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MissTica
3 years ago
5

Approximately 0.8 of middle school students have cell phones. Which of the following fractions describes how many middle school

students
have cell phones?
E 4
5
G. 2
25
H.
100
J. 1
Mathematics
1 answer:
lana [24]3 years ago
8 0

Answer: E. 4/5

Step-by-step explanation: You have to put the decimal (0.8) over its place value. So in this case 0.8 turns into 8/10. Then you must simplify 8/10, by dividing the numerator (8) and the denominator (10) by the greatest common factor (2). Which gives you the answer 4/5.

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The distance from Earth to Mars is about 35,000,000 miles. What is the order of magnitude of this number?. . . . . . . . A.. . 6
Musya8 [376]
The scientific notation of the given, 35,000,000 is 3.5 x 10^7. The order of magnitude of a scientific notation is the exponent of its multiplier, 10. From the derived scientific notation above, the exponent of 10 is 7. Thus, the answer is letter D. 
7 0
3 years ago
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Flura [38]
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7 0
3 years ago
A circle has centre (3,0) and radius 5. The line y = 2x + k intersects the circle in two points. Find the set
lara [203]

A circle with center (3,0) and radius 5 has equation

(x-3)^2+y^2=25 \iff x^2 + y^2- 6 x  = 16

If we substitute y=2x+k in this equation, we have

x^2+(2x+k)^2-6x=16 \iff 5x^2+(4k-6)x+k^2-16=0

This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:

\Delta=b^2-4ac=(4k-6)^2-4\cdot 5\cdot (k^2-16)>0

The expression simplifies to

-4 (k^2 + 12 k - 89)>0 \iff k^2 + 12 k - 89

The solutions to the associated equation are

k^2 + 12 k - 89=0 \iff k=-6\pm 5\sqrt{5}

So, the parabola is negative between the two solutions:

-6-5\sqrt{5}

8 0
3 years ago
Find the lateral area and total surface area of each of the following. GEOMETRY!!! HELP PLS
AlexFokin [52]

(a) The lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.

(b) The lateral surface area of the cone is 136π sq units and the total surface area is 200π sq units.

(c) The lateral surface area of the cylinder is 242π sq units and the total surface area is 484π sq units.

<h3>Lateral surface area of the prism</h3>

L.S.A = Ph

where;

  • P is perimeter of the base
  • h is height of the prism

h² = 17² - 8²

h² = 225

h = 15

L.S.A = (3 x 16) x 15 = 720 sq units

<h3>Total surface area of the prism</h3>

T.S.A = PH + 2B

T.S.A = 720 + 2(16) = 752 sq units

<h3>Lateral surface area of the cone</h3>

L.S.A = πrt

where;

  • t is the slant height = 17

r² = 17² - 15²

r² = 64

r = 8

L.S.A = π(8)(17) = 136π sq units

<h3>Total surface area of the cone</h3>

T.S.A = πrt + πr²

T.S.A = 136π sq units + π(8)²

T.S.A = 200π sq units

<h3> Lateral surface area of the cylinder</h3>

L.S.A = 2πrh

where;

  • r is the radius of the cylinder = 11
  • h is height of the cylinder = 11

L.S.A = 2π(11 x 11) = 242π sq units

<h3>Total surface area of the cylinder</h3>

T.S.A = 2πrh + 2πr² = 2πr(r + h)

T.S.A = 2π(11)(11 + 11)

T.S.A = 484π sq units.

Thus, the lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.

  • the lateral surface area of the cone is 136π sq units and the total surface area is 200π sq units.
  • the lateral surface area of the cylinder is 242π sq units and the total surface area is 484π sq units.

Learn more about surface area here: brainly.com/question/76387

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3 0
2 years ago
Select the correct answer from each drop-down menu. Complete the statements about these similar pyramids. Two square pyramids A
Scrat [10]

The ratio of the heights of these pyramids is 3 : 1, the ratio of the base areas is 9 : 1 and the ratio of the volumes is 27 : 1.

<h3>What is ratio?</h3>

Ratio can be defined as a mathematical expression which denotes the proportion of two (2) or more physical quantities to one another and the total quantities.

The ratio of the heights of these pyramids is given by:

Ratio = Height of pyramid A : Height of pyramid B

Ratio = (3V/lw) : (V/lw)

Ratio = 3 : 1.

The ratio of the base areas of these pyramids is given by:

Ratio = Base area of pyramid A : Base area of pyramid B

Ratio = (3a)² : a²

Ratio = 9a : a

Ratio = 9 : 1.

The ratio of the volumes of these pyramids is given by:

Ratio = Volume of pyramid A : Volume of pyramid B

Ratio = (3l × 3w × 3h)/3 : (l × w × h)/3

Ratio = 27 : 1.

Read more on pyramid here: brainly.com/question/16315790

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8 0
2 years ago
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