Prime numbers are those numbers that have only 1 and the number itself as factors.
If a and b are prime numbers.
The greatest common divisor of a and b is 1.
The lowest common multiple of a and b is ab.
What is a prime number?Prime numbers are those numbers that have only 1 and the number itself as factors.
2 is the only even prime number.
Examples:
2, 3, 5, 7, 11 are all prime numbers
We have,
Two natural numbers a and b.
a and b are prime numbers.
The greatest common divisor of a and b:
The prime numbers have 1 and the number itself as its factors.
So,
a x 1 = a
b x 1 = b
1 is the GCD of a and b.
The lowest common multiple of a and b:
a x b = ab
ab is the lowest common multiple of a and b.
Thus,
The greatest common divisor of a and b is 1.
The lowest common multiple of a and b is ab.
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The GCD of two different prime numbers is 1, and the LCM is the product of the two primes.
GCD(a,b) is the Greatest Common Divisor, which is the largest positive integer that divides both numbers without a remainder. For two different prime numbers a and b, their GCD will be 1 because there are no common factors other than 1. LCM(a,b) is the Least Common Multiple, which is the smallest multiple that is divisible by both numbers. For prime numbers a and b, their LCM will be the product of the two primes.
What is the circumference of the circle? Round your answer to the nearest foot
What is the average speed in miles per hour of a car that’s travels 956.4 miles in 15.9 hours? Round the answer to nearest tenth , explain step by step how to solve it
I would rather to help 6th and 7th grade math
What is the square root of 25p^3 expressed in simplified form?
Greg started with a certain number of quarters. He then decided on a number of quarters he would save each day. He added the quarters he saved to the amount with which he started. At the end of day 2, Greg had a total of 26 quarters saved. At the end of day 5, he had a total of 35 quarters saved.
A. How many quarters does Greg start with? Show or explain your work.
B. Write an equation to model the number of quarters Greg has saved, y, after x days.
C. Using the rate at which Greg is saving, explain why he can never have exactly 100 quarters saved by the end of any given day.
Final answer:
Greg started with 20 quarters. The equation for the number of quarters saved after x days is y = 20 + 3x. With Greg's savings rate of 3 quarters per day, he cannot have exactly 100 quarters on any day since 100 is not a multiple of 3 plus the 20 starting quarters.
Explanation:
To determine how many quarters Greg started with, let 's' be the number quarters Greg started with, and 'd' be the number of quarters he saves each day. After 2 days, he had a total of 26 quarters saved, and after 5 days, he had a total of 35 quarters saved. These can be written as two equations:
s + 2d = 26s + 5d = 35Subtracting the first equation from the second gives:
3d = 9
From which we find that d = 3 (Greg saves 3 quarters a day). Plugging this value back into the first equation:
s + 2(3) = 26
s + 6 = 26
s = 20
Greg started with 20 quarters.
B. The equation to model the number of quarters Greg has saved, y, after x days is:
y = 20 + 3x
C. With the savings rate of 3 quarters a day, Greg's total will always be a multiple of 3 plus the 20 he started with. 100 is not a multiple of 3, meaning he can never save exactly 100 quarters by the end of any given day since 100 minus the 20 quarters he started with leaves 80, which is not divisible by 3.
Final answer:
Greg started with 20 quarters and saves 3 quarters every day afterward. The equation to model the number of quarters saved after x days is y = 20 + 3x. It is impossible for Greg to have exactly 100 quarters saved by the end of any given day because 100 cannot be reached by adding multiples of 3 to the starting amount of 20 quarters.
Explanation:
To solve for the number of quarters Greg started with and the number of quarters he saves each day, we can set up a system of equations. Let's designate q as the number of quarters Greg started with and d as the number of quarters he saves each day. From the problem, we have two points of data: On day 2, Greg has 26 quarters, and on day 5, he has 35 quarters.
The equations representing these two data points are:
q + 2d = 26q + 5d = 35Subtracting the first equation from the second gives us:
3d = 9
Dividing both sides by 3 gives us:
d = 3
Now that we have the value for d, we can substitute it back into the first equation:
q + 2(3) = 26
q + 6 = 26
Subtracting 6 from both sides gives us:
q = 20
Greg started with 20 quarters.
For the equation to model the number of quarters saved, y, after x days, we have:
y = q + dx
This simplifies to:
y = 20 + 3x
To address part C, let's analyze the possibility of Greg having exactly 100 quarters saved. If we set y to 100 in the equation y = 20 + 3x and solve for x, we get:
100 = 20 + 3x
80 = 3x
x = 80/3
x ≈ 26.67
Since x must be an integer because Greg cannot save a fraction of a day, he cannot have exactly 100 quarters by the end of any given day. This is because 100 is not a multiple of 3 (the daily amount Greg saves) when starting from 20. Thus, it's impossible for Greg to have exactly 100 quarters saved by the end of any given day.
whats a prime number
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A cone has a diameter of 9 inches and a height of 12 inches. Find the volume of the cone to the nearest cubic inch.
972 in³
113 in³
324 in³
254 in³
HELP ASAP!!!
1: What is the surface area of a sphere with a radius of 4 meters rounded to the nearest square meter
A: 50 m^2
B: 101 m^2
C: 201 m^2
D: 268 m^2
2: What is the volume of a sphere with a radius of 6 meters rounded to the nearest square meter?
A: 905 m^3
B: 679 m^3
C: 452 m^3
D: 226 m^3
△ABC is similar to △DEF .
AB=5 inches, BC=9 inches, and DE=7.5 inches.
What is EF ?
Double a penny every day for 30 days. How many dollars do you have
PLEASE HELP ME!! A right circular cone has a radius of 6 inches and a volume of 180 cubic inches. What is the height of the cone? Please answer without using pi. Thank you
A. 5 in.
B. 15 in.
C. 25 in.
D. 90 in.
Option B.The height of a cone is 15 inches.
To find the height of the cone, we will use the formula for the volume of a cone:
V = (1/3) * π * r² * h
We know the volume (V) is 180 cubic inches and the radius (r) is 6 inches.
We need to solve for the height (h).
First, let's plug in the known values:
180 = (1/3) * π * (6)² * h
180 = (1/3) * π * 36 * h
540 = π * 36 * h
540 / 36π = h
We can simplify this further, h = 15/π. Since we do not use π for the answer:
By rational observation of given options, B. 15 in. seems accurate.
Smoked salmon is being sold for $15.50 per pound. What is the cost of 6 ounces of salmon?.
When a number x is multiplied by 5, it gives the same result as when 48 are added to twice the number. Form an equation in terms of x. Hence, find the number x
what value of c makes x^2 - 24x + c a perfect square trinomial?
Answer:
Step-by-step explanation:
Quadratic equation is given by x²-24x+c
This is in the form expansion of (a-b)², that is a²-2ab+b²
Comparing
a² = x², a = x
-2ab = -24x
-2xb = -24x
b = 12
c = b² = 12² =144
x²-24x+144 = (x-12)²
Option D is the correct answer
"Our customer retention rate has decreased 10% from last quarter's goal of 250 consumers retained. We need to increase our current rate by at least 16% to meet this quarter's goal."
Employee: "That means our target is __________ consumers retained."
Using proportions, it is found that the correct sentence is:
"That means our target is 261 consumers retained."Decreased 10% from last quarter's goal of 250 consumers retained, hence, the number of customers is:
[tex]0.9(250) = 225[/tex]
The current rate has to be increased by 16%, hence, the goal is:
[tex]1.16(225) = 261[/tex]
Hence, the sentence is:
"That means our target is 261 consumers retained."
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for which data representation is the median the better measure of center
The median is the better measure of center when dealing with data sets that have outliers or extreme values.
The median is the better measure of center when a data set contains several outliers or extreme values. It is less sensitive to measurements with extreme values, providing a more robust estimation of central tendency. The median can be thought of as the middle number in a series, where 50% of the measurements are above it and 50% are below.
Why do elephants have ivory tusks?
Elephants have ivory tusks, which are elongated incisor teeth, primarily for digging, stripping bark, and defense, and they may have evolved for sexual selection and competitive interactions among males.
Elephants have ivory tusks because they are actually elongated incisor teeth. These tusks are composed of dentine and are covered by a layer of enamel, just like our teeth. Elephants use their tusks for various purposes, such as digging for water, stripping bark from trees, and as a weapon for defense. However, the primary reason they have tusks is not entirely understood. It's believed that tusks might have evolved for sexual selection and display, as well as for competitive interactions among male elephants.
i need this rotated 270 degrees clockwise
what is the answer to this question ?
what she got to school she saw that the school has nine buildings each Heaven 30 classrooms how many classrooms does the school have
Final answer:
To find the total number of classrooms in the school, we multiply the number of buildings (9) by the number of classrooms in each building (30), resulting in a total of 270 classrooms.
Explanation:
The question asks how many classrooms are there in total if a school has nine buildings, each with 30 classrooms. To find the answer, we need to multiply the number of buildings by the number of classrooms in each building. This calculation is straightforward:
Multiply the number of buildings (9) by the number of classrooms in each building (30).
This gives us: 9 buildings x 30 classrooms/building = 270 classrooms in total.
Therefore, the school has a total of 270 classrooms.
It takes 24 cups of chicken broth to make chicken soup recipe. How much is this in quarts?
Convert 3 feet to inches.
A) 4 inches
B) 9 inches
C) 12 inches
D) 36 inches
A sign in front of a roller coaster says ''you must be 40 inches tall to ride'' what percentage of this height is A 34 inches and B 54 inches. Please answer both questions if you can.
i need to find the area
there are 3 rectangles and a trapezoid
show how plz
estimate the value of this expression by rounding each number to the nearest
whole unit. (1.94)(7.51)(3.74)
A. 21
B. 42
C. 56
D.64
Please help meeeeeeeee
107=5x+17 simplify your answer as much as possible
is 2x-5y=0 a direct variation
I need help figuring out when to use law of sine or law of cosine?
These are some examples of problems.
Please Help!
Final answer:
Use the law of sines when you have two angles and one side, or two sides and a non-inclusive angle. Use the law of cosines when you have two sides and the included angle or all three sides. Apply trigonometric identities for vector addition and resolving forces.
Explanation:
Deciding when to use the law of sines or the law of cosines depends on the information given in a triangle problem. The law of sines is most useful when you know either two angles and one side (AAS or ASA) or two sides and a non-enclosed angle (SSA). The law states that the ratio of the length of a side to the sine of its opposing angle is consistent for all sides and angles in a triangle, often written as a/sin A = b/sin B = c/sin C.
The law of cosines is handy when you have either two sides and the included angle (SAS) or when you have all three sides (SSS). This law relates the lengths of the sides of a triangle to the cosine of one of its angles, following the formula c² = a² + b² - 2ab cos C.
For vector addition problems or when decomposing forces into components, trigonometric identities involving sine and cosine are employed. If you're resolving a weight into components, you may use sine to find the component opposite the angle and cosine for the component adjacent to the angle.
A right triangle is drawn on a coordinate plane. Two vertices of the triangle are points A(−2,4) and B(3,−2) . The third vertex of the triangle is point C, which lies in the third quadrant of the coordinate plane.
What is the distance from point A to point C?
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