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Zigmanuir [339]
3 years ago
7

An environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sampl

e of vehicles in order to estimate that percentage with a margin of error of 5​% and 95​% confidence. To gauge the size of the​ problem, the agency first picks 50 cars and finds 12 with faulty emissions systems. How many should be sampled for a full​ investigation?
Mathematics
1 answer:
goldenfox [79]3 years ago
3 0

Answer:

197

Step-by-step explanation:

Sample proportion is; p^ = 12/50 = 0.24

Margin of error of 5% is given by the formula;

ME = (z_0.05) √[p^(1 - p^)/n]

Let's make n(number of sample) the subject.

n = ((z_0.05)/ME)²((p^)(1 - p^))

From tables, the z-score of 0.05 is 1.645

Thus;

n = ((1.645)/0.05)²(0.24(1 - 0.24))

n ≈ 197

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It has been said that newspapers are disappearing, replaced by various electronic media. In 2004, newspaper circulation (the num
shutvik [7]

Answer:

A. y=-1.2x+59

B. 42.2 million

Step-by-step explanation:

Part A:

Given:

Newspapers circulated in year 2004, y_{1}=59\textrm{ million}

Newspapers circulated in year 2014, y_{2}=47\textrm{ million}

Let the time x start at the year 2004. So, x_{1}=0

For the year 2014, x_{2}=2014-2004=10

Therefore, linear relationship between newspapers circulated and time passed since 2004 is given as:

y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})\\y-59=\frac{47-59}{10-0}(x-0)\\y-59=-\frac{12}{10}x\\y=-1.2x+59

Therefore, the equation describing the relationship is: y=-1.2x+59

Part B:

For the year 2018, x=2018-2004=14

Plug in 14 for x in the above equation and solve for y. This gives,

y=-1.2(14)+59\\y=-16.8+59\\y=42.2

Therefore, in the year 2018, the newspaper circulation will be 42.2 million.

8 0
3 years ago
state whether the lines represented by the equations y=1/2x-1 and y+4=-1/2(x-2) are parallel, perpendicular, or neither.
Zepler [3.9K]
Parallel because they have the same slope. Y+4= -1/2(x-2) is in point slope form, simplified to y intercept form is y=1/2-5... The slope (m) in both equations is the same, if you graphed the equations they would be parallel
7 0
3 years ago
Square with sides measuring 12in
malfutka [58]
Perimeter = 48in Area =144 in
4 0
3 years ago
Which of the following expressions can be used to find how many cubes with edge length of 1/3 unit fit in a prism that is 5 unit
mash [69]

Answer:

5400 cubes can be fit into the prism.

Step-by-step explanation:

We are given the dimensions of prism as:

5 units by 5 units by 8 units i.e. 5 units×5 units×8 units.

Hence, the volume of the prism is given by:

Volume of prism=5×5×8=200 cubic units

Also the edge length of cube is given by= 1/3 unit.

Hence volume of 1 cube=

Hence volume of 1 cube= (1/27) cubic units.

Let 'n' cubes can be fitted into the prism.

Hence we have the relation as:

Volume of prism=n×Volume of 1 cube.

200=n×(1/27)

n=200×27

n=5400

Hence 5400 cubes can be fitted into the prism.

<h2><u><em>NUMBER THREE</em></u></h2>
8 0
2 years ago
Read 2 more answers
If A=( a,b)and B= (2,4,6} find n(A) * n(B)​
kumpel [21]

Answer:

n(a) X n( b) = 6

Step-by-step explanation:

n(a)= 2

n(b) = 3

n(a) X n( b) = 2x3

=6,,

4 0
3 years ago
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