which one would be the correct answer?

Answer:

Step-by-step explanation:

there is probably a way to do this w/o calculus,  but I cheated and used that.

A = Length * Width

A = x * ( 650 -2x)

A = 650x -2[tex]x^{2}[/tex]

d/dx ( A = 650x -2[tex]x^{2}[/tex])

0=650 -4x

4x = 650

x = 135 m

A= 650*135 -2*[tex]135^{2}[/tex]

A = 51,300  [tex]m^{2}[/tex]

If repetition is allowed then the required passwords generated are 17576.

If repetition is not allowed then the required passwords generated are 15600.

Given that;

We need to get 3 letter passwords using a through z by two case;

(a) If repetition is allowed

(b) If repetition is not allowed

Case (a): If repetition is allowed.

       The total number of letters from a through z are 26

   ⇒ The total number of 3 letter passwords made are;

        = 26³

        = 26 * 26 * 26

        = 17576

If repetition is allowed then the required passwords generated are 17576.

Case (b): If repetition is not allowed.

      ⇒ The total number of 3 letter passwords made are;

         = 26 * 25 * 24

         = 15600

If repetition is not allowed then the required passwords generated are 15600.

Therefore,

If repetition is allowed then the required passwords generated are 17576.

If repetition is not allowed then the required passwords generated are 15600.

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The solution for the given expression -0.5x-3.69=x-1.9-2.3 is x= 0.34

The given problem is related to an algebraic expression which is the thought of expressing numbers utilizing letters or letter sets without indicating their real values, which is made up of factors and constants, at the side of logarithmic operations (expansion, subtraction, etc.). Expressions are made up of terms.

since the  given expression is :

-0.5x-3.69=x-1.9-2.3

=>-0.5x-x=-1.9-2.3+3.69

=>-1.5x=-0.51

=>x=0.34

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Answer:20 dollars per hour

Step-by-step explanation:60/3 = 20

20 dollars per hour

7 x 20 = 140

Answer:27.5 inches

Step-by-step explanation:

We can use both regular and strong induction.

The Fundamentals of Inductive Mathematics (i.e., Regular Induction). If any of the following statements involving a positive number, n, are accurate: The claim is true if and only if n is 1. If the assertion is true for n=k, then it must also be true for n=k+1(x).

In a variation of induction known as strong induction, we make the assumption that the assertion is true for all values before k. This provides us with more information with which to work.

Regular Induction form

N>6 = n=7 in basic case

3n = 37 = 2187

N! = 7! = 5040

For n= 7 3n<n! is true

Induction hypothesis

Let for n= k and k>6

Assume 3k<k! is true

We prove that for k = k+1 the assumption holds true then the assumption must be true for k

K = k+1

3k+1 < (k+1)!

3k. 3 < (k+1) k!

3k < (k+1)/3.k!

For k>6

(k+1)/3 >1 and let (k+1)/3 = p

3k < P.k!

But we assumed that 3k < k! for k > 6 then 3k must be less than p.k1 since P>1

Therefore 3k<k! for k>6

3n < n! for all integers n greater than 6.

Therefore we can use both regular and strong induction

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There are 2 different bad arrangements possible.

We see that there are 5! absolute ways of orchestrating the numbers. Nonetheless, we can constantly turn these numbers so that, for instance, the number 1 is dependably at the highest point of the circle. Consequently, there are just 4! ways under turn, which is easy to drill down. We methodically list out every one of the 24 cases.

Presently, we should inspect assuming they fulfill the circumstances. We can see that by selecting each number, in turn, we can continuously acquire subsets with aggregates 1, 2, 3, 4, and 5. By picking the round trip, we can get 15. By selecting everything aside from 1, 2, 3, 4, and 5, we can get subsets with amounts of 10, 11, 12, 13, and 14.

This implies that we presently just have to check for 6, 7, 8, and 9. Be that as it may, whenever we have found a set adding to 6, we can pick all the other things and get a set adding to 9, and comparably for 7 and 8. Hence, we just have to check each case for whether we can acquire 6 or 7.

We observe that there are just 4 arrangements that fulfill these circumstances. In any case, each of these is an impression of another. We divide by 2 for these reflections to get the final answer of B = 2.

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The geometric system has a length of f = 4 cm and a length of g = 6 cm.

Herein we find a geometric system formed by two rectangles, the rectangle ABCD has an area of 60 square centimeters and the rectangle APQD has an area of 24 square centimeters. The area of a rectangle is equal to the product of the lengths of its base (b) and its height (h), both in centimeters.

First, describe the area formulas for the rectangles ABCD and APQD, both in square centimeters:

Rectangle ABCD

(g + 9) · f = 60        (1)

Rectangle  APQD

g · f = 24                 (2)

Where:

Second, use distributive property in (1):

By (1):

g · f + 9 · f = 60

Third, use substitution by (2) on (1) and determine the value of f:

(2) in (1):

24 + 9 · f = 60

9 · f = 36

f = 4

Fourth, determine the value of g:

By (2):

g = 24 / f

g = 24 / 4

g = 6

The lengths of f and g are 4 and 6 centimeters, respectively.

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Part A

We can get equation B from A by Multiply/divide both sides by the same non-zero constant.

Part B

The two equations are equivalent, they have same solution

The equations are

3(x+2) = 18

x + 2 = 6

Part A

Consider the first equation

3(x + 2) = 18

Divide both side of the equation by 3

3(x+2) / 2 = 18/3

x + 2 = 6

We will get equation B from equation A, if we divide both side of the equation by 3

Part 2

The first equation

3(x+2) = 18

x + 2 = 6

x = 6-2

x = 4

The second equation

x+2 = 6

x = 6-2

x = 4

Both the equation has same solution

Hence,

Part A

We can get equation B from A by Multiply/divide both sides by the same non-zero constant.

Part B

The two equations are equivalent, they have same solution

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The equation of the line in slope intercept form is y = 6x + 5

The given parameters are

Slope, m = 6

Points, (x₁, y₁) = (-2, -7)

A linear equation can be represented as

y = slope * x + y-intercept

i.e.

y = m(x - x₁) + y₁

Substitute the known values in the above equation

So, we have the following equation

y = 6(x + 2) - 7

Expand

y = 6x + 12 - 7

Evaluate the like terms

y = 6x + 5

Hence. the linear equation is y = 6x + 5

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Answer:

Jacob was able to determine there was a problem with the specifications of the triangular sail because of the Pythagorean theorem.

Step-by-step explanation:

Assume the triangular sail is a right triangle.

The Pythagorean theorem says: [tex]A^{2} + B^{2} = C^{2}[/tex]

If A = 4.8, B = 2.5, and C = 7.5, then [tex]4.8^{2} + 2.5^{2} = 7.5^{2}[/tex].

[tex]4.8^{2} + 2.5^{2} = 23.04 + 6.25 = 29.29[/tex]

[tex]7.5^{2} = 56.25[/tex]

In conclusion, [tex]29.29 \neq 56.25[/tex], so there is a problem with the sail.

Answer: Campbell to Hillsboro to Richmond to Winchester

(Note: Not taking the Washington route)

Step-by-step explanation:

Form Campbell all the way to Richmond have no other choices, From Richmond to Winchester has two choices, 12.2 mi +5.2 mi or 15.7 mi

12.2+5.2=17.4 mi while the other choice is only 15.7 mi

So taking the 15.7 mi option is faster

Answer:

x= -7

Step-by-step explanation:

here you go.....

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The total number of medals won by Canada is 3 and Greece's 6,

Here we have to find the number of medals won by Canada and Greece.

The ratio of medals won by Canada and Greece is 1: 2.

The total number of medals won = is 9

The common number is x.

Medal won by Canada = x

Medal won by Greece = 2x

So we get the equation:

x + 2x = 9

3x = 9

x = 3

So the total medal won by Canada = 3

The total medal won by Greece = 2 × 3= 6

Therefore the number of medals won by Canada and Greece is 3 and 6 respectively.

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The range of values for the rectangle  length is  20 ≤ y ≤ 30 .

What is a rectangle made of?

The garden is to be rectangular shape.

Let x = width

Let y = length

Set the equations for perimeter and area.

2(x + y) = 100  -----> perimeter

x + y = 50   ------> perimeter

xy = 600   ---->  area

We have two equations to work with.

x + y = 50                eq1

xy = 600                   eq2

Substitute eq1 into eq2.  We can get eq2 in terms of x.

x(50 - x) = 600

-x2 + 50x = 600

-x2 + 50x - 600 = 0

Divide both sides of the equation by -1, so that we have a positive x2.  The goal is to try to use FOIL to factor.

x2 - 50x + 600 = 0

(x - 30)(x - 20) = 0

x = 30         and           x = 20

Next, we plug in these values of x into eq1 to solve for y.

y = 50 - x                     and                y = 50 - x

y = 50 - 30                                        y = 50 - 20

y = 20                                               y = 30

Based on this, the range of values for the length is

20 ≤ y ≤ 30

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The value of x in the Inequality (7x + 1)/2> 4 is x > 1.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.

In this case, the inequality is given as:

(7x + 1)/2> 4

Cross multiply

7x + 1 > 2 × 4

7x + 1 > 8

Collect like terms

7x > 8 - 1

7x > 7

Divide

x > 7/7

x > 1

Therefore, x > 1.

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Answer:

The equation that is true is equation two

Answer:

$53.8.

Step-by-step explanation:

10% of $538 is like saying 538 times .10. After you multiply, you get $53.8 as the fee that Monica had to pay.

The equation which represents the sentence given; Half the difference of a number and 5 is−2 is; 1/2(x - 5) = -2; 1 half left parenthesis x minus 5 right parenthesis equals negative 2.

It follows from the task content that the expression which best represents the given algebraic expression is to be determined.

First, the difference of a number, x and t is represented as; (x - 5).

Hence, the word phrase; Half the difference of a number and 5; is best represented algebraically as; 1/2(x - 5).

Ultimately, the whole word phrase; Half the difference of a number and 5 is -2 can best be represented as; 1/2(x - 5) = -2.

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It was 33 degrees warm in the afternoon

From the question, we have the following parameters that can be used in our computation:

In the morning = 5 degrees above zero

Afternoon = Rise of 27 degrees

The degree of warmth in the afternoon is then calculated as

Degree of warmth = Temperature In the morning + Rise of the temperature

Substitute the known values in the above equation, so, we have the following representation

Degree of warmth = 5 + 27

Evaluate the sum

Degree of warmth = 33

Hence, the temperature is 33 degrees

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Answer:

x = 1/4p

y = 3/2p

Step-by-step explanation:

2x + 3y =5p__________________equ 1

y = 2x + p____________________equ 2

sub equ 2 for y in equ 1

2x + 3(2x + p) = 5p_______________open brackets

8x = 2p______________________divide both sides by 8

x = 1/4p

sub 1/4p for x in equ 2

y = 2(1/4p) + p___________________open brackets

y = 3/2p

The quadratic equation x² + 16 · x + 80 has two roots: x₁ = - 1 / 10 + i (4 / 5), x₂ = - 1 / 10 - i (4 / 5).

In this question we find a quadratic equation of the form a · x² + b · x + c = 0, whose roots can be found by using the quadratic formula:

x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)

Where b² - 4 · a · c is the discriminant of the quadratic formula, which offers three cases of solutions:

If we know that a = 1, b = 16 and c = 80, then the roots of the quadratic equation are, respectively:

x = - 16 / 160 ± (1 / 160) · √(16² - 4 · 1 · 80)

x = - 1 / 10 ± (1 / 10) · √(- 64)

x = - 1 / 10 ± i (4 / 5)

The roots are - 1 / 10 + i (4 / 5) and - 1 / 10 - i (4 / 5).

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The Number of ways that four people can be seated on the bench so that john is not next to paul is 12

In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.

The arrangement of n items in r ways is given by

Here we have

4 people (John, Paul, George, and Ringo) are seated in a row on a bench

Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24

The number of ways of seating the four people so that john is next to paul is 12

Then the number of ways the four people on the bench so that john is not next to paul can find as given below

= Total No of ways, 4 can be seated - No of ways that john next to paul  

= 24 - 12 = 12        

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Answer:

$180

Step-by-step explanation:

[tex]P\times{(1-0.20)}=144[/tex]

[tex]P\times{0.80}=144[/tex]

[tex]P=\frac{144}{0.80}[/tex]

[tex]P=180[/tex]

1/24 is the probability that the two chosen tiles differ with respect to all three properties

1/2  chance that the tiles materials will be different (wood or plastic). 1/3 chance exists that the tiles will have different colors (r, y or b) 1/4 chance where the tile shapes will change (t, s, p or c)the probability that all three attributes of the two tiles will be different.1/2 * 1/3 * 1/4 = 1/24 The probability of an event occurring is a measure of its likelihood. It assesses the likelihood of an event. P(E) = Number of Favourable Outcomes/Total Outcomes is the probability formula.

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The probability of a family owning a cat given that the family owns a dog is 0.164

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

Here

probability of a family owning a dog is 0.91,

P(dog) = 0.91

probability of a family owning a cat and a dog is 0.15,

P(dog ∩ cat) = 0.15

according to conditional probability

the probability of occurring of B after event A takes place is

P(A|B)=P(A∩B)/P(A)

so, the probability of a family owning a cat given that the family owns a dog is

        P(dog | cat) =P(dog∩cat)/P(dog)

                            = 0.15/0.91

                            =0.164

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If 9 seeds are planted, what is the probability that exactly 3 don't grow will be 1/5832000 as 5% chance are there that plant will not grow.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The chances of seed to be not growing is 1–0.95 =0.05.

For 3 seeds not to grow being simultaneous occurring events have the probability = 0.05×0.05x0.05=0.000125

As 9 seeds being planted the probability of selecting 1 out of 9 is (1/9).

So for 3 mutual occurring case is (1/9)×(1/9)x(1/9)= 1/729

So the probability will be (1/729)×1/8000=1/58,32,000

The likelihood that exactly 3 seeds out of 9 will not germinate is 1/5832000, or 5%, so there is a chance that the plant won't grow.

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