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2 years ago

3. Jalen is a lifeguard at a public swimming pool and is planning to string

Mathematics

1 answer:

m_a_m_a [10]2 years ago

7 0

Answer:

$Flag = 55.90m$

Step-by-step explanation:

Given

$Length = 50m$

$Width = 25m$

Required

Determine the length of the flag

Because the flag crosses through opposite diagonals of the pool. Its length is the length of the diagonal of the pool.

This is calculated using Pythagoras theorem.

$Flag^2 = Length^2 + Width^2$

Substitute values for Length and Width

$Flag^2 = 50^2 + 25^2$

$Flag^2 = 2500 + 625$

$Flag^2 = 3125$

Take positive square root of both sides

$Flag = \sqrt{3125$

$Flag = 55.90m$

<em>Hence, the length of the flag is approximately 55.90m</em>

You might be interested in

SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as

vovangra [49]

Answer:

a) $P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

$P(Z>1.25)=1-P(Z$

b) $P(400$

$P(-1$

c) $z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

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 SAT scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(500,100)$

Where $\mu=500$ and $\sigma=100$

We are interested on this probability

$P(X>625)$

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:

$P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.25)=1-P(Z$

Part b

We are interested on this probability

$P(400$

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:

$P(400$

And we can find this probability with this difference:

$P(-1$

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

$P(-1$

Part c

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

$P(X>a)=0.8$ (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 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

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:

$z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

8 0

3 years ago

Find the range of values of x for which 2x2 – 5x + 2 > 0

Alchen [17]

Answer:

x < 1/2 and x>2

Step-by-step explanation:

first solve the eqn,

2x2 -5x +2 = 2x2 -4x -x +2 = 2x(x-2) - 1(x-2) = (2x-1)(x-2)

since the questions asks for >,

x < 1/2 and x>2

if the question had asked for <,

1/2<x<2

7 0

3 years ago

Im so lost what the answer is

Rainbow [258]

Answer:

Unfortunately, we can't do anything with 41 as it has no factors. Since $3\sqrt{41}$ is already simplified, try submitting that as your answer. If that doesn't work then try un-doing their steps and get rid of the 3: