A quadratic equation of at the origin, estimate the error = 0.000859M
The approximation is valid because is very small.
Calculation of concentration:
Since
0.85 M 0 0
(0.85-x)M x x
Now the value of x should be
x = 0.0000229
So based on this, the above concentration should be determined.
In order to demonstrate that the same value of x may be achieved either way, you will now solve using the quadratic formula rather than iterations. What are the values of a, b, and c and x, where a, b, and c are the coefficients in the quadratic equation [tex]ax^{2} +bx+c=0[/tex] and x is [h3o+], when using the quadratic equation to determine [h3o+] in 0.00250 m hno2? Keep in mind that ka=4.5104.
a : 1
b : 4.5x[tex]10^{-4}[/tex]
c : 1.125x[tex]10^{-6}[/tex]
[[tex]H_{3} O^{+}[/tex]] = 0.000859M
As [tex]HNO_{2}[/tex] is a weak acid, its equilibrium in water is:
[tex]HNO_{2} (aq)+H_{2} O(I)[/tex] ⇄ [tex]H_{3} O^{+} (aq)+N_{2} O^{-} (aq)[/tex]
Equilibrium constant, ka, is defined as:
ka = 4.5x[tex]10^{-4}[/tex] = [[tex]H_{3} O^{+}[/tex]] [NO₂⁻] / [HNO₂] (Equation-1)
Equilibrium concentration of each specie are:
[HNO₂] = 0.00250M - x
[H₃O⁺] = x
[NO₂⁻] = x
Replacing in (1):
4.5x[tex]10^{-4}[/tex] = [tex]\frac{x*x}{0.00250M-x}[/tex]
1.125x10⁻⁶ - 4.5x10⁻⁴x = x²
0 = x² + 4.5x10⁻⁴x - 1.125x10⁻⁶
As the quadratic equation is ax² + bx + c = 0
Coefficients are:
a: 1
b: 4.5x10⁻⁴
c: 1.125x10⁻⁶
Now, solving quadratic equation:
x = -0.0013 → False answer, there is no negative concentrations.
x = 0.000859
As [H₃O⁺] = x; [H₃O⁺] = 0.000859M
Therefore,
A quadratic equation of at the origin, estimate the error = 0.000859M
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a professor at a certain school polled 12 colleagues about the number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period. the summary data are as follows: n
The number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period is [tex]-8.6+3.15[/tex].
What is formula for slope and intercept is?
[tex]$$\begin{aligned}& b=\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& a=\bar{y}-b \bar{x} \\& \hat{y}=a+b x\end{aligned}$$[/tex]
The slope is
[tex]$$\begin{aligned}b & =\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& =\frac{12 \times 318-(12 \times 4)(12 \times 4)}{12 \times 232-(12 \times 4)^2} \\& =3.15\end{aligned}$$[/tex]
The intercept is
[tex]$$\begin{aligned}a & =\bar{y}-b \bar{x} \\& =4-3.13 \times 4 \\& =-8.6\end{aligned}$$[/tex]
The regression equation is
[tex]$$\begin{aligned}\hat{y} & =a+b x \\& =-8.6+3.15 x\end{aligned}$$[/tex]
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3. "Seventeen less than twice a number is -49."
Answer: the number is -16
Step-by-step explanation: if you add 17 to -49, you will get -32. you do this because it is 17 less than NOT more than. that would be called inverse operations. then, you divide that number by 2 to get -16. again, you use inverse operations because you are going backwards to try and find the number.
Answer: -16
Step-by-step explanation: So, to solve, we should write an equation. It should look like this:
2x - 17 = -49
So, using inverse operations, we would add 17 to - 49, which is -32, then divide that by 2, which would be -16. I hope this helped!
P.S. our new equation would look like 2(16) - 17 = -49
32-17 = 49
32 + -17 = 49
49 = 49
It checks out.
i need the answers please
(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.
(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.
(9) We have drawn the graph passing through the point P and parallel to line AB.
(10)We have drawn the graph passing through the point P and perpendicular to line AB.
What is the property of slopes of parallel lines and perpendicular lines?
If two lines are given and they are parallel to each other then the slopes are equal and for perpendicular lines, the product of their slopes is equal to -1.
(7) The line AB is passing through the points (-1, 5/2) and (3/2, -1/2).
Slope = y2 - y2/x2 - x1
= (-1/2 - 5/2)/(3/2-(-1))
= -6/5
As line AB and line CD are parallel in nature so the slope of line CD is also -6/5.
(8) The line AB is passing through the points (1/2, 1) and (5/2, 5/2).
Slope = y2 - y2/x2 - x1
= (5/2 - 1)/(5/2-1/2)
=3/2/2
= 3/4
Line CD is passing through points (1, 1) and (2, 3).
Slope = y2 - y2/x2 - x1
= (3 - 1)/(2-1)
=2/2
= 1
As the product of their slopes is not equal to -1.
So lines are neither parallel nor perpendicular.
(9) Slope of AB can be computed as (-2, 1) and (-5, 5)
Slope = 5 - 1/-5 + 2
= 4/-3.
The slope of line passing through the point P = -4/3 as we have to draw the parallel line.
Point P = (-1, 3)
Equation of the line :
y - 3 = -4/3(x + 1)
3y +9 = -4x - 4
3y = -4x - 13
Now we can draw the line
(10) Slope of line AB = -4/3
So the slope of the line passing through point P should be 3/4 in order to be perpendicular to line AB.
Equation of the line passing through point P:
y - 3 = 3/4(x - (-1))
y - 3 = 3/4(x+1)
Hence,
(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.
(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.
(9) We have drawn the graph passing through the point P and parallel to line AB.
(10)We have drawn the graph passing through the point P and perpendicular to line AB.
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Jeremy has 3/4 pound of fish food if fish food is used to feed 24 fish how much food is there for each fish
Answer:
There is 1/32 pound food for each fish
Step-by-step explanation:
24 fish = 3/4 pound food
1 fish = (3/4)/24 pound food = 1/32 pound food
(Problem solved by using unitary method)
A local entrepreneur would like to know if those who live in an urban or rural community are more likely to buy a real Christmas tree. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the village and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree, and let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree. What is the p-value?
.32
.16
.07
.18
The value of p is 0.16. So the option b is correct.
A local entrepreneur takes a random sample of 100 people.
Of the urban participants, 22 buy a real tree.
Of the rural participants, 28 buy a real tree.
Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree.
Let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree.
We have to find the p-value
p1 = X1/N1
p1 = 28/100
p1 = 0.28
p2 = X2/N2
p2 = 22/100
p2 = 0.22
p = (X1 + X2)/(N1 + N2)
p = (28+22)/(100+100)
p = 0.25
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2
Test statistic
z = (p1 - p2)/√(p*(1-p)*(1/N1 + 1/N2))
z = (0.28-0.22)/√(0.25*(1-0.25)*(1/100 + 1/100))
z = 0.9798
P-value Approach
P-value = 0.16
Hence, the option A is correct. 0.16 is the p-value.
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Refer to the above diagram. Economies of scale: A) are evident over the entire range of output. B) occur over the OQ range of output. C) begin at output 03. D) occur only over the
Economies of scale occur when average cost declines with an increase in output. This occurs up to output level Q1.
Diseconomies of scale occur when average cost increases with an increase in output. This begins at output level Q3.
The phenomenon known as economies of scale occurs when the size or magnitude of the production generated by a business increases while the average cost per unit of output decreases.
The Long Run Average Cost Curve demonstrates how a firm's average expenses change over time. The shift from point A to point B illustrates how the cost per unit decreases as the curve slopes down. Because of economies of scale, the average cost grows less proportionally to output over the downward sloping region of the curve.
Minimum efficient scale is the level of output where economies of scale have been fully exploited.
A competitive firm produces at the minimum point of ATC in the long run and thus achieves productive efficiency.
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What is the slope-intercept equation for this line?
Answer:
y = -1/2x - 2
Step-by-step explanation:
y = mx+b, m = -1/2, and b (the y-intercept) is -2.
Given: ABCD is a parallelogram with AE = 9x−5, AC = 14x + 34. Find AC
The value of AC according to given equation of Parallelogram is 188 units.
What is parallelogram?
In elementary geometry, a parallelogram may be a quadrilateral with 2 pairs of parallel sides. the alternative or facing sides of a quadrangle square {measure} of equal length
Main body:
according to question:
AE = 9X-5
AC = 14X+34
as E is midpoint of AC so , we can say
2AE = AC
2(9x-5)= 14x+34
18x-10= 14x+34
4x = 44
x = 11
Now we need to find AC = 14x+34
= 14*11+34
= 188 units
Hence the value of AC according to given equation of Parallelogram is 188 units.
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Reshawn read 25 pages of his book each day until he finished the book. His book was 400 pages long. Which sketch represents this solution
Graph (C) which has points (0, 400) and (16, 0) represent the solution to the given situation of Rashawn.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Graphs and charts are useful visual aids because they make information accessible and quick to understand.
Therefore, it is not unexpected that print and electronic media frequently use graphs.
When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.
So, Rashawn consumed 25 pages of his book daily till it was finished. There were 400 pages in his book.
400 / 25 = 16 days is the estimated number of days he needs to finish the book.
He will have 400 pages finished in 0 days and 0 pages in 16 days.
As a result, the situation is represented by a graph with a line segment in the first quadrant.
Days are shown on the x-axis, and Pages left are listed on the y-axis.
The line segment's ends are (0, 400) and (16, 0).
Therefore, graph (C) which has points (0, 400) and (16, 0) represent the solution of the given situation of Rashawn.
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Complete question:
Rashawn read 25 pages of his book each day until he finished the book. His book was 400 pages long.
Which sketch represents this situation?
a) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 400 end ordered pair and begin ordered pair 25 comma 0 end ordered pair.
b) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 16 end ordered pair and begin ordered pair 400 comma 0 end ordered pair.
c) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 400 end ordered pair and begin ordered pair 16 commas 0 ends ordered pair.
d) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y-axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 25 ends ordered pair and begin ordered pair 400 commas 0 ends ordered pair.
Write an equation and solve.
When two times the difference of a number x and three is increased by five, the result is nine. What is the number?
With all this information, and reading our question carefully, we can decipher the following:
9(n-3) = 3 + (9n + 3n)
9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)
9n - 27 = 3 + 12n (Step 2. Combine like terms; 9n + 3n = 12n)
-9n -9n (Step 3. Subtract 9n from both sides to isolate the variable)
______________
-27 = 3 + 3n
-3 -3 (Step 4. Subtract 3 from both sides)
________________
-30 = 3n
----- ----
3 3 (Step 5. Divide 3 from both sides)
________________
-10 = n
Therefore, n = -10
What is Distributive property?Distributive property explains that the operation performed on numbers, available in brackets that can be distributed for each number outside the bracket. It is one of the most frequently used properties in Maths. The other two major properties are commutative and associative property.The distributive property is easy to remember. There are a number of properties in Maths which will help us to simplify not only arithmetical calculations but also the algebraic expressions. In this article, you will learn what is distributive property, formula, and solved examples.to learn more about distributive property refer to:
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Determine whether the integers in each of these sets are pairwise relatively prime. a) 11, 15, 19 b) 14, 15, 21 c) 12, 17, 31, 37 d) 7, 8, 9, 11
Note that Option A is pairwise and is relatively prime.
Option B is not relatively primeOption C is also a relatively primeOption D is also relatively prime.What does it mean for a list of integers to be pairwise relatively prime?If every pair of elements in a list of integers is relatively prime, the list is pairwise relatively prime. For example, the numbers 121, 122, and 123 are relatively prime pairwise (even though they are each composite).
You can tell if a set of numbers are relatively prime if they do not share a common factor other than ±
Looking at set a:
11, 15, 19
Writing their prime factorization
11 = 11
15 = 3 x 5
19 = 19, hence since any pair of these numbers does not have any common factor, hence they are relatively prime.
Looking at set b:
14, 15, 21
Writing their prime factorization, we have:
14 = 7 x 2
15 = 3 x5
21 = 3 x 7
15, and 21 share a common factor of 3 while
14 and 21 share a common factor of 7, therefore, they are NOT relatively prime.
Looking at set c)
12, 17, 31, 37
Writing their prime factorization,
12 = 3 x 2²
17 = 17
31 = 31
37 = 37
In this case, no pair of these numbers have any common factor. Hence they are relatively prime.
Looking at set d)
7,8,9, 11, spelling out their prime factorization
7=7
8=2³
9=3²
11=11
Thus, any pair of these numbers do not have a common factor, hence they are relatively prime.
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Cathy was not watching her dog's eating habits and his weight went from 40 pounds to 48
pounds. By what percentage did the dog's weight increase?
Answer:
Step-by-step explanation:
To find the percentage increase in the dog's weight, you can use the following formula:
percentage increase = (final value - initial value) / initial value x 100%
In this case, the initial value is 40 pounds and the final value is 48 pounds, so the percentage increase is:
percentage increase = (48 - 40) / 40 x 100% = 8 / 40 x 100% = 20%
Therefore, the dog's weight increased by 20%.
Please help me with this!
1) express the original claim in symbolic form
2) identify the null and the alternative hypotheses
The alternative hypothesis is often abbreviated as Ha or H1. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < o
What is hypothesis?
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientists typically build their scientific ideas on prior observations that cannot be adequately explained by the current body of knowledge.
In statistics, the null hypothesis is usually denoted by letter H with subscript '0' (zero), such that H0. It is pronounced as H-null or H-zero or H-nought
At the same time, the alternative hypothesis expresses the observations determined by the non-random cause.It is represented by H1 or Ha.
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Can you help me with this
2. Natalie is selling candles to raise money for her softball team. The team has two different options for selling the candles. The first option is to sell a package of 5 candles for $18. The second option is to sell individual candles for $4 each.
(a) The team wants to earn $1404. How many candles do the members need to sell if they sell candles only in packages? How many candles do they need to sell if they sell only single candles? Explain your answer using an equation for each situation.
(b) Describe at least one advantage of selling the candles in packages. Describe at least one disadvantage of selling the candles in packages
a) The amounts that the team needs to sell is given as follows:
Packages: 390 candles.Single candles: 351 candles.b) The advantage and disadvantage is given as follows:
Advantage: Better opportunity cost when a person needs one candle, the person will have to purchase the entire package.Disadvantage: Lower revenue per candle.How to obtain the amounts?The amounts needed are found applying the proportion, considering the costs and the number of candles.
A package of 5 candles for $18, hence the number of candles needed to earn $1404, in packages, is given as follows:
5 candles - $18
n candles - $1404
Applying cross multiplication, we have that:
18n = 5 x 1404
n = 5 x 1404/18
n = 390 candles.
With a single candle, the number of candles is calculated as follows:
1404/4 = 351 candles.
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Does the histogram appear to depict data that have a normal distribution? O A. The histogram appears to depict a normal distribution. The frequencies generally decrease to a minimum and then increase. O B. The histogram does not appear to depict a normal distribution. The frequencies generally increase and the histogram is roughly symmetric. O C. The hidtogram does not appear to depict a normal distribution. The frequencies generally decrease to a minimum and then increase, and the histogram is roughly symmetric. OD. The histogram appears to depict a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is roughly symmetric The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters. Frequency Weight (g) 6.000-6.049 6.050-6.099 6.100-6.149 6.150-6.199 6.200-6.249 6.250 6.299 6.300-6.349 6.350-6.399 Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?
The histogram appears to roughly estimate a normal distribution. The frequencies normally increase to a maximum and then decrease, and the histogram is symmetric.
The Graph of Normal Distribution is bell-shaped. Here the value of y is less for the lower value of x and then the value of y is increased for a larger value of x, but after some time value of y again getting decreases as the value of x increases.
For the Histogram to appear to be a normal distribution, the graph of the histogram must have the same nature. Thus, option B is only the correct option.
The histogram is made up of many columns and bars that are vertical with no gaps between bars with different labels of numeric data of different heights showing the size of the group of different labels.
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State the Domain, Range, in interval notation.
Domain:
Range:
The range and domain of the graph shown is
domain -4 ≤ x < ∞
range ∞ ≤ x < 3
How to find the domain and the rangeAll of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.
The domain of a graph is every value in the graph, from left to right.
Examining the curve the extreme left has x coordinate value of -4 and the right end have an arrow which means the value continues. this is written as
-4 ≤ x < ∞
The graph's entire range, from lower to higher numbers, in the vertical line represents the range.
Examining the curve the lowest point the curve reached in y-coordinate have an arrow which means the value continues and the top end have the value of 3. this is written as
∞ ≤ x < 3
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Each of the 9 reindeer have 8 jingle bells on their collar. There are 12 more bells on the reins. How many bells in all?
Answer: 84 bells
Step-by-step explanation:
12 + 9x8
84
What is the fourth root of 625
The required answer is the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
To find the fourth root of 625, we need to determine the number that, when raised to the power of 4, equals 625. Here's the step-by-step process:
Step 1: Start with the number 625.
Step 2: Take the fourth root of 625.
Since we're looking for the fourth root, we need to find a number that, when raised to the power of 4, equals 625.
Step 3: Determine the number that, when raised to the power of 4, equals 625.
To find this number, we can use the concept of exponentiation. Let's denote the unknown number as "x". Mathematically, we have [tex]x^4 = 625[/tex]..
Step 4: Solve the equation [tex]x^4 = 625[/tex].
To solve this equation, we need to find the value of x. Taking the fourth root of both sides of the equation, we have [tex]\sqrt[4]{(x^4)} =\sqrt[4] {625}.[/tex]
The fourth root of 625 is (625)^(1/4).
Step 5: Simplify the expression.
We can simplify [tex]\sqrt[4]{ 625}[/tex] as follows:
[tex]\sqrt[4]{ 625} = \sqrt[4]{ 5^4}= 5^{4/4} = 5^1 = 5.[/tex]
Therefore, the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
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let w represent the number of attempted experiments to get one experiment that is not successful. the random variable w has a geometric distribution with mean 4 and standard deviation 3.5. which of the following is the best interpretation of the standard deviation? responses a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selecte
The best interpretation of the standard deviation on this problem is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
How to interpret the standard deviation?The standard deviation of a data-set is calculated as the square root of the sum of the differences squared between each observation of the data-set and the mean, divided by the number of observations in the data-set.
The interpretation of this calculation is that the standard deviation represents by how much each value of the distribution is expected to vary from the mean, on average.
This means that the correct statement is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
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Max found a car he wants to buy that costs $16,000. He can
afford to pay $250 a month for the car. His bank offers him a car
loan of 7.3%. How will the length of his loan be for this payment
amount?
Answer: To calculate the length of a loan, you need to know the total cost of the loan, the monthly payment amount, and the interest rate. In this case, the total cost of the car is $16,000, the monthly payment amount is $250, and the interest rate is 7.3%.
First, you need to calculate the total interest that will be paid on the loan. This can be done by multiplying the total cost of the loan by the interest rate, and then dividing by 100 to convert the result to a percentage. In this case, the total interest paid would be $16,000 * 7.3 / 100 = $1,168.
Next, you need to subtract the total interest from the total cost of the loan to find the total amount of the loan that will be used to pay for the car. In this case, the total amount of the loan used to pay for the car would be $16,000 - $1,168 = $14,832.
Finally, you can use this total amount and the monthly payment amount to calculate the length of the loan by dividing the total amount by the monthly payment amount. In this case, the length of the loan would be $14,832 / $250 = 59.32 months, or just over four years. The answer is 59.32 months.
Step-by-step explanation:
A fair coin is tossed 10 times. Find the probability of satisfying the condition that that the coin does not land on tails twice in a row
The probability of tossing 10 tails in a row is [tex]\frac{1}{1024}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
When a fair coin is tossed 10 times, the sample size (n) is:
n = [tex]2^{10}[/tex]
This is so because a fair coin has 2 sides.
So, we have:
n = 1024
There is only one occurrence of having 10 tails in a row in the 1024 possible outcomes.
So, the probability is:
P = [tex]\frac{1}{1024}[/tex]
Therefore,
The probability of tossing 10 tails in a row is [tex]\frac{1}{1024}[/tex]
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-3/2 passes through (-4, 3)
what is the y intercept and equation
(in slope intercept form)
Write the complex equation 8 + 3; in trigonometric form.
The complex equation 8 + 3; in trigonometric form is z = 8.544[cos(20.6) + isin(20.6)}.
What is trigonometric form ?
Here, we'll utilize that fundamental transformation to recast z = a + bi in a different (sometimes more practical) form that is based on the polar transformation. The trigonometric form of a complex number is the name of this new representation.
Given
8 + 3i
Required
Rewrite in trigonometric form.
The trigonometric form of a complex equation is
z = r[cosθ + isinθ]
Let a = 3 and b = 8
Where
r is calculated by
r² = b² + a²
And
θ is calculated by
θ = arctan(a/b)
Substituting 3 for a and 8 for b
r² = a² + b² becomes
r² = 3² + 8²
r² = 9 + 64
r² = 73
√r² = √73
r = √73
r = 8.544
Calculating θ
θ = arctan(a/b) becomes
θ = arctan(3/8)
θ = arctan(0.375)
θ = 20.556°
θ = 20.6 --- Approximated
Hence, z = r[cosθ + isinθ] becomes
z = 8.544[cos(20.6) + isin(20.6)}
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Eli and Amy brought in 3 packs of stickers to give out to their two classes. They had enough for Mrs. O’s 21 students, Mrs. L's 24 students and even had 15 stickers left over! How many stickers were in each pack?
ill give brainliest semester ends tommorow
Answer: We can set up the equation 21 stickers/pack + 24 stickers/pack + x stickers/pack = 15 stickers.
We can solve this equation to find that x, the number of stickers in each pack, is equal to 6 stickers/pack. Answer: 6
Answer: 20
Step-by-step explanation:
24 + 21 = 45
45 + 15 = 60
60 / 3 = 20
A lamina occupies the region inside circle x2 +y2 = 2y but outside circle x2 +y2 = 1. Find the center of mass if the density atany point is inversely proportional to its distance from theorigin.
the answer is {0, [3√3/2(3√3-π)]}
Ф {0, [3√3/2(3√3-π)]}
The poster above has good diagrams ; so , I will just go through the calculations .
The region of integration is with in the circle x ^2+y^2=2y but outside the circle x^2+y^2=1.
I would convert to polar . With polar , we have x^2+y^2=r^2 ,x=rcosФ and y=rsinФ
We thus have the first circle becomes x^2+y^2=2y ⇒r^2=2rsinФ Divide through by r, and you get r=2sinФ(1).
This is the upper circle in the previous posters diagrams .
The other equation of a circle becomes :
x^2 + y^2 = 1 ⇒ r^2 = 1 ⇒ r = 1 (2)
These two curves intersect at :
r= 2sinФ =1 ⇒ sinФ=1/2 ⇒Ф= [tex]\alpha[/tex]/6 or 5[tex]\pi[/tex]/6
From the previous poster's diagrams , we can see that there is as much mass on either side of the positive. y axis or
Ф=[tex]\pi[/tex]/2 axis in polar ; so , the X coordinate of the center of mass is zero
X=0 We can also see from his diagrams that the mass and moment of mass is symmetrical about the Ф=[tex]\pi[/tex]/2
we only need to integrate from Ф=[tex]\pi[/tex]/6 to Ф=[tex]\pi[/tex]/2 ( the answers from to are the same and double )
The differential of area in polar coordinates is
d A=rdrdФ They say the area mass density is inversely proportional to the distance from the origin .
This can be written as : p=k/r. We can thus say the differential of mass is
d M=PDA=
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Error Analysis.
Use mathematical reasoning and appropriate terminology to describe (with words) and correct the error (with work) in simplifying each rational expression.
Error Analysis 1:(x-3)/(x+7)
Error Analysis 2:(x(x-7)(x+3))/2(x+1)(x+9)(x+5)
What is meant by error analysis?Error analysis is a procedure that is usually used to identify the cause of the issue when pupils continually make mistakes. The method entails going over a student's work and looking for patterns of misinterpretation. Mathematical errors can occur for a variety of reasons and can be factual, procedural, or conceptual. The study of the kind and quantity of mistake, or uncertainty, that might be present in the solution to a problem is known as error analysis in mathematics. This issue is particularly common in practical disciplines like statistics and numerical analysis. The teacher can examine a student's errors on a worksheet, test, or progress monitoring tool to do an error analysis for mathematics. In order to grade each problem, the teacher should mark each wrong digit in the student's response, starting from the RIGHT, going to the LEFT for addition, subtraction, and multiplication problems.
Error Analysis 1:
(x²-x-6)/(x²+9x+14)
=(x-3)(x+2)/(x+2)(x+7)
=(x-3)/(x+7)
Error Analysis 2:
(x²-6x-27)/(2x²+2x)÷(x²+14x+45)/(x²)
=(x(x-7)(x+3))/2(x+1)(x+9)(x+5)
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If f(x) = x³ + 14x² + 61x + 84, which of the following is not a factor of f(x)?
Four friends paid a total of $32 for bowling. What is the ratio $32 for 4 people written as a unit rate?
Answer:
$8 per person
Step-by-step explanation:
32 divided by 4 is 8
32 : 4 = 8 : 1
W is the midpoint of SU, TU ⊥ SU and SU ⊥ SV. Complete the proof that Δ SVW ≅ Δ UTW.
Statement Reason
1. W is the midpoint of SU Given
2. TU ⊥ SU Given
3. SU ⊥ SV Given
4. ∠S ≅ ∠U All right angles are congruent
5. ∠ SVW ≅ ∠ UTW Definition of midpoint
6. Δ SVW ≅ Δ UTW.
The proof that Δ SVW ≅ Δ UTW is given by ASA congruence criterion.
What do you mean congruence of triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.
The symbol of congruence is’ ≅’.
Given:W is the midpoint of SU
⇒ SW = WUTU ⊥ SU and SU ⊥ SV
To prove:Δ SVW ≅ Δ UTW
Proof:In Δ SVW and Δ UTWSW = UW (given)
∠S ≅ ∠U (given)
∠ SVW ≅ ∠ UTW (vertically opposite angle)
Therefore, Δ SVW ≅ Δ UTW (by ASA congruence criterion)
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A train travels at 80 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?
1. The domain is distance (d) and the range is time (t).
2. The domain is time (t) and the range is distance (d).
3. The domain is time (t) and the range is 80.
4. The domain is 80 and the range is time (t).
The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.
What are domain and range?
The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
From the given question, and the above definition of domain and range,
the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value
Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.
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