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3 years ago

Write a quadratic equation that has x-intercepts of -1/3 and 5/2

Mathematics

1 answer:

iogann1982 [59]3 years ago

6 0

<h2>Answer: $6x^{2}-13x-5$ </h2>

Step-by-step explanation:

Given that the two roots of the quadratic equation are $\frac{-1}{3}$ and $\frac{5}{2}$ .

If $\alpha$ $,\beta$ are the roots of the quadratic equation,the equation is $(x-\alpha )(x-\beta )$ .

It is given that $\alpha =\frac{-1}{3}$ and $\beta =\frac{5}{2}$ .

So,the equation is

$(x-(\frac{-1}{3}))(x-\frac{5}{2})$

= $x^{2}-\frac{5}{2}x+\frac{x}{3}-\frac{5}{6}$

= $6x^{2}-13x-5$

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A buyer went to the market to buy strawberries. He purchased 120 randomly selected strawberries from a vendor who claimed that n

mafiozo [28]

Answer:

$z=\frac{0.333 -0.25}{\sqrt{\frac{0.25(1-0.25)}{120}}}=2.10$

$p_v =P(z>2.10)=0.018$

At 5% of significance we can conclude that the true proportion of strawberries damage is higher than 0.25

Step-by-step explanation:

Data given and notation

n=120 represent the random sample taken

X=40 represent the number of strawberries damaged

$\hat p=\frac{40}{120}=0.333$ estimated proportion of strawberries damaged

$p_o=0.25$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that no more than 25% of his total harvest of strawberries was damaged.:

Null hypothesis: $p\leq 0.25$

Alternative hypothesis: $p > 0.25$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.333 -0.25}{\sqrt{\frac{0.25(1-0.25)}{120}}}=2.10$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>2.10)=0.018$

At 5% of significance we can conclude that the true proportion of strawberries damage is higher than 0.25

6 0

2 years ago

When solving a system of equations, Jared found y = x + 10 for one equation and substituted x + 10 for y in the other equation.

myrzilka [38]

Both are correct they just chose a different variable to solve for first. they will both get correct answers if they do the rest correctly.

5 0

3 years ago

Read 2 more answers

Evaluate ab + c for a = 2, b = 3, and c = 4.<br><br> 9<br> 10<br> 27

Kazeer [188]

Substituting the values given, we get
(2)*(3) + 4 ;
Using BODMAS
We get
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3 years ago

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How do you get the number 43 with the numbers 2,3,6,8 with using all numbers and only using them once.

iren [92.7K]

Answer:

Multiply 8x6 and subtract 2 and 3

Step-by-step explanation:

8x6=48

48-3=45

45-2=43

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3 years ago

Alenkinab [10]

Answer:

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3 years ago