MATHEMATICS MIDDLE SCHOOL

My Questions is: An addy number is a 5-digit number with the following properties:
• The first (leftmost) digit plus the second digit is the third digit.
• The second digit plus the third digit is the fourth digit.
• The third digit plus the fourth digit is the fifth (rightmost) digit.
• All of the digits are different.
How many different addy numbers are possible?

Answers

Answer 1

Answer:

Three different addy numbers are possible. They are 12358, 21347 and 31459.

Step-by-step explanation:

Let the 1st two digits of the numebr be x and y

Given that, 1st digit = x

2nd digit = y

3rd digit = x + y

4th digit = x + 2y

5th digit = 2x + 3y

None of the diigts can be 0 because then x = y, also none of the digits can be more tan 9 which limits the possible first digits as 1,2 and 3

(i) consider x= 1,hence 2x + 3y < 10

2 + 3y < 10

3y < 8

which makes y < $2(2)/(3)$ , since y cant be 1, it is 2

sub x = 1, y = 2 we get the number as 12358.

(ii) consider x= 2,hence 2x + 3y < 10

4 + 3y < 10

3y < 6

which makes y < 2,then y becomes 1

sub x = 2, y = 1 we get the number as 21347.

(iii) consider x= 3,hence 2x + 3y < 10

6 + 3y < 10

3y < 4

which makes y < $1(1)/(3)$ , then y becomes 1

sub x = 3, y = 1 we get the number as 31459.

Answer 2

Answer:

Final answer:

There are 26 unique addy numbers. The possible first digits for an addy number are only 1 through 4. The rest of the digits are deterministically found by the sums of adjacent digits and condition of each digit being unique.

Explanation:

An 'addy' number is a 5-digit number with specific addition rules between adjacent digits. To determine how many possible addy numbers there are, we need to analyze the rules and work out possible combinations.

Firstly, no digit can be zero because all digits must be a part of the sum which means the minimum value should be 1. And, as we move forward, since each number must be unique, it limits our possibilities of choosing values.

Consider the following: If the first digit is 1, the second could be any number from 2 to 9 (8 choices). The resulting third digit would be uniquely determined since it is the sum of the first two digits. This continues through the rest of the number, with each subsequent digit determined by the sum of the previous two digits. The only restriction is that a digit cannot be repeated, and thus the sum of two digits cannot go above 9.

By trying this approach with different starting numbers (1 through 4), we realize that the maximum number of unique addy numbers can be calculated as the sum of the series 8, 7, 6, 5 which is 26.

Learn more about Addy Numbers here:

brainly.com/question/35422565

#SPJ3

Related Questions

The sum of two numbers is 20. Their difference is 14. Find the numbers.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?A.y = 3x + 4B.c.D.y= 3x - 14y= 3x - 4y=3x + 12
For her cell phone plan, Heather pays $30 per month plus $0.05 per text. She wants to keep her bill under $60 per month. Which inequality represents the number of texts, t, Heather can send each month while staying within her budget? A)t < 600. B) t > 600. C) t < 1,800. D) t > 1,800
If the johnson family used 300 ft3 more water this month than last month then they can expect
How many 2/5 are there in 4?

(Plz answer)Unicorn is writing an equation to represent the perimeter of a rectangle with the width equal to half the length. She knows that the perimeter is equal to 18 units and needs to find the length and width of the rectangle. Which equations represent this relationship? Check all that apply.

1.- x+ 1/2 x = 18

2. 2x + x = 18

3. 2(x) + 2(2x)= 1/2x =18

4. x+ 1/2 x + x + 1/2x= 18

5. 2 [ x + 1/2 x} =18

Answers

The first is wrong

Second is right

Third is wrong

Fourth is right

Fifth is right

A children's birthday party at an indoor play center costs $50 to rent the space and $6.25 per child. Gina wants to spend no more than $100 on her son's fourth birthday party. Write an inequality for the number of children who can attend the birthday party, and solve the inequality.

Answers

Inequality: 50 + 6.25x < 100

50 + 6.25x < 100
-50    -50
   6.25x < 50
   ÷6.25 ÷6.25
   x < 8

Gina can only invite 8 children to attend her son's fourth birthday party and remain within the budget of $100 total cost. In excess of 8 will put Gina beyond budget by 6.50 per extra child.

The line L is a tangent to the curve with equation y= 4x^2 +1 . The line L cuts the y axis at (0,8) and has a positive gradient. Find the equation of L in the form y = mx + c. $y= 4x^(2) +1$

Answers

Final answer:

To find the equation of a line tangent to the given curve, we need to find the derivative of the curve at the point of tangency and substitute the x-coordinate of the point of tangency to find the slope. The equation of the tangent line with 0 slope and y-intercept of 8 is y = 8.

Explanation:

To find the equation of a line tangent to a curve, we need to find the derivative of the curve at the point of tangency.

The given curve is y = 4x² + 1 (equation 1).

First, find the derivative of equation 1, which gives us dy/dx = 8x (equation 2).

Next, substitute the x-coordinate of the point of tangency into equation 2 to find the slope of the tangent line.

Since the line cuts the y-axis at (0,8), the x-coordinate of the point of tangency is 0.

Substituting x=0 into equation 2, we get the slope of the tangent line as m = 8(0) = 0.

The equation of a line in the form y = mx + c, where m is the slope and c is the y-intercept.

Since the slope of the tangent line is 0, the equation of the tangent line is y = 0x + c. And since the line cuts the y-axis at (0,8), the y-intercept is 8.

Therefore, the equation of the tangent line is y = 8.

Learn more about Equation of a tangent line here:

brainly.com/question/39323392

#SPJ3

A generic point on the graph of the curve has coordinates

$(x, 4x^2+1)$

The derivative gives us the slope of the tangent line at a given point:

$f(x) = 4x^2+1 \implies f'(x) = 8x$

Let k be a generic x-coordinate. The tangent line to the curve at this point will pass through $(k, 4k^2+1)$ and have slope $8k$

So, we can write its equation using the point-slope formula: a line with slope m passing through $(x_0, y_0)$ has equation

$y-y_0 = m(x-x_0)$

In this case, $(x_0, y_0)=(k, 4k^2+1)$ and $m=8k$ , so the equation becomes

$y-4k^2-1 = 8k(x-k)$

We can rewrite the equation as follows:

$y-4k^2-1 = 8k(x-k) \iff y = 8kx - 8k^2+4k^2+1 \iff y = 8kx-4k^2+1$

We know that this function must give 0 when evaluated at x=0:

$f(x) = 8kx-4k^2+1 \implies f(0) = -4k^2+1 = 8 \iff -4k^2 = 7 \iff k^2 = -(7)/(4)$

This equation has no real solution, so the problem looks impossible.

Find the area of the semicircle.Either enter an exact answer in terms of or use 3.14 for
and enter your answer as a decimal.
units

Answers

Answer:

14.13

Step-by-step explanation:

The formula for area of a circle is πr^2.

This is a semicircle which is half a circle, so the formula for area of a semicircle is (πr^2)/2

The diameter of the circle is 6, which means that the radius is 3. Since the radius of a circle is always half the diameter. (1/2*6=3)

This means we can plug the known values into our formula.

π(3)^2/2

Simplify.

9π/2

Now we plug 3.14 in for π.

9(3.14)/2

28.26/2

14.13

So we know that the area of a full circle is pi multiplied by radius squared
But for a semicircle the area is pi multiplied by radius squared divided by two
So, we do 3.14*3^2/2
Which is 14.13

A bicyclist rides 1/5 mile in 1/65 hour. Write this rate as a unit rate.

Answers

1/5 over 1/65 hour. as in 1/5 divided by 1/65 hr

Final answer:

The unit rate of the bicyclist's speed is found by dividing the distance covered (1/5 mile) by the time spent (1/65 hour). The result is 13 miles per hour.

Explanation:

In this problem, you're asked to find a unit rate. A unit rate is a rate in which the second term is 1. So, to find a unit rate, you divide the first term with the second term.

In this case, the bicyclist's rate is 1/5 mile in 1/65 hour. If you divide 1/5 by 1/65, you find the rate of bicycle speed per 1 hour, which is the unit rate:

1/5 miles divided by 1/65 hours = (1/5) * (65/1) = 13 miles/hour

So, the bicyclist's unit rate is 13 miles per hour.

Learn more about Unit Rate here:

brainly.com/question/38777061

#SPJ11

In 1950, there were 40.3 million cars registered in the United States. In 1990, there were 133.7 million cars registered in the United States. What was the percent increase of registered cars from 1950 to 1990?

Answers

$(133.7)/(40.3)*100\%\approx331,76\%$

Final answer:

The number of registered cars in the US increased by about 231.76% from 1950 to 1990, calculated by finding the difference between the two given values, then dividing this by the initial value and multiplying by 100 to get the answer as a percentage.

Explanation:

The question is asking for a percent increase in the number of registered cars in the United States from 1950 to 1990. To calculate a percent increase, you first need to determine the amount of the increase, then divide this by the original amount, and multiply by 100 to get the answer in percent form.

The number of registered cars in the United States increased from 40.3 million in 1950 to 133.7 million in 1990. The amount of increase is therefore 133.7 (1990 number) - 40.3 (1950 number) = 93.4 million.

Next, we find the percent increase by dividing the increase by the original (1950) amount and multiplying by 100: (93.4 / 40.3) x 100 = Approximately 231.76%. So, there was roughly a 231.76% increase in the number of registered cars in the United States from 1950 to 1990.

Learn more about Percentage Increase here:

brainly.com/question/20818421

#SPJ3

Other Questions

On a farm, the farmer decides to give pizza to her 15 ducks as a special treat. She orders 3 pizzas, and the total price is $23.46. What is the unit price of each pizza?

Can someone tell me if im right? i think its 3. if im not correct,please tell me what i did wrong.

The equation of the line of best fit of a scatter plot is y = −5x − 2. What is the slope of the equation?1. −5 2.−2 3. 2 4. 5 Please give me the answer if you know it, or help me figure it out.

A cylinder has a diameter of 6cm. The volume of the cylinder is 108 pie cm cube. What is the height number 4