select all values of n making the following statement true: out of a set of 33 positive integers, some two of them share all of their prime factors less than or equal to n.

Answer:

x= -4 + 3i and -4 - 3i

Step-by-step explanation:

solve by cross multiplying

The median for the given sample of data is A. 20.

To find the median for the given sample of data, we need to arrange the numbers in ascending order and then find the middle value.

Arranging the numbers in ascending order: 16, 17, 18, 18, 19, 19, 21, 22, 22, 23, 25

There are 11 numbers in the sample, so the middle value is the (11 + 1) / 2 = 6th value.

The 6th value in the ordered list is 19.

Therefore, the median for this sample of data is A. 20.

To know more about median, refer here:

https://brainly.com/question/300591

#SPJ4

Answer:

The answer is D

Step-by-step explanation:

The answer is D

Therefore , the solution of the given problem of equation comes out to be  it takes 6 hours of labor to make $45 (5 dollars an hour plus the $15 sign-up bonus).

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a singular formula which divides 12 into two parts and can be used to assess data received from y + 7, normalization in this case yields b + 7.

Here,

This scenario can be represented by the equation 5x + 15 = 45, where x is the required number of hours of labor.

The sum you will make after working x hours (5 hours at the rate of $5 plus the $15 welcome incentive) is shown on the left-hand side of the equation at 5x + 15. The total quantity you want to make is shown by the number 45 on the right-hand side of the equation.

Therefore, you must isolate x in order to answer the equation:

=> 5x + 15 = 45

=> 5x = 30

=> x = 6

Consequently, it takes 6 hours of labor to make $45 (5 dollars an hour plus the $15 sign-up bonus).

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

it is option 3

Step-by-step explanation:

-4(5p+3)

by opening brackets, you get

-20p -12

Answer:

72

Step-by-step explanation:

75% of 96 = 0.75 x 96

                 = 72

Answer:

Accounts receivable in January = $68,432.60

Accounts receivable in February = $55,929.20

Accounts receivable in March = $55,958.95

Step-by-step explanation:

65% of sales collected in the month of sales + 25% in the following month + 10% in second month after sales.

In January, total accounts receivable will be the amounts outstanding or unpaid by the end of January. By the end of January, a total of 10% of December sales & 35% of January sales remain outstanding.

Accounts receivable in January = 35% of January sales + 10% of December sales

Accounts receivable in January = (35% * $124298) + (10% * $249283)

Accounts receivable in January = $43504.3 + $24928.3

Accounts receivable in January = $68432.60

In February, total accounts receivable will be the amounts outstanding or unpaid by the end of February. By the end of February, a total of 10% of January sales & 35% of February sales remain outstanding.

Accounts receivable in February = 35% of February sales + 10% of January sales

Accounts receivable in February = (35% * $124284) + (10% * $124298)

Accounts receivable in February = $43,499.4 + $12,429.8

Accounts receivable in February = $55,929.20

In March, total accounts receivable will be the amounts outstanding or unpaid by the end of march. By the end of March, a total of 10% of February sales & 35% of March sales remain outstanding.

Accounts receivable in March = 35% of March sales + 10% of February sales

Accounts receivable in March = (35% * $124373) + (10% * $124284)

Accounts receivable in March = $43530.55 + $12428.4

Accounts receivable in March = $55,958.95

Answer:Your answer should be 0.125 or .125

Step-by-step explanation:Decimals can be negative or positive. In this case it will be negative.

Find an equivalent fraction with a denominator of a power of 10.

In this case we will use  

1000

Answer: A

Step-by-step explanation b. would be in the negative section

c. Would be rashal

d.would be whole number

The set of all points at which the function f(x) = 1/ln(ln(x)) is continuous is (e^(e), infinity).

To find the set of all points at which the function is continuous, we need to check for two things: the function is defined and the limit of the function exists at every point in its domain. For f(x) = 1/ln(ln(x)), the function is defined for x > e^(e), since ln(ln(x)) is only defined for x greater than or equal to e^(e). To check for continuity, we need to evaluate the limit of the function as x approaches a point in its domain. Taking the limit as x approaches e^(e) from the right and from the left gives us infinity. Therefore, f(x) is continuous for x > e^(e).

Note that ln(ln(x)) approaches negative infinity as x approaches e^(e) from the right. This means that f(x) has a vertical asymptote at x = e^(e).

To learn more about the limit of the function click here: brainly.com/question/29795597

#SPJ11

Answer:

a. intersecting

b. parallel

c. skew

d. intersecting

e. parallel

Therefore, the center of pressure on the triangular sail is approximately (1.2, 0.9).

The center of pressure on a boat's sail that occupies a region R in the plane is given by

x = ∬R xydA/∬R ydA` and y = ∬R x²ydA/∬R xydA`.

To calculate the center of pressure on a triangular sail with vertices (0,0),(3,2) and (0,7) we will use the following formulas:

x = ∬R xydA/∬R ydA

y = ∬R x²ydA/∬R xydA

Remember that in this case, the region R in the plane is the triangular sail with vertices (0,0), (3,2), and (0,7).

Hence, the equations for x-bar and y-bar are:x-bar = ∬R xydA/∬R ydA= ∫(x=0 to x=3) ∫(y=0 to y=(7x/3))

=  xy dy dx/ ∫(x=0 to x=3) ∫(y=0 to y=(7x/3)) y dy dx= 42/35= 1.2 units (approx)

And,y-bar = ∬R x²ydA/∬R xydA= ∫(x=0 to x=3) ∫(y=0 to y=(7x/3)) x²y dy dx/ ∫(x=0 to x=3) ∫(y=0 to y=(7x/3)) xy dy dx= 63/70= 0.9 units (approx)

Therefore, the center of pressure on the triangular sail is approximately (1.2, 0.9).

To know more about pressure,

https://brainly.com/question/28012687

#SPJ11

Answer:

\(a^4\) Where (a) is the side length of the hypercube

Step-by-step explanation:

A dimension can be simply defined as a direction in which matter can move it.

We live in a 3-dimensional world, matter can move in three basic directions. The formula for finding the volume of a cube is the following: (\(a^3\)). In the second dimension, a flat world, the area for the volume of a square is as follows: (\(a^2\)). However, a hypercube is a paradox, as it exists in 4-dimensions, thus it cannot exist in our world. However, scientists propose "String theory" which requires that matter can move in more directs than the (3) we know of in our world. In essence, there can be more than 3 dimensions. A hypercube is the 4-dimensional version of a cube. If it follows the area pattern that a square-object follows in all preceding dimensions then the area of a hypercube is (\(a^4\)).

Bear in mind that the area patter for a square-object is generally the following:

\(a^n\)

Where (a) is the side length of the square-object

(n) is the dimension the object is in.

Please keep in mind, this answer was written in the June of 2021, as science keeps progressing and new discoveries are made, this theory can be disproven. Therefore, this answer might be considered correct now, but it can be proven incorrect in the future.

The value of simplified form of the expression is,

⇒ √2 (13 - √3)

We have to given that;

The expression is,

⇒ 3√2-√6+10√2

Now, We can simplify as;

⇒ 3√2 - √6 + 10√2

⇒ 3√2 - √2 × √3 + 10√2

⇒ 13√2 - √2 × √3

⇒ √2 (13 - √3)

Thus, The value of simplified form of the expression is,

⇒ √2 (13 - √3)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

There are total of 152 students in 5th grade, then the number of pencils altogether will be equal to 2,736 pencils.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total number of students in 5th grade = 152

Amount of pencil each student have = 18

Then, the total number of pencils altogether,

= 152 × 18

= 2,736 pencils.

To know more about arithmetic operations:

https://brainly.com/question/13585407

#SPJ1

Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

Learn more about quadratic equation here:

https://brainly.com/question/1214333

#SPJ2

The coordinates of X'' is (-4, 7) after the transformation

From the question, we have the following parameters that can be used in our computation:

X = (4, -7)

Then, we have the transformations to be

X'' = R y axis (R x axis(X))

This transformation means that

Mathematically, this is represented as

(x, y) = (-x, -y)

Substitute the known values in the above equation, so, we have the following representation

(x, y) = (-4, 7)

Hence, the image is (-4, 7)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

The counterexample is if the length of the rectangle is 19.99 and width is 0.01 then the area is 0.1999 and the perimeter still 40.

Counterexample are those examples which is used to make given statement false , Or its an instance of example.

Given ,

The perimeter of the rectangle = 40 units

It is mentioned in the statement that if perimeter is 40 then area must be at least 1 unit .

The counterexample for proven this statement false would be ,

The rectangle whose length is 19.99 unit and width is 0.01 unit have the area 0.1999 square unit  and perimeter is 40 unit .

Hence , It is proved by counterexample that it is not necessary that area must be at least 1 unit when perimeter is 40 unit .

Learn more about Counterexample:

 brainly.com/question/24881803

#SPJ1

SOLUTION

By Definition

Whole numbers are the basic counting numbers 0, 1, 2, 3, 4, 5, 6, …

it sets can be represented as

An Integer is a whole-valued positive or negative number or 0. The set of integers is represented as

hence integers contain whole numbers

Rational numbers are a set of numbers that can be written as a fraction. all integers can be written as a fraction.

Hence we conclude that

Hence we have the diagram as

Therefore the right option is B

If 624 minutes are used, the total cost will be dollars is $2,493.92.

Part A :

With the information given in the problem, we know that (i) "if a customer uses 150 minutes, the monthly cost will be $83" and (ii) "if the customer uses 980 minutes, the monthly cost will be $332."

From the information given in (i), we can set up the equation where y = total monthly payment = 83, x = minutes = 150, and where b = monthly fee which is an unknown value.

This gives the equation : y = mx+b --> 83 = 150m + b

*Note: m = the slope = rate, which can be defined as the $/min.

From the information given in (ii), we can set up the equation where y = total monthly payment = 332, x = minutes = 980, and where b = monthly fee which is an unknown value.

This gives the equation: y = mx + b --> 332 = 980m + b

At this point, we have two equations with two unknown values, m and b which are constant in both equations. The values that were given are the (x,y) values. To find the unknown m and b values, we can first use an equation to isolate one of the variables.

Solving for m:

From the first equation, b = 83 - 150m.

We can substitute this value of b into the second equation: 332 = 980m + (83 - 150m)

Solve for m:

332 - 83 = 980m - 150m

249 = 830m

m = 3.33

Solving for b:

From the first equation, since solving for m, we know that 83 = 150(3.33) + b

Now, we know that b = 83 - (150)3.33 = 416.50

Answer for Part A: y = 3.33 x + 416

Part B:

Using the equation y = 3.33 x + 416, we can substitute 624 minutes for x.

y = 3.33 (624) + 416

y = 2493.92

Answer for Part B: If 624 minutes are used, the total cost will be $2,493.92.

Hence the answer is If 624 minutes are used, the total cost will be dollars is $2,493.92.

To learn more about equations click here https://brainly.com/question/22688504

#SPJ4

Answer: 3x + 2) 12x� + 20x� + 11x + 2

Divide the first term 12x� by 3x: %2812x%5E3%29%2F%283x%29=4x%5E2

and write 4x� above the 20x�:

               4x�__________  

3x + 2) 12x� + 20x� + 11x + 2

Multiply the 4x� by the (3x + 2) getting 4x%5E2%283x%2B2%29=12x%5E3%2B8x%5E2 and

write it under the first two terms and draw a line underneath:

               4x�__________  

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�  

Subtract %2812x%5E3%2B20x%5E2%29-%2812x%5E3%2B8x%5E2%29=12x%5E3%2B20x%5E2-12x%5E3-8x%5E2=12x%5E2,

and write 12x� under the line under 8x�, like this:

               4x�__________  

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x�

Now bring down the next term + llx and write in next to the 12x�

               4x�__________  

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x� + 11x

Divide the first term on the bottom 12x� by 3x: %2812x%5E2%29%2F%283x%29=4x

and write + 4x above the 11x at the top, like this:

               4x� +  4x____

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x� + 11x

Multiply the 4x by the (3x + 2) getting 4x%283x%2B2%29=12x%5E2%2B8x and

write it under the first two terms and draw a line underneath:

               4x� +  4x____

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x� + 11x

              12x� +  8x

Subtract %2812x%5E2%2B11x%29-%2812x%5E2%2B8x%29=12x%5E2%2B11x-12x%5E2-8x=3x,

and write 3x under the line under 8x, like this:

               4x� +  4x____

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x� + 11x

              12x� +  8x

                      3x

Now bring down the last term + 2 and write in next to the 3x

               4x� +  4x____

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x� + 11x

              12x� +  8x

                      3x + 2

Divide the first term on the bottom 3x by the 3x at the left:

%283x%29%2F%283x%29=1 and write + 1 above the + 2 at the top,

like this:

               4x� +  4x + 1

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x� + 11x

              12x� +  8x

                      3x + 2

Multiply the + 1 by the (3x + 2) getting 1%283x%2B2%29=3x%2B2 and

write it under the two terms at the bottom and draw a line

underneath:

               4x� +  4x + 1

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x� + 11x

              12x� +  8x

                      3x + 2

                      3x + 2

Subtract %283x%2B2%29-%283x%2B2%29=3x-3x=0,

and write 0 under the line under 2, like this:

               4x� +  4x + 1

3x + 2) 12x� + 20x� + 11x + 2

       12x� +  8x�

              12x� + 11x

              12x� +  8x

                      3x + 2

                      3x + 2

                           0

Now you are done and the answer is 4x%5E2%2B4x%2B1 and

since the remainder is 0 you do not have to put it over

the divisor 3x+%2B+2 and add it on like you do when

the remainder is not 0.

Step-by-step explanation:

Answer:

Volume of the box is 448 cm^3.

Step-by-step explanation:

It is given that a box is to hold 448 cm^3.

Mathematically we could say , the volume of the box is 448 cubic centimeters.

Answer:

34 = 22 + x

x = 12

Step-by-step explanation:

alternatively, you could say (10x3)+(1x4) = (10x2) + (1x2) + x

Answer:

Second one is the Correct answer

Answer:

z= 117°

y = 34

Hope it helps!

Step-by-step explanation:

(5y - 53) + 63 =180°

5y + 10 =180

5y = 170

y= 34

z and y are congruent (vertical angles)

5 (34) - 53 = z

170 - 53 = z

z = 117

Answer:

\( \frac{9 - 8}{12 } \\ = \frac{1}{12} \\ = 0.8333333...\)

If the average salary of several of the groups was close to $51,000 then least likely to be the average salary of another one of the groups are equal to $41,000.

Random groups of teachers are = 30

If the average salary of several of the groups was close to equal to = $51,000

The mean, or average, salary is the amount derived by adding two or more salary values and dividing the sum by the number of values.

So we can write,

The average wage is known to be close to $41,000

$41,000 < $51,000

Therefore,

The average salary of another one of the groups are equal to $41,000.

To learn more about visit Average salary :

brainly.com/question/22521658

#SPJ1

#6 is 210

Step-by-step explanation:

Just rememder that the circles are 360 degrees

Answer: A,B

Step-by-step explanation: the numbers constantly add up only by 218 or 1240 , C and D would not be correct because the rate of change increases as will with the total sum after each period of time

also tiny hint, if you were to draw an X,Y axis graph, A and B would be a straight line while C and D are curved up-wards