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3 years ago

14

Determine if the side lengths listed create a right triangle, acute triangle, obtuse triangle, or do not make a triangle. 3, 9,

10 Determina si las longitudes de los lados enumeradas crean un triángulo rectángulo, un triángulo agudo, un triángulo obtuso o no forman un triángulo. 3, 9, 10 * 1 point right acute obtuse not a triangle

1 answer:

zimovet [89]3 years ago

4 0

Answer:

Obtuse triangle

Step-by-step explanation:

Given the side lengths :

3, 9, 10

Let :

a = 3 ; b = 9 ; c = 10 (longest side)

If a² + b² = c² (right angle)

If a² + b² > c² (acute angle)

If a² + b² < c² (obtuse angle)

a² + b²

3² + 9²

9 + 81 = 90

c² = 10² = 100

90 < 100

Hence,

a² + b² < c² (then we have an obtuse triangle)

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dolphi86 [110]

Answer:

Below in bold.

Step-by-step explanation:

c) 3 x (9^2)^3/4 x ((81^3)^5/6

= 3 x 81^3/4 x 81^15/6

= 3 x 81^(3/4 + 15/6)

= 3 x 81^13/4

= 3 x 3^13

= 3^14

= 4,782,969.

f) (5x^-1y^2)^-2 / (25 x^2 y - 1)^2

= 5^-2 x^2y^-4 / 625 x^4y^-2

= 5^-2 x^-2 y^-2 / 5^4

= 5^-6 x^-2y^-2

= 0.000064x^-2y^-2.

5 0

3 years ago

You’ve bought a cylindrical thermos 8 in. high with a base 6 in. across. How much coffee can you put in the thermos?

lana66690 [7]

Answer:

3.706 liters

Step-by-step explanation:

Hello

assuming that these measures correspond to the internal measures of the thermos,

we can calculate the volume as, the volume of a cylinder, which is given by

$V=\pi r^{2} h$

where r is the radius of the base, and h the height

also

Diameter=2r

r=Diameter/2

Step 1

let

h=8 in

base = diameter = 6 inch

r=diameter/2

r=6/2 inch,r=3 inch

Step 2

Put the values into the equation

$V=\pi r^{2} h\\V=\pi (3in)^{2} (8 in)\\V=\pi *72 \ in^{3} \\\\V=72\pi\ in^{3} \\\\$

Step 3

Now, the unit (cubic inches) is not an usual unit for measuring coffee, let´s convert cubic inches into liters by knowing

1 inch = 2.54 cm

1 litro = 1000 cubic centimeters

$if\ 1\ inch\ = 2.54\ cm\\(1\ inch)^{3} =(2.54\ cm)^{3}\\\\1\ inch^{3}=16.3870\ cm^{3}$

1 cubic inch = 16.3870 cubic centimeters

$1\ cubic\ inch\ = 16.3870\ cubic\ centimeters\\\\\\72\pi =x?\ cubic\ centimeters\\\\x=\frac{72\pi \cubic \ inch\ \*16.3870 }{1\ cubic\ inch} \\\\x=3706.65\ cubic\ centimeters$

Step 4

Finally, convert cubic centimeters into liters $1000\ cubic\ centimeters =1\ liter \\\\\\3706.65\ cubic\ centimeters = x?\ liters\ centimeters\\\\x=\frac{3706.65 \cubic \ centimeters\ \*1 liter}{1000 cubic centimeters} \\\\x=3706.65\ cubic\ centimeters\\x=3.706 Liters$

I can put 3.706 liters in the thermos

Have a good day

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3 years ago

29 us. 2ft. 11 in. + 55 yd. 1 ft. 10 in. + 13 yd. 1 ft.3 in.

scoundrel [369]

Answer:

99 yd

Step-by-step explanation:

When I add these, I line them up vertically

29 yd. 2ft. 11 in.

+ 55 yd. 1 ft. 10 in.

+ 13 yd. 1 ft. 3 in.

---------------------------

97 yd 4ft 24 in

We know that 12 in = 1 ft

so 24 in = 2ft

Subtract 24 in and add 2 ft

97 yd 4ft 24 in

+2ft -24 in

------------------------------

97 yd 6ft

We know 3 ft = 1yd

so 6ft = 2yd

Subtract 6ft and add 2 yd

97 yd 6ft

+2yd - 6ft

-------------------

99 yd

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3 years ago

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gladu [14]

Answer:

1. 9

2. 8

3. 16

4. 20

5. 27

6. 6

7. 54

8. 70

9. 24

10. 20

11. 15

12. 42

13. 25

14. 44

15. 28

16. 66

17. 36

18. 60

19. 16

20. 9

21. 18

22. 30

23. 4

24. 9

25. <

26. >

27. <

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30. =

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Step-by-step explanation:

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2 years ago

agasfer [191]

Answer:

The 80% confidence interval for the proportion of companies that are planning to increase their workforce is (0.033, 0.331).

A sample size of 8852 is needed.

Step-by-step explanation:

First question:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Only 2 of the 11 companies were planning to increase their workforce.

This means that $n = 11, \pi = \frac{2}{11} = 0.1818$

80% confidence level

So $\alpha = 0.2$ , z is the value of Z that has a pvalue of $1 - \frac{0.2}{2} = 0.9$ , so $Z = 1.28$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1818 - 1.28\sqrt{\frac{0.1818*0.8182}{11}} = 0.033$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1818 + 1.28\sqrt{\frac{0.1818*0.8182}{11}} = 0.331$

The 80% confidence interval for the proportion of companies that are planning to increase their workforce is (0.033, 0.331).

Second question:

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

A poll taken in July 2010 estimates this proportion to be 0.36.

This means that $\pi = 0.36$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.01?

This is n for which M = 0.01. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.01 = 1.96\sqrt{\frac{0.36*0.64}{n}}$

$0.01\sqrt{n} = 1.96\sqrt{0.36*0.64}$

$\sqrt{n} = \frac{1.96\sqrt{0.36*0.64}}{0.01}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.36*0.64}}{0.01})^2$

$n = 8851.04$

Rounding up(as a sample of 8851 will have a margin of error slightly over 0.01):

A sample size of 8852 is needed.

4 0

2 years ago