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2 years ago

Boston, Massachusetts had a population of 617,594 people during January 1 2010, and 675,647 people on January 1 2020.

Mathematics

1 answer:

tigry1 [53]2 years ago

5 0

Answer:

See below

Step-by-step explanation:

Exponential function is:

y = abˣ

If we consider the time difference in years as x and the initial population as a, then we get:

675647 = 617594*b¹⁰

Find the value of b:

b¹⁰ = 675647/617594
b¹⁰ = 1.09399864636
b = 1.09399864636^(1/10)
b = 1.009 (rounded)

The equation we got is:

y = 617594*1.009ˣ

Here we have y- population after x years since 2010, x - the number of years since 2010 and 1.009 is the population growth rate.

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If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95% confident that the d

katen-ka-za [31]

Answer:

We need a sample size of least 119

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Sample size needed

At least n, in which n is found when $M = 0.09$

We don't know the proportion, so we use $\pi = 0.5$ , which is when we would need the largest sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.09 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.09\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.09}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.09})^{2}$

$n = 118.6$

Rounding up

We need a sample size of least 119

6 0

3 years ago

It takes a day to build 2/3 of a model airplane gow many model airplanes can be built in 6 days

Sedaia [141]

Answer:

4 airplanes

Step-by-step explanation:

1 = 2/3

6 = x

cross multiply

x = 6 × 2/3

therefore x = 4

5 0

2 years ago

Read 2 more answers

If x=-2 and y=6 is a solution of equation 3ax+2by=6, then find the value of b

lana66690 [7]

$\text{Substitute the values of x and y to the equation}\\\\x=-2,\ y=6,\ 3ax+2by=6\\\\3a(-2)+2b(6)=6\\\\-6a+12b=6\qquad|\text{add 6a to both sides}\\\\12b=6a+6\qquad|\text{divide both sides by 12}\\\\b=\dfrac{6a}{12}+\dfrac{6}{12}\\\\\boxed{b=\dfrac{1}{2}a+\dfrac{1}{2}}$

7 0

3 years ago

What is the answer to 219 divided by7

KatRina [158]

219 divided by 7

Exact Form:
219/7

Decimal Form: 
31.28571428...

Mixed Number Form: 
31 2/7

7 0

3 years ago

Read 2 more answers

Find the value of x to the nearest tenth

o-na [289]

As the sides shown are same so the base of large triangle is double the base of smaller triangle
That is
2(3x-8) =20
Divide both sides by 2
3x-8 = 10
Add 8 to both sides
3x =18
Divide both sides by 3
x=6

So answer is 6.0

5 0

3 years ago