Answer:
A
Step-by-step explanation:
The problem with this kind of question is that the author tells you what you should see in that sentence. The dogs experienced fear. Any other answer you suggest is not what the author means. So you are guessing. It is adding to the notion that the arctic is not a friendly place and you cannot go sunbathing in and be comfortable in the middle of winter.
A is as good an answer as you are likely to get, but I don't think it's right.
An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes.
Required:
Let x̄ be the sample average lifetime of 64 Duracell and ȳ be the sample average lifetime of 64 Eveready Energizer batteries. What is the mean value of x̄- ȳ(i.e., where is the distribution of -centered)?
Answer:
The mean is of -0.4 hours.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Mean of the sample of 64 Duracell:
By the Central Limit Theorem, 4.1 hours.
Mean of the sample of 64 Eveready:
By the Central Limit Theorem, 4.5 hours.
Mean of the difference?
Subtraction of normal variables, so we subtract the means.
4.1 - 4.5 = -0.4
The mean is of -0.4 hours.
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]
[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]
-27
Which of the following is equivalent to
نان-۴
?
N
O
(197)
NI
12
22
(22)
2².2
Answer:
3rd option
Step-by-step explanation:
(1/2)^-2t
= (2^-1)^-2t
= 2^2t
= (2^2)^t
Answered by GAUTHMATH
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.
18 Geometry question: Use an algebraic equation to find the measure of each angle that is representative in terms of X
Answer:
12x - 28° = 116°
7x + 32° = 116°
Step-by-step explanation:
12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.
Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:
12x - 28° = 7x + 32°
Collect like terms
12x - 7x = 28 + 32
5x = 60
Divide both sides by 5
5x/5 = 60/5
x = 12
✔️12x - 28°
Plug in the value of x
12(12) - 28
= 144 - 28
= 116°
✔️7x + 32°
7(12) + 32
= 84 + 32
= 116°
2 balloons and 3 cakes cost £29.
6 balloons and 4 cakes cost £52.
Find the cost of one of each.
1 balloon is £
1 cake is £
Answer:
1 balloon is 4/ 1 cake is 7
Step-by-step explanation:
2 balloons is 8/ 3 cakes are 21 add together you get 29.
!!!Please help!!!
What is the following quotient?
96
B
O 2.13
4.
2.V22
12
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]
A 90% confidence interval is (35 45). What is the margin of error?
A. 5
B.4.5
C.9
D.10
Answer:
option A 5
I hope it's correct
.....
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
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.
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
What is the area of this figure?
Answer:
22
Step-by-step explanation:
(5x2) + (3x2) + (3x2)
22 square units
Answer from Gauthmath
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
Find the Sample size for 99% confidence level with a margin of error of 4% and p unknown.
Answer:
za/2: Divide the confidence level by two, and look that area up in the z-table: .95 / 2 = 0.475. ...
E (margin of error): Divide the given width by 2. 6% / 2. ...
: use the given percentage. 41% = 0.41. ...
: subtract. from 1.
Please help me with this
Answer:
[tex]\frac{121}{14} = 8\frac{9}{14}[/tex]
Step-by-step explanation:
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 :}
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
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.
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.
Tuition. The tuition at a community college increased from $2,500 to $2,650 per semester. What was the percent of increase in the tuition?
Answer:
6 percent increase
Step-by-step explanation:
2650 divided by 2500 gives you 1.06 which means if 2500 is 100 percent 2650 would be 106 percent so the answer is a 6 percent increase
Answer:
6%
Step-by-step explanation:
another way of doing this type of calculation is...
NEW-OLD = 2650-2500 = 150 = .06 = 6%
OLD 2500 2500
2+4? I am omisha please give me answer
Answer:
6
Step-by-step explanation:
2+4 = 6
..............
Answer:
Here is your answer omisha
2+4=6
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
4 times a certain number less two times that's the same number is 10 what is the number
Answer:
The number is 5
Step-by-step explanation:
Let the number be x,
Four times the number= 4x
two times the same number= 2x
So we have ,
4x – 2x = 10
2x = 10
x = 5
Therefore the number is 5
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
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:
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
The management of a large airline wants to estimate the average time after takeoff taken before the crew begins serving snacks and beverages on their flights. Assuming that management has easy access to all of the information that would be required to select flights by each proposed method, which of the following would be reasonable methods of stratified sampling?
a. For each day of the week, randomly select 5% of all flights that depart on that day of the week.
b. Divide all flights into the following 4 groups on the basis of scheduled departure time: before 9:00 am 9:00 am to 1:00 pm. 1:00 pm to 5:00 pm, and after 5:00 pm. Randomly select 5% of the flights in each group.
c. For each crew member the airline employs, randomly select 5 flights that the crew member works.
d. Divide the airports from which the airline's fights depart into 4 regions: Northeast, Northwest Southwest and Southeast. Randomly select 5% of all flights departing from airports in each region
Answer:
The answer is "Option a, Option b, and Option d".
Step-by-step explanation:
In the given question it is used to stratifying the sampling if the population of this scenario it flights takes off when it is divided via some strata.
In option a, In this case, it stratified the sampling, as the population of planes taking off has been divided into the days of the week. In option b, It also used as the case of stratified sampling. In options c, it is systematic sampling, that's why it is wrong. In option d, It is an example of stratifying the sampling.Answer:
For each day of the week, randomly select 5% of all flights that depart on that day of the week.
Divide all flights into the following 4 groups on the basis of scheduled departure time: before 9:00 am, 9:00 am to 1:00 pm, 1:00 pm to 5:00 pm, and after 5:00 pm. Randomly select 5% of the flights in each group.
Divide the airports from which the airline's flights depart into 4 regions: Northeast, Northwest, Southwest, and Southeast. Randomly select 5% of all flights departing from airports in each region.
Step-by-step explanation:
ll sampling methods that divide the flights into a small number of mutually exclusive categories are appropriate. These methods include all flights on the basis of a characteristic that might be associated with the variable being investigated and randomly selects a proportionate number of flights from each group.
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
