What is the difference between a formal and informal proof?
A) A formal proof is much shorter, whereas an informal proof is longer.
B) A formal proof provides the reasons for steps, whereas an informal proof does not.
C) A formal proof uses equations, whereas an informal proof only uses text.
D) A formal proof uses a table or a list of steps, whereas an informal proof uses paragraphs.

Answer:

Distance = Speed × Time.

Let's break down the problem into two parts:

a) At what time will the cyclists meet on the way?

Let's assume t represents the time in hours when the cyclists meet.

The distance Joel travels in t hours is given by: Distance = Speed × Time = 12t km.

The distance Ryan travels in t hours is given by: Distance = Speed × Time = 8t km.

Since they are cycling towards each other, the sum of their distances should equal the total distance between Kingston and Sunny Place, which is 35 km.

So, we can set up the equation: 12t + 8t = 35.

Simplifying the equation, we have: 20t = 35.

Dividing both sides of the equation by 20, we get: t = 35/20 = 1.75 hours.

Therefore, the cyclists will meet on the way after 1.75 hours, which is equivalent to 1 hour and 45 minutes.

b) How far will each cyclist have traveled when they meet?

To find the distance traveled by each cyclist, we can substitute the value of t into their respective equations:

Distance traveled by Joel = 12t = 12 × 1.75 = 21 km.

Distance traveled by Ryan = 8t = 8 × 1.75 = 14 km.

Therefore, when the cyclists meet, Joel would have traveled 21 km and Ryan would have traveled 14 km.

The volume of the solid obtained by rotating the region over the function is given by the integral and V = 44.46 units³

Given data ,

The volume of the solid obtained by rotating the region underneath the graph of the function f(x)=√x² +9 over the interval [0,2] about the y-axis

The formula for Area under definite integral is

∫ₐᵇ f ( x ) = f ( b ) - f ( a )

Since we are rotating the region about the y-axis, the radius is simply the x-coordinate of each point on the curve, or r = x

The height h of each shell is equal to the difference between the y-coordinates of the curve at x and x + Δx, or h = f(x + Δx) - f(x)

Using these expressions for r and h, we can write the volume of each cylindrical shell as:

V(x) = 2πx[f(x + Δx) - f(x)]Δx

V = ∫₀² 2πx[f(x + Δx) - f(x)]dx

As Δx approaches zero, this integral becomes:

V = ∫₀² 2πx√(1 + (f'(x))²) dx

where f'(x) is the derivative of f(x), which is:

f'(x) = x/√(x² + 9)

Substituting this expression for f'(x) into the integral, we get:

V = ∫₀² 2πx√(1 + (x/√(x² + 9))²) dx

This integral can be evaluated using a substitution, u = x² + 9, du/dx = 2x, and dx = du/2x, to get:

V = ∫₉¹³ 2π(x² + 9)^(3/2)/2 dx

V = [4/5 π(x² + 9)^(5/2)]₉¹³

V = 44.46 units³

Hence , the volume of the solid is 44.46 units³

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Using a system of equations, the quantities of each type of gas sold by the gas station for the business day are as follows:

A system of equations refers to two or more equations solved concurrently.

A system of equations is also known as simultaneous equations because they can be solved at the same time.

                              Regular    Premium

Price per gallon      $2.20       $2.75

Total number of gallons of gas sold = 340

The total receipts for the 340 gallons = $803.

Let the number of gallons of the regular gas = x

Let the number of gallons of the premium gas = y

x + y = 340 ...Equation 1

2.2x + 2.75y = 803 ...Equation 2

Multiply Equation 1 by 2.2:

2.2x + 2.2y = 748 ...Equation 3

Subtract Equation 3 from Equation 2:

2.2x + 2.75y = 803

-

2.2x + 2.2y = 748

0.55y = 55

y = 100

x = 240 (340 - 100)

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Answer:

The correct answer is C, Graph D.

x^2 - 4x + 4 = (x - 2)^2.

To solve for x in terms of y in the equation 23x + 15y = 2, we can start by isolating the term with x on one side of the equation. We can do this by subtracting 15y from both sides of the equation to get 23x + 15y - 15y = 2 - 15y, which simplifies to 23x = 2 - 15y.

Next, we can solve for x by dividing both sides of the equation by 23 to get 23x/23 = (2 - 15y)/23, which simplifies to x = (2 - 15y)/23.

Therefore, the solution for x in terms of y is x = (2 - 15y)/23.

The equation of the line passing through the points (6, 5) and (8, -2) is[tex]y = -\frac{7}{2} x + 26[/tex].

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Determine the slope of the line.

Given the two points are (-7, -3) and (1, 2)

We can find the slope of the line by using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values:

m = (-2 - 5) / (8 - 6)

m = -7/2

Using the point-slope form, plug in one of the given points and slope m = -7/2 to find the equation of the line.

Let's use the point (6, 5):

y - y₁ = m(x - x₁)

[tex]y - 5 = -\frac{7}{2}( x - 6 )\\\\y - 5 = -\frac{7}{2} x + 21\\\\y = -\frac{7}{2} x + 21 + 5\\\\y = -\frac{7}{2} x + 26[/tex]

Therefore, the equarion of the line is [tex]y = -\frac{7}{2} x + 26[/tex].

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Answer:

I'm pretty much confused abt this one bc I didn't get an exact answer. Anyway I think it's 13.1

Step-by-step explanation:

The pic

An ordered pair that describes a point that should be removed from the graph so that the graph represents a function include the following: A. (1, 1).

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the graph shown below, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);

3  → 1

1 → 1

In this context, we can reasonably infer and logically deduce that either (3, 1) or (1, 1) must be removed from the graph in order to represent a function.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The solution of the inequality given is b < 64

the graph is attached

In the equation, let us replace b with x

To solve the inequality x/8 < 8 for x, we need to isolate x on one side of the inequality.

We can do this by multiplying both sides of the inequality by 8, which will cancel out the 8 in the denominator on the left side:

Therefore, the solution to the inequality x/8 < 8 is x < 64.

This means that any value of x that is less than 64 will make the inequality true.

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Answer:

(x, -1/2x + 5/2) or infinitely many solutions

Step-by-step explanation:

We can solve the system of equations using substitution.  We can start by isolating x in the first equation.  Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:

Isolating:

x = -2y + 5

Plugging in and solving for y:

4(-2y + 5) + 8y = 20

-8y + 20 + 8y = 20

20 = 20

We see that we get a constant equal to another constant.  Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:

y = -1/2x + 5/2

Thus, the general rule for the solution to the system of equations is

(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions

You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation.  Let's try 4 for x and 0 for x:

4 for x in first equation:

4 + 2(-1/2(4) + 5/2) = 5

4 + 2(0.5) = 5

4 + 1 = 5

5 = 5

4 for x in the second equation

4(4) + 8(-1/2(4) + 5/2) = 20

16 + 8(0.5) = 20

16 +4 = 20

20 = 20

0 for x in the first equation:

0 + 2(-1/2(0) + 5/2) = 5

0 + 2(2.5) = 5

5 = 5

0 for x in the second equation:

4(0) + 8(-1/2(0) + 5/2) = 20

0 + 8(2.5) = 20

20 = 20

There are 10,080 possible ways for the 15 people to stand if the people from each borough insist on standing together.

If there are 15 people from the Bronx, Brooklyn, Manhattan, Queens, and Staten Island, and each borough has 3 people, then there are 5 groups of 3 people. If the people from each borough insist on standing together, we can treat each group of 3 people as a single entity. So, we have 5 entities that need to be arranged.

The number of ways to arrange these 5 entities is 5!, which is equal to 120. However, within each group of 3 people, there are 3! ways to arrange the people. So, we need to multiply the number of ways to arrange the groups by the number of ways to arrange the people within each group. We will get the answer

5! × (3!)⁵ = 120 × 3⁵ = 10,080

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Answer:

84

Step-by-step explanation:

Trust me

Answer:

84

Step-by-step explanation:

There are 9 pieces of luggage.

We can select the first piece 9 different ways, the second piece 8 different ways, since there are only 8 pieces left.  The third piece can be selected 7 different ways.

9*8*7

504

But order doesn't matter since we are taking 3 pieces.

Divide by (3*2*1)

504/6 = 84

There are 84 different combinations of luggage

Answer:x=-8

Step-by-step explanation:

3.2+(−1/2)x−2=4.8x+2−5.2x

−0.1x=0.8

x=-8

Answer:

x=-8

Step-by-step explanation:

x=-8

The surd forms are simplified to give;

21. 10√6 - 12√10

23. -56a  - 5√2a - 25

25. -4√15x - 25x + 3

Surds are described as values in square root that can no longer be simplified into whole numbers or integers

They are also seen as irrational numbers.

From the information given, we have that;

√15(2√10 - 4√6)

Expand the bracket and multiply the surd forms

2√150 - 4√90

Factorize the forms

2√25 ×√6 - 4√9 × √10

find the square root

10√6 - 12√10

23. (√2a - 5)(7√2a - 5)

expand the bracket

7√4a² - 5√2a - 35√4a² + 25

find the square root, we have;

7×2a - 5√2a - 35×2a + 25

collect the like terms

14a - 70a - 5√2a - 25

-56a  - 5√2a - 25

25. (√3 + √5x)(√3 - 5√5x)

expand the bracket

3 - 5√15x + √15x - 5√25x²

find the square root

3 - 5√15x + √15x - 25x

collect the like terms

-4√15x - 25x + 3

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Answer:

w≤9

Step-by-step explanation:

8w ≤ 72

Divide by 8 on both sides

w ≤ 9

For graph, draw a number line and label a point as 9. Draw a solid line facing to the left and having a closed point at 9. The line should not extend past 9.

To solve the equation -10(x-1.7)=-3 by expanding first, we need to apply the distributive property of multiplication.

Expanding -10(x-1.7), we get

-10x + 17 = -3

Now we can solve for x by isolating the variable on one side of the equation. To do this, we'll add 10x to both sides of the equation

-10x + 17 + 10x = -3 + 10x

Simplifying, we get

17 = 10x - 3

Next, we add 3 to both sides of the equation

17 + 3 = 10x - 3 + 3

Simplifying, we get

20 = 10x

Finally, we divide both sides of the equation by 10 to isolate x

20/10 = 10x/10

Simplifying, we get

2 = x

Therefore, the solution to the equation -10(x-1.7)=-3 by expanding first is x = 2.

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To find the multiplicative inverse of 2i, we need to find a complex number z such that:

(2i) * z = 1

Multiplying both sides by -i, we get:

z = -i/2

Therefore, the multiplicative inverse of 2i is -i/2.

The estimate of the cost for a 20-ft cord is given as follows:

$74.66.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points in the context of the problem are given as follows:

(3, 12.75), (5, 16), (6, 25.99), (50, 185).

Inserting these points into a calculator, the regression equation is given as follows:

y = 3.6794x + 1.06462.

Hence the estimate of the cost for a 20-ft cord is obtained when x = 20 as follows:

y = 3.6794(20) + 1.06462

y = $74.66.

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The correct statements are,

B)It has two faces that are decagons.

C)It has 11 faces.

D)It has 20 edges.

What is decagonal pyramid?

A decagonal pyramid is a solid whose base is a decagon or a ten sided figure, regular or irregular. The surfaces are ten isosceles triangles, in case of a regular decagonal pyramid with all the ten vertices meeting at a point.

Here The decagonal prism is formed by two regular decagons as its bases and 10 squares as its other faces. the top of the decagonal prism is a regular decagon, so is the bottom face.

We know that decagonal pyramid has 11 faces and 20 edges and 11 vertices.

Hence the correct statements are,

B)It has two faces that are decagons.

C)It has 11 faces.

D)It has 20 edges.

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Answer:

Step-by-step explanation:

There are 6 possible outcomes when rolling a single cube (1, 2, 3, 4, 5, or 6). When rolling two cubes, the possible sums range from 2 (1+1) to 12 (6+6). Using the chart provided, we can see that the sum of two cubes being equal to 5 only occurs once in the 36 possible combinations: when one cube shows a 1 and the other cube shows a 4.

To find the expected number of times this sum will occur if Tamara rolls the cubes 180 times, we need to multiply the probability of this event occurring on any given roll by the number of rolls. The probability of rolling a sum of 5 is 1/36, since there is only one way to get a sum of 5 out of the 36 possible combinations. Therefore, the expected number of times this sum will occur in 180 rolls is:

(1/36) x 180 = 5

So Tamara should expect to roll a sum of 5 about 5 times in 180 rolls of two cubes.

The amount of water that the plastic container can hold is -p + 3.

To determine the amount of water that can be held, we will first assume that the container can hold x quantity of water.

So, the glass jug can hold:

p + 6 - x

2 glass jugs and 2 plastic containers can hold 6p quarts of water.

= 2(p + 6 - x) - 2x = 6p

2p + 12 - 2x -2x = 6p

2p + 12 -4x = 6p

12 - 4x = 6p - 2p

-4x = 6p -2p - 12

-4x = 4p -12

x = 4p - 12/-4

x = -p - 3

or -p + 3

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There were no more books checked out in March than in April.

The pictograph provided shows the number of books checked out from the library during the months of December, January, February, March, and April. Each picture represents 5 books.

The pictograph tells us that for each of these months, 5 books were checked out. So, in March, 5 books were checked out, and in April, 5 books were also checked out.

To find the difference between the number of books checked out in March and April, we subtract the number of books checked out in April from the number of books checked out in March:

5 books (March) - 5 books (April) = 0 books

Therefore, The result shows that there were no more books checked out in March than in April. Both months had the same number of books checked out, which is 5.

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Answer: A

Step-by-step explanation:

well i did alll of them and got A

Answer:

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

According to the problem, 2 laps make a difference of 10% as:

Hence the total distance in terms of laps is:

Find the total distance:

Answer:

To find the value of A, we can substitute g(-3) = 2 into the given equation and solve for A.

g(q) = (2q-4) / (q-A)

2 = (2(-3)-4) / (-3-A)

Multiplying both sides by (-3-A), we get:

2(-3-A) = -10 - 2A

Expanding the left side, we get:

-6 - 2A = -10 - 2A

Adding 2A to both sides, we get:

-6 = -10

This is a contradiction, which means that there is no value of A that satisfies the given conditions. Therefore, the answer to the question is:

There is no value of A that satisfies the given conditions.

There were 56 students in Mr Tan's class.

To solve this problem, we can use the formula for average: average = (sum of all values) / (number of values). Let's assume that there were initially n students in Mr Tan's class, and the average amount collected was x. Then, we can write:

nx = sum of all amounts collected

Now, if three students each collected $32 less, the new sum of amounts collected would be:

(nx - 3*32) = (n-3)(x-32)

And the new average would be:

(n-3)(x-32) / n = 146

Similarly, if eight students each collected $18 more, the new sum of amounts collected would be:

(nx + 8*18) = (n+8)(x+18)

And the new average would be:

(n+8)(x+18) / n = 156

Now we have two equations with two unknowns (n and x). We can solve them using algebraic manipulation. After some simplification, we get:

n = 56 and x = 104

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Multiplying is necessary because each larger unit contains a certain number of the smaller units and we need to account for that conversion factor.

For example, when converting from meters to centimeters where we know that 1 meter is equal to 100 centimeters.

To convert 3 meters to centimeters, we need to multiply by the conversion factor of 100 which gives us:

= 3 meters * 100 centimeters/meter

= 300 centimeters

So, without the multiplication, we would not account for the fact that each meter contains 100 centimeters. This principle applies to all conversions from larger units to smaller units and it is important to remember to ensure accurate conversions.

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Using some logarithm properties we will get the expanded expression:

log(y^10) = 10*ln(y)/ln(10)

So there are two logarithm properties that we can use here, these are:

logₙ(x) = ln(x)/ln(n)

and:

logₙ(x^a) = a*logⁿ(x)

Now let's go to our expression, it is:

log(y^10)

Using the second property we can remove the exponent, then we will get:

log(y^10) = 10*log(y)

Now we can use the first rule, remember that log(x) has a base of 10, then we can write:

10*log(y) = 10*ln(y)/ln(10)

That is the expession expanded.

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Answer:

10868

Step-by-step explanation:

11x26=286

286x38=10868