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Olenka [21]
3 years ago
7

Evelyn is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve small rooms that can hol

d 3 people, and large rooms that can hold 5 people. Evelyn reserved 2 more small rooms than large rooms, which altogether can accommodate 54 guests. Write a system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved. Define the variables that you use to write the system
Mathematics
1 answer:
natali 33 [55]3 years ago
6 0

Answer:

Small rooms reserved = 8

Large rooms = 6

Step-by-step explanation:

Let the number of large rooms be x

Evelyn booked 2 more small rooms than the larger rooms.

Therefore the number of small rooms would be x+2.

Given each large room can accommodate 5 people.Therefore the total number of people in large rooms are 5x.

Given each small room can hold 3 people. Therefore the total number of people in large rooms are 3(x+2)

Total number of people accommodated = 54

Total number of guests = total guests in small rooms + total guests in large rooms

54 = 5x + 3(x+2)\\48 = 8x\\x = 6

No of large rooms = x = 6

No of small rooms = (x+2) = (6+2) = 8

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Consider the age distribution in the United States in the year 2075 (as projected by the Census Bureau). Construct a cumulative
MrRissso [65]

Answer:

The cumulative frequency plot is also attached below.

Step-by-step explanation:

The data provided is as follows:

Age Group Frequency

   0 - 9             34.9

  10 - 19             35.7

20 - 29             36.8

30 - 39             38.1

40 - 49             37.8

50 - 59             37.8

60 - 69             34.5

70 - 79             27.2

80 - 89             18.8

90 - 99               7.7

100 - 109       1.7

Consider the Excel output attached.

The cumulative frequency are computed in the Excel sheet.

The cumulative frequency plot is also attached below.

From the cumulative frequency plot it can be seen that in the future most people will belong to a higher age group rather then the lower ones.

8 0
4 years ago
What is central tendency?
Maurinko [17]

Answer:

the tendency for the values of a random variable to cluster round its mean, mode, or median.

8 0
3 years ago
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-19.76x+227=-92.57x+1052
Sergio039 [100]

If you are solving for x then your answer is 11.33

8 0
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Factor over complex numbers 2x^4+36x^2+162
Darina [25.2K]

<u>Answer:</u>

Factor over complex numbers of 2 x^{4}+36 x^{2}+162 is 2(x+3 i)^{2}(x-3 i)^{2}

<u>Solution:  </u>

From question given that

2 x^{4}+36 x^{2}+162  → (1)

On substituting x^{2}=y in equation (1),

=2 y^{2}+36 y+162

Taking 2 as a common in above expression,

=2\left(y^{2}+18 y+81\right)

Rewrite the above expression,

=2\left[y^{2}+2(y)(9)+9^{2}\right]

=2(y+9)^{2}  \left[\text { Using }(a+b)^{2}=a^{2}+2 a b+b^{2}\right]

=2\left(x^{2}+9\right)^{2} \left[\text { since } y=x^{2}\right]

\left[\text { Using } a^{2}+b^{2}=(a+i b)(a-i b), \text { where } i=\sqrt{-1}\right]

=2[(x+3 i)(x-3 i)]^{2}

=2(x+3 i)^{2}(x-3 i)^{2}

Hence Factor over complex numbers of 2 x^{4}+36 x^{2}+162 is 2(x+3 i)^{2}(x-3 i)^{2}

7 0
4 years ago
Tickets for the school play sell for $4 each. Which graph shows the relationship between the number of tickets solo
Xelga [282]

Answer:

I do not see all the graphs but it would be the reverse of what is shown for A. graph. The tickets sold to total income would have to be a 1:4 ratio where every 4 dollar leap in the y-axis is a one point (1 unit change in x).

Step-by-step explanation:

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