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3 years ago

Find the area of a parallelogram with sides of 6 and 12 and an angle of 60°.

Mathematics

1 answer:

Anna007 [38]3 years ago

4 0

ANSWER

36√3 square units.

EXPLANATION

The area of a parallelogram is obtained by multiplying the base by the height.

We use the sine ratio to obtain the height.

$\sin(60 \degree) = \frac{h}{6}$

$h = 6 \sin(60 \degree)$

$h = 3 \sqrt{3}$

The area becomes:

$12 \times 3 \sqrt{3} = 36 \sqrt{3} {units}^{2}$

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Vlada [557]

The least value is 1, the greatest value is 7, and the median is 2.

<h3>How to calculate the median?</h3>

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2 years ago

If measure 4 is 36 degrees what is the measure of angle 2

elena55 [62]

Acute angle between 0 and 90 degrees I think

7 0

3 years ago

Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls on the skin, is essential for stro

tigry1 [53]

Answer:

a) The 98% confidence interval would be given (0.182;0.218).

b) We are 98% confident that the true proportion of of England people who are deficient in Vitamin D is between 0.182 and 0.218.

c) If repeated samples were taken and the 98% confidence interval computed for each sample, 98% of the intervals would contain the population proportion.

d) Yes since the confidence interval not contains the value 0.25, we can refute the claim at 2% of significance.

Step-by-step explanation:

Data given and notation

n=2700 represent the random sample taken

X represent the people in England who are deficient in Vitamin D

$\hat p=0.2$ estimated proportion of England people who are deficient in Vitamin D

$\alpha=0.02$ represent the significance level

Confidence =0.98 or 98%

z would represent the statistic (variable of interest)

p= population proportion of England people who are deficient in Vitamin D

Part a

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 98% confidence interval the value of $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.33$

And replacing into the confidence interval formula we got:

$0.20 - 2.33 \sqrt{\frac{0.2(1-0.2)}{2700}}=0.182$

$0.20 + 2.33 \sqrt{\frac{0.2(1-0.2)}{2700}}=0.218$

And the 98% confidence interval would be given (0.182;0.218).

Part b

We are 98% confident that the true proportion of of England people who are deficient in Vitamin D is between 0.182 and 0.218.

Part c

If repeated samples were taken and the 98% confidence interval computed for each sample, 98% of the intervals would contain the population proportion.

Part d

Yes since the confidence interval not contains the value 0.25, we can refute the claim at 2% of significance.

3 0

3 years ago

Find the slope please

Katarina [22]

Answer:

slope is $-\frac{3}{4}$