The objective is to determine how many numbers must be selected form the set to guarantee that at least one pair of these numbers add up to 16.
Arrange the members of {1, 3, 5, 7, 9, 11, 13, 15} as pigeon holes as follows:
If 5 numbers out of 4 groups are chosen, then by Dirichlet’s principle there is at least 2 numbers in the same group, and their sum will be equal to 16.
It is not sufficient to choose 4 numbers.

The cosine function will be equal to f(x) = 3cos(π(6/7)x) + 4

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

A generic cosine function is written as:

f(x) = Acos(wx + p) + M

where:

A = amplitude

w = angular frequency

p = phase

M = midline.

We know that:

The midline is 4, then  M = 4

The amplitude is 3, then A  = 3

There is no information about the phase, so p = 0.

And we know that the period is 7/3.

The period is written as T, and the relation between the period and the angular frequency is:

T = 2π/w

Then we have:

7/3 = 2π/w

w = (2π)*(3/7) = π  x (6/7)

where π= 3.14

Then we have:

w =  π  x (6/7)

A = 3

M = 4

p = 0

Hence, the cosine function is: f(x) = 3cos(π(6/7)x) + 4

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Answer:

The four main types of factoring are the Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes.

Step-by-step explanation:

Hope it helps!

Answer:

• Two $10 bills

• Four $20 bills

Step-by-step explanation:

We are told that Gerardo received a number of $20 and $10 bills upon changing a $100 bill at the bank. We are also told that he received 2 more $20 bills than $10. Then we are asked to find the number of each kind of bill.

To solve this problem, let's consider the number of $10 bills he received was [tex]x[/tex]. Since he received 2 more $20 bills, he got [tex](2 + x)[/tex] $20 bills. Therefore, in total he received:

[tex]10 \times x + 20 \times (x +2)[/tex]

This should add up to $100 since that is the amount he changed. Solving the resulting equation for [tex]x[/tex] will give us the number of $10 bills he received.

[tex]10 \times x + 20 \times (x +2) = 100[/tex]

⇒ [tex]10x + 20x + 40 = 100[/tex]

⇒ [tex]30x +40 = 100[/tex]

⇒ [tex]30x + 40 - 40 = 100 - 40[/tex] [Subtracting 40 from both sides of equation]

⇒ [tex]30x = 60[/tex]

⇒ [tex]\frac{30}{30}x = \frac{60}{30}[/tex]              [Dividing both sides of the equation by 30]

⇒ [tex]x = \bf 2[/tex]

Therefore, he received 2 $10 bills.

Since the number of $20 bills is 2 more than the number of $10 bills,

no. of $20 bills = 2 + 2

                         = 4

Answer:

109 it is the answer

Step-by-step explanation:

02947 029377393

Answer:

3 x −3

Step-by-step explanation:

Use the given functions to set up and simplify f−x.

Nucleic acids offer variability through their ability to undergo mutations.

Mutation is a process in which a gene or organism undergoes a change in its DNA sequence, resulting in a new trait or altered function. Mutations can occur naturally or be induced by environmental factors such as radiation, chemicals, or viruses. Mutations can be beneficial, harmful, or have no effect on the organism. Some mutations can cause genetic disorders or even cancer.

Mutations are changes in the sequence of nucleotides that make up a gene, resulting in a different form of the gene. These mutations can lead to different traits in the organism, providing a greater range of variability in the gene pool. Mutations can be caused by environmental factors such as radiation or chemicals, as well as random changes that occur as DNA is replicated. The range of variability offered by mutations is one of the main reasons why organisms are able to adapt to their environment.

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Answer:0.3

Step-by-step explanation:

Answer:

Step-by-step explanation: Bro honestly math is some bull

The area of the floor of a square room in square meter whose each side is 800 cm is 640000 cm ^ 2.

The area of a square or square shaped figures is:

area = side x side or (side) ^2

The length of the side of the floor of the given square room is:

800 cm

Therefore, area of the floor of the given square room is:

800 cm x 800 cm = 640000 cm ^ 2.

Thus, the area of the floor of the given square room in square meter whose each side is 800 cm is 640000 cm ^ 2.

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The monthly payment with given simple interest will be $673.

What is simple interest?

Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount.

Simple interest formula is given as:

SI=P*R*T/100

Where SI = simple interest

P = principal

R = interest rate (in percentage)

T = time duration (in years)

In order to calculate the total amount, the following formula is used:

Amount (A) = Principal (P) + Simple Interest (SI)

Now,

Amount to Borrow=$28716

Rate=3.12%

Time=4 years

SI=28716*3.12*4/100

=$3584

Total amount to pay=28716+3584

=$32300

Hence,

        monthly payment for 4 years =32300/48

  monthly payment=$673

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Answer:

17.13953 mph

I just did it these ways with a speed calculator

Step-by-step explanation:

Answer:

4

2

3

4

5

3

7

3

4

5

4

3

2

Step-by-step explanation:

The area of triangle whose sides are 9 cm 12 cm and 15 cm is 54 cm².

The formula to be used for calculating of the area of triangle is -

A = ✓s(s-a) (s-b) (s-c), where a, b and c are sides of triangle. S is (a+b+c)/2.

Let us assume side a to be 9 cm, side b to be 12 cm and side c to be 15 cm. Calculating the value of s.

s = 9 + 12 + 15/2

Adding values on Right Hand Side of the equation

S = 36/2

Performing division

S = 18

Keep the values in formula of area -

A = ✓18 × (18 - 9) × (18 - 12) × (18 - 15)

Performing subtraction

A = ✓18 × 9 × 6 × 3

Performing multiplication

A = ✓2916

Taking square root

A = 54 cm²

Thus, the area of triangle is 54 cm².

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The coordinate of F is (3, 3).

What is the formula to find the midpoints?

Diagonals of a parallelogram bisect each other, meaning they divide each other into equal parts.

The formula is used to find the midpoints are as follows;

(x1 + x2)/2, (y1+y2)/2

DF and EG are diagonals of parallelogram DEFG, therefore:

The midpoint of DF = midpoint of E

Then,

The midpoint of D(0, 2) and F(x, y) is:

(0 + x)/2 , (2 + y)/2

The midpoint of E(-1, 5) and G(4, 0) is;

(-1 + 4)/2, (5 + 0)/2

Comparing the equation;

x/2 = 3/2

x = 3

2+y/2= 5/2

y = 3

Hence, the coordinate of F is (3, 3).

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The option that is not a possible way to evaluate that function and find the correct answer is given as follows:

Answer 1: See what x is when y=-5.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 3x² - 2x + 5.

At x = -5, the numeric value is obtained replacing the two instances of x by -5, hence:

f(-5) = 3(-5)² - 2(-5) + 5 = 90.

Meaning that only answer 1 is incorrect.

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The decay factor for the car will be equal to 0.925 or 92.5%

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Answer:

HK and GJ is the diameter of circle L.

Step-by-step explanation:

Answer:

Either GJ or HK

Step-by-step explanation:

Im not sure if im reading ot correctly bit ye diameter is the full line in the moddle and they both are so it's probably those 2

The difference in the account balance after 30 years if the electrician's investment was compounded continuously instead of twice per year would be $83.63.

Value is the worth of something that is measured in terms of its quality, importance, and usefulness. It is a fundamental concept in economics, finance, and business, as it reflects the perceived benefits of a good or service compared to its cost. Value can be subjective, as it is often based on personal opinion or preference. It can also be quantified and measured in terms of money, time, or resources.

Compound interest is the concept of earning interest on the initial principal and any interest previously earned. When the interest is compounded continuously, the interest is added to the principal more frequently than when it is compounded semiannually, resulting in a larger final balance.

The electrician's initial investment of $9,000 compounded semiannually at 2.45% for 30 years would have a balance of $18,685.71.

However, if the same investment had been compounded continuously at 2.45%, the balance after 30 years would be $18,769.34, which is $83.63 more than the semiannually compounded balance.

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Answer:

$83.63

Step-by-step explanation:

The rest are wrong.

The cost of  the two clubs will be the same after 4 sessions

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Let x represent the number of session

Since One tennis club charges $ 34 per session to play tennis. We can write the cost as:

cost = 34x

And another tennis club charges an annual fee of $ plus $ 22 per session. We can write the cost as:

cost = 48 + 22x

At the same cost, we have:

34x = 48 + 22x

34x - 22x = 48

12x = 48

x = 48/12

x = 4

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Complete Question

One tennis club charges $30 per session to play tennis. Another tennis club charges an annual fee of $48 plus $22 per session. After how many sessions is the cost at the two clubs the same?

According to the lengths of their sides, triangles can be classified into three types which are: Scalene, Isosceles. Equilateral.

Triangles come in six different types and are divided into two groups, namely sides and angles. The three triangles are categorised as equilateral triangles, isosceles triangles, and scalene triangles based on their sides. Triangles can be classified as acute, obtuse, or right-angled depending on the angle at which they are formed.

Triangles are divided into three sorts based on their sides.

Equilateral triangle: A triangle is deemed to be an equilateral triangle if its three sides are all the same length.

Isosceles triangle: An isosceles triangle is one in which each of its sides are equal.

A triangle is said to be a scalene triangle if each of its three sides is a different length.

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The equation of this perpendicular line is Y=-4x+15

What is perpendicular line ?

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The 7 stages of problem-solving are a widely recognized framework for approaching and solving problems. The stages include identifying the problem, collecting information, developing the possible solutions, evaluating those solutions, choosing a solution, implementing it and evaluating the results.

Identifying the problem: This involves clearly defining and understanding the problem, including its scope and the factors that contribute to it.

Gathering information: This involves researching and collecting data to better understand the problem and potential solutions.

Developing possible solutions: This involves generating a list of potential solutions to the problem, including both traditional and creative options.

Evaluating possible solutions: This involves analysing each potential solution to determine its feasibility and potential impact.

Choosing a solution: This involves selecting the best solution based on the evaluation in the previous stage.

Implementing the solution: This involves putting the chosen solution into action, including any necessary planning and preparation.

Evaluating the results: This involves monitoring and assessing the effectiveness of the solution and making any necessary adjustments.

It's important to note that the problem-solving process is not always linear, and it's possible to move back and forth between the stages as new information is gathered or new issues arise. Additionally, it's important to be flexible and open-minded throughout the problem-solving process to consider different possibilities.

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To solve a two-step inequality, you can follow these steps:

Isolate the variable on one side of the inequality by performing the same operation on both sides of the inequality.

If the inequality is a "greater than" or "less than" inequality, you will need to reverse the inequality if you multiply or divide by a negative number.

Solve the inequality by isolating the variable.

Check your solution by plugging it back into the inequality and making sure it is true.

Graph the solution in number line

Example:

x + 2 > 6

x > 4

(x+2) > 6

x > 4 (by isolating x)

It is important to remember that if we multiply or divide by a negative number, we have to reverse the inequality sign.

It is also important to remember that after solving the inequality, it is necessary to check the solution by substituting it back into the original inequality to make sure it works.

The three types of co-ordinates are:

(i) Cartesian co-ordinates

(ii) cylindrical co-ordinates

(iii) spherical co-ordinates

Three digits are used to indicate distances in the three-dimensional flat space of the Cartesian coordinate system, often known as the "rectangular coordinate system." The East/West direction, North/South direction, and Elevation are represented by the first two digits, respectively.

The Cartesian coordinate system is a prime example of a coordinate system. Two perpendicular lines are picked in the plane, and a point's coordinates are assumed to be the signed distances between the lines.

So, three types of co-ordinates are:

(i) Cartesian co-ordinates

(ii) cylindrical co-ordinates

(iii) spherical co-ordinates

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The number -5 represents the rate of decreasing 5 centimeters per hour.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A candle's height is modeled by the equation y = -5x + 30, where x is the hours spent burning, and y is the height of the candle in centimeters.

The number -5 represents the rate of decreasing 5 centimeters per hour and 30 represents the initial length of the candle.

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The number that satisfies the given condition is x= 64.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Let the number be x.

Then one eight of the number can be represented as follows: [tex]\frac{1}{8}x[/tex]

The number 17 exceeds by 9, this is written as [tex]\frac{1}{8}x + 9 =17[/tex]

Using the equation, we find the value of x by isolating the variable:

[tex]\frac{1}{8}x + 9 =17\\\\x+ (8)(9) = (17)(8) \\\\x = 136 - 72\\\\x=64[/tex]

Hence the number x that satisfies the given condition is 64.

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Answer:

x <−11 or x >7

Step-by-step explanation:

Answer:

x < –11 or x > 7p

explanation:

I got it right on the test.

No , 904 is not divisible by 3 because sum of 9+0+4 =13 which is not divisible by 3 so number 904 is not divisible by 3

There are 301 numbers less than 904 divisible by 3, as per arithmetic progression.

What is an arithmetic progression?

"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."

Let, there are 'n' terms less than 904 divisible by 3.

Now, the first term divisible by 3 is(a) = 3.

The second term divisible by 3 is = 6.

Therefore, the common difference between terms divisible by 3 is(d)

The last term that is less than 904 and divisible by 3 is() 903.

Now, if we compare it with arithmetic progression, then:

The required number is 301.

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