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ira [324]
3 years ago
14

The Escobar family and the Johnson family each used their sprinklers last month. The water output rate forthe Escobar family's s

prinkler was 20 gallons per hour. The water output rate for the Johnson family's sprinkler was40 gallons per hour. The families used their sprinklers for a combined total of 32 hours, resulting in a total wateroutput of 960 gallons. How many hours was each family’s sprinkler used?
Mathematics
1 answer:
DENIUS [597]3 years ago
3 0

Answer:

J = 32

E = 0

Step-by-step explanation:

E is the number of hours for the Escobar family

J is the number of hours for the Johnson family

E + J = 32

E * 20 + J * 30 = 960

Multiply the first equation by -20 so we can use elimination

-20 E -20 J = -640

Add this to the second equation

E * 20 + J * 30 = 960

-20 E -20 J = -640

---------------------------------

         10 J = 320

Divide by 10

J = 32

Now find E

E + J = 32

E  + 32 = 32

E = 0

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Pythagorean theorem a=7 and c=14. Can you explain how to find b?​
nikdorinn [45]

Answer:

c squared - a squared = b squared

Step-by-step explanation:

Since a squared + b squared = c squared

With these values it would equal 14 squared - 7 squared = c squared

Then after you find c squared, find the square root of it and there you have go your answer!

8 0
3 years ago
What is the correct unit for this triangle??
natita [175]
The correct unit for this triangle would be cm. Hope this helps!
8 0
3 years ago
Read 2 more answers
1. Consider the following hypotheses:
Andrej [43]

Answer:

See deductions below

Step-by-step explanation:

1)

a) p(y)∧q(y) for some y (Existencial instantiation to H1)

b) q(y) for some y (Simplification of a))

c) q(y) → r(y) for all y (Universal instatiation to H2)

d) r(y) for some y (Modus Ponens using b and c)

e) p(y) for some y (Simplification of a)

f) p(y)∧r(y) for some y (Conjunction of d) and e))

g) ∃x (p(x) ∧ r(x)) (Existencial generalization of f)

2)

a) ¬C(x) → ¬A(x) for all x (Universal instatiation of H1)

b) A(x) for some x (Existencial instatiation of H3)

c) ¬(¬C(x)) for some x (Modus Tollens using a and b)

d) C(x) for some x (Double negation of c)

e) A(x) → ∀y B(y) for all x (Universal instantiation of H2)

f)  ∀y B(y) (Modus ponens using b and e)

g) B(y) for all y (Universal instantiation of f)

h) B(x)∧C(x) for some x (Conjunction of g and d, selecting y=x on g)

i) ∃x (B(x) ∧ C(x)) (Existencial generalization of h)

3) We will prove that this formula leads to a contradiction.

a) ∀y (P (x, y) ↔ ¬P (y, y)) for some x (Existencial instatiation of hypothesis)

b) P (x, y) ↔ ¬P (y, y) for some x, and for all y (Universal instantiation of a)

c) P (x, x) ↔ ¬P (x, x) (Take y=x in b)

But c) is a contradiction (for example, using truth tables). Hence the formula is not satisfiable.

7 0
3 years ago
In 2005, the Summerville Journal had 110,000 subscriptions. The number of subscriptions subsequently decreased by 8% each year.
barxatty [35]

Answer:

The number of subscription will be 26,655 in 2022.

Step-by-step explanation:

In 2005, the number subscription is 110,000 and it is decreased at a rate 8% per year.

After 1 year number of subscription is 110,000- 8% of 110,00

                                                              =110,000(1-8%)

After 2 years  number of subscription is 110,000(1-8%) -8% of 110,000(1-8%)

                                                               =110,000(1-8%)(1-8%)

                                                               =110,000(1-8%)²

After 2 years  number of subscription is 110,000(1-8%)² -8% of 110,000(1-8%)²

                                                               =110,000(1-8%)²(1-8%)

                                                               =110,000(1-8%)³

....

and so on.

After t year the number of subscription is

S(t)=110,000(1-8\%)^t

t= 2022-2005=17 years

\therefore S(t)=110,000(1+0.08)^{17}

          ≈26,655

The number of subscription will be 26,655 in 2022.

6 0
3 years ago
Simplify
Gre4nikov [31]

Answer is 81x^5*y^30/125

8 0
3 years ago
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