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balu736 [363]
3 years ago
5

Paula collected 75 stickers. She shares her stickers with 5 of her friends equally. How many stickers will each get?

Mathematics
1 answer:
Daniel [21]3 years ago
8 0
75 ÷ 5 = 15. So each friend will get 15 stickers. 
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Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interes
Vsevolod [243]

Answer:

  • CDs — $10,000
  • bonds — $80,000
  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

  0.0275c +.045b +0.104s = 8555 . . . . . total income earned

  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

  b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b

  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

  2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

  .0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn

  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

  s = 65000 -2c . . . . . . . expression we can substitute for s

  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

_____

Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

6 0
3 years ago
Which method would be more efiicient to solve the system y=1/2x and 2x+3y=28
Licemer1 [7]
Probably the subsitution method


y=1/2x
subsitute that fr y

2x+3(1/2x)=28
2x+3/2x=28
times 2 both sides
4x+3x=56
7x=56
divide by 7 both sides
x=8
sub back

y=1/2x
y=1/2(8)
y=4

(x,y)
(8,4)
6 0
2 years ago
Z=-3x2+2ey-2y+3 cực trị tự do
topjm [15]

Answer:

z=( -2 , 5/3) can you speak English

5 0
2 years ago
The outer diameter of a spherical shell is 36 pie cm³and its inner diameter is 9 cm. Find the volume of the metal contained the
Leona [35]

Answer:

may be 11.460

sorry to say this but I'm not sure bout my answer

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4 0
2 years ago
Jaime has 5 over 11 spaceof a project completed while Tim has finished 7 over 13 spaceof the same project.
faust18 [17]

Answer:

a. Tim has completed a greater amount of work.

b. Together they have completed \frac{142}{143} part of two projects.

Step-by-step explanation:

Let us assume that the project on which Jaime and Tim are working has x amount of space.

Now, given that Jaime has 5 over 11 space of a project completed while Tim has finished 7 over 13 space of the same project.

Therefore, Jaime has completed \frac{5x}{11} amount of space and Tim has finished \frac{7x}{13} amount of space.

a. Now, (7x) \times 11 > (5x) \times 13

⇒ \frac{7x}{13} > \frac{5x}{11}

Therefore, Tim has completed the greater amount of work. (Answer)

b. Together they have completed (\frac{7x}{13} + \frac{5x}{11}) = \frac{(7 \times 11 + 5 \times 13)}{13 \times 11} x = \frac{142}{143}x amount of space out of 2x amount of space. (Answer)

4 0
3 years ago
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