"Lake superior has roughly 25 times the volume of Lake Erie. If the volume of Lake
Superior is approximately 1.22x10^10 km^3, what is the approximate volume of Lake
Erie?"

3/4 fraction of cupcake have vanilla fronting.

A fraction is a mathematical concept that represents a part of a whole or a ratio of two numbers. It is typically represented as two numbers separated by a line or a slash, with the top number representing the numerator and the bottom number representing the denominator. The numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole.

we have in total 9 cupcakes having vanilla froting and there are total 12 cupcakes.

so the fraction is given as :

9/12

since the HCF of (9,12) is 3

so the fraction in lowest form is 3/4

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The estimate of the no. of people to vote varies by 25% from the actual no. of voters turned out.

Finding the per cent variation of estimated votes from the actual turnout

The no. of people estimated to vote in the election = 7000

The actual no. of people who voted = 5600

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

∴ The per cent by which the estimate vary from the actual turnout is given by,

= [{7000 – 5600}/ {5600}]×100

= [1400/5600]×100

= 0.25×100

= 25%  

Therefore, the 25% of the estimate vary from the actual amount.

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To the nearest tenth of a kilogram, m = 0.6 kg.

What is ttemperature rate ?

With increase in temperature, the rate of the reaction and the rate constant increases. As a generalization, the rate of the reaction (and the rate constant) becomes almost double for every ten degree rise in temperature. This is also called temperature coefficient.

the heat Q required to raise the temperature of water varies jointly as the mass m of the water and the amount of temperature change T, and Q = 20,930 J when m = 1 kg and T = 5°C.

So, write an equation for Q as:

Q = k * m * T

where k is a constant of proportionality.

Substituting the known values, we can find k:

20930 = k * 1 * 5

k = 20930 / (1 * 5) = 4186

Now that we have k, use it to find m when Q = 8349 J and T = 3°C:

8349 = 4186 * m * 3

m = 8349 / (4186 * 3)

To the nearest tenth of a kilogram, m = 0.6 kg.

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The mass of the water m is 0.7 kg.

Since Q varies jointly as m and T, we know that Q = k * m * T where k is a constant of proportionality. Using the given information, we can find the value of k:

Q = 20,930 J when m = 1 kg and T = 5° C

k = Q / (m * T) = 20,930 / (1 * 5) = 4186

Now that we have found k, we can use it to find m when Q = 8,349 J and T = 3°C:

Q = k * m * T

8,349 = 4186 * m * 3

m = 8,349 / (4186 * 3) = 8,349 / 12,558

m = 0.67 kg

To the nearest tenth of a kilogram, m = 0.7 kg.

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The equation of the line is y = 3x-9(slope-intercept form).

The graph of the linear equation y = mx + c is a line with slope m and y-intercept m and c. This is known as the slope-intercept form of the linear equation, and the values of m and c are real numbers.

The slope, m, of a line represents its steepness. Sometimes the slope of a line is referred to as the gradient. A line's y-intercept, b, represents the y-coordinate of the point where the line's graph intersects the y-axis.

Given that,

m = 3

y = 9

Thus, The equation of the line is y = 3x-9(slope-intercept form).

Complete question: A linear function has a slope of 3 and crosses the y- axis at 9. What is the equation of the line?

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To multiply fractions:

First multiply the numerator with numerator, then multiply the denominator with the denominator. Lastly, simplify the resultant fraction, if required.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part of fraction is denominator.

consider a fraction 1/8.

Here, numerator is 1, denominator is 8

When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8

The multiplication of fractions is defined as the product of a fraction with a fraction or the product of a fraction with an integer or the product of a fraction with the variables.

The steps to multiply two fraction are:

1) First multiply the numerator with numerator

2) Then Multiply the denominator with the denominator

3) And lastly simplify the fractions, if required

In case of product of mixed fractions (a fraction which is a combination of a natural number and fraction),

First we change each mixed fraction to an improper fraction. Then multiply the fraction as mentioned above.

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The height of a triangle in Class 7, Height =  (2×Area)/ Base

​

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Answer:

x=5000 I think

Step-by-step explanation:

1800-1600=200$ difference between choices

this difference equals a 4% commission on the amount of furniture she sells during the month

If the amount of sales is x$, then a 4% commission on the amount is 0.04x$

so 0.04x=200

x=200%2F0.04

x=5000$ amount of sales for that two choices will be equal

Answer:

p = 73.21 pounds of strawberries

Step-by-step explanation:

M + 10 = 5.6p - 96

314 + 10 = 5.6p - 96

314 +96 = 410

410 = 5.6p

410/5.6 = p

73.2142857143 = p

p = 73.2142857143

Answer:

75 pounds

Step-by-step explanation:

Replace M in the equation with 314

314 + 10 = 5.6p - 96

324 = 5.6p - 96

5.6p = 324 + 96

5.6p = 420

Divide both sides by 5.6

p = 75

Answer:

x = 7 , VS = 6

Step-by-step explanation:

• If two chords of a circle are equidistant from the centre of the circle then they are congruent.

given ZU and ZV = 5

then the chords QR and ST are equidistant from the centre and are congruent , that is

QR = ST

2x - 2 = 12 ( add 2 to both sides )

2x = 14 ( divide both sides by 2 )

x = 7

---------------------------------------------------

• If a radius is perpendicular to a chord then it bisects it.

radius ZY is perpendicular to chord ST and bisects it, so

VS = [tex]\frac{1}{2}[/tex] × ST = [tex]\frac{1}{2}[/tex] × 12 = 6

Answer:

11

Step-by-step explanation:

the answer is 11 because of therom

The measure of the base of the triangle is 10 millimetres

From the question, we have the following parameters that can be used in our computation:

Area of the triangle = 80 square millimetres

Height of the triangle = 16 millimetres

Using the above as a guide, we have the following:

The base of the triangle = 2 * Area/Height

Substitute the known values in the above equation, so, we have the following representation

The base of the triangle = 2 * 80/16

Evaluate

The base of the triangle = 10

Hence, the base is 10 millimetres

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Complete question

The area of the triangle is 80 square millimeters and the height of the triangle is 16 millimetres.

Calculate the length of the base

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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The polynomial function with zeroes at -2, 0, and 3√2 is (x+2)(x-0)(x-3√2) = [tex](x+2)*(x-3\sqrt{2}) = x^3 - 3x\sqrt{2x} - 2x^2.[/tex]

The polynomial function with zeroes at -1, 3, and 2i is (x+1)(x-3)(x-2i) = [tex](x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]

A polynomial function is a function of the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where n is the degree of the polynomial and the a_i are constants. To find a polynomial function with zeroes at -2, 0, and 3√2, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+2)(x-0)(x-3\sqrt{2}) = (x+2)x(x-3√2) = x^3 - 3x\sqrt{2x} - 2x^2[/tex].

In this case, we can see that x = -2, x = 0, x = 3√2 are the zeroes, so we know that (x+2), x and (x-3√2) are the factors of the polynomial.

Similarly, to find a polynomial function with zeroes at -1, 3, and 2i, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as [tex](x+1)(x-3)(x-2i) = (x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12[/tex]

In this case, we can see that x = -1, x = 3, x = 2i are the zeroes, so we know that [tex](x+1), (x-3), (x^2+4)[/tex]are the factors of the polynomial.

It is worth noting that (x-2i) is a zero of the polynomial, so (x-2i)(x+2i) = [tex]x^2[/tex]+4 is a factor of the polynomial and it is included in the polynomial..

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The tallest lighthouse in the world is the Jeddah Light. It is 133 m tall. A dhow is sailing away from this lighthouse. From the top of the lighthouse, the angle of depression to the dhow is 65° Later, the angle of depression has changed to 40°.

How far did the dhow travel during that time?

To solve this problem, we can use trigonometry and the fact that the angles in a triangle add up to 180°.

Let's call the distance between the lighthouse and the dhow "d".

We know that the angle of depression from the top of the lighthouse to the dhow is 65°, and the angle of depression later changed to 40°.

Let's call the angle between the horizontal and the line of sight from the lighthouse to the dhow, "x"

Since the angles in a triangle add up to 180°, we can say that:

x + 65 + 40 = 180

x = 75

Now, we can use the tangent function to find the distance d. We know that:

tan(x) = d / h

tan(75) = d / 133

d = 133 * tan(75)

Therefore, the dhow traveled 133 * tan(75) distance during that time.

(a)1+2×3×4×5 is equal to 121 which shows it is square integer.

(b)1+3×4×5×6 is equal to 361 that shows it is square integer and 1+4×5×6×7 is equal to 841 that shows it is square integer.

(c)n(n+3) is equal to n²+3n and second expression would be a+2.

(d)The expression in the term of a is a²+2a+1

•Integers are any number, including positive, negative, and zero. The Latin root of the word "integer" means "whole" or "intact." Therefore, integers do not contain decimals or fractions.

•Consequently, both negative and positive whole numbers can be added to create a set of integers.

•An integer, which includes both positive and negative integers, including zero, is a number without a decimal or fractional component. Z stands for an assortment of integers that includes the following.

•If a number is smaller than zero, it is said to be negative. For instance, 1, 2, 3, etc. Zero is defined as not having a positive or negative value. The sum is a whole number.

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Reason: The 90 degree angle means we have a right angle, and it leads to a right triangle. The triangle is also scalene since all three angles are different (it means all side lengths are different).

The absolute value function is increasing on [0,∞) and decreasing on (−∞,0].

There are a few ways to describe what is meant by the absolute value |x| of a real number x. You may have been taught that |x| is the distance from the real number x to the 0 on the number. So, for example, |5| = 5 and | − 5| = 5, since each is 5 units from 0 on the number line.

Another way to define absolute value is by the equation |x| = √x2. Using this definition, we have

|5| = √(5)² = √25 = 5 and | − 5| = √(−5)² = √25 = 5. The long and short of both of these procedures is that |x| takes negative real numbers and assigns them to their positive counterparts while it leaves positive numbers alone.

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When a=9 and c=3, A varies as b and c together. If a=40, b-2, and c=5, B. [tex]40x^{2}[/tex] - 2 x + 5 = 0 and [tex]9x^{2} +3 = 0[/tex] are the quadratic equations.

When a=9 and c=3, A varies as b and c together. If a=40, b-2, and c=5, B. [tex]40x^{2}[/tex] - 2 x + 5 =0 and [tex]9x^{2} +3 =0[/tex] are the quadratic equations.

Domain of [tex]$40 x^2-2 x+5:\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Range of [tex]$40 x^2-2 x+5:\left[\begin{array}{cc}\text { Solution: } & f(x) \geq \frac{199}{40} \\ \text { Interval Notation: } & {\left[\frac{199}{40}, \infty\right)}\end{array}\right]$[/tex]

Axis points of interception [tex]$40 x^2-2 x+5: \quad$[/tex] Y Intercepts: (0,5)

Vertex of [tex]$40 x^2-2 x+5: \quad$[/tex] minimum [tex]$\left(\frac{1}{40}, \frac{199}{40}\right)$[/tex]

Factor [tex]$9 x^2+3: \quad 3\left(3 x^2+1\right)$[/tex]

[tex]$$9 x^2+3$$[/tex]

Replace 9 with 3 - 3.

Put 3 in as 3 - 1.

[tex]$$=3 \cdot 3 x^2+3 \cdot 1$$[/tex]

Exclude common word 3

[tex]$$=3\left(3 x^2+1\right)$$[/tex]

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The degree of the given polynomial 7x³ + 5x + 4x³ + 2x² is 3.

The degree of a polynomial is the highest power of the variable present in the polynomial.

Now the given polynomial is 7x³ 5x 4x³ 2x², and the highest power of x is x³. This indicates that the degree of this polynomial is 3.

It's important to note that when working with polynomials, it's important to pay attention to the signs of the coefficients. In this case, we have 7x³, 5x, 4x³, and 2x². The x³ term has the highest degree, and its coefficient is 7; the x term has the second highest degree, and its coefficient is 5; the x³ term has the same degree as the 7x³ term, but the coefficient is different, and the x² term has the fourth highest degree, and its coefficient is 2.

--The given question is incomplete; the complete question is

"What is the degree of the polynomial 7x³ + 5x + 4x³ + 2x²?"--

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The sampling method described appears to be flawed.

Without additional information about the survey, it is difficult to determine the specific issues with the methodology, but there are a few potential issues that could affect the validity of the results.

First, the sample size of 2030 randomly selected adults may not be representative of the entire population. A larger sample size would be needed to be more representative of the population.

Second, the survey only asked about one specific behavior (sharing passwords) and it is not clear how the survey was conducted (e.g. online, phone, in-person) or if the survey was self-reported or not.

Third, It's not specified if the survey reached a diverse sample, which could be a problem if the survey only reached a certain demographic or geographic area.

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Correctly written question:

In a password survey of 2030 randomly selected adults, 39% said that they never share passwords with anyone. Does this sampling method appear to be sound or flawed?

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 1/2x + 4

put x = 2
= 1/2 × 2 + 4
= 5

Now, another expression

= x + 6 - 1/2x - 2
Put x = 2

= 2 + 6 - 1/2 × 2 -2
= 5

Thus, both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Option A is correct.

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Answer:7.5

Step-by-step explanation:

The median is the middle value of a set of observations when they are arranged in ascending order. Since the observations are already arranged in ascending order and there are 7 observations, the median will be the fourth value.

Given that the median is 32, we know that the fourth value is 32. The observations are:

13, x, 26, 32, 39, 41, 50

So x + 3x + 2 = 32

4x + 2 = 32

4x = 30

x = 7.5

The value of x is 7.5.

The matched solution for given linear inequalities is given in image attached.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

The solution for linear inequalities  is provided in image.

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Answer:

2nd is the correct answer

The side that will be in palce of Questionmark by Similarity of Triangle is WZ.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Since Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Properties:

Similar equivalent side ratios exist.

Triangle WZX and WXY:

Angle WZX = angle WXY= 90 degrees

Angle WXY is a common angle .

So triangle WZX and WXY are similar (AAA similarity)

So, the ratio of sides are equal.

Therefore,

WY / WX = WX / WZ

The side that will be in place of WZ

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Brian has done a mistake in step 3.

What is the linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form of "ax + b = 0" where a and b are constants and x is the variable. The equation will be a line when plotted on a graph.

The given equation is -4g + 11 = 5

Now we can add -11 in step 1,

-4g + 11 -11 = 5 - 11

-4g = -6

Now divide by -4

we get

  g = 3/2

We can see in the given picture in step 3, it should have been divided by -4 so in step 3 mistake was done.

Hence, Brian has done a mistake in step 3.

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In class 9, matter is typically defined as anything that has mass and takes up space. Matter can be found in different forms and states, such as solid, liquid, and gas.

The study of matter in class 9 typically includes the following topics:

Properties of matter: Students learn about the different physical and chemical properties of matter, such as density, melting point, boiling point, and solubility.

States of matter: Students learn about the three states of matter (solid, liquid, and gas) and how they are different from each other in terms of properties such as shape, volume, and compressibility.

Changes of state: Students learn about how matter can change from one state to another, such as melting, freezing, boiling, and condensation.

Mixtures and solutions: Students learn about the different types of mixtures, such as homogeneous and heterogeneous mixtures, and solutions, such as true solutions, colloidal solutions, and suspensions.

Particles of matter: Students learn about the nature of matter and how matter is made up of tiny particles called atoms and molecules. They also learn about the arrangement of these particles in solids, liquids, and gases.

Physical and chemical changes: Students learn about the differences between physical and chemical changes in matter and examples of each.

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The three conditions must be satisfied for a square to be in its simplest form, that is, first, No radicands other than 1 have perfect square factors. Secondly, there isn't a fraction in any radicand and finally, the fraction's denominator has no radicals.

A square root can be reduced to a simple form by first factoring it into primes, then finding the radical's index, and finally moving the group of numbers either inside or outside the radical.

The expressions both inside and outside the radical can then be made simpler by adding up all the numbers inside the radical.

The quotient property of square roots, which can be used to split radical expressions, is another beneficial property for simplifying radical expressions.

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(a) The expression for the width of the rectangle is 7x + 1.

(b) The expression for the perimeter of the rectangle is 14x + 14.

(c) when x = 1/2, the perimeter of the rectangle is 21 in

The area of a rectangle is given by the formula:

A = L × W

where L and W are the length and width of the rectangle respectively

(a) Since A = 42x + 6 sq inches and L = 6 in. We have:

42x + 6 = 6 × W

42x + 6 = 6W

6W = 42x + 6    (divide through by 6)

W = 7x + 1 in

Thus, the expression for the width of the rectangle is 7x + 1

(b) The expression for the perimeter of the rectangle

The perimeter of a rectangle is given by the formula:

P = 2(L + W)

P = 2(6 + 7x + 1)

P = 2(7 + 7x)

P = 14x + 14 in

(c) when x = 1/2

P =  14x + 14

P = 14×(1/2) + 14

P = 7 + 14

P = 21 in

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The complete factor of the polynomial x² + 5x +6 is (x + 3)(x + 2).

You can factor it by using the factorization methods such as

Factor by grouping

Factor by grouping and completing the square

Factoring by using difference of squares

Factoring by using sum and difference of cubes

For example, you can factor it by using the difference of squares method:

x² + 5x +6 = (x² + 6x + 9) - (x +3)

We know x² + 6x + 9 = (x + 3)², So

x² + 5x +6 = (x + 3)² - (x + 3)

Taking (x + 3) common

x² + 5x +6 = (x + 3)(x + 3 - 1)

x² + 5x +6 = (x + 3)(x + 2)

So (x + 3)(x + 2) is complete factor.

--The question is not readable, answering to the question below--

"What is the complete factor of x² + 5x + 6?"

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