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3 years ago

A motorcycle can travel 292.5 miles on 4.5 gallons of gasoline. What is the number of miles per gallon?

Mathematics

1 answer:

Gelneren [198K]3 years ago

6 0

Answer:

65 miles per gallon

Step-by-step explanation:

To determine the number of miles per gallon, take the total number of miles driven and divide by the number of gallons used

292.5 miles/4.5 gallons

65 miles per gallon

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Find the area of the figure.

yanalaym [24]

Answer:

132 cm squared

Step-by-step explanation:

To find the area, find the area of each shape inside it and add together.

Small rectangle - Area of 4*7 = 28

Two triangles - Area of 6*8 = 48

Large rectangle - Area of 8*7 = 56

All together the area is 28 + 48 + 56 = 132

7 0

3 years ago

There are 20 black, 15 white, 12 green, 12 red, 9 blue and 2 yellow candies in a box. How many candies should you take (without

kow [346]

<h3>Answer: 13</h3>

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

Explanation:

The best case scenario is that you get 3 of the same color in a row on the first three attempts. The lower bound is 3.

However, we have to consider the worst case scenario when we want to guarantee something like this, without looking at the candies we selected.

Consider the case of something like this sequence:

black
white
green
red
blue
yellow
black
white
green
red
blue
yellow
black

As you can see above, I've listed the colors in the order presented by your teacher. I pick one candy at a time. Once I reach yellow, I restart the cycle. In slots 1, 7 and 13, we have a black candy selected. This example shows that we must make 13 selections to guarantee that we get at least 3 candies of the same color (that color being black). The order of the candies selected doesn't matter. We could easily use any other color except yellow to do this example. The black candy just happened to be the first listed, so I went with that.

Note how we have 6 unique colors in the set {black, white, green, red, blue, yellow}. If we pick 2 candies of each color, then we've selected 6*2 = 12 candies so far. That 13th candy (some color other than yellow) is guaranteed to be a color we already selected; therefore, we'll be guaranteed to have 3 of the same color. We won't know what color it is but we will know we have a match like this.

For more information, check out the Pigeonhole Principle.

4 0

2 years ago

Suppose you need to deliver 40 terabytes of data to your co-workers in Atlanta (200 km). You have an available 100 Mbps dedicate

Marat540 [252]

Answer: All data will be sent in 89.39 hours

Step-by-step explanation:

Data transfer rate: 100 Mbps=100 $\frac{Mb}{s}$ × $\frac{1Tb}{1024^{2} Mb}$ × $\frac{3600s}{h}$ =0.3433 $\frac{Tb}{h}$

The pigeon can fly 1000 km/day and it needs to fly 400 km (round trip).

Pigeon rate: $\frac{1000km}{24h}$ =41.67 $\frac{km}{h}$

Time of round trip: 400 km÷ $\frac{1000km}{24h}$ =9.6 h

So the pigeon can send 1 Tb every 9.6 hours.

If we sum the rates we can get the time for sending all the data:

40 Tb= (0.3433 Tb/h + 1 Tb/9.6h)×t

T= 89.39 hours

8 0

3 years ago

Can y’all help me please

muminat

Answer:

1. 4m(note this might be switched with 2)

2. 5m(note this might be switched with 1)

3.3m

4. 60

5.60

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

normally distributed with mean 24.6 seconds and standard deviation 0.64 seconds;the lower finishing time, the better. If the qua

marshall27 [118]

Answer:

$z=1.04$

And if we solve for a we got

$a=24.6 +1.04*0.64=25.27$

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.

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".

Solution to the problem

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

$X \sim N(24.6,0.64)$

Where $\mu=24.6$ and $\sigma=0.64$

Solution to the problem

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.15$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.04$

And if we solve for a we got

$a=24.6 +1.04*0.64=25.27$

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.

3 0

2 years ago

A motorcycle can travel 292.5 miles on 4.5 gallons of gasoline. What is the number of miles per gallon?​

A motorcycle can travel 292.5 miles on 4.5 gallons of gasoline. What is the number of miles per gallon?