A recent survey showed that 91 full-time employees out of a sample of 500 did not use all of their vacation days last year. However, 105 of those studied expressed a desire for more vacation time. Based on this sample, if a full-time employee is chosen at random, what is the probability that he or she is content with the vacation allowance? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth

Answer:

After investing for 10 years at 5% interest, your $2,000 investment will have grown to $3,258

Step-by-step explanation:

Your welcome

Answer:

[tex]\huge\boxed{\bf\:1}[/tex]

Step-by-step explanation:

At first, let's factorise the given three numbers.

[tex]12\\= 4 * 3*1\\= \underline {2*2*3*1}[/tex]

[tex]15\\= \underline{5*3*1}[/tex]

[tex]20\\= 4*5*1\\=\underline {2*2*5*1}[/tex]

Here, from the given factors, we can see that the three numbers (12, 15 & 20) don't have any common factors except for 1.

•°• The least numbers divisible by 12, 15 & 20 is 1.

[tex]\rule{150pt}{2pt}[/tex]

The area of the triangle is equal to 12 mm².

The area of a triangle is given by the formula:[tex]A=\frac{bh}{2}[/tex], where:

 b= length of the base;

  h=height

From the figure, it is possible to see that h= base of rectangle - 4 mm. Then, the height of the triangle(h)= 10-4=6 mm.

You can see that the sum of the base of the triangle with the height of the rectangle is equal to 12 mm. The figure also shows that the height of this rectangle is equal to 8 mm. Thus, the  base of the triangle(h)= 12-8=4 mm.

STEP 2 - Find the area of the triangle.

From step 1:

    b= length of the base= 4

    h=height=6

Therefore, the area of the triangle - [tex]A=\frac{bh}{2}=\frac{4 * 6}{2}=\frac{24}{2} =12 mm^2[/tex].

Learn more about the area of compound shapes here:

brainly.com/question/15884960

Answer:

mP = 35

Step-by-step explanation:

QR = 80

QS = 150

The measure of the angle formed by a secant and a tangent intersecting in the exterior of a circle is half the difference between the measures of the intercepted arcs.

This means that (150-80)/2 = mP

mP = 35 degrees

Hope this helps!

Answer:

3x - 6 = 60

Step-by-step explanation:

[tex]\frac{3}{5} =\frac{12}{x-2}[/tex]
5*12 = 3*(x-2)
60 = 3x - 6

Answer:

498.66577718478985990660440293529019346230820547031354236157438292 seconds

Step-by-step explanation:

Answer:

c) 32°

Step-by-step explanation:

The bisector of an angle is the line or line segment that divides the angle into two equal parts.  So Ray HJ divides ∠GHI into 2 equal parts.

Therefore, ∠GHJ = ∠IHJ

As we are told that ∠IHJ = 32° then ∠GHJ = 32°

Answer:

30°

Explanation:

∠LMP + ∠PMN = 180°

[∠LMO + ∠OMP] + [∠PMR + ∠RMN] = 180°

FIND x

(x - 10) + (x + 30) + x + 40 = 180

3x - 10 + 30 + 40 = 180

3x + 60 = 180

3x = 120

x =40

FIND ∠LMO

∠LMO = x - 10

∠LMO = (40) - 10

∠LMO = 30°

Hope this helps and God bless!

Answer:

∠LMO = 30°

Step-by-step explanation:

Angles on a straight line add up to 180°

⇒ (x - 10)° + (x + 30)° + 40° + x° = 180°

⇒ x° + x° + x° - 10° + 30° + 40° = 180°

⇒ 3x° + 60° = 180°

⇒ 3x° = 120°

⇒ x = 40

Substitute found value of x into the expression for ∠LMO:

⇒ ∠LMO = (40 - 10)°

⇒ ∠LMO = 30°

Answer:

11 / 12 or 0.9167

Step-by-step explanation:

Given:

3/4 + 1/6

Find:

Value with expression

Computation:

"3/4 added to number 1/6"

3/4 + 1/6

By taking LCM

[9 + 2] / 12

11 / 12 or 0.9167

brainliest?

Answer:

41.57

Step-by-step explanation:

took the test

Answer:

The answer to 6^4 is 1296

Step-by-step explanation:

2x2x2x2 = 16 (you have to multiply the 2 four times because you have a little four on top of the two)

3x3x3x3 = 81 (you have to multiply the 3 four times because you have a little four on top of the three)

16x81 = 1296 (6^4 = 6x6x6x6 = 1296)

The stem-and-leaf plot for the given different wieghts (in kg) is displayed in the image attached below.

A stem-and-leaf plot is a graphical tool used to display data points, in such a way that, if 26, 27, and 28 are data points, 2 will be the stem in a row and along with 6, 7, 8 as the leaf.

Given the data points, 16, 15, 23, 24, 13, 21, 15, 26, 22, 24, 30, 24, 10, 17, 19, 17, 28, 31, 29, 14, the stem-and-leaf plot is displayed in the image attached below (see attachment).

Learn more about the stem-and-leaf plot on:

https://brainly.com/question/8649311

The probability that a blue marble was drawn followed by a yellow marble is; 0.45.

According to the task content;

On this note , the probability that a blue marble and yellow marble were drawn respectively is;

Read more on probability;

https://brainly.com/question/12971752

Answer:

x = 45 degrees

Step-by-step explanation:

The angles is 90 degrees because it is a corner. Half of 90 is 45.

Answer:

736x-89

Step-by-step explanation:

i think all you can do here is add the numbers that have an X in them so adding 689x+47x=736x and you leave the 89 so it becomes 736x-89

Answer:

736x-89

Step-by-step explanation:

first add the like terms (numbers with the same variables)

so now the equation is 736x-89

Answer:

2

Step-by-step explanation:

h ( x ) = - x - 4

To find : h ( - 6 )

h ( - 6 ) = h ( x )

Here,

x = - 6

h ( - 6 ) = - x - 4

           = - ( - 6 ) - 4

           = 6 + 4

h ( - 6 ) = 2

Step-by-step explanation:

wheres. the. quatation it doesnt say

A circle is a curve sketched out by a point moving in a plane. The measure of x is 60°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given that the measure of the arc AC is 120°. Now, as we know, the diameter divides the circle into two equal chords of 180° each. Therefore, the measure of x can be written as,

[tex]x = {\rm arcAB-arc AC}\\\\x = 180^o-120^o\\\\x = 60^o[/tex]

Hence, the measure of x is 60°.

Learn more about Circle:

https://brainly.com/question/11833983

#SPJ1

Answer:

12 eggs over 2 tablespoons, 24 eggs over 4 tablespoons, and 9 eggs over 1.5 tablespoons

Step-by-step explanation:

1 tablespoon of butter for every 6 eggs makes the ratio 6:1

Now let's make the ratio for all of them:

12:2

15:3

24:4

9:1.5

We can simplify them

6:1

5:1

6:1

6:1

There is your answer,

1) 12 eggs Over 2 tablespoons

2) 15 eggs Over 3 tablespoons

3) 9 eggs Over 1.5 tablespoons

Hope it helped :)

Answer:

30 inches

Step-by-step explanation:

In equilateral triangle all sides are equal. One side of the triangle EB is also the  side of a square.

So, all the sides of the square is 6 inches

Perimeter = sum of all sides

                  = AB  + BC + CD + DE + EA

                  = 6 + 6 + 6 + 6 + 6

                  = 5*6

                   = 30 inches

Answer:

Here,

length of the square BCDE(l)= 6 inches

Also,

length of the equilateral triangle ABE(l)=6 inches

Lastly, Perimeter of figure ABCDE= 5*6

=30 inches

or,Perimeter of the figure ABCDE also=

AB+BC+CD+DE+EA

=6+6+6+6+6

=30inches

Step-by-step explanation:

We know,

length DC of the square BCDE(l)=6inches

So,

DC=BC=BE=DE (All sides of a square are equal)

Again,

length BE of the equilateral triangle ABE=6inches

So,

BE=AB=AE (All sides of a equilateral triangle are equal)

Therefore, Perimeter of figure ABCDE=

AB+BC+CD+DE+EA or, 5*6

(perimeter means to sum all the outer sides a given polygon, in this case it's a Pentagon)

Please read cautiouly with patience

An equation is formed of two equal expressions. There is no solution set of the equation 3x+13 = 3(x+6)+1.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation can be solved in the following manner,

[tex]3x+13 = 3(x+6)+1\\3x+13=3x+18+1\\3x+13=3x+19[/tex]

Since both the sides of the equation are the same in terms of variable and the constant terms are not the same. Therefore, there is no solution set of the equation 3x+13 = 3(x+6)+1.

Learn more about Equation:

https://brainly.com/question/2263981

Answer: ZERO

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Trial and error into (APPROXIMATELY)

y=31,006,000(1+.012)^x

Answer:

24/7 = 3 3/7

Step-by-step explanation:

Always remember the formula:

tan x = (sin x)/(cos x)

[tex]tan \: x = \frac{sin \: x}{cos \: x} \\ = \frac{ \frac{24}{25} }{ \frac{7}{25} } \\ = \frac{24}{7} [/tex]

0.25 is the probability that the randomly selected candy is orange

Answer:
208

Step-by-step explanation:

the formula is:

2*(width*lenght+height*lenght+height*width)

2*(6*8+4*8+4*6)

208

Hey ! there

Answer:

Step-by-step explanation:

In this question we are provided a net of cuboid with ,

And we are asking to find the surface area of the figure ( cuboid ) . We know that ,

[tex] \quad\underline{ \boxed{\sf{Surface \: Area_{(Cuboid)} = 2 ( lw + wh + hl )}}}[/tex]

Where ,

Solution : -

[tex] \longmapsto \qquad \: 2((8 \times 6) + (6 \times 4) + (4 \times 8))[/tex]

[tex] \longmapsto \qquad \: 2(48 + 24 + 32)[/tex]

[tex] \longmapsto \qquad \: 2(48 + 56)[/tex]

[tex] \longmapsto \qquad \:2(104)[/tex]

[tex] \longmapsto \qquad \: \blue{\underline{\boxed{\frak{208 \: m {}^{2} }}}} \quad\bigstar[/tex]

Answer:

B

Step-by-step explanation:

6-1+11 +8

5x+19

therefore the answer is 5x + 19

The expression which is equivalent to 5x - 19 is D) -3x + 4(2x - 6) + 5.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given an expression,

5x - 19

We have to find the equivalent expression.

Find the value of each expression in the options.

A) 7(4 - 2x) + 9 (x - 1) = 28 - 14x + 9x - 9 = -5x + 19

B) 6x - (x - 11) + 8

= 5x + 11 + 8 = 5x + 19

C) 10 - 3(x - 3) - 2x

10 - 3x + 9 - 2x = -5x + 19

D) -3x + 4(2x - 6) + 5

-3x + 8x - 24 + 5 = 5x - 19

Hence the correct option is D.

Learn more about Equivalent Expression here :

https://brainly.com/question/27911936

#SPJ2

Answer:

(a) Reduction

(b) scale factor = 1/2

Step-by-step explanation:

(a)  A reduction is a dilation that creates a smaller image.  

As A'B'C'D' is smaller than ABCD, image A'B'C'D' is a reduction of image ABCD.

(b)  To find the scale factor:

center of dilation = (0, 0)

(0, 0) to point C = 4 units

(0, 0) to point C' = 2 units

⇒ scale factor = 2/4 = 1/2

Answer:

angle one is 23.3

Step-by-step explanation:

yw

Answer:

1/12

Step-by-step explanation:

Needed information

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

The sum of the probabilities of all outcomes must equal 1

Solution

We are told that the probability that the counter is not black is 3/4.  

As the sum of the probabilities of all outcomes must equal 1, we can work out the probability that the counter is black by subtracting 3/4 from 1:

[tex]\sf P(counter\:not\:black)=\dfrac34[/tex]

[tex]\implies \sf P(counter\:black)=1-\dfrac34=\dfrac14[/tex]

We are told that the probability that the counter is not white is 2/3.  

As the sum of the probabilities of all outcomes must equal 1, we can work out the probability that the counter is white by subtracting 2/3 from 1:

[tex]\sf P(counter\:not\:white)=\dfrac23[/tex]

[tex]\implies \sf P(counter\:white)=1-\dfrac23=\dfrac13[/tex]

We are told that there are black, white and grey counters in the bag.  We also know that the sum of the probabilities of all outcomes must equal 1.  Therefore, we can work out the probability the counter is grey by subtracting the probability the counter is black and the probability the counter is white from 1:

[tex]\begin{aligned}\sf P(counter\:grey) & = \sf1-P(counter\:black)-P(counter\:white)\\\\ & =\sf 1-\dfrac14-\dfrac13\\\\ & = \sf \dfrac{12}{12}-\dfrac{3}{12}-\dfrac{4}{12}\\\\ & = \sf \dfrac{12-3-4}{12}\\\\ & = \sf \dfrac{5}{12}\end{aligned}[/tex]