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3 years ago

A square rug has an area of 225ft. How long is each side of the rug?

Mathematics

1 answer:

klio [65]3 years ago

8 0

The area formula is b x h, but since its a square the area would be side squared.

here side squared = 225 ft

Square root of 225 is 15, so each side of the rug measures 15 feet

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At a competition with 6 runners, 2 medals are awarded for first and second

insens350 [35]

Answer:

30 ways

Step-by-step explanation:

The first medal can be awarded in 6 different ways since any of the runners could have it. Once the first medal is awarded, the second medal can only be given to any of the 5 runners available.

So there are 6x5=30 different ways to award the medals

3 0

3 years ago

Write a quadratic relation in the form y = ax2 + bx + c with roots 4 and - 3 and

pochemuha

Answer:

y = 2*x^2 - 2*x - 24

Step-by-step explanation:

If we have a quadratic function with roots a and b, we can write the equation for that function as:

y = f(x) = A*(x - a)*(x - b)

Where A is the leading coefficient.

In this case, we know that the roots are: 4 and -3

Then the function will be something like:

f(x) = A*(x - 4)*(x - (-3) )

f(x) = A*(x - 4)*(x + 3)

Now we need to determine the value of A.

We also know that the graph of the function passes through the point (3, -12)

This means that:

f(3) = -12

Then:

-12 = A*(3 - 4)*(3 + 3)

-12 = A*(-1)*(6)

-12 = A*(-6)

-12/-6 = A

2 = A

Then the equation is:

y = f(x) = 2*(x - 4)*(x + 3)

Now we need to write this in standard form, so we just need to expand the equation:

y = f(x) = 2*(x^2 + x*3 - x*4 - 4*3)

y = f(x) = 2*(x^2 - x - 12)

y = f(x) = 2*x^2 - 2*x - 24

Then the relation is:

y = 2*x^2 - 2*x - 24

4 0

2 years ago

A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w

sergejj [24]

Answer:

a) $a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

b) $P(X \geq 3) = 1-P(X$

c) $P(\bar X \geq 225)=1- P(\bar X$

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".

2) Part a

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

$X \sim N(225,16.5)$

Where $\mu=225$ and $\sigma=16.5$

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

$P(X>a)=0.25$ (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 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

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:

$z=0.674=\frac{a-225}{16.5}$

And if we solve for a we got

$a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

$X\sim Bin(n=10, p=0.25)$