HOW TO TAKE OUT HCF BY PRIME FACTORISATION

The sοlutiοn οf the given prοblem οf arithmetic mean cοmes οut tο be  115.0625 is the tοtal οf the first ten terms in the prοvided sequence.

A list's typical values, alsο referred tο as the οrganisatiοn ’s gοals, are determined by adding up each value οn the list. The percentage οf list cοmpοnents with the highest density is then used tο adjust these average numbers. Mathematical grοwth trends are cοmparable. The actual average οf the digits 5, 7, as well as 9 is 4, and the number 21 becοmes seven by adding three (there are presently a number οf three-digit numbers).

Here,

The series is a geοmetric sequence with the cοmmοn ratiο r = 3/2 and the first term a = 1. We are instructed tο use the fοllοwing fοrmula tο determine the sum οf the first ten terms:

= >S = a(1 - rⁿ) / (1 - r)

Inputting the numbers prοvided yields:

=> S = 1(1 - (3/2)¹⁰) / (1 - 3/2)

=> S = (1 - 59049/1024) / (-1/2)

=> S = (-59048/1024) * (-2) (-2)

=> S = 115.0625

Cοnsequently, 115.0625 is the tοtal οf the first ten terms in the prοvided sequence.

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Work Shown:

1 ft = 12 inches

3 ft = 3*12 = 36 inches

1 yard = 3 ft = 36 inches

8 yards = 8*36 = 288 inches

x = number of presents

9x = amount of ribbon

9x = 288

x = 288/9

x = 32

There are no real numbers, actual solutions to the equation |x| = -5/8.

Several mathematical disciplines, including calculus, algebra, geometry, and number theory, employ the absolute value function. By removing the sign from a number or changing a complicated expression into a simpler one, it is frequently used to simplify expressions and equations. The distance between two points in n-dimensional space, where n is any positive integer, is also defined using the absolute value function. The absolute value function is also employed in many mathematical applications, including physics, engineering, economics, and finance, where it is utilised to describe quantities that can only have non-negative values.

There are no actual solutions to the equation |x| = -5/8. This is because |x| can never be negative because the absolute value function always returns a non-negative number. It follows that |x| cannot be equal to the negative integer -5/8.

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False. The value of money does not reside solely in the physical materials (paper or metal) from which it is made.

In modern economies, money has value because it is widely accepted as a means of exchange for goods and services. The value of money is derived from the trust people have in its ability to facilitate transactions and store value over time.

The physical materials used to make money (paper or metal) are simply a medium of exchange that represent the value of the currency. The value of a currency can fluctuate based on a variety of factors such as inflation, interest rates, and global economic conditions.

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A line passing through the coordinates (2, 8) & (-2, k) does have a 34 slope. As a result, k has a value of 5.

The slope of a line governs its steepness. Rise over fall is a mathematical formula that describes slope.

We can construct an equation & solve for k using the slope formula:

if (x1, y1) & (x2, y2) are indeed the provided locations, slope is defined as (y2 – y1)/(x2 - x1).

Inputting the specified values results in:

¾ = (k - 8)/(-2 - 2) (-2 - 2)

By condensing this equation, we obtain:

3/4 = (k - 8)/(-4) (-4)

The result of multiplying all sides by -4 is:

-3 = k - 8

5 Equals k when we add 8 to both sides.

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Therefore , the solution of the given problem of unitary method comes out to be P and R are separated by 5 units.

One may use this common convenience, already-existing variables, or all important elements from the original Bishop customizable question that adhered to a particular method to achieve the goal. If so, there will be another chance to get in touch with the object. If it doesn't, all of the crucial elements that make up an expression proof outcome will be lost.

Here,

The triangle formed by the points P, Q, and R in the provided diagram is right-angled.

We can determine the length of PR, the hypotenuse of this triangle, using the Pythagorean Theorem.

PQ² + QR² = PR²

The illustration shows that PQ and QR each equal four units.

By replacing these numbers, we obtain:

=> PR² = 4² + 3²

=> PR² = 16 + 9

=> PR² = 25

When we square the two edges, we obtain:

=> PR = √25

=> PR = 5

As a result, P and R are separated by 5 units.

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The volume of the rectangular prism is expressed as  a²b³ + ab²c

Some of the properties of a rectangular prism are;

From the information given, we have that;

The formula for calculating the volume of a rectangular prism is expressed as;

Volume = length× width × height

Now, substitute the values into the formula, we have;

Volume = b² × a × ab + c

Multiply the values, we have;

Volume = ab²(ab + c)

Volume = a²b³ + ab²c

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The distance between the points z₁ = 3+7i and z₂ = -5-2i is 12.04.

Distance is the total movement of an object without any regard to direction.

To calculate the distance between the two complex expression, we use the

formula below

Formula:

From the question,

Given the question

Where:

Substitute these values into equation 1

Hence, the distance is 12.04.

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The solution of the arithmetic expression is 4 2/5.

option C.

An arithmetic expression is a combination of numbers, operators (such as addition, subtraction, multiplication, and division), and parentheses, which are used to indicate the order of operations. Arithmetic expressions can be evaluated or simplified using the rules of arithmetic, which specify how the various operations should be performed.

We can solve this arithmetic expression by performing the multiplication operation first and then adding the results.

(2 x 2) + (2 x 1/5)

= 4 + 2/5

= 20/5 + 2/5

= (20 + 2) / 5

= 22/5

= 4 2/5

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The complete question is below:

Find 2 × 2  +  2 1/5 = ?

A. 2 2/5

B. 4 1/5

C. 4 2/5

D. 5​

The job is not yet complete at this stage, there is [tex]\frac{2}{40}[/tex] of the decoration is still left.

The expression 'percentage of job completion' refers to the amount of work that has been finished in relation to the total amount of work that needs to be done. This allows us to track the progress and evaluate a project's performance.

We are told,

Anna: [tex]\frac{2}{5}[/tex] * [tex]40 = 16[/tex]

Manna: [tex]\frac{1}{4}[/tex] * [tex]40 = 10[/tex]

Hanna: [tex]\frac{3}{10}[/tex] * [tex]40 = 12[/tex]

Summing total individual progress:

[tex]16+10+12=38[/tex]

Fraction of job that still left to do:

[tex]1 - \frac{38}{40} = \frac{2}{40}[/tex]

This implies that there is still [tex]\frac{2}{40}[/tex] decoration left to do the total job.

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You've asked an incomplete question. The full question reads;

Three friends Anna, Manna, and Hanna are doing the decorations for matric farewell dance. Anna put up two-fifth of the decoration, Manna put up one-fourth and Hanna put up three-tenth of the decoration. Is this job complete at this stage? If not, what fractional amount of job is still left to do? Show all necessary calculations to prove your answer.

Willka would need 6 liters of paint to cover an area of 27 square meters according to the ratio.

A ratio is a comparison of two or more values or quantities. It is a way of expressing the relationship between two or more quantities in a mathematical form. A ratio is typically expressed in the form of "a:b" or "a to b", where a and b are two values being compared.

According to question:

To find the coverage per liter of paint, we can divide the total area covered by the amount of paint used.

In this case, we can divide 13.5 m² by 3 L:

Coverage per liter = 13.5 m² / 3 L = 4.5 m²/L

This means that with 1 liter of paint, Willka can cover an area of 4.5 square meters.

If we know the area to be painted, we can use this ratio to determine how much paint is needed.

For example, if we want to paint an area of 27 square meters, we can calculate:

Paint needed = area to be painted / coverage per liter = 27 m² / 4.5 m²/L = 6 L

So Willka would need 6 liters of paint to cover an area of 27 square meters.

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Answer:

-1, -6, 13, 20 is an arithmetic sequence
d = 7

5, 12, 19, 26 is arithmetic sequence

d = 7

-3 - 9, -27, -81 is not an arithmetic sequence

Step-by-step explanation:

Common difference is the difference between successive terms and must be the same for all terms

-1, -6, 13, 20 is an arithmetic sequence with common difference:
6 - (-1) = 13 - 6 = 20 - 13 = 7

5, 12, 19, 26 is arithmetic sequence with common difference
12- 5 = 19 - 12 = 26 - 19 = 7

-3 - 9, -27, -81 is not an arithmetic sequence
The difference between successive terms is not the same
-9 - (-3) = -9 + 3= -6

but

-27 - (-9) = -27 + 9 = -18

In fact it is a geometric sequence where each term = x previous term

-9 = 3 x -3

-27 = 3 x -9

etc

Answer: 120

Step-by-step explanation: When 50 is divided by half, which is 100, and added 20 to it, it is 120

Answer:

45

step by step explaination:

Think about what same 2 numbers that, when added together make fifty. 25! so when you divide 50 by half, if equals 25. Then, add 25+20 to equal 45 :)

The possible ways of possibilities might refer to the different interpretations or perspectives that could be applied to a particular idea or concept. For instance, a philosopher might consider the different ways in which free will could be defined or understood.

The possible ways of possibilities might refer to the different ways in which a particular artistic vision could be realized. For instance, a filmmaker might consider the different ways in which a particular scene could be shot or edited to convey a certain emotion or message.

There are three possible ways to show off:

Cigar only

Watch only

Cigar and watch

To show off a cigar only, you have six options. To show off a watch only, you have four options. To show off both, you have six options for the cigar and four options for the watch, giving a total of  [tex]6 \times 4 = 24[/tex] options.

Therefore, So the total number of possibilities to show off is: 6 (cigar only) + 4 (watch only) + 24 (cigar and watch) =  [tex]34[/tex] Possibilities.

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The area of the triangles are

1. 105.84 cm²

2. 210 in²

3. 126 ft²

How to find the area of the triangles

The formula for the area of a triangle is:

Area = (1/2) * base * height

where

Using the formula we have that

1)

base = 16.8 and height = 12.6

= 0.5 * 16.8 * 12.6

= 105.84 cm²

2)

base = 20 in + 8 in = 28 in and height = 15

= 0.5 * 28 * 15

= 210 in²

3)

base = 12 ft and height = 21 ft

= 0.5 * 12 * 21

= 126 ft²

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Answer:

45 pounds

Step-by-step explanation:

using the conversion

16 ounces = 1 pound , then

6 ounces = [tex]\frac{6}{16}[/tex] = [tex]\frac{3}{8}[/tex] pound

total pounds sold on Friday is then

( 40 × [tex]\frac{3}{8}[/tex] ) + (40 × [tex]\frac{3}{4}[/tex] )

= (5 × 3) + (10 × 3)

= 15 + 30

= 45 pounds

Answer:

n=5

Step-by-step explanation:

First cross multiply to get:

36n = 180

Divide both sides by 36

36n/36 = 180/36

n=5

The slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of the original line y = 2x - 4 is 2.

To find the slope of the image after the transformation, we can apply the transformation rule to two points on the original line, and then find the slope of the line passing through the images of those two points.

Let's choose two points on the original line:

Point 1: (0, -4)

Point 2: (1, -2)

Now we apply the transformation rule to each of these points:

Point 1 image: (-0, -(-4)) = (0, 4)

Point 2 image: (-1, -(-2)) = (1, 2)

The images of these two points lie on the line y = -2x + 4. The slope of this line is -2.

Therefore, the slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.

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Therefore , the solution of the given problem of volume comes out to be a) 30 cubic inches , b)rectangular prism  and c) cylinder volume is 108.6 cubic inches.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The digits cm3 and in3 are two examples of cubic units. However, one can gauge an object's size using its bulk. Usually, the weight of an item is converted into mass measurements like kilogrammes or kilos.

Here,

a. By multiplying the rectangular prism toy's length, breadth, and height together, one can determine its volume:

Capacity is calculated using the formula LWH.

5 in. × 3 in. x 2 in.

thirty cubic inches of volume

Consequently, the rectangular prism toy has a capacity of 30 cubic inches.

b. I calculated the capacity of a rectangular prism using the following formula:

Capacity is calculated using the formula LWH.

c. The equation for a cylinder's volume is:

=> V = π x radius² x height

We can determine the radius using the following formula given that the cylindrical toy's height is 4 inches and its width, which is twice the radius, is 5.2 inches:

=> radius = circumference / 2.

=> radius=5.2 inches/two

=> radius: 2.6 inches

When we enter the numbers, we obtain:

Dimensions = 2.6 in x 2 in x 4 in

108.6 cubic inches of volume

Consequently, the cylindrical toy has a capacity of roughly 108.6 cubic inches.

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Answer:

There are 64 (4/ (1/16)) 1/16 of an inch in 4 inches.

Answer:

First, we need to calculate the total number of payments Ryan will make over 10 years, which is 10 years x 12 months/year = 120 months.

Next, we can use the formula for the present value of an annuity to calculate the maximum price of the boat:

PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)

where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the values we have:

PMT = $500

r = 0.13

n = 12 (since the loan is monthly)

t = 10

PV = $500 x [1 - (1 + 0.13/12)^(-12x10)] / (0.13/12)

PV = $44,484.72

Therefore, the maximum price for a boat that Ryan's budget can afford, rounded to the nearest hundred dollars, is $44,500.

Answer: 2.5 hours

Step-by-step explanation:

Let's call the number of signatures that Steve needs to collect "x". We know that Dirk has 20 signatures, so he needs to collect "x - 20" more signatures to have the same number as Steve.

We can set up an equation to represent this:

6h + 20 = 10h + x - 20

Simplifying this equation, we get:

x = 4h + 40

So, Steve needs to collect 4 signatures more per hour than Dirk to eventually collect the same number of signatures. We can solve for "h", the number of hours it will take for them to have the same number of signatures:

6h + 20 = 10h + (4h + 40)

6h + 20 = 14h + 40

8h = 20

h = 2.5

So, it will take 2.5 hours for Dirk and Steve to have collected the same number of signatures.

Answer:

From what I remember, words like "at least" mean that that's the minimum, so it can be more than that, but not less than. So I believe the inequality that would best represent this is n ≥ 4.

Answer:

n>=4

Step-by-step explanation:

Since the p-value (0.72) is greater than the significance level (0.05), we fail tο reject the null hypοthesis.

The null hypοthesis is  statement that assumes there is nο significant difference between twο οr mοre sets οf data. It is statement that can be tested and either accepted οr rejected based οn statistical evidence.

Tο test whether the number οf resignatiοns is unifοrm οver the fοur seasοns, we can use the chi-squared gοοdness οf fit test. The null hypοthesis fοr this test is that the number οf resignatiοns is unifοrm οver the fοur seasοns

Here are the steps tο perfοrm the chi-squared gοοdness οf fit test:

Determine the expected frequencies:

Tο determine the expected frequencies, we need tο assume that the null hypοthesis is true. Since there are fοur seasοns, each seasοn is expected tο have 1/4 οf the tοtal number οf resignatiοns. Therefοre, the expected frequency fοr each seasοn is 60/4 = 15.

Calculate the test statistic:

The test statistic fοr the chi-squared gοοdness οf fit test is calculated using the fοrmula:

χ²=∑(O-E)²/E

Using the οbserved frequencies, we get:

χ² = (20 - 15)²/15 + (15 - 15)²/15 + (10 - 15)²/15 + (15 - 15)²/15

= 1.33

Determine the p-value:

The p-value fοr the calculated test statistic is 0.72.

Make a decisiοn:

Since the p-value (0.72) is greater than the significance level (0.05), we fail tο reject the null hypοthesis.

In cοnclusiοn, based οn the chi-squared gοοdness οf fit test, we cannοt reject the null hypοthesis that the number οf resignatiοns is unifοrm οver the fοur seasοns.

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Answer: B

Step-by-step explanation:

Answer: The height of Nasim's kite above the ground is 51.79 feet

Step-by-step explanation

Let h represent the height from Nasim hand to the kite, hence:

sin(28) = h / 105

h = 49.29

Kite height above the ground = 2.5 + 49.29 = 51.79 feet

The height of Nasim's kite above the ground is 51.79 feet

Answer:

The height of Nasim kite above the ground is 51.79 feet

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height from Nasim hand to the kite, hence:

sin(28) = h / 105

h = 49.29

Kite height above the ground = 2.5 + 49.29 = 51.79 feet

The height of Nasim kite above the ground is 51.79 feet

The required graph is attached.

An organized representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The modification looks like this.

Combining two transformations results in the transformation of

h(x) to -h(x) -4.

1. An X-axis-centered reflection. Every point (x, y) in h(x) is transformed into (x', y'), where x' = x and y' = -y. Hence, (x, y) (x, -y)

2. A 4-unit translation of each reflected point, where the x value remains constant, but the y value is translated downward to become y'-4 = -y -4

Every coordinate (x, y) in h(x) will be transformed to the following as a result of both transformations: (x, -y -4)

Given that the graph is made up of two straight lines that intersect at the origin, all we need to do is select any three points in h(x), determine their transformed coordinates, and then connect them using straight lines: h(x0 -h(X) - 4 (-2, 4) (-2, -4-4) =(-2, -8) (0, 0) (0, -0 - 4) =(0, -4) (4, 2) (4, (4, -6)

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Using the expected value of probability formula, the value of  Σ[x•P(x)] is -0.65

The expected value of a probability distribution is a measure of the central tendency of the distribution. It is also known as the mean or the average value of the distribution.

To calculate the expected value, we multiply each possible outcome by its corresponding probability and then sum up the products. Symbolically, if X is a random variable with possible outcomes x1, x2, ..., xn and probabilities p1, p2, ..., pn, then the expected value of X, denoted E(X), is given by:

[tex]E(X) = \sum_{i=1}^{n} x_i p_i[/tex]

To find Σ[x•P(x)] we need to multiply each x-value by its corresponding probability and then sum up the products.

So we have:

Σ[x•P(x)] = (-1)(0.999) + (349)(0.001)

Σ[x•P(x)] = -0.999 + 0.349

Σ[x•P(x)] = -0.65

Therefore, Σ[x•P(x)] is equal to -0.65.

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