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iren2701 [21]
3 years ago
8

Assume there are 11 voting districts in the county.  Polly Tician is running for office. She figures she must win at least 7 of

the districts to win the election.  If she has an equal chance of 60% to win any one district, what are her chances of winning the election?
​
Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
5 0

Answer:

53.3%

Step-by-step explanation:

Here we will use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

In this case, n = 11, r ≥ 7, p = 0.6, and q = 0.4.

P = ₁₁C₇ (0.6)⁷ (0.4)⁴ + ₁₁C₈ (0.6)⁸ (0.4)³ + ₁₁C₉ (0.6)⁹ (0.4)² + ₁₁C₁₀ (0.6)¹⁰ (0.4)¹ + ₁₁C₁₁ (0.6)¹¹ (0.4)⁰

P = 0.236 + 0.177 + 0.089 + 0.027 + 0.004

P = 0.533

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lys-0071 [83]

Answer:

32%

Step-by-step explanation:

at least twenty caters long

6 0
3 years ago
The population of a certain town was 10,000 in 1990. The rate of change of the population, measured in people per year, is model
Katena32 [7]

The question is incomplete. The complete question is :

The population of a certain town was 10,000 in 1990. The rate of change of a population, measured in hundreds of people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020?

Solution :

According to the question,

The rate of change of population is given as :

$\frac{dP(t)}{dt}=200e^{0.02t}$  in 1990.

Now integrating,

$\int_0^{20}\frac{dP(t)}{dt}dt=\int_0^{20}200e^{0.02t} \ dt$

                    $=\frac{200}{0.02}\left[e^{0.02(20)}-1\right]$

                   $=10,000[e^{0.4}-1]$

                    $=10,000[0.49]$

                    =4900

$\frac{dP(t)}{dt}=200e^{0.02t}$

$\int1.dP(t)=200e^{0.02t}dt$

$P=\frac{200}{0.02}e^{0.02t}$

$P=10,000e^{0.02t}$

$P=P_0e^{kt}$

This is initial population.

k is change in population.

So in 1995,

$P=P_0e^{kt}$

   $=10,000e^{0.02(5)}$

   $=11051$

In 2000,

$P=10,000e^{0.02(10)}$

   =12,214

Therefore, the change in the population between 1995 and 2000 = 1,163.

8 0
3 years ago
4. A loan made on March 12 is due September 10 of the following year. Find the exact time for the loan in a non-leap year and a
saul85 [17]

Answer:

182 days

Step-by-step explanation:

Given:

Date on which loan is made = March 12

Due date of the loan = September 10

Now,

The months in between March and September and the number of days in the particular months are

Month                          Number of days

April                               30

May                                31

June                               30

July                                 31

August                            31

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

Total number of days =  153

also,

Number of days left in March after 12 are (31 - 12 ) = 19 days

and,

Number of days in September before the due date = 10 days

Hence, the total time for loan = 19 + 153 + 10 = 182 days

since the included months does not have the month of February. Therefore,

the time for both leap year and non-leap year will remain same.

7 0
4 years ago
Positionx (m)
9966 [12]

Answer:

A. 3.0 m/s

Step-by-step explanation:

Based on the graph,

velocity = Area of the graph

v =  \frac{y1 - y2}{x1 - x2}

(y : position and x : time)

Let y1 = 2m and y2 = 14m,

t1 = 0s and t2 = 4s

v = (14 - 2)m/(4-0)s

= 12m/4s

= 3.0 m/s

6 0
3 years ago
Read 2 more answers
Solve the quadratic equation for x. What is one of the roots? (x − 5)2 = 9
Sonja [21]

Answer:

x=8, x=2

Step-by-step explanation:

(x-5)^2=9 Solve by completing the square

Find square root of both sides

|x-5|=3

x=8, x=2

7 0
4 years ago
Read 2 more answers
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