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An equation in which the highest power of the variable is 1 is known as a linear equation. It is also termed a one-degree equation.

There are two types of linear equations, linear equations in one variable and linear equations in two variables. The standard form of a linear equation in one variable is Ax + B = 0. Where x = variable, A = coefficient and B = constant.

The standard form of a linear equation in two variables is Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always formed in a straight line. That is why it is named a 'linear equation'.

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The horizontal line of the graph is known as x axis,

The term graph in math is defined as the visual representation of data or the function in math.

Here we have to find the definition for the horizontal line on a graph.

Here we know that the straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.

On the other hand, we all also know that the straight line that does not make any intercept on the X-axis and it can have an intercept on Y-axis is called horizontal line.

And we all also know that the straight line that is parallel to the x-axis and where all the points on the line have the same y-coordinate and basically all horizontal lines are parallel to each other.

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this question is related to numbers and the solution is as follows,

Rover eats 3/4 can of cat food in a day.

given

in 60 days it will consume 60 x 3/4 cans = 45 cans of cat food

3 cans cost = $5 and a pack contains 3 cans

45 cans is equivalent to= 45/3

= 15 packs

15 packs cost = 15 x $5 = $75

So it will cost $ 75 to feed Rover for 60 days

Bobo eats 1/2 of a can of cat food per day

in 60 days it will consume 60 x 1/2 cans = 30 cans of cat food

3 cans cost $5 and a pack contains 3 cans

30 cans are equivalent to 30/3 = 10 packs

10 packs will cost = 10 x $5 = $50

So it will cost $50 to feed Bobo for 60 days

In total, in 60 days it will cost $75 +$ 50 = $125 to feed both cats in 60 days.

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As calculated from the data we get the result as that $ 125 is required for the cat food of both the cats in a month.

We are given that in 60 days he will consume  ,

60 x 3/4 cans

= 45 cans of cat food

The cost of 3 cans cost = $5

and one pack has 3 cans in it.

Therefore, 45 cans is equivalent to

= 45/3

= 15 packs

So , the cost of 15 cans will be ,

15 packs cost = 15 x $5 = $75

Therefore ,$75 is used for 60 days of cat food for Rover.

Now , we know that Bobo eats 1/2 of a can food in a day.

Therefore, in 60 days he will  eat,

60 x 1/2 cans

= 30 cans of food

As we know, 3 cans cost $5 and a pack contains 3 cans

Therefore, 30 cans = 30/3 = 10 packs

10 packs will cost = 10 x $5 = $50

So , $50 is spend to feed Bobo , in a month.

Therefore , if will combine their cost we will get that ,

$75 +$ 50 = $125 is required to feed both the cats in one month.

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The odds against Arjun taking the longest trail are 4 : 9 .

The probability that when Arjun is hiking from the mountain lodge to the nearby summit, he takes the longest trail, is 5 / 9.

This means that the odds that Arjun will not take the longest trail, or rather, the odds against him taking the longest trail, will be the difference between 1 and the probability that he takes the longest trail:

= 1 - 5 / 9

= 4 / 9

When given as a ratio, this would be:

=  4 : 9

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That would be [tex] \sqrt{113} [/tex]

The option that best explains the relationship between altitude and the boiling point is; A. There is a strong negative correlation between altitude and water's boiling point.​

In correlation coefficient, we know that a positive correlation occurs when both x and y values increase at the same time while negative correlation occurs when y value decreases as x value increases.

Now, we see from the given graph that y-values are decreasing with increasing x-values and as such this is a negative correlation.

Now, we want to determine whether it is a strong or weak correlation.

The scatterplot is close to being a straight line and as such the correlation coefficient will be close to - 1 which makes it a strong negative correlation.

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Answer: A is correct

Step-by-step explanation:

took the test

The required length of the curst on the edge of one piece of pizza 1.5 π. Option D is correct.

Perimeter is the measure of the figure on its circumference. The perimeter of a circle is given as 2πr, where r is the radius of the circle.

here,
A pizza has an 18-inch diameter
Circumference of pizza = 18π

The pizza is sliced into 12 pieces, and the length of the crust on the edge of one piece of pizza is given as,
= 18π/12
= 1.5π

Thus, the required length of the curst on the edge of one piece of pizza is 1.5 π.

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Answer: It gets smaller

Step-by-step explanation: When you divide something by anything, the place value of the digits decreases. The digits move to the right since the number gets smaller, but remember, the decimal point does not move.

The quotient of 1.782 × 10⁹ and 8.1 × 10⁶ in scientific notation is 2.2 × 10². The result is obtained by using the quotient rule.

Several rules for exponents are

Find the quotient of 1.782 × 10⁹ and 8.1 × 10⁶!

Dividing the first number by the second using the quotient rule, it would be

= (1.782 × 10⁹) / (8.1 × 10⁶)

= (1.782/8.1) × (10⁹/10⁶)

= 0.22 × 10⁹⁻⁶

= 0.22 × 10³

In scientific notation, we should write a.b × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

So,

0.22 × 10³ = 2.2 × 10²

Hence, the result of 1.782 × 10⁹ divided by 8.1 × 10⁶ in scientific notation is 2.2 × 10².

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The answer to the iterated integral after the evaluation is 2.

The iterated integral evaluates to the area of the region bounded by the curves x = 0, x = y, and y = π/2, which can be calculated by setting up a double integral. The outer integral is with respect to x, from 0 to π/2, and the inner integral is with respect to y, from 0 to x.

The integrand is xsin(y), meaning that the area of the region is the integral of xsin(y) with respect to y from 0 to x, and then with respect to x from 0 to π/2. The solution is found by evaluating the inner integral first, which yields -xcos(x), and then evaluating the outer integral. The result is 2, which is the area of the given region.

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In Python an operator += is an assignment operator which adds the value on its right to the variable and assigns the result to the variable on its left.

We know that an operator is a symbol that represents a mathematical or logical process.

We know that in Python the operator += provides a convenient way to add a value to an existing variable and assign the new value back to the same variable.

If p += q

This means,  the variable p the left side is getting added to the value on the right side (q), and the result is then reassigned to the variable on the left.

i.e., p = p + q

+= is an assignment operator.

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Answer:47

Step-by-step explanation

Weight of each type of box:

Weight of each big box = 18.75 kg

Weight of each small box = 13.75 kg

The relationship between two terms on either side of a letter is represented by a mathematical formula. Often there is a variable and an equals sign.

The definition of an equation in algebra is a formula that shows the equivalence of two mathematical terms. For example, in the expression 6x + 11 = 14 the two terms 6x + 11 and 14 are separated by the "equals" symbol.

To let

Weight of each big box = x

And the weight of each small box = y

Weight of 3 big boxes:

3 times

5 small box weights:

5 years

3x + 5y = 125 .......................(i)

resemble:

9x + 7y = 265 ......................(ii)

Equation (i) multiplied by -3:

-3 (3x + 5y) = 125 * (-3)

-9x - 15y = -375 ...................(iii)

Under (ii) and (iii):

9x + 7y = 265

-9x - 15y = -375

Adding this gives:

-8y = -110

or y = 110/8

or y = 55/4

y = 13.75

From equation (i), we have:

3x + 5y = 125

or 3x + 5(13.75) = 125

or 3x + 68.75 = 125

3x = 125 - 68.75

3x = 56.25

x = 56.25/3

x = 18.75

Each large box weighs:

18.75 kilograms

Weight of each small box:

13.75 kilograms

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Answer:

5pie/6,0

Step-by-step explanation:

i graphed it

The first figure is dilated to form the second figure, the statement according to will be the scale factor is 0.25.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is.

A ratio divides two quantities in order to compare them.

As per the given information in the question,

We have two side lengths,

First figure: This represents the object length, which is a diamond with a length equal to 5.8.

Second figure:The picture length is then represented by a small diamond with sides that measure 1.45.

So, the scale factor is,

k = Image length/Object length

k = 1.45/5.8

k = 0.25.

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answer:10

Step-by-step explanation:

the graph show it is 1 hour and shows 10 miles and it continues

Answer:

it should be that the miles are 10 times the amount of hours

Step-by-step explanation:

Considering that to bike 10 miles it took 1 hour and to bike 20 miles it took 2 hours it will continue going like that so the miles will always be 10 times the amount of hours

Answer:

x < -18/5

this is the answer of you problem

When Dylan travels 8 miles due north, the distance between the homes of the parents and grandparents is thus 9 miles.

The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides. With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares. The base for more intricate trigonometry ideas, such as the Pythagorean theorem's opposite, is provided by this theorem, which is a very helpful tool.

given

by pythagoras theorem

[tex]c^{2} = a^{2} + b^{2} \\c^{2} = 8^{2} + 5^{2} \\c^{2} = 64 + 25 \\c^{2} = 89 \\c = 9[/tex]

The homes of the parents and grandparents are thus 9 miles apart in a straight line.

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There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:

[tex]H_0: \mu = 8.5[/tex]

At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:

[tex]H_1: \mu \neq 8.5[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

(p-value of 1 - (0.05/2)).

Hence the decision rule is given as follows:

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]

Hence the test statistic is of:

[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]

z = 1.24.

|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

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The Construction is shown below.

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given:

a) Steps for perpendicular line:

b) Perpendicular Bisector for triangle

So, if we extend the bisector they can meet inside, at center and outside the triangle.

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To tell if a log graph is a growth or decaying, look at the slope of the line. If the slope is positive, then it is growth; if the slope is negative, then it is decay.

A positive slope indicates that the value is increasing over time, while a negative slope indicates that the value is decreasing over time. To find the slope, take two points on the line and calculate the change in the y-value divided by the change in the x-value.

If the answer is positive, the graph is growth; if the answer is negative, the graph is decay. Additionally, you can look at the y-intercept of the graph, which is the value where the line meets the y-axis. If the y-intercept is positive, the graph is growth; if the y-intercept is negative, the graph is decay.

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Answer:

$5,775

Step-by-step explanation:

The equation is:

A = P( 1 + rt)

We know

P = $5,500

r = 5% = 0.05

t = 1 month

Let's solve

A = 5,500( 1 + 0.05 x 1)

A = 5,500( 1.05)

A = $5,775

So, his account will be at $5,775 after one month.

Jolene will have 4096 virus cells in her body after 12 divisions

Viruses are something more than living or dead, they are both. Maybe we need a new classification of life for them, a life that lives when the environment is favorable and hibernate when it is not.

The function provided to determine the number of virus cells in the body after h hours is 2^h. To find the number of virus cells after 12 divisions, we can plug in 12 for h in the function.

2^12 = 4096.

So, Jolene will have 4096 virus cells in her body after 12 divisions.

Please note that Jolene would not develop a rash after 12 divisions as it would take 30 divisions (120 hours) for the rash to appear.

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The rate of increase of the radius is 0.025 in/sec.

A three-dimensional object with a sphere-like shape. A sphere has no vertices or edges, unlike other three-dimensional shapes. The distances between each point on its surface and its center are equal.

In other words, the distance between any two points on the surface and the sphere's center is equal. The formula for the Volume of the sphere is given by

Volume of sphere = (4/3)πr³

Where, r = radius of the sphere

Here we have

A sphere is increasing in volume at the rate of 20 in³/s.  

Here we need to find at what rate the radius of the sphere increases when the radius is 4 in.

Let v = Volume of the sphere at time t

=> Change in Volume = dv/dt  = 20

r = Radius of the sphere at time t

As we know, the Volume of the sphere, v = (4/3)πr³

Differentiate the Volume of the sphere with respect to t

=> dv/dt = (4/3)3πr³⁻¹)(dr/dt)

=> dv/dt = 4πr² (dr/dt)

=>  20 = 4πr² (dr/dt)  

=>  5 = πr² (dr/dt)  

Given that radius, r = 4

=> 5 = π4² (dr/dt)  

=> 5 = (22/7) 64 (dr/dt)  

=> 5 = 3.14(64) (dr/dt)  

=> dr/dt = (5/3.14 × 64)  

=> dr/dt = 0.024880573

=> dr/dt = 0.025

Therefore,

The rate of increase of the radius is 0.025 in/sec.

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Answer:

1. 480
2. 30
3. 5
4. 480%

Step-by-step explanation:

1.
25% = 120
100% = 120 x 4 = 480
2.
100% = 120
25% = 120 : 4 = 25
3.
120 = 100%
6 = 6/120 x 100 = 5%
4.
25 = 100%
120 = 120/25 x 100 = 480%

There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.

quadratic equations

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

factoring

factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

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B. A greater percentage of second-lunch students (39%) eat outside.

From the table above, the percentage second-lunch students who eat outside is calculated as follows:

%= number of students who eat outside/total number of students who have second lunch × 100/1

%=18/46 x 100/1

%=39.1%

Percent is usually used to describe data in percentage form. This mathematical science is often used when calculating population percentages, discounts, interest rates, and so on. Percent is a number that represents part or all of the value or goods by forming a ratio of one hundred. Percent has an infinitely high value, while its lowest value is 0 percent. The amount of the percentage is denoted by "%".

This number was born in ancient Rome to be precise from the collection of auction taxes by using a fraction of 1/100 of the auction value or called centesima rerum venalium. the percent symbol has changed several times. Originally the Latin word percento was used. However, in the next generation, the word percento was changed to two symbols, namely the word per which changed to "/" and cento which changed to "00". Until finally the symbol "%" was known.

The simple formula for calculating percent is: Percentage (%) = (Total parts)/(Total amount) X 100%. The general percentage formula for calculating the percentage of a number that is considered as part of the whole is written in percent or 100%.

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Answer:

12.

V. E=(1-a)(1+a)(1+a^2)(1+a^4)(1+a^8)

Step-by-step explanation:

1-a^16=(1-a^8)(1+a^8)

1-a^8=(1-a^4)(1+a^4)

1-a^4=(1-a^2)(1+a^2)

1-a^2=(1-a)(1+a)

1-a^16=(1-a)(1+a)(1+a^2)(1+a^4)(1+a^8)