Write these propositions using p and q and logical connectives (including negations). (a) you do not drive over 65 miles per hour. (b) you drive over 65 miles per hour, but you do not get a speeding ticket. (c) you will get a speeding ticket if you drive over 65 miles per hour

The simplification by combining like terms of -(3z -5) + z is -2z + 5.

According to the given question.

We have an expression -(3z -5) + z.

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression -(3z - 5)  +z.

Here -3z and z both are the like terms.

So, we subtract coeffcients of z to simplify the given expression.

Therefore, the simplification of the expression -(3z - 5)  +z is given by

-(3z - 5) + z

= -3z + 5 + z

= -3z + z + 5

= -2z + 5

Hence, the simplification by combining like terms of -(3z - 5) + z is -2z + 5.

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Does the infinite series converge or diverge? The series converges.

If it converges, what is the sum?

a. 1/2 + 3/4 + 9/8 + . . . . .

The sum of the infinite series is -1

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=\frac{1}{2} \\\\r(\text{ thecommon ratio})=\frac{a_2}{a_1} =\frac{3}{2}[/tex]

Since ,[tex]\vert r\vert < 1[/tex], the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a }{1-r} ; -1 < r < 1\\\\S_\infty=\frac{\frac{1}{2}}{1-\frac{3}{2}}=-1[/tex]

The sum of the infinite series is -1

What is an infinite geometric series?

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Answer:

Step-by-step explanation:

It is given that we need to find the correct measurement indicated by the arrows on the lines to the left​.

Now, let us have a look at the figure;

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Answer:

(-15, -15)

Hope this helps!

Answer:

8,052

Step-by-step explanation:

(2,014 - 2,012) x (2,014 +2,012)

2 x 4,026

8,052

Answer:

c

Step-by-step explanation:

its one full square and 1/4

The measurement of angle ∠2 is 67.50°.

So,

Therefore, ∠2 is 67.50°.

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The correct question is given below:

Given the regular polygon, find the measure of each numbered angle.

m ∠ 2

Answer:

6561

Step-by-step explanation:

You multiply by 3 each time.

Answer:

-24 < -2 < -7/4 < 1/2 < √5

Step-by-step explanation:

The combined cost of 2 yards of yellow and 1 yard of purple fabric is  $17.69.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Length of yellow fabric = 5 yards

Length of purple fabric = 8 yards

Let x be the cost of per yard purple fabric.

Then, cost of per yard yellow fabric = 2 + x

Now since, Total amount paid is $62.80

Therefore,

5(2 + x) + 8x = 62.8

expanding the brackets we get,

10 + 5x + 8x = 62.8

Solving we get,

10 + 12x  = 62.8

or, 12x = 52.8

⇒ x = 62.8/12

⇒ x = $5.23

Thus the cost of per yard purple fabric = $5.23

Similarly, cost of per yard yellow fabric = 2 + 5.23 = $7.23

Thus, combined cost of 2 yards of yellow and 1 yard of purple

fabric = 2*$5.23 + $7.23

= $10.46 + $7.23

= $17.69

Thus, the combined cost of 2 yards of yellow and 1 yard of purple fabric is  $17.69

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According to the question, to calculate the probability of an event which states that flip a coin and not landing on head. That means P = {H,T}

Therefore, the probability can be written as:

Probability of getting tail = [tex]\frac{no of favorable events}{total number of outcomes} = \frac{1}{2}[/tex]

Therefore, the probability of a coin in which head is not landing is [tex]\frac{1}{2}[/tex].

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Answer:

B. Squaring, 2

Step-by-step explanation:

When you Square a number, doing the opposite is finding the square root. When squaring a number, you multiply the number by itself, the number it raises the the power of 2.

Answer:

Step-by-step explanation:

2500+150x=3000+125x

150x-125x=3000-2500

25x=500

x=500/25

x=20 mo

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

2500+150*20=3000+125*20

5500=5500 total paid after twenty months

Hope this helps! ;0

The system of equations that can be used to determine the cost for each pound of jellybeans and almonds is

5x + 3y = 16

2x + 6y = 22

The cost of one pound of jellybeans is $1.25.

The cost of one pound of almonds is $3.25.

Given this two equations:

5x + 3y = 16 equation 1

2x + 6y = 22  equation 2

Take the following steps to determine the required values:

Multiply equation 1 by 2

10x + 6y = 32 equation 3

Subtract equation 2 from equation 3

8x = 10

Divide both sides of the equation by 8: x = 10 / 8

x = 1.25

Substitute for x in equation 1:

5(1.25) + 3y = 16

6.25 + 3y = 16

3y = 16 - 6.25

3y = 9.75

y = 9.75 / 3

y = 3.25

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The most commonly used explicit of an arithmetic sequence is given as,

an = a + (n - 1) d

Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,

2nd row seat = 12+ 1x2

3rd row seat = 12 + 2 x2

nth seat = 12 + (n-1) x 2

16th row seat = 12 + (16–1) x2 = 42

Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows

Average number of seats per row = (12 +42)/2= 27

So total seats = average per row x number of rows

= 27 x 16 = 432.

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The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.

The measure of < LRQ is 112.5.

The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.

An arc is a segment of a circle's circumference. An intercepted arc is thus one formed when one or two different chords or line segments cut across a circle and meet at a common point known as a vertex.

If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.

So, [tex]$m \angle L R Q=\frac{1}{2}(m \overparen{L N Q})$[/tex]

The sum of the measures of the central angles of a circle with no interior points in common is 360 .

Here, 360 is divided into 8 equal arcs and each arc measures

360/ 8 = 45.

Then, m LNQ = m LM + m MN + m NO + m OP + m PQ = 5(45) = 225.

[tex]$m \angle L R Q=\frac{1}{2}(225)=112.5$[/tex].

Therefore, the measure of < LRQ is 112.5.

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The length of A'B' is 2 unit when Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane.

What is Translation ?

Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size.

That is, if the measurement of segment AB is 2 unit then after translation by any factor its measurement will not change,

So, the measurement of segment A'B' would be 2 unit.

Verification :

Let the coordinates of A and B are (x₁, y₁) and (x₂, y₂) respectively,

Also, the rule of translation 6 unit right is,

(x,y) → (x + 6, y)

By the distance formula,

The measure of segment AB = √(x₂- x₁)² + (y₂ - y₁)²

Thus, if A'B' is the transformed segment of segment AB,

Then, coordinates of A' and B' are (x₁ + 6, y₁) and (x₂ + 6, y₂)

So, the measure of segment A'B' =

√(x₂ + 6 - x₁ - 6)² + (y₂ - y₁)² = √(x₂- x₁)² + (y₂ - y₁)²

Hence, the measure of AB = measure of A'B'.

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hope it will help you...good luck

The unknown variable's result of the equation 24² + x² = 26² is 10

To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:

24² + x² = 26²

576 + x² = 676

x² = 676 - 576

x² = 100

x = [tex]\sqrt{}[/tex]100

x = 10

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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The number of books published by a small publishing company is 3240.

Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of books be x.

With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.

That is, 44,714+11.50x

With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.

That is, 17,174+20x

Now, the number of books produced will the costs from the two methods be the same.

So, 44,714+11.50x=17,174+20x

⇒ 44,714-17,174=20x-11.50x

⇒ 8.5x = 27540

⇒ x=3,240

Therefore, the number of books published by a small publishing company is 3240.

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The solution of the simultaneous equation is given by (-7 , 4) .

A pair of simultaneous equations is the most common representation of a pair of straight lines in the cartesian plane.

For solving a pair of simultaneous equation we can use various procedures such as the matrix method, substitution or the method of elimination.

The given pair of simultaneous equation is given as:

x=−2y+1

3x+8y=11

Let us solve the equations by the method of substitution:

From the first equation we take the value of x and put it in the second equation:

3x + 8y = 11

or, 3 ( -2y + 1 ) + 8y = 11

or, -6y +3 +8y = 11

or, 2y + 3 = 11

or, 2y = 8

or, y = 4

Substituting the value of y as 4 in the first equation we get:

x = − 2y + 1

or, x = - 2 × 4 +1

or, x = -8 +1

or, x = -7

Therefore the solution set of the pair of equations is given by (-7 , 4) .

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The minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

In mathematics, area of rectangle refers to the product of length of the rectangle and width of the rectangle. The unit is in square units. Area shows the extent a surface or a plane covers

Given data

size of rectangular plate = 5 cm by 3cm.

the length should be within   = 0.25 of 5 cm  

This means the length, L of the rectangular plate can be mathematically represented as

5 - 0.25 ≤ L ≤ 5 + 0.25

4.75 ≤ L ≤ 5.25

Area of rectangle =  Length × Width.

Width = 3

minimum length = 4.75

maximum length = 5.25

minimum length

= 4.75 * 3

= 14.25 cm^2

maximum length

= 5.25 * 3

= 15.75 cm^2

Therefore, the minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2

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The volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches

The formula for calculating the volume of a cone is expressed according to the formula

V = 1/3 pir²h

where

r is the radius of the cone = 10/2 = 5in

h is the height = 2in

Substitute to have;

V = 1/3pi(5)² × 2

V = 50/3pi

Hence the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches

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The slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.

It follows from the task content that the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) be determined.

On this note, it follows from the slope formula that slope;

m = (y2 - y1)/(x2 - x1)

Therefore, the slope of the line segment joining the two points is;

m = (-1.5 - (-3))/(0 - (-6))

m = 1.5/6

m = 1/4.

Ultimately, the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.

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Answer: 30,000 rounded to 1 significant figure

I hope this helped!

Answer:

Step-by-step explanation:

How many solutions does each of the following equations have?

6(x-3)+12=6x-6

6x - 18 + 12 = 6x - 6

-18 + 12 = -6

-6 = -6

0 = 0