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Tcecarenko [31]
1 year ago
14

The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive l

arge multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. make a system of equations to find the smallest number of busses the orchestra can rent. Let x= the number of busses and y= the number of vans make an equation representing the number of vehicles needed. __________ make an equation representing the total number of seats in vehicles for the orchestra members. __________ Solve the system of equations. How many busses does the orchestra need to rent? ____________ How many 12-passenger vans does the orchestra need to rent? ____________
Mathematics
1 answer:
Nezavi [6.7K]1 year ago
8 0

- Make an equation representing the number of vehicles needed.

We have six drivers so

x + y ≤ 6

That's not really an equation; it's an inequality.  We want to use all our drivers so we can use the small vans, so

x + y = 6

- Make an equation representing the total number of seats in vehicles for the orchestra members.

s = 25x + 12y

That's how many seats total; it has to be at least 111 so again an inequality,

25x + 12y ≥ 111

We solve it like a system of equations.  

x + y = 6

y = 6 - x

111 = 25x + 12y = 25x + 12(6-x)

111 = 25x + 72 - 12x

111 - 72 = 13 x

39 = 13 x

x = 3

Look at that,  it worked out exactly.  It didn't have to.

y = 6 - x = 3

Answer: 3 buses, 3 vans

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Emma's square patio below has been area=31 sq ft. She decides to decrease one dimension by 1 foot and decreases the other dimens
Andreas93 [3]

Answer:

4.57ft  by 1.57 ft

Step-by-step explanation:

We are given that

Emma's square patio has been area=31 sq.ft

One dimension decrease by 1 foot and other dimension decrease by 4 feet.

We have to find the new dimensions of Emma's patio.

Let x be the side of Emma's square patio

We know that

Area of square=x^2

x^2=31

x=\sqrt{31}=5.57 ft

One dimension=5.57-1=4.57 ft

other dimension=5.57-4=1.57 ft

Hence, the new dimension of Emma's patio is given by

4.57ft  by 1.57 ft

5 0
2 years ago
A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space in
GrogVix [38]

Answer:

fdwef

Step-by-step explanation:

4 0
2 years ago
Given the first type of plot indicated in each pair: which of the second plots could not always be generated from it? a. dot plo
Elenna [48]

Answer:

C

Step-by-step explanation:

Dot plot is usually in the form of stem & leaf. The only difference is that, stem& leaf presents the actual values while dot plot usually represent the value in dots. Hence, we can easily generate dot plot from stem & leaf!

For (a) dot plot and box plot, dot plot presents all the data while box plot presents only the five-num statistics, namely:

1. minimum

2. 1st quartile (Q1)

3. median

4. 3rd quartile (Q3)

5. Maximum

And outliers, if any!

Thus, dot plot cannot directly generate box plot

For (b). Histogram and stem & leaf. Although both usually help us understand the skewness of data distribution, however, histogram deals with frequency distribution (counts of number of occurrence) and plotted on the intervals and stem&leaf list the values.

For (d). Even though dot plot shoots up and down like the histogram, the content is different. In dot plot, it is the actual value represented in dots. But in histogram, it is the frequency distribution of the class intervals.

3 0
2 years ago
You sell sporting goods. Your wages depend on the value of your sales. One week you sold $3,500 in sporting goods, earning $950.
Semmy [17]

Answer:

y = 0.2x + 250

Step-by-step explanation:

let the sales be x and y be earnings

thus,

given

x₁ = $3,500 ; y₁ = $950

and,

x₂ = $2,800 ; y₂ = $810

Now,

the standard line equation is given as:

y = mx + c

here,

m is the slope

c is the constant

also,

m = \frac{y_2-y_1}{x_2-x_1}

or

m = \frac{810-950}{\textup{2,800-3,500}}

or

m = 0.2

substituting the value of 'm' in the equation, we get

y = 0.2x + c

now,

substituting the x₁ = $3,500 and y₁ = $950 in the above equation, we get

$950 = 0.2 × $3,500 + c

or

$950 = $700 + c

or

c = $250

hence,

The equation comes out as:

y = 0.2x + 250

7 0
1 year ago
The median of $20, x, 15, 30, 25$ is $0.4$ less than the mean. If $x$ is a whole number, what is the sum of all possible values
34kurt

Answer:

198

Step-by-step explanation:

5 0
1 year ago
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