Suppose the equation for line A is y = 6/5 x - 10 Line A is parallel to line B, which is perpendicular to line C. If line D is perpendicular to line C and perpendicular to line E, what is the slope of line E? Justify your conclusion.

Answer:

A

Step-by-step explanation:

a) ✔️

This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.

b) ❌

There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.

c) ❌

This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.

d) ❌

This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.

Answer:

B. 171

Step-by-step explanation:

Answer:

The answer is 171

Step-by-step explanation:

You do the math in the parentheses first, then the sum to the power of two, then multiply by 4, and then subtract by 5^2.

4×(2+5)^2-5^2

4×(7^2)-5^2

4×(49)-5^2

4×49-5^2

196-5^2

196-25=

171

See Explanation

Step-by-step explanation:

\( \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \\ \\ = 4 \times 1 - 3 \times 2 \\ \\ = 4 - 6 \\ \\ = - 2\)

\( \begin{bmatrix} 4 & 2 & 6 \\ - 1 & - 4 & 5\\ 3 & 7 & 2 \end{bmatrix} \\ \\

=4(-4\times 2-5\times 7)\\ -2(-1\times 2-5\times 3)\\ +6(-1\times 7-(-4)\times 3)\\\\

= 4(-8-35) -2(-2-15) \\+6(-7+12)\\\\

= 4(-43) -2(-17) +6(5)\\\\

= - 172 + 34 + 30\\\\

= 64 - 172\\\\

= - 108 \\\)

In two years, Country F's GDP is projected to be in the millions.

Currently, its GDP stands at $975,875, and it experiences an annual growth rate of 11%. Based on these figures, Country F's GDP in two years can be calculated.

To determine the GDP in two years, we need to calculate the growth rate for each year and apply it to the current GDP.

The growth rate is given as 11% annually, which means it is compounded over each year. To calculate the growth rate, we can use the formula:

GDP in two years = Current GDP × (1 + Growth Rate)^Number of Years

Plugging in the values, we get:

GDP in two years = $975,875 × (1 + 0.11)^2

Simplifying the equation, we have:

GDP in two years = $975,875 × 1.11^2

Evaluating the expression, we find:

GDP in two years ≈ $1,131,586

Therefore, based on the given growth rate of 11% annually, Country F's GDP is projected to be approximately $1,131,586 in two years.

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Answer:

\(\displaystyle 50\)

Step-by-step explanation:

See above image

I am joyous to assist you at any time.

Answer:

50

hope it helps you have a great day keep smiling be happy stay safe

Answer:

That's not full question

Answer:

32ft^2

Step-by-step explanation:

V1=l*w*h

V1=4*2*5

v1=40

V2=4*2*1

V2=8

V1-V2=Volume of the solid

40-8=32

Answer:

392.7

To get the answer multiply Density * Volume

Mass = 0.1785 * 2200

Mass = 392.7

The mass of the helium with a density of 0.1785 kilograms per cubic meter and volume of 2,200 cubic meters  is 392.7 kg

The density of a substance is its mass per unit volume. It can be represented mathematically as follows:

density = mass / volume

Therefore,

mass of the helium = ?

density of the helium = 0.1785  kilograms per cubic meter

volume of helium = 2,200 cubic meters

Therefore,

mass = density × volume

mass =  0.1785 × 2200

mass = 392.7 kg

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Answer:

0.85 × 9.412=8.0002 nearest so 0.25 × 9.421= 2.35525

Step-by-step explanation:

1. A mathematical expression showing the amount Trey will owe for his car is y = 2x.

2. For an 11-day rental, the amount that Trey will owe for his car is $22.

A mathematical expression is a mathematical statement that shows the value of the expression, which is always made up of numbers, variables, constants, coefficients, and mathematical operations.

Mathematical operations include addition, subtraction, division, and multiplication.

Let the daily rental charge = $2

The number of days the car is rented = x

The total rental charge = y

y = 2x.

For an 11-day rental:

y = 2 x 11

y = 22

y = $22

Thus, the expression that shows the amount that Trey would owe for an 11-day rental is $22.

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The prevalence odds ratio is calculated by taking the ratio of the probability of having diabetes for those with access to green spaces over the probability of having diabetes for those without access to green spaces. This can be represented by A/(B*C) or D.

The prevalence odds ratio is a measure of the likelihood of an outcome in one population compared to another. In this case, the odds ratio of diabetes status among those who do versus those who do not have access to green spaces is calculated by taking the ratio of the probability of having diabetes for those with access to green spaces over the probability of having diabetes for those without access to green spaces. This ratio can be represented as A/(B*C) or D, where A is the ratio of those with diabetes among those with access to green spaces over those without diabetes among those with access to green spaces, B is the probability of having diabetes among those with access to green spaces, C is the probability of having diabetes among those without access to green spaces, and D is the ratio of those with diabetes among those without access to green spaces over those without diabetes among those without access to green spaces. It is important to note that the odds ratio only represents relative risk and does not necessarily mean that access to green spaces is a direct cause of diabetes.

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By setting up the equation and solving we get the positive number is 2/5.

A positive number is a number greater than zero. In mathematical terms, it is a number that is greater than zero on the number line. Positive numbers are often represented with a "+" sign in front of them, but this is not always necessary as the positive sign is the default and is usually omitted.

An equation is a mathematical statement that asserts the equality of two expressions. It is a statement that asserts that the two expressions on either side of the "=" sign are equal and have the same value. The expressions on either side of the "=" sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.

For example:

2x + 3 = 7

x(2x+x/2)=x

2x^2+x^2/2=x

5x^2/2=x

5x^2=2x

5x=2

x=2/5

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Complete question is;

Ilona is at a friends home that is several miles from her home. She starts walking at a constant rate in a straight line toward her home.

The expression -2t + 10 gives the distance, in miles, that Ilona is from her home after t hours. Select True or False for each of the following.

1. The friends home is 10 miles from Ilonas home

2. The distance Ilona has walked away from her friends home after t hours is given by the absolute value of -2t

3.The negative sign in the term indicates that Ilona is walking toward her home

4. Ilona is walking at a rate of 10 miles per hour

Answer:

Statements 1 & 2 are correct.

Step-by-step explanation:

We are told that the expression -2t + 10 gives the distance, in miles, that Ilona is from her home after t hours.

Now, we know that distance = speed x time

Now, from the expression -2t + 10

It's clear that 2t is a distance value.

This means that the speed used in going home is 2 miles/hr

This means that at t hours, she has walked 2t miles from her friends home.

Thus, statement 2 is true because an absolute value of -2t will be 2t.

Since 2t is subtracted from 10 in the expression and 2t is the distance she has walked from her friends house at Time, t. It means that 10 miles is the distance from her friends house to her house.

Thus, statement 1 is also true

Answer:

acute equilateral

Step-by-step explanation:

acute is less than 90 angles, and all sides are equal.

Answer:

It looks to me like an Acute Equilateral.

Step-by-step explanation:

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

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By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.

To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.

First, let's examine the given figure and information.

We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.

To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.

Supplementary angles are defined as two angles whose measures sum up to 180 degrees.

We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.

Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.

Now, let's assume that segments HI and JK are not parallel.

In this case, if we extend lines HA and JA, they will eventually intersect at point P.

Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.

However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.

Therefore, our assumption that segments HI and JK are not parallel must be incorrect.

Consequently, we can conclude that segment HI is indeed parallel to segment JK.

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Answer:

SA = 10,800 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 40

w = 60

h = 30

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 60(40) + 30(40) + 30(60) )

SA = 2 ( 2400 + 1200 + 1800 )

SA = 2 ( 5400 )

SA = 10,800 ft²

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Simplify;

The answer is NOT a real number, that is 4i

Answer:

Answer:

Weight of each large box: 18.25kg

Weight of each small box: 13.25kg

Step-by-step explanation:

For this question, we have two unknowns, but we can solve them as we are given two equations.

If we use the variables 'L' for Large and 'S' for small, we  an write out the information given to us as equations:

3L + 5S = 121

6L + 2S = 136

Now we can solve these simultaneous equations by multiplying one of them by a constant so that one of the variable co-efficients are the same so we can cancel them. We can see here that we can easily double the first equation which would result in both having 6L:

2(3L + 5S) = 2(121)

=> 6L+10S=242

Now that we have one term which is the same, we can subtract one equation from the other:

  6L+ 10S = 242

- (6L + 2S = 136)

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

=>0L + 8S = 106

Now we can solve for S:

8S/8 = 106/8

S = 13.25

And use this value of S to solve for L:

3L + 5(13.25) = 121

3L + 66.25 = 121

3L + 66.25 - 66.25 = 121 - 66.25

3L = 54.75

3L/3 = 54.75/3

L = 18.25

Hope this helped!

Given: The box plot shown in the figure

To Determine: The percent of the data that is below 16

Solution

The given box plot can be interpreted as beow

From the abov, we can sobserve that

Therefore, the percent of that data below 16 falls in the 1st quartile.

Hence, the percent of that data below 16 is 25 %

a. The mean of the sample can be found by summing up all the observations and dividing by the sample size:

mean = (33 + 26 + 29 + 35 + 31 + 35 + 31) / 7 = 31.14

c. To find the p-value, we need to find the area under the t-distribution curve with 6 degrees of freedom to the left of -1.31 and to the right of 1.31.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

a. The mean of the sample can be found by summing up all the observations and dividing by the sample size:

mean = (33 + 26 + 29 + 35 + 31 + 35 + 31) / 7 = 31.14

The standard deviation of the sample can be found using the formula for the sample standard deviation:

s = sqrt[Σ(xi - x)² / (n - 1)]

where Σ is the sum, xi is each observation, x is the sample mean, and n is the sample size. Substituting in the values from the sample:

s = sqrt[((33-31.14)² + (26-31.14)² + (29-31.14)² + (35-31.14)² + (31-31.14)² + (35-31.14)² + (31-31.14)²) / 6]

= 2.98 (rounded to 2 decimal places)

b. We can use a t-test since the population standard deviation is not known. The test statistic is given by:

t = (x - μ) / (s / sqrt(n))

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. Substituting in the values:

t = (31.14 - 30) / (2.98 / sqrt(7)) = 1.31 (rounded to 2 decimal places)

c. To find the p-value, we need to find the area under the t-distribution curve with 6 degrees of freedom to the left of -1.31 and to the right of 1.31. Using a t-table or calculator, we find that the area to the left of -1.31.

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Answer:

x = -15

Step-by-step explanation:

Subtract x on both sides

x + 5 = -10

Subtract 5 on both sides

x = -15

Check work:

2(-15) + 5 = -15 - 10

-30 + 5 = -25

-25 = -25

Answer:

Step-by-step explanation:

(3.00 - 2.40)/2.40  = p/100;

Then. 0.60/2.40 = p/100;

1/40 = p/100;

p = 100/40;

p = 2.5;

The percentage increase was 2.5%;

The branch of mathematics that analyses the strategic behavior of decision-makers is known as game theory.

The branch of mathematics that analyzes the strategic behavior of decision-makers is known as Game Theory.

Game theory is the study of the mathematical modeling of social interactions between agents. [1] It has applications in all areas of the social sciences, including logic, systems science, and computer science. It was originally focused on a two-player zero-sum game where each player's win or loss equals the other player's win or loss. In the 21st century, game theory applies to many social relationships; is now the subject of research on decision-making in humans, animals, and computers. The modern theory begins with the idea of ​​a combination of competition in a two-player zero-sum game and its proof by John von Neumann.

Von Neumann's original proof of continuity in a linear system using Brouwer's fixed point theorem has become a standard in game theory and business mathematics. His research was based on the 1944 book Game Theory and Economic Behavior by Oskar Morgenstern, which deals with multiplayer cooperative games. The second edition of this book presents an axiomatic theory of expected utility that enables mathematical statisticians and economists to solve decisions in uncertainty.

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Answer:

the correct answer is B

Step-by-step explanation:

Answer:

the second choise is the answer

The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.

This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.

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Therefore, the probability that the team is comprised of 2 men and 2 women is approximately 0.4545, which is true.

To calculate the probability that the team is comprised of 2 men and 2 women, we need to determine the number of favorable outcomes (teams with 2 men and 2 women) and the total number of possible outcomes (all possible teams).

The number of ways to choose 2 men from 6 men is given by the combination formula: C(6, 2) = 6! / (2! * (6-2)!) = 15.

Similarly, the number of ways to choose 2 women from 6 women is also C(6, 2) = 15.

Therefore, the number of favorable outcomes is the product of the number of ways to choose 2 men and 2 women: 15 * 15 = 225.

Now, let's calculate the total number of possible outcomes. We need to choose 4 members from a total of 12 members, which is given by C(12, 4) = 12! / (4! * (12-4)!) = 495.

The probability that the team is comprised of 2 men and 2 women is the ratio of favorable outcomes to the total number of outcomes: 225/495 = 45/99 ≈ 0.4545 (rounded to four decimal places).

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Answer:

Thank you!

Step-by-step explanation:

Have a nice day/night lol

Answer:

1^2 +68=69

Step-by-step explanation:

by sqrt rooting 2 by 1 is 1