Answer:
9e -3
Step-by-step explanation:
Perform the indicated multiplication:
6 e + 3 (e-1) = 6e + 3e - 3
This, in turn, simplifies to
9e -3, or 3(3e - 1).
Answer:
ANSWER: 9e-3
Step-by-step explanation:
6e+3(e−1)
As we need to simplify the above expression:
First we open the brackets :
3(e-1)=3e-33(e−1)=3e−3
Now, add it to 6e.
So, it becomes,
$$\begin{lgathered}6e+3e-3\\\\=9e-3\end{lgathered}$$
Hence, equivalent expression would be 9e-3.
Please help! picture above plus, part B: write the quadratic expression in the numerator and the dominator in factored form. Part C: cancel the common factor of the numerator and the denominator to write the expression in simplified form.
Answer:
work is shown and pictured
Answer:
Hi, there!!!
The answer would be 2(2x-1)/x(x-4).
See explanation in picture.
Hope it helps...
In kickboxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 7 pounds of pressure to break a board that is 3 feet long, how long is a board that requires 5 pounds of pressure to break?
Answer:
4.2
Step-by-step explanation:
f varies inversly with L can be translated matimatically as:
● f = k/L
It takes 7 pounds of pressure to break a 3 feet long board.
Replace f by 7 and L by 3.
● 7 = k/3 => k=7×3=21
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's find tge length of a board that takes 5 pounds of pressure to be broken.
● 5 = k/L
● 5 = 21/L
● L = 21/5 = 4.2
So the board is 4.2 feet long
8 sin2 x + cos x - 5 = 0
[tex]8 {sin}^{2} x + cos \: x - 5 = 0[/tex]
[tex]recall \: that \: {sin}^{2} x + {cos}^{2} x = 1[/tex]
[tex]then \: {sin}^{2} x = 1 - {cos}^{2} x[/tex]
then substitute,
[tex]8( 1 - {cos}^{2} x) + cos \: x - 5 = 0[/tex]
After Further Simplication,
[tex]8 {cos}^{2} x - cos \: x - 3 = 0[/tex]
[tex]let \: y = \cos(x) [/tex]
[tex]8 {y}^{2} - y - 3 = 0[/tex]
use quadratic formulae
[tex]y = 0.375 \: or \: - 0.25[/tex]
therefore
[tex] \cos(x) = 0.375 \: or \: - 0.25[/tex]
[tex] x = 70degrees \: or \: 104.5degrees[/tex]
75% of this
number is 13.5
Answer:
10.125
Step-by-step explanation:
Hello!
To find this we first have to convert the percentage to a decimal
We do this by moving the decimal point two times left
75.0% = 0.75
Now we multiply this by the number
13.5 * 0.75 = 10.125
The answer is 10.125
Hope this helps!
14. Find the distance between (7,217pi/180 ) and (5,-23pi/36 ) on the polar plane.
Answer: the distance is 3.49 units
Step-by-step explanation:
There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.
When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:
x = R*cos(θ)
y = R*sin(θ)
Then we have:
(7,217pi/180 )
R = 7
θ = (217/180)*pi
x = 7*cos( (217/180)*pi) = -5.59
y = 7*sin( (217/180)*pi) = -4.21
So this point is (-5.59, -4.21) in rectangular coordinates.
And the other point is (5,-23pi/36 )
R = 5
θ = -(23/36)*pi
x = 5*cos( -(23/36)*pi ) = -2.11
y = 5*sin( -(23/36)*pi ) = -4.53
So this point is (-2.11, - 4.53)
Then the point distance between those points is:
D = I (-2.11, -4.53) - (-5.59, -4.21) I
D = I (-2.11 + 5.59, -4.53 + 4.21) I
D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) = 3.49
1 = prt is an example of
O
a variable
an expression
a constant
a formula
Complete Question
I = prt is an example of
• a variable
• an expression
• a constant
• a formula
Answer:
A formula
Step-by-step explanation:
I = prt is an example of a formula called Simple Interest.
Simple Interest can be defined as the formula that is used to calculate the interest that is accumulated on a particular amount of money which was saved in a financial institution or loaned out to a person at a given interest rate for a particular period of time.
The formula for Simple Interest is Expressed as:
I = PRT
Where :
I = Simple Interest
P = Principal = Amount saved, or loaned out
R = Interest rate that is given in percentage form
T = Time that has elapsed in Years.
Answer:
D. A Formula
Step-by-step explanation:
A formula is an equation that uses variables to state a rule.
Hope I was able to help you!
Can someone help me, please?
Answer:
16
Step-by-step explanation:
7x+20+2x-5=159
9x+15=159
9x=159-15
9x=144
x=16
Chris wanted to know how likely he is to win at his favorite carnival game. He conducted 50 tests and won 15 times. What is the probability that he will win next time he plays? All answers are rounded to the nearest hundredth. a.) 0.15 b.) 0.30 c.) 0.50 d.) 0.35 SUBMIT MY ANSWER g
Answer:
b.) 0.30
Step-by-step explanation:
15/50 = 0.3
PLzzzz answer quick will give good rate nd say thanks
What is the slope of the line? 5(y+2)=4(x-3)
A 2/3
B 4/5
C 5/4
D 3/2
Step-by-step explanation:
Here,
[tex]5y = 4x - 12 - 10[/tex]
[tex]y = \frac{4}{5} x - \frac{22}{5} [/tex]
slope is 4÷5
Answer:
The answer is option BStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
5(y+2)=4(x-3)
To find the slope first expand the terms in the equation
That's
5y + 10 = 4x - 12
Write the equation in the form y = mx+ c
That's
5y = 4x - 12 - 10
5y = 4x - 22
Divide both sides by 5 to make y stand alone
y = 4/5x - 22/5
Comparing with the general equation above the slope of the line is
4/5Hope this helps you
Determine the equation of the tangent line to the given path at the specified value of t. (sin(7t), cos(7t), 2t9/2); t=1
Answer:
P(t) = {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)
Step-by-step explanation:
The equation of the tangent line to the given path at the specified value of t is expressed as;
P(t) = f(t0) + f'(t0)(t - t0)
f(t0) = (sin(7t), cos(7t), 2t^9/2)
at t0 = 1;
f(t0) = {sin7(1), cos7(1), 2(1)^9/2}
f(t0) = {sin7, cos7, 2}
f'(t0) = (7cos7t, -7sin7t, 9/2{2t^9/2-1}
f'(t0) = (7cos7t, -7sin7t, 9t^7/2}
If t0 = 1
f'(1) = (7cos7(1), -7sin7(1), 9(1)^7/2)
f'(1) =(7cos7, -7sin7, 9)
Substituting the given function into the tangent equation will give:
P(t) = f(t0) + f'(t0)(t - t0)
P(t)= {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)
The final expression gives the equation of the tangent line to the path.
The circumference of the circle shown below is 75 inches. Which expression
gives the length in inches of DE?
D
A.
. 75
72
O B.
360
75
O C.
361
. 75
O D.
360
75%
Answer:
B. 360 .75
Step-by-step explanation:
The circumference of the circle is represented by π * diameter of the circle. The circumference of the circle is its perimeter. The circumference is arc length of the circle. The perimeter is curve length around the figure of the circle. The circumference of the circle of 75 inches is represented by 75/360.
Answer: 72/360 multiply by 75
Step-by-step explanation:
i just did this question
A simple random sample of 28 Lego sets is obtained and the number of pieces in each set was counted.The sample has a standard deviation of 12.65. Use a 0.05 significance level to test the claim that the number of pieces in a set has a standard deviation different from 11.53.
Answer:
Step-by-step explanation:
Given that:
A simple random sample n = 28
sample standard deviation S = 12.65
standard deviation [tex]\sigma[/tex] = 11.53
Level of significance ∝ = 0.05
The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.
The null hypothesis and the alternative hypothesis can be computed as follows:
Null hypothesis:
[tex]H_0: \sigma^2 = \sigma_0^2[/tex]
Alternative hypothesis:
[tex]H_1: \sigma^2 \neq \sigma_0^2[/tex]
The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.
[tex]X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}[/tex]
[tex]X_0^2 = \dfrac{(28-1)(12.65)^2}{(11.53)^2}[/tex]
[tex]X_0^2 = \dfrac{(27)(160.0225)}{132.9409}[/tex]
[tex]X_0^2 = \dfrac{4320.6075}{132.9409}[/tex]
[tex]X_0^2 = 32.5002125[/tex]
[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}[/tex]
[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}[/tex]
From the chi-square probabilities table at 0.975 and degree of freedom 27;
[tex]X^2_{0.975 , 27}[/tex] = 14.573
[tex]X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}[/tex]
[tex]X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}[/tex]
From the chi-square probabilities table at 0.975 and degree of freedom 27;
[tex]X^2_{0.025 , 27}=[/tex] 43.195
Decision Rule: To reject the null hypothesis if [tex]X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}[/tex] ; otherwise , do not reject the null hypothesis:
The rejection region is [tex]X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573[/tex]
Conclusion:
We fail to reject the null hypothesis since test statistic value 32.5002125 lies between 14.573 and 43.195.
Suppose 232subjects are treated with a drug that is used to treat pain and 50of them developed nausea. Use a 0.01significance level to test the claim that more than 20%of users develop nausea. Identify the null and alternative hypotheses for this test.
A. Upper H0?: p equals 0.20
Upper H1?: p not equals 0.20
B. Upper H0?: p equals 0.20
Upper H1?: p greater than 0.20
C. Upper H0?: p greater than 0.20
Upper H1?: p equals 0.20
D. Upper H0?: p equals 0.20
Upper H1?: p less than 0.20
Identify the test statistic for this hypothesis test. Identify the P-value for this hypothesis test.
Identify the conclusion for this hypothesis test.
A. Reject Upper H 0. There is sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
B. Fail to reject Upper H 0. There is sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
C. Reject Upper H 0. There is not sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
D. Fail to reject Upper H 0. There is not sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
Answer:
A
The correct option is B
B
[tex]t = 0.6093[/tex]
C
[tex]p-value = 0.27116[/tex]
D
The correct option is D
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 232[/tex]
The number that developed nausea is X = 50
The population proportion is p = 0.20
The null hypothesis is [tex]H_o : p = 0.20[/tex]
The alternative hypothesis is [tex]H_a : p > 0.20[/tex]
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{50}{232}[/tex]
[tex]\r p = 0.216[/tex]
Generally the test statistics is mathematically represented as
=> [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p )}{n} } }[/tex]
=> [tex]t = \frac{ 0.216 - 0.20 }{ \sqrt{ \frac{ 0.20 (1- 0.20 )}{ 232} } }[/tex]
=> [tex]t = 0.6093[/tex]
The p-value obtained from the z-table is
[tex]p-value = P(Z > 0.6093) = 0.27116[/tex]
Given that the [tex]p-value > \alpha[/tex] then we fail to reject the null hypothesis
The weights of a sample of college textbooks has a bell-shaped distribution with a mean of 8.1 p o u n d s ( l b s ) and a standard deviation of 2.1 l b s . According to the Empirical Rule, what percent of all college textbooks will weigh between 1.8 and 14.4 l b s ?
Answer:
The interval ( 1,8 ; 14,4 ) will contains 99,7 % of all values
Step-by-step explanation:
For Normal Distribution N ( μ ; σ ) the Empirical Rule establishes that in the intervals:
( μ ± σ ) we find 68,3 % of all values
( μ ± 2σ ) we find 95,4 % of all values
( μ ± 3σ ) we find 99,7 % of all values
Then we have a normal distribution N ( 8,1 ; 2,1 )
3*σ = 3* 2,1 = 6,3
And 8,1 - 6,3 = 1,8 8,1 + 6,3 = 14,4
Then the interval ( 1,8 ; 14,4 ) will contains 99,7 % of all values
Write each expression in a simpler form that is equivalent to the given expression. Let F be a nonzero number. f-4
Answer:
f-4
Step-by-step explanation:
f-4 cannot be simplified
This is the simplest form
Answer:
[tex]\large \boxed{f-4}[/tex]
Step-by-step explanation:
[tex]f-4[/tex]
[tex]\sf f \ is \ a \ nonzero \ number.[/tex]
[tex]\sf The \ expression \ cannot \ be \ simplified \ further.[/tex]
20
#1. Which statement is the converse to: If a polygon is a triangle, then it
has 3 sides. *
O A polygon is a triangle, if and only if, it has 3 sides.
If a polygon has 3 sides, then the polygon is a triangle.
If the polygon does not have 3 sides, then it is not a triangle
If a polygon is not a triangle, then it does not have 3 sides
Answer:
If a polygon has 3 sides, then the polygon is a triangle.
Step-by-step explanation:
Bold = hypothesis
Italic = conclusion
Statement:
If p, then q.
Converse: If q, then p.
To find the converse, switch the hypothesis and conclusion.
Statement:
If a polygon is a triangle, then it has 3 sides.
Now we switch the hypothesis and the conclusion to write the converse of the statement.
If it has 3 sides, then a polygon is a triangle.
We fix a little the wording:
If a polygon has 3 sides, then it is a triangle.
Answer: If a polygon has 3 sides, then the polygon is a triangle.
The converse statement will be;
⇒ If a polygon has 3 sides, then the polygon is a triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The statement is,
''If a polygon is a triangle, then it has 3 sides. ''
Now,
Since, The statement is,
''If a polygon is a triangle, then it has 3 sides. ''
We know that;
The converse of statement for p → q will be q → p.
Thus, The converse statement is find as;
⇒ If a polygon has 3 sides, then the polygon is a triangle.
Learn more about the triangle visit:
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what is PI numbers?
Answer:
These are the first 100 digits of pi: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067
Step-by-step explanation:
Pi goes on continuously forever, so this is a reduced version, by including the first 100 digits.
Help plz! Jim is climbing a mountain that has a base 150 feet above sea level. If he climbs 233 feet then descends into a cave 64 feet, how far above sea level is Jim
Answer:
150+233-64=319
Jim is 319 ft above sea level.
Step-by-step explanation:
g A modal class in a histogram is the class that includes a. the largest number of observations. b. the smallest observation in the data set. c. the largest observation in the data set. d. the smallest number of observations.
Answer:
a. the largest number of observations.
Step-by-step explanation:
The mode is the variable in a data that has the highest frequency. Which implies that it occurs more than other variables.
When plotting a histogram, the modal class is one that has the greatest number of observations. Showing that the variables comprised in the class has more occurrence than others. Therefore, the required answer to the question is option a.
Draw a Venn diagram and use the given information to fill in the number of elements in each region.
Answer: Check out the diagram below for the filled in boxes
14 goes in the first box (inside A, but outside B)
7 goes in the overlapping circle regions
5 goes in the third box (inside B, outside A)
3 goes in the box outside of the circles
==============================================================
Explanation:
[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.
n(A) = 21 means there are 21 items in A
n(B) = 12 means there are 12 items in B
We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]
It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.
--------
[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]
So there are 7 items in both regions.
This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.
Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.
Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.
The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.
Again the diagram is posted below with the filled in values.
A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
The filled Venn diagram is given below.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
n(A) = 21
This is the total of all the items included in Circle A.
n(B) = 12
This is the total of all the items included in Circle A.
n(A') = 8
The items that are not in circle A.
n(A U B ) = 26
The items that are in both circle A and circle B.
Now,
n (A U B) = n(A) + n(B) - n(A ∩ B)
26 = 21 + 12 - n(A ∩ B)
n(A ∩ B) = 33 - 26
n(A ∩ B) = 7
Thus,
The filled Venn diagram is given below.
Learn more about the Venn diagram here:
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Fresno County, California is the largest agricultural producing county in the country and almonds are an important crop with more than 99,000 acres harvested. Each acre produces about a ton of almonds and sold at a price of $4300 a ton. The Sagardia Brothers grew 600 acres of almonds . How many tons would the brothers sell if they priced the almonds at $4500 a ton?
Answer:
0 ton
Step-by-step explanation:
The question states that 99,000 acres are harvested. This suggest that there are plenty sellers of almonds.The Sagardia Brothers grew 600 acres of almonds. this is a small percentage of the total output of almonds. This suggests that the market for almonds is perfectly competitive.
In this type of market, if the price of a seller is above equilibrium price, zero units of the commodity would be bought. This is because the goods sold are homogenous and buyers can easily purchase from other buyers that sell at the market price
You have a $5,000 limit on your credit card. What is the largest balance you should carry on this card to maintain an acceptable debt ratio? Recall that your debt ratio should never exceed 50% of your limit
Answer:
Amount of balance maintain = $2,500
Step-by-step explanation:
Given:
Limit of credit card = $5,000
Debt ratio = 50%
Find:
Amount of balance to maintain
Computation:
Amount of balance to maintain = Limit of credit card × Debt ratio
Amount of balance to maintain = $5,000 × 50%
Amount of balance to maintain = $2,500
create an equation with a solution closest to 0 using digits 1 to 9
Complete Questions:
Create an equation with a solution closest to 0 using digits 1 to 9
_x + _ = _x + _
Answer:
See Explanation
Step-by-step explanation:
Given
_x + _ = _x + _
Required
Fill in the gap using 1 to 9 to give a result close to 0
First, you have to determine what kind of numbers that are close to 0;
In this case, I'll work with -0.4 to 0.4 because the number in this range approximate to 0;
Next, is to fill in the gaps using trial by error method
5x + 2 = 2x + 3
Checking the above expression
Collect Like Terms
[tex]5x - 2x = 3 - 2[/tex]
[tex]3x = 1[/tex]
Divide equation by 2
[tex]x = 0.33[/tex] (Approximated)
Another trial is
6x + 8 = 2x + 7
Checking the above expression
Collect Like Terms
[tex]6x - 2x = 7 - 8[/tex]
[tex]4x = -1[/tex]
Divide equation by 4
[tex]x = -0.25[/tex] (Approximated)
I'll stop here but note that, there are more expressions that can fill in the gaps
m= -1/2 and the point (3, -6) which is the point -slope form of the equation
Answer:
y+6=-1/2(x-3)
Step-by-step explanation:
Point slope form: y-y1=m(x-x1)
Given that:
m=-1/2 and point (3, -6), you just add these numbers into the equation, and this gives:
y+6=-1/2(x-3)
Hope this helped!
Have a nice day!
Find the probability.
Two dice are rolled. Find the probability that the score on the dice is either 5 or
10.
Answer:
7/36
Step-by-step explanation:
1 die has 6 faces
When two dice are rolled, the total number of outcomes
= 6 × 6 = 36
The Probability of having(5) =
(1 & 4), (2 & 3) , ( 3 & 2), (4 & 1)
= 4
The probability of having (10) =
(5 & 5), (4 & 6) , ( 6 & 4)
= 3
The probability that the score on the dice is either 5 or 10.
P(5) + P(10)
= 4/36 + 3/36
= 7/36
Answer: 7/36
Step-by-step explanation:
36 outcomes
4 chances of getting 5 (1+4, 2+3, 4+1, 3+2)
3 chances of getting 10 (4+6, 5+5, 6+4)
4+3=7
so 7/36 chance
URGENT, PLEASE HELP! (3/5) -50 POINTS- !please no wrong answers for the points.! A) [tex]y = \frac{9}{2} x + \frac{1}{2}[/tex] B) [tex]y = - \frac{1}{2} x + \frac{7}{2}[/tex] C) [tex]y = -4x + 9[/tex] D) [tex]y = 4x + 15[/tex]
Answer:
B y = -1/2x + 7/2
Step-by-step explanation:
We know that it has a negative slope since the points go from the top left to the bottom right
We can eliminate A and D
The y intercept is where it crosses the y axis
It should cross somewhere between 2 and 4
C has a y intercept of 9 which is too big
Lets verify with a point
x = -4
y = -4(-4)+9 = 16+9 = 25 (-4,25) not even close to being near the points on the graph
checking B
y = -1/2 (-4) +7/2
= 2 + 7/2 = 11/2 = 5.5 it seems reasonable
Answer:
[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]
Step-by-step explanation:
Using a graph,
we can see that the line y = -1/2x + 7/2 best fits for the data.
Let U = {q,r,s,t,u,v,w,x,y,z}, A={q,s,u,w,y}, B={q,s,y,z}, and C={v,w,x,y,z}. List the elements in the set open parentheses A union B close parentheses to the power of apostrophe intersection C
[tex]A\cup B=\{q,s,u,w,y,z\}\\(A\cup B)'=\{r,t,v,x\}\\\boxed{(A\cup B)'\cap C=\{v,x\}}[/tex]
If Company X has 1600 employees and 80% of those employees have attended the warehouse training course how many employees have yet to attend?
Answer:
320
Step-by-step explanation:
Total no of employees = 1600
% of employees attended the training = 80%
no. of employee who attended the training = 80/100* 1600 = 1280
No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training = 1600-1280 = 320
Thus, 320 employees have yet to attend the training
Find a particular solution of the differential equation
-(5/4)y" + 2y' + y = 3x*e^(3x)
using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).
Find the following particular solution
yp= ?
Note that the characteristic solutions to this ODE are [tex]e^{-2x/5}[/tex] and [tex]e^{2x}[/tex], so we can safely assume a particular solution of the form
[tex]y_p=(ax+b)e^{3x}[/tex]
with derivatives
[tex]{y_p}'=ae^{3x}+3(ax+b)e^{3x}=(3ax+a+3b)e^{3x}[/tex]
[tex]{y_p}''=3ae^{3x}+3(3ax+a+3b)e^{3x}=(9ax+6a+9b)e^{3x}[/tex]
Substitute these expressions into the ODE and solve for a and b. Notice that each term on either side contains a factor of [tex]e^{3x}[/tex], which we can cancel.
[tex]-\dfrac54(9ax+6a+9b)+2(3ax+a+3b)+(ax+b)=3x[/tex]
[tex]-\dfrac{17a}4x-\left(\dfrac{11a}2+\dfrac{17b}4\right)=3x[/tex]
[tex]\implies\begin{cases}-\frac{17a}4=3\\\frac{11a}2+\frac{17b}4=0\end{cases}[/tex]
[tex]\implies a=-\dfrac{12}{17}\text{ and }b=\dfrac{264}{289}[/tex]
So the particular solution is
[tex]y_p=\left(-\dfrac{12x}{17}+\dfrac{264}{289}\right)e^{3x}=\boxed{\dfrac{12}{289}(22-17x)e^{3x}}[/tex]
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is false. A sampling distribution is normal only if n30. B. The statement is false. A sampling distribution is normal if either n30 or the population is normal. C. The statement is true. D. The statement is false. A sampling distribution is never normal.
The statement is false. A sampling distribution is normal if either n > 30 or the population is normal.
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Explanation:
If the underlying population is normally distributed, then so is the sample distribution (such as the distribution of sample means, aka xbar distribution).
Even if the population isn't normally distributed, the xbar distribution is approximately normal if n > 30 due to the central limit theorem. Some textbooks may use a higher value than 30, but after some threshold is met is when the xbar distribution is effectively "normal".
Choice A is close, but is missing the part about the population being normal. If we know the population is normal, then n > 30 doesn't have to be required.
