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3 years ago

Calculate a rough estimate of the total lineal footage of lumber needed for a rectangular house 35’ x 40’?

Mathematics

1 answer:

Maru [420]3 years ago

7 0

Answer:

B. 1,500’

Step-by-step explanation:

Given;

dimension of the rectangular house, = 35’ x 40’

The actual total linear footage of lumber needed = 35’ x 40’ = 1,400'

The rough estimate should be greater than the actual estimate in 100s;

rough estimate = 1,400' + 100' = 1,500'

Therefore, the rough estimate of the total linear footage of lumber needed is 1,500'.

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Find the generating function for the sequence 1,-2,4,-8, 16, ...

kirill [66]

Answer:

$a(x)=\dfrac{1}{1+2x}$

Step-by-step explanation:

The generating function a(x) produces a power series ...

$a(x)=a_0+a_1x+a_2x^2+a_3x^3+\dots$

where the coefficients are the elements of the given sequence.

We observe that the given sequence has the recurrence relation ...

$a_0=1;a_n=-2a_{n-1} \quad\text{for n $>$ 0}$

This can be rearranged to ...

$a_n+2a_{n-1}=0$

We can formulate this in terms of a(x) as follows, then solve for a(x).

$\sum\limits^{\infty}_{n=1} {a_{n}x^n} =a(x)-a_0 \quad\text{and}\\\\\sum\limits^{\infty}_{n=1} {2a_{n-1}x^n} =(2x)a(x) \quad\text{so}\\\\\sum\limits^{\infty}_{n=1} {(a_n+2a_{n-1})x^n}=0=a(x)-a_0+2xa(x)\\\\a(x)=\dfrac{a_0}{1+2x}=\dfrac{1}{1+2x}$

The generating function is ...

a(x) = 1/(1+2x)

3 0

3 years ago

Read 2 more answers

Find the rate of change of the line below. I

Talja [164]

Answer:

-1/4

Step-by-step explanation:

6 0

3 years ago

How many sundaes are possible using one flavor of ice cream and three different toppings?

ratelena [41]

There are three different possibilities.
Ice cream + x
Ice cream + x
Ice cream + x
x = toppings

8 0

3 years ago

American adults are watching significantly less television than they did in previous decades. In 2016, Nielson reported that Ame

goldenfox [79]

Answer:

1. 0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.

2. 0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the normal distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\lambda$ is the mean in the given interval, which is the same as the variance.

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

The Poisson distribution can be approximated to the normal with $\mu = \lambda, \sigma = \sqrt{\lambda}$

In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day.

This means that $\lambda = 320n$ , in which n is the number of days.

1. Find the probability that an average American adult watches more than 309 minutes of television per day.

One day, so $\mu = 320, \sigma = \sqrt{320} = 17.89$

This probability is 1 subtracted by the pvalue of Z when X = 309. So

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

$Z = \frac{309 - 320}{17.89}$

$Z = 0.61$

$Z = 0.61$ has a pvalue of 0.729

1 - 0.729 = 0.271

0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.

2. Find the probability that an average American adult watches more than 2,250 minutes of television per week.

$\mu = 320*7 = 2240, \sigma = \sqrt{2240} = 47.33$

This is 1 subtracted by the pvalue of Z when X = 2250. So

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

$Z = \frac{2250 - 2240}{47.33}$

$Z = 0.21$

$Z = 0.21$ has a pvalue of 0.583

1 - 0.583 = 0.417

0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.

6 0

3 years ago

What initial investment must be made to accumulate $60000 in 17 years if the money is invested in a mutual fund that pays 12% an

mars1129 [50]

$7881.18

Step-by-step explanation:

Let the initial Investment be $P_{0}$ . The Interest is compounded on a monthly basis at 12% annual interest rate. After 17 years, the Investment amounts to $60,000.

As the annual interest rate is 12%, the monthly interest rate is 1%.

Since this is a compound interest problem, the total amount can be modeled as follows: $P(t)=P_{0}(1+\frac{i}{100})^{t}$

Here $i$ is the interest rate, i.e $1$ , and t is the number of time periods, i.e $17\textrm{ years x }12\frac{\textrm{months}}{\textrm{year}}$ = $204\textrm{ months}$

$60,000=P_{0}\textrm{ x }(\frac{101}{100})^{204}$

$P_{0}=7881.18$

∴ Initial Investment = $7881.18

4 0

3 years ago