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Bismuth-214 has a half life of about 20 minutes. Find the amount of Bismuth-214 left from a 30-gram sample after 1 hour

R ==30 x  1/2^(60/20)

R ==30 x   o.125

R ==3.75 grams remain after 60 minutes, or 1 hour.

A 6% alcohol salt solution is added to a 12% salt solution to produce a 3-liter 10% salt solution. How much of each solution was used? Show your solution.​

Let the volume of 6% solution==S

Then, the nolume of 12%salt solution ==3 - S

0.06S  +  0.12[3  -  S] ==0.10 *3, solve for S

S ==1 Liter of 6%solution

3 - 1 ==2 Liters of 12% salt solution.

tan a + tan b = -7/8.

The samllest distance is 9/2.

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right, sorry my bad.

i did that wrong, the correct answer should be (3, -1/2). please ignore my first answer

There are two numbers which add up to 17. If one number is 13 more than the other, find the two numbers. 

Let X stand for the smaller of the two numbers.  

X + (X + 13) = 17   

2X + 13 = 17  

2X = 17 – 13   

X = 2  and of course the other number is 15  

_.

C==Chocolates,  S==Sweets, A=Chocolates sold, B==Sweets sold.
C  -  S==184
C/A ==8/3
B /[S - B]==2/3
S  -  B==1/2[C  - A], solve for A, B, C, S

A = 144 and B = 80 and C = 384 and S = 200
144 - 80 ==64 more chocolates were sold than sweets.

8/9 n = 2/3 s

s = 4/3 n

n+s = total number

n / (n + 4/3 n) = Nadia fraction of total

n / 7/3 n

Nadia fraction = 3/7

6 X 4 X 8 X 7 = ____________ ways

6/(6+11)= 6/17ths are professors     6/17 * 136=  48 profs

B==Black, Y==Yellow, W==White
Y - W==184,
0.75Y - B ==87,
W ==2/3B, solve for B, Y, W

B==102, Y==252,  W==68
[102 + 252 + 68] ==422 - shirts altogether.

2/5B ==1/3G,
1/4(B + G)==A,
5G  - 8A ==1,600, solve for A, B, G

A==550 - adults at the fair.
B==1,000 - boys at the fair.
G==1,200 - girls at the fair.

4,700 / 5 ==940 km/h - its speed against the wind.

9,520 / 7==1,360 km/h - its speed with the wind.

[940  +  1,360] / 2 ==1,150 km/h - its speed in still air.

[1,360  -  940 ] / 2 ==210 km/h - speed of the wind.

5^400 mod 29==24 -the remainder

.03 (60)     =  .018 ( 60 + w)    solve for 'w'

4700 / (a-w) = 5         9520 / (a+w) = 7     <===== re-arrange to solve for 'a' :    (9520-7w) / 7 = a  = 1360 -w

Sub in the red equation for 'a' then solve for 'w' :

4700/ (1360-w - w) = 5

w = 210 km/hr

a = 1360 -210 = 1150 km/hr

The degree of  f(x)+kg(x) will be 5 unless k=0. 

If k=0   then   f(x)+kg(x)=f(x)     and so the degree will be 4

SHOW YOUR WORK.

N mod 4 ==3,

N mod 6==3, solve for n

LCM[4, 6] ==12

N==12C + 3, where C==0, 1, 2, 3.........etc.

When C==1,  N==12 + 3 ==15 -Least number of apples in the carton.

What is an equation of the line that passes through the point (-5,7) and is parallel to the line y = 5x + 7?

Hello Guest!

\(y = 5x + 7\\ m=5\\ y=m(x-x_P)+y_P\\ y=5(x-(-5))+7=5x+25+7\)

\(y=5x+32\)

  !

or:

∠BMC : ∠A = 2 : 1

∠A = 210 / 3

Angle AMC => x

(180 - x) + 1/2(180 - x) = 210

x = 40

Angle B = x/2

XY = 44.3760157

There are 4 pairs of congruent triangles.