For each Diagram, write an unsimplified and simplified equation that represents the relationship between x and y.

I need the unsimplified equations on the left side of the chart from what I know it should be equal to the simplified equation across from it.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-8}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{(-4)}}} \implies \cfrac{-11}{-6 +4} \implies \cfrac{ -11 }{ -2 } \implies \cfrac{11 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-7}-\underset{x_1}{(-7)}}} \implies \cfrac{2 +1}{-7 +7} \implies \cfrac{ 3 }{ 0 } \implies \stackrel{\textit{vertical line}}{{\Large \begin{array}{llll} unde fined \end{array}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{9}}} \implies \cfrac{ 0 }{ -15 } \implies \stackrel{\textit{horizontal line}}{\text{\LARGE 0}}[/tex]

keep in mind that whenever you notice the x-coordinates are the same, it's a vertical line, and whenever the y-coordinates are the same, is a horizontal line.

The slope of segment EF and AB is same but the length of segment EF is half of the length of segment AB.

What is Line segment ?

An unmoving portion of a line is called a line segment. Two points serve as its ends. By the termination points, it is identified.

Let's assume the length of EF to be "x"

from the figure, we can clearly see that AB is made up of two segments which are of same length as EF.

So, we can say that AB = 2 times of the length of EF

i.e. AB = 2 x

Hence, By comparing, we conclude that AB's length is double of EF.

Now, if we look at slope,

Slope of EF = CE/CF

and, Slope of AB = BC/AC

But, we know that AC = 2 CF and BC = 2 CE

So, Slope of  EF = CE/CF

and, Slope of AB = 2 CE / 2 CF

                             = CE/CF.

Hence, Both segments have same slope direction.

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Answer:

61/10

Step-by-step explanation:

Convert the mixed number to an improper fraction

28 / 5 + 1 / 2

= 61/10

Answer:

Simplified form: 6 1/10

Improper form: 61/10

Step-by-step explanation:

5 3/5 + 1/2

= 28/5 + 1/2

Then, you multiply both fractions so that the denominator is the same number. In this case, multiply the fraction (numerator and denominator) on the left by 2 and on the right by 5.

= 56/10 + 5/10

This way, you can add the numbers because they have the same denominator.

=61/10

The total number of possible passwords is 17,576,000.

There are several steps involved in calculating the total number of possible passwords.

Step 1: Determine the number of possible choices for the first lowercase letter. Since there are 26 letters in the alphabet, and the password consists of lowercase letters, there are 26 choices for the first letter.

Step 2: Determine the number of possible choices for the second lowercase letter. Since there are 26 letters in the alphabet and repetition is allowed, there are 26 choices for the second letter.

Step 3: Determine the number of possible choices for the capital letter. Since the password requires a capital letter, there are 26 choices for this position.

Step 4: Determine the number of possible choices for the first digit. Since there are 10 digits (0-9), there are 10 choices for the first digit.

Step 5: Determine the number of possible choices for the second digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the second digit.

Step 6: Determine the number of possible choices for the third digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the third digit.

Step 7: Determine the number of possible choices for the fourth digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the fourth digit.

Step 8: Multiply the number of choices for each position together to get the total number of possible passwords.

Using the multiplication rule of counting, we get:

Total number of possible passwords = (Number of choices for the first lowercase letter) x (Number of choices for the second lowercase letter) x (Number of choices for the capital letter) x (Number of choices for the first digit) x (Number of choices for the second digit) x (Number of choices for the third digit) x (Number of choices for the fourth digit)

Total number of possible passwords = 26 x 26 x 26 x 10 x 10 x 10 x 10

Total number of possible passwords = 17,576,000

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The toothpicks lennon should use in each row is 185.

Algebra is the study of abstract symbols, and logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction also. This approach is used to answer the given problem correctly and completely.

We are given that;

Total number of toothpicks= 3330

Number of rows= 18

Now,

To find the number of toothpicks in each row

=3330/18

=1665/9

=185

Therefore, by algebra the answer will be 185.

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The probability of the sample mean annual insurance cost being greater than $620 is very low, that is 0.00317% which indicating that it is unlikely to happen by chance.

Probability is a branch of mathematics that deals with the likelihood of an event happening. It is used in various fields, such as insurance, finance, and science.

To calculate the probability, we need to use the central limit theorem, which states that the distribution of sample means of a population approaches a normal distribution as the sample size increases. We also need to know the mean and standard deviation of the population.

Assuming that the population is normally distributed, we can use the following formula to calculate the probability:

z = (x - μ) / (σ / √(n))

where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we don't know the population mean and standard deviation, but we can use the sample mean and standard deviation as estimates. Let's say we have a sample of 100 insurance costs with a mean of $600 and a standard deviation of $50.

Now, we can calculate the z-score:

z = (620 - 600) / (50 / √(100)) = 4

The z-score of 4 indicates that the sample mean of $620 is 4 standard deviations away from the mean of $600. We can use a standard normal distribution table or a calculator to find the probability of getting a z-score of 4 or higher. The probability is very small, approximately 0.0000317 or 0.00317%.

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Due to the fact that secured loans often have lower interest rates than unsecured loans, they are less expensive. They require collateral. They are less risky for the financial institution. The correct option is D.

A secured loan is one in which the borrower pledges an asset as security for the loan, turning the pledged asset into a secured debt owing to the lender (the creditor).

Some loans may be backed by assets other than your house; for instance, they may be backed by your automobile, jewelry, or other possessions. Because lenders can collect the asset in the event of a default on a secured loan, secured loans often have lower interest rates than unsecured loans.

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The profit made on the transaction by the dealer was Rs. 7,750.

To calculate the profit made by the second hand car dealer, you can subtract the cost of buying the car and the transaction costs from the selling price.

Profit = Selling Price - Cost of Car - Transaction Costs

Profit = 93,000 - 85,000 - 250

Profit = 7,750

So the dealer made a profit of Rs. 7,750 on the transaction.

Profit and Loss (P&L) is a statement that summarizes a company's revenues and expenses over a specific period of time, typically a quarter or a year. The purpose of a P&L statement is to show a company's ability to generate revenue, as well as the cost of doing so. The difference between a company's total revenue and total expenses is referred to as net profit or net loss

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Answer:

see explanation

Step-by-step explanation:

(a)

given m varies directly as n then the equation relating them is

m = kn ← k is the constant of variation

to find k use the condition m = 14 when n = 7

14 = 7k ( divide both sides by 7 )

2 = k

m = 2n ← equation of variation

(b)

when n = 16 , then

m = 2 × 16 = 32

(c)

when m = 30 , then

30 = 2n ( divide both sides by 2 )

15 = n

A manufacturer working at the 430 gram setting, and a 21 bag sample had a mean of 421 grams with a standard deviation of 15. The p-value of test statistic is 0.0074.

To test whether the bag filling machine works correctly at the 430 gram setting, we can conduct a one-sample t-test. The null hypothesis is that the true mean weight of the bags filled by the machine is equal to 430 grams, and the alternative hypothesis is that the true mean weight is less than 430 grams.

The test statistic is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values given in the problem, we get:

t = (421 - 430) / (15 / sqrt(21)) = -2.77

The degrees of freedom for the t-distribution are n - 1 = 20.

Using a t-table or calculator, we can find the p-value associated with a t-score of -2.77 and 20 degrees of freedom. The p-value turns out to be 0.0074 (rounded to four decimal places).

Since the p-value is less than the level of significance of 0.1, we can reject the null hypothesis and conclude that the bag filling machine is underfilling the bags at the 430 gram setting.

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If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are 15000 * (1/20) = 750 tourists daily.

And if 1/15 of the tourists are travel bloggers, then there would be 750 * (1/15) = 50 travel bloggers daily.

If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are

15000 * (1/20) = 750 tourists daily

So, there would be a total of 50 tourist passengers on domestic flights who are travel bloggers.

It is important to note that these are average numbers and the actual number of tourists and travel bloggers on domestic flights can vary from day to day. However, this calculation provides a general idea of the proportion of tourist passengers who are travel bloggers on domestic flights.

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Answer:

13

Step-by-step explanation:

The value of length of z is 5.06 cm.

The value of length of z is calculated by determining the radius of the sector as shown below;

The formula for the perimeter of a sector is given as;

P = 2r  +  (θ/360) × 2πr

where;

20 cm = 2r  + (40/360) x 2πr

20 = 2r  +  0.7r

20 = 2.7r

r = 20/2.7

r = 7.4 cm

A perpendicular bisector of 40⁰ will cut line z into two equal parts, the length of half of z is calculated as;

sin (20) = (z/2) / r

r x sin (20) = (z/2)

2r x sin (20) = z

2 x 7.4 cm x sin(20) = z

5.06 cm = z

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The primary difference between writing the name of a segment and the name of a line is the use of symbols.

A symbol is an object, image, or action that stands for or represents something else. Symbols can be used to convey a wide variety of ideas and concepts, from the literal, such as a heart to represent love, to the abstract, such as a peace sign to represent a call for world peace. Symbols are often used to communicate complex ideas quickly and easily.

To denote a segment, a line is usually written with two arrows pointing in opposite directions, such as ↔. To denote a line, the line is usually written with a single arrow pointing in one direction, such as →.

For example, if you were writing the name of a segment called "AB", then you would use the symbol ↔ AB. If you were writing the name of a line called "AB", then you would use the symbol → AB.

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Step-by-step explanation:

the area of a circle is

pi×r²

r being the radius (1.68 m).

the area of half a circle is therefore

pi×r²/2

in our case

pi× 1.68²/2 = pi× 2.8224/2 = pi×1.4112 =

= 4.433415553... m² ≈ 4.43 m²

The area of the shaded semicircle is  1.11 meters squared.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed shape, two-dimensional .

The area of shape is the space enclosed within the perimeter or the boundary of a given shape.

The area of a circle is expressed as ;

A = π[tex]r^{2}[/tex]

where r is the radius of the circle.

Therefore the area of a semi circle will be :

A = 1/2  π[tex]r^{2}[/tex]

r = d/2

r = 1.68/2 =0.84

A = 1/2 × 3.14 × 0.84 ×0.84

 = 1.11 meter squared.

Therefore the area of the shaded semi circle is 1.11 meters squared.

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The area of the figure is 52 square units

The perimeter of the figure is 36 units

The graph is attached

The perimeter of the figure is found by summing the length of the sides

F(-5, 2) - G(-3, 2) = 2 units

G(-3, 2) - H(-3, 4) = 2 units

H(-3, 4) - J(1, 4) = 4 units

J(1, 4) - K(1, 1) = 2 units

K(1, 1) - L(4, 1) = 3 units

L(4, 1) - M(4, -2) = 3 units

M(4, -2) - N(6, -2) = 2 units

N(6, -2) - P(6, -3) = 1 units

P(6, -3) - Q(-5, -3) = 11 units

Q(-5, -3) - F(-5, 2) = 5 units

The perimeter = 2 + 2 + 4 + 2 + 3 + 3 + 2 + 1 + 11 + 5 = 36 units

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The largest square that Mr. Stanley can use to plant in his farm is a square with a side length of 8 meters.

To find the greatest common factor of 24 and 40, we can list the factors of both numbers and find the highest factor that they have in common:

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

The highest factor that 24 and 40 have in common is 8.

Factors are numbers that can be multiplied together to get a given number. For example, the factors of 6 are 1, 2, 3, and 6 because 1 x 6 = 6 and 2 x 3 = 6. Factors can be prime or composite. Prime factors are those that are only divisible by 1 and themselves. Composite factors are those that have more than two factors.

Factors are important in math because they can be used to simplify fractions, find common denominators, and solve equations. They also play a crucial role in number theory and cryptography, where they are used to encrypt and decrypt messages. 150 is a composite number, which means it has factors other than 1 and itself. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. To find these factors, you can divide 150 by each number smaller than it and see if the remainder is 0.

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Answer:

A

=

1.50c + 18

where

A

is amount and

c

is toppings added

Step-by-step explanation:

The constant price is

18

dollars, which never changes and for every topping you get, it costs

$

1.50

. If you got no toppings, sub in

0

for

c

to get

$

18

.

1 ton = 2000 pounds

2000/2.5 = 800 months

800/12 = ~66.67 years

Answer:

your answer would be 66.6: do the math: 2.5 a month times 12 months in a year=30. 1 ton =2000 pounds. 2000 divided by 2.5 =800. 800 divided by 12=66.6

Step-by-step explanation:

The cost to ship a box of 250 grams, with 10 books of weight of 8.5kg by natalie is $ 29.75.

The total weight of the books and the box is:

10 books × 810 grams/book + 250 grams = 8,250 grams + 250 grams = 8,500 grams

To convert this to kilograms, we divide by 1000:

8,500 grams ÷ 1000 = 8.5 kg

The cost of shipping will be based on the weight, so we can multiply the weight in kilograms by the shipping cost per kilogram:

8.5 kg × $3.50/kg = $29.75

Therefore, it will cost Natalie $29.75 to ship the books of 8.5 kg

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a) The simple interest that will be owed the bank by Diane after 76 days is $343.59.

b) The final amount that Diane will repay the bank after 76 days is $17,443.59.

The simple interest is an interest system that does not compound interest.

Compounding interest means that interest is added to the principal before subsequent interests are computed.

But under the simple interest system, interest is based on the principal from one period to the next.

The loan amount = $17,100

Simple interest rate = 9.65%

Loan period = 76 days

Total interest = $17,100 x 9.65% x 76/365 = $343.59

Final amount = $17,443.59 ($17,100 + $343.59)

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Approximately 70 miles separated Harold's home at his grandparents' home from his own home. Accordingly, Harold travelled the following distance overall on his birthday: 70 + 74.46 + 70 ≈ 214.46

What is a distance? . Regardless of the start or end point, distance can be defined as the amount of space object has to cover.

The metre serves as the SI unit of distance (m). Centimeters (cm) are a common unit of measurement for short distances, whereas kilometres (km) are used for longer distances (km). You could measure a piece of paper's length in centimetres, for instance, by measuring from the bottom to the top.

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Answer: To find out how many students attend chess club on Wednesdays, we need to calculate 3% of the 800 students at Steven's high school. To do this, we multiply the number of students by 3% (which is equivalent to 0.03):

800 x 0.03 = 24

So, 24 students attend chess club on Wednesdays.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x=5, y=1

Step-by-step explanation:

2x-y=9

2(5)=10

10-1=9

4x+y=21

4(5)=20

20+1=21

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The function f(x) is translated 3 units right and 5 units down then the function f(x) is coincident with the function g(x).

A function is an assertion, conception, or regulation that establishes a partnership between two variables.

The functions f(x) and g(x) are given below.

f(x) = 1 / x

g(x) = 1 / (x - 3) - 5

Translate the function 3 units right, then replace x with (x - 3). And translate the function 5 units down, then replace f(x) with (g(x) + 5). Then we have

g(x) + 5 = 1 / (x - 3)

g(x) = 1 / (x - 3) - 5

The function f(x) is translated 3 units right and 5 units down then the function f(x) is coincident with the function g(x).

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r as a percent is a) a = 79, b = 1.002, and r = 0.2%.

The formula given, q = abt = a(1+r)t, represents exponential growth, where a is the starting value, b is the growth factor, r is the growth rate, t is the time period, and q is the final value after t periods.

Given q = 79(1.002)^t, we can see that:

a = 79 (the starting value)

b = 1.002 (the growth factor)

r = 0.2% or 0.002 (the growth rate, expressed as a decimal)

So, the correct answer is a) a = 79, b = 1.002, and r = 0.2%.

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The percentage of the data values are greater than 24 is 75%.

A box and whisker plot is a special type of graph that is used to show groups of number data and how they are spread. It shows the median, which is the middle value of the numbers in your data, the lowest number, the highest number and the quartiles, which divides the data into four equal groups.

So as per the given question box-whisker plot represents some data set. There is a number 24 just corresponding to it there is a vertical line which shows that 24 is the first quartile of the data and here 24 is the 75th percentile.

It means that there is 75% values are greater than 24.

Therefore, the percentage of the data values are greater than 24 is 75%.

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On solving the provided question, we can say that Volume of cuboid - L X B X H=> volume = (x+6)*(x-2)*(x-1) => [tex]V = x^3 + 3x^2 - 16x + 12[/tex]

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

The dimensions are:

Length =(x + 6), Width = (x - 2) and Height = (x -1)

Volume of cuboid - L X B X H

volume = (x+6)*(x-2)*(x-1)

[tex]V = (x+6)(x^2 - 3x +2)[/tex]

[tex]V = x^3 - 3x^2 + 2x + 6x^2 - 18x + 12[/tex]

[tex]V = x^3 + 3x^2 - 16x + 12[/tex]

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