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2 years ago

The perimeter of a triangle is 170 ft and the sides are in the ratio of 25:14:12. Find the area of the triangle

Mathematics

1 answer:

EastWind [94]2 years ago

8 0

using the ratio, the length of the sides are:

25x + 14x + 12x = 170

51x = 170

x = 170 / 51

x = 3 1/3

The lengths of the sides are: 25 * 3 1/3 = 83 1/3 feet

14 x 3 1/3 = 46 2/3 feet

12 x 3 1/3 = 40 feet

Using Heron's formula

the semi perimeter (S) = 170/2 = 85 ft.

The area of the triangle = SQRT(S*(S-83 1/3) * (S - 46 2/3) * (S-40))

= SQRT (85 * (85-83 1/3) * (85 - 46 2/3) * (85-40)

= SQRT (85 * 1 2/3 * 38 1/3 * 45)

= SQRT(244374)

= 494.34 square feet ( round answer as needed).

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A bicycle wheel has an inside radius of 12 inches. Which expression could be used to find the inside circumference of this wheel

il63 [147K]

Step-by-step explanation:

We have given that,

The inner radius of a bicycle wheel is 12 inches.

It is required to find the expression to find the inside circumference of this wheel.

The outer surface of the wheel is equal to its circumference. It is given by :

$C=2\pi r$

r is radius of wheel

$C=2\times 3.14\times 12\\\\C=75.36\ \text{inches}$

This is the required explanation.

5 0

2 years ago

The average annual cost of the first year of owning and caring for a large dog is $1,843 (US News and World Report, September 9,

ICE Princess25 [194]

Answer:

a. Error is 0.14

b. between 1913.68 to 1772.32

Step-by-step explanation:

Requirement a)

The margin of error is a statistic expressing the amount of random sampling error in a survey's results.

Given,

Size of the sample n = 50

We know, At 95% confidence interval,

The margin of error,

= 0.98/√n

= 0.98/√50

= 0.98/7.07

= 0.13859 ~ 0.14

So the margin of error at 95% confidence level is 0.14.

Requirement b)

Given,

Standard deviation σ = 255

Population mean z = 1814

Size of the sample n = 50

We know, At 95% confidence interval,

(z-µ)/(σ/√n) < Z_0.05

= - Z_0.05 < (z-µ)/(σ/√n) < Z_0.05

= - 1.96 * σ/√n < (z-µ)/(σ/√n)* σ/√n < 1.96 * σ/√n [ in two tail Z test the value of Z_0.05 is 1.96 ]

= - 1.96 * 255/√50 < Z-µ < 1.96 * 255/√50

= -70.6828 < Z-µ < 70.6828

= 70.6828 > µ - Z > -70.6828

= 70.6828 + Z > µ > -70.6828 + Z

= 70.6828 + 1814 > µ > -70.6828 + 1814

=1913.68 > µ > 1772.32

So, the sample mean would be between 1913.68 to 1772.32.

7 0

2 years ago

You are checking the intermediate results of a phone app that calculates the weight of an object in kilograms given the weight i

Illusion [34]

The wrong step is step 4, because you only need one conversion.

The formula to convers pounds to kilograms is

$\text{weight in pounds} = 2.2 \times \text{weight in kilograms}$

Obviously, the inverse formula is

$\text{weight in kilograms} = \cfrac{\text{weight in pounds}}{2.2}$

So, you're given an input of 142 pounds. To convert it in kilograms, plug that value into out formula:

$\text{weight in kilograms} = \cfrac{142}{2.2} \approx 64.5$

and this is the answer you're looking for, so you need no more steps.

4 0

2 years ago

In 2011, a train carried 8% more passengers than in 2010. In 2012 , it carried 8% more passengers than in 2011. Find the percent

konstantin123 [22]

Answer:

there was a 16% increase since 2010 to 2012

Step-by-step explanation:

lets say the train had 100 people on it in 2010 and in 2011 it had an 8% increase which then brings you to 8 plus 100 and you get 108.

Now in 2012 there was an increase 8%, so you will add 8 to your previous answer 108 and receive 116. So now there was 16 more passengers in 2012 than in 2010. Transfer the 16 passengers into 16% and you now have your answer.

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2 years ago

The cylinder below has a volume of 785 ft^3. and the cone has a volume of 314 ft^3.

Tanya [424]

Answer:

The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.

6 0

2 years ago

Read 2 more answers