According to the desired test, the hypothesis are given by:
D) H0: μ=210
Ha: μ ≠ 210
At the null hypothesis, it is tested if the population mean is of 210 lbs, that is:
[tex]H_0: \mu = 210[/tex]
At the alternative hypothesis, it is tested if the population mean differs from 210 lbs, that is:
[tex]H_a: \mu \neq 210[/tex]
Hence, the correct option is:
D) H0: μ=210
Ha: μ ≠ 210
A similar problem is given at https://brainly.com/question/25707631
[infinity]
Substitute y(x)= Σ 2 anx^n and the Maclaurin series for 6 sin3x into y' - 2xy = 6 sin 3x and equate the coefficients of like powers of x on both sides of the equation to n= 0. Find the first four nonzero terms in a power series expansion about x = 0 of a general
n=0
solution to the differential equation.
У(Ñ)= ___________
Recall that
[tex]\sin(x)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex]
Differentiating the power series series for y(x) gives the series for y'(x) :
[tex]y(x)=\displaystyle\sum_{n=0}^\infty a_nx^n \implies y'(x)=\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]
Now, replace everything in the DE with the corresponding power series:
[tex]y'-2xy = 6\sin(3x) \implies[/tex]
[tex]\displaystyle\sum_{n=0}^\infty (n+1)a_{n+1}x^n - 2\sum_{n=0}^\infty a_nx^{n+1} = 6\sum_{n=0}^\infty(-1)^n\frac{(3x)^{2n+1}}{(2n+1)!}[/tex]
The series on the right side has no even-degree terms, so if we split up the even- and odd-indexed terms on the left side, the even-indexed [tex](n=2k)[/tex] series should vanish and only the odd-indexed [tex](n=2k+1)[/tex] terms would remain.
Split up both series on the left into even- and odd-indexed series:
[tex]y'(x) = \displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} + \sum_{k=0}^\infty (2k+2)a_{2k+2}x^{2k+1}[/tex]
[tex]-2xy(x) = \displaystyle -2\left(\sum_{k=0}^\infty a_{2k}x^{2k+1} + \sum_{k=0}^\infty a_{2k+1}x^{2k+2}\right)[/tex]
Next, we want to condense the even and odd series:
• Even:
[tex]\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2k+2}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2(k-1)+1}x^{2k}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2k-1}x^{2k}[/tex]
[tex]=\displaystyle a_1 + \sum_{k=1}^\infty \bigg((2k+1)a_{2k+1} - 2a_{2k-1}\bigg)x^{2k}[/tex]
• Odd:
[tex]\displaystyle \sum_{k=0}^\infty 2(k+1)a_{2(k+1)}x^{2k+1} - 2\sum_{k=0}^\infty a_{2k}x^{2k+1}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2(k+1)}-2a_{2k}\bigg)x^{2k+1}[/tex]
[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1}[/tex]
Notice that the right side of the DE is odd, so there is no 0-degree term, i.e. no constant term, so it follows that [tex]a_1=0[/tex].
The even series vanishes, so that
[tex](2k+1)a_{2k+1} - 2a_{2k-1} = 0[/tex]
for all integers k ≥ 1. But since [tex]a_1=0[/tex], we find
[tex]k=1 \implies 3a_3 - 2a_1 = 0 \implies a_3 = 0[/tex]
[tex]k=2 \implies 5a_5 - 2a_3 = 0 \implies a_5 = 0[/tex]
and so on, which means the odd-indexed coefficients all vanish, [tex]a_{2k+1}=0[/tex].
This leaves us with the odd series,
[tex]\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1} = 6\sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!}[/tex]
[tex]\implies 2(k+1)a_{2k+2} - 2a_{2k} = \dfrac{6(-1)^k}{(2k+1)!}[/tex]
We have
[tex]k=0 \implies 2a_2 - 2a_0 = 6[/tex]
[tex]k=1 \implies 4a_4-2a_2 = -1[/tex]
[tex]k=2 \implies 6a_6-2a_4 = \dfrac1{20}[/tex]
[tex]k=3 \implies 8a_8-2a_6 = -\dfrac1{840}[/tex]
So long as you're given an initial condition [tex]y(0)\neq0[/tex] (which corresponds to [tex]a_0[/tex]), you will have a non-zero series solution. Let [tex]a=a_0[/tex] with [tex]a_0\neq0[/tex]. Then
[tex]2a_2-2a_0=6 \implies a_2 = a+3[/tex]
[tex]4a_4-2a_2=-1 \implies a_4 = \dfrac{2a+5}4[/tex]
[tex]6a_6-2a_4=\dfrac1{20} \implies a_6 = \dfrac{20a+51}{120}[/tex]
and so the first four terms of series solution to the DE would be
[tex]\boxed{a + (a+3)x^2 + \dfrac{2a+5}4x^4 + \dfrac{20a+51}{120}x^6}[/tex]
A coffee pot holds 3 3/4 quarts of coffee. How much is this in cups.
Answer: 15 cups
Step-by-step explanation:
At a university of 25,000 students, 18% are older than 25. The registrar will draw a simple random sample of 242 of the students. The percentage of students older than 25 in the sample has an expected value of 18% and a standard error of:______.
Answer:
Standard error of: 2.47%
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
18% are older than 25.
This means that [tex]p = 0.18[/tex]
Simple random sample of 242 of the students.
This means that [tex]n = 242[/tex]
Standard error:
By the Central Limit Theorem:
[tex]s = \sqrt{\frac{0.18*0.82}{242}} = 0.0247[/tex]
0.0247*100% = 2.47%
Standard error of: 2.47%
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
8.6
Step-by-step explanation:
VW = WX / cos (36°)
= 7 / 0.81
= 8.6
Answer:
8.65
Step-by-step explanation:
cos 36° = 7 / VW
VW = 7 / cos 36°
VW = 8.65
The graph f(x)=x^5 is transformed to form a new function, g(x). Which set of transformations takes f(c) to g(x) in the correct order?
- translation 2 units to right,vertical stretch by a factor 1/3, translation 1 unit up
-translation 2 units to the right, vertical stretch by a factor of 3, translation 1 unit up
-translation 2 units to the right,translation 1 unit up,vertical stretch by a factor of 1/3
-translation 2 units to the right,translation 1 unit up,vertical stretch by a factor of 3
Answer:
Translation 2 units to the right
Vertical stretch by a factor of 3
Translation 1 unit up
Step-by-step explanation:
Correct on plato :}
Of all the people applying for a certain job 75% are qualified and 25% are not. The personnel manager claims that she approves qualified people 80% of the time, she approves unqualified people 30% of the time. Find the probability that a person is qualified if he or she was approved by the manager The probability is:_______.
Type an integer or decimal rounded to four decimal places as needed)
Answer:
The probability is: 0.8889.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Approved
Event B: Qualified
Probability of a person being approved:
80% of 75%(qualified)
30% of 25%(not qualified). So
[tex]P(A) = 0.8*0.75 + 0.3*0.25 = 0.675[/tex]
Probability of a person being approved and being qualified:
80% of 75%, so:
[tex]P(A \cap B) = 0.8*0.75[/tex]
Find the probability that a person is qualified if he or she was approved by the manager.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.8*0.75}{0.675} = 0.8889[/tex]
The probability is: 0.8889.
Determine if the table below represents a linear function. If so, what's the rate of change?
A) No; it's a non-linear function.
B) Yes; rate of change = 4
C) Yes; rate of change = 2
D) Yes; rate of change = 3
Answer:
A
Step-by-step explanation:
Its not a linear function; there is no consistent rate of change between each of the points.
7 root 3 by 3 minus 3 root 2 by root 15 minus 3 root 2 minus 2 root 5 by root 6 + root 5
Answer:
Hill doctoral tricot trivial paint Tahiti he who Olney of Accokeek if Dogtown k park pectin rabbit tabernacle numbed.
Make x the subject
y = 4(3x-5)/9
Answer:
3/4y +5/3 = x
Step-by-step explanation:
y = 4(3x-5)/9
Multiply each side by 9
9y = 4(3x-5)/9*9
9y = 4(3x-5)
Divide each side by 4
9/4 y = 4/4 (3x-5)
9/4y = 3x-5
Add 5 to each side
9/4y +5 = 3x-5+5
9/4y +5 = 3x
Divide by 3
9/4 y *1/3 +5/3 = 3x/3
3/4y +5/3 = x
- 2/3 (2 - 1/5) use distributive property
Answer:
-6/5
Step-by-step explanation:
- 2/3 (2 - 1/5)
Distribute
-2/3 *2 -2/3 *(-1/5)
-4/3 + 2/15
Get a common denominator
-4/3 *5/5 +2/15
-20/15 +2/15
-18/15
Simplify
-6/5
37. The trip between 2 towns is exactly 90 miles. You have gone 40% of this distance. How far have
you gone?
Answer:
36 miles
Step-by-step explanation:
We want to find 40% of 90 miles
40% * 90
.40 * 90
36 miles
We have to find travelled distance inorder to find this we have to find 40℅ of 90miles
[tex]\\ \Large\sf\longmapsto 90\times 40\℅[/tex]
[tex]\\ \Large\sf\longmapsto 90\times \dfrac{40}{100}[/tex]
[tex]\\ \Large\sf\longmapsto 9\times 4[/tex]
[tex]\\ \Large\sf\longmapsto 36miles [/tex]
Find Easy question For yall
Answer:
V = 64.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos V = adj side/ hypotenuse
cos V = 3/7
Taking the inverse cos of each side
cos ^-1 ( cos V) = cos ^-1 (3/7)
V=64.62306
Rounding to the nearest tenth
V = 64.6
Answer:
V=64.6
Step-by-step explanation:
the same thing as other guy, lol
If we add one unit to the length (l) of a rectangle that has width (w), what is its new area (NA) in terms of its old area (A)?
NA = A x w
NA = A + w
NA = A + l
NA = A
NA = A + W
By adding one unit to length, we increase the overall area by the width of the rectangle. This is because the formula for the area of a rectangle is A = l x w. So, NA = (l + 1) x w = (l x w) + w = A + w.
How many unit cubes are on each layer of the cube?
6
3
12
9
Answer:
6
Step-by-step explanation:
Remember: Each layer has 6 cubes. Step 3 Count the cubes. cubes Multiply the base and the height to check your answer. So, the volume of Jorge's rectangular prism is cubic centimeters. if wrong very sorry
Answer:
9
Step-by-step explanation:
took the test
!!!Please help!!!
What is the following quotient?
96
B
O 2.13
4.
2.V22
12
plz help with this:)
9514 1404 393
Answer:
-4
Step-by-step explanation:
The point (x, y) = (0, 0) is on the line, so it represents a proportional relation. Any ratio of y to x will be the slope. The choice that makes this computation easiest is ...
x = 1, y = -4
y/x = -4/1 = -4
The slope of the line is -4.
True or False: A line perpendicular to x=7 has a slope of 0
Answer:
True, I believe
Step-by-step explanation:
Answer:
The answer is yes because its horizontal
If $500 were deposited into an account paying 5% interest, compound monthly, how much would be in the account in 4 years?
Please show me proper work and a good explanation on how you got said answer.
Answer:
610.48
Step-by-step explanation:
The formula for compound interest is
A = P(1+r/n) ^nt where
A is the amount in the account
P is the principle
r is the interest rate
n is the number of times the interest is compounded per year
t is the time in years
A = 500(1+.05/12) ^12*4
A = 500(1+.0041666666) ^48
A = 500(1.0041666666) ^48
A = 500*1.220895355
A =610.4476775
Rounding to the nearest cent
A = 610.48
Name
MATH 1342
Lab 12 - Ch.10 - Hypothesis Testing
Critical Thinking, Communication Skills, Empirical/Quantitative Skills
2. A machine is designed to fill jars with 16 ounces of coffee. A quality control inspector
suspects that the machine is not filling the jar with the full 16 ounces. A sample of 20 jars has
a mean of 15.8 ounces and a standard deviation of 0.32 ounce. Is there enough evidence to
support the inspector's claim that the mean number of ounces of coffee in the jars is less than
16? Use a = .05.
1.
Hand H
2.
3.
Critical value(s)
4.
Graph
5.
Test Statistic
6.
P-value
7.
Reject H. or Do Not Reject H.
8.
Conclusion
1 & 2:The null and alternate hypotheses are
H0 : u = 16 vs Ha: u < 16
The null hypothesis is that the mean is 16 ounces against the claim that it is less than 16 ounces.
3:The significance level is 0.05
4. Critical Value:
The critical region for significance level = 0.05 for one tailed test is z< ± 1.645
5.The test statistic
The test statistic to be used is
z= x- μ/σ/√n
z= 15.8-16/0.32/√20
z= -0.2/ 0.071556
z= -2.7950
6. The p-value ≈ 0.00259 for one tailed test.
7. Reject H0
Since the calculated value of z= -2.7950 is less than z∝= -1.645 we reject the null hypothesis.
8. Conclusion:
There is enough evidence to support the inspector's claim that the mean number of ounces of coffee in the jars.
https://brainly.com/question/15980493
Graph
If 2x - 5y – 7 = 0 is perpendicular to the line ax - y - 3 = 0 what is the value of a ?
A) a =2/3
B) a =5/2
C) a = -2/3
D) a = -5/2
Answer:
D) a = - 5/2
Step-by-step explanation:
2x -5y - 7 = 0
5y = 2x - 7
y = 2/5 x - 7
the slope of this line is therefore 2/5 (factor of x).
the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.
WILL GIVE BRAINIEST PLEASE WRITE IN ''f(x) = a(b)^x'' ORDERAn industrial copy machine has the ability to reduce image dimensions by a certain percentage each time it copies. A design began with a length of 16 inches, represented by the point (0,16). After going through the copy machine once, the length is 12, represented by the point (1,12).
Answer:
f(x) = 16*0.75^x
Step-by-step explanation:
first off let's use this coordinate (the one given) :
(0,16)
let's substitute this into the equation with x being 0 and f(x) being 16
16 = a*b^0
*anything to the power of 0 is 1*
so:
a = 16
now use the second coordinate :
(1,12)
and do the same by substituting 1 for x and 12 for f(x), we also know what 'a' is:
12 = 16*b^1
12 = 16 * b
b = 3/4
so :
f(x) = 16*0.75^x
Answer:
f(x) = 16(.75)^x
Step-by-step explanation:
How to multiply
(c+7)(3x-2)
Answer:
3cx - 2c + 21x - 14
Step-by-step explanation:
( c + 7 ) ( 3x - 2 )
= c ( 3x - 2 ) + 7 ( 3x - 2 )
= c ( 3x ) - c ( 2 ) + 7 ( 3x ) - 7 ( 2 )
= 3cx - 2c + 21x - 14
Answer:
3cx-2c+21x-14
Step-by-step explanation:
try to expand it by multiplying everything in the first brackets by every thing in the second brackets.
c(3x-2)+7(3x-2)
3cx-2c+21x-14
I hope this helps
If a seed is planted, it has a 90% chance of growing into a healthy plant.
If 6 seeds are planted, what is the probability that exactly 2 don't grow?
Answer:
[tex]\displaystyle\frac{19,683}{200,000}\text{ or }\approx 9.84\%[/tex]
Step-by-step explanation:
For each planted seed, there is a 90% chance that it grows into a healthy plant, which means that there is a [tex]100\%-90\%=10\%[/tex] chance it does not grow into a healthy plant.
Since we are planting 6 seeds, we want to choose 2 that do not grow and 4 that do grow:
[tex]\displaystyle \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}[/tex]
However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):
[tex]\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15[/tex]
Therefore, we have:
[tex]\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%[/tex]
Answer:
[tex] {?}^{?} However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):
\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15(26)=2!6⋅5=230=15
Therefore, we have:
\begin{gathered}\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%\end{gathered}P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅(26),P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅15,P(exactly 2 don’t grow)=200,00019,683≈9.84%
[/tex]
morgan got 17/20 of the questions on a science test correct. what percent of the questions did she get correct?
Answer:
85%
Step-by-step explanation:
100% = 20
1% = 100%/100 = 20/100 = 0.2
now, how often does 1% fit into the actual result of 17 ? and that tells us how many %.
17/0.2 = 17/ 1/5 = 17/1 / 1/5 = 5×17 / 1 = 5×17 = 85%
Answer:
17/20×100=
85%
=85%
hope this helps
There is a path of width 2.5 m inside around a square garden of length 45m.
(a) Find the area of the path.
(b) How many tiles will be required to pave in the path by the square tiles of length 0.5m? Find it.
Help ! 도와주세요, 제발 :(
Answer:
2.5+2.5+45+45
=95.0m
therefore area of the square= 95.0m
45m×0.5=45.5÷95=
Step-by-step explanation:
2.5m
2.5 m tiles are required
[tex]area = 2.5 \times 45 = 192.5 \: squared \: cenimetre \\ \\ no \: of \: tiles = 0.5 \times 0.5 = 0.25 \\ 192.5 \div 0.25 = 770tiles[/tex]
What is the area of this figure?
Answer:
22
Step-by-step explanation:
(5x2) + (3x2) + (3x2)
22 square units
Answer from Gauthmath
F(x) = x +3; G(x) = 2x^2 -4 Find (f*g)(x)
9514 1404 393
Answer:
(f·g)(x) = 2x^3 +6x^2 -4x -12
Step-by-step explanation:
The distributive property is used to find the expanded form of the product.
(f·g)(x) = f(x)·g(x) = (x +3)(2x^2 -4) = x(2x^2 -4) +3(2x^2 -4)
= 2x^3 -4x +6x^2 -12
(f·g)(x) = 2x^3 +6x^2 -4x -12
Write the inequality shown in this graph.
Answer:
y > -1/2 x + 4
Step-by-step explanation:
Equation of a line : (y-y1)/(y2-y1) = (x-x1)/(x2-x1)
(y-4)/(2-4)= (x-0)/(4-0)
(y-4)/-2 = x/4
(-y+4)/2 = x/4
-y+4 = 1/2 x
-y = 1/2 x - 4
y = -1/2 x + 4
the solutions of the inequality are the points above this line, so
y > -1/2 x + 4
Solve for x
X/6 = 10
A) X = 4
B) X = 10
C) X = 16
D) X = 60
hi
x/6 = 10
In a equation , you can use every math operation you know as long as you do the same thing on both sides.
Here we have x/6 = 10
But what I want is x .
Here X is split in 6. So I 'm going to multiplicate all by 6 to find the original amount of X
In bold operation that are often not written but that you must understand to do that kind of exercices.
So : x/6 = 10
(x/6) *6 = 10 *6
6x/6 = 60
x = 60
I need help ASAP please
Answer:
yes how can I help you???
