If s and t are integers greater than 1 and each is a factor of the integer n, then the product nst must be divisible by both s and t. This is because s and t are factors of n, which means that n is divisible by s and t.
The product of two integers is divisible by the factors of each of those integers. Therefore, since n is divisible by s and t, and nst is the product of n, s, and t, nst must also be divisible by s and t. This can be proven by the definition of divisibility: if a number, in this case n, is divisible by an integer, in this case s or t, then the product of that number and another integer, in this case t or s, is also divisible by the initial integer.
For example, if n = 24, s = 4, and t = 3, we can see that 4 and 3 are factors of 24, since 24 is divisible by 4 and 3. The product of 24, 4 and 3 is 2443 = 288. 288 is also divisible by 4 and 3.
In summary, if s and t are integers greater than 1 and each is a factor of the integer n, then s and t must be factors of nst.
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easy please help!! Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.
A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.
The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of the large container of popcorn is _______ in.^3
OPTIONS FOR BLANK :
A) 56.52
B) 84.78
C)127.17
D) 169.56
This is ______ times the volume of the small container.
OPTIONS FOR THIS BLANK :
A) 2.88
B) 2.25
C) 1.8
D) 1.5
Answer:
127.17 cubic inches2.25 timesStep-by-step explanation:
You want to know the volume of a cylindrical container 6 inches in diameter and 4.5 inches high, and you want to know how many times larger this volume is than if the diameter were 4 inches.
VolumeThe volume of a cylinder is given by the formula ...
V = πr²h
where r is half the diameter, and h is the height.
The volume of your large popcorn container is ...
V = 3.14·(3 in)²·(4.5 in) = 127.17 in³
The volume of the large container is 127.17 in³.
RatioFor a given height, the volume ratio is the square of the ratio of diameters. That ratio is given as 3/2, so the volume ratio is ...
(3/2)² = 9/4 = 2.25
The large container is 2.25 times the volume of the small container.
2. you are given two ropes that when lit burn in one hour. which one of the following time periods cannot be measured with your ropes? a) 50 min b) 30 min c) 25 min d) 35 min. (asked by citadel)
We cannot the time period of 25 min using two ropes that when lit burn in one hour. Hence, option C is the correct answer.
This problem is an example of a mathematical puzzle. In order to measure a time period of 30 min, all we need to do is burn one rope from both ends. Since it takes 60 minutes for the rope to burn when lit from one end, it will take half that time i.e., 30 min to burn when lit from both ends.
We can also measure a time period of 35 min if we burn one rope from both ends and the other a bit differently. If we burn a rope from both ends, it will take 30 mins. As for the extra 5 mins, we can take the other rope and first burn it from both ends and then burn it from the middle again. That makes 2 separate ropes and thus the burning time is 15 min. We can then again burn one of these from the middle and wait until one of them completely burns out. This will give us a time period of 35 minutes.
As for 50 minutes, we can use the same method as above for burning one rope completely from both ends and the other from the ends and the middle. We can't really burn the ropes in a way that will give us the time period of 25 min so option C is the correct answer.
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What are the solutions to the system of equations? y = 1/2 * x ^ 2 - 4; y = x - 4 Graph the system of equations to solve. (0, - 4) and (2, - 2); (- 2.75, 0) and (2.75, 0); (2, - 2) and (4, 0); (4, 0) and (0, - 4)
The graph of a system of two equations is a pair of lines in the plane for the two variables (x and y).
What is meant by system of equations?Simple sets of two or more linear equations make up a system of linear equations. A system of two equations has a graph that is a pair of lines in the plane for two variables (x and y).
Equations with the same variables are grouped together as systems of equations. The only difference is that you're using inequalities as opposed to equations when working with a system of inequalities. To resolve such a system, you must identify the values of the variables that will cause each inequality to be true simultaneously.
The first equation:
[tex]$y=\frac{1}{2} x+3$$[/tex]
[tex]$5 \stackrel{?}{=} \frac{1}{2}(4)+3 \quad$[/tex]
Plug in x = 4 and y = 5
5 = 5
The second equation:
y = x + 1
[tex]$5 \stackrel{?}{=} 4+1 \quad$[/tex] Plug in x = 4 and y = 5
5 = 5
(4,5) is indeed a solution.
Therefore, the correct answer is option b) (- 2.75, 0) and (2.75, 0).
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Amenys earns a#$ 35.00 a month after taxes and his brother Esinam earns three timer as much, how much is their income after five years
Solve for the empty box for question 6
Using the associative property of multiplication the missing value of (x × 8) × 2 = 4 × (2 × 8) is 4.
What is associative property of multiplication?The associative property of multiplication tells us how we group factors that does not alter the result of the multiplication. Therefore, the associative property of multiplication can be represented as follows:
a x (b x c) = (a x b) x c
where
a, b and c are variables representing numbers.Therefore, let's use the associative property of multiplication to solve the following.
(x × 8) × 2 = 4 × (2 × 8)
Hence, using the rule, of associative property of multiplication, a x (b x c) = (a x b) x c, the missing variable is 4.
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What is 9 out of 20?
The diagonals of rhombus ABCD intersect at E. Given that m∠BAC=53°, DE=8 and EC=6, Find AC.
AC=?
[tex]\it AC=2\cdot EC=2\cdot6=12[/tex]
How many groups of 1/3 in 9? Evaluate. 9÷ 3 7
The number of groups of one third in 9 is 27
How to evaluate the expressionThe problem requires the use of division
To determine the number of groups of 1/3 in 9, we can divide 9 by 1/3:
= 9 / (1/3)
= 9 * 3
= 27
Therefore, there are 27 groups of 1/3 in 9.
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Simplest form 6m-2(-3m+8)
[tex]6m - 2( - 3m + 8)\\ Multiplying :\ each \\ term \\ - 18m + 48m + 6m - 16 \\ - 18m + 54m - 16 \\ 36m - 16 \\ 2(18m - 8)[/tex]
find the trapezoidal riemann sum approximation of the integral from 1 to 5 of the square root of quantity x squared plus 3 close quantity times dx using four equal partitions.
Answer:
14.115
Step-by-step explanation:
Recall Trapezoidal Rule
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx=\frac{1}{2}\biggr(\frac{b-a}{n}\biggr)\biggr[f(x_0)+2\bigr(f(x_1)+f(x_2)+\text{... }+f(x_{n-1})\bigr)+f(x_n)\biggr][/tex]
Make necessary substitutions and evaluate
[tex]\displaystyle \int\limits^5_1 {\sqrt{x^2+3}} \, dx=\frac{1}{2}\biggr(\frac{5-1}{4}\biggr)\biggr[2+2\bigr(\sqrt{7}+\sqrt{12}+\sqrt{19}\bigr)+\sqrt{28}\biggr]\approx14.115[/tex]
Note that the actual value of the integral is [tex]\displaystyle \int\limits^5_1 {\sqrt{x^2+3}} \, dx\approx14.078[/tex], so we can see how accurate the Trapezoidal rule is with just a few equal partions.
Teds farm 4 horses, 12 goats, 2 sheep & 18 cows. Find the angle measure of yhe sextor of a circle graph for each animal animal represents. Fill in the boxes
The angle for each animal is;
Horse - 40 degrees
Goats - 120 degrees
Sheep - 20 degrees
Cows - 180 degrees
What is the measure of the angle in each case?We can see that we want to plot the data that we have on the circle graph and each of the values is going to occupy a given part of the sector and would subtend an angle. We are to obtain the angle that is subtended by each value.
We have;
Total number of farm animals = 4 + 12 + 2 + 18 = 36 animals
Angle for horses = 4/36 * 360 = 40 degrees
Angle for goats = 12/36 * 360 = 120 degrees
Angle for sheep = 2/36 * 360 = 20 degrees
Angle for cows = 18/36 * 360 = 180 degrees
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Missing parts
Ted’s farm has 4 horses, 12 goats, 2 sheep, and 18 cows. Find the angle measure of the sector of a circle graph that represents each animal. Enter the correct answers in the boxes.
find the point on the shore line from which the angle from the boat is response area. then, measure the distance that the boat travels until the angle from the boat to that point is response area. that distance is the same as the distance between the boat and the shore line because the triangle formed is a(n) response area
The triangle formed is an isosceles triangle since two sides of the triangle are equal .
The point on the shoreline is the point of tangency between the shoreline and the circle centered at the boat with a radius equal to the distance between the boat and the shoreline. The angle from the boat to that point is equal to the angle of the central angle of the circle whose radius is equal to the distance between the boat and the shoreline.
Let the radius of the circle be r and the angle from the boat to the point on the shoreline be θ. Then the formula for the distance between the boat and the shoreline is:
r = θ × (2π/360)
To calculate the distance traveled by the boat, we need to use the formula for the circumference of a circle:
C = 2πr
Substituting the above formula for r into the formula for the circumference of a circle, we get:
C = 2π(θ × (2π/360))
Therefore, the distance traveled by the boat is:
C = (2π)2 × θ/360
The triangle formed is an isosceles triangle since two sides of the triangle are equal (the radius of the circle and the distance between the boat and the shoreline).
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Surveying A triangular parcel of ground has sides of lengths 725 feet, 650 feet, and 575 feet. Find the measure of the largest angle.
cos⁻¹ ( 7/23) is the measure of the largest angle.
What is known as a triangle?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.
The triangle's three angles add up to a total of 180 degrees.
The lengths are given as a = 725 feet, b = 650 feet, and c = 575 feet.
Since, we know the fact that angle opposite to largest side is greatest. Hence, the largest angle would be opposite to side a.
Now, use the law of cosine
cosA = b² + c² - a²/2bc
On substituting the values, we get
cosA = (650)² + ( 575 )² - ( 725)²/2*650*575
= 422500 + 330625 - 525625/747500
= 227500/747500
= 7/23
A = cos⁻¹ ( 7/23)
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Find the inverse function of function B, your answer should begin with y=...
Answer: To find the inverse of a function, we first need to make sure that the function is one-to-one, meaning that no two different input values map to the same output value.
If the function B is one-to-one, we can find the inverse by switching the x and y values, and then solving for y.
y = B^-1(x)
We can then use algebraic manipulation to solve for y.
For example, if B(x) = 2x + 1, we can find the inverse by switching x and y:
x = 2y + 1
Solving for y:
y = (x - 1)/2
So the inverse function of B(x) = 2x + 1 is B^-1(x) = (x - 1)/2
Please note that if the function B is not one-to-one, it will not have an inverse.
Step-by-step explanation:
3
Which is different?
O Add-4.5 and 3.5.
O What is -4.5 increased by 3.5?
What is the distance between-4.5 and 3.5?
O Find the sum of -4.5 and 3.5.
Find "both" answers.
Answer for the "different" question:
Answer for the "same" questions:
Answer for the "different" question: The distance between -4.5 and 3.5 is 8.
Answer for the "same" questions:
O Add -4.5 and 3.5: -4.5 + 3.5 = -1
O What is -4.5 increased by 3.5: -4.5 + 3.5 = -1
Find the sum of -4.5 and 3.5: -4.5 + 3.5 = -1
Answer: What is the distance between -4.5 and 3.5?
Step-by-step explanation:
The distance between -4.5 and 3.5 and will be different than all the others because the distance it's asking for the distance between the absolute values, not adding them together.
Find "both" answers.
➜ Answer for the "different" question:
What is the distance between -4.5 and 3.5? = 4.5 + 3.5 = 8
➜ Answer for the "same" questions:
Add -4.5 and 3.5 = -4.5 + 3.5 = -1
What is the result if the product of 5 and 75 is divided by 3?
Answer: 125
Step-by-step explanation: product of 5 and 75 = 5*75 = 375 divided by 3 which is 375/3 = 125.
PLEASE PLEASE HELP ME SOMEONE
Find the slope of the line.
Answer: The slope is 2.
Step-by-step explanation:
We can use this formula to help us solve:
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Given:
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Substitute values and simplify to solve:
[tex]\displaystyle \frac{6--6}{2--4}=\frac{6+6}{2+4}=\frac{12}{6} =2[/tex]
Answer:
The slope is 2
Step-by-step explanation:
The formula for slope is y2-y1/x2-x1
So just fill out the points and do the calculations.
PLEASE HELP, i have done the work 3 times and i keep on getting the same answer
Let A1,A2,⋯ be Lebesgue-measurable subsets of [0,1] of measure 1/2, and let A denote the set of points x such that x belongs to infinitely many of the sets An. How we can show that the Lebesgue measure of A is at least 1/2.
Lebesgue outer measure in this instance is a complete extension of Lebesgue measure that meets all other criteria.
What exactly is a Lebesgue measure?The translation invariant is the Lebesgue measure, and the length of the interval I is the same for that measure when it is on the interval I. The Lebesgue measure of E, for instance, is given by λ(E) = l if E is any collection of real numbers (E).
As with a single point or a countable number of points, every set that is a finite collection of points has a Lebesgue measure of zero. The measure of finite and countable unions of disjoint sets has the property of being equal to the total of the measures.
An interval's length is its Lebesgue value. The formal foundation for probability theory is measure theory.
(1) When working with function spaces, the Lebesgue integral is important since it is resistant to a variety of limiting procedures. (2) It easily expands to quite an abstract context and creates a fundamental language of probability theory, as numerous users have noted.To learn more about Lebesgue measure, refer to:
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prove that the continuous function of order 3 is continuous of order 1 after being differentiated twice.
We use the concepts of continuity and differentiability to prove that a continuous function of order 3 is continuous of order 1 after being differentiated twice.
Let us assume the function x³ as the function of order 3. We know that its 1st derivative will be 3x² and its 2nd derivative will be, 6x. Now, let's check both of their continuities at any point "a" on the function. By putting a limit x tending to a to the function
= lim (x³) = a³
x→a
and putting a directly to the equation i.e, f(a) = a³ therefore, x³ is a continuous function at a. Similarly, by putting a limit x tending to a to the function
= lim (6x) = 6a
x→a
and putting a directly to the equation i.e, f(a) = 6(a) therefore, 6x is also a continuous function at a. Hence we can say that the continuous function of order 3 is continuous of order 1 after being differentiated twice.
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It’s sales season, and there are 15 bags of potato chips in Cecilia shop.Alfred told me that there are 5 times fewer bags of potato chips in Cecilia shop than there are in his. Work out how many bags of potato chips there are in Alfred shop
Using multiplication, In Alfred's store, there are 75 bags of potato chips.
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication.
The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.
In Cecilia's store, there are five times fewer bags of potato chips than there are in Alfred's. This indicates that Alfred's has five times as many bags as Cecilia's does. We must multiply to determine how many bags there are in Alfred's store:
15 x 5 = 75
In Alfred's store, there are 75 bags of potato chips.
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Simplify and evaluate 25 POINTS TO WHO EVER SOLVES IT
Answer: -2 i think
Step-by-step explanation:
(5-4)-3*(5-4)
1-3*1
1-3=-2
Answer:
The value is 0
The simplified expression is
3• (5 - 4) -3 (5 - 4)
Step-by-step explanation:
hope it helps<3Applications of linear equations
One number is 7 more than another number. If the smaller number is doubled and added to 3 times the larger number, the sum is 86. Find the two numbers.
Smaller number=
Larger number=
(Type the integers or decimals.)
Answer:
Bigger number: 20
Smaller number: 13
Step-by-step explanation:
Let smaller number = x
Bigger number. = x + 7
From the question; 2x + 3(x + 7) = 86
2x + 3x + 21 = 86
5x + 21 = 86
5x = 86 - 21
5x = 65
x = 13
Therefore the smaller number is 13, and the bigger number is 13 + 7 = 20
A car dealership wants to conduct a survey of
100
100 people who bought a new or used car at the dealership in the last three months. Of the people who bought a car at the dealership in the last three months,
2
,
000
2,000 bought a new car
1
,
600
1,600 of the new car buyers received a loan
500
500 bought a used car
300
300 of the used car buyers received a loan
Complete the table below to show the number of people the dealership should survey in each group so that the sample is representative of whether the buyers bought a new car or a used car and whether the buyers received a loan
According to the report, 80% of those who purchased new cars received loans, compared to 60% of those who purchased older cars.
How do you determine the population size for a survey?The population size estimate is calculated by dividing the total number of people getting a service or the total number of unique items delivered (M) by the percentage of people reporting receiving the service or item in a representative survey (P).
Given a car dealership wants to conduct a survey of 100 people who bought a new or used car at the dealership in the last three months.
number of people new car old car received Loan No loan
2,000 yes No 1600 400
500 No Yes 300 200
Percentages of people who received Loans bought new cars:
Percentage = 2000-400 / 2000
Percentage = 1600/2000
Percentage = 80%
Percentages of people who received Loans bought used cars:
Percentage = 300 * 100 / 500
Percentage = 3/5 * 100
Percentage = 60%
Therefore, According to the survey, 60% of the people Who bought used cars got loans while 80% of people who bought new cars gets loan.
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the coefficient of static friction between the right bar and the surface at a is. what are the largest angles
The coefficient of static friction is a dimensionless value that represents the ratio of the maximum static friction force to the normal force. It is used to determine the maximum angle at which an object can be inclined on a surface without slipping. The coefficient of static friction between the right bar and the surface at point A is not given in the information provided.
To determine the largest angles at which the right bar can be inclined without slipping on the surface at point A, one would need to know the coefficient of static friction between the bar and the surface, as well as the weight of the bar and the normal force acting on it. The coefficient of static friction multiplied by the normal force must be greater than or equal to the weight of the bar in order for it to remain in static equilibrium.
It is also worth mentioning that the coefficient of static friction varies depending on the materials of the two surfaces in contact and the normal force acting on it. The coefficient of static friction can be measured experimentally and is usually provided in the material properties of the surfaces.
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A water tank already contains 55 gallons of water in Baxter begins to fill it. water flows into the tank at a rate of 8 gallons per minute. write a linear equation to model this situation. Find the volume of the water in the sink 25 minutes after Baxter begins filling the tank.how many minutes will Baxter fill the tank if the maximum volume of water is 395 gallons?
Answer:42.5
Step-by-step explanation:
A linear equation can be used to model this situation, where the volume of water in the tank (V) is equal to the initial volume plus the rate of flow multiplied by the number of minutes (t).
V = 55 + 8t
This equation can be used to find the volume of the water in the tank at a specific time. To find the volume of the water in the tank 25 minutes after Baxter begins filling it, we can substitute 25 for t in the equation:
V = 55 + 8(25) = 55 + 200 = 255 gallons
To find how many minutes it will take for Baxter to fill the tank if the maximum volume of water is 395 gallons, we can use the equation to solve for t.
395 = 55 + 8t
Subtract 55 from both sides:
340 = 8t
Divide both sides by 8:
t = 42.5
So, it will take 42.5 minutes for Baxter to fill the tank with a maximum volume of 395 gallons.
A linear equation can be used to model a situation where a quantity is changing at a constant rate.
Let V be the volume of water in the tank at time t in minutes.
The rate of change of the volume of water is 8 gallons per minute, so we can write the equation as:
V = 55 + 8t
This equation tells us that the volume of water in the tank is 55 gallons when t = 0 (at the start of filling the tank) and it increases by 8 gallons for every minute after that.
To find the volume of water in the tank 25 minutes after Baxter starts filling it, we can plug in t = 25 into the equation:
V = 55 + 8(25)
V = 55 + 200
V = 255 gallons
To find how many minutes it will take to fill the tank to the maximum volume of 395 gallons, we can use the equation and solve for t:
V = 55 + 8t
395 = 55 + 8t
340 = 8t
t = 340/8
t = 42.5 minutes
So it will take 42.5 minutes to fill the tank to the maximum volume of 395 gallons.
determine the number of positive integers less than that contain at least one in their decimal representation.
There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.
There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation. This can be determined by counting the number of possible combinations of digits that can be formed with the numbers 0-9. Since there are five digits in a number less than 100,000, the total number of combinations is 10^5 (10 to the power of 5). Of these combinations, 1/10th will contain at least one "1" as there are 10 possible ways to include a "1" in the five-digit number. Thus, 10^5/10 = 9,999. This means that there are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.
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which of the following statements could be used to generate a random number between 1 and 9, inclusive, and assign it to the variable dice?
The result is between 1 and 9, which is assigned to the variable dice.
To generate a random number between 1 and 9, inclusive, we can use the formula: (Math.random() * (9 - 1 + 1)) + 1. This formula randomly generates a number between 0 and 1, and then multiplies it by the range (9 - 1 + 1) to give us a result between 0 and 8. We then add 1 to this result to ensure that the final number is between 1 and 9.
To assign this number to the variable dice, we can use the following statement:
var dice = Math.floor((Math.random() * (9 - 1 + 1)) + 1);
Math.random() generates a random number between 0 and 1, which is then multiplied by the range (9 - 1 + 1) to give us a result between 0 and 8. Math.floor rounds this number down to the nearest whole number. We then add 1 to ensure that the result is between 1 and 9, which is assigned to the variable dice.
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Simplify the expression and combine like terms. -3(4k + 7)
Answer: -12k-21
Step-by-step explanation:
you must distribute the -3
the decisions at this level are generally made with the least amount of data and have the longest time horizon
Decisions at this level are typically strategic in nature and involve long-term planning and goal setting. These decisions may involve large amount investments of resources and have a significant impact on the organization's future.
Decisions at this level are typically strategic in nature and involve long-term planning and goal setting. These decisions may involve large investments of resources and have a significant impact on the organization's future. Examples of decisions at this level include setting the overall strategy, developing new products and services, entering new markets, and deciding on organizational structure. Due to the nature of these decisions, they require extensive data analysis and research. It is important for decision makers at this level to have knowledge about the industry, the marketplace, and the competitive environment in order to make informed decisions. Additionally, since these decisions have a long-term impact, it is important to consider the potential risks and opportunities associated with them. Furthermore, the decisions made at this level must align with the overall mission and vision of the organization. As such, these decisions must be made with careful consideration, as they can have far-reaching implications for the entire organization.
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