Write a proof sequence for each of the following assertions. Justify each step.p→¬qr → (p ∧ q) ｝⇒ ¬r

The answer for the given question is 67.

An equation is a mathematical statement made up of two expressions connected by an equal sign. 2x - 4 = 16 is an example of an equation. We get the value of the variable x as x = 10 after solving this equation.

Coefficients, variables, operators, and constants are all components of an equation.

An equation is formed by joining two expressions with an equal sign ("=").. The two expressions on either side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side" The right-hand side of an equation is usually assumed to be zero. This will not reduce generality because we can balance it by subtracting the right-hand side expression from the expressions on both sides.

Let x be Vidya's height.

The equation will be determined by the given conditions:

x – 19 = 48

move the variable to the equation's left side:

x = 48 + 19

x = 67

Hence, the correct value for the given question is 67

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The probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors is 0.02712.

Probability of natural occurrences = 0.82Probability of outside factors = 0.18To find the probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors, we have to consider two possibilities:

The first two patients are due to natural occurrences, or the first two patients are due to outside factors.If the first two patients are due to natural occurrences, the probability of the third patient being the first due to outside factors is:0.82 x 0.82 x 0.18 = 0.12272

If the first two patients are due to outside factors, the probability of the third patient being the first due to outside factors is:0.18 x 0.82 x 0.82 = 0.12272

Therefore, the total probability of the third patient being the first due to outside factors is the sum of these two probabilities:0.12272 + 0.12272 = 0.24544But, we have counted the case where all three patients have outside factors twice, so we need to subtract that probability once:0.24544 - 0.01836 = 0.22708

Therefore, the probability that the 3rd patient with heart failure that enters the emergency room is the first one due to outside factors is 0.22708 or approximately 0.02712.

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Answer:15 twice

Step-by-step explanation:

There are 28 ounces of essential oil is needed for 728 ounces of wax.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

There are 8 ounces of essential oil is used for 208 ounces of wax.

Now,

Number of ounces of essential oil is used in 1 ounces of wax;

= 8 ÷ 208

= 8 / 208

= 1 / 26

Thus, For 728 ounces of wax, number of ounces of essential oil is;

= 728 × 1/26

= 728 / 26

= 28

Therefore,

There are 28 ounces of essential oil is needed for 728 ounces of wax.

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Answer:

A

Step-by-step explanation:

using the cosine ratio in the right triangle

cos? = \(\frac{adjacent}{hypotenuse}\) = \(\frac{17}{27}\) , then

? = \(cos^{-1}\) ( \(\frac{17}{27}\) ) ≈ 51° ( to the nearest degree )

The number of periods is approximately 26.98.

To calculate the number of periods it takes to double your money at 5.25 percent interest, you can use the formula for compound interest:

Future value = Present value * (1 + interest rate) ^ number of periods

In this case, the future value is twice the present value, so the equation becomes:

2 = 1 * (1 + 0.0525) ^ number of periods

To solve for the number of periods, you can take the logarithm of both sides:

log(2) = log((1 + 0.0525) ^ number of periods)

Using the logarithmic properties, you can bring the exponent down:

log(2) = number of periods * log(1 + 0.0525)

Finally, you can solve for the number of periods:

number of periods = log(2) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 13.27.

To calculate the number of periods it takes to quadruple your money at 5.25 percent interest, you can follow the same steps as above, but change the future value to four times the present value:

4 = 1 * (1 + 0.0525) ^ number of periods

Solving for the number of periods using logarithms:

number of periods = log(4) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 26.98.

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74100

170000

36000

I believe this is right!

The function is an exponential growth since it is increasing with time and k is positive

Given that at t =6, P = 167075

Then;

167075 =110.8e^6k

167075/110.8 = e^6k

1507.9 = e^6k

ln(1507.9) = 6k

k = ln(1507.9)/6

k = 1.2

Thus in the year 2020;

P = 110.8e^20(1.2)

P = 2.9 * 10^12

In the year 2025;

P = 110.8e^25(1.2)

P = 1.18 * 10^15

To reach 290,000

290,000 = 110.8e^1.2t

290000/110.8 = e^1.2t

2617.3 = e^1.2t

t = ln(2617.3 )/1.2

t = 7 years

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Step-by-step explanation:

A³B = 4T

A³=4T/B

A = cbrt 4T/B. or

³√(4T/B)

hope this helps.

Therefore, the distance between the two points is simply the difference in their x-coordinates, this makes sense since both points lie on the same horizontal line, and so the vertical distance between them is zero.

Distance is a numerical measurement of how far apart two objects or points are from each other. It is a scalar quantity that is usually expressed in units of length, such as meters, kilometers, miles, or feet. Distance is often used in physics, mathematics, and engineering to describe the spatial separation between two objects or points. It is also used in everyday language to describe how far away something is, such as the distance between two cities or the distance from a person's house to their workplace.

By the question.

The distance between two points on a coordinate plane can be found using the distance formula:

distance =\(\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-x_{1}^{2} ) }\)

In this case, the two points are (0, b) and (a, b). We can substitute these values into the distance formula:

distance = \(\sqrt{(a-0)^{2}+(b-b)^{2} }\)

distance = \(\sqrt{a^{2}+0 }\)

distance = a

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So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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Answer:

1.

Blank 1: y

Blank 2: x

2.

Blank 1: x

Blank 2: y

Step-by-step explanation:

The reflection of a point along y-axis means the y value stays the same and the x-value changes its sign.

Blank 1: y

Blank 2: x

The reflection of a point along x-axis means the x value stays the same and the y-value changes its sign.

Blank 1: x

Blank 2: y

Answer:

answer is

D. 45. hhhisukwk

Answer:

The '=' sign.

Step-by-step explanation:

The equals sign ( = ). for example:

3x + 1 = 8.

The  equals sign was invented by Robert Recorde of Tenby, South Wales, UK in the early part of the 16th century.

The domain of g(x) is all real numbers, and the range is (61, ∞) and the range is (61, ∞).

The domain of a function is the set of all possible input values for which the function is defined, while the range is the set of all possible output values.

For the given function g(x) = -1/4 (x−17)² + 61, the domain is all real numbers since there are no restrictions on the input values.

To find the range, we can use the fact that the vertex of the parabola is at (17, 61) and the coefficient of the squared term is negative, indicating a downward opening parabola.

Thus, the maximum value of the function occurs at the vertex and is 61, which is also the minimum possible value. Therefore, the range is (61, ∞).

In summary, the domain of g(x) is all real numbers, and the range is (61, ∞).

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The probability that the mean length of 10 randomly chosen terms is less than 10.2 inches is 0.6368

Using the central limit theorem, the distribution of sample means will also be normally distributed with a mean of 9 inches and a standard deviation of (14 inches/sqrt(10)) = 4.427 inches.

To find the probability that the mean length is less than 10.2 inches, we need to standardize this value by subtracting the mean and dividing by the standard deviation:

z = (10.2 - 9) / 4.427 = 0.347

Using a standard normal distribution table or calculator, we can find the probability that z is less than 0.347:

P(z < 0.347) = 0.6368

Therefore, the probability that the mean length of 10 randomly chosen terms is less than 10.2 inches is 0.6368 (rounded to four decimal places).

Note that the central limit theorem is applicable when the sample size is large enough (n > 30) or when the population distribution is normal.

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The correct option is A, the lower quartile (Q1) and it is 75.

We must comprehend the quartiles of the box plot in order to calculate the number below which 25% of the data lies.

A box plot's interquartile range (IQR), which contains the middle 50% of the data, is represented by the box.

The median, which splits the data into two equally sized half, is shown by the line inside the box.

Here, the box has a line at 79 and spans from 75 to 82.

Accordingly, the lower quartile (Q1) and the upper quartile (Q3) are both situated near the box's boundary, which is 75 and 82, respectively.

The line inside the box, which is 79, is the median (Q2).

The first quartile (Q1) or the 25th percentile must be identified in order to establish the number below which 25% of the data lies.

The first quartile in a box plot symbolizes the number below which 25% of the data is found.

Since Q1 is located at the lower boundary of the box, which is 75, 25% of the data lies below the score of 75.

Hence the correct option is A.

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Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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Answer:

Discrete

Step-by-step explanation:

Given the function:

f(x) = 100x + 300

Where ;

x = number of attendees

At least 4 students but no more than 9 students will attend the fieldtrip due to transportation and chaperone restrictions

Range of attendees :

4 ≤ x ≤ 9

Is this a discrete or continuous situation?

It is a discrete because the number of students who will attend the science weekend are finite and countable.

The number of attendees range from:

4, 5, 6, 7, 8 and 9.

Answer:

Move all terms that don't contain  x to the right side and solve.

x = 3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

3x + 2 = 11

Subtract by 2 on both sides

3x = 9

Divide by 3 on both sides

x=3

Answer:

no solution

Step-by-step explanation:

hope this helps have a good day :)

Answer: 18in

Step-by-step explanation:

0.50x 3 = 1.50

50 divided by 5 is 10

1in every 10 cent

ok

Possible prices

Toy 1 Toy 2 Total Price

$12 $4 $16

$8 $8 $16

$4 $12 $16

These are the possible prices:

STEP - BY - STEP EXPLANATION

What to find?

The new the new account balance after 9 months.

Given:

Principal (p) = $20 000

Rate(R) = 8

Time(t) = 9 months = 9/12 year = 0.75 years.

We will solve the given problem using the steps below:

Step 1

State the formula that will be use to solve the problem.

Where I is the interest.

Step 2

Substitute the values into the formula.

Hence, interest(I) = $1200

But;

Amount = principal + Interest

= 20 000 + 1200

=21200

Therefore, the account balance after 9 months is $21200

ANSWER

$21200

The Formula of Area of Obtuse Triangle is equal to ½ × b× h .

and by using Heron's formula,

A = √(S(S-a)(S-b)(S-c)) ; S = (a+b+c)/2

A closed two-dimensional figure with three sides of equal or unequal length and three corners of equal or unequal angles is called a triangle.

Obtuse triangle: A type of triangle with the following properties:

Area formula of obtuse triangle :

Area of obtuse triangle = ½ × b × h

where b --> base of triangle

h ---> height of triangle.

The area of a triangle can also be found using Heron's formula.

A = √(S(S-a)(S-b)(S-c)),

where s is half the perimeter of the triangle and a, b, c are the three sides of the triangle.

the perimeter of the triangle = a + b + c cm then

S = (a + b + c)/2

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The minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.

The minimum and maximum mass measurement is determined from the uncertainty in the measurement.

For a given uncertainty of 2.2%, the minimum and maximum mass measurement is calculated as follows;

2.2% of 1.5 kg = 0.022 x 1.5 kg = 0.033 kg

minimum mass = 1.5 kg - 0.033 kg = 1.467 kg

maximum mass = 1.5 kg + 0.033 kg = 1.533 kg

Thus, the minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.

The complete question is below:

what is the minimum and maximum mass of 1.5 kg if the uncertainty in measurement is 2.2%?

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The correct option of the given statement "Janice's funds to triple if she has $5,000 invested in a bank that pays 9.4% annually" is 11.86 years.

To solve the problem, we can use the formula for the future value of a single sum.

FV = PV (1 + i)ⁿ

Where,

PV is the present value of the investment

"i" is the annual interest rate

n is the number of years

FV is the future value of the investment.

So, we can say that the future value (FV) of Janice's investment will be 3 times her present value (PV). Thus,

FV = 3 PV

    = 3 × 5,000

    = $15,000

Now, we can substitute the given values in the formula:

FV = PV (1 + i)ⁿ

15,000 = 5,000(1 + 0.094)ⁿ

Dividing both sides by 5,000, we get:

3 = (1 + 0.094)ⁿ

Taking the logarithm of both sides:

log 3 = log (1 + 0.094)ⁿ

log 3 = n log (1 + 0.094)

n = log 3 / log (1 + 0.094)

n = 11.86 years

Therefore, it will take approximately 11.86 years for Janice's funds to triple.

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The required expression that describes the shaded region is (A'∩B) ∪ (A ∩ B'). Option A is correct.

GIven that,
For the given Venn diagram which expression represents the shaded area

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,
The total area of A and B
= AUB
Area of unshaded area,
= (A'∩B) ∪ (A ∩ B')

Thus, the required expression that describes the shaded region is (A'∩B) ∪ (A ∩ B'). Option A is correct.

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