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natali 33 [55]
2 years ago
7

The coordinates of the vertices of quadrilateral HIJK are H (-2, -1), I (2, 1), J (5, 0), and K (-1, -3). Isabella states that q

uadrilateral HIJK is a parallelogram. Is Isabella correct? Support your answer and show all work.
Mathematics
1 answer:
Firlakuza [10]2 years ago
7 0

Answer:

Step-by-step explanation:

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a single die is rolled one time. Find the probability of rolling a number greater than 4 or less than 3​
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less then 3

Step-by-step explanation:

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Solve for x: −10x+5= -6x-35
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There are $400$ pages in Sheila's favorite book. The average number of words per page in the book is $300$. If she types at an a
Pepsi [2]

Answer:

50hours

Step-by-step explanation:

Given that there are 400 pages in Sheila's favorite book.

The average number of words per page in the book is 300

She types an average rate of 40words per minute.

So to type 400pages of the book

Total number of words in the pages = 400×300 = 120000 words

Typing rate : 40words ------- 1minute

120000 words ----------- x minutes

Hence we have 40 × X mins = 120000 × 1min

Make X the subject

40X = 120000minutes

X = 120000/40

X = 3000minutes

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3000minutes = 3000minutes/60

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5 0
3 years ago
The Westbrook Pharmaceutical Company manufactures atorvastatin pills, designed to lower cholesterol levels. Listed below are the
Sloan [31]

Solution :

Given :

$\mu = 24$

n = 15

$\overline x = 24.89$

s = 0.5902

The hypothesis :

$H_0 : \mu = 25$

$H_a : \mu \neq 25$

This is a 2 tailed test.

The significance level is $95 \% \ ( \alpha =0.05)$

The test statistic :

$Z=\frac{\overline x - \mu}{\frac{\sigma}{\sqrt n}}$

$Z=\frac{24.89-25}{\frac{0.5902}{\sqrt 15}}$

   = -0.72

The p value : The p value for Z = -0.72 is 0.4716

The critical value : the critical value at α = 0.05 is +1.96 to -1.96

The decision rule :

If $Z_{observed} > Z_{critical}$ or if $Z_{observed} < -Z_{critical}$, then reject $H_0$.

Also if p value is less than α, then reject $H_0$.

The decision :

Since the Z falls in between +1.96 and -1.96, we fail to reject the $H_0$. Also since p value is greater than α, we fail to reject  $H_0$.

The conclusion :

There is not sufficient evidence at the 95% significance level to warrant rejection of the claim that the pills come from a population in which the amount of the atorvastatin is equal to 25 mg.

Now calculating the mean and the standard deviation :

$\text{Mean} = \frac{\text{sum of observation}}{\text{total observations}}$

Standard deviation = $\sqrt{\text{variance}}$

Variance = $\frac{\text{sum of squares(SS)}}{n-1}$

Where, SS = $\sum (X - \text{mean})^2$

X                   Mean                 $(X-\text{mean})^2$

24.1               24.89                    0.62

24.4              24.89                     0.24

24.3              24.89                    0.35

24.9             24.89                       0

24.1              24.89                    0.62

24.2             24.89                    1.72

24.1              24.89                    0.04

26.2             24.89                    0.04

25.1              24.89                   0.24

25                24.89                    0.01

24.7             24.89                    0.04

25.1             24.89                    0.04

25.3             24.89                   0.17

25.5             24.89                   0.37

25.5            24.89                   0.37

n                                                   15

Sum                                           373.3

Average                                    24.89

SS                                              4.8775

Variance = $\frac{SS}{n-1}$                       0.348392857

Standard deviation                    0.5902      

3 0
2 years ago
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