1. Start the search among 2-digit numbers. A dropdown number (DDN) with 2 digits is a number [tex]ab[/tex] such that
[tex]\dfrac{a+b}2 = a \implies a + b = 2a \implies b = a[/tex]
or
[tex]\dfrac{a+b}2 = b \implies a+b = 2b \implies a=b[/tex]
but both of these solutions violate the requirement that the digits are distinct, so there are no 2-digit DDNs.
A 3-digit DDN [tex]abc[/tex] is such that
[tex]\dfrac{a+b+c}3 = a \implies a+b+c = 3a \implies b+c = 2a[/tex]
or [tex]a+c=2b[/tex] if the average is [tex]b[/tex], or [tex]a+b=2c[/tex] if the average is [tex]c[/tex]. The smallest possible value for [tex]a[/tex] is 1 since we require 3 digits. Then [tex]b+c=2[/tex], and we can pick [tex]b=0[/tex] and [tex]c=2[/tex] to get the smallest DDN, 102.
2. In a 4-digit DDN [tex]abcd[/tex], we have
[tex]\dfrac{a+b+c+d}4 = a \implies a + b + c + d = 4a \implies b+c+d=3a[/tex]
or [tex]a+c+d=3b[/tex] or [tex]a+b+d=3c[/tex] or [tex]a+b+c=3d[/tex].
We're free to fix [tex]a=1[/tex] and [tex]b=0[/tex] to try to get the smallest DDN. This leaves us with [tex]c+d=3[/tex] or [tex]c+d=-1[/tex] or [tex]1+d=3c[/tex] or [tex]c=3d[/tex].
The first two cases are impossible - the only choices for [tex]c,d[/tex] such that [tex]c+d=3[/tex] are 1 and 2, and the sum of two positive integers must be positive. The smallest possible value of [tex]c[/tex] is 2; this leaves us with [tex]1+d=6[/tex] or [tex]2=3d[/tex], but the latter case is impossible because 3 does not divide 2. So [tex]d=5[/tex], and the smallest 4-digit DDN is 1025.
To find the largest DDN, start with the largest possible values for [tex]a[/tex] and [tex]b[/tex]. Let [tex]a=9[/tex] and [tex]b=8[/tex]. Then [tex]c+d=19[/tex] or [tex]c+d=15[/tex] or [tex]17+d=3c[/tex] or [tex]17+c=3d[/tex]. At most, we can have [tex]c+d=13[/tex] with 7 and 6, so the first two cases are impossible. If we maximize [tex]c=7[/tex], then either [tex]17+d=21\implies d=4[/tex] or [tex]24=3d\implies d=8[/tex] (which we don't want). So the largest 3-digit DDN is 9874.
3. I don't have an analytical solution to this, but using brute force (program) the total count is 112.
4. It is possible; consider 1249 and 1250, with digital averages
[tex]\dfrac{1+2+4+9}4=4 \text{ and } \dfrac{1+2+5+0}4=2[/tex]
which happens to be the smallest pair. (Also found with brute force.)
Ellison wants to purchase a backpack for $76. The tax in his area is 7%. What would his total cost be?
Answer:
The cost is $81.32
Step-by-step explanation:
Answer: $81.32
Step-by-step explanation:
Its about Numerical Representations
Lyndie is making reduced copies of a photo 25 centimeters in height. She sets the copy machine to an 80% size reduction.
PART A
Write a percent equation that represents the relationship of the height of the first copy to the height of the original photo.
PART B
Lyndie wants to make another copy that will have a height of 17 cm. The copy machine settings increase or decrease in increments of 5%. Which photo should she make her copy from, the original or her first copy? Explain.
Answer:
80% x 25cm = 20cm
First Copy
Step-by-step explanation:
80% x 25cm = 20cm
1.25 is 5% of 25 25-17=8
8/1.25= 6.4 which doesn't go in evenly.
1 is 5% of 20 20-17=3
3/1= 3 which goes in evenly.
Elliot is moving a table through a doorway. The table is 2 and StartFraction 5 Over 8 EndFraction ft wide and the doorway is 2 and three-fourths ft wide. Which statement explains if the table will fit through the door?
The table will fit because 2 and StartFraction 5 Over 8 EndFraction < 2 and three-fourths.
The table will fit because 2 and StartFraction 5 Over 8 EndFraction > 2 and three-fourths.
The table will not fit because 2 and StartFraction 5 Over 8 EndFraction < 2 and three-fourths.
The table will not fit because 2 and StartFraction 5 Over 8 EndFraction > 2 and three-fourths.
Answer:
The table will fit
Step-by-step explanation:
Table: 2 3/8 = 19/8
Door: 2 3/4 = 11/4
(Mixed fraction to Improper fraction)
Door: 2 3/4 = 11/4 = 11/4*2 = 22/8
19/8 (Table) > 22/8 (Door)
(Hopefully thats the answer 'cause the question isn't very readable)
If a person walks 1/2 mile in 1/4 hour, how far does that person walk in 2 hours?
Please see photo. I don't know where to begin
art A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.
Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation.(2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
I need the most help for part c.
Answer: PART A:
Recall that the equation of a line in standard form is of the form:
ax + by = c
where a, b, and c are constants.
The equation of a line passing through two points:
and
is given by:
Given that Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113.
This,
and
Thus, the equation of the line is given by:
Therefore, the equation of the line in standard form is
PART B:
To write the equation with a function notation, we first express y in terms of x and then change y notation to f(x) notation.
Recall from part 1:
Therefore, the equation obtained in Part A written using function notation is given by:
PART C:
To graph the equation obtained above, we draw the x- and y- axis with the x-axis labelled 'number of hours' and the y-axis labelled 'total rent'.
Next, we choose appropriate scales for x- and y- axis. Depending on the size of your graph book, you can choose an interval of 1 unit for the x-axis and an interval of 10 units for the y-axis.
From part A, we know that the line of the equation passes though points (3, 43) and (8, 113), mark these points and draw a straight line passing theough these points.
Step-by-step explanation:
Mrs. Lowry is ordering car decals for each family to put on their cars for the upcoming baseball season. She ordered 25 decals. She got a deal on them and they will be $2 cheaper for each decal. The total came to $250. Write an equation to find the amount, d, for the normal cost of each car decal without the deal.
What is the normal cost of each decal without the deal?
Answer:
$12----------------------
Let the cost of each car decal is d.
After applying a discount of $2 the total for 25 decals came to $250.
Set up an equation:
25(d - 2) = 250Solve it for d:
25(d - 2) = 250d - 2 = 250/25d - 2 = 10d = 10 + 2d = 12The normal cost of each decal is $12.
helpppppppppppppppppppppppppppppppppppppppppp
Answer: 565.49 inch^3
Step-by-step explanation:
if your looking for volume, the solution is V= πr^2h
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write a list of steps that are needed to find the measure of ∠B.
Answer:
5 degree75 drgreeStep-by-step explanation:
hope I was correct
Answer: hope this helps ♡
The measure of ∠B is 41°
HELP! Use the distributive property to find an expression that is equavilent to 2( x + 7) - (3x + 1)
Answer: -x + 13
Step-by-step explanation:
2 ( x +7 ) - (3x + 1 )
2x + 14 - 3x +1
Please Help!!!!!!!!!!!!
Answer: For the $18 sweatshirt, DISCOUNT 2 is the best.
For the $30 sweatshirt, DISCOUNT 3 is the best.
Step-by-step explanation: For the $18 sweatshirt, 20% off would be $14.4. If she uses the $5 rebate, shes getting $5 off or back. She can't use the 3rd discount because it's not over $20.
For the $30 sweatshirt, 20% off of that makes it $24. $5 back from the rebate makes it $25, and half off (50%) makes it $15. Which is the cheapest.
Answer:
discount 2 would be the best for $18 sweatshirt
discount three would be the best for the $30 sweatshirt
Step-by-step explanation:
the person who answered first was correct!
I need help ASAP .....
Answer:
(d + 1)(d + 2)
Step-by-step explanation:
the thing is that you want to find a number that goes into 2 and adds to 3. so like this one 1 x 2 is 2 and the numbers add to 3
Combining Like Terms- Thank you!!
Answer:
-1(3e-9) is NOT equivalent to 4-10e+7e-13.
Step-by-step explanation:
See the image attached
First, you must begin by combining the like terms.Once you combine like terms, evaluate them.Form the final expression.Look through the answer choices:The first choice is the expression we just derived (-3e-9).-3(e+3) evaluates to (-3e-9) via PEMDAS.-1(3e+9) evaluates to (-3e-9) via PEMDAS.-1(3e-9) evaluates to (-3e+9) via PEMDAS.Please let me know if this helped!!
A wire is first bent into the shape of a square. Each side of the square is 5 in long. Then the wire is unbent and reshaped into a rectangle. If the length of the rectangle is 6, what is its width?
Can you solve this for me? Thank you! :>
Answer:8.5
Step-by-step explanation:
x+2.25=10.75
do the opposite from the equation(always the one with the variable) to the value given
x+2.25-2.25=10.75-2.25
Sum it all up
x=8.5
Hope this helps good luck!
The width of a new barn is 27 meters across. Nine meters is equal to approximately ten yards. How many yards wide is the new barn?
Answer:
If 9 meters is equal to 10 years, then you just need to find out how many times 9 goes into 27 and then multiply that by 10!
9 * 3 = 27
3 * 10 = 30!
Step-by-step explanation:
Hope it helps! =D
PLEASE HELP I HAVE NO CLUE WHAT TO DO I DROPED THE FILE SO PLEASE HELP
Answer:
y = 3/4x -1/4
Step-by-step explanation:
First, find the slope using the points (3, 2) and (-1, -1):
Slope = m = y2 -y1 / x2 -x1 = -1 -2 / -1 -3 = -3/-4 = 3/4
Find the y-intercept, b, by substituting x = -1, y = -1 and m = ¾ in y = mx + b.
-1 = ¾(-1) + b
-1 = -¾ + b
Add ¾ to both sides
-1 + ¾ = b
(-4 + 3)/4 = b
-¼ = b
Substitute m = ¾ and b = -¼ in y = mx + b.
The equation would be:
✅ Y = 3/4x - 1/4
There are 63 students in Grade 6. If the ratio of students who have black shoes to white shoes is 3:4, how many students have black shoes?
Answer: 27 students have black shoes.
Step-by-step explanation:
There are 3 people who have black shoes out of 7 (3+4=7)
You have: 3/7
Find the variable: 3/7: x/63
63 divided by 7 = 9
3x9=27 students who have black shoes
what is the equation of the line slope intercenpt form that passes through the point (8,9) and is parallel to the graph of y=3/4x-2? please explain.
Answer:
Slope-intercept form is y= 4x - 30
Step-by-step explanation:
Step 1: Substitute the slope from original line into the equation of the line
Here slope , m is 4
y= mx +b
where m is the slope
b is the y intercept
So Substituting slope we get,
y= 4x +b--------------------------------------------(1)
Step 2 :Substitute the given point (8,2) into the x and y values of equation (1)
y = 4x +b
2 =4(8) + b
Step 3: Solve for y intercept values
2 = 32+ b
2-32 =b
-30 =b
Now the y intercept value b= -30
Step 3: Substitute this value for 'b' in the slope intercept form equation
Substituting the value in eq (1) we get,
y= 4x +(-30)
y= 4x - 30
hope this helps!
Which of the following fractions is equivalent to 4/20? 2/12, 3/15, 3/19, 1/10
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The probability of landing on yellow is less than the probability of landing on blue.
Explanation:
The probability of landing on yellow is 2/8, while the probability of landing on blue is 3/8. 2/8 is less than 3/8
None of the other answers can be right, because:
the probability of landing on purple (2/8) is greater than the probability of landing on orange (1/8),
the probability of landing on orange (1/8) is less than the probability of landing on yellow (2/8),
and the probability of landing on purple (2/8) is less than the probability of landing on blue (3/8)
Eman walks from the store to her friend’s house, 2 miles away. It takes her 35 minutes.
A. What fraction represents her constant speed, C ?
B. Write the fraction that represents her constant speed, C , if she walks y miles in 10 minutes.
C. Write and solve a proportion using the fractions from parts (a) and (b) to determine how many miles she walks after 10 minutes. Round your answer to the hundredths place.
D. Write a two-variable equation to represent how many miles Eman can walk over any time interval.
Answer:
A is 17.5
B is y/10
C in 10 minutes she walks 0.57 miles (0.92 km)
Step-by-step explanation:
Solve the equation −108 = 6x for x.
−102
−18
18
114
Answer:
-18
Step-by-step explanation:
-108=6x
÷6 ÷6
X=-18
-108=6(-18)
-108=-108
helpppppppppppp fasttttttttttttttt
Answer:
Step-by-step explanation:
it 2
I just did this
Is it clear now? And PLEASE help me with it
At the Wild West amusement park, Florence's favorite ride is the Blazing Bullet roller coaster. The roller coaster normally has a lot of seats to choose from, but Florence noticed that 12 of the seats are now reserved for season pass holders. There are 42 seats remaining for people without season passes. Let s represent the total number of seats on the Blazing Bullet roller coaster. Which equation models the problem?
Answer:
s=42+12
if there were 42 seats remaining and 12 seats reserved, adding both of them together would give you the total number of seats
Answer: s-12=42
Step-by-step explanation:
We don’t see any multiple choice problems but I think the answer would be this.
s-12=42
Dani's estimate for the cost of tiling her bathroom floor is $50 plus $3 per square foot. Write a linear equation showing the total cost.
Include in Your Answer:
The linear equation written in y=mx + b format.
1 to 2 sentences explaining how you determine the correct linear equation.
Answer:
The linear equation showing the total cost of tiling Dani's bathroom floor is: y = 3x + 50
The equation is in the form of "y = mx + b", where y represents the total cost, x represents the number of square feet, m represents the cost per square foot ($3), and b represents the fixed cost ($50). The linear equation is determined by using the information provided in the problem, which is the cost per square foot and the fixed cost.
Step-by-step explanation:
pls help soon someone
also commment down below if can help me with these questions and i will message you
please do it because i dont have money to pay for a one on one toutor i just need help for 7 questions
Answer:
The first blank is -88
The second blank is - 120
and the last blank is -32
Step-by-step explanation:
I am good at Math TRUST me
hope you get a good grade :)
Question
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Answer:13.8
Step-by-step explanation: Divide 27.60 by 2