

$P(X > 3.5) = P(Z > \frac{3.5 - 3.0}{1.4} )$

$P(X > 3.5) = P(Z > 0.3571 )$

From the z-table the value of

$P(Z >0.3571 )=0.36051$

So $P(X > 3.5) = 0.36051$

5 0

3 years ago

Chapter 11 lesson 1 math homework math in my world

kvv77 [185]

I’m sorry but what???

7 0

3 years ago

HELPP PLEASE DUE TOMMOROW PLEASE ANSWER QUESTION B

marin [14]

Answer:

28 non-blue marbles.

Step-by-step explanation:

Initial probability of choosing a blue marble = 4/12

Let the number of non-blue marbles to be added be x.

$\frac{4}{12+x} =\frac{1}{10}$

$12+x=40$ (cross multiply)

$x=28$

4 0

4 years ago