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Leto [7]
3 years ago
11

If a4 = 625, what does (a) equal?

Mathematics
1 answer:
Reika [66]3 years ago
4 0

I'm assuming you meant to write a^4 = 625.

If that is the case, then note how 625 = 25^2, and how a^4 is the same as (a^2)^2

So we go from this

a^4 = 625

to this

(a^2)^2 = 25^2

Apply the square root to both sides and you'll end up with: a^2 = 25

From here, apply the square root again to end up with the final answer: a = 5 or a = -5

As a check:

a^4 = (-5)^4 = (-5)*(-5)*(-5)*(-5) = 25*25 = 625

a^4 = (5)^4 = (5)*(5)*(5)*(5) = 25*25 = 625

Both values of 'a' work out

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Find the maxmium area of a rectangular plot of land which can be enclosed by rope of length 60 metres​
mario62 [17]

Answer:

225 m²

Step-by-step explanation:

If W is the width of the rectangle, and L is the length, then:

60 = 2W + 2L

A = WL

Use the first equation to solve for one of the variables:

30 = W + L

L = 30 − W

Substitute into the second equation:

A = W (30 − W)

A = 30W − W²

This is a parabola, so we can find the vertex using the formula x = -b/(2a).

W = -30 / (2 × -1)

W = 15

Or, we can use calculus:

dA/dW = 30 − 2W

0 = 30 − 2W

W = 15

Solving for L:

L = 30 − W

L = 15

So the maximum area is:

A = WL

A = (15)(15)

A = 225

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Pic included> a or c?
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2 years ago
Do oddsmakers believe that teams who play at home will have home field advantage? Specifically, do oddsmakers give higher point
anygoal [31]

Complete question is;

Do oddsmakers believe that teams who play at home will have home field advantage? Specifically, do oddsmakers give higher point spreads when the favored team plays home games as compared to when the favored team plays away games?

Two samples were randomly selected from three complete National Football League seasons (1989, 1990, and 1991). The first sample consisted of 50 games, where the favored team played in a home game, while the second sample consisted of 50 games, where the favored team played in an away game. The oddsmakers’ point spreads (which are the number of points by which the favored team is predicted to beat the weaker team) were then collected.

If µ1 and µ2 represent the mean point spread for home games and away games, respectively, which of the following is the appropriate.

A) H0: μ1 - μ2 = 0

Ha: μ1 - μ2 < 0

B) H0: μ1 - μ2 = 0

Ha: μ1 < μ2

C) H0: μ1 - μ2 > 0

Ha: μ1 - μ2 = 0

D) H0: μ1 - μ2 = 0

Ha: μ1 - μ2 > 0

E) None of the above

Answer:

D) H0: μ1 - μ2 = 0

Ha: μ1 - μ2 > 0

Step-by-step explanation:

We want to find out if oddsmakers give higher point spreads when the favored team plays home games as compared to when the favored team plays away games.

Now, since µ1 and µ2 represent the mean point spread for home games and away games, respectively;

It means we want to find out if µ1 > µ2 as the alternative hypothesis.

Thus, alternative hypothesis is;

Ha: µ1 - µ2 > 0

Meanwhile null hypothesis assumes that equal point spreads are given when the favored team plays home games as well as when the favored team plays away games.

Thus, null hypothesis is;

H0: μ1 - μ2 = 0

The only correct option is D.

8 0
2 years ago
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