Answer:
12.04
Step-by-step explanation:
Because the questions are true and false, that is, there are only two answer options, therefore, you have a success probability = 1/2 = 0.5
The standard deviation can be calculated as follows:
Standard Deviation = (n*p* (1-p)] ^ (1/2)
replacing we have:
SD = (290 * (1-0.5)] ^ (1/2) = 12.04
That is, the standard deviation is 12.04
The null hypothesis for this ANOVA F test is: the population mean load failures for the three etch times are all different the population mean load failure is lowest for the 15‑second condition and highest for 60‑second condition at least one population mean load failure differs the sample mean load failure is lowest for the 15‑second condition and highest for 60‑second condition the sample mean load failures for the three etch times are all different the population mean load failures for the three etch times are all equal
Answer:
The population mean load failures for the three etch times are all equal
Step-by-step explanation:
For an ANOVA F test, the null hypothesis always assumes that mean which is also the average value of the dependent variable which is continuously are the same/ there is no difference in the means. The alternative is to test against the null and it is always the opposite of the null hypothesis.
Carlos is almost old enough to go to school! Based on where he lives, there are 666 elementary schools, 333 middle schools, and 222 high schools that he has the option of attending.
Answer:
There are 36 education paths available to Carlos based on the schools around where he lives.
Step-by-step explanation:
Complete Question
Carlos is almost old enough to go to school. Based on where he lives, there are 6 elementary schools, 3 middle schools, and 2 high schools that he has the option of attending. How many different education paths are available to Carlos? Assume he will attend only one of each type of school.
Solution
We can use mathematics or manually writing out the possible combinations of elementary, middle and high school that Carlos can attend.
Using Mathematics
There are 6 elementary schools, meaning Carlos can make his choice in 6 ways.
There are 3 middle schools, meaning Carlos can make his choice in 3 ways.
Together with the elementary school choice, Carlos can make these two choices in 6 × 3 ways.
There are 2 high schools, Carlos can make his choice in 2 ways.
Combined with the elementary and middle school choices, Carlos can make his choices in 6×3×2 ways = 36 ways.
Manually
If we name the 6 elementary schools letters A, B, C, D, E and F.
Name the 3 middle schools letters a, b and c.
Name the 2 high schools numbers 1 and 2.
The different combinations of the 3 choices include
Aa1, Aa2, Ab1, Ab2, Ac1, Ac2
Ba1, Ba2, Bb1, Bb2, Bc1, Bc2
Ca1, Ca2, Cb1, Cb2, Cc1, Cc2
Da1, Da2, Db1, Db2, Dc1, Dc2
Ea1, Ea2, Eb1, Eb2, Ec1, Ec2
Fa1, Fa2, Fb1, Fb2, Fc1, Fc2
Evident now that there are 36 ways in which the 3 stages of schools can be combined. There are 36 education paths available to Carlos based on the schools around where he lives assuming that he will attend only one of each type of school.
Hope this Helps!!!
Answer:
36 education paths
Step-by-step explanation:
Hope this helps!
What is the area of this triangle?
Answer:
Option (D)
Step-by-step explanation:
Formula for the area of a triangle is,
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
For the given triangle ABC,
Area of ΔABC = [tex]\frac{1}{2}(\text{AB})(\text{CD})[/tex]
Length of AB = [tex](y_2-y_1)[/tex]
Length of CD = [tex](x_3-x_1)[/tex]
Now area of the triangle ABC = [tex]\frac{1}{2}(y_2-y_1)(x_3-x_1)[/tex]
Therefore, Option (D) will be the answer.
When planning a more strenuous hike, Nadine figures that she will need at least 0.6 liters of water for each hour on the trail. She also plans to always have at least 1.25 liters of water as a general reserve. If x represents the duration of the hike (in hours) and y represents the amount of water needed (in liters) for a hike, the following inequality describes this relation: y greater or equal than 0.6 x plus 1.25 Which of the following would be a solution to this situation?
Answer:
The solution for this is:
y = (0.6 * x) + 1.25
Hope it helps! :)
Answer:
Having 3.2 liters of water for 3 hours of hiking
Step-by-step explanation:
If x represents the number of hours and y represents the number of liters of water, then we can plug the possible solutions into our inequality to see which solution(s) work.
The first option is having 3 liters of water for 3.5 hours of hiking. We will plug 3 in for y and 3.5 in for x:
y > 0.6x + 1.25
3 > 0.6(3.5) + 1.25
3 > 3.35
But since 3 is not greater than 3.35, this does not work.
The next option is having 2 liters of water for 2.5 hours of hiking:
2 > 0.6(2.5) + 1.25
2 > 2.75
But 2 is not greater than 2.75, so this does not work.
Option c is having 2.3 liters of water for 2 hours of hiking:
2.3 > 0.6(2) + 1.25
2.3 > 2.45
Since 2.3 is not greater than 2.45, this solution does not work.
The last option is having 3.2 liters of water for 3 hours of hiking:
3.2 > 0.6(3) + 1.25
3.2 > 3.05
3.2 IS greater than 3.05, so this solution works!
. A bag contains 6 red and 3 black chips. One chip is selected, its color is recorded, and it is returned to the bag. This process is repeated until 5 chips have been selected. What is the probability that one red chip was selected?
Answer:
The probability that one red chip was selected is 0.0053.
Step-by-step explanation:
Let the random variable X be defined as the number of red chips selected.
It is provided that the selections of the n = 5 chips are done with replacement.
This implies that the probability of selecting a red chip remains same for each trial, i.e. p = 6/9 = 2/3.
The color of the chip selected at nth draw is independent of the other selections.
The random variable X thus follows a binomial distribution with parameters n = 5 and p = 2/3.
The probability mass function of X is:
[tex]P(X=x)={5\choose x}\ (\frac{2}{3})^{x}\ (1-\frac{2}{3})^{5-x};\ x=0,1,2...[/tex]
Compute the probability that one red chip was selected as follows:
[tex]P(X=1)={5\choose 1}\ (\frac{2}{3})^{1}\ (1-\frac{2}{3})^{5-1}[/tex]
[tex]=5\times\frac{2}{3}\times \frac{1}{625}\\\\=\farc{2}{375}\\\\=0.00533\\\\\approx 0.0053[/tex]
Thus, the probability that one red chip was selected is 0.0053.
Answer:
0.0412
Step-by-step explanation:
Total chips = 6 red + 3 black chips
Total chips=9
n=5
Probability of (Red chips ) can be determined by
=[tex]\frac{6}{9}[/tex]
=[tex]\frac{2}{3}[/tex]
=0.667
Now we used the binomial theorem
[tex]P(x) = C(n,x)*px*(1-p)(n-x).....Eq(1)\\ putting \ the \ given\ value \ in\ Eq(1)\ we \ get \\p(x=1) = C(5,1) * 0.667^1 * (1-0.667)^4[/tex]
This can give 0.0412
In the fall semester of 2009, the average Graduate Management Admission Test (GMAT) of the students at a certain university was 500 with a standard deviation of 90. In the fall of 2010, the average GMAT was 570 with a standard deviation of 85.5. Which year's GMAT scores show a more dispersed distribution
Answer:
Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution
Step-by-step explanation:
To verify how dispersed a distribution is, we find it's coefficient of variation.
Coefficient of variation:
Mean of [tex]\mu[/tex], standard deviation of [tex]\sigma[/tex]. The coefficient is:
[tex]CV = \frac{\sigma}{\mu}[/tex]
Which year's GMAT scores show a more dispersed distribution
Whichever year has the highest coefficient.
2009:
Mean of 500, standard deviation of 90. So
[tex]CV = \frac{90}{500} = 0.18[/tex]
2010:
Mean of 570, standard deviation of 85.5. So
[tex]CV = \frac{85.5}{570} = 0.15[/tex]
Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution
2009's GMAT scores show a more dispersed distribution.
Given that in 2009: Mean = 500 and standard deviation = 90.
In 2010: Mean = 570 and standard deviation = 85.5.
If the standard deviation is higher then the scores will be more dispersed.
Note that: 90 > 85.5. And 90 corresponds to 2009.
So, 2009's GMAT scores show a more dispersed distribution.
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Please answer this correctly
Answer:
6 pizzas
Step-by-step explanation:
At least 10 and fewer than 20 makes it 10-19
So,
10-19 => 6 pizzas
6 pizzas have at least 10 pieces of pepperoni but fewer than 20 pieces of pepperoni.
The histogram shows the number of miles driven by a sample of automobiles in New York City.
What is the minimum possible number of miles traveled by an automobile included in the histogram?
Answer:
0 miles
Step-by-step explanation:
The computation of the minimum possible number of miles traveled by automobile is shown below:
As we can see that in the given histogram it does not represent any normal value i.e it is not evenly distributed moreover, the normal distribution is symmetric that contains evenly distribution data
But this histogram shows the asymmetric normal distribution that does not have evenly distribution data
Therefore the correct answer is 0 miles
Answer:
2,500
That is your correct answer.
please - i got this wrong so plz help
Answer:
Area = 108 cm^2
Perimeter = 44 cm
Step-by-step explanation:
Area, -->
24 + 30 + 24 + 30 -->
24(2) + 30(2)
48 + 60 = 108 cm^2
108 = area
10 + 12 + 10 + 12, -->
10(2) + 12(2) = 44 cm
44 = perim.
Hope this helps!
Answer:
Step-by-step explanation:
Draw the diagram.
This time put in the only one line for the height. That is only 1 height is 8 cm. That's it.
The base is 6 + 6 = 12 cm.
The slanted line is 10 cm
That's all your diagram should show. It is much clearer without all the clutter.
Now you are ready to do the calculations.
Area
The Area = the base * height.
base = 12
height = 8
Area = 12 * 8 = 96
Perimeter.
In a parallelagram the opposite sides are equal to one another.
One set of sides = 10 + 10 = 20
The other set = 12 + 12 = 24
Both sets = 20 + 24
Both sets = 44
Answer
Area = 96
Perimeter = 44
In d e f, d f equals 16 and F equal 26. Find Fe to the nearest tenth
Answer:
14.4 units
Step-by-step explanation:
In Trigonometry
[tex]\cos \theta =\frac{Adjacent}{Hypotenuse}\\[/tex]
In Triangle DEF,
[tex]\cos F =\dfrac{EF}{DF}\\\cos 26^\circ =\dfrac{EF}{16}\\EF=16 \times \cos 26^\circ\\=14.4$ units (correct to the nearest tenth).[/tex]
Let f(x)= x^3 −6x^2+11x−5 and g(x)=4x^3−8x^2−x+12. Find (f−g)(x). Then evaluate the difference when x=−3 x=−3 .
Answer: (f-g)(x)= -138
Step-by-step explanation:
Solve for X. Show all work
Answer:
About 11.77 centimeters
Step-by-step explanation:
By law of sines:
[tex]\dfrac{50}{\sin 62}=\dfrac{x}{\sin 12} \\\\\\x=\dfrac{50}{\sin 62}\cdot \sin 12\approx 11.77cm[/tex]
Hope this helps!
Solve: x + 7 < 3 plsss help me
Answer:
The answer is -4.
Step-by-step explanation:
You should get this answer if you do 3 - 7.
The cost of unleaded gasoline in the Bay Area once followed a normal distribution with a mean of $4.74 and a standard deviation of $0.16. Sixteen gas stations from the Bay area are randomly chosen. We are interested in the average cost of gasoline for the 15 gas stations. What is the approximate probability that the average price for 15 gas stations is over $4.99?
Answer:
Approximately 0% probability that the average price for 15 gas stations is over $4.99.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 4.74, \sigma = 0.16, n = 16, s = \frac{0.16}{\sqrt{16}} = 0.04[/tex]
What is the approximate probability that the average price for 15 gas stations is over $4.99?
This is 1 subtracted by the pvalue of Z when X = 4.99. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.99 - 4.74}{0.04}[/tex]
[tex]Z = 6.25[/tex]
[tex]Z = 6.25[/tex] has a pvalue very close to 1.
1 - 1 = 0
Approximately 0% probability that the average price for 15 gas stations is over $4.99.
What is the simplified form of the expression 3cubed root b^2
Answer:
Step-by-step explanation:
[tex](\sqrt{b^{2}})^{3}=b^{3}\\\\[/tex]
or If it is
[tex]\sqrt[3]{b^{2}} =(b^{2})^{\frac{1}{3}}=b^{2*\frac{1}{3}}=b^{\frac{2}{3}}[/tex]
Please help me or assist me in answering this Thank you 5 2/3 X 6 7/8
Answer: 38 23/24
Step-by-step explanation:
Turn the mixed numbers into improper fractions
5 * 3 = 15
15 + 2 = 17
17/3
————————
6 * 8 = 48
48 + 7 = 55
55/8
————————
Now multiply the improper fractions
17/3 * 55/8
17 * 55 = 935
3 * 8 = 24
Divide 935 by 24 to get the answer as a mixed number.
935 / 24 = 38.95833
0.95833/1 = 23/24
935/24 as a mixed number is 38 23/24
Answer: 119 / 4
Step-by-step explanation:
5 2/3 x 6 7/8
= 17/3 x 6 x 7/8
= 17 x 2 x 7/8
= 17 x 2 x 7/8
= 17 x 7/4
= 119 / 4
The equation f(x) is given as x2_4=0. Considering the initial approximation at
x0=6 then the value of x1 is given as
Select one:
O A. 10/3
O B. 7/3
O C. 13/3
O D. 4/3
Answer:
The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.
Step-by-step explanation:
This exercise represents a case where the Newton-Raphson method is used, whose formula is used for differentiable function of the form [tex]f(x) = 0[/tex]. The expression is now described:
[tex]x_{n+1} = x_{n} - \frac{f(x_{n})}{f'(x_{n})}}[/tex]
Where:
[tex]x_{n}[/tex] - Current approximation.
[tex]x_{n+1}[/tex] - New approximation.
[tex]f(x_{n})[/tex] - Function evaluated in current approximation.
[tex]f'(x_{n})[/tex] - First derivative of the function evaluated in current approximation.
If [tex]f(x) = x^{2} - 4[/tex], then [tex]f'(x) = 2\cdot x[/tex]. Now, given that [tex]x_{0} = 6[/tex], the function and first derivative evaluated in [tex]x_{o}[/tex] are:
[tex]f(x_{o}) = 6^{2} - 4[/tex]
[tex]f(x_{o}) = 32[/tex]
[tex]f'(x_{o})= 2 \cdot 6[/tex]
[tex]f'(x_{o}) = 12[/tex]
[tex]x_{1} = x_{o} - \frac{f(x_{o})}{f'(x_{o})}[/tex]
[tex]x_{1} = 6 - \frac{32}{12}[/tex]
[tex]x_{1} = 6 - \frac{8}{3}[/tex]
[tex]x_{1} = \frac{18-8}{3}[/tex]
[tex]x_{1} = \frac{10}{3}[/tex]
The value of [tex]x_{1}[/tex] is given by [tex]\frac{10}{3}[/tex]. Hence, the answer is A.
To collect data on the signal strengths in a neighborhood, Briana must drive from house to house
and take readings. She has a graduate student, Henry, to assist her. Briana figures it would take her
12 hours to complete the task working alone, and that it would take Henry 18 hours if he completed
the task by himself.
Answer: Working together, they can complete the task in 7 hours and 12 minutes.
Step-by-step explanation:
Ok, Briana needs 12 hours to complete the task.
Then we can find the ratio of work over time as:
1 task/12hours = 1/12 task per hour.
This means that she can complete 1/12 of the task per hour.
Henry needs 18 hours to complete the task, then his ratio is:
1 task/18 hours = 1/18 task per hour.
This means that he can complete 1/18 of the task in one hour.
If they work together, then the ratios can be added:
R = 1/12 + 1/18 = 18/(12*18) + 12/(18*12) = 30/216
we can reduce it to:
R = 15/108 = 5/36
So, working together, in one hour they can complete 5/36 of the task, now we can find the number of hours needed to complete the task as:
(5/36)*x = 1 task
x = 36/5 hours = 7.2 hours
knowing that an hour is 60 minutes, then 0.2 of an hour is 60*0.2 = 12 minutes.
then x = 7 hours and 12 minutes.
Show all work to identify the asymptotes and zero of the faction f(x) = 4x/x^2 - 16.
Answer:
asymptotes: x = -4, x = 4zeros: x = 0Step-by-step explanation:
The vertical asymptotes of the rational expression are the places where the denominator is zero:
x^2 -16 = 0
(x -4)(x +4) = 0 . . . . . true for x=4, x=-4
x = 4, x = -4 are the equations of the vertical asymptotes
__
The zeros of a rational expression are the places where the numerator is zero:
4x = 0
x = 0 . . . . . . divide by 4
Multi step equation a-2+3=-2
Answer:
-3
Step-by-step explanation:
a-2+3=-2
-3 -3
a-2=-5
+2 +2
a=-3
// have a great day //
Answer:
a = -3
Step-by-step explanation:
a - 2 + 3 = -2
Add like terms.
a + 1 = -2
Subtract 1 on both sides.
a = -2 - 1
a = -3
The value of a in the equation is -3.
I need help pleaseee!
Step-by-step explanation:
we can use o as the center of the circle
OB=13
EB=12
OE=?
OE^2 +EB^2=OB^2
OE^2+12^2=13^2
OE^2=169-144
OE=
√25
OE=5
OC=OE+EC
EC =13-5
EC=8
What is the measure of AC?
Enter your answer in the box.
Answer:
21
Step-by-step explanation:
Since angle ABC is an inscribed angle, its measure is half that of arc AC. Therefore:
[tex]2(3x-1.5)=3x+9 \\\\6x-3=3x+9 \\\\3x-3=9 \\\\3x=12 \\\\x=4 \\\\AC=3(4)+9=12+9=21[/tex]
Hope this helps!
Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is, 21°.
What is the Inscribed Angle theorem?We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.
Given that,
The inscribed angle is, (3x - 1.5)
And the Intercepted arc AC is, (3x + 9)
So, We get;
(3x - 1.5) = 1/2 (3x + 9)
2 (3x - 1.5) = (3x + 9)
6x - 3 = 3x + 9
3x = 9 + 3
3x = 12
x = 4
Thus, The Intercepted arc AC is,
(3x + 9) = 3×4 + 9
= 21°
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I. In the testing of a new production method, 18 employees were selected randomly and asked to try the new method. The sample mean production rate for the 18 employees was 80 parts per hour and the sample standard deviation was 10 parts per hour. Provide 90% confidence intervals for the populations mean production rate for the new method, assuming the population has a normal probability distribution.
Answer:
The 90% confidence interval for the mean production rate fro the new method is (75.9, 84.1).
Step-by-step explanation:
We have to calculate a 90% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=80.
The sample size is N=18.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{10}{\sqrt{18}}=\dfrac{10}{4.24}=2.36[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=18-1=17[/tex]
The t-value for a 90% confidence interval and 17 degrees of freedom is t=1.74.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.74 \cdot 2.36=4.1[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 80-4.1=75.9\\\\UL=M+t \cdot s_M = 80+4.1=84.1[/tex]
The 90% confidence interval for the mean production rate fro the new method is (75.9, 84.1).
anyone please answer this
Answer:
21
Step-by-step explanation:
1/5 of 30 is 6
10% of 30 is 3
3+6=9
30-9=21
which is 7/10
Answer:
Simon has 7/10 of the cakes left.
The life of an electric component has an exponential distribution with a mean of 8.9 years. What is the probability that a randomly selected one such component has a life more than 8 years? Answer: (Round to 4 decimal places.)
Answer:
[tex] P(X>8)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] F(x) = 1- e^{-\lambda x}[/tex]
And if we use this formula we got:
[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]
Step-by-step explanation:
For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:
[tex]X \sim exp (\lambda =\frac{1}{8.9}) [/tex]
And we want to find the following probability:
[tex] P(X>8)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] F(x) = 1- e^{-\lambda x}[/tex]
And if we use this formula we got:
[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]
A manager bought 12 pounds of peanuts for $30. He wants to mix $5 per pound cashews with the peanuts to get a batch of mixed nuts that is worth $4 per pound. How many pounds of cashews are needed
Answer:
18 pounds of cashews are needed.
Step-by-step explanation:
Given;
A manager bought 12 pounds of peanuts for $30.
Price of peanut per pound P = $30/12 = $2.5
Price of cashew per pound C = $5
Price of mixed nut per pound M = $4
Let x represent the proportion of peanut in the mixed nut.
The proportion of cashew will then be y = (1-x), so;
xP + (1-x)C = M
Substituting the values;
x(2.5) + (1-x)5 = 4
2.5x + 5 -5x = 4
2.5x - 5x = 4 -5
-2.5x = -1
x = 1/2.5 = 0.4
Proportion of cashew is;
y = 1-x = 1-0.4 = 0.6
For 12 pounds of peanut the corresponding pounds of cashew needed is;
A = 12/x × y
A = 12/0.4 × 0.6 = 18 pounds
18 pounds of cashews are needed.
multiply and remove all perfect square roots. Assume y is positive. √12
Answer:
2√3
Step-by-step explanation:
Step 1: Find perfect square roots
√4 x √3
Step 2: Convert
2 x √3
Step 3: Answer
2√3
Solve for x. 9x-2c=k
A grasshopper sits on the first square of a 1×N board. He can jump over one or two squares and land on the next square. The grasshopper can jump forward or back but he must stay on the board. Find the least number n such that for any N ≥ n the grasshopper can land on each square exactly once.
Answer:
n=N-1
Step-by-step explanation:
You can start by imagining this scenario on a small scale, say 5 squares.
Assuming it starts on the first square, the grasshopper can cover the full 5 squares in 2 ways; either it can jump one square at a time, or it can jump all the way to the end and then backtrack. If it jumps one square at a time, it will take 4 hops to cover all 5 squares. If it jumps two squares at a time and then backtracks, it will take 2 jumps to cover the full 5 squares and then 2 to cover the 2 it missed, which is also 4. It will always be one less than the total amount of squares, since it begins on the first square and must touch the rest exactly once. Therefore, the smallest amount n is N-1. Hope this helps!
The smallest value of n is N-1.
What is a square?Square is a quadrilateral of equal length of sides and each angle of 90°.
Here given that there are 1×N squares i.e. N numbers of squares in one row.
The grasshopper can jump either one square or two squares to land on the next square.
Let's assume the scenario of 5 squares present in a row.
Let the grasshopper starts from the first square,
so the grasshopper can cover the full 5 squares in 2 methods;
one method is that it will jump one square at a time and reach at last square.
another method is it will jump all the squares to the finish and then backtrace.
If the grasshopper jumps one square at a time, it will take 4 jumps to cover all 5 squares.
Similarly, If a grasshopper jumps two squares at a time and then backtrace, it will take 2 jumps to reach the 5th square and then it will jump 1 square and then 2 squares to cover the 2 squares it missed, for which the number jump is also 4.
From the above it is clear that the number of jumps will always be one less than the total number of squares if the grasshopper begins from the first square and touch every square exactly once.
Therefore, the smallest value of n is N-1.
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According to a report an average person watched 4.55 hours of television per day in 2005. A random sample of 20 people gave the following number of hours of television watched per day for last year. At the 10% significance level, do the data provide sufficient evidence to conclude that the amount of television watched per day last year by the average person differed from that in 2005? 1.0 4.6 5.4 3.7 5.2 1.7 6.1 1.9 7.6 9.1 6.9 5.5 9.0 3.9 2.5 2.4 4.7 4.1 3.7 6.2 a. identify the claim and state and b. find the critical value(s) and identify the rejection region(s), c. find the standardized test statistic Sketch a graph decide whether to reject or fail to reject the null hypothesis, and d. interpret the decision in the context of the original claim. e. Obtain a 95%confidence interval
Answer:
a. The claim is that the amount of television watched per day last year by the average person differed from that in 2005.
b. The critical values are tc=-1.729 and tc=1.729.
The acceptance region is defined by -1.792<t<1.729. See the picture attached.
c. Test statistic t=0.18.
The null hypothesis failed to be rejected.
d. At a significance level of 10%, there is not enough evidence to support the claim that the amount of television watched per day last year by the average person differed from that in 2005.
e. The 95% confidence interval for the mean is (2.29, 7.23).
Step-by-step explanation:
We have a sample of size n=20, which has mean of 4.76 and standard deviation of 5.28.
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{20}(1+4.6+5.4+. . .+6.2)\\\\\\M=\dfrac{95.2}{20}\\\\\\M=4.76\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{19}((1-4.76)^2+(4.6-4.76)^2+(5.4-4.76)^2+. . . +(6.2-4.76)^2)\\\\\\s=\dfrac{100.29}{19}\\\\\\s=5.28\\\\\\[/tex]
a. This is a hypothesis test for the population mean.
The claim is that the amount of television watched per day last year by the average person differed from that in 2005.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=4.55\\\\H_a:\mu\neq 4.55[/tex]
The significance level is 0.1.
The sample has a size n=20.
The sample mean is M=4.76.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=5.28.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.28}{\sqrt{20}}=1.181[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.76-4.55}{1.181}=\dfrac{0.21}{1.181}=0.18[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=20-1=19[/tex]
The critical value for a level of significance is α=0.10, a two tailed test and 19 degrees of freedom is tc=1.729.
The decision rule is that if the test statistic is above tc=1.729 or below tc=-1.729, the null hypothesis is rejected.
As the test statistic t=0.18 is within the critical values and lies in the acceptance region, the null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the amount of television watched per day last year by the average person differed from that in 2005.
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=4.76.
The sample size is N=20.
The standard error is s_M=1.181
The degrees of freedom for this sample size are df=19.
The t-value for a 95% confidence interval and 19 degrees of freedom is t=2.093.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.093 \cdot 1.181=2.47[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 4.76-2.47=2.29\\\\UL=M+t \cdot s_M = 4.76+2.47=7.23[/tex]
The 95% confidence interval for the mean is (2.29, 7.23).