Topic: Linear Diophantine Equation
Solve: Find x,y∈Z such that 123x + 360y = 99

Answer:

(what is the question).

There are 5 possible combinations for Jacob's lock combination with increasing digits from left to right, and the product of the digits being 84.

Multiplication is a mathematical operation that involves combining two or more quantities to find their total or product. It is often represented by the "x" symbol or the multiplication sign "⋅". Multiplication is a fundamental operation in arithmetic and is used to calculate the total or result of repeated addition or groups of equal quantities.

The product of the digits being 84 implies that the possible combinations of digits are limited to those whose product is 84. The prime factorization of 84 is 2^2 * 3 * 7. Since the digits must be increasing from left to right and cannot repeat, the possible combinations of digits are:

1, 2, 42

1, 3, 28

1, 4, 21

2, 3, 14

2, 6, 7

So, there are 5 possible combinations for Jacob's lock combination.

Therefore, There are 5 possible combinations for Jacob's lock combination with increasing digits from left to right, and the product of the digits being 84.

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Answer:

x = 10.20240940

Step-by-step explanation:

[tex]x(2x + 9) = 2x^2 + 9x[/tex]

[tex]2x^2 + 9x = 300[/tex]

- 300 on both sides

[tex]2x^2 + 9x - 300 = 0[/tex]

solve using the quadratic formula

[tex]x = -b +/- \ \text{all root} (b)^2 - 4(a)(c) \ \text{All over} \ 2(a)[/tex]

When all the values are plugged in:

When using "+" in the equation you should get:

x = 10.20240940

When using "-" in the equation you should get:

x = −14.70240940

Now.. you CANNOT have a negative length, so you cross of the negative value leaving you one value for x which is 10.20240940.

Your answer is: x   =  10.20240940

The slope of a line is a measure of its steepness and is defined as the ratio of the change in y (vertical distance) to the change in x (horizontal distance) between any two points on the line.

We can use the point-slope form of the equation of a line to find the equation of the line that passes through the point (2, 5) and has a slope of -3. The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Substituting the values we have, we get:

y - 5 = -3(x - 2)

Simplifying this equation, we get:

y - 5 = -3x + 6

Adding 5 to both sides, we get:

y = -3x + 11

Therefore, the equation of the line that passes through the point (2, 5) and has a slope of -3 is y = -3x + 11.

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The cost is minimized when all the remaining requirements are met by Food B, we can purchase 36 units of Food A and 30 units of Food B to meet all the requirements and minimize the cost.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Let x be the number of units of Food A and y be the number of units of Food B.

The objective is to minimize the cost, which is given by the expression 2x + y.

The constraints are:

50x + 20y >= 2400 (minimum vitamin requirement)

30x + 20y >= 1800 (minimum mineral requirement)

10x + 40y >= 1200 (minimum calorie requirement)

x >= 0, y >= 0 (non-negative quantities)

We can use linear programming to solve this problem. The standard form is:

Minimize: 2x + y

Subject to:

50x + 20y >= 2400

30x + 20y >= 1800

10x + 40y >= 1200

x >= 0, y >= 0

Therefore, the minimum cost is $30, and it is achieved by purchasing 30 units of Food B.

To find the number of units of Food A, we can use one of the constraints, for example:

50x + 20y >= 2400

50x + 20(30) >= 2400

50x >= 1800

x >= 36

So, we need at least 36 units of Food A to meet the vitamin requirement.

Since the cost is minimized when all the remaining requirements are met by Food B, we can purchase 36 units of Food A and 30 units of Food B to meet all the requirements and minimize the cost.

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The right number that fits the sequence 54 , 48 , 18 , 24 , 6 , 12 , is 2

To find the next number in the sequence, we need to look for a pattern in the given numbers.

So, we have

54 .. 18 .. 6 ... division by 3

48 .. 24 .. 12 .. division by 2

So, it seems that we are dividing each pair of consecutive numbers by a certain factor.

So, the factor by which we are dividing each pair of consecutive numbers seems to be decreasing by a factor of 3 each time, for the first sequence.

Therefore, the next number in the sequence should be:

6/3 = 2

So, the complete sequence is:

54, 48, 18, 24, 6, 12, 2

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Answer: x-2

Use A=Lw

A/L=w

if you factor and cancel, you are left wirh x-2.

We need to mix 3.2 units of the 25% orange juice with 0.8 Units of the 100% orange juice to get a 4-unit mixture with a 25% concentration of pure orange juice.

The first thing we need to do is figure out how much of each type of orange juice we need to mix together to get the desired 25% concentration. Let's call the amount of the 25% orange juice "x" and the amount of the 100% orange juice "y".

We know that the total amount of juice we want to end up with is "4" (since the function f(x) is equal to 4 + 2). So we can write an equation based on that:

x + y = 4

We also know that we want the final concentration to be 25%, which means that the amount of pure orange juice in the mixture should be 25% of the total volume. To calculate that, we can use the formula:

0.25 = (0.25x + y) / 4

Simplifying that equation, we get:

0.25x + y = 1

Now we have two equations with two unknowns (x and y), which we can solve using substitution or elimination. I'll use substitution here:

x = 4 - y (from the first equation)
0.25(4 - y) + y = 1 (substituting for x in the second equation)
1 - 0.25y + y = 1
0.75y = 0
y = 0

Uh-oh, that's not good. It looks like we can't use any of the 100% orange juice, or we'll end up with a concentration greater than 25%. Let's double-check our equations and see if there's a mistake.

x + y = 4
0.25x + y = 1

Hmm, it looks like we made a mistake in the second equation. The 0.25x term should be multiplied by the concentration of the 25% orange juice, which is 0.25 (or 25% as a fraction). So the correct equation should be:

0.25(0.25x) + y = 1

Now let's solve for y:

0.0625x + y = 1
y = 1 - 0.0625x

Substituting that into the first equation, we get:

x + (1 - 0.0625x) = 4
0.9375x = 3
x = 3.2

So we need to mix 3.2 units of the 25% orange juice with 0.8 units of the 100% orange juice to get a 4-unit mixture with a 25% concentration of pure orange juice.

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Answer:

13

Hope this helps!

Step-by-step explanation:

Answer:

200ft²

Step-by-step explanation:

SA = 8(15) + (8+15+17) 20

= 120+ (4)(20)

= 120+80

= 200ft²

Answer: 2.4

(Hopefully this helps! If you can, please mark me brainliest tomorrow)

Explanation:

We divide the feet by 5280 to find that amount in miles.

12,672/5280 = 2.4

Therefore, the answer is 2.4 miles.

The mean of the remaining stock is 5

To find the mean amount of remaining stock, we need to add up the amounts of remaining stock for each garment and divide by the total number of garments.

So, we can start by adding up the amounts of remaining stock:

5 + 4 + 5 + 3 + 8 + 5 + 5 = 35

Now we can divide by the total number of garments (which is 7) to find the mean:

35 / 7 = 5

Therefore, the mean amount of remaining stock is 5.

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According to the given information, the equation that represents the proportional relationship is y = (1/4)x

What is proportion?

Proportion is a mathematical concept that describes the equality of two ratios. In other words, it is a statement that two ratios or fractions are equal.

For example, if we have two fractions, a/b, and c/d, we can say that they are in proportion if:

a/b = c/d

We can see that the ratio between X and Y is always 4:1, which means that Y is one-fourth of X. We can write this as:

Y = (1/4)X

Therefore, the equation that represents the proportional relationship is:

y = (1/4)x

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Toy Cost Percentage

Aditya Kashyap

ohn spent 20% of his money on food. He spent 2/5 of the remainder on a toy. The toy cost $12.

(a) What percentage of his money did he spend on the toy?

b) How much money did he have at first?

(a) To find the percentage of his money that John spent on the toy, we need to first find the total amount of money he had left after spending 20% on food.

Let's say John had x amount of money initially.

Then, he spent 20% of x on food, which is 0.2x.

So, he had (x - 0.2x) = 0.8x amount of money left.

Next, he spent 2/5 of this remaining amount on a toy, which cost $12.

Therefore, 2/5 of 0.8x = $12

Simplifying this, we get:

0.32x = $12

x = $37.50

So, John had $37.50 initially.

Now, to find the percentage of his money that he spent on the toy, we can use the formula:

Percentage = (Amount spent on toy / Total initial amount) x 100

Amount spent on toy = $12

Total initial amount = $37.50

Plugging these values into the formula, we get:

Percentage = (12 / 37.50) x 100

Percentage = 32%

Therefore, John spent 32% of his money on the toy.

(b) John had $37.50 at first.

The inverse probability of drawing either an 8 or a 9 from a deck of cards is 0.852.

What is probability?

The likelihood of an occurrence can be determined using probability. It can only be applied to determine how likely an event is to occur. a scale with 0 being impossible and 1 being a specific occurrence.

We know that there are 52 cards in a deck consisting of 4 cards of each number.

So,

⇒ Probability of drawing 8 = [tex]\frac{4}{52}[/tex]

⇒ Probability of drawing 8 = [tex]\frac{1}{13}[/tex]

Similarly,

⇒ Probability of drawing 9 = [tex]\frac{4}{52}[/tex]

⇒ Probability of drawing 9 = [tex]\frac{1}{13}[/tex]

Now,

Let event A be drawing a 8 and event B drawing a 9.

So,

⇒ P (A ∪ B) = [tex]\frac{1}{13}[/tex] + [tex]\frac{1}{13}[/tex]  - ([tex]\frac{1}{13}[/tex] * [tex]\frac{1}{13}[/tex] )

⇒ P (A ∪ B) = [tex]\frac{2}{13}[/tex] - [tex]\frac{1}{169}[/tex]

⇒ P (A ∪ B) = [tex]\frac{25}{169}[/tex]

⇒ P (A ∪ B) = 0.148

Inverse probability = 1 - 0.148

Inverse probability = 0.852

Hence, the inverse probability of drawing either an 8 or a 9 from a deck of cards is 0.852.

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Answer:

3.17

Step-by-step explanation:

First change 63.4 to 634/10

Then simplify

You get 317 over 5 then divide by 20 and get

3.17000

Then round

Rounding to the nearest unit, the average annual rate of change during this time period is 10,797.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can be solved to find the value of the variable that makes the statement true. Equations are used in many areas of mathematics and science, as well as in everyday life, to model relationships and solve problems.

Here,

To find the average annual rate of change, we need to calculate the total change in subscribers over the 6-year period and divide by the number of years. The total change is the final value minus the initial value, or:

335,244 - 270,461 = 64,783

The number of years is 6.

So the average annual rate of change is:

64,783/6 = 10,797.17

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The article's development of key ideas by showcasing the importance of precise criteria and the ever-evolving nature of scientific knowledge. The IAU's decision on Pluto serves as a prime example of these concepts in action.

Lines 25 and 26 contribute to the development of key ideas in the article "Ideas That Work... And Those That Don't" from "When is a Planet Not a Planet? The Story of Pluto" by providing a comparison between two concepts in the field of astronomy. These lines state, "The IAU's decision to demote Pluto was based on a more nuanced understanding of what constitutes a planet."

Firstly, this statement demonstrates that the International Astronomical Union (IAU) relies on a "nuanced understanding" to define what a planet is, emphasizing the importance of precise criteria in categorizing celestial bodies. The IAU's decision-making process shows that some ideas work, such as establishing clear guidelines for planetary classification, while others don't, like the previous, less accurate definition of a planet.

Secondly, by mentioning the demotion of Pluto, the article highlights the impact of changing scientific perspectives on our understanding of the solar system. This reinforces the idea that knowledge is constantly evolving, and sometimes previously accepted ideas must be reconsidered or discarded to make way for more accurate information.

In summary, lines 25 and 26 contribute to the article's development of key ideas by showcasing the importance of precise criteria and the ever-evolving nature of scientific knowledge. The IAU's decision on Pluto serves as a prime example of these concepts in action.

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To create a 95% confidence interval for the proportion of all U.S. adults living with chronic conditions, we can use the following formula:

CI = p ± zsqrt(pq/n)

where:

p is the sample proportion (0.453)

q is the complement of p (1 - p = 0.547)

z is the z-score associated with a 95% confidence level (1.96)

n is the sample size (unknown)

We need to find the sample size (n) in order to calculate the confidence interval. We can do this by using the margin of error formula:

ME = zsqrt(pq/n)

where ME is the margin of error (0.035)

Solving for n, we get:

n = (z^2 * p * q) / ME^2 = (1.96^2 * 0.453 * 0.547) / 0.035^2 = 580.04

Rounding up to the nearest whole number, the sample size is 581.

Now we can substitute the values into the confidence interval formula:

CI = 0.453 ± 1.96sqrt(0.4530.547/581)

CI = 0.453 ± 0.035

The 95% confidence interval for the proportion of all U.S. adults living with chronic conditions is:

CI = (0.418, 0.488)

So we can say with 95% confidence that the true proportion of all U.S. adults living with chronic conditions is between 0.418 and 0.488.

The job would need to pay $500 to cover Cole's expenses.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Let's define some variables to represent the unknowns in this problem:

Let x be the number of hours that the server will work at the next job.

Let y be the total amount of money that Cole will make from the next job.

With these variables, we can set up a system of equations:

The cost of the equipment and server hire is $100 plus the server's hourly wage multiplied by the number of hours worked:

100 + 16x = total cost

The amount that Cole will make from the next job is the base pay of $50 plus the server's hourly wage multiplied by the number of hours worked:

y = 50 + 18x

We want to find the value of y that will make up for the $100 expense. In other words, we want to find the value of x that satisfies the equation:

total cost = y

Substituting the second equation into the first equation, we get:

100 + 16x = 50 + 18x

Solving for x, we get:

x = 25

Substituting x = 25 into the second equation, we get:

y = 50 + 18(25) = 500

Therefore, the job would need to pay $500 to cover Cole's expenses.

We can graph the two equations to visualize the solution:
   y = 50 + 18x          y = 100 + 16x

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

x = 0 |        50      |   |        100      |

    |               |   |               |

    |               |   |               |

    |               |   |               |

    |               |   |               |

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

              25                      25

The point where the two lines intersect is (25, 500), which represents the solution to the system of equations.

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absolute value inequality |x - 2| <= 7 and (x <= 9 or x >= -5)

To create an absolute value inequality that has the solution set x < 9 or x >= -5, we first need to find the midpoint between -5 and 9, which is:

Midpoint = (-5 + 9) / 2 = 2

now, we need to find the distance between the midpoint and either endpoint.

Distance = |9 - 2| = 7

Now we can use the formula:

|x - b| <= c

where b is the midpoint and c is the distance.

putting the values we found,

|x - 2| <= 7

To get the solution set x < 9 or x >= -5, we can split this inequality into two parts:

x - 2 <= 7 or -(x - 2) <= 7

Simplifying each part, we get:

x <= 9 or x >= -5

Combining the two inequalities we get :

|x - 2| <= 7 and (x <= 9 or x >= -5)

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The true statement about the value of a in comparison to 0 and 1 is that it is a real number between 0 and 1.

A graph of y = f⁻¹(x) is shown below.

An equation for f⁻¹(x) is [tex]y=\frac{1}{a^x}[/tex].

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of f(x), we can logically deduce that [tex]a^x[/tex] is positive for all values of x and as such, all values of a must also be positive:

0 < a

Additionally, the exponential function [tex]a^x[/tex] represent a decreasing function, so for any values of x, we have:

[tex]a^x > a^{x+1}[/tex]

1 > a

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Tara invests $555 into a savings account that has an interest rate of 12.6% and is compounded quarterly. It will take 18.6 years for the account to reach a balance of $5,600.

The amount that the lender charges the client above and beyond the initial amount is referred to as the interest rate. Given the time worth of money, a person who deposits money in a bank or other financial organisation also gets extra revenue known as interest received by the depositor.

Using the quarter compound formula given below-

[tex]$ \rm A = P (1 + \frac{r}{4})^{4 \times t}[/tex]

Where,

Interest in a year (r)= 12.6% = 12.6/100= 0.126

Actual amount (P)= $555

Final amount (A)= $5,600

Lets solve:

[tex]5,600 = 555(1+0.126/4)^{4t[/tex]

Or, [tex](4.126/4)^{4t}= 5600/555[/tex]

Or, 4t ln(4.126/4)= ln 5600/555

Or, 4t =74.532

Or, t ≈ 18.6

Hence the correct answer is 18.6 years

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Answer:

A 30 degree angle is an acute angle cause its less than 90 degrees

Answer:

A thirty degree angle is an acute angle.

A thirty degree angle is formed when two lines meet or intercept at a point .

A thirty degree angle is one in which the measure is less than 90 degrees

Answer:

Of course! The value of 3 log 4 is approximately 4.7712. Does that match your answer?

Answer:

B. S(15) - S(10) = -40 means that there were 40 less students in 2010 than there were in 2015. This statement is true because S(15) represents the number of students in the year 2015, and S(10) represents the number of students in the year 2010. Subtracting S(10) from S(15) gives the change in the number of students over that 5-year period.

C. S(0) = 2,000 means that there were no students in the year 2000. This statement is also true because S(t) represents the number of students in terms of the number of years after 2000. Therefore, S(0) represents the number of students in the year 2000, which is the starting point for the function.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given:

1 furlong has 660 feet

1 yard has 0,5 fathom

Find:

How many fathoms are there in one furlong?

.

We know that 1 yd has 3 ft, that means:

There's 660 ft in one furlong and 3 ft in 0,5 of a fathom (6 ft in one fathom)

Now, in order to find how many fathoms are there in one furlong, we have to divide the number of feet in a furlong by the number of feet in a fathom:

[tex] \frac{660}{6} = 110 \: fathoms[/tex]

Answer:

center:(0,0)

Radius:7

Step-by-step explanation:

the equation of circle:

(x-h)^2+(y-k)^2=r^2

the point h and k are the center of the circle
(h,k)  ———-> (0,0)

since r^2 =49

So, the radius will be the square root of that number
[tex]r^{2} =49[/tex]

[tex]\sqrt{r^{2} } =\sqrt{49}[/tex]

[tex]r=7[/tex]

Answer:

Let's start with the distance each person covers in 3 minutes.

Beth's distance = 70 meters/minute x 3 minutes = 210 meters

Liz's distance = 60 meters/minute x 3 minutes = 180 meters

Now we can find their distance apart after 3 minutes.

Distance apart = Initial distance - distance covered

Distance apart = 520 meters - (210 meters + 180 meters)

Distance apart = 520 meters - 390 meters

Distance apart = 130 meters

Therefore, Beth and Liz are 130 meters away from each other after walking towards each other for 3 minutes.

Answer:

247277 cubic in

Step-by-step explanation: