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fgiga [73]
3 years ago
13

To rent a meeting room a college charges a reservation fee of $14 an additional fee of four dollars per hour. The chemistry club

wants to spend less than $50 in renting a room. What are the possible numbers of ours a chemistry club could rent the meeting room?
Mathematics
1 answer:
Anettt [7]3 years ago
7 0
They can rent a meeting room for 8 hours
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What is the square root of 12 simplified? Is it 2 times the square root of 3?
blagie [28]

Answer: Yes, it is 2\sqrt{3}

Step-by-step explanation:

To simplify square roots, you can factor the number inside the square root into its lowest common denominators.

\sqrt{12}=\sqrt{4*3}  =\sqrt{2*2*3}

Any value that appears twice can be "taken out" of the square root and moved to the left of it:

2\sqrt{3},

What you are doing is essentially taking the square root of 4 and the square root of 3. Because the square root of 4 can be simplified, and the square root of 3 cannot, this is the most simplified version of the expression we can reach.

4 0
3 years ago
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Draw your own rectangle, with an area of 24 square units, on the coordinate plane. Then, identify the vertices of your rectangle
Gnoma [55]

Answer:

First you should remember that the formula for calculating area of a rectangle is;

Area=Length × width

You can decide to have a rectangle with different dimensions provided the area is 24 square unit

For this case, lets choose a rectangle with vertices at (1,0), (7,0),(1,4), (7,4)

After plotting these coordinates, you will notice your rectangle has a length of 6 units and a width of 4 units

A single unit is 1 square unit.When you Count the number of units inside the rectangle formed you realize you have 24 units covered inside

The area of the 24 units will be;

24×1 square unit= 24 square units

6 0
2 years ago
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Please help!
kogti [31]
I and III seem to be correct, II doesn't because, for example, if x = w = z = t = 70 and y = u = 40, then all three pairs of vertical angles in the figure have equal measure and the given condition x + y = u + w stands. But it means y is not equal to w.
3 0
3 years ago
Read 2 more answers
I need help on both problems
Lerok [7]
Number 1 is d.50 because 10= 1 mile and there are 5 miles 10times5=50
8 0
3 years ago
A total of 12 players consisting 6 male and 6 female badminton players are attending a training camp
abruzzese [7]

Step-by-step explanation:

<em>"A total of 12 players consisting 6 male and 6 female badminton players are attending a training camp."</em>

<em />

<em>"(a) During a morning activity of the camp, these 12 players have to randomly group into six pairs of two players each."</em>

<em>"(i) Find the total number of possible ways that these six pairs can be formed."</em>

The order doesn't matter (AB is the same as BA), so use combinations.

For the first pair, there are ₁₂C₂ ways to choose 2 people from 12.

For the second pair, there are ₁₀C₂ ways to choose 2 people from 10.

So on and so forth.  The total number of combinations is:

₁₂C₂ × ₁₀C₂ × ₈C₂ × ₆C₂ × ₄C₂ × ₂C₂

= 66 × 45 × 28 × 15 × 6 × 1

= 7,484,400

<em>"(ii) Find the probability that each pair contains players of the same gender only. Correct your final answer to 4 decimal places."</em>

We need to find the number of ways that 6 boys can be grouped into 3 pairs.  Using the same logic as before:

₆C₂ × ₄C₂ × ₂C₂

= 15 × 6 × 1

= 90

There are 90 ways that 6 boys can be grouped into 3 pairs, which means there's also 90 ways that 6 girls can be grouped into 3 pairs.  So the probability is:

90 × 90 / 7,484,400

= 1 / 924

≈ 0.0011

<em>"(b) During an afternoon activity of the camp, 6 players are randomly selected and 6 one-on-one matches with the coach are to be scheduled.</em>

<em>(i) How many different schedules are possible?"</em>

There are ₁₂C₆ ways that 6 players can be selected from 12.  From there, each possible schedule has a different order of players, so we need to use permutations.

There are 6 options for the first match.  After that, there are 5 options for the second match.  Then 4 options for the third match.  So on and so forth.  So the number of permutations is 6!.

The total number of possible schedules is:

₁₂C₆ × 6!

= 924 × 720

= 665,280

<em>"(ii) Find the probability that the number of selected male players is higher than that of female players given that at most 4 females were selected. Correct your final answer to 4 decimal places."</em>

If at most 4 girls are selected, that means there's either 0, 1, 2, 3, or 4 girls.

If 0 girls are selected, the number of combinations is:

₆C₆ × ₆C₀ = 1 × 1 = 1

If 1 girl is selected, the number of combinations is:

₆C₅ × ₆C₁ = 6 × 6 = 36

If 2 girls are selected, the number of combinations is:

₆C₄ × ₆C₂ = 15 × 15 = 225

If 3 girls are selected, the number of combinations is:

₆C₃ × ₆C₃ = 20 × 20 = 400

If 4 girls are selected, the number of combinations is:

₆C₂ × ₆C₄ = 15 × 15 = 225

The probability that there are more boys than girls is:

(1 + 36 + 225) / (1 + 36 + 225 + 400 + 225)

= 262 / 887

≈ 0.2954

7 0
3 years ago
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