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Maksim231197 [3]
1 year ago
13

A quadrilateral has vertices A(4, 5), B(2, 4), Q4, 3), and D(6, 4). Which statement about the quadrilateral is true?

Mathematics
1 answer:
Igoryamba1 year ago
7 0

The true statement about the quadrilateral is ABCD is a rhombus with non-perpendicular adjacent sides.

<h3>How to determine the true statement?</h3>

The coordinates are given as:

A(4, 5), B(2, 4), Q4, 3), and D(6, 4).

Next, we plot the graph of the quadrilateral ABCD

See attachment

From the attached graph, we have the following highlights:

  • Opposite sides are equal
  • Opposite sides are parallel
  • Adjacent sides are not perpendicular

This means that the quadrilateral is ABCD is a rhombus

Read more about quadrilateral at

brainly.com/question/4812739

#SPJ1

<u>Complete question</u>

A quadrilateral has vertices A(4, 5), B(2, 4), C(4, 3), and D(6, 4). Which statement about the quadrilateral is true?

1) ABCD is a parallelogram with noncongruent adjacent sides.

2) ABCD is a trapezoid with only one pair of parallel sides.

3) ABCD is a rectangle with noncongruent adjacent sides.

4) ABCD is a square.

5) ABCD is a rhombus with non-perpendicular adjacent sides.

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If f(1) = 10 and f '(x) ≥ 3 for 1 ≤ x ≤ 6, how small can f(6) possibly be?
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In a sample of 170 students at an Australian university that introduced the use of plagiarism-detection software in a number of
Kisachek [45]

Answer:

p_v =P(Z>4.146)=0.0000169  

Based on the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who NOT belief that such software unfairly targets students is higher than 0.5 or 50% .  

Step-by-step explanation:

1) Data given and notation  

n=170 represent the random sample taken  

X=58 represent the student's who belief that such software unfairly targets students

\hat px=\frac{58}{170}=0.341 estimated proportion of students who belief that such software unfairly targets students

\hat p=\frac{112}{170}=0.659 estimated proportion of students who NOT belief that such software unfairly targets students

p_o=0.50 is the value that we want to test  

\alpha=0.05 represent the significance level (no given)  

z would represent the statistic (variable of interest)  

p_v represent the p value (variable of interest)  

p= proportion of student's who belief that such software unfairly targets students

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that that a majority of students at the university do not share this belief. :  

Null hypothesis:p\leq 0.5  

Alternative hypothesis:p>0.5

We assume that the proportion follows a normal distribution.  

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,higher or less) from a hypothesized value p_o.  

<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np_o =170*0.5=85>10

n(1-p_o)=170*(1-0.5)=85>10

3) Calculate the statistic  

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

z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{170}}}=4.146  

4) 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 significance level provided is \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a one right side test the p value would be:  

p_v =P(Z>4.146)=0.0000169  

Based on the p value obtained and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who NOT belief that such software unfairly targets students is higher than 0.5 or 50% .  

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