Home / Assignment Help / 8.01)Ben takes a random sample of 25 students in his seventh-grade class and finds that 85% of the sample prefers math over science. There are 150 students in the seventh grade. Based on the sample proportion, about how many students in the seventh grade would be expected to prefer math over science? 25 85 150 128 08.01)Carla wants to know how many students in her school enjoy watching reality TV shows. She asks all 22 students in her science class and finds that 40% of her classmates enjoy watching reality TV shows. She claims that 40% of the school’s student population would be expected to enjoy watching reality TV shows. Is Carla making a valid inference about her population? No, it is not a valid inference because she asked all 22 students in her science class instead of taking a sample from her music class No, it is not a valid inference because she asked all 22 students in her science class instead of taking a sample of the students in her school Yes, it is a valid inference because she asked all 22 students in her science class Yes, it is a valid inference because her classmates make up a random sample of the students in the school

8.01)Ben takes a random sample of 25 students in his seventh-grade class and finds that 85% of the sample prefers math over science. There are 150 students in the seventh grade. Based on the sample proportion, about how many students in the seventh grade would be expected to prefer math over science? 25 85 150 128 08.01)Carla wants to know how many students in her school enjoy watching reality TV shows. She asks all 22 students in her science class and finds that 40% of her classmates enjoy watching reality TV shows. She claims that 40% of the school’s student population would be expected to enjoy watching reality TV shows. Is Carla making a valid inference about her population? No, it is not a valid inference because she asked all 22 students in her science class instead of taking a sample from her music class No, it is not a valid inference because she asked all 22 students in her science class instead of taking a sample of the students in her school Yes, it is a valid inference because she asked all 22 students in her science class Yes, it is a valid inference because her classmates make up a random sample of the students in the school

Answer:

60 feet

Step-by-step explanation:

The area of the school is

165(300) = 49500 square feet.

The area of the parking lot with the school is

(165+75)(300+75) = 240(375) = 90000 square feet.  This means the area of just the parking lot is

90000-49500 = 40500 square feet.

The area of the new expanded lot will be doubled; this means it will be

2(40500) = 81000 square feet.  Adding back the area of the school, this means the total lot will be

81000+49500 = 130500 square feet.

The width will be 375+x and the length will be 240+x; this gives us

130500 = (375+x)(240+x)

Multiplying the binomials gives us

130500 = 90000+375x+240x+x²

130500 = 90000+615x+x²

To solve this, we first set it equal to 0.  We do this by subtracting 130500 from each side:

130500-130500 = 90000+615x+x²-130500

0 = x²+615x-40500

We will use the quadratic formula:

x=frac{-bpm sqrt{b^2-4ac}}{2a}

Substituting our values for a, b and c,

x=frac{-615pm sqrt{615^2-4(1)(-40500)}}{2(1)}\\=frac{-615pm sqrt{378225--162000}}{2}\\=frac{-615pm sqrt{378225+162000}}{2}\\=frac{-615pm sqrt{540225}}{2}\\=frac{-615pm 735}{2}\\=frac{-615+735}{2}text{ or }frac{-615-735}{2}\\=frac{120}{2}text{ or }frac{-1350}{2}\\=60text{ or }-675

We do not use negative numbers for measurement, so x = 60.

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