MATHEMATICS HIGH SCHOOL

What is the square root property of:

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Answer 1

Answer:

The square root property seems to be another name for completing the square

x^2 + 5x + 6 = 0

We move the constant to the other side

x^2 + 5x = -6

We square half the linear coefficient and add that to both sides

x^2 + 5x + (5/2)^2 = -6 + 25/4

Now the left side is a perfect square,

(x + 5/2)^2 = 1/4

Here's the square root property part, we take the square root of both sides, remembering the ±

x + 5/2 = ± 1/2

x = -5/2 ± 1/2

Answer: x = -3 or x=-2

We check by plugging in these values to the original equation, and they work.

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x^2 + 6x = 16

Again we add half the linear coefficient, squared, to both sides

x^2 + 6x + 3^2 = 16 + 9

(x + 3)^2 = 25

Here comes the square root property, taking the square root of both sides:

x + 3 = ±5

x = -3 ± 5

x = 2 or x = -8

Again we check by substitution, and they both work

Answer: x = 2 or x = -8

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8)What is the opposite of the opposite of -9|

How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads?

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The theoretical probability of getting heads is 50%. 50% of 50 is 25. So, 20 % more than 50% is 20% * 25 + 25 = 5 + 25 = 30. That means that the coin should show 30 heads fo have an experimental probability of 20% more than the theoretical probability. You can check that 30 out of 50 is 0.6. Which is 0.1 more than 0.5. And 0.1 is 20% of 0.5. Then 0.6 is 20% more than 0.5.

Final answer:

In a series of 50 coin tosses, a coin needs to land heads 30 times to have an experimental probability 20% greater than the theoretical probability.

Explanation:

The subject of focus here is the allusion to the theory of probability, particularly in relation to a fair coin flip. The theoretical probability of obtaining either heads or tails in a coin flip is 0.5. However, the student is interested in having an experimental probability 20% greater than the theoretical probability.

We can first calculate the theoretical counts of expected heads per 50 tosses, which is (0.5 * 50) = 25. This result represents the notion that if a coin is thrown 50 times, on average, will land heads 25 times based on the theoretical probability.

To achieve an experimental probability 20% greater than the theoretical probability, we need to find a count of heads that corresponds to a probability that is 20% more than 0.5 (the theoretical probability). This new probability is therefore 0.6 and the corresponding count of heads required would be (0.6 * 50) = 30. Hence, in 50 tosses, the coin would need to show heads 30 times to have an experimental probability 20% greater than the theoretical probability of getting heads.

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A bag has five red marbles, six blue marbles, and four black marbles. What is the probability of picking a blue marble, replacing it, and then picking another blue marble?A. 1/15
B. 8/75
C. 4/25
D. 1/9

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The total number of marbles is 15. The probability of picking a blue marble is 6/15. After putting the marble back, the probability of picking another blue marble is probably 1/9.

Answer: the probability of picking two blue marbles in a row is 1/9.

Answer:

4/25 is the answer guys!

Step-by-step explanation:

Name the missing numbers from the function table and write the function rule.

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3rd one down on x is 6.because they are all subtracting 12.same goes for the last one on y.it is -22 because you are subtracting 12 from -10

Find correct two decimal places, the radius of the circle with the given circumference: 35cm

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$C=2 \pi r$
C - circumference, r - radius

$C=35 \ [cm] \n \n35=2 \pi r \nr=(35)/(2 \pi) \nr=(17.5)/(\pi) \n\boxed{r \approx 5.57 \ [cm]}$

$C=2\pi r=35\n2\pi r=35\nr=(35)/(2\pi)\approx5.57\text{ cm}$

Doris put $4000 in a 2 year cd paying 6% interest, compounding monthly. after 2 years, she withdrew all her money. what was the amount of the withdraw?

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For the answer to the question above asking what was the amount of the withdraw if Doris put $4000 in a 2-year cd paying 6% interest, compounding monthly. after 2 years, she withdrew all her money?

First year Interest: I(1) = 4000[(1.005)^12 - 1] = 246.71 = penalty for early withdrawal
Value after two years: P(2) = 4000(1.005)^24 = 4508.64

Value after 2 years with penalty: V = 4000(1.005^24 - 1.005^12 + 1) = $4261.93

Answer:

Value after two years: P(2) = 4000(1.005)^24 = **** 4508.64 ***

(8^3)^4 ⋅ 8^−9/ 8^3
Answer???

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Answer: 1

Step-by-step explanation:

What is the square root property of:​

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Final answer:

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What is the square root property of: