There are 40 hoses with loose fittings should the manufacturer expect out of 2,900 hoses.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
A hose manufacturer tests the fittings on every 20th hose on an assembly line.
And, Out of 145 hoses tested, 2 had issues with loose fittings.
Let number of hoses with loose fittings should the manufacturer expect out of 2,900 hoses = x
So, By definition of proportion, we get;
⇒ 2 / 145 = x / 2900
⇒ 2×2900 / 145 = x
⇒ x = 40
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you are buying a flower arrangement. the florist has 9 types of flowers and 7 types of vases. if you can afford exactly 2 types of flowers and need only 1 vase, how many different arrangements can you buy?
The total number of different arrangements is 36 * 1 = 36
Permutation and Combination:
Permutation and combination are the ways to represent a group of objects by selecting them in a set and forming subsets. It defines the various ways to arrange a certain group of data. When we select the data or objects from a certain group, it is said to be permutations, whereas the order in which they are represented is called a combination.
There are 9 types of flowers and you are choosing 2 of them, so the number of ways to choose the flowers is 9 choose 2 which is equal to (98)/(21)=36.
There is 1 vase and you are choosing 1 of them, so the number of ways to choose the vase is 1 choose 1 which is equal to 1.
The total number of different arrangements is 36 * 1 = 36.
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What is the system of inequalities associated with the following graph?
A. x + y >2
2x - y < 1
B. x + y < 2
2x - y > 1
C. x + y > 2
2x - y > 1
D. x + y < 2
2x - y < 1
Answer:
This leads to C: x + y > 2 and 2x - y > 1
Step-by-step explanation:
All of the answer options have the same structure, with the exception of the < and > signs. We can assume the the two lines on the graph conform to the line defined by:
x + y =2, and
2x - y = 1
See the attached graph. The lines y = -x+2 and y = 2x-1 match the provided graph.
But the equations are all inequalities. So the darker areas represent the possibilities of values for x and y. The darkeest area is where the solutions for both equations overlap, so look for equations that would satisfy that situation. As shown, the equations are:
y<2x-1, and
y>-x+2
Rearrange these to match the options:
y-2x < -1, and
y + x > 2
---
Note that y-2x < -1 is the same as 2x-y > 1
This leads to C: x + y > 2 and 2x - y > 1
please help.......................??
x axis described as the independent variable
What is horizontal line?
A horizontal line is a straight line that goes from left to right or right to left. In coordinate geometry, a line is said to be horizontal if two points on the line have the same Y- coordinate points. It comes from the term “horizon”. It means that the horizontal lines are always parallel to the horizon or the x-axis.A horizontal line is a line extending from left to right. When you look at the sunrise over the horizon you are seeing the sunrise over a horizontal line. The x-axis is an example of a horizontal lineA horizontal line is one that goes from left to right across the page. This is because horizontal lines are parallel to the horizon. This fact can help children to remember the meaning of horizontal lines. It comes from the word “horizon”, which refers to the visible line that separates the earth from the sky.To learn more about horizontal plane refers to:
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x-axis is the horizontal line dividing the plane into parts. The x-axis is also described as the abscissa and it used for independent variable.
Tell us about the horizontal line.A horizontal line is any straight path that runs from left to right or from right to left. In coordinate geometry, a line is said to be horizontal if two points on it have the same Y-coordinates. Its origins are in the term "horizon." In other words, the horizontal lines and the horizon, or x-axis, are always parallel.
A line that moves from left to right is said to be horizontally oriented. When you look beyond the horizon, you are seeing the dawn over a horizontal line. The x-axis serves as a representation of a horizontal line.
A horizontal line is one that extends from left to right across the full page. This is explained by the fact that horizontal lines are parallel to the horizon. By considering this fact, children can maintain the meaning of horizontal lines. Its root word, "horizon," refers to the line that may be seen separating the earth from the sky.
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how to get a between number
You can get a number between two numbers by adding the two numbers together and then dividing by two.
How to get a between number?For example, if you wanted to get a number between 3 and 5, you could add 3 and 5 together to get 8, and then divide by 2 to get 4.One way to get a number between two other numbers is to use the average of the two numbers. To calculate the average, add the two numbers together and divide the sum by two. For instance, if one number is 10 and the other is 20, the average of the two numbers would be 15.Another way to get a number between two other numbers is to use the midpoint. To calculate the midpoint, add the two numbers together and divide the sum by two. The midpoint is the same as the average, but it is also the exact middle number of the two numbers. For instance, if one number is 10 and the other is 20, the midpoint of the two numbers would be 15.In conclusion, there are several ways to get a number between two other numbers. The most accurate methods involve using the average, the midpoint, interpolation, or formulas. However, it is also possible to simply guess a number between two other numbers.To learn more about to get a between number refer to:
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If you were to make a scatter plot of data, you would be able to determine the line of best fit. Using the regression equation y = 1.73x + 0.39, Predict the number of representatives for Oregon, which has a population of about 3.3 million.
A. 5 representatives
B. 6 representatives
C. 7 representatives
D. 28 representatives
The number of representatives for Oregon, which has a population of about 3.3 million is 6 Representatives (Option B).
The regression equation y = 1.73x + 0.39 is the equation of the line of best fit. To use this equation to predict the number of representatives for Oregon, which has a population of about 3.3 million, we need to substitute the population of Oregon (x = 3.3 million) into the equation and solve for y.
y = 1.73x + 0.39
y = 1.73(3.3) + 0.39
y = 5.659 + 0.39
y = 6.049
So the number of representatives for Oregon is approximately 6.049. The closest answer to that is
B. 6 representatives
Therefore, The number of representatives for Oregon, which has a population of about 3.3 million is 6 Representatives (Option B).
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if 1,000,000 people are exposed to 10 msv, then what is the expected number of radiation induced cancers according to the linear no threshold model of cancer induction
The expected number of radiation induced cancers according to the linear no threshold model of cancer induction is 500
Radiation is defined as the energy that comes from a source and travels through space at the speed of light.
Here we have given that 1,000,000 people are exposed to 10 msv and here we need to find the the expected number of radiation induced cancers according to the linear no threshold model of cancer induction.
As we all know that the amount of dose depends on the type of x-ray examination. A CT examination with an effective dose of 10 milli Sieverts
And it may be associated with an increase in the possibility of fatal cancer of approximately 1 chance in 2000.
therefore, here we have the total number as 1,000,000
Then the expected number if calculated as,
=> 1,000,000/2000
=> 500
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The first step in the K-means clustering algorithm is to randomly assign each observation within the data set to a cluster from 1 to k.
True or False?
So the Statement the first step in the K-means clustering algorithm is to randomly assign each observation within the data set to a cluster from 1 to k.
Hence, The first step in the K-means clustering algorithm is to randomly assign each observation within the data set to a cluster from 1 to k.
K-means cluster algorithm:
K-Means Clustering is an unsupervised learning algorithm that is used to solve clustering problems in machine learning or data science. In this topic, we will learn what is K-means clustering algorithm is, how the algorithm works, along with the Python implementation of k-means clustering.
The first step in the K-means clustering algorithm is to randomly assign each observation within the data set to one of the k clusters. This initial assignment is done randomly in order to ensure that the algorithm is not influenced by any initial ordering of the observations. The subsequent steps of the algorithm involve iteratively re-assigning observations to clusters and updating the cluster centroids until convergence is reached.
As a result, the K-means clustering algorithm's first step is to randomly assign each observation inside the data set to one of the k clusters, ranging from 1 to k.
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a farmer finds that if she plants 95 trees per acre, each tree will yield 80 bushels of fruit. she estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. how many trees should she plant per acre to maximize her harvest?
She should plant 118 trees per acre to maximize her harvest area. This will yield 96 bushels per tree.
95 trees per acre x 80 bushels per tree = 7600 bushels
96 trees per acre x 77 bushels per tree = 7392 bushels
97 trees per acre x 74 bushels per tree = 7158 bushels
98 trees per acre x 71 bushels per tree = 6938 bushels
99 trees per acre x 68 bushels per tree = 6732 bushels
100 trees per acre x 65 bushels per tree = 6500 bushels
101 trees per acre x 62 bushels per tree = 6262 bushels
102 trees per acre x 59 bushels per tree = 6038 bushels
103 trees per acre x 56 bushels per tree = 5828 bushels
104 trees per acre x 53 bushels per tree = 5532 bushels
105 trees per acre x 50 bushels per tree = 5250 bushels
106 trees per acre x 47 bushels per tree = 4978 bushels
107 trees per acre x 44 bushels per tree = 4716 bushels
108 trees per acre x 41 bushels per tree = 4452 bushels
109 trees per acre x 38 bushels per tree = 4188 bushels
110 trees per acre x 35 bushels per tree = 3925 bushels
111 trees per acre x 32 bushels per tree = 3663 bushels
112 trees per acre x 29 bushels per tree = 3407 bushels
113 trees per acre x 26 bushels per tree = 3151 bushels
114 trees per acre x 23 bushels per tree = 2895 bushels
115 trees per acre x 20 bushels per tree = 2300 bushels
116 trees per acre x 17 bushels per tree = 1972 bushels
117 trees per acre x 14 bushels per tree = 1638 bushels
118 trees per acre x 11 bushels per tree = 1306 bushels
Therefore, 118 trees per acre will yield the highest harvest of 1306 bushels.
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g what are differences or similarities between everyday logic and mathematical logic? how can the study of mathematical logic help you in your everyday life?
The study of mathematical logic can help you in your everyday life by developing your ability to think logically and critically.
Everyday logic and mathematical logic are similar in that they both involve reasoning and drawing conclusions based on evidence or information. However, mathematical logic is a more formal and precise system of reasoning that is used in mathematics, computer science, and other fields. It involves using symbols and formal languages to represent statements and arguments, and it often involves the use of mathematical proofs to demonstrate the validity of a conclusion.
The study of mathematical logic can help you in your everyday life by developing your ability to think logically and critically. It can also help you understand the foundations of computer science and the way that computers process information. Additionally, it can help you become more comfortable with using formal language and reasoning, which can be useful in fields such as law, philosophy, and science.
Thus, the study of mathematical logic can help you in your everyday life by developing your ability to think logically and critically.
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On the $xy$-plane, the origin is labeled with an $M$. The points $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$ are labeled with $A$'s. The points $(2,0)$, $(1,1)$, $(0,2)$, $(-1, 1)$, $(-2, 0)$, $(-1, -1)$, $(0, -2)$, and $(1, -1)$ are labeled with $T$'s. The points $(3,0)$, $(2,1)$, $(1,2)$, $(0, 3)$, $(-1, 2)$, $(-2, 1)$, $(-3, 0)$, $(-2,-1)$, $(-1,-2)$, $(0, -3)$, $(1, -2)$, and $(2, -1)$ are labeled with $H$'s. If you are only allowed to move up, down, left, or right by one unit at each step, starting from the origin, how many distinct paths can be followed to spell the word MATH
On solving the provided question, we can say that there are 66 ways , on counting .
What is counting?Calculating the number of components in a limited collection of objects is the process of counting. H. Calculate the set's size. Calculating the quantity or overall number of items in a collection or group is the definition of counting in mathematics. In other words, counting something entails reciting the number in order and individually valuing each item in the group. To count objects, use the count number. 1, 2, 3, 4, 5, and so forth are examples of counting numbers. In daily life, people employ the numbers required to count items, items, money, etc. Because of this, count numbers cannot be fractions, integers, negative numbers, or decimals.
here in question,
there are 66 ways.
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There is a 25% chance that you will have to work tonight and cannot study for the big
math test. if you study, then you have an 80% chance of earning a good grade. if
do not study, you only have a 30% chance of earning a good grade.
you
Therefore ,as a result, the answer to the probability problem is 67.5% chance that you get good scores.
What exactly does the probability process entail?Probability theory is a branch of mathematics that focuses on calculating the likelihood that a statement is true or that an event will occur. Any number in 0 and 1, with 1 signifying certainty and 0 generally reflecting the likelihood of occurrence, can be used to represent a chance. Probability is a diagrammatic model of range the chance or likelihood that an event will occur.
Here,
Given : There is a 0.25 percent probability that we work tonight without studying,
a 0.80 percent chance that you study and get high grades, and
a 0.30 percent chance that you don't study and get a good grade.
To calculate the likelihood that we will receive high marks,
multiply by: 0.25 * 0.30 + 0.75 * 0.8
=> 0.075 + 0.60 => 0.675
You have a 67.5% chance of getting good grades.
As a result, the answer to the probability problem is 67.5% chance that you get good scores.
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What is the x-intercept of the line graphed above? What is the y-intercept of the line? What is the slope of the line? Write an equation for the line.
Answer:
a) (-2,0) is the x-intercept of the line.
b) (0,4) is the y-intercept of the line.
c) "2" is the slope of the line.
d) 2x + 4 = y (Equation of the Line)
Step-by-step explanation:
All linear equations have a general form: mx+n.
When we figure out two points on the line, we can use them in this general formula and find out the equation for the line.
We can use x and y intercepts of the line for that, they are also asked to find.
The x-intercept of the line is (-2,0) because this is where the line crosses the x axis, this point is named as x-intercept.
Except the axis, y-intercept has no more difference than x-intercept. So, the y-intercept of a line is where the line crosses the y axis.
We can see that the line crosses y axis at (0,4).
Now, we know two specific points on the line. This means that we can find the slope and write the equation for this line.
We can find the slope using the formula below:
y1 - y0 / x1 - x0 = Slope
This would give us the slope for the line, no matter which point you take as (x1, y1). The order is not important.
If you use the given points on the formula above, you would get "2" as the slope of the line.
In the general form of a linear equation, the coefficient of "x" is equal to the slope of the line. This means that "m" is equal to "2". (y = 2x + n)
Finally, you can use one of the known points to find out the real equation for the line.
Let's use (0,4):
2x + n = y (Use 0 for "x" and 4 for "y" variable.)
We can conclude that "n" is equal to 4.
So, the equation of this line is equal to "2x + 4 = y".
find the slope 1. (3,4) and (-1,,2)
2. (-2,0) and (5,-3)
3. (4,-5) and (4,2)
4. (-1,3) and (5,3)
note show your solution:
Answer:
Step-by-step explanation:
1. To find the slope between the two points (3,4) and (-1,2), we can use the slope-intercept form of a line, y = mx + b. The slope (m) is equal to the rise (change in y) over the run (change in x), or (y2-y1)/(x2-x1). In this case, the rise is (2-4) = -2 and the run is (-1-3) = -4, so the slope is (-2)/(-4) = 1/2.
2. To find the slope between the two points (-2,0) and (5,-3), we can use the same formula, (y2-y1)/(x2-x1). The rise is (-3-0) = -3 and the run is (5-(-2)) = 7, so the slope is (-3)/7 = -3/7
3. To find the slope between the two points (4,-5) and (4,2), we can use the same formula, (y2-y1)/(x2-x1). The rise is (2- (-5)) = 7 and the run is (4-4) = 0, so the slope is 7/0 which is undefined.
4. To find the slope between the two points (-1,3) and (5,3), we can use the same formula, (y2-y1)/(x2-x1). The rise is (3-3) = 0 and the run is (5-(-1)) = 6, so the slope is 0/6 = 0.
Find the ratio, n, between the length of side DE and length of the corresponding side AB.
ratio between side length AB and side length DE = 1
What is point coordinate?In a coordinate plane location of a particular point is represented by the
pair of two numerical terms that is bounded by a parenthesis. That is called coordinate pair.
What is the ratio, n between the length of side DE and length of the corresponding side AB?From the triangle ABC and triangle DEF that plotted in the XY coordinate plane, we measured from the point coordinate that side length AB = side length DE
side length DF = side length BC
side length EF = side length AC
we also observed that the three corresponding angles of ABC is equal to the corresponding angles of DEF.
The above statement is true for congruence theorem.
hence the above two triangles are congruent.
from the graph, we find point coordinate A (1,1), B(4, 1), D (-1, 1) and E (-4, 1)
length formula = √(x₂ - x₁) ² + (y₂- y₁) ²
length of AB = √(4-1) ²+ (1-1)² = 3
length of DE = √( -4+1) ²+ (1-1) ² = 3
ratio, n = length AB/ length DE = 3/3 =1
n= 1
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Consider kite FGHJ. What are the values of a and b? A = 14, b = 6 a = 14, b = 8 a = 17, b = 6 a = 17, b = 8
The value of a=17 cm and b=6 cm as FGHJ is a kite.
Kite has property their adjacent sides are equal. The top two sides of the kite are equal and the bottom two sides of the kite are equal.
Any quadrilateral with two sets of congruent successive sides is referred to as a kite (in contrast to a parallelogram where the opposite sides are congruent). Connecting points G and J, draw a section. Triangle GHJ and triangle GFJ are congruent. The information that GH = GF and FJ = HJ will be used.
FG=GH because of ∠F=∠H.
30=2a-4
2a=34
a=17 cm
Similarly, ∠F=∠H
FJ=HJ
3b+6=24
3b=18
b=6 cm
Hence, The value of a=17 cm and b=6 cm
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Answer:
a=17 and b=6
Step-by-step explanation:
took the test
luis is saving money to purchase a new video game. he has a total of 30 coins consisting of nickels and dimes. the value of the coins is $2.20. let n represent the number of nickels and let d represent the number of dimes. which system of equations can be used to determine the number of nickels and the number of dimes luis has? a system of equations. n plus d equals 2.20. 10 n plus 5 d equals 30. a system of equations. n plus d equals 2.20. 10 n plus 5 d equals 30. a system of equations. n plus d equals 2.20. 0.5 n plus 0.1 d equals 30. a system of equations. n plus d equals 30. 0.5 n plus 0.1 d equals 2.20.
The correct system of equations to determine the number of nickels and dimes that Luis has is: n + d = 30 and 0.5n + 0.1d = 2.20.
What is Equation?
In mathematics, an equation is a statement that two expressions are equal. It consists of two expressions connected by an equal sign (=). For example, the equation "2 + 2 = 4" states that the sum of two and two is equal to four. Equations are used to describe relationships between different variables, as well as to solve unknown values.
This system of equations can be used to solve for n and d. The first equation states that the total number of coins is equal to 30, while the second equation states that the total value of the coins is equal to $2.20. By solving these two equations, it can be determined how many nickels and dimes Luis has.
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As $n$ ranges over the positive integers, what is the maximum possible value that the greatest common divisor of $13n 8$ and $5n 3$ can take
Therefore , the solution of GCD problem comes out to be the greatest common factor of 252 and 60 is 223 = 12.
What is Greatest common divisor?The number that divides two or more numbers most precisely by itself is said to be the largest common denominator (GCD) of those numbers. It is also known as the highest common denominator (HCF). Since both 15 and 10 can be divided by 5, for instance, the highest common factor of these two numbers is 5.
Here,
The highest common factor (hcf), greatest common factor, and the greatest common divisor (gcd) are other names for it (gcf).
The highest integer which divides both numbers is known as the largest common series of 2 numbers.
We must choose the number that divides 252 and 60 most equally.
252's prime factorization is as follows:
252 = 2×2×3×3×7
the prime factors that make up 60 are.
60 = 2×2×3×5
These common elements are: 2 2 3
Therefore, the greatest common factor of 252 and 60 is 223 = 12.
Therefore , the solution of GCD problem comes out to be the greatest common factor of 252 and 60 is 223 = 12.
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If during her first three months at
college a student's long distance
phone bills are $119. 68, $84. 36,
and $68. 49, and her local phone
bill is $21. 00 per month, what is her
total average monthly phone bill?
Please help
Her entire monthly phone bill is $153.37, which includes long distance calls of $119.68, $84.36, and $68.49, as well as local calls of $21.00.
How to solve this equation?To figure out the student's total average monthly phone expense, combine her long distance phone bills ($119.68 + $84.36 + $68.49) and her local phone bill ($21.00), then divide the total by three (the number of months). The sum of the three long distance phone bills is $272.53, which is added to the $21.00 local phone charge for a total of $293.53. By dividing this sum by three, we get a monthly phone charge of $153.37. In summary, the student's total average monthly phone bill is $153.37, which includes long distance calls of $119.68, $84.36, and $68.49, as well as local calls of $21.00.
Here,
Long distance phone bills total:
$119.68 + $84.36 + $68.49
= $272.53
Local phone bill: $21.00
Total: $272.53 + $21.00
= $293.53
Average monthly phone bill:
$293.53 / 3
= $153.37
Her entire monthly phone cost is $153.37, which includes $119.68, $84.36, and $68.49 for long distance calls and $21.00 for local calls.
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This meal originally costs $75.00.
Fatima used a 20% off coupon and then tax was added.
The total after coupon and tax was $75.00.
What was the tax rate?
The discount given on the cost of the meal is $15
How to calculate tax on a given price?When a government imposes an obligational fee or financial charge on an individual or group in order to raise funds for public projects that support the best facilities and infrastructure, the action is referred to as a tax.
step1
According to the question, we are given the following information
The original cost of the meal = $75
Off coupon = 20%
step2
Required
The number of coupons given
coupon amount = 0.2 * 75
coupon amount = $15
Hence the discount given on the cost of the meal is $15
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If the original price was $75 and Fatima used a 20% coupon, then Fatima saved $15.
0.20 x 75 = 15
This means the cost of the meal that was taxed was a $60 meal.
Now we also know that after tax, the price of the meal came back to a $75 cost. This means that the amount of tax was also $15, but it's a $15 tax on a $60 meal, so this is a 25% tax.
$15 tax / $60 meal = 0.25 = 25%
The trick here is that in the beginning, the savings is based on the $75 meal, while the tax is based on a $60 meal, so the percentages are not the same.
Monique made several batches of soup for a potluck supper. Each batch required Three-fourths of a pound of potatoes, and she used a total of 6 and one-half pounds of potatoes. How many batches of soup did Monique make?
Which division and multiplication problems could represent this scenario? Check all the apply.
Three-fourths divided by StartFraction 13 over 2 EndFraction
StartFraction 13 over 2 EndFraction divided by three-fourths
Three-fourths (StartFraction 13 over 2 EndFraction)
StartFraction 13 over 2 EndFraction (three-fourths)
StartFraction 13 over 2 EndFraction (four-thirds)
Answer:Answer: B,E or 2nd answer and last
Step-by-step explanation: i did this test two week ago and made 100 own it good look to you
Step-by-step explanation:
Answer:
yo
Step-by-step explanation:
its B and E on edge
or
StartFraction 13 over 2 EndFraction divided by three-fourths
StartFraction 13 over 2 EndFraction (four-thirds)
Lydia has n nickels and d dimes. She has no more than $1 worth of coins altogether. Write this situation as an inequality.
Answer:
.10d + .05n ≤ 1.00
Step-by-step explanation:
a dine with worth 10 cents and a nickel is worth 5 cents. Together this amount cannot be over 1 dollar.
What is the solution for the equation?
a + StartFraction 8 over 3 EndFraction = two-thirds
The solution to the algebraic equation (a + 8/3) = 2/3 is given by a = -2
How to solve fractional equation?(a + 8/3) = 2/3
open parenthesis
a + 8/3 = 2/3
collect like terms
a = 2/3 - 8/3
a = (2-8) / 3
a = -6/3
a = - 2
Check:
(a + 8/3) = 2/3
-2 + 8/3 = 2/3
(-6+8) / 3 = 2/3
2/3 = 2/3
In conclusion, -2 is the solution to the unknown in the equation (a + 8/3) = 2/3
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Solve the equation. 4x - 6 = 2x + 8 x = _____
Answer:
x=-1
Step-by-step explanation:
4x-6=2x+8x; 4x-6=10x; -6=6x; x=-1.
Answer:
x=-1
Step-by-step explanation:
4x-6=2x+8x=
4x-6=10x
-6=10x-4x
-6=6x
x=6/-6
x=-1
four girls take turns flipping a fair coin until a head appears. what is the probability that the first girl is the first to flip a head
the probability of "heads" on the first flip of this coin will be 1/2.
What is probability and example?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
"Heads" is the result of the latest flip and the preceding four flips. The total sample space for the heads.
P(A^B)=(1/2)^5
The preceding four flips in a row all resulted in "heads."
P(B)=(1/2)^4
The probability that the 5th flip lands head is;
⇒P(A^B)/p(B)= (1/2)⁵/(1/2)⁴
⇒P(A^B)/p(B)= 1/2
Hence, the probability of "heads" on the next (5th) flip of this coin will be 1/2.
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Round 21245 to the nearest thousand
Answer:
21245 rounded to the nearest thousand is 21000.
Rounding to the nearest thousand means finding the number that is closest to the original number, but ends in three zeroes. In this case 21000 is the nearest number ending in three zeroes to 21245.
Answer:
21000
Step-by-step explanation:
If the hundreds place is 500 or bigger, round to 22000, if the number is 499 or under it will be 21000.
factorize fully 2(x-y)² - x+y
Answer: (2x-2y-1)(x-y)
Step-by-step explanation:
To factor 2(x-y)² - x+y, we first recognize that the expression is a difference of squares, which means it can be factored into the form (a-b)(a+b). To identify the values of a and b, we can look for common factors between the two terms, which are 2(x-y)² and -x+y.
The common factor between 2(x-y)² and -x+y is x-y. We can factor it out by dividing both terms by x-y:
2(x-y)² - x+y = (x-y) * (2(x-y) - 1)
Now we can write the expression as (x-y)(2x-2y-1) .
As you can see (x-y) is common in both the term, so we can factor it out, and we are left with (2x-2y-1)(x-y)
A multiple-choice quiz contains 5 questions. Each question has answer choices labeled a, b, c, and d.
How many different ways can a student answer the five questions?
A multiple-choice quiz contains 5 questions. Each question has answer choices labeled a, b, c, and d. There are 256 different ways can a student answer the five questions.
Permutation and Combination:
Permutations and combinations form counting principles, which are applied in many different situations. A permutation is the number of different arrangements that can be made from a given set. When it comes to permutations, the details matter because the order or order matters. The three country names are spelled differently: {US, Brazil, Australia} or {Australia, US, Brazil) or {Brazil, Australia, US}, and the order in which the country names appear is important. In combination, the names of the three countries are just one group, and the order or sequence does not matter.
When asked how many ways an object can be combined, dispersed, mixed or split, in this case the answer is to use the counting method to calculate the number of ways.
In this case, DDDD can be answered from AAAA, AAAB, AAAC, AAAD, AABA, AABB, ..., CADB. To calculate that number, we have to consider that for every possible answer to one question, there are four alternatives to the other question. So for the 4 choices for question 1, there are 4 choices for question 2, and for each question 3, and so on.
Therefore, the answer is 4*4*4*4 = 256 questions.
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Carly's age is 3 more than twice her sister's age, s. Which of the following expressions represents Carly's age? 2s + 3 3s + 2 2(s + 3) s2 + 3
Answer:
c = 2s + 3
Step-by-step explanation:
Let c be Carly's age.
Carly is 3 more . . . than twice her sister's age.
We can translate "twice her sister's age" into 2s.
Carly is 3 more than 2s.
We can translate this into:
Carly is 3 + 2s.
c = 2s + 3
JK has endpoints (-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a
ratio of 2:1.
What are the two possible locations of L?
(-9, 0.5)
(-7, 0.25)
(0, -1)
(-6, 0)
(1, -1.5)
(-4,-0.5)
If JK has endpoints (-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1 then the possible locations of L is at (-7, 0.25)
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0
L divides JK into two parts with lengths in a ratio of 2:1
so JL:LK is either 2:1 or 1:2
Let us solve the midpoint of JK
Midpoint=(-10+2/2, 1-2/2)
M=(-4,-1/2)
Midpoint of JM is (-10-4/2, 1-1/2/2)
L: (-7, 1/4)
Hence, the possible locations of L is at (-7, 0.25)
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Find the equation of the surface obtained by rotating the parabola y=x^2 about y-axis. What type of quadric surface is this?
On solving the provided question, we can say that this is from integral type of quadric surface [tex]SA = (\pi / 6) * 26 = > SA = (13 * \pi) / 3[/tex]
what is integral?In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration.
We concentrate on the x distance from the y-axis since the rotation is about the y-axis.
function for x, which is
x = + or - sqrt(y)
x = sqrt(y)
This is function is g(y) = sqrt(y)
g(y) about the y-axis on the closed interval [c, d], that is, y is an element of [c, d] is
Surface Area(SA) = 2 * pi * integral from c to d of ( g(y) * sqrt(1 +(g’(y))^2 ) *dy
The given interval is x=0 to x=sqrt(2), using the given function y = x^2 we obtain y = 0 to y = 2
g(y) = sqrt(y) and g’(y) = 1/(2 * sqrt(y))
SA = 2 * pi * integral from 0 to 2 of sqrt(y) * sqrt(1 +(1/(2*sqrt(y)))^2) * dy
SA = 2 * pi * integral from 0 to 2 of sqrt(y *(1 +(1/(4*y)) * dy
SA = 2 * pi * integral from 0 to 2 of sqrt(y +(1/4) * dy
Apply u substitution, let u = y +(1/4), then take derivative of u which gives us du = dy. As part of the substitution, we need to change the bounds to 1/4 and 9/4
SA 2 * pi * integral from 1/4 to 9/4 of u^(1/2) du
[tex]f u^(1/2) is 2u^(3/2) / 3[/tex]
[tex]SA = evaluate 2 * \pi * ( 2u^(3/2) / 3 ) from 9/4 to 1/4\\SA = [ 2 * \pi * ( 2 * (9/4)^(3/2) / 3) ] - [ 2 * \pi * ( 2 * (1/4)^(3/2) / 3) ]\\2 * \pi * 2 * (1/3)\\SA =((4 * \pi) / 3) * { [ (9/4)^(3/2) / 3) ] - [ (1/4)^(3/2) / 3) ] }\\ 4^(3/2) = sqrt(64) = 8\\SA = ((4 * \pi) / 3) * [ ( 9^(3/2) -1) / 8 ]\\SA = (\pi / 6) * ( 27 -1)\\SA = (\pi / 6) * 26\\SA = (13 * \pi) / 3\\[/tex]
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