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4 years ago

What is indicated by arrowheads on a line?

1 answer:

5 0

Arrows on a line mean that the line continues forever in that direction. If there are two arrows in both directions along a line, then you have a geometric line. If you only have one arrow, then it is a ray. Having no arrows indicates a segment.

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A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the roo

lidiya [134]

Answer:

r=$14,400

The hotel should charge $120

Step-by-step explanation:

Revenue (r)= p * n

where,

p = price per item

n = number of items sold

A change in price leads to a change in number sold

A variable to measure the change in p and n needs to be introduced

Let the variable=x

Such that

p + x means a one dollar price increase

p - x means a one dollar price decrease

n + x means a one item number-sold increase

n - x means a one item number-sold decrease

for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)

know that at $60 per room, the hotel rents 210 rooms

r = (60 + 2x) * (210 - 3x)

=12,600-180x+420x-6x^2

=12,600+240x-6x^2

r=2100+40x-x^2

= -x^2 +40x+2100=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a= -1

b=40

c=2100

x= -b +or- √b^2-4ac / 2a

= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)

= -40 +or- √1600-(-8400) / -2

= -40 +or- √ 1600+8400 / -2

= -40 +or- √10,000 / -2

= -40 +or- 100 / -2

x= -40+100/-2 OR -40-100/-2

=60/-2 OR -140/-2

= -30 OR 70

x=70

The quadratic equation has a maximum at x=70

p+2x

=60+2(30)

=60+60

=$120

r= (60 + 2x) * (210 - 3x)

={60+2(30)}*{(210-3(30)}

r=(60+60)*(210-90)

=120*120

=$14,400

7 0

3 years ago

how long will it take an investment of $300 to triple, if the interest rate is 3.5% per year, compounded continuously?

Rashid [163]

Answer:

31 years to triple the investment

Step-by-step explanation:

Initial investment = 300

Triple amount that is final amount = 300*3= 900

rate of interest = 3.5 % = 0.035

we need to find out number of years (t)

for compounded continuously we use formula

$A= Pe^{rt}$

A is the final amount

P is the initial amount

r is the rate of interest

t is the number of years

$900 = 300e^{0.035*t}$

Divide both sides by 300

$3 =e^{0.035*t}$

take 'ln' on both sides

$ln(3) =ln(e^{0.035*t})$

ln(3) = 0.035t ln(e)

ln(e)= 1

$\frac{ln(3)}{0.035} = t$

t= 31.3889

Round to nearest whole number

t= 31 years

4 0

3 years ago

A spinner is divided into four equal sections that are numbered 2, 4, 7, and 9. The spinner is spun twice.How many outcomes have

shusha [124]

The spinner is divided into four equal sections: 2, 4, 7, 9. This represents 4 possibilities

If the spinner is spun twice, the sample space is:

$\text{Sample space = 4}^2\text{ = 16}$

For product less than 30, the number of outcomes is shown below:

The number of outcomes that have a product less than 30 = 10

The sample space that shows possibilities of an odd number combination:

The number of outcomes that contains at least one odd number = 12

The number of outcomes that have a product less than 30 and contain at least one odd number is shown below. These outcomes are outcomes circled in both cases shown above,

The outcomes circled represents the number of outcomes that has a product less than 30 and contains at least one odd number

Answer: 6 (option B)

7 0

1 year ago

Show work please :)

fgiga [73]

Answer:

Step-by-step explanation:

90/100 = 54

Cross multiplying:

100 * 54 / 90

5400/90

4 0

2 years ago

Which expression represents the calculation a (3x6)+5<br> B 6+(5x3) C 3+(6x5) D 3x(5+6)

Dahasolnce [82]

Answer:

Step-by-step explanation:

<h2>BEACAUSE ITS FORMED PROPERLY</h2>

5 0

3 years ago