Find the measure of the arc

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and th

Marizza181 [45]

Answer:

$\mu = 8.8\\\sigma = 1.9$

Now we are supposed to find probabilities that the response time is between 5 and 10 minutes i.e P(5<x<10)

Formula : $z= \frac{x-\mu}{\sigma}$

at x = 5

$z= \frac{5-8.8}{1.9}$

$z=-2$

at x = 10

$z= \frac{10-8.8}{1.9}$

$z=0.6315$

P(-2<z<0.6315)=P(z<0.6315)-P(z<-2)

Refer the z table

P(-2<z<10)=0.7357-0.0228=0.7129

So, the probability that response time is between 5 and 10 minutes is 0.7129

b)the response time is less than 5 minutes

at x = 5

$z= \frac{5-8.8}{1.9}$

$z=-2$

P(x<5)=P(z<-2)=0.0228

So, the probability that the response time is less than 5 minutes is 0.0228

c)the response time is more than 10 minutes

at x = 10

$z= \frac{10-8.8}{1.9}$

$z=0.6315$

P(x>10) = 1-P(x<10) = 1-P(z<0.63) = 1-0.7357 = 0.2643

So, The probability that the response time is more than 10 minutes is 0.2643

4 0

2 years ago

Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle

Nina [5.8K]

The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as $x$ .
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
$cos(59)= \frac{19}{h}$
$h= \frac{19}{cos(59)}$
$h=36.9$
Now we can use the law of sines to find the distance $x$ between Paul and Jose:
$\frac{sin(43)}{36.9} = \frac{sin(16)}{x}$
$x= \frac{36.9sin(16)}{sin(43)}$
$x=14.9$

Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
$19m+14.9=33.9m$

We can conclude that Jose is 33.9m from the base of the tree.

3 0

3 years ago

Solve for the variable c in this equation a(c + b) = d

noname [10]

Multiply everything in the parenthesis by a.

ac + ab = d

Subtract ab from both sides.

ac = d - ab

Divide a on both sides.

c = d - ab / a

Hope this helps!

3 0

3 years ago

For each function, do the following: a) state the name of the function, b) identify the independent and dependent variable, c) i

Lostsunrise [7]

Answer:

Given the function in the question

f(x) = |x-3| + 2

a) state the name of the function

Absolute value function

since it is similar to f(x) = |x|

b) identify the independent and dependent variable

x = independent variable (input variable)

f(x) or y = dependent variable (output variable)

The variable which we assign the value we call the independent variable, and the other variable is the dependent variable, since it value depends on the independent variable.

c) identify the rule

A function is an equation that has only one answer for y for every x.

d) evaluate the function

given x = -5

f(-5) = |-5 - 3| + 2

= |-8| + 2

= 8 +2

= 10

8 0

2 years ago

I need help with these two problems

erastova [34]

Number 5 is 15.9 kilograms

And number 6 is 6 million cubic feet per minute

You just cross multiply

5 0

2 years ago