What is the range of the function?
f(x)=3^x-1 -6
Enter your answer, in interval notation, in the box.
range:

The probability that all adjacent points differ in color is given as follows:

1/10. (second option).

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the total outcomes, we have an arrangement of 6 elements, due to the six points, with 3 and 3 repetitions, as 3 are green and 3 are red, hence the number of total outcomes is calculated as follows:

[tex]T = A_6^{3,3} = \frac{6!}{3!3!} = 20[/tex]

For the desired outcomes, there are two, given as follows:

This means that the probability that all adjacent points differ in color is calculated as follows:

p = 2/20 = 1/10.

Hence the second option is the correct option.

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The percentage of total hours was spent skiing is 10%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, total number of hours =5+20+10+5+10 =50

Number of spent on skiing is 5

Now, percentage is 5/50 ×100

=10%

Therefore, percentage of hours spent on skiing is 10%

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"Your question is incomplete, probably the complete question/missing part is:"

What percentage of total hours were spent skiing?

Soccer 5

Jogging 20

walking 10

skiing 5

football 10

Luianne earns $4340 weekly by working as waitress at a local emerald Monday restaurant.

As per the known fact, one week comprises of seven days. Concerning this, the formula to be used for calculation is -

Regular weekly pay = Numbers of hours of work × number of days in a week × pay per hour

Keep the values in formula to find the regular weekly pay

Regular weekly pay = 40 × 7 × 15.50

Performing multiplication on Right Hand Side of the equation

Regular weekly pay = 4340

Hence, she earns $4340 weekly.

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The equations of the lines parallel and perpendicular to the lines f (y = 2), ang g (y = 2·x - 1), with the parallel lines passing through the point P(-2, -1), and the perpendicular line passing through the point Q(3, -2) are;

A. The equation of the line parallel to the line f and passing through the point P is; y = -1

B. Equation of the parallel line to g and passing through P is; y = 2·x + 3

C. Equation of the line perpendicular to f passing through P is; x = 3

D. The equation of the line perpendicular to g and which passes through P is y = -0.5·x - 0.5

Perpendicular lines are lines that intersect forming (right angles) an angle of 90°.

The equation that represents the line f is y = 2

The equation that represents the line y = 2·x - 1

A. The slope of a line parallel to another line are the same, therefore;

The equation of the line parallel to the line y = 2, has a slope which is the coefficient of x of 0.

The line f is parallel to the x-axis

The equation that is parallel to line f and passes through the point P(-2, -1)  therefore has the same y-value as the point P of -1 and an x-value of 0, the equation is therefore;

B. The slope of the line g, y = 2·x - 1 is 2

The slope of the graph of the equation of the line that is parallel to the line g, is also 2

The equation of the line parallel to the line g and passing through the point (-2, -1) is; y - (-1) = 2·(x - (-2)) = 2·x + 4

y + 1 = 2·x + 4

y = 2·x + 4 - 1 = 2·x + 3

The equation of the line parallel to the line g and passing through the point P(-2, -1) is therefore;

C. The line f is parallel to the x-axis, therefore, the line perpendicular to the line f is perpendicular to the x-axis or parallel to the y-axis

The equation of the line perpendicular to the line f and passing through the point Q(3, -2), is therefore;

D. The slope of the line perpendicular to the line g, has a slope that is the negative inverse of the slope of the line g

The slope of the line g is 2, therefore, the slope of the perpendicular line is -1/2

The equation of the perpendicular line to the line of the equation g and passing through the point Q(3, -2) in point-slope form is therefore;

y - (-2) = (-1/2)·(x - 3) = -x/2 + 3/2

y = -x/2 + 3/2 - 2 = -x/2 - 1/2 = -0.5·x - 0.5

y = -0.5·x - 0.5

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"2 more than a number" is equivalent to the mathematical expression X+2.

"2 more than a number" denotes addition because of the word "more." Since we aren't given a definite number, we use a variable in its place (such as x). So, x+2 can be used to represent "2 greater than a number."

An arithmetic value used to indicate an amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. You can think of a number as a count, like when we yell, "3, 2, 1, GO!" during a race, or as a measurement, like John Cena's weight of 275 lbs. There are also decimals like 3.14 and fractions like 22/7.

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The answer that is entirely correct based on the sales of popcorn is;

A: Jorge will raise more money because he is selling the popcorn for $3 per bag, and Alan is selling the popcorn for $2 per bag.

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, For Alan, we are told that her popcorn sales can be represented by the equation; y = 2x

where;

x is the number of bags of popcorn sold.

y is the amount of money raised.

Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $2

Now, for Jorge, looking at the graph, we can see that;

y -intercept = 0

Slope = (15 - 6)/(5 - 2)

Slope = 3

Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $3.

Looking at the options, the correct one are Options A,

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Answer:

t ≈ 7.7

Step-by-step explanation:

                   r         ^nt

A = P ( 1 + ------- )

                  n

A = 3000

P = 1500

n = 12

r = 0.09

t = ?

                             0.09        

3000 = 1500 ( 1 + ------- ) ^(12)(t)

                               12

                             0.09        

3000 = 1500 ( 1 + ------- ) ^(12)(t)

÷1500  ÷1500         12

              0.09        

2 =  ( 1 + ------- ) ^(12)(t)

               12

Change into logs and divide

  log 2

----------------------    =   12t

              0.09

log (1 + ----------)

               12

multiply both sides by (1/12)

                 log 2

(1/12) ----------------------    =   12t (1/12)

                    0.09

      log (1 + ----------)

                     12

7.7304805 = t

7.7 ≈ t

I hope this helps!

Answer: B, D, E (2^-1; subtract exponents)

Step-by-step explanation:

B > 1/2 = 2^-1

D > 2^-1 = 2^-1

E > Add exponents 2 + -5 = -1

Moving this barrel up a ramp required around 339.41 foot-pounds of labour from Alexa.

W = F.d

When the dot product is expanded, we get:

W=Fd cos(Ф)

We can plainly see from the given statement that:

applied force = F = 120 pounds

d = 4 feet for displacement.

F's angle with the horizontal is Ф = 45 degrees.

When the formula's values are substituted, we obtain:

W = 4 * 120 * cos (45)

W equals 339.41 foot pounds.

This indicates that lifting the barrel up this ramp required roughly 339.41 foot-pounds of labour from Alexa.

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The complete question is-

Alexa is pushing a construction barrel up a ramp 4 feet long into the back of a truck. She is using a force of 120 pounds in a horizontal direction and the ramp is 45 degrees from the horizontal. How much work is Alexa doing?

Answer:

Step-by-step explanation:

So basically you can always use bodmas( Brackets of division multiplication addition substractions)

or if it is like 5-4=8+9

then u can   5= 8+9+4

so.................. 5= 21

then................ 21-5=16

We found that after simplifying , He have 13 dimes and 10 quarters.

Given,

A man has 23 coins in his pocket.

The total value of his change is 380 cents.

Now,

23 = x + y

23 - x = y

As we know that

A dime=10 cents

So the cost of x dime is 10x.

A quarter=25 cents

so the cost of y quarters is 25y.

380 = 10x + 25y

Substitute the first equation, so

389 = 10x + 25 (23 - x)

380 = 10x + 575 - 25x

15x = 195

x = 13 dimes

Therefore,

y = 23 - 13 = 10 quarters

y = 10 quarters

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The standard deviation is 4.95.

The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean.

A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean. The standard deviation and the mean together can tell you where most of the values in your frequency distribution lie if they follow a normal distribution.

Dataset: 1,2,4,7,8

So, n = 5 (because the sample size is 5)

We calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values:

X = 1+2+4+7+8/5

X=22/5 = 4.4

So, the average is 4.4

For standard deviation calculation,

$ = [tex]{\sqrt{(x-X)^2/n-1} }[/tex]

Thus, the standard deviation is 4.95.

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a) Natural number: [tex]12[/tex]

b) Integer that is not a natural number:[tex]-8[/tex]

c) Rational number that is not an integer: [tex]\frac{5}{10} or 0.5[/tex]

d) An Irrational number: [tex]\sqrt{3}[/tex]

A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5,6[/tex]  etc. Natural numbers are also known as counting numbers.

An integer is a whole number (not a fraction) that can be positive, negative, or [tex]0[/tex]. Examples of integers are: [tex]-5,0,1,5,10.[/tex]

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]-\frac{1}{2},\frac{3}{4},0.75, etc.[/tex]

Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi (3.14), \sqrt{2}, etc.[/tex]

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a) Natural number: 12

b) Integer that is not a natural number:-8

c) Rational number that is not an integer: [tex]\frac{5}{10}[/tex]

d) An Irrational number: [tex]\sqrt{5}[/tex]

A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5[/tex]  etc. Natural numbers are also known as counting numbers.

An integer is a whole number (not a fraction) that can be positive, negative, or 0. Examples of integers are: [tex]-1,5, etc[/tex]

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]\frac{1}{2} ,0.5[/tex]

Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi ,\sqrt{6}[/tex]

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If it is important to detect a mean difference in score of one point with the probability of at least 0.90 , then the number of pairs that should be used is  10 .

What is a Probability ?

The term probability of an event  is defined as ⇒ number of favorable outcomes / total number of outcomes  .

It is given that ,

the probability is at least 0.90 ,

So , in the paired t test ,

testing mean paired difference is = 0

alpha = 0.05 , the assumed standard deviation of paired difference = 0.441

So the output is

Difference = 1 , Size = 5 power(probability) = 0.90 ,

So , the actual probability is = 0.95190

From the output above , the required sample size is n = 5 .

We observe that , under the given conditions the sample size is = 5 .

but the researcher  considered 10 pairs ,

So , the sample size 10 is used for this study .

Therefore , 10 pairs should be used .

The given question is incomplete ,the complete question is

It is important to detect a mean difference in score of one point with a probability of at least 0.90. how many pairs should have been used ?

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(2, 1,985.5) is not a solution of the equation y = 2200(0.95)x.

What is solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Consider, the given equation

y = 2200(0.95)x

And the point given is, (2, 1985.5).

From this x = 2, y = 1985.5

Plug x = 2 in the above equation,

y = 2200(0.95)(2)

y = 4180 ≠ 1985.5

Hence, the given point (2, 1985.5) is not a solution to the equation

y = 2200(0.95)x.

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Answer:

y = 0.028t + 230,000

Step-by-step explanation:

We know

t = number of years since the start of the study

y = be the city's population

Each year the population has grown by 2.8%, this is the slope

The city had 230,000 people, this is the y-intercept

2.8% = 0.028

The equation is y= mx + b

So, our equation in this case is

y = 0.028t + 230,000

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There are 10 dimes and 50 nickels.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Susan has a collection of 60 nickels and dimes.

And, The number of nickels is five times the number of​ dimes.

Now,

Let number of dimes = x

Then, The number of nickels = 5x

Since, Susan has a collection of 60 nickels and dimes.

Hence, We get;

⇒ x + 5x = 60

⇒ 6x = 60

⇒ x = 10

Thus, The number of dimes = x

                                           = 10

Then, The number of nickels = 5x

                                             = 5 × 10

                                             = 50

Therefore, There are 10 dimes and 50 nickels.

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The true statements regarding the construction are statement 2) and statement 5)

"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.

Given that, A design began from the construction of a regular hexagon.

The true statements made on the construction is;

2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.

5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.

Hence, The true statements regarding the construction are statement 2) and statement 5)

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Six Sigma provides a continuous improvement framework and it has two methodologies.

DMAIC - Define, Measure, Analyze, Improve and Control.

DMADV - Define, Measure, Analyze, Design and verify

What is Six Sigma ?

According to the Six Sigma philosophies, every work can be broken down into discrete processes that may be measured, evaluated, improved, and managed.

                     Processes result in outputs after requiring inputs (x) (y). You can manage the outputs if you manage the inputs. This is typically written as y = f. (x).

What is a fundamental principle of Six Sigma?

The management practice known as "six sigma" aims to reduce errors. It is based on the idea that reducing defects is essential for improving margins, that costs can be cut, and that increasing customer loyalty can help because it is expensive to harbor defects.

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Answer:

Below

Step-by-step explanation:

( Your question asks for m^2 discharge......I think you need m^3 discharge per minute)

Find the volume of a cylinder that is 8 meters long with radius of 8cm ( .08 m)

area = pi r^2 = pi (.08)^2 = .0201 m^2

    area * 8 m   = volume PER SECOND

        volume PER SECOND  *  60 = volume per minute

                 .0201   * 8 * 60 = 9.65 m^3 / min  discharge

Answer:

m-2

Step-by-step explanation:

to start simplify

-3(7/2-2/3m)+17/2-m

-21/2+6/3m+17/2-m

-21/2+17/2+2m-m

-4/2+m

-2+m

m-2

hopes this helps

Answer: decimal 0.03 fraction 3/10

Step-by-step explanation:

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

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26 points are scored in the fifth game.

The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

First four games, a netball team scores an average of 31 points per game.

x/4=31

Let x represents four games

x=124

After the fifth game, the average for the first five games is 30

y/5=30

Let y represents five games

y=150

We need to find the number of points scored in fifth game.

x-y

124-150

26

Hence, 26 points are scored in the fifth game.

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By using percentage, it can be calculated that

2% of the product of 19 and the average of 63,500, 65,000 and 66,500 = 24700

What is percentage?

Suppose, there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example, 7% means [tex]\frac{7}{100}[/tex]. Here, 7 is expressed as a percentage of 100.

This is a problem on percentage

The numbers are 63,500, 65,000 and 66,500

Average = [tex]\frac{63500 + 65000 + 66500}{3}[/tex] = 65000

Product of 19 and 65000 = 65000 [tex]\times[/tex] 19 = 1235000

2% of 1235000 = [tex]\frac{2}{100} \times 1235000[/tex] = 24700

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Answer: 3ft to 1cm

Step-by-step explanation:

Store B is offering the best unit rate for bananas.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Grocery Store A is selling bananas for $0.75 for 12 pounds.

The unit rate will be = 0.75/12 = 0.06

Grocery Store B is selling 5 pounds of bananas for $3.75.

The unit rate will be = 3.75/5 = 0.75

Hence, Store B is offering the best unit rate for bananas.

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