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Illusion [34]
3 years ago
10

The quadratic equation (3k-2)x^2 +12x+3(k+1) =0 has equal roots. Find the two possible values of k.

Mathematics
1 answer:
romanna [79]3 years ago
5 0
x_1=x_2 \Rightarrow \Delta=0\\
\Delta=12^2-4\cdot(3k-2)\cdot3(k+1)\\
\Delta=144-(36k-24)(k+1)\\
\Delta=144-36k^2-36k+24k+24\\
\Delta=-36k^2-12k+168\\
-36k^2-12k+168=0\\
-3k^2-k+14=0\\
-3k^2+6k-7k+14=0\\
-3k(k-2)-7(k-2)=0\\
-(3k+7)(k-2)=0\\
k=-\frac{7}{3} \vee k=2
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denis23 [38]

Answer: 2x-5y

Step-by-step explanation:

The common term in this expression (GCF) is 5. When you take out the 5, you get 2x-5y. This is the answer.

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5 0
3 years ago
utomobiles arrive at the drive-through window at a post office at the rate of 7 every 10 minutes. The average service time is 7
Arlecino [84]

Answer:

The answers to the questions are well numbered below.

Step-by-step explanation:

We have arrival rate

λ = 7 in every 10 minutes = 0.7

Service time u = 7 minutes

1. Average time a car is in system

W = 1/u - λ

= 1/7-0.7

= 0.1587

= 0.16 to 2 decimal places

2. Average number of cars in system

= λ/u-λ

= 0.7/7-0.7

= 0.1111

= 0.11 to 2 decimal places

3. Average time that cars spend to receive service

= λ/u(u-λ)

= 0.7/7(7-0.7)

= 0.01587

= 0.016 to 2 decimal places

4. Average number of cars in line behind customer receiving service

= λ²/u(u-λ)

= 0.7²/7(7-0.7)

= 0.49/44.1

= 0.011 to 2 decimal places

5. Probability no cats at window

1-λ/u

= 1-0.7/7

= 0.9 = 9%

6. Percentage of time postal clerk is busy

= λ/u = 0.7/7 = 0.1 = 10%

7. Probability of exactly 2 cars

= λ²e^-λ/2!

= 0.7²e^-0.7/2!

= 0.1217

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8 0
3 years ago
n testing the reliability of DNA results used in crime labs, the new procedure matched DNA results to suspects 46 out of 50 time
timurjin [86]

Answer:

Step-by-step explanation:

Given that in testing the reliability of DNA results used in crime labs, the new procedure matched DNA results to suspects 46 out of 50 times.

i.e population proportion = 46/50 = 0.92

For 99% success rate

Here p the proportion follows normal distribution with mean = 0.92 and

Std error = \sqrt{0.92*0.08/50} \\=0.038

Margin of error for 99% = ±2.58*0.038 = ±0.099

Confidence interval lower bound = 0.92-0.099 = 0.8210

Upper bound = 0.92+0.0999 ~1

so Confidence interval - (0.821,1)

(p cannot exceed 1 so 1 is taken)

We are 99% sure the that this new DNA match procedure correctly identifies susspects between (0.821, 1)

since 99% confidence interval contians 1, there is evidence at the .01 level that this procedure will successfully match DNA results 99% of the time

8 0
3 years ago
Half of the sum of 17 and 9 anyone??
adoni [48]

MATHEMATICALLY WE WRITE THIS AS

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