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2 years ago

This line plot shows something about trails in a state park. What is true about the data in this line plot?

Mathematics

2 answers:

Zepler [3.9K]2 years ago

4 0

Answer:

The total length of the Dogwood Trail is 24 kilometers

The difference between the lengths of the trails is 6 kilometers

Step-by-step explanation:

The complete and correct question is

The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.

Which of the following statements are true about the lengths of the trails? Check all that apply.

1.The total length of the Dogwood Trail is 16 kilometers.

2.The total length of the Dogwood Trail is 24 kilometers.

3.The Elm Trail is longer than the Dogwood Trail.

4.The difference between the lengths of the trails is 2 kilometers.

5.The difference between the lengths of the trails is 6 kilometers.

The picture in the attached figure

step 1

Find the value of a

Applying the Pythagorean Theorem in the right triangle ABC

$13^2=a^2+5^2\\a^2=169-25\\a^2=144\\a=12\ km$

step 2

Find the value of b

Applying the Pythagorean Theorem in the right triangle CDE

$5^2=b^2+3^2\\b^2=25-9\\b^2=16\\b=4\ km$

step 3

Find the total length of the Dogwood Trail (solid blue line)

The total length is equal to

$AD=AB+BC+CE+ED$ ---> by segment addition postulate

substitute the given values

$AD=a+5+b+3=(a+b+8)\ km$

substitute the value of a and b

$AD=(12+4+8)=24\ km$

step 4

Find the total length of the Elm Trail (dashed red line)

The total length is equal to

$AD=AC+CD$ ---> by segment addition postulate

substitute the given values

$AD=13+5=18\ km$

Verify the following statements

Part 1) The total length of the Dogwood Trail is 16 kilometers

The statement is false

Because

The total length of the Dogwood Trail is 24 kilometers (see the explanation)

Part 2) The total length of the Dogwood Trail is 24 kilometers

The statement is true (see the explanation)

Part 3) The Elm Trail is longer than the Dogwood Trail

The statement is false

Because

The Elm Trail is smaller than the Dogwood Trail

$18\ km < 24\ km$

Part 4) The difference between the lengths of the trails is 2 kilometers

The statement is false

Because

The difference is equal to

$24-18=6\ km$

Part 5) The difference between the lengths of the trails is 6 kilometers

The statement is true

Because

The difference is equal to

$24-18=6\ km$

kenny6666 [7]2 years ago

4 0

Answer:

2 thirds of the trails are longer than 5 Km

Step-by-step explanation:

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2 years ago

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The rodriquez Family is taking a 1,311 mile train ride. If the train travels 57 miles per hour, how many hours will the ride las

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Answer:

57x = 1311

x = 23 hours

Step-by-step explanation:

I don't know how you would model this with two equations but the answer is 23 hours.

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2 years ago

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A function of the form f(x) = abx is modified so that the b value remains the same but the a value is increased by 2. How do the

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Answer:

The range stays the same.

The domain stays the same.

Step-by-step explanation:

The function $f(x)=ab^{x}$ is an exponential function, where a is the coefficient, b is the base and x is the exponent.

The domain for this kind of functions is: All real numbers.

And the range is: (0,∞); this happen because the exponential functions are always positive when a>0.

Therefore, if the value of a is increased by 2, the domains will stay the same and the range will stay the same: (0,∞). The coefficient does not change the domain or the range if it keeps the same sign.

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2 years ago

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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:

"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" is about 0.8749.

Step-by-step explanation:

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

The normal distribution is determined by two parameters: the population mean, $\\ \mu$ , and the population standard deviation, $\\ \sigma$ . 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 cumulative standard normal distribution to find the probability.
Find the z-score for the raw score given in the question, that is, x = 6 hours per day.
With the z-score at hand, we can find this probability using a table with the values for the cumulative standard normal distribution. This table is called the standard normal table, 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 standard normal distribution because we can "transform" any raw score into standardized values, which represent distances from the population mean in standard deviations units, where a positive value indicates that the value is above the mean and a negative value that the value is below it. A standard normal distribution has $\\ \mu = 0$ and $\\ \sigma = 1$ .

The formula for the z-scores is as follows

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

Solving the question

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

x = 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 z 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 z, we can consult the cumulative standard normal table, 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, "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" 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.

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Ashley recently opened a store that sells only natural ingredients. She wants to advertise her products by distributing bags of

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With 6 people preparing bags, they would be able to prepare 6 bags every 2 minutes.

900/6 * 2 = the total minutes

Divide that answer by 60 to get the numbe of hours.

The answer is 5 hours.

Hope that helps.- UF aka Nadia

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2 years ago

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