A shop makes £2,750 in March. It has an Easter sale and the profit for April is £3,162.50 Work out the percentage increase

Answer:

2

Step-by-step explanation:

3(6+x) = 24

18 + 3x = 24

3x = 24 - 18

3x = 6

x = 6/3

= 2

Answer:

25%

Step-by-step explanation:

5 out of (15+5 ) are cats

5/20 = .25 = 25 %

Answer:

25%

5 out of (15+5 ) are cats

5/20 = .25 = 25 %

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The most appropriate units for the rate of change in the table is automobiles per hour.

What is rate of change?

The rate of change function describes the rate at which one quantity changes in proportion to another quantity. The rate of change is determined, to put it simply, by dividing the amount of change in one item by the same amount of change in another. The rate of change formula provides a relationship indicating how one quantity changes in relation to a change in another quantity.

We are given that city planners study how many automobiles pass through a particular intersection over several hours.

This means that the graph depends on the automobiles that pass through a particular intersection every hour.

Hence, the most appropriate units for the rate of change in the table is automobiles per hour.

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The meridian at 180° longitude is commonly known as the International Date Line. As you pass the International Date Line, you either add a day (going west) or subtract a day (going east.)

The prime meridian and the International Date Line create a circle that divides Earth into the Eastern and Western Hemispheres.

The prime meridian has been set up in Greenwich, UK. It is an imaginary line that represents O degrees of longitude. This line, like all other meridians, runs from the North Pole to the South Pole and has the same length as all of the other meridians.

From the prime meridian, there are 180 degrees west and 180 degrees east. This is the line that divides the world in the Western and Eastern Hemispheres. The prime meridian is also the line from which time is counted either plus or minus, as it is at 0+ time zone, and everything east of it is plus, while everything west is minus. On the opposite side of the world of the prime meridian, we have the line that represents the start of time.

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Gong must have driven the truck for 149 miles as per the given problem.

Let’s discuss the problem in detail.

In addition to the base rate of $19.95, there was an extra fee of 71 cents for every mile driven. When Gong returned the truck, he was required to pay $125.74.

Now we have to calculate how far did he drive the truck before stopping.

First, let’s convert all dollars into cents.

Base fee = 1995 cents.

71 cents for each mile.

Total Gong gave 12574 cents.

Assume Gong drive for x miles.

Therefore,  12574 = 1995 + 71 * x

= 71x = 12574 - 1995

= 71x = 10579

= x = 10579/71 = 149 miles.

Hence, Gong drove the truck for 149 miles before stopping.

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Answer: 392

Surface area of a prism formula:  A= 2(l*w*h)

2*(5*8*12*5*8*12) =392

Step-by-step explanation:

Hope this helps :))))

Answer:

225 minutes

Step-by-step explanation:

[tex]\displaystyle \frac{40\text{ gallons}}{\text{min}}=\frac{9000\text{ gallons}}{\text{x min}}\\\\x=\frac{9000\text{ gallons}}{40 \text{gallons}}=225\text{ min}[/tex]

Answer:

The answer is 37.5%

Step-by-step explanation:

Answer:

37.5

Step-by-step explanation:

1% of 40= 0.4

0.4 x 25 = 62.5

100-62.5 = 37.5

The converse of the conditional statement is "if a ray divides an angle into two congruent angles, then it is an angle bisector"

The conditional statement is given as:

"An angle bisector is a ray that divides an angle into two congruent angles"

The converse of the conditional statement is such that:

The hypothesis and the conclusion are switched

So, we have the converse statement to be:

"if a ray divides an angle into two congruent angles, then it is an angle bisector"

Also, the converse of the statement is true

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We can use the Law of Cosines. The Law of Cosines states that for a triangle ABC with sides a, b, and c, and angle A opposite side c, the measure of angle A can be found: cos A = (b^2 + c^2 - a^2) / (2bc)

Measure or determine the lengths of all three sides of the triangle (a, b, and c). Let's say a = 5, b = 6, and c = 7.

Substitute the side lengths into the formula above and solve for cos A. cos A = (6^2 + 7^2 - 5^2) / (267) = 0.6

Use the inverse cosine function to find the measure of angle A in degrees or radians. In this case, A = 60 degrees.

To find the length of side HI in triangle HIG, we can use the Pythagorean Theorem. The Pythagorean Theorem states that for any right triangle, the length of the hypotenuse (the side opposite the right angle) is equal to the square root of the sum of the squares of the other two sides.

Measure or determine the lengths of the two legs of the triangle (HG and GI). Let's say HG = 8 and GI = 6

Substitute the side lengths into the formula HI^2 = HG^2 + GI^2 and solve for HI. HI = √(8^2 + 6^2) = √(64+36) = √100 = 10

Therefore, the length of side HI is 10.

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The complete question is:To find the measure of ∠A in ∆ABC, use the___(Pythagorean Theorem, Law of Sines, Law of Cosines). To find the length of side HI in ∆HIG, use the____(Pythagorean Theorem, Law of Sines, Law of Cosines) .

As the sides of the triangle 10 cm, 24 cm and 26 cm are triplets, the triangle will be a right angle triangle with side having length 26 cm as hypotenuse.

What is meant by triangle?

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The mark of the angles and sides of the triangle indicate that they are congruent.

Triangle diagram with side and angle indicators. To demonstrate if two or more sides are congruent, indicator marks are utilized (equal in measure).

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance.

When two angles and the included side of one triangle are equal to two angles and the included side of another triangle, two triangles are said to be congruent. PB = DE. The matching triangle portions are equal since the triangles are congruent.

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By square root 5 this we get the value √5 = 2.2360…Or √5 ≈ 2.24 with correct two decimal number fraction .

1. First, the number 5 can be expressed as 5.00000000, or 5 = 5.00 00 00 00.

2.Take the number whose square is less than five. The perfect square of the number 2 is 4, which comes after the number 5.

3..Enter 2 in both the divisor and quotient places so that it may be multiplied by 2 to get the answer 4. Add 4 to 5 to obtain the answer, which is 1.

4.Write two zeros after one and add them to the quotient. Add the decimal point after the first zero.

5.Now multiply by 2 to make 4 in the divisor. Pick a number that will go next to 4, ensuring that the result of multiplying the combination with that number will be less than or equal to 100. In order to make 42 times 2 equal 84, which is less than 100, we shall use 2 in this instance. To get the remainder, take 100 out of it immediately. The remainder is therefore 16.

6.Repetition of Step 5 up to 4 places of decimals with the addition of two more zeros.

7.Ultimately, you arrive at the quotient value, which is 2.2360, or around 1.236.

In light of this, the value of root 5 is, √5 = 2.2360… Or √5 ≈ 2.24

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The Pythagorean Triplets states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the right triangle. The Pythagorean Triplets is (3,4,5).

Pythagorean triplets:

The Pythagorean numbers consist of three positive integers a, b, and c such that a2 + b2 = c2. Such triples are usually written as (a, b, c), with a familiar example being (3, 4, 5). If (a, b, c) are Pythagorean numbers, then (ka, kb, kc) for all positive integers k. A primitive Pythagorean number is one in which a, b, and c are relatively prime (that is, they have no common divisors greater than 1). For example, (3, 4, 5) is a primitive Pythagorean number, but (6, 8, 10) is not. A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle and is always a right triangle.

Based on the Question:

Let the smallest even number be 2m

(i) (3,4,5)

  2m = 4

⇒ m = 2

⇒ m² −1 = 4−1 = 3

⇒ m² +1 = 4+1 = 5

∴(3,4,5) is a Pythagorean triplet.

(ii) (10,24,26)

  2m = 10

⇒ m = 5

⇒ m²−1 = 25−1 = 24

⇒ m²+1 = 25+1 =26

∴(10,24,26) is not a Pythagorean triplet.

(iii) (6,7,8)

  2m = 6

⇒ m = 3

⇒ m² −1 = 9−1 = 8

⇒ m² +1 = 9+1 = 10

∴(6,7,8) is not a Pythagorean triplet.

(iv) (2,3,4)

2m=2

⇒m=1

m² −1 = 1−1 = 0

m²+1 = 1+1 = 2

∴(2,3,4) is not a Pythagorean triplet.

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Equality is a fundamental human right, and it is essential for the development of any society. Equality is a complex concept that can be broken down into five distinct types.

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Answer:

The answer is rational.

I just got it right on the test.

The table of values of the function f(x) = 5x³ + 2x² - 6x + 7 are illustrations of polynomial functions

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The values on the table can be represented as:

(x, g(x)) = (-3, 0.375) (-1, 0.75) (1, 1.5) (3, 3) (5, 6) (7,12) (9, 24)

The above values show that as the values of x increases by 2, the values of function g(x) doubles.

Only an exponential function has this property.

Hence, the table of values represents an (a) exponential function.

3. Example of a polynomial function

A polynomial function is represented as:

y = ax^n  + bx^n-2 + .......... + d

Using the above format, the function that is a polynomial function is (a) f(x) = 5x3 + 2x2 – 6x + 7

4. Key features in the functions

The functions are given as,

f(x) = 2x² + 7x + 6

g(x) = 2x + 5

Set x to 0 to calculate the y-intercept

f(0) = 2(0) + 7(0) + 6 = 6

g(x) = 2⁰ + 5 = 6

Hence, both functions have the same (c) y-intercept

Questions 1 and 5 are not properly presented

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If the scale factor is 1/2, then every coordinate point of the original triangle is multiplied by the scale factor 1/2. Dilation with scale factor 1/2, then multiply by 1/2.

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Binary is also known as Base 2. This means it is composed of only 0's and 1's. For example 9 in binary/base 2 is 1001.

The binary number system or base two number system is a system of writing numbers using two symbols, namely 0 and 1.The modern binary number system was discovered by Gottfried Wilhelm Leibniz in the 17th century. This number system is the basis of all digital-based number systems. From the binary system, we can convert it to the Octal or Hexadecimal number system. We can also refer to this system as Bits, or Binary Digits. Binary groupings on a computer always add up to 8, with the term 1 Byte/byte. In computer terms, 1 Byte = 8 bits. Computer design codes, such as ASCII, American Standard Code for Information Interchange use a 1 Byte coding system.

In modern digital communication systems, where data is transmitted in the form of binary bits, a system is needed that is resistant to noise contained in the transmission channel so that the transmitted data can be received correctly. Errors in sending or receiving data are fundamental problems that have a very significant impact on communication systems.[2] The commonly used binary has 8 digit numbers and only contains the numbers 1 and 0, no other numbers. Base-2 ; Position Value: 2 · 2 ; Digit Value: 128s. 64s ; Binary Number: 1. 1.

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It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are greater than three sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 10.2 and 5.8

10.2 + 5.8 > 4.5

16 > 4.5

Now we add 5.8 and 4.5

5.8 + 4.5 > 10.2

10.3 > 10.2

Now we add 10.2 and 4.5

10.2 + 4.5 > 5.8

14.7 > 5.8

It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are greater than three sides.

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Every possible input value results in exactly one output value in a function. "The output is a function of the input," we state. The domain is made up of the input values, while the range is made up of the output values.

What do you mean by relation of a function?

A relation that states that there should be only one output for each input is known as a function. Alternatively, we could say that a special sort of relation (a set of ordered pairs) that adheres to the rule that every X-value should be associated with only one y-value is known as a function.

To ascertain whether a graph accurately depicts a function, use the vertical line test. If there are multiple points where the vertical line intersects the graph, the graph is not a function.

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Therefore , the solution of fraction is both of the options are incorrect in this case since the given expression results in a different equation than the ones chosen.

A part makes up the whole. In maths, the excess is divided by the denominator to represent a statistical as a divide. Both are integers in a simple fraction. The prime or the denominator of a complex fraction both contain a fraction. A proper fraction has an equal numerator.

Here,

The sentence that is given

13/15 | 2 - x | = 4/15

there are

| 2- x | = 1/15

Identify the absolute value.

=> 13/15 | 2- x | = 1/15

=> | 2- x | = 4 * 15 / 15 * 13

=> 1/13 = | 2- x |  

Therefore, if your query is complete, the appropriate answer is none of the above options. Neither choice is appropriate in this case since the given expression results in a new equation that isn't the same as the options made.

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The probability that a randomly selected customer purchases lettuce is 3/5.

What is Probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given that there are 100 customers the farmer provides.

The number of customers purchasing lettuce is 60.

The probability that a randomly selected customer purchases lettuce,

P(L) = Number of customers purchasing lettuce ÷ Total number of customers

[tex]\implies P(L) = \frac{60}{100} \\\implies P(L) = \frac{3}{5}[/tex]

Therefore, the probability that a randomly selected customer purchases lettuce is 3/5.

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Answer:

20 feet

Step-by-step explanation:

Using the Pythagorean theorem, the distance is [tex]\sqrt{12^2+16^2}=20[/tex] feet.

Answer: 45

Step-by-step explanation: 3 x 3 = 9 x 5 = 45

The measure of angle 3 in the given triangle is 141 degrees.

Angle 1 + Angle 2 + Angle 3 = 180°

So, Angle 3 = 180° - (Angle 1 + Angle 2)

Angle 3 = 180° - (28° + 11°)

Angle 3 = 141°

The sum of the three angles in a triangle is 180 degrees, so to calculate the measure of angle 3, we can subtract the measures of angles 1 and 2 from 180 degrees. In this case, angle 1 measures 28 degrees and angle 2 measures 11 degrees, so the measure of angle 3 is 180 degrees minus (28 degrees + 11 degrees), or 141 degrees.

The measure of angle 3 in the given triangle is 141 degrees.

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choose 50 distinct numbers between 0 and 99. For starlings and geese, follow the same procedure.

Measurement of the likelihood that an event will occur or a claim is true is done via probability theory, a branch of mathematics. The probability of an occurrence is a number between 0 and 1, with 1 denoting certainty and 0 roughly indicating how likely it is that the event will occur. A probability is a numerical representation of how likely it is that a certain occurrence will take place. Probabilities can also be expressed as ranges of 0% to 100% or 0 to 1. the proportion of occurrences in a whole set of equally likely options that lead to a particular event relative to the entire number of outcomes.

given

All of the blackbirds were numbered and tagged from 00 to 99. With a random number generator,

choose 50 distinct numbers between 0 and 99. For starlings and geese, follow the same procedure.

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the correct question is :- In search of a mosquito repellent that is safer than the ones that are currently on the market, scientists have developed a new compound that is rated as less toxic than the current compound, thus making a repellent that contains this new compound safer for human use. Scientists also believe that a repellent containing the new compound will be more effective than the ones that contain the current compound. To test the effectiveness of the new compound versus that of the current compound, scientists have randomly selected 100 people

The formula of an image in a straight line is y = mx + c, where m is the slope of the line, x is the x-coordinate of the point and c is the y-intercept.

A straight line is a line whose points all lie in the same plane and all have the same distance from each other, making them all equidistant. The line does not curve or bend in any way, and can extend infinitely in either direction. Straight lines are the most basic form of geometric shape and are the foundation of all other shapes. The line is defined by two points, known as its endpoints, and any point that lies on the line is called a point on the line. Straight lines are important in mathematics, as they are used to describe relationships between points on a graph, and they can also be used to define equations and boundaries.

The y-intercept is the point at which the line crosses the y-axis. The slope of the line is determined by the ratio of the change in the y-coordinate to the change in the x-coordinate. To calculate the slope of a line, the formula m = (y2 - y1)/(x2 - x1) is often used, where (x1, y1) and (x2, y2) are two points on the line. Using the slope and the y-intercept, the formula can be used to plot the points of the image along a straight line.

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The mass of the marble in kg is 486 kg .

Now, According to the question:

A sculptor needs to lift a piece of marble.  

It is a cuboid with dimensions 1 m by 0.6 m by 0.3 m.  

Marble has a density of 2.7 g/cm³.

We need to find what is the mass of the marble in kg .

Let's find out :

Volume of Cuboid = Length × Width × Height

Volume = (1m)(0.6m)(0.3m)

Volume = 0.18[tex]m^3[/tex]

Also , We know that

Density = [tex]\frac{Mass}{Volume}[/tex]

Density = 2.7[tex]\frac{g}{cm^3}[/tex]

Density = 2.7 [tex]\frac{10^-^3kg}{(10^-^2m)^3}[/tex]

Density = 2.7[tex]\frac{10^-^3kg}{(10^-^6m)}[/tex]

Density = 2.7[tex](10^-^3^+^6)kgm^-^3[/tex]

Density = 2.7[tex](10^6)kgm^-^3[/tex]

Now, Density = [tex]\frac{Mass}{Volume}[/tex]

2.7[tex](10^6)[/tex] = [tex]\frac{Mass}{0.18}[/tex]

Mass = [tex]2.7(10^6)[/tex] × 0.18

Mass = 486kg

Therefore , the mass of the marble in kg is 486 kg .

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