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NARA [144]
3 years ago
15

The following table shows the data collected from a random sample of 100 middle school students on the number of hours they play

outdoor games every week: Weekly Duration of Outdoor Games Time (in hours) 0–2 3–5 6–8 9–11 Number of Students 30 62 8 0 There are 1,200 students in the school. Based on the sample proportion, how many students in the school would be expected to play outdoor games for at least three hours every week? 744 840 960 1,104
Mathematics
2 answers:
ra1l [238]3 years ago
8 0
I believe your answer is 840. Hope this helps!
n200080 [17]3 years ago
6 0

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Weekly Duration of Outdoor Games      Number of students

                             0-2                                            30

                             3-5                                            62

                             6-8                                             8

                             9-11                                            0

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

                            Total                                         100

so, Probability of getting number of students for at least three hours every week is given by

\dfrac{62+8}{100}=\dfrac{70}{100}

Since the number of students = 1200

so, Expected number of students in the schools is given by

\dfrac{70}{100}\times 1200\\\\=840

Hence, Second option is correct.

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Solve each inequality, and then drag the correct solution graph to the inequality.
Nesterboy [21]

The correct solution graph to the inequalities are

4(9x-18)>3(8x+12)  →  C

-\frac{1}{3}(12x+6) \geq -2x +14  → A

1.6(x+8)\geq 38.4  →  B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

4(9x-18)>3(8x+12)

First, clear the brackets,

36x-72>24x+36

Then, collect like terms

36x-24x>36+72\\12x >108

Now divide both sides by 12

\frac{12x}{12} > \frac{108}{12}

∴ x > 9

For the second inequality

-\frac{1}{3}(12x+6) \geq -2x +14

First, clear the fraction by multiplying both sides by 3

3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)

-1(12x+6) \geq -6x +42

Now, open the bracket

-12x-6 \geq -6x +42

Collect like terms

-6 -42\geq -6x +12x

-48\geq 6x

Divide both sides by 6

\frac{-48}{6} \geq \frac{6x}{6}

-8\geq x

∴ x\leq  -8

For the third inequality,

1.6(x+8)\geq 38.4

First, clear the brackets

1.6x + 12.8\geq 38.4

Collect likes terms

1.6x \geq 38.4-12.8

1.6x \geq 25.6

Divide both sides by 1.6

\frac{1.6x}{1.6}\geq  \frac{25.6}{1.6}

∴ x \geq  16

Let the graphs be A, B and C from left to right

The first graph (A) shows x\leq  -8 and this matches the 2nd inequality

The second graph (B) shows x \geq  16 and this matches the 3rd inequality

The third graph (C) shows x > 9 and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

4(9x-18)>3(8x+12)  →  C

-\frac{1}{3}(12x+6) \geq -2x +14  → A

1.6(x+8)\geq 38.4  →  B

Learn more here: brainly.com/question/17448505

8 0
2 years ago
if 36 cookies cost $4.00 what is the unit rate in cookies per dollar. Using the same information what is the unit rate for 1 coo
pogonyaev

Answer:

9 cookies per dollar

Step-by-step explanation:

This is a fraction equal to

36 cookies ÷ 4 dollars

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 4

36 cookies ÷ 4

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

4 dollars ÷ 4

=  

9 cookies

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

1 dollar

=  

9 cookies

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

dollar

= 9 cookies per dollar

3 0
3 years ago
The lines y1 = 2x - 6, y2 = -3x + 4, y3 = -1/2x + 4 intersect to form the sides of a right triangle. Find the perimeter and area
tino4ka555 [31]

The area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

<h3>Determining the perimeter and area of the triangle giving line equation</h3>

In order to determine the area and perimeter of the lines, we will plot the giving lines, determine the point of intersection and then use the Pythagoras theorem to determine the dimension of the right triangle.

The points of intersection of the line are;

(x₁, y₁) = (- 0.4, 5.2),

(x₂, y₂) = (-0.8, 4.4),

(x₃, y₃) = (0, 4)

Determine the base

b² = c² -a²

b = √(-0.8)² + (4 - 4.4)²

b = 2√5 / 5

Determine the height

h = √((- 0.4) - (- 0.8))² + (5.2 - 4.4)²

height = 2√5 / 5

For the hypotenuse

r = √2 · b

r = 2√10 / 5

<h3>Determine the Perimeter and area</h3>

Perimeter = s1+s2+s3

Perimeter = 2√5 / 5 + 2√5 / 5 + 2√10 / 5

Perimeter = (2√10 + 4√5) / 5 units

<u>For the area</u>

area = 1/2* base * height

A = 0.5 · (2√5 / 5) · (2√5 / 5)

A = 2/5 square units

Hence the area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

Learn more on area and perimeter of triangles here: brainly.com/question/12010318

#SPJ1

3 0
1 year ago
Identify radicand of 2 either as a rational or irrational
faltersainse [42]
The radicand of 2 is irrational
6 0
3 years ago
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The graph below shows the solution set of which inequality ?? HELP FASTTT
Maru [420]

<u>Answer:</u>

<h2>A.</h2>

The graph shows the solution set of the equality √x < -1

<em>(No Solutions)</em>

4 0
2 years ago
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