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2 years ago

15

Un automóvil recorre 1000 Km y consume 95 L de gasolina. Si la gasolina tiene un precio de $18.75 por cada litro ¿cuánto cuesta

recorrer cada Km, en $/Km? (redondear a tres decimales)

1 answer:

Shkiper50 [21]2 years ago

6 0

Answer:

$1781.25

1 x 95= 95

18.75 x 95= 1781.25

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Carl scored 32 on the ACT mathematics Test and 730 on the mathematics portion of the SAT. If the ACT Math Test had a mean score

Shtirlitz [24]

Answer:

Carl's ACT grade had a higher z-score, which means that he earned a better score with respect to his peers on the ACT test.

Step-by-step explanation:

Z-score

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.

On which exam did Carl earn a better score with respect to his peers?

On whichever exam he had the higher z-score.

SAT

Scored 730, mean 516, standard deviation 116. So

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

$Z = \frac{730 - 516}{116}$

$Z = 1.84$

ACT

Scored 32, mean 21, standard deviation 5.3. So

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

$Z = \frac{32 - 21}{5.3}$

$Z = 2.08$

Carl's ACT grade had a higher z-score, which means that he earned a better score with respect to his peers on the ACT test.

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2 years ago

Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average

enot [183]

Then, 15 - x is the distance ran in the second part.
The time, t1, for the first part is t1 = xmi / 8mi/h
The time, t2, for the second part is t2 = (15 - x)mi / 20mi/h
The total time is t1 + t2 = 1.125 h
Then x/8 + (15 - x) / 20 = 1.125
To solve for x, multiply both sides by 40 (this is the least common multiple)
5x + 30 - 2x = 45
3x = 15

to find x divide: 15/3=5

And 15 - x = 10 mi.
First part:
Speed: 8mi/h
Distance: 5 mi
Time: 5mi/8mi/h = 5/8 h = 37.5 minutes
Second part
Speed: 20 mi/h
Distance: 10 mi
Average speed: 15mi/1.125h =13.33 mi/h
Distance: 15mi
Time: 1.125 h = 67.5 minutes

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2 years ago

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Determine the distance between point (x1, y1) and point (x2, y2), and assign the result to pointsdistance. the calculation is: d

taurus [48]

For this case what you should know is that the distance between two points can be thought of as a line. To find the length of this line, you can use the formula:
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Example,
for points (1.0, 2.0) and (1.0, 5.0):
d: √ [(1 - 1) ^ 2 + (5 - 2) ^ 2]
d: 3.0
Answer:
the distance between point (x1, y1) and point (x2, y2) is:
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2 years ago

Josh can split a truckload of logs in 8 hours, but working with his dad, they can get it done in 3 hours. How long would it take

grin007 [14]

Answer: 4.8 hrs

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

Josh: $\frac{1}{8}$

Dad: $\frac{1}{x}$

Together: $\frac{1}{3}$

Josh + Dad = Together

$\frac{1}{8}$ + $\frac{1}{x}$ = $\frac{1}{3}$

$\frac{1}{8}*(24x)$ + $\frac{1}{x}*(24x)$ = $\frac{1}{3}$ (24x)

3x + 24 = 8x

<u> -3x </u> <u> -3x </u>

24 = 5x

<u> ÷5 </u> <u>÷5 </u>

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2 years ago

For the angles α and β in the figures, find cos(α + β)?

Blababa [14]

Answer:

$\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})$

Step-by-step explanation:

Let the hypotenuse of the smaller triangle be h units.

Then; from the Pythagoras Theorem.

$h^2=4^2+2^2$

$h^2=16+4$

$h^2=20$

$h=\sqrt{20}$

$h=2\sqrt{5}$

From the smaller triangle;

$\cos (\alpha)=\frac{4}{2\sqrt{5} }=\frac{2}{\sqrt{5} }$ and $\sin(\alpha)=\frac{2}{2\sqrt{5} }=\frac{1}{\sqrt{5} }$

From the second triangle, let the other other shorter leg of the second triangle be s units.

Then;

$s^2+4^2=6^2$

$s^2+16=36$

$s^2=36-16$

$s^2=20$

$s=\sqrt{20}$

$s=2\sqrt{5}$

$\cos(\beta)=\frac{2\sqrt{5} }{6}=\frac{\sqrt{5} }{3}$

and

$\sin(\beta)=\frac{4}{6}=\frac{2}{3}$

We now use the double angle property;

$\cos(\alpha +\beta)=\cos(\alpha)\cos(\beta) -\sin(\alpha)\sin(\beta)$

we plug in the values to obtain;

$\cos(\alpha +\beta)=\frac{2}{\sqrt{5} }\times \frac{\sqrt{5} }{3}-\frac{1}{\sqrt{5} }\times \frac{2}{3}$

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2 years ago

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