ATCs are required to undergo periodic random drug testing.
A simple, low-cost urine test is used for initial screening. It has been reported that this particular test has a sensitivity and specificity of 0.96 and 0.93. This means that if there is drug use, the test will detect it 96% of the time. If there is no drug use, the test will be negative 93% of the time.
Based on historical results, the FAA reports that the probability of drug use at a given time is approximately 0.007 (this is called the prevalence of drug use).
Draw a probability tree for the situation. (Use this order for the tree: Drug Use(yes/no) -> Test Result(+/-) -> Joint Probabilites)
A positive test result puts the air traffic controller’s job in jeopardy. What is the probability of a positive test result?
Find the probability an air traffic control truly used drugs, given that the test is positive.

Given:

The numbers are [tex]-5,0,6,-3.5,-1\dfrac{2}{3}[/tex].

To find:

The number line one which each of the given number is plotted correctly.

Solution:

The given numbers are [tex]-5,0,6,-3.5,-1\dfrac{2}{3}[/tex].

To plot [tex]-5,0,6[/tex], we need to make dots at [tex]-5,0,6[/tex] respectively.

To plot [tex]-3.5[/tex], we need to make a dot in the mid of -4 and -3.

To plot [tex]-1\dfrac{2}{3}[/tex], we need to make a dot between -2 and -1. That point divides the segment between -2 and -1 in 1:2

In option A, -5 is not plotted correctly. So, option A is incorrect.

In option B, -3.5 is not plotted correctly and [tex]-1\dfrac{2}{3}[/tex] is not plotted. So, option B is incorrect.

In option C, all the points are plotted correctly. So, option C is correct.

In option D, [tex]-1\dfrac{2}{3}[/tex] is not plotted correclty. So, option D is incorrect.

Therefore, the correct option is C.

Answer:

7/9

Step-by-step explanation:

this equation is true:

21/27 = 7/9

If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.

7/9 = Proper Fraction

Answer:

i believe its D

Step-by-step explanation:

Answer: it’s true i just did the quiz

Step-by-step explanation:

Chord BC is a diameter of the circle as passes from the center O of the circle and its end points B,C lies on the circle so the statement is true.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

O is the center of the Circle

Chord BC is the line segment passing from the center of circle

Chord is a line segment whose end points lies on the circle.

Diameter is defined as a line segment passing from the center of the circle whose end point lies on the circle.

A chord that passes through the centre of a circle is called a diameter, and it is the longest chord.

Hence, chord BC is a diameter of the circle as passes from the center O of the circle and its end points B,C lies on the circle so the statement is true.

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Answer:

I think B but not so sure

Answer:

Step-by-step explanation:

radius of semi circle=8/2=4 in

height of triangle=14-4=10 in.

area of composite figure=1/2×8×10+π×4²=40+16 π≈90.3 sq. in

Answer:

a)

We know that:

a, b > 0

a < b

With this, we want to prove that a^2 < b^2

Well, we start with:

a < b

If we multiply both sides by a, we get:

a*a < b*a

a^2 < b*a

now let's go back to the initial inequality.

a < b

if we now multiply both sides by b, we get:

a*b < b*b

a*b < b^2

Then we have the two inequalities:

a^2 < b*a

a*b < b^2

a*b = b*a

Then we can rewrite this as:

a^2 < b*a < b^2

This means that:

a^2 < b^2

b) Now we know that a.b > 0, and a^2 < b^2

With this, we want to prove that a < b

So let's start with:

a^2 < b^2

only with this, we can know that a*b will be between these two numbers.

Then:

a^2 < a*b < b^2

Now just divide all the sides by a or b.

if we divide all of them by a, we get:

a^2/a < a*b/a < b^2/a

a < b < b^2/a

In the first part, we have a < b, this is what we wanted to get.

Another way can be:

a^2 < b^2

divide both sides by a^2

1 < b^2/a^2

Let's apply the square root in both sides:

√1 < √( b^2/a^2)

1 < b/a

Now we multiply both sides by a:

a < b

Answer:

4761

Step-by-step explanation:

69 times 69 since it is to the power of 2.

Answer:

4761

Step-by-step explanation:

[tex]69 *69=4761[/tex]

please give brainliest I need to feed my children

Answer:

the answer is 2 1/4 cups of oil

Step-by-step explanation:

if he wants to triple the ingredient then you would triple the numerator and than simplify your new fraction

3 times 3 is 9 = 9/4

9 divided by 4 is 2.25 = 0.25 is equal to 1/4 so it would be 2 1/4 cups of oil

Answer:

The car would need 12 gallons of gas to go 360 miles

Step-by-step explanation:

360÷30=12

Answer:

it would take 12 gallons of gas

Step-by-step explanation:

[tex]360 \div 30 = 12[/tex]

Answer:

32/9

Step-by-step explanation:

2 to the fifth power is 32. 3 to the second power is 9.

Answer:

84 possible paths

Step-by-step explanation:

Given

[tex]N =3[/tex] --- 3 blocks north

[tex]E = 6[/tex] --- 6 blocks east

Required

Number of distinct path

To solve this question, we make use of the following formula

[tex]^{m+n}C_n \ =\ ^{m+n}C_m[/tex]

The above formula implies that;

On a single path, there is a total of m + n steps to get to a particular position, where each path is either in m direction or n direction.

In this case:

[tex]m = 3[/tex]

[tex]n = 6[/tex]

So, we have:

[tex]^{m + n}C_n = ^{3+6}C_6[/tex]

[tex]^{m + n}C_n = ^9C_6[/tex]

Apply combination formula

[tex]^{m + n}C_n = \frac{9!}{(9-6)!6!}[/tex]

[tex]^{m + n}C_n = \frac{9!}{3!*6!}[/tex]

Expand the numerator

[tex]^{m + n}C_n = \frac{9*8*7*6!}{3!*6!}[/tex]

[tex]^{m + n}C_n = \frac{9*8*7}{3!}[/tex]

Expand the denominator

[tex]^{m + n}C_n = \frac{9*8*7}{3*2*1}[/tex]

[tex]^{m + n}C_n = \frac{504}{6}[/tex]

[tex]^{m + n}C_n = 84[/tex]

Hence, there are 84 possible paths

[tex]^{m + n}C_m[/tex] will also give the same result

Answer:

       7 / 28

Step-by-step explanation:

7 / 28 = 0 . 28

Answer:

Juan invested $ 11,800 in Fund A and $ 7,200 in Fund B.

Step-by-step explanation:

Given that Juan invested $ 19000 in two mutual funds, and Fund A earned 7% profit during the first year, while Fund B earned 3% interest, if he received a total of $ 1042 profit, to determine how much she had invested in each mutual fund the following calculation must be performed:

19000 x 0.07 + 0 x 0.03 = 1330

15000 x 0.07 + 4000 x 0.03 = 1170

11000 x 0.07 + 8000 x 0.03 = 1010

11500 x 0.07 + 7500 x 0.03 = 1030

11800 x 0.07 + 7200 x 0.03 = 1042

Therefore, Juan invested $ 11,800 in Fund A and $ 7,200 in Fund B.

B

Step-by-step explanation:

Step-by-step explanation:

to find area

A = Pi x r^2

r = d/2 = 10/2 = 5

The mixed number equivalent to 38 divided by 7 is 5 3/7.

To find the mixed number equivalent to 38 divided by 7,

we need to divide 38 by 7 and express the result as a mixed number.

=38 ÷ 7

= 5 remainder 3

Or      7 | 38 | 5

              35

         ______

                3

So, the quotient is 5 and the remainder is 3.

So, the mixed number equivalent to 38 divided by 7 is 5 3/7.

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Answer:

C

Step-by-step explanation:

2:3 = x:60

3 → 60 (*20)

2*20=40

Answer:

40 green houses

Step-by-step explanation:

Because the ratio is given, you can use the criss-cross method.

2:3

?:60

All you do is multiply 60 by 2 then divide by 3

(60×2)/3=40

Answer:

a

Step-by-step explanation:

it is a because the shape is moving to the side

Answer:

The answer is B!

Answer:

175 ÷ 12.50 = 14

Step-by-step explanation:

Answer:

x=6 y=12

Step-by-step explanation:

30-60-90 triangle

shorter leg is x

longer leg is [tex]x\sqrt{3}[/tex]

hypotenuse is 2x

since the longer leg is [tex]6\sqrt{3}[/tex] than makes x=6

and y=2(6)=12

Answer:

1, 2.5 at the top and 50 at the bottom

Answer:

I think B is your answer if so then comment me and you can mark me as brainliest and please follow me

Answer:

This link should help

Step-by-step explanation:

http://www.uvm.edu/~eclark/Math017LectureNotes.pdf

Answer:

0.50

Step-by-step explanation:

Because decimals are correlated with fractions, and fractions are correlated with percentage.

Essentially, everything is out of a hundred. For example, 100% is max capacity(aka the votes in this question).

In decimals, 0.50 is half of 1.00 which is essentially also max capacity. Following this logic, if you convert 50% into decimal form, it will be 0.50, and 0.50 is one half of 1.00. The other half must be 0.50 then, because if you subtract it, that's what you get, and you can check by adding it together.

Hope this helps.

Answer:

Symmetry in a regular nonagon

A regular nonagon has 9 lines of symmetry and a rotational symmetry of order 9, meaning that it can be rotated in such a way that it will look the same as the original shape 9 times in 360°. Nine 40° of rotation about the center.

Step-by-step explanation:

Answer:

15 feet

Step-by-step explanation:

Forumula: Multiply the length value by 3.

5*3= 15 feet

Hope this  helped! :)

Answer:

15 feet

Step-by-step explanation:

okay so in 1 yard is 3 feet

is it is 5 yards so there is 15 feet

Answer:

8 of them would probably fit on there