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Vilka [71]
2 years ago
12

In 2012, Gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that

random samples of 100 respondents were selected from both Vermont and Hawaii. From the survey, Vermont had 65.3% who said yes and Hawaii had 62.2% who said yes. What is the value of the sample proportion of people from Hawaii who exercised for at least 30 minutes a day 3 days a week?
Mathematics
1 answer:
enot [183]2 years ago
7 0

Answer:

0.622

Step-by-step explanation:

According to the question,

62.2% of the respondents from Hawaii said that they had exercised more than 30 minutes a day for 3 days out of the week.

So, value of the sample proportion of people from Hawaii who exercised for at least 30 minutes a day for 3 days in a week is given by,

\frac {62.2}{100}

= 0.622  

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Clay can run one lap around the track in 1/4 of an hour. How many hours will it take him to run 5 1/3 laps around the track?
Jet001 [13]

Answer: It will take him 1 hour and 35 min

8 0
1 year ago
Which graph represents the function f(x)=x4+4x3−12x2−32x+64?
sp2606 [1]

f(x)=x^4+4x^3-12x^2-32x+64

The degree of f(x) is 4. Also the leading coefficient is 1 and it is positive

So  as x approaches infinity then y approaches infinity

as x approaches -infinity then y approaches infinity

The first and fourth graph goes up and it satisfies the above . so we ignore the second and third graph.

Now we check the x intercepts of the first  graph

x intercepts of first graph is -4  and 2

Plug in -4 for x in f(x) and check whether we get 0

f(x)=x^4+4x^3-12x^2-32x+64

f(x)=(-4)^4+4(-4)^3-12(-4)^2-32(-4)+64=0

Now plug in 2 for x and check

f(x)=(2)^4+4(2)^3-12(2)^2-32(2)+64=0

So -4  and 2  are the x intercepts that satisfies f(x)

Hence first option is the graph of f(x)=x^4+4x^3-12x^2-32x+64





5 0
2 years ago
Read 2 more answers
Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her comm
Stels [109]
We are given with
x1 = 20 min
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x2 = 30 min
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p = 0.9
Condition (x > 25)

We need to get the t-value between the two means and comparing it wit the t-value for the time of 25 minutes given that there is a 90% probability that the weather will be good. Simply use the t-test formula and use the t-test table to get the probability.
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2 years ago
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Darren invests $4,500 into an account that earns 5% annual interests. How much will be in the account after 10 years if the inte
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We have been given that Darren invests $4,500 into an account that earns 5% annual interests. We are asked to find the amount in his account after 10 years, if the interest rate is compounded annually, quarterly, monthly, or daily.

We will use compound interest formula to solve our given problem.  

A=P(1+\frac{r}{n})^{nt}, where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

5\%=\frac{5}{100}=0.05  

When compounded annually, n=1:

A=4500(1+\frac{0.05}{1})^{1\cdot 10}

A=4500(1.05)^{10}

A=4500(1.6288946267774414)

A=7330.025820498\approx 7330.03

When compounded quarterly, n=4:

A=4500(1+\frac{0.05}{4})^{4\cdot 10}

A=4500(1.0125)^{40}

A=4500(1.6436194634870132)

A=7396.28758569\approx 7396.29

When compounded monthly, n=12:

A=4500(1+\frac{0.05}{12})^{12\cdot 10}

A=4500(1.00416666)^{120}

A=4500(1.64700949769)

A=7411.542739605\approx 7411.54

When compounded daily, n=365:

A=4500(1+\frac{0.05}{365})^{365\cdot 10}

A=4500(1.0001369863013699)^{3650}

A=4500(1.6486648137656943695)

A=7418.9916619456\approx 7419.00

Since amount earned will be maximum, when interest is compounded daily, therefore, Darren should use compounded daily interest rate.

4 0
2 years ago
According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adult
mezya [45]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 Yes the selection of 15 is a binomial  experiment

b

   P(r =  15) =  3.2768 *10^{-11}

c

  P(r  =  5) =  0.1032

d

P(r \ge 1 ) =  0.9648

Step-by-step explanation:

considering question a

Generally for and experiment to be binomial

The trial must be independent

There must be only two outcomes for each trial

Generally given that that the 15 adults are selected randomly which mean that the trials will be independent and that desired outcome is ''ether the adult save something for retirement or the adult saves nothing for retirement ''

Then we can say that the selection of 15 adult at is a binomial experiment

Considering question b

Generally the probability that all of the adults save nothing for retirement is mathematically represented as

P(r =  n) =  ^nC_r * p^r *  q^{n-r}

Here C stands for combination

r = 15 i.e all the selected adults

      n is the sample size with value  15

From the question p = 0.20

and q is calculated as

q =  1 - p

=> q =  1 - 0.20

=> q =  0.80

So

P(r =  15) =  ^{15}C_{15} * p^{15} *  q^{15-15}

P(r =  15) =  3.2768 *10^{-11}

Considering question c

Generally the probability that exactly five of the selected adults save nothing for retirement is mathematically represented as

P(r  =  5) =  ^{15} C_5 * (0.20)^5 *  (0.80)^{15}

P(r  =  5) =  0.1032

Considering question d

Generally the probability that at least one of the selected adults saves nothing for retirement is mathematically represented as

P(r \ge 1 ) =  1 - P (r = 0 )

P(r \ge 1 ) =  1 - [ ^{15} C _ 0 *  (0.20)^{0} * (0.80 )^{15}]

P(r \ge 1 ) =  1 - 0.0352

P(r \ge 1 ) =  0.9648

4 0
2 years ago
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