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KIM [24]
3 years ago
11

Find the sum and product of the roots. 3x^ 2 - 4x - 7 = 0

Mathematics
1 answer:
victus00 [196]3 years ago
6 0
Given the quadratic function, to get the roots we factorize:
3x²-4x-7=0

3x²+3x-7x-7=0
3x(x+1)-7(x+1)=0
(3x-7)(x+1)=0
thus the roots are
x=-1 or x=3/7
thus the sum of the roots will be:
-1+3/7
=-4/7
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Susan had 28 ft of ribbon to complete a wreath project. She needs 3 1/4 ft of ribbon for each wreath project. How many wreaths w
olya-2409 [2.1K]

Answer:

She will be able to make 8 wreaths

Step-by-step explanation:

I got my answer by first converting 3 1/4 into 13/4. I then divide 28 by 13/4 which was multiplying 28 by 4/13.

I got 112 when I did 28 × 4

I then divided 112 by 13

and got 8.615.

Since they are asking for how much wreaths she could make, it is going to be 8

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3 years ago
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3 years ago
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There are 12 red pens, 20 blue pens and 5 black pens in a bag. What is the probability that you will pick a black pen? Round
Vlada [557]

Answer:

The probability of getting a black pen from the bag is 13.5%.

Step-by-step explanation:

To determine the percentage probability that a black pen will be obtained from the bag, the following calculation must be performed:

12 + 20 + 5 = 37

37 = 100%

5 = X

(5 x 100) / 37 = X

500/37 = X

13.5 = X

Thus, it is determined that the totality of pens is 100%, and through a cross multiplication the percentage of the 5 black pens with respect to the total of pens is obtained.

Therefore, the probability of getting a black pen from the bag is 13.5%.

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3 years ago
A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confid
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Answer:

The 95% confidence interval for the true proportion of all voters in the state who favor approval is (0.4384, 0.5050).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 865, \pi = \frac{408}{865} = 0.4717

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4717 - 1.96\sqrt{\frac{0.4717*0.5283}{865}} = 0.4384

The upper limit of this interval is:

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The 95% confidence interval for the true proportion of all voters in the state who favor approval is (0.4384, 0.5050).

6 0
3 years ago
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