The degree of the function is 3, and the end behavior is that as x gets very large or very small the function increases or decreases without bound respectively.
What is the End Behavior?Generally, The degree of a polynomial function is the highest power of the variable in the function. In this case, the highest power of x is 3, so the degree of the function is 3.
The end behavior of a polynomial function refers to how the function behaves as the value of x gets very large or very small (i.e., as x approaches positive or negative infinity).
To find the end behavior, we look at the leading term, which is the term with the highest degree. In this case, the leading term is 3x³. Since the coefficient of x³ is positive, the end behavior of the function as x approaches positive infinity is positive infinity, and as x approaches negative infinity, the end behavior of the function is negative infinity.
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solve the differential equation
The solution of the differential equation y(3)=29/9.
Given a differential equation y'+(y/x)=x for y(1)=1.
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.
We will solve this differential equation by using the integrating factor method.
Firstly, we will find the integrating factors by using the formula, we get
[tex]I.F=e^{\int Pdx}[/tex]
Here P=1/x and substitute this in the formula, we get
[tex]\begin{aligned}I.F.&=e^{\int \frac{1}{x}dx}\\ &=e^{\log x}\\ &=x\end[/tex]
Now, we will substitute the values in the formula
[tex]y\times I.F.=\int Q\times I.F.dx[/tex]
Here Q=x an substitute this in the above formula, we get
[tex]\begin{aligned}y\times x&=\int x\times xdx\\ yx&=\int x^{2} dx\\ yx&=\frac{x^3}{3}+C\end[/tex]
Further, we will divide both sides with x, we get
y=(x²/3)+(C/x) ......(1)
Given that y(1)=1 means when x=1 then y=1 so substitute this in equation (1) to find the value of C, we get
1=(1/3)+C
1-(1/3)=C
2/3=C
Substitute the value of C in equation (1), we get
y=(x²/3)+(2/(3x))
Now find the value of y when x=3, we get
y=(9/3)+(2/9)
y=3+(2/9)
y=29/9
Hence, in the differential equation y'+(y/x)=x for y(1)=1 then y(3) is 29/9.
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You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 98% confident that you estimate is within 2% of the true population proportion. How large of a sample size is required?
Using the z-distribution, it is found that a sample size of 3,385 is required.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.
We have no prior estimate, hence [tex]\pi = 0.5[/tex] is used, which is when the largest sample size is needed. To find the sample size, we solve the margin of error expression for n when M = 0.02, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.02\sqrt{n} = 2.327 \times 0.5[/tex]
[tex]\sqrt{n} = \left(\frac{2.327 \times 0.5}{0.02}\right)[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.327 \times 0.5}{0.02}\right)^2[/tex]
n = 3,385.
A sample size of 3,385 is required.
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What type of line is PQ¯¯¯¯¯¯¯¯?
A. altitude
B. median
C. side bisector
D. angle bisector
The line PQ is altitude of the triangle. This can be obtained by understanding what an altitude is.
What is altitude of a triangle?Altitude of a triangle: the perpendicular drawn from the vertex of the triangle to the opposite side.Commonly known as height of the triangle.Properties of altitude of a triangle:
A triangle has 3 altitudes from the three vertices of the triangle.The 3 altitudes intersect at a point known as the orthocenter of the triangleThe altitude of the triangle is the shortest distance from the vertex to the opposite side.In the given triangle,
it is clear that angle Q is 90° and therefore PQ is a perpendicular line from the point P.
Since the perpendicular line, which is PQ, is drawn from the vertex, which is P of the triangle to the opposite side, which is SR.
Thus PQ is the altitude of the triangle.
Hence in the given figure, the line PQ is the altitude of the triangle.
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29) Selecting a blue marble, a white marble, and then a red marble.
O a.) 4/19
Ob.) 4/91
Oc.) 3/19
Od.) 7/91
Answer:
4/91
Step-by-step explanation:
There are a total of 15 marbles. In the first selection there are 15 marbles and 6 are blue. That would be 6/15.
Since we are not replacing marbles, we now have 14 marbles and we want to select one of the 5 white marbles. That would be 5/14.
Lastly we now only have 13 marbles and of those we want to select one of the 4 red ones. That would be 4/13.
Now we take these 3 fractions and multiply them together.
6/15(5/14)(4/13). I am going to try to make this a little easier and see if I can find any factors that any top number shares with any bottom number.
I see 5 on the top shares a common factor with 15 on the bottom. I will divide these numbers by 3, so now I have
6/3(1/14)(4/14). I think that I can do better than that. I see that 6 on the top and 3 on the bottom share a common factor of 3. I will divide both of these numbers by 3. Which will give me:
2/1(1/14)(4/13) I see a 4 on top and a 14 on the bottom. Those are both divisible by 2 so, I will divided them both by 2 and that leaves me with
2/1(1/7)(2/13) That is a lot easier, now I will just multiple the top numbers and multiply the bottom numbers to get
4/91
Can you please help me identify the property that justifies the work between step 3 and step 4
Answer:
Division property of inequality
Step-by-step explanation:
24<4x
24/4<4x/4
6<x
(1/4)×24 < (1/4) ×4x
6 < x
please solve this question and plot the graph using GeoGebra it must plotted in the GeoGebra like same as shown in the given question. Using any of these Colors blue, green, orange, black, gray. graph must in the form of GeoGebra or any computerize form not in hand writing. please use only given colors when you plot the graph.
See below for the complete table and graph of y = x + 4
How to complete the table?The function is given as:
y = x +4
Where x = -2, 0, 2, 6 and 8
So, we have
y = -2 +4 = 2
y = 0 +4 = 4
y = 2 +4 = 6
y = 6 +4 = 10
y = 8 +4 = 12
The above computation implies that the complete table is
Input x x + 4 Output, y (x, y)
-2 -2 + 4 2 (-2,2)
0 0 + 4 4 (0,4)
2 2 + 4 6 (2,6)
6 6 + 4 10 (6,10)
8 8 + 4 12 (8,12)
See attachment for the graph of y = -x + 4
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Compare and contrast the relative frequency for the whole table in part B with the two-way frequency table given in the activity introduction. What trends or generalizations can you identify from the data in the tables?
The way to convert counts into relative frequencies in a Two Way Relative Frequency Table is to divide the count by the total number of items
What is a Frequency Table?
This refers to the depiction of the number of times in which an event occurs in the form of a table.
Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.
Please note that your question is incomplete as you did not provide the frequency table needed and also the trends and generalizations to find, so a general overview was given.
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Answer:
The relative frequency table shows a trend that a majority of people prefer coffee over tea: the ratio in the total row for coffee is 0.65 and just 0.35 for tea. Similarly, more people are night owls than early birds: the total column for night owl is 0.6, but the early bird column is only 0.4.
14) 8 people from a group of 15
O a.) 5435
Ob.) 6345
O c.) 6435
Od.) 6543
Answer: 6435
Step-by-step explanation:
[tex]\binom{15}{8}=6435[/tex]
Write a word problem involving finding two real numbers that could be solved with the
equation x(9-x)=14 .
The word problem that depicts this algebraic equation is;
The sum of the weight of my son and my daughter is 9 kg but the product of their weights is 14. Find the weights of each person.
How to write Algebraic Word Problems?We want to write a word problem with the equation;
x(9 - x) = 14
The word problem that depicts this algebraic equation is;
The sum of the weight of my son and my daughter is 9 kg but the product of their weights is 14. Find the weights of each person.
Now, the word problem above is correct because if we assume their weights are x and y, then we can say that;
x + y = 9
xy = 14
Now, y = 9 - x
Thus, equation 2 is;
x(9 - x) = 14
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which of the following best describes the graph below?
Answer:
I think it's B
Step-by-step explanation:
because it's a function,it's 5 to 4 not one to one
PLEASE someone help me with this question, I’ve been stuck on it for so long :(
Help is greatly appreciated! I know what the answer is ( back of my textbook) but i dont know how to figure it out
Oh also if it’s possible could you please take a picture of your handwritten answer instead of typing it since its easier for me to understand , but either way is fine :)
Answer:
13.5 litres
Step-by-step explanation:
the ratios are 2 : 3 : 4 = 2x : 3x : 4x ( x is a multiplier )
given Henrietta produced 1.5 litres more than Gladys , then
4x = 3x + 1.5 ( subtract 3x from both sides )
x = 1.5
then total milk produced by the 3 cows is
total = 2x + 3x + 4x = 9x = 9 × 1.5 = 13.5 litres
(1/2)(-27Divided by 1/3) 2/3
The value of the quotient is - 27
How to determine the quotientTo determine the quotient, first, we have
(1/2)(-27Divided by 1/3) 2/3
[tex] \frac{1}{2} \times \frac{ - 27 \times 3}{1} \times \frac{2}{3} [/tex]Multiply the numerator and denominator
=
[tex] \frac{ - 162}{6} [/tex]
Then divide the numerator by the denominator, we get
= - 27
Thus, the value of the quotient is - 27
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plsss right away will be amazing
Which is the graph of f(x)=√/-x?
Graph 3
Because
y=³√xThe graph is like the first graph
When x approaches+oo y approaches+oo
But when x is negative the reverse thing happens
Hence Graph C is correct
Answer:
Graph 3
Step-by-step explanation:
Given function:
[tex]f(x)=\sqrt[3]{-x}[/tex]
Therefore, the parent function is:
[tex]f(x)=\sqrt[3]{x}[/tex]
(The graph of the parent function is the first graph in the answer options).
The transformation that takes the parent function to the given function is:
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Therefore, the graph of the given function is the third graph in the given answer options (see attached).
For number 9 and 10 what do I put for the distance between the points?
Answer:
I have wrote just answers
Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures.
m∠3=(50x−100)∘, m∠5=(25x+25)∘
Using the corresponding angles postulate:
m∠3 = 150°
m∠5 = 150°
What is the Corresponding Angles Postulate?According to the corresponding angles postulate, corresponding angles, ∠3 and ∠5 are congruent to each other.
Thus, we would have the following equation:
m∠3 = m∠5
Plug in the values
50x - 100 = 25x + 25
50x - 25x = 100 + 25
25x = 125
x = 125/25
x = 5
m∠3 = 50x − 100 = 50(5) − 100 = 150°
m∠5 = 25x + 25 = 25(5) + 25 = 150°
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Evaluate:
(3,251)(30)
Answer: 97350
Step-by-step explanation:
The numbers (3251)(30) are separated by using parentheses by multiplying the numbers we get 97350.
What is multiplication?
When we notice two or more numbers together that exist divided by parentheses, then the parentheses exist pointing us to multiply. In math, multiplying indicates adding equivalent groups. When we multiply, the number of things in the group rises. The two elements and the product exist as regions of a multiplication problem.
Given: (3251)(30)
Here, the numbers are separated by using parentheses, then the parentheses exist pointing us to multiply.
Therefore, by multiplying the numbers we get
(3,251)(30) = 97350
Therefore, the correct answer is 97350.
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Which point on the graph represents the y-intercept?
Answer:
Step-by-step explanation:
It would be point B. Since y-intercept is when the x is at 0, the answer would be point B.
Which of the following is most likely the next step in the series
Answer:
A
Step-by-step explanation:
The pattern is quadrilateral (4-gon), pentagon (5-gon), and hexagon (6-gon). Therefore the next figure would be a heptagon (7-gon).
10 workers can finish the job in 15 days. For the first 5 days, only 6 workers worked on the job. Then for the next 3 days 2 more workers joined them. To finish the job, 4 more workers joined
them. After how many days was the whole job done?
A. 8days
B. 12days
C. 16days
D. 18days
Answer:
C. 16 days
Step-by-step explanation:
Let´s say each worker does 1 ¨work¨, for each day, in order to complete the job in 15 days. That´s a total of 150 work.
If only 6 workers worked for the first 5 days, then we only do 30 by Day 5.
2 more workers join, so they do 8 work each day, 24 work in 3 days, 54 work by Day 8.
4 more workers join to complete the job, so we now do 12 work each day.
150 - 54 = 96
96 work is left to do, which would be done in 8 days by 12 workers.
8 days + 8 days = 16 days
In the following month 10 percent savings on other cost are expected
A shop has this offer.
£5 reduction if you spend more than £100
or
£10 reduction if you spend more than £140
or
£20 reduction if you spend more than £180
At the shop, shirts cost £49 each.
Tim buys 3 shirts
Craig buys 5 shirts
How much more than Tim does Craig pay?
Optional working
Answer: £
Claire has 18 nail polish bottles while Becky has 2/3 of that amount. How many bottles of nail polish does Becky have?
Answer: 12
Step-by-step explanation:
f(x)=x^2+4x-6
a. f(x) can be written in the form (x+m)^2+n. Find the value of m and the value of n
My answer: m= 2; n=-10
b. Use your answer to part (a) to find the positive solution to x^2+4x-6=0
x=
Answer:
[tex]x \approx 1.16[/tex]
Step-by-step explanation:
a.
To find the values of m and n, we have to first expand [tex](x + m)^2 + n[/tex] :
[tex](x + m)^2 + n[/tex]
⇒ [tex]x^2 + 2mx + m^2 + n[/tex]
[tex]f(x) = x^2 + 4x - 6[/tex]
Now compare the coefficients of the x-terms:
• [tex]2mx = 4x[/tex]
⇒ [tex]\bf m = 2[/tex]
• [tex]m^2 + n = -6[/tex]
⇒ [tex]2^2 + n = -6[/tex]
⇒ [tex]n = -10[/tex]
b.
[tex]x^2 + 4x - 6 = 0[/tex]
∴ [tex](x + 2)^2 - 10 = 0[/tex]
⇒ [tex](x + 2)^2 = 10[/tex]
⇒ [tex]x + 2 = \sqrt{10}[/tex]
⇒ [tex]x = \sqrt{10} -2[/tex]
⇒ [tex]x \approx 1.16[/tex]
Is the answer e? I think it is
Answer: I am pretty sure you are correct from my standpoint
Step-by-step explanation:
If you look closely he is pretty close to the answer or it is the answer or this is just answer on my point or if its wrong try b
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 46 and a standard deviation of 5. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 36 and 56?
The approximate percentage of daily phone calls numbering between 36 and 56 by the receptionists is 95.44%.
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 46 and a standard deviation of 5.
Hence, Mean,μ=46 and Standard deviation,σ=5.
To find the probability of daily phone calls numbering between 36 and 56,
P(36≤X≤56)
To convert the X score to Z score, use the formula, Z=(X-μ)/σ
Then we get,
P((36-46)/5 ≤ Z ≤ (56-46)/5) = P(-2 ≤ Z ≤ 2)
By using the property of the normal bell curve, we get
P(-2 ≤ Z ≤ 2) = P(2 ≤ Z) - P(-2 ≤ Z)
As per the normal distribution table,
P(2 ≤ Z) - P(-2 ≤ Z) = 0.9772-0.0228
∴ P(36≤X≤56) = 0.9544
Hence, the approximate percentage of daily phone calls numbering between 36 and 56 by the receptionists is 95.44%.
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Please someone help me!
If the red lines are medians, and segment AE=33 would be the length of the segment AO?
22
bc I know that is 22 so just put that
Write the equation of the line of best fit using the slope-intercept formula y=mx+b. Show all your work, including the points used to determine the slope and how the equation was determined.
The equation of the line of best fit using the slope-intercept formula y=mx+b is y = x - 5
Equation of the line of best fitA line is the shortest distance between two points. The equation in point-slope form is expressed as:
y =. mx + b
m is the slope
b is the y intercept
Using the coordinate points (25, 20) and (60, 55)
Slope = 55-20/60-25
Slope = 35/35
Slope = 1
For the intercept
20 = 1(25) + b
b = 20 - 25
b = -5
Substitute
y = x + (-5)
y = x - 5
Hence the equation of the line of best fit using the slope-intercept formula y=mx+b is y = x - 5
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You reported to work one day and found out that the staffs are on strike over non payment of the previous year's bonus. Placards indicted the human resources director on this. Management is so worried about this situation and has asked you as the director of public relations to come out with a comprehensive report on the matter. What steps would you consider to undertake this assignment?
As the person that is in charge of public relations the steps that you would take to deal with the issue on ground would be:
Identify what the issue is.Set a priority based on the issueGet you position on the issueGet a way to respondTake actionMonitor the situationWhat is public relations?This is the term that is concerned with the part of management that is concerned with the maintenance of a positive image for an organization.
The director has to take proactive steps in order to take care of the issue in a timely and good manner.
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Which parent function is represented by the graph?
Answer:
Absolute value parent function
Explanation:
What is an Absolute value function?
It is a function in Algebra in where the variable is inside the absolute value bars (| |)
f(x)=|x|
y=x on the right side and y=-x on the left side of the graph
Hope it helps!
I need help with my homework please!!
Extremely confused!
I need all the equations imputations and how to solve for everything!
Answer:
what do you need person jjff