There are 120 numbers between 650 and 780 that leave remainders of 4 when divided by 7 and remainders of 6 when divided by 11.
To find the numbers between 650 and 780 that leave remainders of 4 when divided by 7 and remainders of 6 when divided by 11, we can analyze the problem systematically.
For a number to leave a remainder of 4 when divided by 7, it must be of the form [tex]\(7k + 4\)[/tex].
Similarly, for a number to leave a remainder of 6 when divided by 11, it must be of the form [tex]\(11m + 6\).[/tex]
We need to find the intersection of these two sets of numbers between 650 and 780.
Let's start by finding the smallest number of the form \(7k + 4\) greater than or equal to 650:
[tex]\[7k + 4 \geq 650\][/tex]
[tex]\[7k \geq 646\][/tex]
[tex]\[k \geq \frac{646}{7} \approx 92.2857\][/tex]
Since [tex]\(k\)[/tex] must be an integer, the smallest integer greater than or equal to [tex]\(92.2857\)[/tex] is 93.
So, the smallest number of the form [tex]\(7k + 4\)[/tex] greater than or equal to 650 is [tex]\(7 \times 93 + 4 = 655\).[/tex]
Now, let's find the largest number of the form [tex]\(7k + 4\)[/tex] less than or equal to 780:
[tex]\[7k + 4 \leq 780\][/tex]
[tex]\[7k \leq 776\][/tex]
[tex]\[k \leq \frac{776}{7} \approx 110.857\][/tex]
Again, since [tex]\(k\)[/tex] must be an integer, the largest integer less than or equal to [tex]\(110.857\)[/tex] is 110.
So, the largest number of the form [tex]\(7k + 4\)[/tex] less than or equal to 780 is [tex]\(7 \times 110 + 4 = 774\).[/tex]
Next, let's find the smallest number of the form [tex]\(11m + 6\)[/tex] greater than or equal to 650:
[tex]\[11m + 6 \geq 650\][/tex]
[tex]\[11m \geq 644\][/tex]
[tex]\[m \geq \frac{644}{11} \approx 58.5455\][/tex]
Since [tex]\(m\)[/tex] must be an integer, the smallest integer greater than or equal to [tex]\(58.5455\)[/tex] is 59.
So, the smallest number of the form [tex]\(11m + 6\)[/tex] greater than or equal to 650 is[tex]\(11 \times 59 + 6 = 655\).[/tex]
Finally, let's find the largest number of the form[tex]\(11m + 6\)[/tex]less than or equal to 780:
[tex]\[11m + 6 \leq 780\][/tex]
[tex]\[11m \leq 774\][/tex]
[tex]\[m \leq \frac{774}{11} \approx 70.3636\][/tex]
Since [tex]\(m\)[/tex] must be an integer, the largest integer less than or equal to [tex]\(70.3636\)[/tex] is 70.
So, the largest number of the form [tex]\(11m + 6\)[/tex] less than or equal to 780 is [tex]\(11 \times 70 + 6 = 776\).[/tex]
Now, we need to find the intersection of the sets of numbers [tex]\([655, 774]\) and \([655, 776]\).[/tex]
This can be done by finding the range of overlap between these two sets.
The range of overlap is [tex]\([655, 774]\),[/tex] which contains 774 - 655 + 1 = 120 numbers.
So, there are 120 numbers between 650 and 780 that leave remainders of 4 when divided by 7 and remainders of 6 when divided by 11.
Please help with this math question graph
Answer:
its the first one
Step-by-step explanation:
on his fifth birthday ,paul was 42 inches tall. on his seventh birthday he was 48inches tall
Answer:
Paul grew 6 inches in 2 years
Step-by-step explanation: he was 42 inches before now he is 48 inches
Point A is located at (-5, 2) and is reflected in the y-axis. What are the coordinates of point A'?
A.(-5, -2)
B.(5, 2)
C.(5, -2)
When a point is reflected across the Y axis, the Y coordinate remains the same and the X coordinate becomes the opposite of the original value.
Points are written as ( X,Y)
The original point is (-5,2)
The opposite x value would be 5 and the Y value stays the same.
The reflected point would be (5,2)
The answer is B.
A.(-5, -2). The reflected point A' after reflecting point A with coordinates (-5, 2) in the y-axis will have coordinates (5, 2).
Explanation:When point A, which is located at (-5, 2), is reflected in the y-axis, you have to switch the sign of the x-coordinate while keeping the y-coordinate the same. This is because reflection across the y-axis means that the point's position will be mirrored over the y-axis, resulting in the same vertical (y) positioning but an opposite horizontal (x) positioning. Therefore, the reflected point A', will be at (5, 2), which corresponds to answer B.
What is the solution to the following system of equations?
It has infinitely many solutions.
It has no solution.
It has one solution (2, –3).
It has one solution (4, 0).
Answer:
A. Infinite solutions.
Step-by-step explanation:
3x - 2y = 12
6x - 4y = 24
The second equation can be formed by multiplying the first by 2. So if we graphed them they would give the same line. So the equations are identical and there are infinite solutions.
A.Infinite solutions
Whats a comparison between the value of the 3 in 17,235 and the value of 3 in 17,352?
Answer: The 3 in 17,235 is in the tens digit and the 3 in 17,352 is in the hundreds digit
There were some toads in the pond. 3 more jump in. 2 toads jumped out of the pond. There are now 6 toads in the pond. How many toads were in the pond to begin with?
Answer:
5
Step-by-step explanation:
do reverse calculations
we know that we ended with 6
since 2 jumped out we add them back in
6+2 = 8
we remove the toads that jumped in because they are not part of the original group
8-3 = 5
there were 5 toads in the beginning
There were originally 5 toads in the pond. This is determined by reverse calculation of the toads jumping in and out.
Explanation:To solve this math problem you can use a process of reverse calculation. At the end of the toad jumping in and out, there were 6 toads in the pond.
If we take into account the events that happened before we have that 2 toads jumped out so there must have been 8 toads before that(6 + 2).
Further back, 3 toads jumped in which means there must have been 8 - 3 = 5 toads in the pond to begin with.
So, initially, before any of the jumping happened, there were 5 toads in the pond.
Learn more about Toads Herehttps://brainly.com/question/34442054
#SPJ2
What is -5 1/4 written as a decimal
Answer:
-5.25
Step-by-step explanation:
1/4 is equal to 0.25
4*3-(24divided6)+8=?
Answer:
16
Step-by-step explanation:
Follow the correct order of operations.
4 * 3 - (24 divided 6) + 8 =
Parentheses first.
= 4 * 3 - 4 + 8
Now, the multiplication.
= 12 - 4 + 8
Now additions and subtractions in the order they appear from left to right.
= 8 + 8
= 16
One side of a triangle is 3 1/3 cm, another side is 2/3 cm shorter than the first side, and the third side is 1 2/3 cm longer than the first side. What is the perimeter of the triangle?
Thanks so much
Good evening ,
_______
Answer:
perimeter = 22/3 cm
____________________
Step-by-step explanation:
Look at the photo below for the details.
:)
Write the expression 10 + 25 in a different way,
using the commutative law of addition, and show
that both expressions result in the same answer.
What is the absolute value of -3/8? A. 0 B. -3/8 C. 3/8 D. -3/8 or 3/8
The answer is 3/8. The absolute value of a number is its distance from zero on the number line.
Answer:
The answer is 3/8. The absolute value of a number is its distance from zero on the number line.
Step-by-step explanation:
Will give brainliest 9 +10
What is 4,226 - 2,958
Answer:
1268
Step-by-step explanation:
4226-2958=1268 mark the brainliest
The difference between 4,226 and 2,958 is 1,268.
Explanation:The question is asking for the difference between 4,226 and 2,958. To solve this, we subtract 2,958 from 4,226. Starting from the rightmost digit, subtract 8 from 6 which gives us 2. Then subtract 5 from 2 and you get a negative number so we need to borrow from the next digit. Borrow 1 from the leftmost digit, which makes it 3, then subtract 5 from 13 and you get 8. Finally, subtract 2 from 3, giving us 1. The answer is 1,268.
Learn more about Subtraction here:https://brainly.com/question/20438352
#SPJ2
Find the pay per hour if you earned $102.67 for 16 hours worked.
Answer:
heyooo!
the correct answer is youll be making 6.41 an hour.
hope this helps!!
Step-by-step explanation:
if you divide 102.67 by 16 hours youll end up with your hourly pay which is 6.41
Greta added 3/6 of a cup of sugar to her cake mix then sprinkled 1/6 of a cup of sugar over the top of the finished which fraction represents the total amount of sugar that Greta used for the cake? Express the answer in the lowest terms?
a: 1/6 of a cup
b: 1/3 of a cup
c: 3/6 of a cup
d: 2/3 of a cup
Answer:
D
Step-by-step explanation:
4/6 reduced is d
Explain the difference between a markup and a margin.
Answer:
Step-by-step explanation: mark up would be a fixed percentage, say you mark up your goods 50% your cost is $1 and 50% m-up would mean a selling price of 1.50. given this , your margin is 50cents. but margin may vary, there are indirect costs, example. store a charges, 1% display fee, store b charges 3% display fee. so, in store by your margin decreases. other factor that may affect margin are commission, local taxes, store charges.
Answer:
The answer is
Profit margin is sales minus the cost of goods sold. Markup is the percentage amount by which the cost of a product is increased to arrive at the selling price. Markup is the retail price for a product minus its cost, but the margin percentage is calculated differently.
on edg 2020
Step-by-step explanation:
Which of the following numbers could not be represent a probability
3(b+1)=4b-1 I need help
Answer:
3b + 3 = 4b - 1
3= b - 1
b= 4 is the solution
Chase makes 2 gallons of soup for a dinner party. He serves 10 cups of soup to his guests. How many cups of soup will he have left over?
Answer:
d
Step-by-step explanation:
Answer:
22 cups
Step-by-step explanation:
Answer:
22 Cups of soup Left
Step-by-step explanation:
Given: 2 gallons of soup and 10 cups of soup served to guest.
To find: No. of cups of soup left.
We know that , 1 US Gallon = 16 US cups
⇒ 2 gallon of soup = 2 × 16 = 32 cups of soup
So, Remaining No. of Cups of soup = 32 - 10
= 22
Therefore, 22 Cups of soup Left
How do you turn 1/8 into a decimal and a percent
Divide 1 by 8 which is 0.125, for a decimal. Then to turn it into a percent move the decimal 2 places to the right, then add the percent to the end; 12.5%
The fraction 1/8 can be converted into a decimal by dividing the numerator by the denominator, yielding 0.125. This decimal can then be converted into a percent by multiplying by 100, yielding 12.5%.
Explanation:To convert the fraction 1/8 into a decimal and a percent, we need to perform two types of conversions: a fraction-to-decimal conversion and a decimal-to-percent conversion.
First, converting the fraction to a decimal. To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). In this case, that gives us 1 ÷ 8 = 0.125.
Then, converting the decimal to a percent. A decimal can be converted to a percent by multiplying it by 100. So 0.125 * 100 = 12.5%. Therefore, the fraction 1/8 is equal to 0.125 as a decimal and 12.5% as a percentage.
Learn more about Fraction to Decimal and Percent Conversion here:https://brainly.com/question/30596385
#SPJ3
is 19 2/9 a integer
Answer:No
Step-by-step explanation: Integers are whole numbers that can be positive or negatives no decimals or fractions.
Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.
5 - 2x^2 = -15
5-2x2=-15
Two solutions were found :
x = ± √10 = ± 3.1623
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5-2*x^2-(-15)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(5 - 2x2) - -15 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
20 - 2x2 = -2 • (x2 - 10)
Trying to factor as a Difference of Squares :
3.2 Factoring: x2 - 10
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 10 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 3 :
-2 • (x2 - 10) = 0
Step 4 :
Equations which are never true :
4.1 Solve : -2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.2 Solve : x2-10 = 0
Add 10 to both sides of the equation :
x2 = 10
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 10
The equation has two real solutions
These solutions are x = ± √10 = ± 3.1623
Two solutions were found :
x = ± √10 = ± 3.1623
To solve the equation 5 - 2x^2 = -15 using inverse operations, we need to isolate the variable x on one side of the equation.
1. Start by adding 15 to both sides of the equation to eliminate the constant term on the right side:
5 - 2x^2 + 15 = -15 + 15
20 - 2x^2 = 0
2. Next, divide both sides of the equation by -2 to isolate the x^2 term:
(20 - 2x^2) / -2 = 0 / -2
-10 + x^2 = 0
3. Now, move the constant term to the other side by adding 10 to both sides:
-10 + x^2 + 10 = 0 + 10
x^2 = 10
4. To solve for x, we need to take the square root of both sides of the equation:
√(x^2) = √(10)
x = ±√(10)
To check the solutions, substitute them back into the original equation and see if they make it true:
For x = √(10):
5 - 2(√(10))^2 = -15
5 - 2(10) = -15
5 - 20 = -15
-15 = -15 (True)
For x = -√(10):
5 - 2(-√(10))^2 = -15
5 - 2(10) = -15
5 - 20 = -15
-15 = -15 (True)
So, the solutions to the equation 5 - 2x^2 = -15 are x = √(10) and x = -√(10).
What term describes this polygon?
heptagon
dodecagon
17-gon
12-gon
Step-by-step explanation:
heptagon = 7 sides
dodecagon = 12 sides
heptadecagon = 17 sides
What is the perimeter of this rectangle?
Step-by-step explanation:
The perimeter of a rectangle is 2(l+b)
l= x2-x1
b=y2-y1
2(l+b)=2(x2-x1+y2-y1)
The temperature changed from 7°f at 6pm to -5°f at midnight. What was the difference between the high an low temperatures? Whats was the average change in temperature per hour?
Answer:
Difference between high and low temperatures: 12°F
Average change in temperature per hour: 2°F
Step-by-step explanation:
The difference between high and low temperatures was: 7 - (-5) = 12 (°F)
Midnight is 12am, so 6pm to midnight is 6 hours.
The average change in temperature per hour is: 12 / 6 = 2 (°F)
2. Simplify the expression.
7 + 10x - 7 + 7x
Please Help!!!
Answer:
17x
Step-by-step explanation:
10+7 = 17
7-7 = 0
Given l||m and m∠1 = 60°, select all angles that are also equal to 60°.
you can choose more than one
the answer choices are
2
3
4
5
6
7
8
Answer:
m∠2
m∠3
m∠4
Step-by-step explanation:
we know that
m∠2=m∠1 ----> by vertical angles
m∠3=m∠1 ---- by corresponding angles
m∠4=m∠1 ----> by alternate exterior angles
Answer:
m<3
m<2
m<4
Step-by-step explanation:
2. Write the number in standard form.
4 ten thousands, 1 thousand, 9 hundreds,
8 tens, and 4 ones
21.1984
The number "4 ten thousands, 1 thousand, 9 hundreds, 8 tens, and 4 ones" written in standard form is 41,984.
To write the number 4 ten thousands, 1 thousand, 9 hundreds, 8 tens, and 4 ones in standard form, we can add up the value of each place:
4 ten thousands = 4 × 10,000 = 40,000
1 thousand = 1 × 1,000 = 1,000
9 hundreds = 9 × 100 = 900
8 tens = 8 × 10 = 80
4 ones = 4
Now, add up these values:
40,000 + 1,000 + 900 + 80 + 4
= 41,984
Therefore, the number "4 ten thousands, 1 thousand, 9 hundreds, 8 tens, and 4 ones" written in standard form is 41,984.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ6
A path starts and ends at the same vertex.
False
No it does not. False
Plz answer all questions!!! 20 points!!!
Questions:
(question A) What two points are a distance of 5 from -2 on a number line?
(question B) What two points are a distance of 4 from 5 on a number line?
(question C) What two points are a distance of 7 from -1 on a number line?
(question D) What two points are a distance from 3 from 7 on a number line?
(question E) What two points are a distance of 10 from 2 on a number line?
(question F) What two points are a distance of 1 from -5 on a number line?
Answer:
A: -7 and 3
B: 1 and 9
C: -8 and 6
D: 4 and 10
Step-by-step explanation:
you just count the distance as your going:
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
......^.........................................^
-7 and 3 are both 5 away from -2