Question

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Answer 1

Part 1.

Given that Yolanda is 4 yrs younger than 3 times her daughters age and that the sum of their ages are greater than 88.

Let the age of Yolanda's daughter be x, then Yolanda's age is 3x - 4.

x + 3x - 4 > 88
4x - 4 > 88
4x > 88 + 4
4x > 92
x > 92 / 4
x > 23

Therefore, the youngest age Yolanda's daughter can be is 23 years old.



Part 2.

Given that a towns recreation department is updating its parks and that the parks must have slides and swings.

Thus, x > 0 and y > 0

Given that there are x number of swing sets and y number of slides and that the number of new slides must be more than 3 times the number of new swing sets.

Thus,
$y > 3x$

Given that each swing set costs $275 and each slide costs $168 and that they can spend no more than $1250.

Thus,
$275x + 168x \leq1250$

Therefore, the constraints of the parks improvement plan are:

$275x+168y\leq1250\\ x>0\\ y>0\\ y>3x$



Part 3.

For any complex number, the real part is the part without an "i" while the imaginary part is the part with an "i".

Given the complex number -6 - i, the real part is -6 and the complex part is -i.



Part 4.

Given that the weights if loaves of rye bread at a bakery are normally distributed with a mean of 16oz and a standard deviation of 0.5oz and that the bakery produces 120 loaves of rye bread each day.

The proportion of the number of loaves each day that are expected to weigh between 16oz and 16.5oz is obtained as follows:

$P(16\ \textless \ X\ \textless \ 16.5)=P(X\ \textless \ 16.5)-P(X\ \textless \ 16)\\ \\=P\left(z\ \textless \ \frac{16.5-16}{0.5} \right)-P\left(z\ \textless \ \frac{16-16}{0.5} \right)=P(z\ \textless \ 1)-P(z\ \textless \ 0)\\ \\=0.84134-0.5=0.34134$

Since, the bakery produces 120 loaves of rye bread each day, the number of loaves each day that are expected to weigh between 16oz and 16.5oz is 0.34134 x 120 = 40.9608 ≈ 41




Part 5.

Given that the results of a poll show that the percent of registered voters in a town who plan to vote in favor of a new library is in the interval (0.52, 0.58) and that there are 185,500 people in the city.

The point estimate for the percent of people in the city who plan to vote for the new library is given by (0.52 + 0.58) / 2 = 1.1 / 2 = 0.55 = 55%

The polls margin of error is given by 0.55 - 0.52 = 0.03 or 3%

Based on the poll, the interval for the number of people in the city who plan to vote for the new library is given by (0.52 x 185,500, 0.58 x 185,500) = (96,460, 107,590)