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3 years ago

The product of two consecutive room numbers is 420. find the room numbers.

2 answers:

7 0

Hello :
the consecutive room numbers are : n , n+1
n(n+1) =420
n²+n -420 = 0
the discriminant delta = b² - 4ac ( a = 1 and b = 1 and c = - 420
delta = (1)²-4(1)(-420) =1681= 41²
n = (-1 -41)/2 ( refused negatif number)
or
n = (-1+41)/2 =20
<span> the room numbers.are : 20 , 21</span>

Gnesinka [82]3 years ago

3 0

Step-by-step explanation:

Let the first number is x and other number is (x+1). The product of two consecutive room numbers is 420.

So, according to question,

$x\times (x+1)=420$

$x^2+x-420=0$

On solving the above quadratic equation, we get the value of x as:

x = 20

and

(x+1) = 21

So, two numbers are 20 and 21.

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A man pays rs.1440 for income tax at rate of rs.2 per rs.100.Find his income.

KengaRu [80]

Total tax paid = 1440

Tax rate = Rs 2 per Rs 100

ATQ

1440 ÷ 2

= 720

720 × 100

Rs 72,000

His income is Rs 72,000

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7 0

3 years ago

Find the slope of the graph of the relation y^3 − xy = −6 at the point (7, 2).

mezya [45]

Yay, implicit differnentiation

when you take the derivitive of y, you multiply it by dy/dx
example
dy/dx y^2=2y dy/dx

for x, the dy/dx dissapears

ok
so differnetiate and solve for dy/dx

3y² dy/dx-(y+x dy/dx)=0
expand
3y² dy/dx-y-x dy/dx=0
3y² dy/dx-x dy/dx=y
dy/dx (3y²-x)=y
dy/dx=y/(3y²-x)

so at (7,2)
x=7 and y=2
dy/dx=2/(3(2)²-7)
dy/dx=2/(3(4)-7)
dy/dx=2/(12-7)
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answer is 2/5

5 0

3 years ago

Grace is planning on purchasing an Akai Professional MPC5000 drum machine for $2195. She's been pre-approved to finance her purc

Genrish500 [490]

1) Her monthly payment is $40.97 if she finance the total amount

2) She will pay $2458.2 for the MPC5000

3)Her monthly payment will be $26.50 if she pay her saved up money upfront

4) She will pay $2365.4 for the MPC5000

5) Yes, I recommend to pay the $775 upfront . If she pay upfront, then the amount she needs to pay for the MPC5000 is less.

Step-by-step explanation:

The cost of the drum machine is $2195

The APR is 12% over 60 months

1) the APR for 60 months is 12%

So, the APR for 1 month is

12/60 = 0.2%

The interest per month = 0.2% of 2195

= (0.2 x 2195) / 100

= 4.39

The amount to be paid per month is

= monthly amount + interest

= (2195/60) + 4.39

= 36.58 + 4.39

=$ 40.97

2) If she pays $40.97 per month then the total payment (for 60 months) for the drum machine

= 40.97 x 60

= $ 2458.2

3) the total cost is $2195 out of which she pays $775 upfront.

So she have to borrow less .

The amount to be financed is

2195- 775= $1420

The monthly interest is,

(0.2 x 1420) /100 = 2.84

Monthly she have to pay

23.66+ 2.84= $26.50

4) If she pay $775 upfront then the remaining $1420 is financed

Her monthly payment is $26.50

Then for 60 months she will pay,

26.50 x 60= $1590.4

The total amount paid for the drum machine is

775+1590.4 =$2365.4

4 0

3 years ago

Suppose a simple random sample of size nequals36 is obtained from a population with mu equals 74 and sigma equals 6. (a) Descri

OlgaM077 [116]

Part a)

The simple random sample of size n=36 is obtained from a population with

$\mu = 74$

and

$\sigma = 6$

The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.

Therefore the sampling distribution has a mean of

$\mu = 74$

The standard error of the means becomes the standard deviation of the sampling distribution.

$\sigma_ { \bar X } = \frac{ \sigma}{ \sqrt{n} } \\ \sigma_ { \bar X } = \frac{ 6}{ \sqrt{36} } = 1$

Part b) We want to find

$P(\bar X \:>\:75.9)$

We need to convert to z-score.

$P(\bar X \:>\:75.9) = P(z \:>\: \frac{75.9 - 74}{1} ) \\ = P(z \:>\: \frac{75.9 - 74}{1} ) \\ = P(z \:>\: 1.9) \\ = 0.0287$

Part c)

We want to find

$P(\bar X \: < \:71.95)$

We convert to z-score and use the normal distribution table to find the corresponding area.

$P(\bar X \: < \:71.95) = P(z \: < \: \frac{71.9 5- 74}{1} ) \\ = P(z \: < \: \frac{71.9 5- 74}{1} ) \\ = P(z \: < \: - 2.05) \\ = 0.0202$

Part d)

We want to find :

$P(73\:$

We convert to z-scores and again use the standard normal distribution table.

$P( \frac{73 - 74}{1} \:< \: z$

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3 years ago

3/x+3+2/x What is the common denominator in this rational expression? Answers should be given in fully factored form.

Inga [223]

Answer:

x(x+3).

Step-by-step explanation:

The C, D. of x and x+3 is x(x+3).

7 0

2 years ago