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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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The number of pages that Carolyn wrote in her journal each day from Monday to Friday is shown below: 9, 8, 12, 6, 10. What is th

cricket20 [7]

Answer:

She wrote 9 pages per day on average

Step-by-step explanation:

The number of pages that Carolyn wrote in her journal each day from Monday to Friday is shown below:

Monday = 9

Tuesday =8

Wednesday = 12

Thursday = 6

Friday = 10

$Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean =\frac{9+8+12+6+10}{5}$

Mean=9

Hence She wrote 9 pages per day on average

4 0

2 years ago

A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trou

Mrrafil [7]

Answer:

Check the explanation

Step-by-step explanation:

(a)

H0: Population mean = 8.46

H1: Population mean is not equal to 8.46

The test statistic (t) is given by the following expression -

${t=\frac{\overline{x}-\mu_0}{s/\sqrt{n}}}$

We have calculated the sample mean (8.421) and sample standard deviation (0.0461). Therefore, the test statistic (t) will be -

t = (8.421 - 8.46)/(0.0461/sqrt(49)) = -5.92

The left-sided critical value from t-distribution (two-tailed) is -2.01. Thus the test statistic falls in the rejection region and we reject the null hypothesis at 95% confidence level and conclude that the population mean is different from 8.46 inches.

(b)

There are the following four assumptions for a single sample t-test.

The observations are in ratio scale.

The observations have been taken in such a manner that every single observation is independent and uncorrelated from the others.

There should not be any significant outliers in the sample observations.

The sample data should be approximately normal.

(c)

The first assumption is true as the data is in inches. The second assumption cannot be tested now. It will depend upon the situation and study design which we assume as correct in this case. The third assumption is checked by plotting a box plot and finding the outliers. The final assumption can be checked using the Anderson-Darling normality test.

Kindly check the graphical table in the attached images below.

(d)

The data is normal (the p-value of Anderson-Darling test in > 0.05). However, two points in the Box plot are outliers though not grossly different from the entire sample data set. So, we conclude that the assumptions are valid in this case for conducting the t-test.