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elena55 [62]
3 years ago
10

Gabriel has $0.80 worth of pennies and

Mathematics
1 answer:
Juliette [100K]3 years ago
4 0

Answer:

nickels=13 and pennies=15

Step-by-step explanation:

0.05n+0.01p=0.80

-0.01(n+p=28)

0.05n+0.01p=0.80

-0.01n-0.01p= -0.28

0.04n=0.52

n=13

p=15

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Solve the differential equation 3ydx+(xy+5x)dy=0
Brrunno [24]

The ODE is separable:

3y\,\mathrm dx+(xy+5x)\,\mathrm dy=0\implies x(y+5)\,\mathrm dy=-3y\,\mathrm dx\implies\dfrac{y+5}y\mathrm dy=-\dfrac3x\,\mathrm dx

Integrating both sides gives

\displaystyle\int\left(1+\frac5y\right)\,\mathrm dy=-3\int\frac{\mathrm dx}x\implies y+5\ln|y|=-3\ln|x|+C

4 0
3 years ago
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An experiment consists of rolling two fair number cubes. What is the probability that the sum of the two numbers will be >3
liraira [26]

Answer:   \bold{\dfrac{5}{12}}

<u>Step-by-step explanation:</u>

greater than 3 means the sum is either 4, 5, or 6.

There are 15 permutations that meet the criteria:

(1, 3), (1, 4), (1, 5), (1,6)

(2, 2), (2, 3), (2, 4), (2, 5), (2,6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3,6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4,6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6,6)

There are 6²= 36 total permutations for 2 dice.

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3 0
3 years ago
A cake that costs $32 is on sale for 15% off and there are no taxes. Explain why the expression
Darya [45]

Answer:

$27.2

Step-by-step explanation:

A cake that costs $32 is on sale for 15% off and there are no taxes. Explain why the expression (0.85).32 represents the final price of the cake in dollars.

This is explained in the calculation below

= A cake that costs $32 is on sale for 15% off

The amount off the cake is calculated as

= 15% of $32

= 15/100 × 32

= $4.8

The amount he is paying for the cake =>$32 - $4.8

= $27.2

The above expression is obtained as

(0.85).32

= (100% - 15%) × 32

=( 1 - 0.15) × 32

= 0.85 × 32

= $27.2

The final price of the cake = $27.2

7 0
3 years ago
A retail store sells two types of shoes, sneakers and sandals. The store owner pays $8 for the sneakers and $14 for the sandals.
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Sneakers= x, sandals= y

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Sneakers are more profitable, so it should be maximized.

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8x+14y≤2000

x+y≤200

if we assume the maximum of 200 shoes stocked, then:

x= 200-y

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Answer:

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Step-by-step explanation:

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