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2 years ago

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. 4x^2-7x+2=0

Mathematics

1 answer:

Svetach [21]2 years ago

5 0

Answer:

Discriminant is 17 and it has 2 real roots.

Step-by-step explanation:

To find the number of real roots for a quadratic, we apply the discriminate. The discriminate is the inside portion of the square root from the quadratic formula.

• $b^2-4ac>0$ yields 2 real roots

• $b^2-4ac=0$ yields 1 real root

• [tx]b^2-4ac<0[/tex] yields no real roots

$4x^2-7x+2=0$ where a=4, b=-7, and c=2

$b^2-4ac=(-7)^2-4(4)(2)=49-32=17$ .

It has 2 real roots

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According to 2013 report from Population Reference Bureau, the mean travel time to work of workers ages 16 and older who did not

gregori [183]

Answer:

a) 48.80% probability that his travel time to work is less than 30 minutes

b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.

c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 30.7, \sigma = 23$

a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?

This is the pvlaue of Z when X = 30. So

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

$Z = \frac{30 - 30.7}{23}$

$Z = -0.03$

$Z = -0.03$ has a pvalue of 0.4880.

48.80% probability that his travel time to work is less than 30 minutes

b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.

$n = 36$

Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is $s = \frac{23}{\sqrt{36}} = 3.83$

c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?

This is 1 subtracted by the pvalue of Z when X = 35. So

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

By the Central Limit Theorem

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

$Z = \frac{35 - 30.7}{3.83}$

$Z = 1.12$

$Z = 1.12$ has a pvalue of 0.8687

1 - 0.8687 = 0.1313

13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

8 0

3 years ago

Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the favorite

Trava [24]

Answer:

The data are at the <u>Nominal</u> level of measurement.

The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement.

Step-by-step explanation:

The objective here is to Identify the level of measurement of the data, and explain what is wrong with the given calculation.

The data are at the <u> Nominal </u> level of measurement due to the fact that it portrays the qualitative levels of naming and representing different hierarchies from 100 basketball, 200 basketball, 300 football, 400 anything else

b) We are being informed that, the average (mean) is calculated for 597 respondents and the result is 256.1.

The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement. At nominal level this type of data set do not measure at all , it is not significant to compute their average (mean).

6 0

2 years ago

A ticket to a movie theatre for a student is $7. The cost for an adult is $2 more than for a student. How much would it cost 13

MakcuM [25]

Answer: it would cost a total of $194

Step-by-step explanation:

A ticket to a movie theatre for a student is $7. The cost for an adult is $2 more than for a student.

If student ticket costs $x, adult ticket would cost x + 2

This means that the cost for an adult is

7 + 2 = $9

The cost of 13 adult tickets to the movie theatre would be

13 × 9 = $117.

The cost of 11 student tickets to the movie theatre would be

11 × 7 = $77

Total cost of 13 adult tickets and 11 student tickets would be

117 + 77 = $194

3 0

3 years ago

Explain The probability of tossing a prime number when you toss the cube with numbers one through six

asambeis [7]

Probability is (desired outcomes)/(total possible outcomes)

ok, you must make a choice
1. if you believe that 1 is prime (which I don't) go to AAAAAAAAAAA
2. if you believe that 1 is NOT prime, go to BBBBBBBBBBB

AAAAAAAAAAAA
prime numbers from 1 to 6 are
1,2,3,5
desired outcomes=4
total possible =6
4/6=2/3

BBBBBBBBB
prime numbers from 1 to 6 are
2,3,5
3 desired outcomes
6 total possible

3/6=1/2

if you belive that 1 is prime, then 2/3 is probability
if you believe that 1 is NOT prime then 1/2 is probability

5 0

3 years ago

Read 2 more answers

Why am i so bad at math ;w;

zalisa [80]

D might be the answer I am pretty sure it is D if not then sorry

4 0

2 years ago

Read 2 more answers