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Georgia [21]
3 years ago
7

A new radar device is being considered for a certain missile defense system. The system is checked by experimenting with aircraf

t in which a kill or a no kill is simulated. Two research group A and B participated the simulation, and it was found that 63 kills occur out of 100 trials by group A, and 59 kills occur out of 125 trials by group B. Is there a significant difference between the proportions of group A and B's simulation? Use P-value with significance level of 0.05 to draw a conclusion.
Mathematics
1 answer:
adell [148]3 years ago
6 0

Answer:

There is significant difference between the proportions of group A and group B.

Step-by-step explanation:

In this question we need to perform an hypothesis test on the difference of proportions (Δπ) and determine if there is any significant difference between the two proportions.

The null and alternative hypothesis are:

H_0: \Delta \pi=0\\\\H_1: \Delta \pi\neq0

The proportion of group A is p_1=63/100=0.630.

The proportion of group B is p_2=59/125=0.472.

The weighted average of p (to calculate s) is:

p=\frac{n_1*p_1+n_2*p_2}{n_1+n_2}=\frac{100*0.630+125*0.472}{100+125}=\frac{63+59}{100+125}=\frac{122}{225}=0.542

The estimated standard deviation is:

s=\sqrt{\frac{p(1-p)}{n_1}+\frac{p(1-p)}{n_2} } =\sqrt{\frac{0.542(1-0.542)}{100}+\frac{0.542(1-0.542)}{125}} =\sqrt{\frac{0.248}{100} +\frac{0.248}{125} } \\\\s=\sqrt{0.00447} =0.067

Then we can calculate z as

z=\frac{p_1-p_2}{s}=\frac{0.630-0.472}{0.067}=\frac{0.158}{0.067}=2.36

The P-value for z=2.36 is 0.009, which is less that the significance level of 0.05. The effect is significant and the null hypothesis is rejected.

There is significant difference between the proportions of group A and group B.

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I need to know what the answer to that question is and I need to know how to do it
mel-nik [20]

Answer:

\frac{59}{8}  or 7\frac{3}{8}

Step-by-step explanation:

\frac{80}{4}  - 12\frac{5}{8}

First you need to make the 12 5/8 into an improper fraction by multiplying 12 by 8 and then adding the total by 5.

12\frac{5}{8} -> \frac{101}{8}

Now you have \frac{80}{4} - \frac{101}{8} so you need a common denominator by multiplying the first fraction by 2

\frac{80}{4} -> \frac{160}{8}

Then you subtract 160 - 101 which equals 59.

\frac{59}{8}  or 7\frac{3}{8}

5 0
3 years ago
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At the circus, a clown is shot from a cannon. This situation can be modeled by the function: h = – 16t2 + 45t + 15, where 'h' is
weeeeeb [17]

Answer:

The maximum height is 46.64 feet.

Step-by-step explanation:

If we take the derivative of h whit respect to t and equal this to zero we would find the value of t which corresponds to the maximum h.

So, we have the function h(t):

h(t)=-16t^{2} + 45t + 15

Taking the derivative, we have:

\frac{dh(t)}{dt}=-32t + 45=0

Now, we solve it for t:

t=\frac{45}{32}=1.4\: s

Finally, we put this value of t into the original equation.

h(t)=-16(1.4)^{2} + 45(1.4) + 15

h_{max}=46.64\: ft      

Therefore, the maximum height is 46.64 feet. All the given options are wrong, the one that comes closest is option A.

I hope it helps you!          

4 0
3 years ago
Still timed. More math needing help with, i'll double points and mark brainliest! 1. (y - 6) (y + 3) 2. (4x - 5) (x - 7) 3.(3x -
wlad13 [49]

Answer:

1. y² - 3x - 18

2. 4x² - 33x + 35

3. 12x² - 11x + 2

Step-by-step explanation:

All we do with these questions are expanding the factored binomials. Use FOIL:

1. y² + 3y - 6y - 18

y² - 3y - 18

2. 4x² - 28x - 5x + 35

4x² - 33x + 35

3. 12x² - 3x - 8x + 2

12x² - 11x + 2

3 0
3 years ago
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A city park commission received a donation of playground equipment from a parents' organization. The area of the playground need
dalvyx [7]

Answer:

Length = 20.49 yards and Width = 12.49 yards.

Step-by-step explanation:

The area of the rectangular playground is given by 256 yards square. It is also known that one of the sides of the playground is 8 yards longer than the other side. Therefore, let the smaller side by x yards. Then the longer side will be (x+8) yards. The area of the rectangle is given by:

Area of the rectangle = length * width.

256 = x*(x+8)

x^2 + 8x = 256. Applying the completing the square method gives:

(x)^2 + 2(x)(4) + (4)^2 = 256 + 16

(x+4)^2 = 272. Taking square root on both sides gives:

x+4 = 16.49 or x+4 = -16.49 (to the nearest 2 decimal places).

x = 12.49 or x = -20.49.

Since length cannot be negative, therefore x = 12.49 yards.

Since smaller side = x yards, thus smaller side = 12.49 yards.

Since larger side = (x+8) yards, thus larger side = 12.49+8 = 20.49 yards.

Thus, the length and the width to minimize the perimeter of fencing is 20.49 yards and 12.49 yards respectively!!!

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Find the surface area of the cylinder in terms of pi.
Svet_ta [14]
I think the answer is c

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3 years ago
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