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3 years ago

7

Find the number of distinct triangles with the measurements a = 5, b =2, and a = 51 degrees.

1 answer:

elixir [45]3 years ago

4 0

The answer is the option b. 1.

Two sides and one angle determine one unique triangle.

If the angle is the between the two sides, you just can use the rule known as SAS, Side Angle Side.

When that is the case you use the cosine rule.

When the known angle is not between the two sides but one of the others, you use sine theorem.

Then in any case when you know two sides and one angle of a triangle the other side and angles are determined, which implies that there is only one possible triangle.

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A boy wants to jump onto a carousel that is spinning at a rate of 14 revolutions per minute. If the carousel is 23 feet in diamt

nirvana33 [79]

Answer:

16.86 ft/s

Step-by-step explanation:

Given that

Speed of the carousel, s = 14 rpm

Distance from the carousel, d = 23 ft

To start with, we convert the given speed to revolution per second, so that

s = 14/60 rev/sec

To find the needed speed, we use the formula

v =2πnR, remember that Diameter = 2R, so we substitute D for 2R and get πnD

v = πnD, and we use this to find our needed velocity

v = 3.142 * 14/60 * 23

v = 72.266 * 14/60

v = 16.86 ft/s

Therefore the boy must run at a speed of 16.86 ft/s in order to be able to match the carousel and jump on it

6 0

3 years ago

The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the

Darya [45]

Answer:

Brand 1 Brand 2 Difference

37734 35202 2532

45299 41635 3664

36240 35500 740

32100 31950 150

37210 38015 −805

48360 47800 560

38200 37810 390

33500 33215 285

Sum of difference = 2532+ 3664+740+150 −805+ 560 +390 +285 = 7516

Mean = $d=\frac{7516}{8}$

Mean = $d=939.5$

a) d= 939.5

$\text{Sample Standard deviation, s} = \sqrt{\dfrac{(x-\bar{x})^2}{n-1}}$

$=\sqrt{\dfrac{(2532-939.5)^2+(3664-939.5)^2+(740-939.5)^2 ...+(285-939.5)^2}{8-1}}$

=1441.21

b)SD= 1441.21

c)Calculate a 99% two-sided confidence interval on the difference in mean life.

confidence level =99%

significance level =α= 0.01

Degree of freedom = n-1 = 8-1 =7

So, $t_{\frac{\alpha}{2}}=3.499$

Formula for confidence interval $= \left( \bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}} \right)$

Substitute the values

confidence interval $= 939.5 \pm 3.499 \times \frac{1441.21}{\sqrt{8}} \right)$

confidence interval $= 939.5 - 3.499 \times \frac{1441.21}{\sqrt{8}} \right)$ to $= 939.5 + 3.499 \times \frac{1441.21}{\sqrt{8}} \right)$

Confidence interval $−843.396\$ to $2722.396$

8 0

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natita [175]

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OLEGan [10]

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Ksju [112]

Answer:

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