What type of proofs did they use?

Answer:

Step-by-step explanation:

To construct an infinite set of sets of natural numbers such that all of their pairwise symmetric differences are infinite, we can define the following sequence of sets:

S_1 = {1, 2, 3, ...}

S_2 = {2, 3, 4, ...}

S_3 = {1, 3, 5, ...}

S_4 = {2, 4, 6, ...}

S_5 = {1, 4, 7, ...}

S_6 = {2, 5, 8, ...}

...

In general, S_n is the set of natural numbers that are congruent to n mod 2. For example, S_1 is the set of all odd natural numbers, S_2 is the set of all even natural numbers, and so on.

To show that all of their pairwise symmetric differences are infinite, we can consider any two distinct sets S_n and S_m. Without loss of generality, assume that n < m. Then, the symmetric difference between S_n and S_m is the set of natural numbers that are congruent to n or m mod 2, but not both:

S_n Δ S_m = {k ∈ N : (k ≡ n mod 2) XOR (k ≡ m mod 2)}

Since n < m, we can see that every other natural number is in this set, and therefore it is infinite. Hence, the sequence {S_n} is a set of sets of natural numbers such that all of their pairwise symmetric differences are infinite

According to the information it can be inferred that the heaviest dog is 20 ounces heavier than the lightest dog.

To calculate the difference in weight between the heaviest and lightest dogs we must identify the values of the lines according to the above, it can be inferred that the lightest dog is in the 0.5 pound position, while the heaviest dog is in the the 1.75 pound position.

To know the difference in ounces we must convert these values to ounces with the following information:

So, we must apply a rule of three as shown below:

Based on the above, the difference in ounces would be 20 ounces.

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Answer:320000

Step-by-step explanation:

Answer:

90  berries

Step-by-step explanation:

Answer:

Step-by-step explanation:

If f(x) is an even function, that means it has symmetry across the y-axis. In other words, if (a,b) is a point on the graph of f(x), then (-a,b) must also be on the graph.

We are given that f(2) = -5. Since 2 is a positive number, we know that (-2) is the corresponding negative value that also lies on the y-axis. Therefore, we can say that f(-2) = f(2) = -5.

So, the other point that must be on the graph of f(x) is (-2,-5).

Answer:

Step-by-step explanation:

125.

The distance from Philadelphia to Outer Banks is given by A = 10.294 miles

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the distance on the map be represented as

1 inch = 50 miles

So , the distance between Philadelphia to Outer Banks is = ( 7 / 34 ) inches

And , the distance between Philadelphia to Outer Banks = ( 7/34 ) x 50 miles

On simplifying the equation , we get

The distance between Philadelphia to Outer Banks A = 0.20588 x 50

The distance between Philadelphia to Outer Banks A = 10.294 miles

Hence , the distance is 10.294 miles

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Kenny need to buy 4 quarts.

It cost $14.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The mailbox is splitted into two shapes.

One is rectangle and the other is hemisphere.

Length of the rectangle = 2.4 ft

Width of the rectangle = 1.5 ft

Height of the rectangle = 3 ft

Surface area of the given rectangle

                  = 2(lw + wh + lh) – lw

                  = 2(2.4 × 1.5 + 1.5 × 3 + 2.4 × 3) – (2.4 × 1.5)

                  = 2(3.6 + 4.5 + 7.2) – 3.6

                  = 2(15.3) – 3.6

                  = 27

Surface area of the given rectangle = 27 square feet

Radius of the hemisphere = 1.2 ft

Curved surface area of hemisphere

                 = 2*pi*r^2

                  = 9.0432 square feet

Curved surface area of hemisphere = 9.0432 square feet                                      

Total surface area of the mailbox  = 27 + 9.0432

                                                        = 36.0432 square feet

To find how many quarts are needed to cover the mailbox.

1 Quart covers = 10 square feet

36.0432 sq. ft = 36.0432 ÷ 10

                      = 3.60432 quarts

                      ≈ 4 quarts (approximately)

Hence Kenny need to buy 4 quarts.

Cost of 1 quart = $3.50

Cost of 4 quart = 4 × 3.50

                        = 14

Hence it cost $14.

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There are total 15 students who take all three subjects.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We know that;

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C)- n(A ∩ C)+ n(A∩B ∩C)

Here, Total number of students in the school = 62

Hence, By using theorem;

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C)- n(A ∩ C)+ n(A∩B ∩C)

Here, Let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry

so putting values,

62 =  40 + 42 + 38 - 20 - 28 - 25 + n(A∩B ∩C)

62 + 73 - 120 = n(A∩B ∩C)

n(A∩B ∩C) = 15

Therefore, There are total 15 students who take all three subjects.

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Answer:

b = 82

Step-by-step explanation:

Given

a =46 degrees

c = 52 degrees

Since XY is a straight line, it has an angle of 180 degrees

So, Angle a + angle b + angle c = 180 degrees

46 + angle b + 52 = 180

angle b + 98 = 180

angle b = 180 - 98

angle b = 82 degrees

Therefore angle b is equal to 82 degrees

Answer:

180 in a straight line

Step-by-step explanation:

there is 180⁰ in straight line.

46 + 52 is 98

180 - 98 is 82

We do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.

Probability is a method for assessing how likely something is to happen. Many occurrences cannot be foreseen with 100% accuracy. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

We cannot determine whether the probability of an adult being a full-time college student and 65 or older is nonzero based on the given information alone.

To see why, consider the following two scenarios:

Scenario 1: The proportion of adults who are both full-time college students and 65 or older is 0%.

In this case, the events "full-time college student" and "65 or older" are mutually exclusive. That is, no adult can be both a full-time college student and 65 or older. Therefore, P(full-time college student and 65 or older) = 0%.

Scenario 2: The proportion of adults who are both full-time college students and 65 or older is greater than 0%.

In this case, the events "full-time college student" and "65 or older" are not mutually exclusive. That is, there may be some adults who are both full-time college students and 65 or older. Therefore, P(full-time college student and 65 or older) is greater than 0%.

Since we do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.

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In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In option (c) A boxplot of the data has a large outlier, we would not be safe constructing the interval based on an SRS of size 24 from the population.

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

Constructing a one-sample t interval for a population mean is generally safe when the population is not Normal, as long as the sample size is large enough (usually at least 30) or the sample is taken from a population that is not too skewed or has outliers.

Therefore, options (a), (b), and (e) suggest that the sample may come from a population that is roughly Normal or can be transformed to be Normal, and so constructing the interval based on an SRS of size 24 would be safe.

Option (d) suggests that the sample standard deviation is large, but this does not necessarily mean that constructing the interval would not be safe.

It may reduce the precision of the interval, but as long as the sample size is sufficient, the interval can still be constructed.

Option (c) suggests that the sample has a large outlier, which may significantly affect the distribution of the sample and the calculation of the interval.

Therefore, in this circumstance, constructing the interval based on an SRS of size 24 would not be safe.

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Answer:

see explanation

Step-by-step explanation:

using the rules of radicals

• [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

• [tex]\sqrt{\frac{a}{b} }[/tex] ⇔ [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

(1)

[tex]\sqrt{108}[/tex]

= [tex]\sqrt{36(3)}[/tex]

= [tex]\sqrt{36}[/tex] × [tex]\sqrt{3}[/tex]

= 6[tex]\sqrt{3}[/tex]

(2)

[tex]\sqrt{14}[/tex] × [tex]\sqrt{35}[/tex]

= [tex]\sqrt{14(35)}[/tex]

= [tex]\sqrt{490}[/tex]

= [tex]\sqrt{49(10)}[/tex]

= [tex]\sqrt{49}[/tex] × [tex]\sqrt{10}[/tex]

= 7[tex]\sqrt{10}[/tex]

(3)

[tex]\sqrt{\frac{28}{64} }[/tex]

= [tex]\frac{28}{\sqrt{64} }[/tex]

= [tex]\frac{\sqrt{28} }{8}[/tex]

= [tex]\frac{\sqrt{4(7)} }{8}[/tex]

= [tex]\frac{\sqrt{4}(\sqrt{7}) }{8}[/tex]

= [tex]\frac{2\sqrt{7} }{8}[/tex]

= [tex]\frac{\sqrt{7} }{4}[/tex]

Answer:

$154.37

Step-by-step explanation:

$617.48 * 0.25 = $154.37

The price of shipping and handling is $154.37.

Please mark brainlyest.

The Fibonacci numbers are defined by the following recursive formula: f0 = 1, f1 = 1, fn = fn−1 + fn−2 for n ≥ 2. Thus, each number in the sequence (after the first two) is the sum of the previous two numbers.

Imagine you draw a straight line down the middle of a piece of paper. This line is the line of symmetry. Anything you draw on one side of the line is going to have a mirror image on the other side of the line that looks exactly the same.

Now, if you have a point on the line of symmetry, that means the point is exactly in the middle of the line. And since the line is the same on both sides, that means the point is going to be the same on both sides too! So, the point on the line of symmetry stays in the same place and looks the same on both sides of the line.

- Dante

Answer:

Step-by-step explanation:

To find the x-intercepts of the polynomial function f(x) = x^4 - x^2, we need to set f(x) = 0 and solve for x. That is, we need to find the values of x that make the function equal to zero.

f(x) = x^4 - x^2

Setting f(x) = 0, we get:

x^4 - x^2 = 0

Factoring out x^2, we get:

x^2(x^2 - 1) = 0

Using the zero product property, we get:

x^2 = 0 or x^2 - 1 = 0

Solving for x in each case, we get:

x = 0 or x = ±1

Therefore, the x-intercepts of the polynomial function f(x) = x^4 - x^2 are (0, 0), (1, 0), and (-1, 0).

Answer:

No real solutions

Step-by-step explanation:

If lines are parallel, it means that they will never meet each other indicating that there are no real solutions.

Answer:

x = 40° , y = 43° , z = 97°

Step-by-step explanation:

∠ DAC = y = ∠ ACB = 43°

• opposite angles in a parallelogram are congruent , then

z = ∠ D = 97°

the sum of the 3 angles in Δ ACD = 180° , that is

x + y + 97° = 180°

x + 43° + 97° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

then

x = 40° , y = 43° , z = 97°

The requried, percentage of students who study less than 2.50 hours a day is approximately 25.14 percent.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

We need to convert 2.50 hours to a standard score (z-score) using the formula,

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

z = (2.50 - 3.00) / 0.75

z = -0.67

This means that 2.50 hours is 0.67 standard deviations below the mean.

We can use a standard normal distribution table or a calculator to find the percentage of the distribution that falls below this standard score. For example, using a standard normal distribution table, we can look up the area to the left of z = -0.67 and get:

P(z < -0.67) = 0.2514

So the correct answer is (a) 25.14 percent.

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Simplifying, the exponents expression, we have 63y/xu⁴

Exponents are the powers to which a particular number is raised.

Given the expression 3y⁻⁴ . 3y⁵x⁸u⁻⁵.7x⁻⁹. To simplify the expression, we use the product rule of exponents which states that for a given base x, xᵃ xᵇ = xᵃ⁺ᵇ.

So, applying this rule to the expression and collecting common bases, we have that

3y⁻⁴ . 3y⁵x⁸u⁻⁵u.7x⁻⁹ = 3y⁻⁴ × 3y⁵ × x⁸ × 7x⁻⁹ × u⁻⁵ × u

= 3 × 3 × y⁻⁴ × y⁵ × 7 × x⁸ × x⁻⁹ × u⁻⁵ × u

Applying the product rule, we have that

= 3 × 3 × y⁻⁴ ⁺ ⁵ × 7 × x⁸ ⁺(⁻⁹) × u⁻⁵ ⁺ ¹

= 3 × 3 × y⁻⁴ ⁺ ⁵ × 7 × x⁸ ⁻ ⁹ × u⁻⁵ ⁺ ¹

= 3 × 3 × y × 7 × x⁻¹ × u⁻⁴

= 3 × 3 × 7 × y × x⁻¹ × u⁻⁴

Using the reciprocal rule that x⁻ⁿ = 1/xⁿ, we have that

= 3 × 3 × 7 × y × x⁻¹ × u⁻⁴

= 63 × y × 1/x × 1/u⁴

= 63y/xu⁴

So, simplifying, we have 63y/xu⁴

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Answer:

How many centimeters are there in 58 inches?

1 in. = 2.54 cm

Step-by-step explanation:

Answer:  22.50

Step-by-step explanation:

25 x 0.1

25 - 2.5

Answer:

The correct answer is 22.50

Person's diastolic blood pressure at 6:00am is  94.5 mmHg.

Diastolic blood pressure is the lower number in a blood pressure reading. It indicates the pressure in the arteries when the heart muscle is resting between beats and refilling with blood. A normal diastolic blood pressure is between 80 and 90 mmHg (millimeters of mercury).

For example, if a person's blood pressure reading is 120/80 mmHg, the diastolic blood pressure is 80 mmHg. This means that the pressure in the arteries when the heart is at rest is 80 mmHg. High diastolic blood pressure (greater than 90 mmHg) is a risk factor for heart attack, stroke, and other cardiovascular problems.

The formula for diastolic blood pressure at time t is given by B(t) = 90 + 9 sin(t/12). To find the diastolic blood pressure at 6:00am, need to plug in t = 6 into the formula.

B(6) = 90 + 9 sin(6/12) = 90 + 9 sin(0.5) = 90 + 9(0.4794) = 94.5 mmHg.

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The magnitude of the earthquake, as measured on the Richter Scale, is 2.5.

What is Richter Scale ?

The Richter Scale is a logarithmic scale used to measure the magnitude of earthquakes. It was developed by seismologist Charles Richter in the 1930s and is named after him.

The Richter Scale measures the amplitude of the seismic waves produced by an earthquake, which are detected by seismographs. The amplitude is a measure of the size of the earthquake, and is related to the amount of energy released by the earthquake.

Given by the question:
The Richter Scale equation for the magnitude (R) of an earthquake is:

R = log(A/A0)

where A is the amplitude of the earthquake and A0 is a standard wave amplitude.

We are given that the earthquake amplitude (A) is 288 times as great as the standard wave amplitude (A0):

A = 288 A0

Substituting this into the Richter Scale equation, we get:

R = log(288 A0 / A0)

R = log(288)

Using a calculator or a logarithm table, we can evaluate the logarithm of 288 to get:

R = 2.46

Rounding this to one decimal place, we get:

R ≈ 2.5

Therefore, the magnitude of the earthquake, as measured on the Richter Scale, is 2.5.

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The remainder theorem can be used to determine the volume of a cage with a 15-inch height since b = 15, which results in a volume of 2160 inch3.

The size of an item in 3 directions is the area that is covered by its boundaries. The amount of room an object occupies in three aspects is measured by its height, which is given in cubic inches. A few of illustrations of cubic units are cm3 and in3. On the other perspective, an item's mass is used to measure what more matter it contains. The typical method to ascertain an object's mass is to weigh it, either in pounds or kilograms. Unlike the fundamental equations for the area of a rectangular box, which is length, breadth, and height, the primary equation for volumes is length, width, and height.

given

Height is listed as b and is 18 inches.

B = 18 s= b-3 (from I = 18 - 3 s = 15 as a result.

Therefore, volume

volume of a rectangle = l x b x h V= 18 x 15 x 15 = 4,050 inch3

3) Height = 15 then b = 15 b -15 = 0 if height = 15.

The remaining theorem's definition is:

To get a smaller polynomial and a remainder, we divide a polynomial P(x) by the factor (x - a). The polynomial does not have to contain the factor.

= 2160

The remainder theorem can be used to determine the volume of a cage with a 15-inch height since b = 15, which results in a volume of 2160 inch3.

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a. The proportion of adults who took zinc are 17/100.

b. The proportion of adults who took vitamin C reported NOT having a cold in the last 30 days are 41/56.

c. The proportion of adults who reported having a cold took Echinacea are 3/13.

The solution has been obtained by using proportions.

What is proportion?

The comparison of two numbers in mathematics, is known as a proportion. According to the law of proportion, two sets of provided numbers are deemed to be directly proportionate to one another if they increase or decrease in the same ratio. They are inversely proportional if not.

We are given a table showing the results of the survey.

a. Out of 200, 34 adults took zinc. So, the proportion comes out to be

34/200 = 17/100

b. From the table, we can see that 82 adults out of 112, were reported of not having cold in the last 30 days. So, the proportion comes out to be

82/112 = 41/56

c. It is given that total 52 people were reported of having cold. Out of this, 12 adults took Echinacea. So, the proportion comes out to be

12/52 = 3/13

Hence, the required proportions have been obtained.

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Answer:

19. x = 60

20. x= 27

Step-by-step explanation:

19. Given 2 triangles are congruent

so BQ/BC = BR/BD

30/84 = x/168

84x = 30(168)

84x = 5040

x = 5040/84 = 60

20. Given 2 triangles are congruent

QS/QP = ST/PR

18/x = 10/15

10x = 18(15)

10x = 270

x = 270/10 = 27

Both Student A and Student B's representations of the expression 9/y³ⁿ are incorrect.

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a meaningful way. An expression can represent a value, a quantity, a function, or some other mathematical object. Expressions can be made up of one or more terms. A term is a group of numbers, symbols, and/or variables that are separated by a plus or minus sign. Expressions can also include mathematical operations, such as addition, subtraction, multiplication, and division, as well as exponents and parentheses. Expressions are used in various areas of mathematics, including algebra, calculus, and statistics, to represent mathematical relationships and to solve problems.

Here,

Student A represents the expression as the product of 9 and y times the product of 3 and t, which can be written as: 9 * y * 3 * t = 27yt.

This representation is incorrect because it does not include the exponent 3 in the denominator. The correct representation of the expression is: 9 / y^3t.

Student B represents the expression as the quotient of 9 and y times the sum of 3 and t, which can be written as: 9 / y * (3 + t) = (27 + 9t) / y.

This representation is also incorrect because it incorrectly combines the sum of 3 and t in the denominator. The correct representation of the expression is: 9 / y^3t.

To represent the expression correctly, we need to include the exponent 3 in the denominator, indicating that y is being raised to the power of 3, and include t as a separate factor in the denominator. Therefore, the correct representation of the expression is: 9 / (y^3 * t).

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Answer:

Student A says prodact of Tandy, but 9 is 9 y so it's quotient.

Step-by-step explanation:

The length of the center of the circle is approximately 391.9 cm

Let's call the point where the two chords intersect point P. To find the length of the center of the circle to point P, we need to find the distance between point O (the center of the circle) and point P.

To do this, we first need to find the distance from point O to each chord. We can use the Pythagorean theorem to do this. Let's call the midpoint of the first chord point A, and the midpoint of the second chord point B. Then:

OA = √((360 cm)^2 - (280 cm)^2) = 160√2 cm

OB = √((360 cm)^2 - (320 cm)^2) = 40√17 cm

Next, we need to find the distance from each midpoint (A and B) to point P. We can use the formula for the length of a chord that passes through the center of a circle:

AP = BP = √(2r^2 - d^2)

where r is the radius of the circle and d is the length of the chord. Then:

AP = BP = √(2(360 cm)^2 - (560 cm)^2) = 320√2= 320√(2) cm

Now we can use the Pythagorean theorem again to find the distance from point O to point P:

OP = sqrt(OA^2 - AP^2) = √(160√2 cm)^2 - (320√(2) cm)^2) ≈ 391.9 cm

Therefore, the length of the center of the circle to the crossing point of the chords is approximately 391.9 cm.

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Answer: 280cm

Step-by-step explanation:

Use some graph paper and draw the question scaling it down by 0.01.

5.6cm 6.4cm and the radius 3.6cm.

Then multiply the answer by 100.

This is one way to get the answer, but I am sure there are more and one way to get to the 280cm.

Good luck, and share your ideas.