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Simora [160]
3 years ago
6

a contractor digs a rectangular hole that is 40 feet long and 10 1/2 feet deep. what is the width of the hole if 6510 cubic feet

of dirt is removed?
Mathematics
2 answers:
dolphi86 [110]3 years ago
4 0
40 * 10.5 * w = 6510
420 w = 6510
w = 15.5 ft
sweet-ann [11.9K]3 years ago
3 0
Well, since we know (or should know) that cubic feet is found by LxWxH. We take 6510/ 10.5=620 then take the 620/ 40= 15.5. Thus your width is equal to 15.5ft
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For the data in the table, write an equation for the direct variation.
melisa1 [442]

The equation of direct variation is,

\begin{gathered} y=kx \\ k=\frac{y}{x} \end{gathered}

Substitute the values of <em>y</em> and <em>x</em>.

\begin{gathered} k=\frac{5.4}{4} \\ k=1.35 \end{gathered}

So, the obtained equation will be <em>y</em>=1.35(x).

Let's check with the values of <em>x</em>.

1) If <em>x</em>=4

\begin{gathered} y=1.35x \\ y=1.35(4) \\ y=5.4 \end{gathered}

2) If <em>x</em>=2

\begin{gathered} y=1.35x \\ y=1.35(2) \\ y=2.7 \end{gathered}

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9 months ago
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Total = 2,500 (1.021)^t

Step-by-step explanation:

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3 years ago
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces
nadya68 [22]

Answer:

a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less

b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

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Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

P(X \leq x) = \frac{x - a}{b-a}

The probability of being higher than x is:

P(X > x) = \frac{b - x}{b-a}

The probability of being between c and d is:

P(c \leq X \leq d) = \frac{d-c}{b-a}

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

This means that a = 8.5, b = 12

a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

P(X \leq x) = \frac{x - a}{b-a}

P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286

0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.

b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

P(X > x) = \frac{b - x}{b-a}

P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857

0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

P(c \leq X \leq d) = \frac{d-c}{b-a}

P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714

0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.

d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

Proportion of iPad Minis with a battery life of at least 9 hours.

P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571

Out of 100:

0.8571*100 = 85.71

To the nearest whole number

86 should have a battery life of at least 9 hours.

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