Which of the following are propositions? Give the truth value of each proposition.


(a) What time is dinner?


(b) It is not the case that π is not a rational number.


(c) x / 2 is a rational number.


(d) 2x + 3y is a real number.


(e) Either π is rational and 17 is a prime, or 7 < 13 and 81 is a perfect square.


(f) Either 2 is rational and π is irrational, or 2π is rational.


(g) Either 5π is rational and 4.9 is rational, or there are exactly four primes less than 10.


(h) −3.7 is rational, and either 3π < 10 or 3π > 15.


(i) It is not the case that 39 is prime, or that 64 is a power of 2.


(j) There are more than three false statements in this book, and this statement is one of them.

The cost of 1 ft² grass sod is $3 and the cost of 1 geranium is $10.

This is found using simultaneous equations.

What are simultaneous equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations.

Let,

    x = Cost of 1 ft² grass sod

   y = Cost of 1 geranium

In Shayna's case

Grass sod = 2ft²

Geranium bought = 1

Cost = $16

Equation

2x + y = 16 ⇒ (1)

In Arjun's case

Grass sod = 1 ft²

Geranium = 7

Cost = $73

Equation

x + 7y = 73 ⇒ (2)

Solving the equation (1) and (2)

From (1)

y = 16 - 2x

Substituting the above in (2)

x + 7 (16-2x) = 73

-13x = -39

  x = 3  

   y = 16 - 2*3 = 10

Therefore from the solution of the above simultaneous equations, we can conclude that the cost of 1 ft² grass sod is $3 and the cost of 1 geranium is $10.

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Answer:

2 < x < 12

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the interval

difference of 2 sides < x < sum of 2 sides , that is

7 - 5 < x < 7 + 5

2 < x < 12

third side could be 3, 4, 5, 6, 7, 8, 9, 10, 11

Answer:

Each interior angle measures 108 degrees. All of the angles are congruent. The sum of the measures of the interior angles is 180(5 – 2)°.

Answer:

It equals 0

Step-by-step explanation:

Hope it helps!

The Values of missing angles are shown below.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

6. Using Angle sum property

<1 + 72 + 57 = 180

<1 = 51

Now, <2 +72 = 90

<2 = 18

<and, <3+ 57 = 180 (linear pair)

<3 = 123

Now, <4 = 180- 123- 18

<4 = 39

7. <1 = 180- 129 = 51 (linear pair)

<2 = 180- 51 - 95 = 34 (Angle sum property)

<3 = 95 (Vertical opposite angle)

<4= 180- 47 - 95 = 38

<5 = 47  (Vertical opposite angle)

<7= 180-121= 59

<6= 180-59-47= 74

8. Using Angle sum property

13x+ 2 + 5x - 7 + 3x -4 = 180

21x -9 = 180

21x = 189

x= 9

So, angles are 13x+2 = 119, 5x-7 = 38 and 3x-4 = 23

9. Using Exterior Angle property

19x- 18 = 7x+1 + 10x- 9

19x - 18 = 17x  - 8

2x = 10

x= 5

So, angles are 19x-18 = 77, 7x+1 = 36 and 10x-9 = 41

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Answer:

y = -[tex]\frac{1}{2}[/tex]x+6

Step-by-step explanation:

First off, you need to know what slope-intercept form is: y = mx+b

y = mx+b

b = the y-intercept, or where the line meets with (0,y), which is value of the coordinate is the y-intercept.

Looking at your yellow dot on the y axis, (0,6), could be the perfect fit to find the y-intercept.

So, know we know: y = mx+6

m = the slope of the line - you have to find two coordinates

in this case, it could be the two yellow points

(0,6)

(6,3)

use the following two coordinates to find the slope:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case, it would be 3-6/6-0, which equals to -1/2.

So, finally, we get:

y = -[tex]\frac{1}{2}[/tex]x+6

An ordered pair is a set of two values, (x,y), that represents a point on a coordinate plane. To solve an ordered pair means to find the coordinates (x,y) of a point on a coordinate plane.

To solve two ordered pairs, you would need to know the coordinates of both points, and then you can graph them on a coordinate plane to visualize the relationship between the two points.

For example, if you have the ordered pairs (2,3) and (4,5), you can graph them on a coordinate plane with the x-axis and y-axis, where x represents the horizontal position and y represents the vertical position. The point (2,3) would be located at 2 on the x-axis and 3 on the y-axis, and the point (4,5) would be located at 4 on the x-axis and 5 on the y-axis.

Once you have plotted the points on a coordinate plane, you can use them to make a conclusion about the relationship between the two points, for example if they are in the same line, if the distance between them, if they form a slope, etc.

The five algebraic properties of equality are: Reflexive, Symmetric, Transitive, Addition, and Multiplication properties

These properties are the foundation of algebraic manipulation and are used to solve equations and simplify expressions.

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The area of the right triangle with base 5 cm and altitude 4 cm will be 10 cm².

The area of right triangle is calculated using the formula -

Area = 1/2 × b × h. In the formula, the b is base of triangle and h is height of triangle.

Keep the values in formula to find the area of the right triangle.

Area = 1/2 × 5 × 4

Performing division on Right Hand Side of the equation

Area = 5 × 2

Performing division on Right Hand Side of the equation

Area = 10 cm²

Therefore, the area of right hand triangle will be 10 cm².

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Answer:

.35

Step-by-step explanation:

Experimentally   7 hearts were drawn with 20 tries

7/20 = .35

Answer: A: 0.13

Step-by-step explanation:

The distance between these two points is √53 units.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The two points of a triangle are (−3,−6) and (4,−8)

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

=√(4+3)²+(-8+6)²

=√7²+2²

=√49+4=√53

So the distance between these two points is √53 units

Hence, the distance between these two points is √53 units.

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Answer:

Anything to the 0 power is equal to 1

Step-by-step explanation:

Answer:

Anything to the zero power equals 1.

So on solving the provided question we cans ay that function f(3) is f(x) = -5 so x = 3

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here, we have

f(3) is f(x) = -5

so x = 3

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Sidney should buy 3 1-quart jugs of cider.

What is mean by pint?

The pint is a liquid amount that is equal to one eighth of a gallon and it is also equal to one half of a quart.

Sidney wants to drink a pint of cider. She also wants to bring a pint of cider to each of her 5 friends.

So, she needs total 6 pints of cider.

As per standard metric unit, 1 liquid pint = 0.5 liquid quart

                                    6 liquid pints = (6 × 0.5) liquid quart = 3 quarts

So, Sidney should by 3 quarts of apple Cider that means 3 amounts of 1 -quart jugs of cider.

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If a metalworker has a metal alloy that is 30​% copper and another alloy that is 60​% copper. The amount of  kilograms of each alloy is:  20kg of 30% copper alloy must be combined with 30kg of 60% copper alloy to obtain 50 kg of 48% copper alloy.

Let a be the amount of 30% copper alloy and b be the amount of 60% copper alloys. The combined alloys must be 50 kilograms.

a + b = 50 kg

The total copper in the mixture:

0.30a + 0.60b = 0.48(50)

Substitute by making use of the first equation

0.30(50-b) + 0.60b = 24

15 -0.30b + 0.60b =24

0.30b= 9

Divide both side by 0.30b

b = 9/0.30

b = 30

The amount of 30% copper alloy needed is:

a= 50-b

a = 50 -30

a = 20

Therefore 20 kg of 30% copper alloy must be combined with 30 kg of 60% copper alloy to obtain 50 kg of 48% copper alloy.

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Answer:

Dilation of 2

Step-by-step explanation:

Note that [tex]SR=2[/tex] and [tex]S'R'=4[/tex].

The scale factor is defined as the ratio of the length of the side of the image to the length of the corresponding side of the preimage.

So, the scale factor is [tex]\frac{4}{2}=2[/tex].

Place value blocks should be exchanged as

30 tenths and 18 hundredths for modeling 3.18/6 .

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. For example, the place value of 7 in 3,743 is 7 hundreds or 700. However, the place value of 7 in 7,432 is 7 thousands or 7,000.

Given,

Number to model = 3.18/6 = 0.53

The number is 3 wholes 1 tenths and 8 hundredths.

To divide it into 6 equal shares she has to exchange place value blocks as

30 tenths and 18 hundredths

Making its equal shares

30/6 tenths and 18/6 hundredths

5 tenths and 3 hundredths

Hence, 30 tenths and 18 hundredths is the way to exchange place value blocks for modeling 3.18/6.

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The end behavior will be as x approaches infinity, and negative infinity, f(x) approaches infinity.

Function is a type of relation, or rule, that maps one input to specific single output.

The function f(x) is defined as:

→ f(x)= 80x* 2 + 640 - 400x - 52

We need the degree and the leading coefficient to determine the behavior.

Since our leading coefficients has a leading even degree of 5, and a positive number,

The function will Rises to the left and falls to the right.

The end behavior will be as x approaches infinity, and negative infinity, f(x) approaches infinity.

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a) The probability that the randomly chosen injury took place on a Thursday would be 0.17.

b) The probability that the injury took place on a weekday (Monday through Friday) would be 0.84.

c) The probability that it took place on a Monday would be 21.4%.

What is the probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.

(a) To find the probability that the injury took place on a Thursday, we need to find the value of x in the probability table:

Day: Sunday Monday Tuesday Wednesday

Probability: 0.06 0.18 0.17 0.17

Day: Thursday Friday Saturday

Probability: x 0.15 0.09

The sum of the probabilities for each day must equal 1. So we can set up an equation to find x:

0.06 + 0.18 + 0.17 + 0.17 + x + 0.15 + 0.09 = 1

0.83 + x = 1

x = 0.17

The probability that the injury took place on a Thursday is 0.17.

(b) To find the probability that the injury took place on a weekday (Monday through Friday), we sum the probabilities for Monday, Tuesday, Wednesday, Thursday, and Friday:

0.18 + 0.17 + 0.17 + 0.17 + 0.15 = 0.84

The probability that the injury took place on a weekday is 0.84.

(c) Given that an injury took place on a weekday, we can use Bayes' Theorem to find the probability that it took place on a Monday. Let A be the event that the injury took place on a weekday, and B be the event that the injury took place on a Monday. Then:

P(B|A) = P(B and A) / P(A)

P(B and A) = P(B) = 0.18

P(A) = 0.84 (from (b))

So:

P(B|A) = 0.18 / 0.84 = 0.214 or 21.4%

The probability that the injury took place on a Monday, given that it took place on a weekday, is 21.4%.

Hence,

a) The probability that the randomly chosen injury took place on a Thursday would be 0.17.

b) The probability that the injury took place on a weekday (Monday through Friday) would be 0.84.

c) The probability that it took place on a Monday would be 21.4%.

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904 is a composite number.

Prime factorization: 904 = 2 × 2 × 2 × 113, which can be written 904 = 2³ × 113.

What is a factor in math?

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product

The exponents in the prime factorization are 3 and 1. ...

Factors of 904: 1, 2, 4, 8, 113, 226, 452, 904.

Factor pairs: 904 = 1 × 904, 2 × 452, 4 × 226, or 8 × 113.

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The Poisson law states that the probability of at least 2 different changes daily is 0.0263. Thus, 0.0263% of changes happen twice or more each day.

The mathematical method it explains for calculating probability calculates all the probabilities of something occurring in the setting of specific random events. A probability's proximity to the unit value and, conversely, its distance from zero can make one less comfortable in the outcome. The confidence level is based on how close the probability value is, which is calculated using a range from 0 and 1

Here,

The conditional probability function for X is the amount of times the incident occurs over a specific period of time.

In this experiment, the frequency, or x, at which an event occurs is counted.

The likelihood of the event happening throughout each period is equal.

The number of events in one period is independent of the number in other intervals.

The first step is to set the discrete stochastic process X to the number of website content updates.

Let's say that there are on average x content changes every day.

The Poisson distribution law states that the probability of at least 2 changes each day is 0.0263.

0.0263% of changes occuring twice or more as a result per day.

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410.3005

thats the answer but i need to add more characters ignore this

Answer:

Fibonacci sequence

Step-by-step explanation:

A sequence where a term in the sequence is the sum of the 2 previous terms , is a Fibonacci sequence , that is

1 + 1 = 2

2 + 1 = 3

3 + 2 = 5

5 + 3 = 8

m = 5/4 is the solution to the equation

An indices equation is an equation that relates the indices of two or more variables or functions in a mathematical expression. The indices are the exponents of the variables or functions, and the equation states the relationship between them.

The equation can be simplified as follows:

[tex]\frac{1}{\sqrt{8} } = 4^{m-2}[/tex]

[tex]\frac{1}{8^{\frac{1}{2} } } = 4^{m-2}[/tex]

[tex]8^{-\frac{1}{2} } = 4^{m-2}[/tex]

[tex](2^{3})^{-\frac{1}{2} } = 2^2^{(m-2)}[/tex]

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

Equate the powers or exponents:

-3/2 = 2(m-2)

-3/2 = 2m - 4

2m = -3/2 + 4

2m =5/2

m = 5/4

The solution to the equation is m = 5/4

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The growth factor in an exponential function is the constant multiplier that is used to generate the next value in a sequence. It is usually represented by the letter r or b.

The growth factor in an exponential function is a constant multiplier that is applied to each successive value in the series to generate the next value.

The growth factor is essentially the rate of growth of the exponential function, and is calculated by taking the ratio of two successive values of the function.

The growth factor is an important concept in exponential functions, as it helps describe how quickly the function is growing or decaying.

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Answer:

the answer is A

Step-by-step explanation:

did it not the long ago

Answer:94

Step-by-step explanation:

English is not my first language, so I don't know if you understand what I meant in the explanation.

Answer:

1) (-1;4), (4;3)

2) (-1;4), (0;0)

Step-by-step explanation:

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