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3 years ago

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George's sandbox requires 32 cubic feet of sand to fill how many bags of sand does he need to fill the sand box if each bag hold

s 2/3 cubic feet of sand

1 answer:

luda_lava [24]3 years ago

7 0

Answer:

48 bags are needed by George to fill his sandbox.

Step-by-step explanation:

Given:

Total capacity of the sandbox (V) = 32 cubic feet

Capacity of each bag = (B) = $\frac{2}{3}$ cubic feet

Now, number of bags required (N) = ?

The formula to find the total number of bags required to fill the sandbox is given as:

$Number\ of\ bags=\frac{Total\ capacity\ of\ sandbox}{Capacity\ of\ each\ bag}\\\\N=\frac{V}{B}$

Now, plug in the given values and solve for 'N'. This gives,

$N=32\div\frac{2}{3}$

In order to multiply a whole number with a fraction, we replace the division sing by multiplication and take the reciprocal of the fractional number. This gives,

$N=32\times \frac{3}{2}\\\\N=\frac{32\times 3}{2}\\\\N=16\times 3=48$

Therefore, 48 bags are needed by George to fill his sandbox.

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Using the quadratic formula, the solutions are:

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<h3>What is a quadratic function?</h3>

A quadratic function is given according to the following rule:

$y = ax^2 + bx + c$

The solutions are:

$x_1 = \frac{-b + \sqrt{\Delta}}{2a}$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a}$

In which:

$\Delta = b^2 - 4ac$

Item a:

The coefficients are a = 2, b = -3, c = -4, hence:

$\Delta = (-3)^2 - 4(2)(-4) = 41$

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$x_2 = \frac{3 - \sqrt{41}}{4}$

Item b:

The coefficients are a = 1, b = 2, c = 2, hence:

$\Delta = (2)^2 - 4(1)(2) = -4$

$x_1 = \frac{2 + \sqrt{-4}}{2} = 1 + 2i$

$x_2 = \frac{2 - \sqrt{-4}}{2} = 1 - 2i$

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2 years ago

Please help!!!! Describe how you would graph the equation y= -20x + 150.

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3 years ago

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lara [203]

Answer:

a) 0.1587 = 15.87% probability that a battery will break down during the warranty period.

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c) The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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This means that $\mu = 40, \sigma = 16$

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$Z = \frac{X - \mu}{\sigma}$

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$Z = -1$

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0.1587 = 15.87% probability that a battery will break down during the warranty period.

b. What is the expected profit of the auto store on a battery?

1 - 0.1587 = 0.8413 probability of a profit of $20.

0.1587 probability of a loss of $10. So

$E = 0.8413*20 - 0.1587*10 = 15.239$

The expected profit of the auto store on a battery is of $15.239.

c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month?

Multiplying the average for a battery by 500. So

15.239*500 = $7,619.50

The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.

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3 years ago

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sukhopar [10]

Answer:

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Step-by-step explanation:

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