which function has a period of pi

The first term and the last term in the arithmetic progression are -2.5 and 22.5 respectively.

In Mathematics, the sum of a geometric sequence is given by this mathematical expression:

[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]

Where:

Mathematically, the sum of an arithmetic sequence is calculated by using this expression:

Sn = n/2(2a₁ + (n - 1)d)

Where:

Since the sum of all the terms in the geometric progression is equal to the sum of all the terms in the arithmetic progression, we have:

256(1 - 0.5^8)/(1 - 0.5) = 51/2(2a₁ + (51 - 1)0.5)

256(1 - 0.00390625)/(0.5) = 25.5(2a₁ + 25)

255/0.5 = 51a₁ + 637.5

510 = 51a₁ + 637.5

51a₁ = -127.5

a₁ = -2.5

For the last term, we would use the following formula:

aₙ =  a₁ + (n - 1)d

a₅₁ =  -2.5 + (51 - 1)4

a₅₁ =  -2.5 + (50)0.5

a₅₁ = 22.5.

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Answer:

Below

Step-by-step explanation:

The shaded area is the area GREATER than ('>') the graph (it is ABOVE the graph)

the two zeroes (where it crosses the x -axis) of the graph are - 6 and 18

so the parabola   is  y = (x+6)(x-18)

  but we want the shaded region so it becomes   y> (x+6)(x-18)

      It is '>' because the shaded area DOES NOT INCLUDE the graph line (that is why it is a dashed line)

The initial value problem calculator is a tool used to calculate differential equations.

An instrument for solving ordinary differential equations with initial conditions is an initial value problem calculator. Finding a function that solves a given differential equation and a set of initial conditions is the goal of this calculator, a particular kind of differential equation problem. The differential equation, the beginning conditions, and other pertinent parameters are entered into the calculator, which then generates a solution that fulfils the initial conditions.

Usually, the answer is provided as a function that specifies how the system behaves over time. In disciplines like physics, engineering, and economics, where differential equations are regularly employed to represent dynamic systems, these calculators are widely used. They can be helpful for obtaining an understanding of a system's behavior and for predicting its upcoming trends

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The value of "5.5 inches" after conversion to millimeter is equivalent to 139.7mm .

To convert the number 5.5 inches to millimeters, we use the conversion factor ;

The Conversion Factor is defined as a mathematical ratio which is used to convert a measurement from one unit to another unit .

We know that  1 inch is approximately equal to 25.4 millimeters,

So , the conversion factor is 25.4 mm ;

On multiplication , we get ;

⇒ 5.5 inches × 25.4 millimeters/inch = 139.7 millimeters .

Therefore, 5.5 inches is equal to 139.7 millimeters .

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20 kg is approximately equal to 44.0925 pounds ( rounded to four decimal places )

The conversion factor to convert kg to pounds is 2.20462

1 kg = 2.20462 pounds

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in pounds = The mass in kg × conversion factor

Substitute the values in the equation

1 kg = 2.20462 pounds

20 kg =  20 × 2.20462

Multiply the numbers

= 44.0925 pounds  ( rounded to four decimal places )

Therefore, 20 kg is 44.0925 pounds

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The length of the line segment AB is 38.6 m. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle falls under the umbrella of the branch of mathematics known as trigonometry.

We are given a right angled triangle, with angle ACB = 90° and angle CAB = 75°.

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos θ = 10/x

Here, θ = 75°

So,

⇒cos 75° = 10/x

⇒x = 10/cos 75°

⇒x = 38.6

Hence, the length of the line segment AB is 38.6 m.

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250 milliliters is equal to 0.25 liter

The conversion factor to convert milliliter to liters is 0.001

Therefore, the equation will be,

1  ml = 0.001 liter

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The volume in liters = The volume in ml × conversion factor

Substitute the values in the equation

1 ml = 0.001 liters

250 ml =  0.001 × 250

Multiply the numbers

= 0.25 liters  

Therefore, 250 ml is 0.25 liters

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The equation of the line through (1, 2) which is perpendicular to y =(-1/5)x + 1 is y = 5x - 4

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

The standard form of a linear function is:

y = mx + b

where m is the rate of change (slope) and b is the y intercept

Two lines are perpendicular if the product of their slope is -1.

Given the line y =(-1/5)x + 1. The line perpendicular to y =(-1/5)x + 1 would have a slope of 5.

The line  perpendicular to y =(-1/5)x + 1 that includes the point (1, 1), is:

y - y₁ = m(x - x₁)

substituting:

y - 1 = 5(x - 1)

y = 5x - 4

The equation of the line is y = 5x - 4

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Answer:5:1

Step-by-step explanation:

Answer: $5938.92

Step-by-step explanation:

GST = original price * 10% = $5999 * 0.1 = $599.90

The total GST inclusive price would be the sum of the original price and the GST, which is:

GST inclusive price = original price + GST = $5999 + $599.90 = $6598.90

Sale price = (GST inclusive price + GST) * (1 - 10%) = ($6598.90 + $599.90) * 0.9 = $6598.80 * 0.9 = $5938.92

Therefore, the correct sale price should have been $5938.92, and the car yard should have paid the 10% GST on each sale, as advertised.

The hypergeometric distribution should be used instead of the binomial distribution. The correct option is d. Sampling does not involve replacement,

What is binomial distribution ?
The binomial distribution is a probability distribution that describes the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The probability of getting exactly k successes in n trials with probability of success p is given by the formula:

[tex]P(k) = (n choose k) * p^k * (1 - p)^(n - k)[/tex]

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items out of n, and is equal to:

[tex](n choose k) = n! / (k! * (n - k)!)[/tex]

where n! represents n factorial, which is the product of all positive integers up to n.

Given by the question:
The correct answer is d. sampling does not involve replacement.

Therefore, when sampling does not involve replacement, the hypergeometric distribution should be used instead of the binomial distribution.

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30 centimeter is approximately equal to 11.8110 inches ( rounded to four decimal places )

To convert 30 cm to inches, we can use the following formula:

1 cm = 0.393701 inches

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in centimeter

Substitute the values in the equation

30 cm = 30 x 0.393701

Multiply the numbers

= 11.8110 inches ( rounded to four decimal places )

Therefore, 30 centimeter is 11.8110 inches

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The converted value of 100 percent to a decimal is equal to 1 which is denoted by 1.00.

Converting 100 percent to decimal is divide 100 by 100 we get

1 percent is ( 1 / 100 )decimal

Substitute the required value of 100 percent we get,

⇒ 100 percent = ( 100 / 100 ) decimals

⇒ 100 percent = ( 1.00 ) decimals

Therefore, the conversion of 100 percent to decimal is given by 1.00 .

The above question is incomplete , the complete question is:

How to convert 100 percent as a decimal ?

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Answer:

The value of x would make the ratio 1:1 is 6.

Step-by-step explanation:

The given ratio is:

Surface Area : Volume = 6x^2 : x^3

To find the value of x that makes this ratio 1:1, we need to set the two parts of the ratio equal to each other and solve for x:

6x^2 = x^3

Divide both sides by x^2 to obtain:

6 = x

Therefore, the value of x that makes the ratio 1:1 is x = 6.

Answer:

100.48ft

Step-by-step explanation:

Use circumference formula

C=2(pi)r

Answer:

[tex]15.6 \div 100 = .156[/tex]

Step-by-step explanation:

100 is 10 to the second power. Since you are dividing, move the decimal point in 15.6 two places to the left. So .156 is your answer.

Answer:0.156

Step-by-step explanation:

It takes approximately 35.35 seconds to fill the glass 50%. Rounded to two decimal places, the answer is 35.35 seconds.

The volume of the cylindrical glass can be calculated as:

V = πr²h

where r is the radius (half of the diameter), h is the height, and π is the mathematical constant π (approximately 3.14).

Since the diameter is 3 inches, the radius is 1.5 inches. The height is 10 inches. Therefore, the volume of the glass is:

V = π(1.5)²(10) ≈ 70.69 cubic inches

To fill the glass 50%, we need half of the volume:

V/2 ≈ 35.35 cubic inches

The faucet dispenses water at a rate of 1 cubic inch per second, so the time it takes to fill the glass 50% is:

t = (V/2) / (1 cubic inch per second) ≈ 35.35 seconds

Therefore, it takes approximately 35.35 seconds to fill the glass 50%. Rounded to two decimal places, the answer is 35.35 seconds.

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The vertex form of a parabola is  y = a(x - h)² + k , where: a — Same as the a coefficient in the standard form; h — x-coordinate of the parabola vertex; and. k — y-coordinate of the parabola vertex.

The extremal value of a quadratic curve is represented by the vertex of a parabola, which is a point. The quadratic portion is still valid because two is our variable's most important power (x). For a parabola to open up, the vertex can either be a minimum or a maximum (for a parabola opening down).

As an alternative, we might state that the parabola's vertex is where its symmetry axis meets it.

The vertex is typically represented by the point P(h,k), where h stands for the x-coordinate and k for the y-coordinate.

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On converting 168 lbs to Kilogram , we get that 168 lbs is equivalent to  76.188 Kg .

The conversion factors can be used to convert between pounds and kilograms. For example ;

To convert 1 pound to kilograms: We multiply the number of pounds by 0.4535  .

We have to convert 168 pounds to kilograms ;

So , we multiply the given weight in pounds with 0.4535 .

On multiplying ,

We get ;

⇒ 168 pounds = 168 × 0.4535 Kg ;

⇒ 168 pounds = 76.188 Kg .

Therefore , 168 lbs is approximately equal to 76.188 Kg .

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Option C is the correct answer, as it states that the difference between 3 1 4 and 1 2 3 is 1 7 12The question is asking if Emily has 123 more cups of flour than sugar.

To check if this is true, we can subtract the amount of sugar from the amount of flour, and see if the difference is equal to 123.

Emily uses 1 2 3 cups of sugar and 3 1 4 cups of flour.

Therefore, the difference between the amount of flour and the amount of sugar is:

3 1 4 − 1 2 3 = 12/4 + 3/4 - 3/12 = 9/12 + 9/12 - 1/12 = 17/12

The difference between the amount of flour and the amount of sugar is 17/12, not 123. Therefore, we cannot agree with Emily's statement that she has 123 more cups of flour than sugar.

Option C is the correct answer, as it states that the difference between 3 1 4 and 1 2 3 is 1 7 12, which is the same as our calculation above. Options A and B are incorrect because they give incorrect values for the difference. Option D is incorrect because it gives the sum of the two quantities, not the difference.

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Answer:

its c. all credits go to the girl/boy up there.

Step-by-step explanation:

Answer:

the next fraction in the sequence is 5/7.

Step-by-step explanation:

If int j = 3, then the value of J++ is 3.

The post-increment operator ++ increments the value of the variable by 1, but returns the original value of the variable. So when j++ is executed, j is incremented to 4, but the expression evaluates to the original value of j, which is 3.

To see the effect of the increment operator, you could print the value of j before and after the j++ operation:

int j = 3;

System.out.println(j);  // output: 3

j++;

System.out.println(j);  // output: 4

Note - that the pre-increment operator, ++j, would increment the value of j and return the new value, so ++j would evaluate to 4.

j++ is a shorthand notation in many programming languages, including Java and C++, which increments the value of the variable j by 1.

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The value of 7*2 will be = 14

As per question,

We need to find the value of 7*2

For finding the value of given expression, we will use the identity of multiplication.

So, applying the multiplication identity:

We can write the above as:

(7*2) = (7+7) = 14

Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilise every day.

Multiplication is the process of taking one integer and multiplying it by a certain number of times. 5 multiplied by 4 is 5 + 5 + 5 + 5 = 20. We took the number 5 and multiplied it by four. This is why multiplication is often known as "times".

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The probability that Ben will find two worthless $10 bills in his wallet is practically impossible.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.

The probability that each bill will be a worthless $10 bill is very low. This is because the US Federal Reserve has discontinued the production of $10 bills in 2006, so the likelihood of finding two of them in circulation is highly unlikely. Additionally, bills are often replaced after a certain amount of time due to wear and tear, so the probability of finding two bills in circulation that are both from the discontinued series is even lower.

The chances of finding two $10 bills from the discontinued series in circulation is so extremely rare that it has been estimated to be one in ten million. Even though it is possible to find two bills from the discontinued series, it is extremely unlikely that one would carry two of them in their wallet. Therefore, the probability that Ben will find two worthless $10 bills in his wallet is practically impossible.

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The perimeter of the room is approximately 49.272 feet.If the area of a rectangular room is 150 square feet, and one side of the room is 11 feet, we can find the length of the other side by dividing the area by the length of the known side:

Length × Width = Area

Width = Area ÷ Length

Width = 150 ÷ 11

Width ≈ 13.636 feet

Now that we know the length and width of the room, we can calculate the perimeter by adding up the length of all four sides:

Perimeter = 2 × Length + 2 × Width

Perimeter = 2 × 11 + 2 × 13.636

Perimeter ≈ 49.272 feet

Therefore, the perimeter of the room is approximately 49.272 feet.

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Connie's total bill is sum of trail mix and water will be  $9.13.

What is sum ?
In mathematics, the sum refers to the result of adding two or more numbers together. It is a basic arithmetic operation, often used in many different mathematical concepts and calculations. The symbol for addition is '+', and the sum of a set of numbers is often represented using the capital Greek letter sigma (∑).

According to the question:

Connie's total bill would be the sum of the cost of the trail mix and the cost of the water, which is:

Total bill = cost of trail mix + cost of water

Total bill = $6.98 + $2.15

Total bill = $9.13

Therefore, Connie's total bill was $9.13.

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Based on the conversion factor, 35km is equivalent to approximately 21.75 miles.

Kilometers and miles are units of distance measurement used in different parts of the world. While kilometers are the standard unit of distance in most countries, miles are widely used in the United States, the United Kingdom, and a few other countries.

A kilometer is approximately 0.621371 miles, which means that 1 mile is roughly 1.609344 kilometers.

To convert 35km to miles, we need to use this conversion factor. We can start by setting up a proportion:

35 km = x miles

1 km = 0.621371 miles

Multiplying both sides by the conversion factor, we get:

35 km x 0.621371 miles/1 km = x miles

Simplifying this expression, we get:

21.748485 miles = x miles

In conclusion, measurements are essential in our daily lives, and knowing how to convert one measurement to another can be beneficial. In this article, we explored what 35km in miles means and how we can convert kilometers to miles. Remember that 1km is approximately 0.621371 miles, and we can use this conversion factor to convert any distance measurement from kilometers to miles or vice versa.

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The given system of equations, option C. The system has a nontrivial solution.

When given a system of three equations with three unknowns, it is possible to determine if the system has a nontrivial solution by using row operations and Gaussian elimination. Nontrivial solutions are solutions that are not all 0.

In the given system of equations, the left-hand side of each equation consists of 3 variables, 4x₁-6x₂+13x₃, 4x₁-10x₂-x₃, and 8x₁+4x₂+14x₃. By performing row operations on the equations, the augmented matrix can be reduced to the form of the identity matrix.

The first row operation performed is to subtract the first row from the second row, resulting in

=> 4x₁-10x₂-x₃ = -2x₁-2x₂+13x₃.

The second row operation is to subtract twice the first row from the third row, resulting in

=> 8x₁+4x₂+14x₃ = 0.

The third row operation is to divide the second row by -2, resulting in

=> 4x₁-10x₂-x₃ = x₁+x₂-13x₃.

This reduced form of the augmented matrix can then be rearranged to the form of the identity matrix, indicating that the system of equations has a nontrivial solution.

Therefore, the answer to the question is that the system has a nontrivial solution

Hence the option (c) is correct.

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The six trigonometric functions are mathematical functions used in geometry and trigonometry to describe the relationships between angles and sides of triangles.

The six trigonometric functions are:

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle.

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle.

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side of a right triangle.

Cotangent (cot): The cotangent of an angle is the ratio of the length of the adjacent side to the length of the side opposite the angle of a right triangle.

Secant (sec): The secant of an angle is the reciprocal of the cosine of the angle, or the ratio of the hypotenuse to the adjacent side of a right triangle.

Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of the angle, or the ratio of the hypotenuse to the opposite side of a right triangle.

The six trigonometric functions can be used to solve various problems in mathematics, physics, and engineering, among other fields.

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