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3 years ago

18. You run along a path at a constant speed of 5.5 miles per hour. How far do you travel in 1.5 hours? in 3.8 hours?

Mathematics

2 answers:

emmainna [20.7K]3 years ago

8 0

distance = 5.5 mph x 1.5 hrs = 8.25 miles

distance = rate x time

ANSWER 2: You travel 20.9 miles in 3.8 hours.

Anettt [7]3 years ago

5 0

Answer:

the travel of only 1.5 hours:8.25

The travel in 3.8 hours:20.9

Step-by-step explanation:

1.5(5.5)

1.5(3.8)

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Use the Pythagorean theorem to find the unknown side of the right triangle.

Nesterboy [21]

The length of hypotenuse is 39.

Step-by-step explanation:

Given,

Vertical side = a = 15

Horizontal side = b = 36

Hypotenuse = c

Using pythagorean theorem

$a^2+b^2=c^2\\(15)^2+(36)^2=c^2\\225+1296=c^2\\1521=c^2\\c^2=1521$

Taking square root on both sides

$\sqrt{c^2}=\sqrt{1521}\\c=39$

The length of hypotenuse is 39.

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3 years ago

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JulsSmile [24]

Answer: n = -4

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Add 3 to both sides

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-n = 4

Divide by -1 on both sides

n = -4

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3 years ago

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The original price of a computer was reduced by 120 dollars. The new,

wariber [46]

Answer:

x-120=899

Step-by-step explanation:

(x=1019)

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2 years ago

At one point the average price of regular unleaded gasoline was $3.41 per gallon. Assume that the standard deviation price per

Aleonysh [2.5K]

Answer:

a) $1-\frac{1}{k^2} =1- \frac{1}{2^2}= 1-0.25 = 0.75$

So we expected about 75% within two deviations from the mean

b) $1-\frac{1}{k^2} =1- \frac{1}{1.5^2}= 1-0.4444 = 0.556$

So we expected about 55.6% within 1.5 deviations from the mean

And the limits are:

$Lower = 3.41 -1.5*0.09 = 3.275$

$Upper = 3.41 +1.5*0.09 = 3.545$

c) We can calculate how many deviations we are within the mean with the limits with this formula:

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

And using the lower limit we got:

$z = \frac{3.05-3.41}{0.09}=-4$

And with the upper limit we got:

$z = \frac{3.77-3.41}{0.09}=4$

So then the value of k =4 and the percentage is given by:

$1-\frac{1}{k^2} =1- \frac{1}{4^2}= 1-0.0625 = 0.9375$

Step-by-step explanation:

Previous concepts and Data given

$\mu =3.41$ reprsent the population mean

$\sigma=0.09$ represent the population standard deviation

The Chebyshev's Theorem states that for any dataset

• We have at least 75% of all the data within two deviations from the mean.

• We have at least 88.9% of all the data within three deviations from the mean.

• We have at least 93.8% of all the data within four deviations from the mean.

Or in general words "For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least: $1-\frac{1}{k^2}$

Part a

For this case we can find the percentage required replaincg k =2 and we got:

$1-\frac{1}{k^2} =1- \frac{1}{2^2}= 1-0.25 = 0.75$

So we expected about 75% within two deviations from the mean

Part b

For this case we can find the percentage required replaincg k =2 and we got:

$1-\frac{1}{k^2} =1- \frac{1}{1.5^2}= 1-0.4444 = 0.556$

So we expected about 55.6% within 1.5 deviations from the mean

And the limits are:

$Lower = 3.41 -1.5*0.09 = 3.275$

$Upper = 3.41 +1.5*0.09 = 3.545$

Part c

We can calculate how many deviations we are within the mean with the limits with this formula:

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

And using the lower limit we got:

$z = \frac{3.05-3.41}{0.09}=-4$

And with the upper limit we got:

$z = \frac{3.77-3.41}{0.09}=4$

So then the value of k =4 and the percentage is given by:

$1-\frac{1}{k^2} =1- \frac{1}{4^2}= 1-0.0625 = 0.9375$

3 0

3 years ago

(20 POINTS) One side of a trapezoid is extended and the dotted line forms a right angle with the extended line.

RUDIKE [14]

Answer: p = 115* (degrees)

<h3>Explanation:</h3>

What we know:

The trapezoid forms a right triangle
The right triangle has the angles 25*, 90*, and an unknown
The internal angles of a triangle add up to 180*
The unknown value p is a supplementary angle to the right triangle's unknown angle

How to solve:

By finding the degree of the 3rd angle in the right triangle, we can use the rules of supplementary angles to find the value of p.

We will use D to represent the total amount of degrees, which will equal 180*. X will represent an unknown angle. An asterisk represents the degree symbol.

<h3>Process:</h3>

Missing right triangle angle

Set up equation D = 25 + 90 + x

Substitute 180 = 25 + 90 + x

Simplify 180 = 115 + x

Isolate variable -115 -115

Solution 65* = x

Value of p using supplementary angles

Set up equation D = x + p

Substitute 180 = 65 + p

Isolate variable -65 -65

Solution 115* = p

<h3>Answer: p = 115*</h3>

Check:

We can do a check based on estimation. Assuming that the trapezoid and triangle form a box with all 90* corners and that p = 115*, then adding p and all of the other trapezoid angles should result in 360*

Firstly, we need the values of these 4 angles.

The first angle, labeled p, should be 115*. If our equation is untrue, then this value will fail the check.

The second angle will be the one at the bottom-left, which is 90* according to our box statement.

The third angle is the one located at the bottom-right, which is also 90* from the box statement.

The fourth angle is not 90* or 115*, but we can solve its value.

Because we have stated that the right triangle and trapezoid form a box with 4 90* corners, the sum of the fourth angle and the 25* from the right triangle must form a right angle. Let's find the value:

D = 25 + x

90 = 25 + x

(90 = 25 + x) - 25

65* = x

Therefore, the fourth angle has 65*

Now, adding the degrees from all 4 angles should result in a total of 360*. If it does, then our value of p = 115* will pass the check.

D = 90 + 90 + p + x

360 = 90 +90 + 115 + 65

360 = 180 + 180

360 = 360

Therefore, p = 115*

6 0

2 years ago

Read 2 more answers