Identify the slope of the equation. Write your answer as an

Sven shoots a cannon ball out of a cannon and the path of the ball is modeled in the graph. After 8 seconds how high is the cann

DedPeter [7]

Answer:

20 feet

Step-by-step explanation:

7 0

3 years ago

According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated e

slamgirl [31]

Answer:

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that $p = 0.09$

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

So

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$

So

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{12,0}.(0.09)^{0}.(0.91)^{12} = 0.3225$

$P(X = 1) = C_{12,1}.(0.09)^{1}.(0.91)^{11} = 0.3827$

$P(X = 2) = C_{12,2}.(0.09)^{2}.(0.91)^{10} = 0.2082$

$P(X = 3) = C_{12,3}.(0.09)^{3}.(0.91)^{9} = 0.0686$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3225 + 0.3827 + 0.2082 + 0.0686 = 0.982$

Finally

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.982 = 0.0180$

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

6 0

3 years ago

In centimeters, what is the unknown length in this right triangle

Ilya [14]

Answer:

11

Explanation:

(next time, it would be helpful to include a picture)

If you were on the same test as I was, than that means that the triangle you're looking for is the one below.

Using the Pythagorean Theorem,

a² + b² = c² is the same as c² - b² = a²

c = 61

61^2 = 61 X 61 = 3,721

b = 60

60^2 = 60 X 60 = 3,600

Next, we subtract:

3,721 - 3,600 = 121

√121 = 11

(x = 11 cm)

so 11 is your answer

3 0

3 years ago

Read 2 more answers

Find - 4 - 2 1/2 expression on the number line by drawing an arrow

Tema [17]

Answer:

Step-by-step explanation:

4 0

3 years ago

Emma is standing 10 feet away from the base of a tree and tries to measure the angle of elevation to the top. She is unable to g

Vaselesa [24]

The complete question in the attached figure

step 1
find the tree height for an angle of elevation of 55°
tan 55°=opposite side angle 55°/adjacent side angle 55°
opposite side angle 55°=the tree height h1
adjacent side angle 55°=10 ft
so
tan 55°=h/10-------> h=10*tan 55°-----> h=14.28 ft

step 2
find the tree height for an angle of elevation of 75°
tan 75°=opposite side angle 75°/adjacent side angle 75°
opposite side angle 75°=the tree height h2
adjacent side angle 75°=10 ft
so
tan 75°=h2/10-------> h2=10*tan 75°-----> h2=37.32 ft

therefore

the height of the tree is within the range [14.26,37.32]

Part 1) 4.2 ft

the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable

Part 2) 14.7 ft

the value is in the interval [14.26,37.32]
therefore
it is Reasonable

Part 3) 24.4 ft

the value is in the interval [14.26,37.32]
therefore
it is Reasonable

Part 4) 33.9 ft

the value is in the interval [14.26,37.32]
therefore
it is Reasonable

Part 5) 39.1ft

the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable

Part 6) 58.7 ft

the value is not in the interval [14.26,37.32]
therefore
it is Not Reasonable

4 0

3 years ago