6. The police department of a major city has found that the average height of
their 1,250 officers is 71 inches, with a standard deviation of 2.3 inches. Using
the normal curve table, answer the following:
a. How many officers are at least 75 inches tall?
b. How many officers are between 65 and 72 inches tall?
c. If an officer is at the 35th percentile in terms of height, how tall is she or he?
d. Assuming an equal amount of service, the top 10% of the police officers in
terms of height also make higher salaries than their less favored fellow of-
ficers. How tall does an officer have to be to get a better salary?
e. What is the probability of encountering an officer who is 66 inches tall or
less?
f. What heights are so deviant that their probability of occurrence is .05 or
less?

Answer:

Step-by-step explanation:

A=(1,2,3)

B=(0,1,2)

A×B=(1,2,3)×(0,1,2)

A×B=((0,1),(1,1),(1,2),(0,2),(1,2),(2,2),(0,3),(1,3),(2,3))

Answer:

since 4y=12 and 4y=2x then 4y=12=2x or 12=2x

Answer:

D i think sorry if wrong

Step-by-step explanation:

A parallelogram is a figure which has its opposite sides to be equal and parallel. The missing reason in the proof is:

B. Substitution Angle Angle Postulate.

A parallelogram is a type of quadrilateral that has its opposite sides to be equal and parallel. The sum of its internal angles is [tex]360^{o}[/tex].

To prove that ∠ BAD ≅ ∠ DCB, we have:

Given parallelogram ABCD;

<BAC ≅ <ACD (alternate angle theorem)

<DAC ≅ <ACB (alternate angle theorem)

<BAC + <DAC = <BAD

Also,

<BCA + <DCA = <BCD

Therefore,

<BAD ≅ <DCB (Substitution Angle Angle Postulate)

Thus, the missing reason in the partial proof is:

option B. Substitution Angle Angle Postulate

A sketch is attached to this question for more clarifications.

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Answer:

3²

Step-by-step explanation:

3³x3³=3^6

3^6÷3^4=3²

Answer:

8

Step-by-step explanation:

100 = x^2 + AC^2

17^2 = AC^2 + (21 - x)^2

289 = AC^2 + 21^2 + x^2 - 2*21*x

289 = AC^2 + 441 + x^2 - 42x

from 1st equation AC^2 + x^2 = 100

289 = 441 + 100 - 42x

289 = 541 - 42x

42x = 541 - 289 = 252

x = 252/42 = 6

so AC^2 = 100 - 6^2 = 100 - 36 = 64

AC = 8

Answer:

Step-by-step explanation:

Answer:

c)  1 foot per 2 hours

Step-by-step explanation:

1/6 of a foot (which is 12 inches) is 2 inches

1/3 of an hour (which is 60 minutes) is 20 minutes

2 inches in 20 minutes is the same as 12 inches (which is 1 foot) in 120 minutes (which is 2 hours)

Step-by-step explanation:

the most usual firm of line equation is

y = ax + b

a is the slope of the line and is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-interception (the bake of y when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and solve for b.

the slope a :

x changes by +3 (from 3 to 6)

y changes by +8 (from -1 to 7)

so, the slope is +8/+3 = 8/3

our line equation now looks like

y = (8/3)x + b

let's simply use the first point

-1 = (8/3)×3 + b

-1 = 24/3 + b = 8 + b

-9 = b

and the full line equation is

y = (8/3)x - 9

The explicit rule for the sequence is Tn = 2n - 1

Given the sequence 1, 3, 5, 7, 9...

The explicit formula for the nth term is expressed as:

[tex]T_n=a+(n-1)d[/tex]

a is the first term = 1

d is the common difference = 3 - 1 = 5 - 3 = 2

n is the number of terms

Substitute the given parameters into the formula to have;

[tex]T_n = 1+(n-1)(2)\\T_n=1+2n-2\\T_n=2n-1[/tex]

Hence the explicit rule for the sequence is Tn = 2n - 1

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Answer:

1st: 1+(k-1)2

2nd: 399

3rd: C

4th: 40,000

Answer:

-24

Step-by-step explanation:

-7 +3 is -4

-4+-20 is -24

-7 + 3 - 20

= -4 - 20

= -4 + -20

= -24

______

Hope it helps ⚜

Answer:

26, 28

Step-by-step explanation:

2n , 2n + 2

2n + 2n + 2 = 54

4n + 2 = 54

4n = 52

n = 13

2n = 26

2n + 2 = 28

Answer:

Step-by-step explanation:

The sum of two consecutive even numbers is 54 find the answer

(54 - 2) : 2 = 26

26 + 2 = 28

----------------------

check

26 + 28 = 54

[tex]y +1 = 2x~~~...(i)\\\\y^2 = 3x -2~~~...(ii)\\\\\text{From equation (i):}\\\\y +1 = 2x \\\\\implies y = 2x -1~~~....(iii)\\\\\text{Substitute} ~y = 2x-1~ \text{in equation (ii):}\\\\(2x-1)^2 = 3x-2\\\\\implies 4x^2 - 4x +1 = 3x -2\\\\\implies 4x^2 -4x -3x +3 =0\\\\\implies 4x(x-1) -3(x-1)=0\\\\\implies (x-1)(4x-3)=0\\\\\implies x =1 ~\text{or}~ x = \dfrac 34\\\\\text{Substitute x = 1 in equation (iii):}\\\\y = 2 -1 =1\\\\[/tex]

[tex]\text{Substitute}~ x = \dfrac 34 ~\text{in equation (iii):}\\\\\\y = 2\left(\dfrac 34 \right) -1 = \dfrac 32 -1 = \dfrac 12\\\\\text{Hence,}\\\\(x,y) = (1,1)\\\\\text{And}\\\\(x,y) = \left(\dfrac 34 , \dfrac 12 \right)[/tex]

Answer:

336

Step-by-step explanation:

12×1×4×7=336

not sure just a try

Answer:

if you need to plot what percent they have left its 75%, i you have to plot how much decreased it would be 25%> Hope this helped!

Step-by-step explanation:

[tex]-4[/tex] is a part of the solution set to all of the inequalities

We will consider each inequality in turn:

For [tex]x>-5[/tex]:

The solution set is [tex]\{{-4,-3,-2,-1,...\}[/tex]

So [tex]-4[/tex] is a part of the solution set of [tex]x>-5[/tex]

For [tex]2>x[/tex], or [tex]x<2[/tex]:

The solution set is [tex]\{{1,0-1,-2,-3,-4,...\}[/tex]

So [tex]-4[/tex] is a part of the solution set of [tex]2>x[/tex]

For [tex]3x+4\ge -8[/tex]:

We have to solve first

[tex]3x+4\ge -8\\3x\ge -8-4\\3x\ge -12\\x\ge -4\\[/tex]

The solution set is [tex]\{{-4,-3,-2,-1,0,...\}[/tex]

So [tex]-4[/tex] is a part of the solution set of [tex]3x+4\ge -8[/tex]

For [tex]5x\le 2x-3[/tex]:

We have to solve first

[tex]5x\le 2x-3\\5x-2x\le-3\\3x\le-3\\x\le-1[/tex]

The solution set is [tex]\{{-1,-2,-3,-4,-5,...\}[/tex]

So [tex]-4[/tex] is a part of the solution set of [tex]5x\le 2x-3[/tex]

For [tex]-6<4-2x[/tex]:

We have to solve first

[tex]-6<4-2x\\2x<4+6\\2x<10\\x<5[/tex]

The solution set is [tex]\{{4,3,2,...,-3,-4,-5,...\}[/tex]

So [tex]-4[/tex] is a part of the solution set of [tex]-6<4-2x[/tex]

So, [tex]-4[/tex] is a part of the solution set of all the inequalities.

Learn more about inequalities here: https://brainly.com/question/278997

Answer:

C. $20,660

Step-by-step explanation:

Letter c is the answer

Answer:

A(-3,2)B(3,7) and C(4,-4)

Step-by-step explanation:

these are the new coordinate

Answer:

30

Step-by-step explanation:

The answer is said in the question. It said that 30 students of them have a birthday in the summer so it's 30

Answer:

I can even see anything can you reupload your answer, please?

Step-by-step explanation:

Answer:

2 days

Step-by-step explanation:

12 - 4 = 8

8/3 = 2.7

Answer:

3 5/6 = 3 10/12

2 1/3= 2 4/12

3-2=1

10/12-4/12= 6/12=1/2

so Kyle read 1 1/2 more books then Jan

Answer:

Kyle read [tex]1 \frac{1}{2}[/tex] books more than Jan

Step-by-step explanation:

[tex]3 \frac{5}{6}-2\frac{1}{3}[/tex]

They have different denominators so let's look for the [tex]LCM[/tex] to find our common denominator

Definition of LCM - LCM stands for least common multiple. The least common multiple of two numbers is the smallest number that is a multiple of both of them.

Now let's find our LCM

[tex]6:6,12,18,24,30,36,42\\\\3:3,6,9,12,15,18,21,24,27,30[/tex]

as you can see our [tex]LCM[/tex] is [tex]6[/tex]

[tex]3\frac{5}{6}-2\frac{2}{6}=1 \frac{3}{6}[/tex] this can be reduced to [tex]1 \frac{1}{2}[/tex]

Kyle read [tex]1 \frac{1}{2}[/tex] books more than Jan

Answer:

-4/5

Step-by-step explanation:

To find this we can look for the [tex]LCD[/tex] between all the numbers

Here are our [tex]LCD's[/tex] (Least Common Denominator)

-22/30 and -25/30

It wouldn't be -1 because it isn't in between those numbers

It isn't -7/10 because if we turn it into our [tex]LCD[/tex] it would be -21/30 which isn't in between those numbers

It is -4/5 because if we turn in into our [tex]LCD[/tex] it would be -24/30 which is between those numbers

This means we have our right answer we know our last one is incorrect

Answer:

∠K = 123°

∠L = 97°

∠O = 83°

∠N = 40°

Step-by-step explanation:

∠K and ∡57° are Supplementary, so their sum is equal to 180°

180 - 57 = 123

∠K = 123°

∠N and ∡140° are also Supplementary

180 - 140 = 40

∠N = 40°

The area of a triangle is equal to 180 when all angles are added together

40 + 57 = 97

180 - 97 = 83

∠O = 83°

∠L is an outside angle, which is equal to the sum of the 2 further angles (in this case ∡57° and ∠N) which we found was 97° when solving for ∠O

∠L = 97°

Now to check ∠K we add ∠O and ∠N

83 + 40 = 123

Now we also check ∠O with ∡140°

140 - 57 = 83

So all of the angles check out correctly

Answer:

3925

Step-by-step explanation:

25x

25*157

Answer:

202

Step-by-step explanation:

Answer:

let the shares be 4x and 1x (4:1)

total share = 4x + 1x = 5x

total amount = 10£

5x = 10£

x = 2£

1st share = 4x = 4*2£ = 8£

2nd share = 1x = 1*2£ = 2£

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