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2 years ago

What are the zeros of the quadratic function f(x)=8x^2-16x-15

Mathematics

1 answer:

____ [38]2 years ago

3 0

Step-by-step explanation:

<u>Step 1: Use the quadratic formula to find the zeros</u>

<u /> $x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}$

$x=\frac{-(-16)\pm \sqrt{(-16)^2-4(8)(-15)} }{2(8)}$

$x=\frac{16\pm \sqrt{736} }{16}$

$x=\frac{16\pm 4\sqrt{46} }{16}$

$x=\frac{4\pm \sqrt{46} }{4}$

Answer: $x=\frac{4\pm \sqrt{46} }{4}$

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3000 + 70 + 2

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Can someone create two expressions that are equivalent to 3(4j + 4 + j). Please show all steps in your work.

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3 years ago

Read 2 more answers

True or false.200centimeters=2meter

katovenus [111]

Answer:

Step-by-step explanation:

1 meter = 100 centimeters

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3 years ago

Jake draws a drinking glass with a scale of 2 units on his graph paper represents 2.5 cm. The glass is 8 units tall in the drawi

alexandr1967 [171]

Answer:

Ratio 2= 2.5

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10cm

Step-by-step explanation:

Ratios and multiply each side by 4 to get the ratio 2:2.5 to 8:10

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3 years ago

A fair coin is to be tossed 20 times. Find the probability that 10 of the tosses will fall heads and 10 will fall tails, (a) usi

lbvjy [14]

Using the distributions, it is found that there is a:

a) 0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

b) 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

c) 0.1742 = 17.42% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item a:

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.

In this problem:

20 tosses, hence $n = 20$ .
Fair coin, hence $p = 0.5$ .

The probability is <u>P(X = 10)</u>, thus:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{20,10}.(0.5)^{10}.(0.5)^{10} = 0.1762$

0.1762 = 17.62% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item b:

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
The binomial distribution is the probability of <u>x successes on n trials, with p probability</u> of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

The probability of an exact value is 0, hence 0% probability that 10 of the tosses will fall heads and 10 will fall tails.

Item c:

For the approximation, the mean and the standard deviation are:

$\mu = np = 20(0.5) = 10$

$\sigma = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.5)} = \sqrt{5}$

Using continuity correction, this probability is $P(10 - 0.5 \leq X \leq 10 + 0.5) = P(9.5 \leq X \leq 10.5)$ , which is the <u>p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 9.5.</u>