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2 years ago

Determine the number of real solutions for the equation: 6x^2+8x=7

Mathematics

1 answer:

densk [106]2 years ago

7 0

Answer:

Step-by-step explanation:

You could factor this to find out how many real roots you have, but it's easier to use the rule of the discriminate. The discriminate comes from the quadratic formula:

$b^2-4ac$

Plug in the numbers from the quadratic and see what the value of it is. If the:

discriminate < 0, you have 2 imaginary roots

discriminate = 0, you have 1 real root, multiplicity 2 and

discriminate > 0, you have 2 real roots

Our b is 8, our a is 6 and our c is -7 (remember you have to set the polynomial equal to 0 to do this).

$8^2-4(6)(-7)=232$

Because 232 is > 0, we have 2 real roots.

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The University of Washington claims that it graduates 85% of its basketball players. An NCAA investigation about the graduation

Nonamiya [84]

Probabilities are used to determine the chances of events

The given parameters are:

Sample size: n = 20
Proportion: p = 85%

<h3>(a) What is the probability that 11 out of the 20 would graduate? </h3>

Using the binomial probability formula, we have:

$P(X = x) = ^nC_x p^x(1 - p)^{n -x}$

So, the equation becomes

$P(x = 11) = ^{20}C_{11} \times (85\%)^{11} \times (1 - 85\%)^{20 -11}$

This gives

$P(x = 11) = 167960 \times (0.85)^{11} \times 0.15^{9}$

$P(x = 11) = 0.0011$

Express as percentage

$P(x = 11) = 0.11\%$

Hence, the probability that 11 out of the 20 would graduate is 0.11%

<h3>(b) To what extent do you think the university’s claim is true?</h3>

The probability 0.11% is less than 50%.

Hence, the extent that the university’s claim is true is very low

<h3>(c) What is the probability that all 20 would graduate? </h3>

Using the binomial probability formula, we have:

$P(X = x) = ^nC_x p^x(1 - p)^{n -x}$

So, the equation becomes

$P(x = 20) = ^{20}C_{20} \times (85\%)^{20} \times (1 - 85\%)^{20 -20}$

This gives

$P(x = 20) = 1 \times (0.85)^{20} \times (0.15\%)^0$

$P(x = 20) = 0.0388$

Express as percentage

$P(x = 20) = 3.88\%$

Hence, the probability that all 20 would graduate is 3.88%

<h3>(d) The mean and the standard deviation</h3>

The mean is calculated as:

$\mu = np$

So, we have:

$\mu = 20 \times 85\%$

$\mu = 17$

The standard deviation is calculated as:

$\sigma = np(1 - p)$

So, we have:

$\sigma = 20 \times 85\% \times (1 - 85\%)$

$\sigma = 20 \times 0.85 \times 0.15$

$\sigma = 2.55$

Hence, the mean and the standard deviation are 17 and 2.55, respectively.

Read more about probabilities at:

brainly.com/question/15246027

8 0

2 years ago

A line is to be graphed through the point (–3, 0). Which points can be used to create a line with an undefined slope through (–3

irina1246 [14]

Answer:-3.0

Step-by-step explanation:

5 0

3 years ago

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Which one is more <br> –3\5 or –2/3<br> Please help

Kaylis [27]

Answer:

-3/5

Step-by-step explanation:

the smaller negative is still greater, because its negative.

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2 years ago

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On some graph paper, graph these points in a coordinate plane: (-2, 3), (2, 3), (2, -3), (-2, -3). Connect all the points. Descr

Alisiya [41]

Awnser is in the photo like fr?

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2 years ago

A number is increased by 2 and then multiplied by 3. The result is 24. What is this number

Sav [38]

Answer:

The answer is 6.

Step-by-step explanation:

To find this answer, divide 24 by 3 and you get 8. 8 minus 2 is 6.

3 0

2 years ago