six friends all throw their coats on the bed in the spare room when they show up for teesha's birthday party. at the end of the party they all enter the dark room and randomly grab a coat and put it on without knowing if it is actually their coat. what is the probability that exactly three of the friends got the right coat? express your answer as a common fraction.

The answer is A) 10,000,000 seven-digit numbers; B) The number is  20,000 ; C)  5,314,410 identification numbers are possible if no two adjacent digits are the same.

Seven-digit identification number:

A.) The number of possible identifying numbers

Possible digits are 0 up to 9.

Total number of digits: 10

Any of the 10 digits may be used for each;

Hence,

10×10×10×10×10×10×10 equals 10,000,000 potential outcomes.

B.) For it to start begin with either 023 and 003.

- the first digit must be 0 (1 possible value)

- 2nd digit must be 2 or 0 (2 possible values)

- 3rd digit must be 3 (1 possible value)

- 4th and 5th can be filled with any digit (10 × 10 possible values)

Which gives

1×2×1×10×10×10×10 = 20,000

3.) no two adjacent digits are the same that is no two digits that follows each other are the same.

In this case only one digit have 10 possible values.

The other four digits have 9 possible values each.

Which gives:

10×9×9×9×9×9×9 = 10× [tex]9^{6}[/tex] = 5,314,410

The full question:

A certain identification number is a sequence of seven digits. (a) How many identification numbers are possible? (b) How many of them begin with either 023 or 003? (c) How many identification numbers are possible if no two adjacent digits are the same? (For example, 123-4-567 is permitted, but not 123-3-456.).

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Answer:

third choice in image. √(16³)

the squareroot of 16 to the third power

Step-by-step explanation:

Fractional exponents tell you that you have roots. Could be squareroot or thirdroot, fourth root, fifth root...etc. You know which because you look at the bottom number (denominator) of the fraction. I use the phrase "down and out" to help remember that the bottom number in the fractional exponent is the "outside number" (index) on the radical sign.

The top number (numerator) of the fraction is an exponent. It can be either inside the radical right there on the shoulder of the 16 or it could also be outside the whole entire radical.

16^ (3/2) = √(16³)  = (√16)³  

Answer:

C

Step-by-step explanation:

you can use the website desmos and literally type the exact equations in and it will show the graph.

Answer:

3

Step-by-step explanation:

A = 3 × (1ft)²

A = 3 × 1 ft²

A = 3ft²

Answer: Infinitely many solutions

Answer:

Below

Step-by-step explanation:

15x + 3y = 27     divide through by 3 to get

5x + y = 9    <====== this is the same equation as the first one so they are the SAME line ....meaning INFINITE solutions

The measurement of each diagonal is;

i. DB = 23.32 inches

ii. RY = 25.05 inches

A diagonal is a line drawn from one edge of a shape to another, which divides it into two equal shapes produced. Thus a diagonal is not the same as the line of symmetry.

NB: A shape may have more than one diagonal.

In the given question, we can apply Pythagoras theorem to have;

i. From triangle DHB,

/Hyp/^2 = /Opp/^2 + /Adj/^2

 DB^2 = DH^2 + HB^2

           = 20^2 + 12^2

           = 400 + 144

DB^2 = 544

DB = (544)^1/2

     = 23.324

DB = 23.32 inches

ii. From triangle HKR,

/Hyp/^2 = /Opp/^2 + /Adj/^2

KR^2 = HR^2 + HK^2

         = 16^2 + (8.72)^2

         = 256 + 76.0384

KR^2 = 332.0384

KR = (332.0384)^1/2

     = 18.2219

KR = 18.22

but,

YR = YK + KR

     = 6.83 + 18.22

     = 25.05

YR = 25.05 inches

The measurement of the diagonals are: DB = 23.32 inches, and  RY = 25.05 inches.

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Answer: a/2

I believe for this problem all they’re asking is how you would write the expression.

(n-1) x (n-2)! ways of seating arrangements are possible if Fred (a boy) and Carrie (a girl) must be seated next to each other.

A permutation is the act of putting things or numbers in a certain order. Combinations are a method of picking things or numbers from a set of objects or collections without regard for their order.

Let's say there are n seats in total.

Then, there are (n-1) gaps between the seats that Fred and Carrie can be placed in.

If we place Fred and Carrie in one of these gaps, there will be (n-2)! possible arrangements for the rest of the seats.

Therefore, there will be (n-1) x (n-2)! total possible seating arrangements for Fred and Carrie if they must be seated next to each other.

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The constant term for the expression 5g³ + 2 is 2.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the expression,

5g³ + 2,

a linear equation consists of three terms,

variables, coefficient of variables, and constant.

A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Compared with the given expression,

g is the variable and 5 is the coefficient,

2 is the constant term.

Hence 2 is constant.

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Answer: I think the answer is A

Step-by-step explanation: It goes from 128 to 150.

Answer: Y=1/4x-2. slope intercept form is y=mx+b

we have our b and our m and that’s all we need. so the equation would be y=1/4x-2

Step-by-step explanation:

Answer: X= 90

Step-by-step explanation:

There is a 90-degree symbol. So I think X= 90.

Thank you

The value of f in the pentagon is 72 degrees.

A pentagon is a polygon with 5 sides. A regular pentagon is a polygon with 5 sides equal to each other. Therefore, In the regular pentagon, all of the exterior angles marked f are the same size.

Let's find the value of f as follows:

Therefore, the sum of exterior angles of a pentagon is 360 degrees.

Hence,

5f = 360 degrees

divide both sides of the equation by 5

5f / 5 = 360 / 5

f = 72 degrees

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True. An outlier in a data set can significantly affect the value of the mean but not the median.

This is because the median is the middle value in a data set and is not affected by extreme values, while the mean is calculated by adding all the data values and then dividing by the total number of values, which can be significantly affected by extreme values or outliers.

To illustrate this, let's consider the data set {1, 2, 3, 4, 1000}. The median value of this data set is 3, since that is the middle value. The mean of this data set is 205, since it is calculated by adding all the values (1+2+3+4+1000) and dividing by the total number of values (5). The outlier value of 1000 has a significant effect on the mean, changing it from an average of 3.2 (1+2+3+4/4) to an average of 205 (1+2+3+4+1000/5). The median, however, remains unchanged (3). Therefore, it can be concluded that an outlier in a data set can significantly affect the value of the mean but not the median.

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The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).

Mean time that employees spend on personal issues each week(M) = 4.9 hours

Standard deviation = 0.35 hours

The following formula is used to get the confidence interval for the sample mean and standard deviation given:

μ = M ± t(sM)

where; M = sample mean

t = T-statistic based on confidence interval

Degree of freedom = n - 1

From the question, n = 55

Degree of freedom = 55 - 1

Degree of freedom = 54

(Standard errors)sM = √(s^2/n)

Now putting the value

sM = √(0.352/55)

sM = 0.05

t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)

Now the confidence interval

μ = M ± t(sM)

μ = 4.9 ± 2.005 × 0.05

μ = 4.9 ± 0.095

μ = (4.9 - 0.095, 4.9 + 0.095)

μ = (4.805, 4.95)

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Jill should expect an additional 30 to 45 hours of homework each week.

As a general rule of thumb, students can expect to spend 2-3 hours of homework for each hour spent in class. This means that for a 15 credit hour course load, Jill can expect to spend an additional 30 to 45 hours on homework each week.

However, this is just a rough estimate and the actual amount of time required will depend on the difficulty of the courses, the teaching style of the instructors, and the individual study habits and ability of the student. Additionally, some courses may require more time spent on projects, reading, or other assignments that are not factored into this estimate.

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The quantity of kilograms of paper that Madelyn's office would have recycled after 4 weeks would be = 28kg

The recycling activities of Madelyn's office in weeks is listed below:

The total quantity of paper recycled for 3 weeks = 21 kg

Then, after 4 weeks would be = xkg

To calculate the unit rate is to find out the quantity recycled per week;

That is,

3 weeks = 21 kg

1 week = X

Make X the subject of formula;

X = 21/3

X= 7 kg

Then if 7 kg = 1 week

X kg = 4weeks

X kg = 7×4/1

= 28 Kilograms

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Answer:y=2x-15

Step-by-step explanation:

First, we find the slope of the first line
Slope equation:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Plug-in values

[tex]\frac{6-2}{6-(-2)}[/tex]

=[tex]\frac{4}{8}[/tex]=[tex]\frac{1}{2}[/tex]

Slope=1/2

Remember that parallel lines have the same slope.

Now, we use the slope to get the y-intercept.

We start from (8,-1)

We go up 1 (rise) and right 2 (run), or the opposite of the slope (-1 rise, -2 run).

We get a y-intercept of -5.

Plug into y=mx+b

y=1/2x-5

The greatest positive integer n such that [tex]$2^n$[/tex]divides k is 18.

The product k can be expressed as [tex]$(b - a)_{1 \le a < b \le 20}$[/tex] . Since [tex]$2$[/tex] is the only even number between [tex]$1$[/tex] and [tex]$20$[/tex], the product can be written as [tex]$(2 - 1)_{1 \le a < b \le 20}$[/tex]. Since the product of [tex]$(b - a)$[/tex]  is the same for all pairs of integers a and b that satisfy [tex]$1 \le a < b \le 20$, $k$ is equal to $(2 - 1)^{19}$.[/tex]

To determine the greatest positive integer n such that [tex]$2^n$[/tex]divides k, we need to calculate the largest exponent m  such that [tex]$2^m$[/tex] is a factor of [tex]$(2-1)^{19}$[/tex]. To do this, we can factor [tex]$(2-1)^{19}$[/tex] using the equation [tex]$(2-1)^{19} = 2^{19} - 1$[/tex]. This equation can be written as [tex]$2^{19} = (2-1)^{19} + 1$[/tex], which can be rewritten as [tex]$2^n(2^{19-n}+1) = (2-1)^{19}$[/tex]  for any positive integer n. Since the factor [tex]$(2-1)^{19}$[/tex] is odd, the greatest positive integer n such that [tex]$2^n$[/tex] divides k is 18, since [tex]$2^{19}$[/tex] is the greatest power of 2 that divides [tex]$(2-1)^{19}$.[/tex]

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Answer:

the answer is 128 fluid ounce

Step-by-step explanation:

Answer:

x₁ × x₂ = 3

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the product of the roots = [tex]\frac{c}{a}[/tex]

3x² + 15x + 9 = 0 ← is in standard form

with a = 3 and c = 9 , then

x₁ × x₂ = [tex]\frac{9}{3}[/tex] = 3

The value of the fractions will be:

1. 4/10 + 2/10 = 6/10

2. 9 /12 + 3/12 = 1

3. 6/10 + 4/10 = 1

4. 2/8 + 3/8 = 5/8

5. 2/7 + 6/7 = 1 1/7

6. 11/9 + 8/9 = 2 1/9

7. 5/13 + 10/13 = 1 2/13

8. 3/5 + 7/10 = 1 3/10

9. 7/8 + 13/16 = 1 11/16

10. 9/30 + 3/5 = 9/10

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

It should be noted that in order to add the numbers it's essential to have a common denominator. For example, 7/8 + 13/16 will be:

= 7/8 + 13/16

= 14/16 + 13/16

= 27/16

= 1 11/16

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A linear function is a mathematical function that defines a straight line when plotted on a coordinate plane.

It is defined by an equation of the form:

[tex]$y = mx + b$[/tex]

where [tex]$y$[/tex] is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope of the line is the rate at which the dependent variable changes with respect to the independent variable. In other words, it represents how much the dependent variable will change for each unit change in the independent variable.

In the case of the cost of renting a car for a day, the dependent variable is the cost (C) and the independent variable is the number of miles driven (x). The equation for the cost is:

[tex]$C = 42 + 0.65x$[/tex]

The slope of the line is 0.65, which means that for each additional mile driven, the cost of renting the car will increase by $0.65. The units of the slope are dollars per mile, since it represents the additional cost per mile driven.

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The system of equations has one solution, it is (-3,-5)

Here we have the system of equations:

y = -8x - 29

y = 7x + 16

Because y is isolated in both of the equations, we can write:

-8x - 29 = 7x + 16

-29 - 16 = 7x + 8x

-45 = 15x

-45/15 = x

-3 = x

And the value of y is what we get when we evaluate one of the equations in x = -3

y = 7x + 16 = 7*(-3) + 16

                 = -21 + 16 = -5

The solution is (-3, -5)

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If the difference of two numbers is 52 and larger number is six times the smaller number , then the smaller number is 11 , larger number is 63 .

Let  the smaller number be denoted by  "x".

according to the information that, "larger number is three less than six times the smaller number" ;

So,  the larger number can be represented as 6x - 3.

The difference between the two numbers is 52,

that means ; (6x - 3) - x = 52

On Solving for x ;

we get ;

⇒ 5x = 55

⇒ x = 11

Therefore , the smaller number is 11, and the larger number is 6×11-3 = 63.

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Answer:

2½ years

Step-by-step explanation:

I =PxRxT

$625=$5000 x 5/100 x T

$ 625= $250 T

625/250=T

T = 2.5

Answer:

At the beginning of the 11th day, the mass of the radioactive sample was 201.87 grams.

Step-by-step explanation:

Let's call the mass of the substance after n days "m". We can calculate the mass for each day using the formula:

m = 1300 * (1 - 0.14)^n

Plugging in n = 11:

m = 1300 * (1 - 0.14)^11

m = 1300 * 0.15572634

m = 201.87 grams

So at the beginning of the 11th day, the mass of the radioactive sample was 201.87 grams.

Answer:

$2.60

Step-by-step explanation:

10% = 0.1

26 times 0.1 = $2.60

So, Chad pays $2.60 tax.

Answer:$28.60-26= 2.60

Step-by-step explanation:

$26 = 100%

sales tax = +10%

total price 26 x 110%

The number is 60.

A multiple is defined as the the number resulting form the process of multiplication of two numbers.

For example, 6 is a multiple of 2 and 3 since 2 × 3 = 6.

Let x be the number.

x < 70

Multiples of 12 less than 70 = 12, 24, 36, 48, 60

Multiples of 15 less than 70 = 15, 30, 45, 60

Multiple common to 12 and 15 = 60

Hence the number here is 60.

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