An executive for a large company is considering a change to health insurance plans offered to the employees. To
assess employee satisfaction with the current plan, the executive sends an email to all company employees asking
their opinion of the current plan. A summary of the results received shows that 27% of company employees are
"highly satisfied" with the current health insurance plan. Which statement about the results is most likely to be true?

Answer:

Step-by-step explanation:

1) ML // JK , MK is transversal,

∠LMK = ∠MKJ   {Alternate interior angles are congruent}

∠LMK = 30°

In ΔMKO,

30 + 115 + ∠ JLM = 180  {Angle sum property of triangle}

        145 +∠ JLM  = 180

∠ JLM  = 180 - 145

∠ JLM = 35°

2) AB // CD , AC is transversal

∠DCA = ∠BAC     {Alternate interior angles are congruent}

∠DCA = 23

∠BCD = ∠DCA + ∠BCA

          = 23 + 37

          = 60

3) EF // HG ; FH  is transversal

∠FHG = ∠HFE   {Alternate interior angles are congruent}

 ∠FHG = 77

4) ZY // WX ;  WY is transversal

∠ZYW = ∠XWY         {Alternate interior angles are congruent}

            = 65

ZY // WX ;  WY is transversal

∠ZWY = ∠WYX   {Alternate interior angles are congruent}

           = 36

In  ΔWZY

36 +  65 + ∠z = 180

        101 +∠Z = 180

∠Z = 180 - 101

∠Z = 79

Answer:

Yes, she will be able to retrieve the item

Step-by-step explanation:

The information with regards to the research historian interest in finding a sunken treasure are;

The depth from which the equipment can recover items = 5,000 m

The speed of sound through water, v = 1,530 m/s

The time it takes the echo from the item to return to the sonar detector, t = 6.2 s

Let d, represent the depth at which the item is located

Given that an echo travels from the sonar detector to the item and back to the sonar detector, the distance traveled by the sound wave which is received as an echo by the sonar detector = 2 × d

Velocity, v = Distance/time

∴ Distance = Velocity × Time

The distance traveled by the echo = 2 × d = v × t

2 × d = v × t

∴ 2 × d = 1,530 m/s × 6.2 s

d = (1,530 m/s × 6.2 s)/2 = 4,743 m

The depth at which the item is located, d = 4,743 m is less than the maximum depth the equipment can recover items, therefore, she will be able to retrieve the item.

Answer:

18

Step-by-step explanation:

The interior and exterior angle of a polygon is supplementary

let interior be I

let exterior be E

I + E = 180

Since the interior angle is 8 times that of an exterior angle,

8E + E = 180          [replacing I with 8E]  

9E = 180                

E = 20                      

The exterior angle is 20 degrees

I + E = 180          

I + 20 = 180      

I = 160              

The interior angle is 160 degrees.

The equation to find the interior angle of a polygon with 'n' number of sides is:

I = ( (n − 2) × 180 ) ⁄ n

We know the interior angle, so plug it in and solve for n:

160 = ( (n − 2) × 180 ) ⁄ n      

160n = (n − 2) × 180            

160n = 180n − 360                  

-20n = -360                            

n = 18                                  

Answer:

The correct answer is - C.  11.45 ounces to 11.75 ounces.

Step-by-step explanation:

According to the empirical rule of the distribution for 68% falls under the normal curve falls within 1 standard deviation of the mean.

That is:

μ±δ

From the given information, the mean is

μ = 11.60

and the standard deviation is

δ = 0.15

We substitute the given parameters to obtain;

11.60±0.15

11.75 and 11.45

This means the lower limit is

11.45

and the upper limit is

11.75

==========================================================

Explanation:

It helps to add point labels. Let's place point A at the very top point of the triangle. Then point B will be at the 90 degree angle. Point C is the far left point. Lastly, point D is on segment BC such that DC = 3.

Since BC = 8 and CA = 17, we can use the pythagorean theorem to get...

(AB)^2 + (BC)^2 = (AC)^2

(AB)^2 + (8)^2 = (17)^2

(AB)^2 + 64 = 289

(AB)^2 = 289-64

(AB)^2 = 225

AB = sqrt(225)

AB = 15

Now focus on triangle ABD and apply the pythagorean theorem again to find side AD

(AB)^2 + (BD)^2 = (AD)^2

AD = sqrt(  (AB)^2 + (BD)^2  )

AD = sqrt(  (AB)^2 + (BC-CD)^2  )

AD = sqrt( (15)^2 + (8-3)^2 )

AD = sqrt(250)

AD = sqrt(25*10)

AD = sqrt(25)*sqrt(10)

AD = 5*sqrt(10) .... answer is choice B

Answer:

Question 16 = 22

Question 17 = 20 cm²

Step-by-step explanation:

Concepts:

Area of Square = s²

Area of Triangle = bh/2

Diagonals of the square are congruent and bisect each other, which forms a right angle with 90°

Segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Question # 16

Step One: Find the total area of two squares

Large square: 5 × 5 = 25

Small square: 2 × 2 = 4

25 + 4 = 29

Step Two: Find the area of the blank triangle

b = 5 + 2 = 7

h = 2

A = bh / 2

A = (7) (2) / 2

A = 14 / 2

A = 7

Step Three: Subtract the area of the blank triangle from the total area

Total area = 29

Area of Square = 7

29 - 7 = 22

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Question # 17

Step One: Find the length of PT

Given:

PT = PR + RT [Segment addition postulate]

PT = (4) + (6)

PT = 10 cm

Step Two: Find the length of S to PT perpendicularly

According to the diagonal are perpendicular to each other and congruent. Therefore, the length of S to PT perpendicularly is half of the diagonal

Length of Diagonal = 4 cm

4 ÷ 2 = 2 cm

Step Three: Find the area of ΔPST

b = PT = 10 cm

h = S to PT = 2 cm

A = bh / 2

A = (10)(2) / 2

A = 20 / 2

A = 10 cm²

Step Four: Find the length of Q to PT perpendicularly

Similar to step two, Q is the endpoint of one diagonal, and by definition, diagonals are perpendicular and congruent with each other. Therefore, the length of Q to PT perpendicularly is half of the diagonal.

Length of Diagonal = 4 cm

4 ÷ 2 = 2 cm

Step Five: Find the area of ΔPQT

b = PT = 10 cm

h = Q to PT = 2 cm

A = bh / 2

A = (10)(2) / 2

A = 20 / 2

A = 10 cm²

Step Six: Combine area of two triangles to find the total area

Area of ΔPST = 10 cm²

Area of ΔPQT = 10 cm²

10 + 10 = 20 cm²

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Just want the points

Step-by-step explanation:

Answer:

33/4

Step-by-step explanation:

Let n = number

2/3 * n = 11

Multiply each side by 3/2

3/2 * 2/3 n = 11 * 3/2

n = 33/2

We want to find 1/2 of n

1/2 * 33/2 = 33/4

Answer: D

Step-by-step explanation:

formula=V=(π)r2h

Answer:

9

Step-by-step explanation:

Using the rules of logarithms

log[tex]x^{n}[/tex] = nlogx

[tex]log_{b}[/tex] b = 1

Then

[tex]log_{x}[/tex] [tex]x^{9}[/tex]

= 9[tex]log_{x}[/tex] x

= 9

Answer:

B (x+7, y-6)

Step-by-step explanation:

It goes right 7 and down 6

Answer:

(x,y) --> (x+7, y-6)

Step-by-step explanation:

Good luck with your exam! :DD

Answer:

it should be the second one I hope this help

Answer: See explanation

Step-by-step explanation:

The perimeter of a pentagon is gotten through the summation of its five sides. Let the first side be represented by x. Since each side of a pentagon is 10 cm greater than the previous side, then the sides will be:

First side = x

Second side = x + 10

Third side = x + 10 + 10 = x + 20

Forth side = x + 30

Fifty side = x + 40

Therefore,

x + (x + 10) + (x + 20) + (x + 30) + (x + 40) = 500

5x + 100 = 500

5x = 500 - 100

5x = 400

x = 400/5

x = 80

Therefore, the lengths will be:

First side = x = 80cm

Second side = x + 10 = 80 + 10 = 90cm

Third side = x + 20 = 80 + 20 = 100cm

Forth side = x + 30 = 80 + 30 = 110cm

Fifty side = x + 40 = 80 + 40 = 120cm

The conversion rate US dollars to Euros is represented with the function:

E(n)=0.72n

n- number of dollars

E(n) - Euros as a function of US dollars

The conversion rate Euros to Dirhams is :

D(x)=5.10x

x- number of Euros

D(x)- Dirhams as a function of Euros

We are trying to find D(x) in terms of n.

D(x) = 5.10x

x can be rewritten as E(n)

D(x) = 5.10(E(n))

D(x) = 5.10(E(n))

D(x) = 5.10(0.72n)

D(x) = 3.672n

According to this the following statement is true:

A) (D x E)(n) = 5.10(0.72n)

Answer:

x <= -4 or x >= 2

Step-by-step explanation:

so, it actually says

|x+1| >= 3

so, then, this is valid for all x >= 2 (then x+1 is 3 or higher), and for all x <= -4 (then x+1 is -3 or lower, and |x+1| is still 3 or higher)

6√5 + 3√6 = 6√5 + 3√6 [cannot be simplified]

; roots do not contain any perfect squares, and the roots are not similar.

6√5(3√6) = 18√30 [can be simplified]

; although roots do not contain any perfect squares, the product rule can be applied to create a singular expression.

Answer:

A

Step-by-step explanation:

Firstly x cannot be -5 because the expression on th left would be undefined so it's only between choices a and c.

Create a number line with makes the expression on left 0 and undefined...so at 6 and -5 this happens.

-------(-5)--------(6)---------

Let's test the 3 intervals by choosing a value from that interval to see if all numbers from that interval will make the expression on left less than 0.

Number before -5 is -6:

(-6-6)/(-6+5)=-12/-1=12 >0 so this interval is not a part of our solution.

Number between -5 and 6 is 0:

(0-6)/(0+5)=-6/5<0 so this interval is a part of our solution

Number after 6 like 7:

(7-6)/(7+5)=1/12>0 so this interval is not a part of our solution.

The winner is everything between-5 and 6 so answer is A.

Answer:

x=10

Step-by-step explanation:

I hope this will help you

Answer:

81/16

Step-by-step explanation:

(⅔)-⁴

81/16

= 5.0625

Answer:

C, 40 degrees

Step-by-step explanation:

All the angles of a triangle add to 180 degrees according to the Triangle Sum Theorem.

Since all angles sum to 180, we can set all the values to add to 180.

We have:

[tex]2y+y+10+50=180[/tex]

Combining like terms, we have:

[tex]3y+60=180[/tex]

Subtracting 60 from both sides gets us

[tex]3y=120[/tex]

Dividing by 3 from both sides equals

[tex]y=40[/tex]

Answer:

I think the value of y is 40

Step-by-step explanation:

Initial value is your y intercept, and to find that you just need to substitute 0 for x. Anything to the power of 0 is just 1. So you get 34.2(1), which means that your initial value is 34.2.

Answer:

4

Step-by-step explanation:

y = kx

Use point (3, 12).

12 = k * 3

k = 12/3 = 4

y = 4x

Answer: 4

Divide y by x:

12/3 = 4

36 / 9 = 4

The constant of variation is 4

========================================================

Explanation:

The two points mentioned in bold are midpoints of segments AB and AC respectively.

To find the coordinates of a midpoint, you add up the x coordinates and divide by 2. Do the same with the y coordinates.

For example, points A and B are at (7,6) and (1,-2)

If we add up the x coordinates and divide by 2, then we get (7+1)/2 = 4. Do the same for the y coordinates to get (6+(-2))/2 = 2. So that's how (4,2) is the midpoint of segment AB. You'll use similar logic to find that (8,2) is the midpoint of segment AC.

A slight alternative is that once you find one midpoint is (4,2), you can draw a horizontal line until you reach (8,2). We're using the idea that the midsegment is parallel to BC which is also horizontal.

Answer:

oi ngl levi is hawt I like your pfp ^^

Step-by-step explanation:

my name is Riley

Answers:

==============================================================

Explanation:

Refer to the diagram below.

The segment AB is the player's height of 6 ft.

The segment CD is the hoop's height, which is 10 ft.

There is a point E on CD such that rectangle BACE forms. This will help us form ED later.

Angle EBD is what we're after, which I'll call x.

Since the free throw line is 15 ft from the basket, this means segments EB and AC are 15 ft each.

In rectangle BACE, the side EC is opposite AB. So both of those sides are 6 ft each.

Since CD = 10 and EC = 6, this must mean ED = CD-EC = 10-6 = 4.

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

To summarize, we found that ED = 4 and EB = 15.

We'll focus our attention entirely on triangle EBD

We have two known legs of the triangle, specifically the opposite and adjacent sides.

So we'll use the tangent ratio.

tan(angle) = opposite/adjacent

tan(B) = ED/EB

tan(x) = 4/15 .... is the equation to solve

x = arctan(4/15) .... same as inverse tangent or [tex]\tan^{-1}[/tex]

x = 14.931417 ..... make sure to be in degree mode

x = 15 ..... rounding to the nearest whole degree

So that unknown angle in the diagram is approximately 15 degrees

i am not getting it what are you asking

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle \Large \boldsymbol{} a_1=70 \ ; \ d=-5 \\\\S_n=\frac{a_1+a_n}{2} \cdot n \ ; \ a_n=a_1+(n-1)d \Longrightarrow \\\\\\ S_{30}=\frac{70+70-29\cdot5}{2} \cdot 30 =-75 \\\\\\Answer: S_{30}=-75[/tex]

Answer:

112

Step-by-step explanation:

The volume is given by l*b*h=4*4*7=112