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2 years ago

7

A golf-course architect has fivefive linden trees, fourfour white birch trees, and threethree bald cypress trees to plant in

a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?

1 answer:

adell [148]2 years ago

7 0

Answer:

27,720 ways

Step-by-step explanation:

The number of permutations of non-distinct items is determined by the following expression:

$P = \frac{(N_1+N_2+N_3)!}{N_1!N_2!N_3!}$

If there are five linden trees, four white birch trees, and three bald cypress trees:

$P = \frac{(5+4+3)!}{5!4!3!}\\P=27,720\ ways$

The landscaper can plant the trees is 27,720 distinct ways.

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In a factory, two thirds of the floor are is taken up by the production line.Out of the remaining floor area,three fifths is tak

KATRIN_1 [288]

Answer:the floor area of the production line is 20000 m^2

Step-by-step explanation:

Let x represent the total area of the factory.

In the factory, two thirds of the floor are is taken up by the production line. This means that the area of the production line is 2/3 × x = 2x/3 m^2

The remaining floor area would be

x - 2x/3 = x/3 m^2

Out of the remaining floor area,three fifths is taken up by the office space. This means that the area taken up by the office space would be 3/5 × x/3 = x/5 m^2

The remaining area would be

x/3 - x/5 = 2x/15

The rest is warehouse space. The warehouse space occupies 2000m2. This means that

2x/15 = 2000

2x = 15 × 2000 = 30000

x = 30000/2 = 15000m^2

The floor area of the production line would be

(2 × 30000)/3 = 20000 m^2

8 0

2 years ago

9. The average diameter of an atom is 2 x 10-8 m. What if the average diameter of an atom was 1 cm? How tall would you be?

ozzi

Answer:

You'd be $2 * 10^{-6}$ times tall

Step-by-step explanation:

Given

Represent the previous and new diameter by D1 and D2;

$D_1 = 2 * 10^{-8}m$

$D_2 = 1\ cm$

To determine how tall you'd be, we need to divide D2 by D1;

$Ratio = \frac{D_2}{D_1}$

Substitute values for D2 and D1

$Ratio = \frac{2 * 10^{-8}m}{1\ cm}$

Convert cm to m

$Ratio = \frac{2 * 10^{-8}m}{1 * 0.01\ m}$

$Ratio = \frac{2 * 10^{-8}m}{0.01\ m}$

Convert denominator to exponents

$Ratio = \frac{2 * 10^{-8}m}{10^{-2}\ m}$

$Ratio = \frac{2 * 10^{-8}}{10^{-2}}$

Apply Law of indices

$Ratio = 2 * 10^{-8} * 10^2$

$Ratio = 2 * 10^{-8+2}$

$Ratio = 2 * 10^{-6}$

Hence;

<em>You'd be </em> $2 * 10^{-6}$ <em> times tall</em>

4 0

2 years ago

Before leaving to visit Mexico, levant traded 270 american dollars and received 3000 mexican pesos. When he returned from mexico

Makovka662 [10]

Levant will receive about 9 american dollars when he exchanges his pesos.

According to this question, 1 american dollar is worth about 11 pesos. In order to find that, you need to divide 3000/270 which gives you around 11. In order to find out how many dollars he will receive for his pesos, you need to divide 100 by 11 which gives you about 9 dollars.

4 0

2 years ago

Read 2 more answers

g Assume that the distribution of time spent on leisure activities by adults living in household with no young children is norma

OLga [1]

Answer:

"<em>The probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day</em>" is about 0.8749.

Step-by-step explanation:

We have here a <em>random variable</em> that is <em>normally distributed</em>, namely, <em>the</em> <em>time spent on leisure activities by adults living in a household with no young children</em>.

The normal distribution is determined by <em>two parameters</em>: <em>the population mean,</em> $\\ \mu$ , and <em>the population standard deviation,</em> $\\ \sigma$ . In this case, the variable follows a normal distribution with parameters $\\ \mu = 4.5$ hours per day and $\\ \sigma = 1.3$ hours per day.

We can solve this question following the next strategy:

Use the <em>cumulative</em> <em>standard normal distribution</em> to find the probability.
Find the <em>z-score</em> for the <em>raw score</em> given in the question, that is, <em>x</em> = 6 hours per day.
With the <em>z-score </em>at hand, we can find this probability using a table with the values for the <em>cumulative standard normal distribution</em>. This table is called the <em>standard normal table</em>, and it is available on the Internet or in any Statistics books. Of course, we can also find these probabilities using statistics software or spreadsheets.

We use the <em>standard normal distribution </em>because we can "transform" any raw score into <em>standardized values</em>, which represent distances from the population mean in standard deviations units, where a <em>positive value</em> indicates that the value is <em>above</em> the mean and a <em>negative value</em> that the value is <em>below</em> it. A <em>standard normal distribution</em> has $\\ \mu = 0$ and $\\ \sigma = 1$ .

The formula for the <em>z-scores</em> is as follows

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Solving the question

Using all the previous information and using formula [1], we have

<em>x</em> = 6 hours per day (the raw score).

$\\ \mu = 4.5$ hours per day.

$\\ \sigma = 1.3$ hours per day.

Then (without using units)

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{6 - 4.5}{1.3}$

$\\ z = \frac{1.5}{1.3}$

$\\ z = 1.15384 \approx 1.15$

We round the value of <em>z</em> to two decimals since most standard normal tables only have two decimals for z.

We can observe that z = 1.15, and it tells us that the value is 1.15 standard deviations units above the mean.

With this value for <em>z</em>, we can consult the <em>cumulative standard normal table</em>, and for this z = 1.15, we have a cumulative probability of 0.8749. That is, this table gives us P(z<1.15).

We can describe the procedure of finding this probability in the next way: At the left of the table, we have z = 1.1; we can follow the first line on the table until we find 0.05. With these two values, we can determine the probability obtained above, P(z<1.15) = 0.8749.

Notice that the probability for the z-score, P(z<1.15), of the raw score, P(x<6) are practically the same, $\\ P(z$ . For an exact probability, we have to use a z-score = 1.15384 (without rounding), that is, $\\ P(z$ . However, the probability is approximated since we have to round z = 1.15384 to z = 1.15 because of the use of the table.

Therefore, "<em>the probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day</em>" is about 0.8749.

We can see this result in the graphs below. First, for P(x<6) in $\\ N(4.5, 1.3)$ (red area), and second, using the standard normal distribution ( $\\ N(0, 1)$ ), for P(z<1.15), which corresponds with the blue shaded area.

5 0

2 years ago

The starting salary for a particular job is 1.2 million per annum. The salary increases each year by 75000 to a maximum of 1.5mi

Vlada [557]

<h2>Answer:</h2>

In the 5th year

<h2>Step-by-step explanation:</h2>

For the first year, the salary is 1.2million = 1,200,000

For the second year, the salary is 1.2million + 75000 = 1,200,000 + 75,000 = 1,275,000

.

.

.

For the last year, the salary is 1.5million = 1,500,000

This gives the following sequence...

1,200,000 1,275,000 . . . 1,500,000

This follows an arithmetic progression with an increment of 75,000.

<em>Remember that,</em>

The last term, L, of an arithmetic progression is given by;

L = a + (n - 1)d ---------------(i)

<em>Where;</em>

a = first term of the sequence

n = number of terms in the sequence (which is the number of years)

d = the common difference or increment of the sequence

<em>From the given sequence,</em>

a = 1,200,000 [which is the first salary]

d = 75,000 [which is the increment in salary]

L = 1,500,000 [which is the maximum salary]

<em>Substitute these values into equation (i) as follows;</em>

1,500,000 = 1,200,00 + (n - 1) 75,000

1,500,000 - 1,200,000 = 75,000(n-1)

300,000 = 75,000(n - 1)

$\frac{300,000}{75,000} = n - 1$

4 = n - 1

n = 5

Therefore, in the 5th year the maximum salary will be reached.

3 0

2 years ago