What is the median of the data represented in the dot plot below?

Old faithful in Yellowstone National Park shoots water 60 feet into the air that casts a shadow of 42 feet. What is the height o

Serhud [2]

Answer:

The height of near by tree will be 90 feet.

Step-by-step explanation:

Considering the water triangle as shown in figure a.

As the old faithful shoots water 60 feet into the air that casts a shadow of 42 feet.

Considering the tree triangle as shown in figure a. The tree triangle has a shadow 63 feet long.

Let x be the height of near by tree that cost a shadow 63 feet long.

Assuming that the triangles are similar

So,

the ratios of similar triangles will be related as:

$\frac{63}{42}=\frac{x}{60}$

$\mathrm{Switch\:sides}$

$\frac{x}{60}=\frac{63}{42}$

${x}=60.\frac{63}{42}$

$x=90$ feet

Therefore, the height of near by tree will be 90 feet.

Keywords: ratio, similar triangle

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7 0

2 years ago

What was a consequence of Julius Caesar's assassination?

Andrews [41]

Answer: it’s b incomplete public improvement projects

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers t

gregori [183]

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial probability distribution because:

In the question it is given that the sprinklers activate correctly or not independently.
The number of outcomes are two i.e. sprinklers activate correctly or not.

A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = $C_{n,x}*p^{x} * (1 - p)^{n-x}$

b = binomial probability also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

$C_{n,x}$ is calculated as:

$C_{n,x}$ = n! / x!(n – x)!

= 10! / 10!(10-10)!

= 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = $C_{n,x}*p^{x} * (1 - p)^{n-x}$

= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

= 1 * 0.0282 * (0.3) ⁰

= 1 * 0.0282 * 1

P(X=x) = 0.0282

5 0

2 years ago

Factorise : 16x^2 +72xy + 81y^2 -12x +27y

never [62]

Hello!!

It will be the same since there is no common factor. You just need to arrange in order.

6x^2 + 72xy - 12x + 81y^2 + 27y

Good luck :)

5 0

2 years ago

According to a Pew Research survey, about 27% of American adults are pessimistic about the future of marriage and the family. Th

IgorLugansk [536]

Answer:

P(X≤5)=0.5357

Step-by-step explanation:

Using the binomial model, the probability that x adults from the sample, are pessimistic about the future is calculated as:

$P(x)=\frac{n!}{x!(n-x)!} *p^{x}*(1-p)^{n-x}$

Where n is the size of the sample and p is the probability that an adult is pessimistic about the future of marriage and family. So, replacing n by 20 and p by 0.27, we get:

$P(x)=\frac{20!}{x!(20-x)!}*0.27^{x}*(1-0.27)^{20-x}$

Now, 25% of 20 people is equal to 5 people, so the probability that, in a sample of 20 American adults, 25% or fewer of the people are pessimistic about the future of marriage and family is equal to calculated the probability that in the sample of 20 adults, 5 people of fewer are pessimistic about the future of marriage and family.

Then, that probability is calculated as:

P(X≤5)= P(1) + P(2) + P(3) + P(4) + P(5)

Where:

$P(0)=\frac{20!}{0!(20-0)!}*0.27^{0}*(1-0.27)^{20-0}=0.0018$

$P(1)=\frac{20!}{1!(20-1)!}*0.27^{1}*(1-0.27)^{20-1}=0.0137$

$P(2)=\frac{20!}{2!(20-2)!}*0.27^{2}*(1-0.27)^{20-2}=0.0480\\P(3)=\frac{20!}{3!(20-3)!}*0.27^{3}*(1-0.27)^{20-3}=0.1065\\P(4)=\frac{20!}{4!(20-4)!}*0.27^{4}*(1-0.27)^{20-4}=0.1675\\P(5)=\frac{20!}{5!(20-5)!}*0.27^{5}*(1-0.27)^{20-5}=0.1982$

Finally, P(X≤5) is equal to:

P(X≤5) = 0.0018+0.0137 + 0.0480 + 0.1065 + 0.1675 + 0.1982

P(X≤5) = 0.5357

3 0

2 years ago