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2 years ago

The area of a planned garden can be modeled by the equation A= -4w2 + 64w,

Mathematics

2 answers:

lakkis [162]2 years ago

6 0

Answer:

8 feet, 256 ft^2

Step-by-step explanation:

The function of the area can be graphically rapresented with a parabola that opens downwards

in this specific case the vertex is the maximum point of the parabola.

(X) Vertex = -64/-8 = 8 feet

(Y) Vertex = -4(64) + 512 = -256 + 512 = 256 ft^2

valentinak56 [21]2 years ago

5 0

Answer:

Maximum Width = 8 feet.

Maximum area = 256 ft^2.

Step-by-step explanation:

Part A.

A = -4w^2 + 64w

Finding the derivative:

dA/dw = -8w + 64 = 0 for maxm/minm, so

-8w = -64

w = 8

The second derivative is -8 so w = 8 gives a maximum.

Part B.

The maximum area = -4(8)^2 + 64*8

= -256 + 512

= 256 ft^2.

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The weights of adult male birds of a certain species are normally distributed with a mean of 27.5 grams and a standard deviation

Korvikt [17]

Answer:

The z-score of a male bird of this species with a weight of 29.37 grams is 1.7.

Step-by-step explanation:

We are given that the weights of adult male birds of a certain species are normally distributed with a mean of 27.5 grams and a standard deviation of 1.1 grams.

Let X = weights of adult male birds of a certain species

So, X ~ Normal( $\mu=27.5,\sigma^{2} =1.1^{2}$ )

The z score probability distribution for normal distribution is given by;

Z = $\frac{ X-\mu}{\sigma } }$ ~ N(0,1)

where, $\mu$ = population mean weight = 27.5 grams

$\sigma$ = standard deviation = 1.1 grams

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

SO, the z-score of a male bird of this species with a weight of 29.37 grams is given by;

Z score = $\frac{ X-\mu}{\sigma } }$ = $\frac{ 29.37-27.5}{1.1 } }$

= 1.7

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2 years ago

Martin charges 10$ for every 5 bags of leaves he rakes .last weekend , he raked 24 bags of leaves how much money did he earn

V125BC [204]

The answer is 25/12

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2 years ago

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snow_tiger [21]

Answer:

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Step-by-step explanation:

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3 years ago

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ivanzaharov [21]

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allochka39001 [22]

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3 years ago