Brine is a solution of salt and water. If a tub contains 50 gallons of a 5% solution of brine, how much water must evaporate to change it to an 8% solution?

Answers

Answer 1

Answer: Let x = amt of water evaporated :.05(50) = .08(50-x) 2.5 = 4 - .08x .08x = 4 - 2.5 .08x = 1.5 x = 18.75 lb of water evaporated : ; Check; amt of salt remains the same, only the percentage is different, right? .05(50) = .08(50-18.75) .05(50) = .08(31.25) 2.5 = 2.5

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A nest of ants initially contains 500 individuals. The population is increasing by 12% each week.a) How many ants will be there after :
i. 10 weeks
ii. 20 weeks

b)How many weeks will it take for the ant population to reach 2000.

Answers

Answer:

a) (i) 1553 ants

(ii) 4823 ants

b) 12 weeks

Step-by-step explanation:

Given,

The initial number of ants, P = 500,

Also, the rate of increasing per week, r = 12% = 0.12,

So, the number of ants after x weeks,

$A=P(1+r)^x$

$\implies A=500(1+0.12)^x=500(1.12)^x$

a) (i) If x = 10 weeks,

The number of ants would be,

$A=500(1.12)^(10)=1552.92\approx 1553$

(ii) If x = 20 weeks,

The number of ants would be,

$A=500(1.12)^(20)=4823.15\approx 4823$

b) If A = 2000

$\implies 2000 = 500(1.12)^x$

$4=(1.12)^x$

Taking log both sides,

log(4) = xlog(1.12)

⇒ x = 12.23 ≈ 12 weeks

A)4, 823
B)13 Weeks

A: 500 (1 + .12)^x (which is 500 (1 + .12)^20 now)
= 4823. 15 which is ≈ 4823.

B: 2000/ y1 = 500 (1 + .12)^x / y2

12.23 so 13 weeks

Find last year's salary if, after a 5% pay raise, this year's salary is $38,325?

Answers

To answer the question above,
This means that
This year my salary is: 105% ( up 5% from 100%) ;
Salary = $31500
and last year. 100% ( base year) ; Let the Salary = $x

Now let us solve,
x / 100 = 31500/105
so x = 31500 * 100/105 =
$30 000
I hope my answer helped you I've included the formula on how I got the answer.

5% of 38325 is 1916.25

subtract the answer from this years salary

38325
- 1916.25
that would be 36408.75

now add comma and dollar sign and last year's salary is $36,408.75

The 4 in 0.47 stands for

Answers

Its 4 tenths.

Hope This Helps You!
Good Luck Studying :)

The diameter of a bacteria colony that doubles every hour is represented by the graph below. What is the diameter of the bacteria after 9 hours? (0,1) (1,2) (2,4) (3,8)Answers:
128
256
512
1024

Answers

As the colony doubles every hour, the population $p$ is modeled by:

$p = 2^t$

Where $t$ is the time in hours.

We can see this because:

$2^0 = 1 \n 2^1 = 2 \n 2^2 = 4$

Notice that the x coordinate of the graph corresponds to the time, and the y coordinate corresponds to the population.

Thus at $t=9$

$p=2^9 \n \n p = \boxed{512}$

Solve for m in the following equation:
x= 3k(n + m)

Answers

The correct answer is m=x/3k-n

Find the area of a sector with a central angle of 110° and a diameter of 6 cm. Round to the nearest tenth.

Answers

=1/2* r^2 * theta
r=D/2=3 cm
theta=110 deg= 1.92 radian.
area=1/2*3*3*1.92 cm2 =8.64 cm2
=8.6 cm2 (approx.)

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