Mom is getting food ready for my birthday party! Including me, there will be 28 people at the party. Mom is baking cookies for us! She can bake 24 cookies per batch. How many batches should I tell Mom to make so we can each have 5 cookies?​

The sum of the multiples of 9 till 81 is 405 by arithmetic progression.

We have to sum the multiples of 9 up to 81

= 9 + 18 + … +  45  + …+ 72 + 81

We will use arithmetic progression for this.

we get that:

initial term = a = 9

Common difference = d = 9

n = 9

Sum of terms = n / 2 ( 2 a + ( n - 1) d )

Sum = 9 / 2 (2( 9) + 8 ( 9))

sum = 9 / 2 (18 + 72)

Sum = 9 / 2 ( 90)

Sum = 810 / 2

Sum = 405

Therefore, we get that, the sum of the multiples of 9 till 81 is 405 by arithmetic progression.

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Answer:

a bunch of gas money

Step-by-step explanation:

Answer:

Increased towing capacity

Step-by-step explanation:

?

Only function 2 represent a linear function.

Herein we find four cases of functions, of which we are asked to determine if each function is linear or not. A function is linear if and only if the change between every pair of two consecutives values of x and y is the same. Now we proceed to check each case:

Function 1

Δx = - 1 - (- 3) = 2; Δy = 6 - 2 = 4

Δx = 1 - (- 1) = 2; Δy = 18 - 6 = 12

Δx = 3 - 1 = 2; Δy = 54 - 18 = 36

The function is not linear.

Function 2

Δx = 5 - 1 = 4; Δy = - 1 - 1 = - 2

Δx = 9 - 5 = 4; Δy = - 3 - (- 1) = - 2

Δx = 13 - 9 = 4; Δy = - 5 - (- 3) = - 2

The function is linear.

Function 3

Δx = 5 - 4 = 1; Δy = - 10 - (- 5) = - 5

Δx = 6 - 5 = 1; Δy = - 13 - (- 10) = - 3

Δx = 7 - 6 = 1; Δy = - 15 - (- 13) = - 2

The function is not linear.

Function 4

Δx = 1 - (- 2) = 3; Δy = 5 - 4 = 1

Δx = 4 - 1 = 3; Δy = 6 - 5 = 1

Δx = 7 - 4 = 3; Δy = 1 - 6 = - 5

The function is not linear.

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The value of x is 12.

Given on a line lie three points e, f and g.

therefore, ef = x ₋ 4

fg = 2x ₋ 9 and

eg = 13

we can say that ef and fg must add upto eg.

⇒ ef ₊ fg = eg

⇒ x ₋ 4 ₊ 2x ₋ 19 = 13

⇒ 3x ₋ 23 = 13

⇒ 3x = 13 ₊ 23

3x = 36

x = 36/3

x = 12

hence we get the value of x as 12.

now substitute x value to get ef and fg values.

ef = x ₋ 4  = 12 ₋ 4 = 8

fg = 2x ₋ 19 = 2(12) ₋ 19 = 24 ₋ 19 = 5

Hence we get the value of x as 12.

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The answers to both the subparts are as follows:

So, the cycle's velocity-time graph:

Now,

Then,

Therefore, the answer to both the subparts are as follows:

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Zeros of a Polynomial Function

An important consequence of the Factor Theorem is that finding the zeros of a

polynomial is really the same thing as factoring it into linear factors. In this section we

will study more methods that help us find the real zeros of a polynomial, and thereby

factor the polynomial.

Rational Zeros of Polynomials:

The next theorem gives a method to determine all possible candidates for rational zeros

of a polynomial function with integer coefficients.

Rational Zeros Theorem:

If the polynomial ( ) 1

1 1 ... n n P x ax a x ax a n n

− = + ++ − + 0 has integer

coefficients, then every rational zero of P is of the form

p

q

where p is a factor of the constant coefficient 0 a

and q is a factor of the leading coefficient n a

Example 1: List all possible rational zeros given by the Rational Zeros Theorem of

P(x) = 6x

4

+ 7x

3

- 4 (but don’t check to see which actually are zeros) .

Solution:

Step 1: First we find all possible values of p, which are all the factors

of . Thus, p can be ±1, ±2, or ±4. 0 a = 4

Step 2: Next we find all possible values of q, which are all the factors

of 6. Thus, q can be ±1, ±2, ±3, or ±6. n a =

Step 3: Now we find the possible values of p

q by making combinations

of the values we found in Step 1 and Step 2. Thus, p

q will be of

the form factors of 4

factors of 6 . The possible p

q are

12412412412

, , , , , , , , , , ,

11122233366

± ± ± ± ± ± ± ± ± ± ±±

4

6

50 books can be purchased with $ 350.

We have the data:

Books Cost (dollars)    Amount left (dollars)

            1                                    343

            2                                   336

            3                             336 - 7 = 329

            4                             329 - 7 = 322

            7                             322 - 21 = 301

           14                             301 - 49 = 252

Cost of 1 book = $ 7

Cost of b books = 7 × b = 7 b    

Amount of budget after b books = 350 - 7 b

We can buy = 350 / 7 = 50 books before spending the entire amount.

Therefore, we get that 50 books can be purchased with $ 350.

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Answer:

135

Step-by-step explanation:

135 > 13.1 > 13.09 > √169 (√169 = 13)

I hope I could help ^^

Answer:

Step-by-step explanation:

Favorite hobby is gaming

Favorite activity is football

Using proportions, her commission would be of $3,700.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Her commissions are divided as follows:

Hence the total commission is:

0.15 x 5000 + 0.25 x 1000 + 0.3 x 9000 = $3,700.

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Answer:

D

Step-by-step explanation:

Area equal LxWxH

2x2.5x3.5=17+5

The amount of material needed to make the box is 41.5 ft².

The surface area of a figure is the number of unit squares it takes to cover the entire surface without gaps or overlaps. If a three-dimensional figure has flat sides, the sides are called faces. The surface area is the total of the areas of the faces.

Given that, a rectangular storage box is to be made with length is 3.5 feet, the width is 2 feet, and the height is 2.5 feet.

For finding the same, we will find the surface area of the box,

Surface area of the box = 2(length·width + width·height + height·length)

Therefore,

SA = 2(3.5x2+2x2.5+3.5x2.5)

SA = 2 x 20.75

SA = 41.5

Hence, the amount of material needed to make the box is 41.5 ft².

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The correct option is c. True.

If the intquantity and decprice variables contain the numbers 3 and 15.75, respectively, the condition if intquantity > 0 and also intquantity < 10 or else decprice > 20 will evaluate to "True."

C++ is an object-oriented programming (OOP) language that many consider to be the best for developing large-scale applications.

C++ is a subset of the C programming language. Java is a programming language that is similar to C++ but is optimized for the dispersion of program objects over a such as the Internet.

Now, as per the question, construct a program in C++.

#include <iostream>

using namespace std;

int main()

{

  int intQuantity = 3;

  int decPrice = 15.75;

    if (intQuantity >0 && intQuantity <10 || decPrice>20){

      cout<<"True";

   }

   else{

      cout<<"False";

   }

  return 0;

}

Because the condition if (intQuantity >0 && intQuantity 10 || decPrice >20) evaluates to true, the output from in this program will be "True." The reason for this is that in programming, the Logical Or (| |) evaluates to true when either or both conditions are met.

Although the condition decPrice>20 is false in the question, the very first condition intQuantity >0 && intQuantity 10 is true, so the OR evaluates to true.

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The complete question is -

If the intQuantity and decPrice variables contain the numbers 3 and 15.75, respectively, the condition If intQuantity > 0 And Also intQuantity < 10 OrElse decPrice > 20 will evaluate to ____.

a.No

b.Yes

c.True

d.False

Answer:

give me one second brooo

Explanation:

The inequality that represents the possible area of the triangle is 2/7a < 10

The solution to the inequality is a < 35

From the question, we are to write and solve an inequality that represents the possible area, a, of the triangle

From the given information,

The base of the triangle is given by

b = 2/7a

Also, from the given information,

The base of the triangle is less than 10

That is,

b < 10

Then,

we can write that

2/7a < 10

This is the inequality that represents the possible area of the triangle

Now, solve the inequality

2/7a < 10

Multiply both sides of the equation by 7/2

7/2× 2/7a < 7/2× 10

a < 7 × 5

a < 35

Hence, the inequality that represents the possible area of the triangle is 2/7a < 10

The solution to the inequality is a < 35

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Answer:

thank me that's is my answer

The number of players in the team will be 18.

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;

Total cost to go to a tournament = $1885.50

Rent for bus = $949.50

Budget for meal for each player = $52

Now,

Let the number of players = x

So, We can formulate;

⇒ $949.50 + $52x = $1880.50

Solve for x, as;

⇒ $949.50 + $52x = $1880.50

Subtract 949.50 both side, we get;

⇒ $949.50 + $52x - $949.50 = $1880.50 - $949.50

⇒ $52x = $931

⇒ x = $17.90

After round we get;

⇒ x = $18

Thus, The number of players in the team will be 18.

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The population that would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases is All 513 bolts that were randomly selected.

Generalizing the conclusions from a study can only be done with a sample that is well-represented. The question here says that all 513 bolts were chosen without bias. This means that a fair conclusion can be reached from the sample.

So, the results that occur from studying the 513 bolts can be sure to produce accurate results. Moreso, the population is large, thus, the population can be used to generalize conclusions.

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No, the triangle with vertices (-1, -1), (2, 3), (-4, 3) is not equilateral.

An equilateral triangle is a triangle that has all three sides of equal length, also known as a "regular" triangle.

Now, as per the given question.

The vertices are given as (-1, -1), (2, 3), (-4, 3).

Find the distance between the two corresponding vertices.

First, find distances between (-1, -1), (2, 3) lets say 'c'.

c² = (-1-3)² + (-1-2)²

c² = 4² + 3²

c² = 16 + 9

c² = 25

c = 5

Now, find the distance between (2, 3), (-4, 3), let say it 'd'.

d² = (-4-2)² + (3-3)²

d² = 36

d = 6

Now, find the distance between (-1, -1), (-4, 3) say it 'p'

p² = (-1-(-4 ))² +(-1-3)²

p² = 3² +4²

p² = 25

p = 5

As, all three distances are not same. Thus, the given vertices does not form equilateral triangle.

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The correct question is-

An equilateral triangle has sides of equal length. Determine whether the triangle with vertices (-1, -1), (2, 3), (-4, 3) is equilateral.

The piecewise function represented by the graph is:

A piecewise function is a function that has different definitions, depending on the input.

For x to the left of 0, inclusive, the function is constant at y = -3, hence the definition is:

f(x) = -3, x ≤ 0.

For x to the right of 0, with an open interval, the function is linear, with an intercept of 3(when x = 0, y = 3) and a slope of -3(the function fell from y = 3 to y = 0 when x moved from x = 0 to x = 1), hence:

f(x) = 3 - 3x, x > 0.

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Jason is incorrect, because inequality signs change when we multiply/divide by negative numbers, and we need to follow the signs to make sure we use the correct one.

Well, Jason says that you can solve an inequality by replacing the sign by an equal sign, solve the equation as you already have done a thousand times, and then put the inequality sign again.

Now, this is clearly incorrect, because inequalities have a really nice property. If you multiply or divide both sides of the inequality by a negative number, then the "direction" of the sign changes.

This means that if we have an inequality like:

-2x > 10

And we divide both sides by -2, we should get:

x < 10/-2

x < -5

Where the direction of the sign changed.

If you did what Jason said, the direction of that sign would not have changed, and thus, you would have got an incorrect solution for the inequality.

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The parametric equation of our line is;

x = 1 + 3t

y = -1 + 3t

z = 4 + 8t

We want to find parametric equations for the line through (3, 3, 8) that is perpendicular to the plane x − y + 4z = 5

A vector perpendicular to the plane ax + by + cz + d = 0 is given by (a, b, c).

So a vector perpendicular to the plane x − y + 4z - 5 = 0 is (1, -1, 4)

The parametric equation of a line through (x₀, y₀, z₀) and parallel to the vector (a, b, c) is;

x = x₀ + ta

y = y₀ + tb

z = z₀ + tc

So the parametric equation of our line is;

x = 1 + 3t

y = -1 + 3t

z = 4 + 8t

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If a chip is randomly drawn from the bag, the probability it will be a red or a blue one is P(red or blue) = 10/19.

Probability of an event A is the number of event A divided by all possible outcomes. Mathematically,

P(A) = n(A)/n(S)

where:

n(A) = number of event A

n(S) = number of all possible outcomes or sample space.

Suppose A and B are independent outcomes, then:

P(A or B) = P(A) + P(B)

In the given problem:

Number of chips:

Blue = 3

Red = 7

Yellow = 4

Green = 5

Total chips = 3 + 7 + 4 + 5 = 19

If a chip is randomly drawn, the probability it will be a red one is:

P(red) = 7/19

Similarly,

P(blue) = 3/19

Using the probability formula for independent outcomes:

P(red or blue) = P(red) + P(blue)

                      = 7/19 + 3/19 = 10/19

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Answer:

121°

Step-by-step explanation:

These are supplemental angles.  a straight angle is 180 degrees.

180 - 59 = 121

Answer: m2=121 degrees

Step-by-step explanation:

m1+m2=180 ==> m1 and m2 are on a straight line. Straight lines measure 180 degrees and are called straight angles. m1 and m2 are supplementary angles, so they add up to 180 degrees.

59+m2=180

59-59+m2=180-59

m2=180-59

m2=121 degrees

Answer:

9

Step-by-step explanation:

Answer:

F is inversely proportional to d^2when F=9,d=

Step-by-step explanation:

The equation of Leo's line is given by: 3 (y - G) = ( F - x)

Given: An equation of a line on a grid, about which another line is perpendicularly.

To find: Equation of the perpendicular line.

Finding:

=> m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{4-1}{2-1}=\frac{3}{1} = 3[/tex]

The equation of the line becomes:  [tex]y-y_0=3(x-x_0)[/tex]

    2. Since the line passes through (1,1), the final equation of the line can be given by:

=> y - 1 = 3 ( x - 1)

=> y = 3x - 3 + 1

=> y = 3x - 2

=> m' = -1/m

=> m' = -1/3

=> [tex]3(y-y_0)=(x_0-x)[/tex]

    2. Since the perpendicular line passes through the point (F,G), the equation of the line will be: 3 (y - G) = ( F - x).

Hence, The equation of Leo's line is given by: 3 (y - G) = ( F - x).

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!!Figure is not clear!! Formulae is provided below.

To fence the triangular section Mr. Johnson has to find the perimeter of the triangular field.

To find the perimeter of the triangle one has to add the length of all the three sides of the triangle.

Similarly we can also find the perimeter of other plane figures by adding the lengths of all the sides of the figure.

Suppose if the length of the sides of a triangle is a,b and c units.

Then the perimeter of the triangular field will be = (a + b + c) units.

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Answer:its 180 cm

Step-by-step explanation:

Answer:D

Step-by-step explanation:

√81 - √25 = 9 - 5 = 4

√64 + √25 = 8 + 5 = 13

√64 - 31 = 8 - 31 = -23

Answer:

Hope this helps :)

If it is seven and three thousandths then the answer would be...

7.003

This is because after the decimal the first place is tenths, then, hundredths, and lastly, thousandths. So the 3 would be in the thousandths place. Also, 7 is in the ones place which is before the decimal.

Answer: -19.7        

Step-by-step explanation:

62.7 - 82.4=

-(82.4-62.7)= -19.7        ==> switch the numbers and negate the expression to get the same answer