Fifteen students were divided into two classrooms in a ratio of 1:2.
How many students were in each classroom?

The polynomial that should be subtracted from the dividend first is; x³ + 2x²

The long division we are given is;

        __________

x + 2 ) x³ + 3x² + x

Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².

Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;

(x + 2) * (x²) = x³ + 2x²

Thus, the polynomial to be subtracted is x³ + 2x²

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The equation represents a population of 370 animals that increases at an annual rate of 11% is .

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1.

Given that,

A population of 370 animals that increases at an annual rate of 11%

a = 370, r = 11%

[tex]p=a(1+r)^{t}[/tex]

  = [tex]370(1+0.11)^{t}[/tex]

p  =  [tex]370(1.11)^{t}[/tex]

Hence, The equation represents a population of 370 animals that increases at an annual rate of 11% is .

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The number that has to fill the blank to make the trinomial a perfect square is 72x

From the question, we are to determine the number that makes the given trinomial a perfect square

The given trinomial is

9x² + ___+ 144

For any given trinomial ax² + bx + c, the trinomial is a perfect square if

b² = 4ac

In given trinomial,

a = 9, c = 144, b = ?

Now, we will determine the value of b

Putting the values into the equation,

b² = 4ac

b² = 4×9×144

b² = 5184

b = √5184

b = 72

Thus,

The trinomial will become 9x² + 72x+ 144

Hence, the number that has to fill the blank to make the trinomial a perfect square is 72x

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[tex] \rm log_{5}(125) \\ \rm log_{5}( {5}^{3} ) \\ \rm1 \cdot3 \\ 3 \\ \therefore \tt log_{5}(125) = 3[/tex]

The last digit of the product of all the numbers between 11 and 29 is 0.

A product is something that has undergone one or more multiplications.

Here, we're looking for the final digit of the product of all whole numbers greater than 11 and less than 29.

Next, we have the product as: 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28

Now take note of the 20 that is present.

Any number multiplied by 20 will result in a zero, so:

Product = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)

Using only that, we can infer that 0 represents the final digit in the product of all the numbers between 11 and 29.

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The dot product associated to sides AB and BC is 0.

In this question we must find the dot product of two vectors associated with two surrounding sides of a triangle. First, we need to find the vectors associated to sides AB and BC:

Side BA

BA = (5, 3) - (0, 0)

BA = (5, 3)

Side BC

BC = (- 3, 5) - (0, 0)

BC = (- 3, 5)

By definition of dot product, the result associated to the two sides of the triangle is:

BA • BC = (5, 3) • (- 3, 5)

BA • BC = (5) · (- 3) + (3) · (5)

BA • BC = - 15 + 15

BA • BC = 0

The dot product associated to sides AB and BC is 0.

The statement is poorly formatted, the correct form is shown below:

If A(x, y) = (5, 3), B(x, y) = (0, 0) and C(x, y) = (- 3, 5) are the vertices of a triangle then the value of the dot product between vectors AB and BC is:

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For a bedroom measuring 6 3/4" by 4 1/2" on the drawing, the dimensions of the bedroom are 18 ft. by 27 ft.

Option (C) is correct.

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

According to the question,

The scale of an architectural sketch is 1/4" = 1'. If, according to the drawing, a bedroom has the dimensions 6 3/4 by 4 1/2 inches.

Then, the dimensions of the bedroom in feets are calculated as follows:

As 1/4" = 1'

6 3/4" = 27'= 27 ft.

Similarly,

4 1/2" = 18' =18 ft.

Thus, the dimensions of the bedroom are: 18 ft. by 27 ft.

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Answer:

4

Step-by-step explanation:

1. Convert from mixed number to fraction

[tex]5\frac{1}{2} =\frac{5(2)+1}{2} =\frac{11}{2}[/tex]

[tex]1\frac{3}{8}=\frac{(1)(8)+3}{8} =\frac{11}{8}[/tex]

2. Divide fractions

[tex]\frac{\frac{11}{2} }{\frac{11}{8} } =\frac{(11)(8)}{(11)(2)} =\frac{8}{2} =4[/tex]

Hope this helps

The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.

According to the statement

We have given that the there is a algorithm which is used to data cleanup problem of removing 0 values from a data set, and scans a list from left to right and copies every legitimate value into a new list.

and we have to explain about that algorithm.

So,

Here we given that the algorithm copies and paste the values in the new files then

the algorithm is called the copy over algorithm.

So, The copy over algorithm is a a single specimen of something that occurs in a multiple edition, such as a book, article, etc. a matter to be reproduced in print or an imitation or reproduction of an original.

So, The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.

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Answer:

D. 25pi

Step-by-step explanation:

"circumscribed" means the rectangle is inside the circle and just the corners (vertices) of the rectangle are touching the circle. This means the diagonal of the rectangle is the diameter of the circle. See image. If the sides of the rectangle are 6 and 8 then the third side that makes the triangle(half the rectangle) is 10. You can find this using Pythagorean Theorem or Pythagorean triples (shortcut)

6^2 + 8^2 = d^2

36 + 64 = d^2

100 = d^2

d = 10

This is the diameter of the circle. The radius would then be 5.

Area of a circle is:

A = pi•r^2

= pi•5^2

= 25pi

The ratio of white to black horses is 2:5.

Ratio expresses the relationship between two or more numbers. Ratio is used to compare two or more numbers with each other. It shows the frequency that one value is contained within other value(s).

The ratio of white to black horses = number of white horses : number of black horses

The ratio of white to black horses = 6 : 15

6 : 15 is not expressed in its simplest form yet. To convert the ratio to its simplest form, divide the numbers by a common factor of 6 and 15. A common factor is a number that divides two or more numbers perfectly with leaving any remainder. A common factor of both numbers is 3

(6/3) : (15/3) =  2 : 5

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24 is the answer! Its all about isolation, i tried to show it a little better in the image attached. Hope this helps!!

Answer:

Step-by-step explanation:

x+3y=1

Answer:

-3/(b-6) = 3/(-b+6) = 3/(6-b)

Step-by-step explanation:

7/(b-6) + 10/(6-b)

= 7/(b-6) + 10/(-b+6)

= 7-10/(b-6)

= -3/(b-6) = 3/(-b+6) = 3/(6-b)

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{6 - b} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{ - (b - 6)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} - \cfrac{10}{ b - 6} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ - 3}{ b - 6}\:\:\: or \:\:\: \dfrac{3}{6-b} [/tex]

The name of the polygon is (B) hexagon.

To find the name of the polygon:

Therefore, the name of the polygon is (B) hexagon.

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The complete question is given below:

A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. What is the name of the polygon?

A) Octagon

B) Hexagon

C) Heptagon

D) Quadrilateral

Answer:

see explanation

Step-by-step explanation:

basically Gauss' method simplifies to

Sum = (number of terms) ÷ 2 × (1st term + last term)

43

S₂₀₀ = 200 ÷ 2 × (1 + 200) = 100 × 201 = 20,100

44

S₄₀₀ = 400 ÷ 2 × (1 + 400) = 200 × 401 = 80,200

45

S₈₀₀ = 800 ÷ 2 × (1 + 800 ) = 400 × 801 = 320,400

46

S₂₀₀₀ = 2000 ÷ 2 × (1 + 2000) = 1000 × 2001 = 2,001,000

Answer:

Sum = (number of terms) = 2 x (1st term + last term) 43

43. S200 = 200 = 2 × (1+200) = 100 201 = X 20,100

44 400 400 = 2 × (1+400) = 200 × 401 = 80,200

45 S800 = 800 = 2 × (1+800) = 400 × 801 = 320,400

46 S2000 = 2000 2 × (1+ 2000) = 1000 × 2001 = 2,001,000

The graph that matches the polynomial function that has x-Intercepts at -2, ;, and 2 and a relative maximum at x = -1 is: graph A.

We are given that the polynomial function has the following characteristics:

Relative maximum at x = -1, this implies that the peak point of the graph has an x-value that is equal to -1. In order words, the "mountain" is at x = -1.

Graph A has a "mountain" that is at x = -1.

We are given the x-intercepts of the polynomial function as:

-2, 1/2, and 2. This means that the graph intercepts the x-axis at -2, 1/2, and 2.

Graph A in the image attached has x-intercepts of -2, 1/2, and 2.

Therefore, we can conclude that the graph that matches the polynomial function that has x-Intercepts at -2, ;, and 2 and a relative maximum at x = -1 is: graph A.

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Answer:

300 points

Step-by-step explanation:

Since we have a constant rate (12.5 points/game), we can find the number of points by setting up a proportion:

[tex]\frac{12.5}{1}=\frac{x}{24}\\\\x=(12.5*24)=300[/tex]

The value of x from the given set of values is 5

A rectangle is a 2 dimensional shape with 4 sides and angle. The formula for calculating the area and perimeter is given as:

Area = length * width

Perimeter = 2(length + width)

If the length of a rectangle is 2 inches more than its width and the perimeter of the rectangle is 24 inches, the resulting equation will be:

2x + 2(x + 2) = 24,

Expand and determine the value of "x"

2x+ 2x + 4 = 24

4x + 4 = 24

Subtract 4 from both sides

4x = 24 - 4

4x = 20

Divide both sides by 4

4x/4 = 20/4

x = 5

Hence the value of x from the given set of values is 5

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Complete question

The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x is the width in inches, represents this situation. The value of x from the set {1, 3, 5, 7} that holds true for the equation is . So, the width of the rectangle is inches and its length is inches.

The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2/3x + 5/2y = 15

4x + 15y = 12

Multiply the first equation by 6, to eliminate the fractions.

6 * (2/3x + 5/2y = 15)

This gives

4x + 15y = 90

Subtract the equation 4x + 15y = 90 from 4x + 15y = 12

4x - 4x + 15y - 15y = 12 - 90

Evaluate the difference

0 + 0 = -78

Evaluate the sum

0 = -78

The above equation is the same equation as option (b) 0 = 26

This is so because they both represent that the system of equations have no solution

Hence, the equation that could represent a linear combination of the system is 0 = 26

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Complete question

The system of equations below has no solution.

2/3x + 5/2y = 15

4x + 15y = 12

Which equation could represent a linear combination of the system?

From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).

According to the statement

we have given that the a rectangle on the graph with the two given points and we have to find the another points of the graph.

So, to find the points of the rectangle

firstly the given points are:

E(2,3) And G(-2,-2) and we have to find the point H and F.

So, The point H :

For the point H the lines of rectangle meet with each other at the 3 from origin on the x axis to the negative side and at the 3 from origin on the y axis.

So, the point H become H(-3,3)

And for point F:

For the point F the lines of rectangle meet with each other at the 2 from origin on the x axis to the positive side and at the 2 from origin on the y axis on the negative side.

So, the Point F become F(2,-2).

So, From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).

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For function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

For given question,

We have been given a function k(x, y) = -x² - y² + 4x + 4y

We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

First we find the partial derivative of function k(x, y) with respect to x.

⇒ [tex]k_x=-2x+4[/tex]

Now, we find the partial derivative of function k(x, y) with respect to y.

[tex]\Rightarrow k_y=-2y+4[/tex]

To find the critical point:

consider    [tex]k_x=0[/tex]     and      [tex]k_y=0[/tex]

⇒       -2x + 4 = 0     and    -2y + 4 = 0

⇒          x = 2            and       y = 2

This means, the critical point of function is (2, 2)

We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

Consider k(0, 0)

⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)

⇒ k(0, 0) = 0

Consider k(3, 3)

⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)

⇒ k(3, 3) = -9 - 9 + 12 + 12

⇒ k(3, 3) = -18 + 24

⇒ k(3, 3) = 6

Therefore, for function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

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The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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The valid prediction for the mean of the population possible using these samples is C. Yes, the variation of the sample means is small

It should be noted that a sample mean is an average of a set of data . Also, the sample mean can be used to calculate the standard deviation, central tendency, and the variance of a data set.

The sample mean can be applied to a variety of uses, including calculating population averages.

Here, the sample variance is a measure of the degree to which the numbers in a list are spread out. Here, the numbers given are close to each other.

If the numbers in a list are all close to the expected values, the variance will be small and if they are far away, the variance will be large.

Therefore, the correct option is C.

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Answer:

C: Yes, the variation of the sample means is small.

Step-by-step explanation:

Correct answer on edge

The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

According to the statement

we have given that the radius of the clock face is 10 inches and the face of a clock is divided into 12 equal parts.

And we have to choose the three statements which are correct from the given options.

So,

Check the all given options to find the correct options.

So, OPTION A :

360/12=30 degrees between each number

3-1 = 2 2*30 = 60 degrees so A is FALSE

Now, OPTION B:

C=2 x π x r

r=10

using 3.14 for PI = 10*3.14 =31.4 x 2 = 62.8 so B is TRUE

Now OPTION C:

30 x 4 = 120 degrees = TRUE

Now, OPTION D:

10-3 = 7

7/12 x 62.8 = 0.5833*62.8 = 36.63 inches = FALSE

Now, OPTION E:

1/12=0.0833 x 62.8 = 5.23 rounded to 5.2 = TRUE

So, The options C and E is a correct options which are

C. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

Disclaimer: This question was incomplete. Please find the full content below.

Questions:

The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle.

Which statements about the clock are accurate? Check all that apply.

A. The central angle formed when one hand points at 1 and the other hand points at 3 is 30°.

B. The circumference of the clock is approximately 62.8 inches.

C.The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°.

D. The length of the major arc between 3 and 10 is approximately 31.4 inches.

E. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

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The general solution of the given system of odes is

m=1 ; m=4    (real roots)

In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.

the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.

It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.

dx/dt = 2x+2y =   x^1 = 2x+2y     1

dy/dt = x+3y =    y^1 = x+ 3y        2

differentiating 1 with respect to 't'

x^11 = 2x^1+ 2y^1

y^1 = x+3y

x^11 = 2x^1= 2(x+3y)

x^11 = 2x^1+ 2x+ 6y

x^11 = 2x^1+ 2x+ 6(x^1-2x/2)

x^11 = 2x^1+ 2x+ 3x^1- 6x

x^11 = 5x^1 - 4x

x^11 -5x^1 - 4x

x^11 - 5x^1 -4x =0

Auxillary equation is m^5- 5m+4=0

m^2 - m - 4m + 4 = 0

m(m-1) -4 (m-1) =0

(m-1) (m-4) = 0

m=1 ; m=4    (real roots)

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Answer:

  (-∞, ∞)

Step-by-step explanation:

Unless there are restrictions on the domain, the range of any odd-degree polynomial function is "all real numbers."

The given function is a linear function, degree 1. This is an odd degree, so the range of the function is "all real numbers."

  -∞ < f(x) < ∞

  (-∞, ∞) . . . . . in interval notation

Using the remainder theorem, the value of k in f(x) = 3x^2 + kx - 7 is 10

The given parameters are:

f(x) = 3x^2 + kx - 7

Divisor = x - 4

Remainder = 81

To solve for k, we use the remainder theorem

Set the divisor to 0

x -4 = 0

Add 4 to both sides of the above equation

x - 4 + 4 = 0 + 4

This gives

x = 4

Substitute x = 4 in the function f(x) = 3x^2 + kx - 7

f(4) = 3(4)^2 + k * 4 - 7

Evaluate the exponents

f(4) = 3 * 16 + k * 4 - 7

Evaluate the products

f(4) = 48 + 4k - 7

So, we have:

f(4) = 41 + 4k

The remainder is 81.

So, we have

41 + 4k = 81

Subtract 41 from both sides

4k = 40

Divide both sides of the above equation by 4

4k/4 = 40/4

Evaluate the division

k = 10

Hence, the value of k in f(x) = 3x^2 + kx - 7 is 10 using the remainder theorem

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Answer:

Step-by-step explanation:

We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:

[tex]5x+10x=510[/tex]

Solve for x

[tex]15x=510\\x=34[/tex]

Now multiply x by the corresponding percentages to find how much was invested into each percentage.

[tex]34*5=170[/tex]

[tex]34*10=340[/tex]

Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.

We can of course check our answer by adding 170+340 which equals our original investment of 510.

$1800 is invested at 5% and the remainder, $4200, is invested at 10%.

percentage, a relative value indicating hundredth parts of any quantity.

Let us consider the amount invested at 5% x.

The amount invested at 10% is then the remainder, which is:

$6000 - x

Now we can set up an equation for the total interest earned:

0.05x + 0.10($6000 - x) = $510

Simplifying and solving for x:

0.05x + $600 - 0.10x = $510

-0.05x + $600 = $510

-0.05x = -$90

Divide both sides by 0.05

x = $1800

Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.

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The probability that at least $15$ cents worth of coins come up heads is

P(H)=1/16

This is further explained below.

Generally, We are doing a simultaneous toss of four coins. How likely is it that every coin will land with the head side facing up?

It has been established by everyone who has participated so far that the solution is 116, which can be written as

(1/2)4=1/16.

On the other hand, a person who is just starting out can benefit from another method to see things.

I'm going to go ahead and make the assumption that each coin is balanced and that each side has an equal chance of facing up.

Each coin has the potential to exist in either of two states (heads or tails). Therefore, there are

2^4 = 16 different permutations (states) that the four coins may be in together as a group.

Only one of these possible permutations results in all heads. This results in the correct value of 1/16.

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