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3 years ago

(a): How many miles does the train travel per gallon? (b):What is the slope of the graph?

Mathematics

1 answer:

drek231 [11]3 years ago

5 0

since the graph has direct variation as data in x axis increases y also increases.

so we need to find how many miles travelled per galloon .

we distance travelled per gallon =total distance travelled/galoons of fuel used.

$Distance travelled per gallon=200 miles/400 gallons=0.5 litres travelled per gallon$

for part b) slope=rise/run

$m=(y2-y1)/(x2-x1)$

$y2=400 y1=0 x1=0 x2=200$

$m=(400-0)/(200-0)=2$

slope of the graph is 2

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PLEASE HELP ME on #57 WITH ALL WORK SHOWN!!<br><br> Tmr is my exam pls help...

-Dominant- [34]

<h3>Answer: x = 1/2</h3>

=========================================================

Explanation:

Recall that quadratic form is ax^2+bx+c.

So we need an x^2 term followed by an x term, then a constant at the end.

It may not look it, but the given equation is nearly in quadratic form.

Rewrite 9^(2x) as (9^x)^2

We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0

From here, let's make w = 9^x. Replace every copy of '9^x' with 'w' and we end up with this new simpler equation: w^2 - 2w - 3 = 0

From here we can use the quadratic formula or factor. I'll factor.

w^2 - 2w - 3 = 0

(w - 3)(w + 1) = 0

w-3 = 0 or w+1 = 0

w = 3 or w = -1

---------------------

Now we use these values of w to find x

If w = 3, then,

w = 9^x

3 = 9^x

log(3) = log(9^x)

log(3) = x*log(9)

x = log(3)/log(9)

x = log(3)/log(3^2)

x = log(3)/(2*log(3))

x = 1/2

At the last step, we have the log(3) terms cancel.

Repeat for w = -1

w = 9^x

-1 = 9^x

log(-1) = log(9^x)

We run into a problem. The log of any negative number is not a real number output. In other words, 9^x is never negative. Raising any positive number to a real number output leads the result to be positive. Take a look at the graph of y = 9^x to confirm this.

In short, w = -1 is extraneous so it doesn't lead to any x value solution.

So only w = 3 is useful.

Ultimately, the only solution is x = 1/2.

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3 years ago

Determine the amount of potential energy of a 5.0 N book that is moved to three different shelves on a bookcase. The height of e

Aleks [24]

Answer:

Ep = weight x height = 5 x 1 = 5N ; 5 x 1.5 = 7.5N; 5 x 2 = 10N

Step-by-step explanation:

Hope that helps

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3 years ago

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

Alja [10]

Answer:

a) Let X the random variable that represent the blood pressure for people of a population, and for this case we know the distribution for X is given by:

$X \sim N(128,23)$

Where $\mu=128$ and $\sigma=23$

b) $P(X\geq 135)=P(\frac{X-\mu}{\sigma}\geq \frac{135-\mu}{\sigma})=P(Z\geq \frac{135-128}{23})=P(Z\geq 0.304)$

And we can find this probability using the complement rule:

$P(Z\geq 0.304)=1-P(Z$

And in order to find this probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(Z\geq 0.304)=1-P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the blood pressure for people of a population, and for this case we know the distribution for X is given by:

$X \sim N(128,23)$

Where $\mu=128$ and $\sigma=23$

Part b

We are interested on this probability

$P(X\geq 135)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(X\geq 135)=P(\frac{X-\mu}{\sigma}\geq \frac{135-\mu}{\sigma})=P(Z\geq \frac{135-128}{23})=P(Z\geq 0.304)$

And we can find this probability using the complement rule:

$P(Z\geq 0.304)=1-P(Z$

And in order to find this probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(Z\geq 0.304)=1-P(Z$

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3 years ago

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Sonja [21]

Another easy way to remember the area of a square is s*s, or side times side.

if one side is 6 centimeters, then the other 3 are also 6 because it's a square.

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Step2247 [10]

Answer:

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Step-by-step explanation:

Consider the provided information.

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It is given that Smith always bets on the numbers 1 through 12.