All categories

3 years ago

Five years ago, Nina was twice as old as Sam. In five years, she will be 1.5 times as old as Sam. How old are Nina and Sam now?

Mathematics

1 answer:

Margarita [4]3 years ago

4 0

Answer:

age of Sam= 15 years

age of Nina = 25 years

Step-by-step explanation:

Let Nina's age be X years

Let Sam's age be Y years

Five years ago Nina's age will be X- 5 years

Five years ago Sam's age will be Y- 5 years

Given in question

Five years ago, Nina was twice as old as Sam

writing it mathematically using X and Y we have

Nina's age = 2 * Sam's age

X- 5 = 2 *(Y- 5)

X = 2 *(Y- 5) + 5 = 2Y - 10 + 5 = 2Y - 5 _________________equation A

__________________________________________________________

Five years in future Nina's age will be X+ 5 years

Five years ago Sam's age will be Y+ 5 years

Given in question

In five years, she will be 1.5 times as old as Sam

writing it mathematically using X and Y we have

Nina's age = 1.5 * Sam's age

X+5 = 1.5 *(Y+ 5)

X = 1.5*(Y+5) -5 = 1.5Y +7.5 - 5 = 1.5Y +2.5 _________________equation B

_______________________________________

in equation A we have X = 2Y - 5

in equation B we have X = 1.5Y + 2.5

equating equation A and B we have

2Y - 5 = 1.5Y +2.5

=> 2Y - 1.5Y = 2.5 + 5

=> 0.5Y = 7.5

=> Y = 7.5/0.5 = 15

from equation A we have

X = 2Y - 5 (substituting the value of Y = 15 in equation we have)

X = 2*15 - 5 = 25

Therefore age of Sam= 15 years

age of Nina = 25 years

You might be interested in

HELP PLEASE SHOW ME HOW TO DO THIS

katovenus [111]

Answer:

Step-by-step explanation:

Salary increase in 2 years = Salary in fifth year - salary in 3rd year

= 87,023 - 43,250

= $ 43,773

Salary increase per year= 43773/2 = $ 21,886.50

6 0

3 years ago

According to charles law, the pressure P in pascals of a fixed volume of gas is linearly related to the temperature T in degrees

garik1379 [7]

If my memory serves me well, according to charles law, use this formula: m=(P2−P1)/(T2−T1). This is A.
In this cotext, slope is the constant.

8 0

4 years ago

Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting

slega [8]

Answer:

(a) λ = 2.

(b) P (X = 0) = 0.1353; P (X = 1) = 0.2706;

P (X = 2) = 0.2706; P (X = 3) = 0.1804

Step-by-step explanation:

Let X = number of arrivals at the drive-up teller window.

The average number of arrivals at the drive-up teller window per minute is,

p = 0.4 customers/ minute.

(1)

Compute the expected number of customers at the drive-up teller window in n = 5 minutes as follows:

$E(X)=\lambda\\=np\\=5\times 0.4\\=2$

Thus, the mean number of customers that will arrive in a five-minute period is λ = 2.

(2)

The random variable X follows a Poisson distribution with parameter λ = 2.

The probability mass function of X is:

$P(X=x)=\frac{e^{-2}2^{x}}{x!};\ x=0,1,2,3...$

Compute the probability of exactly 0 arrivals in 5 minutes as follows:

$P(X=0)=\frac{e^{-2}2^{0}}{0!}=\frac{0.1353\times 1}{1}=0.1353$

Compute the probability of exactly 1 arrivals in 5 minutes as follows:

$P(X=1)=\frac{e^{-2}2^{1}}{1!}=\frac{0.1353\times 2}{1}=0.2706$

Compute the probability of exactly 2 arrivals in 5 minutes as follows:

$P(X=2)=\frac{e^{-2}2^{2}}{2!}=\frac{0.1353\times 4}{2}=0.2706$

Compute the probability of exactly 3 arrivals in 5 minutes as follows:

$P(X=3)=\frac{e^{-2}2^{3}}{3!}=\frac{0.1353\times 8}{6}=0.1804$

Thus, the values are:

P (X = 0) = 0.1353

P (X = 1) = 0.2706

P (X = 2) = 0.2706

P (X = 3) = 0.1804

(3)

Delays occur in the service time if there are more than three customers arrive during any five-minute period.

Compute the probability that there are more than 3 customers as follows:

P (X > 3) = 1 - P (X ≤ 3)

$=1-\sum\limits^{3}_{x=0}{\frac{e^{-2}2^{x}}{x!}}\\=1-(0.1353+0.2706+0.2706+0.1804)\\=1-0.8569\\=0.1431$

Thus, the probability that delays will occur is 0.1431.

3 0

4 years ago

Consider the function.

Licemer1 [7]

Answer:

Option 4

Step-by-step explanation:

Given function is,

$f(x)=2\frac{1}{2}-3\frac{1}{3}x$

Steps to get the inverse of the given function,

Step 1,

Convert the function into equation,

$y=2\frac{1}{2}-3\frac{1}{3}x$

Step 2,

Interchange the variables 'x' and 'y',

$x=2\frac{1}{2}-3\frac{1}{3}y$

Step 3,

Solve the equation for the value of y,

$x-2\frac{1}{2}=-3\frac{1}{3}y$

$x-\frac{5}{2}=-\frac{10}{3}y$

$-x+\frac{5}{2}=\frac{10}{3}y$

$-3x+\frac{15}{2}=10y$

$-\frac{3}{10}x+\frac{15}{20}=y$

$y=-\frac{3}{10}x+\frac{3}{4}$

Step 4,

Convert the equation into inverse function,

$f^{-1}x=-\frac{3}{10}x+\frac{3}{4}$

For x-intercepts,

Substitute y = 0,

$0=-\frac{3}{10}x+\frac{3}{4}$

$\frac{3}{10}x=\frac{3}{4}$

$x=\frac{10}{4}$

$x=\frac{5}{2}$

$x=2\frac{1}{2}$

Therefore, x-intercept of the inverse function is $(2\frac{1}{2},0)$ .

Option 4 will be the answer.

8 0

3 years ago

In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 41) and matching the nu

puteri [66]

Answer:

1 / 2,787,760,560

Step-by-step explanation:

The number of permutations is:

41 × 40 × 39 × 38 × 37 × 31 = 2,787,760,560

So the probability of winning the jackpot is 1 / 2,787,760,560.

6 0

4 years ago