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3 years ago

A city's population has increased 40% in the last 5 years and is now 53,782 people.

Mathematics

1 answer:

zheka24 [161]3 years ago

6 0

Given:

A city's population has increased 40% in the last 5 years and is now 53,782 people.

To find:

The population 5 years ago.

Solution:

Let x be the population 5 years ago.

A city's population has increased 40% in the last 5 years.

So, present population is

$x+x\times \dfrac{40}{100}=x+0.4x=1.4x$

It is given that the present population is 53782.

$1.4x=53782$

$x=\dfrac{53782}{1.4}$

$x=38415.7142857$

$x\approx 38416$

Therefore, the population 5 years ago was about 38416.

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$\frac{9x+6}{18}=\frac{20x+4}{3x}$

Cross multiply. Distribute...
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plug these values into the quadratic formula and simplify.)
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3 years ago

Read 2 more answers

Consider estimating a population proportion p. What is the most conservative sample size (erring on the large size) required in

just olya [345]

Answer:

The most conservative sample size is 2401.

Step-by-step explanation:

We are given the following in the question:

We are not given any approximation of s]ample proportion, thus,

$\hat{p} = 0.5$

We have to construct a 95% confidence interval.

Margin of error = 2% = 0.02

Formula for margin of error =

$z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get,

$0.02 = 1.96\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\0.02 = 1.96\times \sqrt{\dfrac{0.5(1-0.5)}{n}}\\\\\sqrt{n} = 1.96\times \dfrac{\sqrt{0.5(1-0.5)}}{0.02}\\\\\sqrt{n}=49\\n = 2401$

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3 years ago

Evaluate f(-7). f(x)=3x^2 a) -441 b) -147 c) 78 d) 147

vlabodo [156]

Answer:

Step-by-step explanation:

replace x with -7

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3 years ago

Serena is making a large meatloaf that contains ground beef and ground pork. The beef is $3.50 per Pound and the pork is $2.00 p

I am Lyosha [343]

Hi there! :)

Answer:

Serena bought 0.75 pounds of pork and about 3.93 pounds of beef.

Step-by-step explanation:

Lets start by laying out the important information we know:

- Beef = $3.50/pound → 1 pound of beef = $3.50

- Pork = $2.00/pound → 1 pound of pork = $2.00

- Buys 0.75 pounds of pork → buys 0.75 of 1 pound of pork

- Buys x pounds of beef

- Spends $15.25 in total → 0.75 pounds of pork + x pounds of beef = $15.25

Once this is done, it's much easier to see what we are dealing with (when it's just a bunch of words it's a lot harder to understand).

Creating your algebraic equation:

Algebraically, your equation needs to be equal to the total amount that Serena spent on pork and beef.

She bought 0.75 of 1 pound of pork, which in other words means that she bought 0.75 of $2.00. The word "of" is the same thing as a multiplication sign. SO, all of this would translate into this: (0.75 × 2)

She then bought beef, but we don't know how much. What we can do is replace the "amount of pounds of beef she bought" with the letter "x". Remember, 1 pound of beef is $3.50. SO, all of this would translate into this: 3.50x

Your algebraic equation should look like this:

(0.75 × 2) + 3.50x = 15.25

Now all you need to do is solve this equation by isolating "x":

(0.75 × 2) + 3.50x = 15.25

1.5 + 3.50x = 15.25

Subtract 1.5 from each side of the equation → 15.25 - 1.5 = 13.75

3.50x = 13.75

Divide each side of the equation by 3.50 → 13.75 ÷ 3.50 = 3.92857143...

x ≈ 3.93

There you go! I really hope this helped, if there's anything just let me know! :)

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Answer:

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Step-by-step explanation:

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4 years ago