Each person that works at a company is given a 5-digit code. These employees must enter their codes on a keypad to enter and exit the office building. The company has 80 employees.
a) How many codes are possible if there are no restrictions?
b) What is the probability of someone entering a 5-digit code at random and gaining entry?

Answer: 0.126?

Step-by-step explanation:

A decimal number between 0.25 and 0.125 could be 0.2 or 0.15. These numbers sit within the specified range and comply with the principles of decimal number placement.

The task here is to identify a decimal number that lies between 0.25 and 0.125. To achieve this, we can carefully select a decimal value that stands in the middle of these two numbers. An example of a suitable decimal would be 0.2, as it comfortably sits within this specified range. Another example could be 0.15. These are both valid decimal numbers that reside between 0.25 and 0.125, and their selection adheres to the principles of decimal number placement on a number line.

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The  expression is equivalent to 8/9 divided by 3/4 is 32/27.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

We have to divide the fraction 8/9 by 3/4.

As, the fraction does not allow division then we will perform the multiplication.

So, 8/9 x 4/3

= 32 / 27

Thus, the required fraction is 32/27.

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Answer:

The total discounted price is 34.93

Step-by-step explanation:

The items in the cart are:

Total cart = $ 41.10

Discount = 41.10 * 0.15 = $ 6.17

Discounted total price = 41.10 - 6.17

Discounted total price = 34.93

Answer:

34.94.

Step-by-step explanation:

First we must find the total price of all the items: =$6.35+$6.35+$12.50+$13.40+$2.50=$41.10.

Next, we can calculate the discount: =(15/100)×$41.10=$6.165.

Therefore, our discounted price is $41.10−$6.165=$34.935≈$34.94.

Answer:

Here, we have used the unit rate i.e. speed of 30 mph to get the distance traveled in 5 number of units i.e. 5 hours.

Step-by-step explanation:

We are asked the way to use a unit rate to solve a rate problem for any number of units.

Let, us assume that a car is moving at a unit rate of 30 miles per hour. And we have to calculate the distance it travels in 5 units of time i.e. 5 hours.

Now, the distance traveled in 5 hours will be given by 30 × 5 = 150 miles.

Since  [tex]\textrm {Speed} = \frac{\textrm {Distance}}{\textrm {Time}}[/tex] and here, speed is 30 miles per hour and the time is 5 hours. (Answer)

Answer:

0.33

Step-by-step explanation:

Aight so all we do is use the formula, as shown here:

[tex]\frac{\Delta x}{\Delta y}[/tex]

[tex]x[/tex] is this amount it changed, which is 0.99. So we plug that for [tex]\Delta x[/tex]:

[tex]\frac{0.99}{\Delta y}[/tex]

Then, we find the amount of times the storm changed, and we plug that for [tex]\Delta y[/tex]:

[tex]\frac{0.99}{3}[/tex]

So, now that we have utilized the formula, we can now solve!

[tex]\frac{0.99}{3} = 0.33[/tex]

Good luck!

Answer:

0.33

Step-by-step explanation:

Answer:

5 liters of water.

Step-by-step explanation:

Let [tex]y[/tex] be the liters of water that must be added to 15 liters of 40% sugar syrup.

Initially, we have [tex]0.4(15)=6[/tex] liters of sugar syrup, and since adding water does not add any new syrup, the amount of sugar syrup must be the same after the water has been added. After the water has been added, 30% of the solution is sugar syrup, or

[tex]Sugar\:syrup =0.3(15+y)[/tex]

And since this must equal the amount of syrup we had before:

[tex]0.3(15+y)=0.4(15)[/tex]

[tex]4.5+0.3y=6[/tex]

[tex]0.3y=1.5[/tex]

[tex]\boxed{y=5}[/tex]

Thus, 5 liters of water must be added to obtain 30% sugar syrup.

Answer:

5 liters of water

Quotient = 2

Solution:

Given expression is [tex]22x^2y^2\div11x^2y^2[/tex].

To find the quotient.

[tex]22x^2y^2\div11x^2y^2=\frac{22x^2y^2}{11x^2y^2}[/tex]

In numerator 22 can be written as 2 × 11.

[tex]\frac{22x^2y^2}{11x^2y^2}=\frac{2\times11x^2y^2}{11x^2y^2}[/tex]

Take common term out in the numerator and denominator.

[tex]\frac{22x^2y^2}{11x^2y^2}=\frac{(11x^2y^2)(2)}{11x^2y^2}[/tex]

Common terms in the numerator and denominator will be cancelled.

[tex]\frac{22x^2y^2}{11x^2y^2}=2[/tex]

Hence the quotient is 2.

Answer:

The guy up top is right its 2 with no mistake.

Step-by-step explanation:

There are 5 short essay questions on test

Solution:

Let "a" be the number of multiple choice questions

Let "b" be the number of short essay questions

Worth of each multiple choice questions = 3 points

Worth of each short essay questions = 8 points

There are 25 questions in total

number of multiple choice questions + number of short essay questions = 25

a + b = 25

a = 25 - b --------- eqn 1

The test is worth 100 points. Theerefore, we frame a equation as:

number of multiple choice questions x Worth of each multiple choice questions + number of short essay questions x Worth of each short essay questions = 100

[tex]a \times 3 + b \times 8=100[/tex]

3a + 8b = 100 --------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

3(25 - b) + 8b = 100

75 - 3b + 8b = 100

5b = 100 - 75

5b = 25

b = 5

Thus there are 5 short essay questions on test

The number of short essay questions on the test is 5.

The science test is worth 100 points and has 25 questions. Let's represent the number of multiple-choice questions as 'x' and the number of short essay questions as 'y'. Each multiple-choice question is worth three points, so the total number of points for the multiple-choice questions is 3x. Each short essay question is worth eight points, so the total number of points for the short essay questions is 8y. We can write two equations to represent the given information:

x + y = 25 (since there are 25 questions in total)

3x + 8y = 100 (since the total points for the test is 100)

To find the number of short essay questions on the test, we need to solve these two equations. By substituting x = 25 - y into the second equation, we can solve for y.

3(25 - y) + 8y = 100

75 - 3y + 8y = 100

5y = 25

y = 5

Therefore, there are 5 short essay questions on the test.

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Answer:

1. a ≥ –4 and a ≤ 4

Step-by-step explanation:

Rule : | a | ≤ 4 ⇔ -4 ≤ a ≤ 4

:)

Answer:

The decimal that represents the unshaded portion of the model is 0.4

Step-by-step explanation:

we know that  

Camille shaded 18/30 of a model

That means

The total parts of the model is equal to 30

The shaded parts of the model is 18

To find out the unshaded parts of the model subtract the shaded parts from the total parts

[tex]30-18=12[/tex]

To find out the decimal that represents the unshaded portion of the model, divide the unshaded parts of the model by the total parts of the model

so

[tex]\frac{12}{30}=0.4[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6= -6, -3.4=3.4, 2.25=-2.25, 8 1/5=-81/5

Answer:

d 10x=-3

Step-by-step explanation:

The missing figure is attached down

The length around the outside of the track is about 431 feet

Step-by-step explanation:

A running track has the shape of a rectangle capped with a semicircle on each end

We need to estimate the length around the outside of the track

The length of the outside the track is the length of two semi-circle and two straight lengths of the rectangle

∵ The track is 80 feet wide

- From the figure the width of the track is the diameter of the

  semi-circles

∴ The diameter of each semi-circle = 80 feet

∵ The radius of a circle is half its diameter

∴ The radius of each semi-circle = [tex]\frac{1}{2}[/tex] × 80 = 40 feet

∵ The length of a circle = 2πr

∴ The length of a semi-circle = πr

∴ The length of two semi-circle = 2 × πr

- Substitute r by 40

∴ The length of two semi-circle = 2 × π(40) = 80π feet

∵ The rectangular portion of the track is 90 feet tall

∴ The length of the rectangle = 90 feet

∴ The two straight parts of the track = 2 × 90 = 180 feet

- Add the length of the two semi-circles and the two straight

   parts to find the length of the track

∵ Length of the track = 80π + 180

- Substitute π by 3.141

∴ Length of the track = 80(3.141) + 180

∴ Length of the track = 431.28 ≅ 431 feet

The length around the outside of the track is about 431 feet

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Answer:

12r+6

Step-by-step explanation:

2(6r+3)

2(6r)+2(3)

12r+6

Answer:

x^3-x^2-17x+12

Step-by-step explanation:

(x+4)(x^2-5x+3)

x^3-5x^2+3x+4x^2-20x+12

x^3-5x^2+4x^2+3x-20x+12

x^3-x^2-17x+12

Answer:

x is equal to 2

Step-by-step explanation:

2x+4=8

2x=4

x=2

Answer:

x = 2

Step-by-step explanation:

First you must subtract x to both sides leaving you with 2x + 4=8 and you subtract 4 to both sides giving you 2x=4 and lastly to get the x by itself you divide both sides by 2 leaving you with x=2

The corresponding element in the range when 7 is an element  in the domain is f(5)=179/5

Step-by-step explanation:

Given that the 5 is an element in the domain of f(x)

The function f is defined by f(x)=8x-21/5

To find the corresponding element in the range:

That is put x=5 in the given function f(x)

Therefore f(x) becomes

f(5) = 8(5)-21/5

     =40-21/5

     =179/5

Therefore corresponding element in the range when 5 is an element  in the domain is f(5)=179/5

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hello that is a hard question but the answer is your face

Answer:

im so sorry about the kid that said that. that was mean

Step-by-step explanation:

Answer: -3 and +3

Step-by-step explanation:

The length of side walk is 500 feet

Solution:

Given that, A rectangle park measures 300 ft by 400 ft

Length = 300 feet

Width = 400 feet

A sidewalk runs diagonally from one comer to the opposite corner

We have to find the length of side walk

Which means, we have to find the length of diagonal of rectangle

The diagonal of rectangle is given by formula:

[tex]d = \sqrt{w^2+l^2}[/tex]

Where,

d is the length of diagonal

w is the width and l is the length of rectangle

Substituting the values in formula, we get

[tex]d = \sqrt{400^2+300^2}\\\\d = \sqrt{160000+90000}\\\\d = \sqrt{250000}\\\\d = 500[/tex]

Thus length of side walk is 500 feet

Answer:

53 teachers

Step-by-step explanation:

Basically, what we need to do here is to find how many teachers there need to be, first. If there are 6,734 students in the school district and if maximum class size is 25, then the number of teachers needed is:

6,734 / 25 = 269.36

Of course, it's obvious that we can't have a decimal number of teachers, so we need to find integer (269 or 270).

If we take 269 teachers and 25 students per class, we get:

269 • 25 = 6,725 students, which is not enough, since there are 6,734 students.

That means that the number of teachers needed is 270.

It is given that there are already 217 teachers, meaning that 270-217=53 teachers have to be supplemented.

52 more teachers must the district have to supplement their staff of 217 teachers.

Given that,

A school district has a student population of 6,734 students.

If the maximum class size is 25 students.

We have to determine,

How many more teachers must the district have to supplement their staff of 217 teachers?

According to the question,

Total number of students = 6,734

Maximum class size = 25 students

Then,

The number of teachers needed is,

[tex]= \dfrac{6734}{25}\\\\= 269.36[/tex]

Here, 269 teachers are needed for each group of 25 students.

Therefore,

The number of more teacher must the district have to supplement their staff of 217 teachers is,

269 - 217 = 52

Hence, 52 more teachers must the district have to supplement their staff of 217 teachers.

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Answer:

Step-by-step explanation:

the quotient is the result of division

the quotient of 6 and z...

6/z <===

** pay attention to the wording...because if it would have said : the quotient of z and 6, it would have been z/6

Answer:

original weight of the box = 15 / 16 pounds

Step-by-step explanation:

The correct answer is D. (3x2 + 5)(x + 3). Here’s how you can use the grouping method to factor the polynomial completely:

Group the first two terms and the last two terms: (3x3 + 9x2) + (5x + 15)

Factor out the greatest common factor from each group: 3x2(x + 3) + 5(x + 3)

Factor out the common binomial factor: (3x2 + 5)(x + 3)

So, the polynomial 3x3 + 9x2 + 5x + 15 can be factored completely as (3x2 + 5)(x + 3).

Hope it helps.

Answer:

12(3+4)

Step-by-step explanation:

Answer:

Etc: 12 34

Step-by-step explanation:

The simplified answer is [tex]5\frac{2}{9}[/tex].

Option: C.

Step-by-step explanation:

To simply [tex]-3\frac{1}{9} - (-8\frac{1}{3} )[/tex]:

First convert this improper fraction into normal fraction.

[tex]-3\frac{1}{9}[/tex] = [tex]\frac{-28}{9}[/tex].

[tex]-8\frac{1}{3}[/tex] = [tex]\frac{-25}{3}[/tex].

Now we have to simplify [tex]-\frac{28}{9} - (-\frac{25}{3} )[/tex].

= [tex]-\frac{28}{9} + \frac{25}{3}[/tex].

After applying LCM to the denominators, Multiply the second term with 3 in both numerator and denominator.

= [tex]-\frac{28}{9} + \frac{75}{9}[/tex].

=[tex]\frac{-28+75}{9}[/tex].

=[tex]\frac{47}{9}[/tex].

Convert the answer in improper fraction form.

[tex]\frac{47}{9}[/tex] = [tex]5\frac{2}{9}[/tex].

Thus the simplified answer is [tex]5\frac{2}{9}[/tex].

Answer:

no

Step-by-step explanation:

bc

15/18 cant be simplified no matter what

Answer:

No

Step-by-step explanation:

15/18 can not be simplified

Answer:

Step-by-step explanation:

108 = 2*2*3*3*3=2² * 3³

120 = 2*2*2*3*5=2³*3*5

LCM = 2³*3³*5 = 8*27*5= 1080

To find the LCM of 108 and 120, first find their prime factorizations and then multiply the highest power of each prime factor.

To find the Lowest Common Multiple (LCM) of 108 and 120, we can first find their prime factorizations. The prime factorization of 108 is 2 × 2 × 3 × 3 × 3, while the prime factorization of 120 is 2 × 2 × 2 × 3 × 5. We can then find the LCM by taking the highest power of each prime factor from both numbers. So, the LCM of 108 and 120 is 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2,160.

The Lowest Common Multiple (LCM) of 108 and 120 is 1080. This is found by finding the prime factors of each number, and then multiplying together the highest power of each factor.

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