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tigry1 [53]
2 years ago
12

the national park service is building a 16 mile hiking trail. They will post a sign every 1/8 mile along the trail, including on

e at the end. There will not be a sign posted at the beginning of the trail. How many signs will they post along the trail?
Mathematics
2 answers:
Andreyy892 years ago
7 0

Answer: There are 2 signs will be posted along the trail.

Step-by-step explanation:

Since we have given that

Total length of hiking trail = 16 miles

They will post a sign every \dfrac{1}{8}\ mile along the trail, including one at the end.

No sign posted at the beginning of the trail.

Number of signs will be posted along the trail is given by

\dfrac{1}{8}\times 16\\\\=2

Hence, there are 2 signs will be posted along the trail.

lesya [120]2 years ago
3 0
The nation park will post 128 sign post

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A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. Th
Kisachek [45]

Answer:

Subtracting the volume of the cylinder from the volume of the prism, the volume of metal in the hex nut to the nearest tenth is 23.6 cm^3 (second option)

Step-by-step explanation:

Diameter of the cylinder: d=1.6 cm

Apothem of the hexagon: a=2 cm

Assuming the thickness of the steel hex nut: t=2 cm

Volume of metal in the hex nut: V=?

V=Vp-Vc

Volume of the prism: Vp

Volume of the cylinder: Vc


Prism:

Vp=Ab h

Ab=n L a / 2

Number of the sides: n=6

Side of the hexagon: L

Height of the prism: h=t=2 cm

Central angle in the hexagon: A=360°/n

A=360°/6

A=60°

tan (A/2)=(L/2) / a

tan (60°/2)=(L/2) / (2 cm)

tan 30° = (L/2) / (2 cm)

sqrt(3)/3=(L/2) / (2 cm)

Solving for L/2:

(2 cm) sqrt(3)/3 = L/2

2 sqrt(3)/3 cm = L/2

Solving for L:

2 (2 sqrt(3)/3 cm)=L

4 sqrt(3)/3 cm = L

L=4 sqrt(3)/3 cm

Ab=n L a / 2

Ab=6 (4 sqrt(3)/3 cm)(2 cm) / 2

Ab=24 sqrt(3)/3 cm^2

Ab=8 sqrt(3) cm^2

Vp=Ab h

Vp=(8 sqrt(3) cm^2)(2 cm)

Vp=16 sqrt(3) cm^3

Vp=16 (1.732) cm^3

(1) Vp=27.712 cm^3


Cylinder:

Vc=(π d^2/4) h

π=3.14

d=1.6 cm

Height of the cylinder: h=t=2 cm

Vc=[3.14 (1.6 cm)^2 / 4] (2 cm)

Vc=[3.14 (2.56 cm^2) / 4] (2 cm)

Vc=(2.0096 cm^2) (2 cm)

Vc=4.019 cm^3


V=Vp-Vc

V=27.712 cm^3 - 4.019 cm^3

V=23.693 cm^3

V=23.6 cm^3

4 0
2 years ago
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Three different divers kept track of the number of treasure boxes they've found this year.
steposvetlana [31]
Choice a i'm pretty sure !
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1 year ago
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(HELP PLEASE) The cost for a company to produce x smartphones can be modeled by C(x)= 2x+35 and the company's total profit after
Juliette [100K]
This is the concept of algebra, the revenue of the smart phone sells is given by:
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C(x)=2x+35

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P(x)=-x^2+120x-435
Thus the revenue will be:
R(x)=-x^2+120x-435+2x+35
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7 0
2 years ago
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John should drive to his workplace and back to home. On the way to the workplace it was raining, so he drove at speed of 42mph.
elixir [45]

Answer:

47.25 mph

Step-by-step explanation:

Represent the total distance traveled as 2x. Average speed= total distance/total time

When going at 42 mph, the time would be x/42 and when going at 54 mph the time would be x/54 to travel x distance. Add x/42 and x/54 together to get 16x/378. Then divide 2x by 16x/378 to get 47.25 mph. Also this is RSM innit?

5 0
2 years ago
Factor the expression given below. Write each factor as a polynomial in
kherson [118]

The factorization of the expression of 43x³ + 216y³ is

(7x + 6y)(49x² - 42xy + 36y²)

Step-by-step explanation:

The sum of two cubes has two factors:

1. The first factor is \sqrt[3]{1st} + \sqrt[3]{2nd}

2. The second factor is ( \sqrt[3]{1st} )² - ( \sqrt[3]{1st} ) ( \sqrt[3]{2nd} ) + ( \sqrt[3]{2nd} )²

Ex: The expression a³ + b³ is the sum of 2 cubes

The factorization of a³ + b³ is (a + b)(a² - ab + b²)

∵ The expression is 343x³ + 216y³

∵ \sqrt[3]{343x^{3}} = 7x

∵ \sqrt[3]{216y^{3}} = 6y

∴ The first factor is (7x + 6y)

∵ (7x)² = 49x²

∵ (7x)(6y) = 42xy

∵ (6y)² = 36y²

∴ The second factor is (49x² - 42xy + 36y²)

∴ The factorization of 43x³ + 216y³ is (7x + 6y)(49x² - 42xy + 36y²)

The factorization of the expression of 43x³ + 216y³ is

(7x + 6y)(49x² - 42xy + 36y²)

Learn more:

You can learn more about factors in brainly.com/question/10771256

#LearnwithBrainly

6 0
2 years ago
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