One-seventh of a number, increased by twelve?

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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If three points that are provided are not collinear then the only possible polygon that can be formed by connecting these points would be a triangle.

A polygon is a closed two-dimensional shape made up of straight line segments called sides. It is formed by connecting three or more points (vertices) in a specific order. The sides of a polygon do not intersect, and each vertex is connected to exactly two sides. The region enclosed by the sides of a polygon is called its interior, while the points outside the polygon but on the same plane are called its exterior.

If three points are provided and they are not collinear (i.e., they do not lie on the same straight line), then the only possible polygon that can be formed by connecting these points would be a triangle(refer image attached). A triangle is a polygon with three sides and three angles.

The specific type of triangle (e.g., equilateral, scalene, isosceles) would depend on the lengths of the sides and the measure of the angles formed by connecting these points in a specific order. Different orders of connecting the points may result in different types of triangles.

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The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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Answer:

25 in²

Step-by-step explanation:

formula for area of a triangle:

1/2(bxh)

1/2(5x10)

1/2(50)

25

Answer:

D. \(25^{2}\)

Step-by-step explanation:

Answer: ):

Step-by-step explanation:

Answer:

second side is 16

third side is 38

Step-by-step explanation:

x + (x - 8) + (x + 14) = 78

3x + 6 = 78

3x = 78 - 6

3 x = 72

x = 72/3

x = 24

24 + (24 - 8) + (24 + 14) = 78

24 + 16 + 38 = 78

Answer:

Step-by-step explanation:

Answer:

$343.45

Step-by-step explanation:

$318.75 x 1.0775 = $343.45

or

$318.75 x 0.0775 = $24.70

$318.75 + $24.70 = $343.45

The selling price of the lawn mower is $343.45 if the customer purchased a lawn mower for a total purchase price of $318.75.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We have a customer purchased a lawn mower for a total purchase price of $318.75.

Sales tax rate = 7.75%

Sales tax amount = 7.75% of $318.75

Sales tax amount = $24.64 ≈ $24.70

Original price = 318.75 + $24.70 = $343.45

Thus, the selling price of the lawn mower is $343.45 if the customer purchased a lawn mower for a total purchase price of $318.75.

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a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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200 pounds need to collect to earn the $50.00. Divide the cost per pound from the total amount needed, \(\frac{50.00}{0.25}\)= 200 pounds.

The official money of the U.k. and its regions is the GBP, or British pound sterling. The Pound is the earliest currency that is still accepted as legal tender in the entire world. The GBP, represented by pound sign (£), has one of the greatest trade volumes worldwide.

The development of the pounds sterling -The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from. During the years, the pound banknotes underwent various revisions before being initially printed by the Bank of England and over 300 years ago.

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The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Answer: A) 6x = 54; x = 9 times older

Step-by-step explanation:

9 x 6 = 54

Answer:

The value of e is approximately 2.71828.

Step-by-step explanation:

An exponential function is of the form:

\(y=a^{x}\)

Here a is any value that is more than 0.

The natural form of an exponential function is:

\(y=e^{x}\)

Here e is known as the Euler's number.

The value of e is approximately 2.71828.

Answer:

A P value of 0.05 is considered as the gold standard of the significance level, but it depends on the type of study

Step-by-step explanation:

The scientists make experiments to collect relevant data and their conclusions are often based on statistical analyses of their results. In scientific method, the correct interpretation of the statistical results may be critical for obtaining conclusions. The statistical significance level or 'P value' is an index aimed at summarizing the results of a research. Karl Pearson created the term P value in 1900 and used this index in association with his chi-square test. The P-value can be defined as the probability of observing statistical results that are equal to or more extreme than the one observed when null hypothesis is correct. A P value of 0.05 is generally considered to be correct in many studies; however, this index may change according to the level of significance required for a particular case. It is also important to note the factors that may lead to errors in P value calculation (P>0.05): small sample sizes, errors in study design, errors in measurement methods, etc.

Answer:

2. C. 50.3 ft²

3. A. 75.4 ft²

Step-by-step explanation:

The lateral surface area of a cylinder is the area of the curved surface of the cylinder. It is calculated by multiplying the circumference of the base by the height of the cylinder. The formula for the lateral surface area of a cylinder is:

Lateral Surface Area = 2πrh

Where:

The total surface area of a cylinder is the area of the lateral surface plus the area of the two circular bases. The formula for the total surface area of a cylinder is:

Total Surface Area = 2πrh + 2πr^2

Where:

2.

r=2 ft

h=4 ft

Lateral Surface Area = 2πrh=2*22/7*2*4=50.3 ft²

3.

Total Surface Area = 2πrh + 2πr^2=2*22/7*2*4+2*22/7*2

=50.3+25.1=75.4 ft²

The sum (A+B)(x) and difference (A-B)(x) of two quadratic functions A(x) and B(x) were found, along with their values for x=5, vertices, intercepts, and where they are increasing/decreasing.

To find (A+B)(x), we simply add the two functions:

(A+B)(x) = A(x) + B(x) = (\(-0.25x^2+20x\)) + (\(-0.19x^2+15.2x\)) = \(-0.44x^2\) + 35.2x

To find (A-B)(x), we simply subtract B(x) from A(x):

(A-B)(x) = A(x) - B(x) = (\(-0.25x^2+20x\)) - (\(-0.19x^2+15.2x\)) = \(-0.06x^2\) + 4.8x

When x=5, we can evaluate each expression:

(A+B)(5) = \(-0.44(5)^2\) + 35.2(5) = 60

(A-B)(5) = \(-0.06(5)^2\) + 4.8(5) = 12

To find the vertices and intercepts of the functions A(x) and B(x), we can use the vertex and intercept formulas for quadratic functions:

For A(x):

Vertex = (-b/2a, f(-b/2a)) = (-20/-0.5, A(20/-0.5)) = (40, 400)

x-intercepts: 0 = \(-0.25x^2\) + 20x, so x = 0 or x = 80

y-intercept: A(0) = 0

For B(x):

Vertex = (-b/2a, f(-b/2a)) = (-15.2/-0.38, B(15.2/-0.38)) = (40, 304)

x-intercepts: 0 = \(-0.19x^2\) + 15.2x, so x = 0 or x = 80

y-intercept: B(0) = 0

Both functions are decreasing for x < 40, and increasing for x > 40. The vertex (40, 400) is the maximum point for A(x), and the vertex (40, 304) is the maximum point for B(x).

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she could have scored the 10 points in 302400 ways.

The given parameters are

n= total points =10

r1 =one-point free throw = 1

r2 = two-point field goals = 2

r3 =  three-point field goals = 3

The number of ways (k) she could have scored the points is:

k=(n!)/(r1!×r2!×r3!)

The factorial function is a mathematical formula represented by an exclamation mark "!".

k= 10!/(1!×2!×3!)

k= 3628800/(1×2×6)

k= 302400

so.. she could have scored the 10 points in 302400 ways.

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

The difference in the maximum values of the functions ​g(x) ​and ​f(x)​ is 3

The functions are given as

f(x) = -(x - 3)² + 9

Table of g(x)

x    −3 −4 −2 0 −1  4

g(x) 0   8   1  12  2  8

The maximum value of f(x) is when the root expression is 0

i.e. -(x - 3)² = 0

So, we have

Max f(x) = 0 + 9

Max f(x) = 9

For the table of values, we have

Max g(x) = 12

The difference between these values is

Difference = 12 - 9

Evaluate

Difference = 3

Hence, the difference is 3

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The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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it a centimeter question

Answer:

-15

-26

-29

-43

Step-by-step explanation:

Answer:

\(\boxed{x \geq 353}\)

Step-by-step explanation:

Hey there!

Info Given

- Dot is solid

- Line goes to the right

- Dot is at 353

So by using the given info we can conclude that the inequality is,

x ≥ 353

Hope this helps :)

Answer:

Inequality: 100 + 50w ≥ 18000

What to put on graph: w ≥ 358

Lagrange interpolation process to obtain a polynomial to approximate these data points is L(x) = (7/6)x³ - (5/3)x² + (19/6)x + 7

The polynomial interpolation is a technique that is used to find a polynomial function that passes through a given set of points. This is particularly useful in situations where we have a set of data points, and we want to find a smooth function that connects these points.

The given set of data points can be represented as (x0, y0), (x1, y1), ... , (xn, yn), where xi and yi represent the x and y coordinates of the ith point. In our case, the data points are (0, 7), (2, 11), (3, 28), and (4, 63).

To find the polynomial function that passes through these points, we can use a method called linear system. In this method, we assume that the polynomial function has the form:

pn(x) = a0 + a1x + a2x^2 + ... + anxn

Alternatively, we can use the Lagrange interpolation process to obtain a polynomial to approximate these data points. In this process, we construct a polynomial that passes through the data points by using the Lagrange basis polynomials. The Lagrange basis polynomial Li(x) is defined as:

Li(x) = (x - xi) / (xi - xj)

where i and j are indices that range from 0 to n, and i is not equal to j.

Using the Lagrange basis polynomials, we can construct the Lagrange polynomial L(x) as:

L(x) = y0L0(x) + y1L1(x) + ... + ynLn(x)

where yi is the y-coordinate of the ith point. This polynomial L(x) is the polynomial that passes through the given set of data points.

In this one, the Lagrange polynomial can be written as:

L(x) = (7/6)x³ - (5/3)x² + (19/6)x + 7

This polynomial can be used to approximate the values of y for any x within the range of the data points.

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9514 1404 393

Answer:

  (c)  16

Step-by-step explanation:

The figure will be a parallelogram when opposite angles are congruent. We already know X and Z are congruent, so we need to find x so that W = Y.

  x +3 = 2x -13

  16 = x . . . . . . . . . . add 13-x to both sides

Answer:

The suspect possesses 0.4 ounces of cocaine.

Step-by-step explanation:

Mass Units Conversion

The mass can be expressed in several units like grams, kilograms, ounces, pounds, etc. Each unit can be converted to any other multiplying by a fixed number.

The international conventions state that 1 gr = 0.035274 ounces.

If a suspect is in possession of 10 grams of cocaine, its equivalent to ounces can be calculated as 10*0.035274=0.35 oz. Rounding to the nearest tenth it would be 0.4 oz.

Since 1/8 = 0.125 and 1/2 is 0.5, our subject should be charged as a Class C felony

The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).

We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.

To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.

Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.

To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.

This is the equation of the line in standard form.

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Using proportions, it is found that they need 750 white beads and 150 red beads.

A proportion is a fraction of a total amount.

Researching the problem on the internet, it is found that the pattern states the following:

Hence:

\(\frac{5}{6} \times 900 = 750\)

\(\frac{1}{6} \times 900 = 150\)

They need 750 white beads and 150 red beads.

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