Answer:
Step-by-step explanation:
Hello!
According to a study regarding the average age of female and male kids to complete toilet training is:
Females:
Average age 32.5 months
The standard deviation of 6.7 months
n= 126
Males:
Average age 35.0 months
The standard deviation of 10.1 months
n= 141
The parameter of study is the difference between the age of females are successfully toilet trained and the average age that males are successfully toilet trained. μf - μm (f= female and m= male)
a.
Assuming that both variables have a normal distribution to choose whether you'll use an unpooled or pooled-t to calculate the confidence interval you have to conduct an F-test for variance homogeneity.
If the variances are equal, then you can usee the pooled-t, but if the variances are different, you have to uses Wlche's approach:
H₀: δ²f = δ²m
H₁: δ²f ≠ δ²m
Since both items b. and c. ask for a 95% CI I'll use the complementary significance level for this test:
α: 0.05
[tex]F= \frac{S^2_f}{S^2_m} * \frac{xSigma^2_f}{Sigma^2_m} ~~~F_{(n_f-1); (n_m-1)}[/tex]
[tex]F= \frac{(6.7^2)}{(10.1)^2} *1= 0.44[/tex]
Critical values:
[tex]F_{125;140;0.025}= 0.71\\F_{125;140;0.975}= 1.41[/tex]
The calculated F value is less than the lower critical value, 0.77, so the decision is to reject the null hypothesis. In other words, there is no significant evidence to conclude the population variances of the age kids are toilet trained to be equal. You should use Welch's approach to construct the Confidence Intervals.
[tex]Df_w= \frac{(\frac{S^2_f}{n_f} + \frac{S^2_m}{n_m} )^2}{\frac{(\frac{S^2_f}{n_f} )^2}{n_f-1} +\frac{(\frac{S^2_m}{n_m} )^2}{n_m-1} }[/tex]
[tex]Df_w= \frac{(\frac{6.7^2}{126} + \frac{10.1^2_m}{141} )^2}{\frac{(\frac{126^2}{126} )^2}{126-1} +\frac{(\frac{10.1^2}{141} )^2}{141-1} } = 254.32[/tex]
b.
The given interval is:
[0.3627; 4.6073]
Using Welch's approach, the formula for the CI is:
(X[bar]f- X[bar]m) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]
or
(X[bar]m- X[bar]f) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]
As you can see either way you calculate the interval, it is centered in the difference between the two sample means, so you can clear the value of that difference by:
(Upper bond - Lower bond)/2= (4.6073-0.3627)/2= 2.1223
The average age for females is 32.5 months and for males, it is 35 months.
Since the difference between the sample means is positive, we can say that the boys were considered "group 1" and the girls were considered "group 2"
You have a95% confidence that the parameter of interest is included in the given confidence interval.
c.
None of the statements is correct, the interval gives you information about the difference between the average age the kids are toilet trained, that is between the expected ages for the entire population of male and female babies.
This represents a guideline but is not necessarily true to all individuals of the population since some male babies can be toilet trained before that is expected as some female babies can be toiled trained after the average value.
I hope it helps!
Dylan wanted to find the average number of hours per day that the students in his class practiced their instruments. He chose three students by drawing their names from a hat. What should he do to ensure that he has an accurate average for the class?
A dot plot going from 0 to 4. There is 1 dot above 0, 1 dot above 0.5, and 1 dot above 4.
He should add the three numbers and divide by 3 because that is how one finds an average.
He should poll more students to eliminate the variability caused by a sample size that is too small.
He should take the middle number as his average since he has three observations.
He should just find the average of 0.5 and 4 since 0 does not change anything when adding.
Answer:
D
Step-by-step explanation:
hope I was correct
To get the average he should add the three numbers and divide by 3.
What is average?The mean of a group of numbers is the average of the numbers. It is given by:
Average = (sum of all numbers) / total number of numbers
From the dot plot:
Average = (1 * 0 + 1 * 0.5 + 1 * 4) / 3 = 1.5
To get the average he should add the three numbers and divide by 3.
Find out more on mean at: https://brainly.com/question/1136789
Suppose he makes two stops of 10 minutes each during his journey. Will he be
able to reach the town in 4 hours if he keeps the speed the same?
Answer:
No, he would not be able to reach the town in 4 hours with two 10 minutes stops and same speed
Completed question;
Max travels to see his brother's family by car. He drives 216 miles in 4 hours. What is his rate in miles per hour? Suppose he makes two stops of 10 minutes each during his journey. Will he be able to reach the town in 4 hours if he keeps the speed the same?
Step-by-step explanation:
Average speed = total distance travelled/time taken
Given;
Total distance travelled= 216 miles
Total time taken = 4 hours
Average speed v = 216/4 = 54 miles per hour
v = 54 mph
Suppose he makes two stops of 10 minutes each during his journey.
Total time on stops = 2 × 10 = 20 minutes = 0.33 hours
Total time spent on motion = 4 - 0.33 hours = 3.67 hours
Total distance covered in 4 hours with two stops;
d = 3.67 × 54 mph = 198.18 miles
Since d < 216 miles
No, he would not be able to reach the town in 4 hours with two 10 minutes stops and same speed
Create an expression that simplifies to sin x
Answer:
[tex]2\cdot \sin 0.5x \cdot \cos 0.5x[/tex]
Step-by-step explanation:
Here is one example:
[tex]2\cdot \sin 0.5x \cdot \cos 0.5x[/tex]
[tex]\sin 0.5x \cdot \cos 0.5x + \cos 0.5x\cdot \sin 0.5x[/tex]
[tex]\sin (0.5x + 0.5x)[/tex]
[tex]\sin x[/tex]
Where is the treasure?
A treasure is hidden under a number on the hundreds chart.
Use the clues to shade the other 99 numbers. The number
that is left unshaded holds the treasure.
• Shade the numbers in the patterns described below.
A. Start at 3. The rule is: Subtract 2, and then add 5.
B. Start at 2. The rule is: Add 6.
C. Start at 5. The rule is: Add 12.
D. Start at 83. The rule is: Subtract 12.
E. Start at 1. The rule is: Add 3.
Answer:
The treasure is hidden under 95.
Step-by-step explanation:
The numbers are:
[tex]1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\\21, 22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40\\41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60\\61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80\\81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,100[/tex]
Clue A:Start at 3. The rule is: Subtract 2, and then add 5.
3-2+5=6
6-2+5=9
Therefore, this rule eliminates all multiples of 3.
[tex]1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20\\22, 23, 25,26, 28, 29, 31, 32, 34, 35, 37, 38, 40\\41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, \\61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80\\82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100[/tex]
Clue B:Start at 2. The rule is: Add 6.
The numbers are:2,8,14,...
We have left:
[tex]1, 4, 5, 7, 10, 11, 13, 16, 17, 19, \\22, 23, 25, 28, 29, 31, 34, 35, 37, 40\\41, 43, 46, 47, 49, 52, 53, 55, 58, 59, \\61, 64, 65, 67, 70, 71, 73, 76, 77, 79, \\82, 83, 85, 88, 89, 91, 94, 95, 97, 100[/tex]
Clue C: Start at 5. The rule is: Add 12.
The numbers are: 5,17,29,...
We have left:
[tex]1, 4, 7, 10, 11, 13, 16, 19, \\22, 23, 25, 28, 31, 34, 35, 37, 40\\ 43, 46, 47, 49, 52, 55, 58, 59, \\61, 64, 67, 70, 71, 73, 76, 79, \\82, 83, 85, 88, 91, 94, 95, 97, 100[/tex]
Clue D: Start at 83. The rule is: Subtract 12.
The numbers are 83,71,59,...
We have left:
[tex]1, 4, 7, 10, 13, 16, 19, \\22, 25, 28, 31, 34, 37, 40\\ 43, 46, 49, 52, 55, 58, \\61, 64, 67, 70, 73, 76, 79, \\82, 85, 88, 91, 94, 95, 97, 100[/tex]
Clue E: Start at 1. The rule is: Add 3.
The numbers are 1,4,7,...
We are left with:
[tex]95[/tex]
The treasure is hidden under 95.
A commuter must pass through five traffic lights on her way to work, and she will have to stop at each one that is red. After years of commuting she has developed the following probability distribution for the number of red lights she stops at each day on her way to work: No. of red lights x 0 1 2 3 4 5 Probability .05 .25 .30 .20 .15 .05 Note that the standard deviation of the above probability distribution is SD(X) = 1.27.
Answer:
Step-by-step explanation:
Hello!
You have the information about the number of red lights a commuter pass on her way to work and the probability of them stoping her:
Be x: number of red lights
X: 0, 1, 2, 3, 4, 5
hi: 0.05, 0.25, 0.30, 0.20, 0.15, 0.05
a. What is the expected number of red lights at which she will stop on her way to work?
The expected number of red lights is the sample mean, you can calculate it using the following formula:
[tex]X[bar]= sum Xi*hi= (0*0.05)+(1*0.25)+(2*0.30)+(3*0.20)+*(4*0.15)+(5*0.05)=2.3[/tex]
She's expected to be stopped by 2.3 red lights on the way to work.
b. Suppose each red light delays the commuter 1.8min. What is the standard deviation od the number of minutes that she is delayed by red lights?
If each light delays the commuter 1.8 min then you can determine a new variable of interest:
Be Y: the time a commuter is delayed by red lights on the way work, then Y= X*1.8min
Meaning if X= 0, then Y=0 (the commuter will be delayed 0 min), if X=1, then Y= 1.8min, if X=2, then Y= 3.6min and to on....
The properties of variance state that if
Y= X*k (Where K= constant)
Then the sample variance of Y will be
V(Y)= V(X*k)= k²*V(X)
Then the standard deviation of Y will be the constant k by the standard deviation of X:
Sy= k*Sx= 1.8 * 1.27= 2.286
I hope it helps!
Ignoring those who said they weren't sure, there were 297 men asked, and 183 said yes, they had driven a car when they probably had too much alcohol. Does this provide statistically significant evidence that a majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, if asked
Answer:
[tex]z=\frac{0.616-0.5}{\sqrt{\frac{0.5(1-0.5)}{297}}}=3.998[/tex]
[tex]p_v =2*P(z>3.998)=0.0000639[/tex]
With the most common significance levels used [tex]\alpha= 0.1, 0.05, 0.01[/tex] we see that the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can say that the true proportion is significantly higher than 0.5
Step-by-step explanation:
Information given
n=297 represent the random sample of male taken
X=183 represent the men who said yes, they had driven a car when they probably had too much alcohol
[tex]\hat p=\frac{183}{297}=0.616[/tex] estimated proportion of men who said yes, they had driven a car when they probably had too much alcohol
[tex]p_o=0.5[/tex] is the value that we want to test
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Hypothesis to test
We need to conduct a hypothesis in order to test the claim that the majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, and the system of hypothesis are:
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
After replace we got:
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.616-0.5}{\sqrt{\frac{0.5(1-0.5)}{297}}}=3.998[/tex]
Decision
We have a right tailed test so then the p value would be:
[tex]p_v =2*P(z>3.998)=0.0000639[/tex]
With the most common significance levels used [tex]\alpha= 0.1, 0.05, 0.01[/tex] we see that the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can say that the true proportion is significantly higher than 0.5
0.000000452 in scientific notation
0.000000452 in scientific notation would be 4.52 × [tex]10^{-7}[/tex]
Indicate whether each of the following statements is true or false (brie y explain your reason). (a) [1pt] Consider a standard LP with four variables and three constraints. Then two basic solutions (0; 0; 0; 4; 0; 12; 18) and (3; 0; 0; 1; 0; 2; 0) are adjacent. (b) [1pt] If a linear program has no optimal
Answer:
Indicate whether each of the following statements is true or false (brie y explain your reason). (a) [1pt] Consider a standard LP with four variables and three constraints. Then two basic solutions (0; 0; 0; 4; 0; 12; 18) and (3; 0; 0; 1; 0; 2; 0) are adjacent. (b) [1pt] If a linear program has no optimal solution, then it must have an unbounded feasible region. (c) [1pt] Consider the shadow prices of a standard form of LP. The vector formed by the shadow prices is a feasible solution of the dual problem of this LP. (d) [1pt] A linear program can have exactly 10 feasible solutions. (e) [1pt] Consider a primal problem of maximizing c^Tx and a dual problem of minimizing b^Ty (both subject to some constraints). If for a primal feasible solution x and a dual solution y, we have c^Tx > b^Ty, then y must be dual infeasible. (i.e not a feasible solution for the dual problem). (f) [1pt] In a two player zero sum game, there exists at least one Nash equilibrium.
Step-by-step explanation:
a. true
Because two basic feasible solution stands to be adjacent in case they possess basic variable in common. Two distinct basic solutions with respect to set related with linear constraint under is considered to be adjacent.
b.False.
If a linear problem has no solution it may have null feasible region not important to have unbounded feasible region.
c.True.
If Shadow price is feasible for standard form of LP then it will be feasible solution of dual problem of this LP.
d. False.
As there will be 'n' variables 'm' constraints having nCm feasible solutions.
e.True.
As stated in weak duality theorem
f.True
For every zero-sum 2-player normal-form game, a Nash equilibrium exists. Moreover, a pair of mixed strategies (p,q)(p,q) for the two players is a Nash equilibrium if and only if each strategy is a maximin strategy.
Members of an online gaming group have been increasing by 25% every year. The group started with 75 members. How many members will the group have after 4 years?
183 member will the group have after 4 years, if the members of an online gaming group have been increasing by 25% every year. The group started with 75 members.
Step-by-step explanation:
The given is,
Members of an online gaming group is 75
Increasing by 25% every year
Step:1
Formula to calculate the members in gaming group after few years with an rate of increase,
[tex]F = P(1+r)^{t}[/tex].......................(1)
Where, F - Members in gaming group after 4 years
P - Members in gaming group in initially
r - Rate of increase in year
t - No. of years
Step:2
From the given,
P = 75 members
r = 25 %
t = 4 years
Equation (1) becomes,
[tex]F = 75(1+0.25)^{4}[/tex]
[tex]= 75(1.25)^{4}[/tex]
= ( 75 ) ( 2.441406 )
= 183.105
F ≅ 183 members
Result:
183 member will the group have after 4 years, if the members of an online gaming group have been increasing by 25% every year. The group started with 75 members
The triangles below are similar. Triangle G H F. Angle G is 65 degrees, H is 24 degrees, F is 91 degrees. Triangle J K L. Angle J is 24 degrees, K is 91 degrees, L is 65 degrees. Which similarity statement expresses the relationship between the two triangles? Triangle F G H is similar to Triangle K L J Triangle F G H is congruent to Triangle K L J Triangle F G H is similar to triangle J K L Triangle F G H is similar to triangle J K L
Answer:
Triangle F G H is similar to Triangle K L J
Step-by-step explanation:
Angle H = Angle J
Angle G = Angle L
Angle F = Angle K
KLJ is similar to FGH
If the lengths are also equal, then they're congruent
Triangle FGH is similar to triangle JKL.
To express the relationship between the two triangles using a similarity statement, we need to match corresponding angles.
Since the triangles are similar, corresponding angles are congruent.
In triangle FGH,
the angles are 65° , 24° , and 91 °
In triangle JKL,
the angles are 24° ,91° , and 65°
We see that the angles 24° , 91°, and 65° in triangle JKL match the angles in triangle FGH respectively.
So, the similarity statement expressing the relationship between the two triangles is:
Triangle FGH is similar to triangle JKL.
What is an open line of credit?
a. A line of credit which has no current balance
b. A line of credit with a variable interest rate.
c. A line of credit against which additional debt may be drawn.
d. A line of credit which has no credit history requirements.
Please select the best answer from the choices provided
Answer:
c. A line of credit against which additional debt may be drawn
Step-by-step explanation:
A line of credit is "open" if there are no specific payoff requirements (except perhaps a minimum payment according to the balance). There is usually a limit to the available credit, but as long as the amount borrowed is less than that limit, additional funds may be borrowed at any time.
A credit card is an example of an open line of credit.
Find the perimeter 8ft 11ft
Answer:
38ft
Step-by-step explanation:
I'm assuming that you mean that the dimensions are 8ft by 11ft
If so, you need to add all the sides together, there should be two 8ft sides and two 11ft sides
8*2 = 16 (or 8+8
11*2= 22 (or 11+11
16+22 = 38
An isosceles triangle has slant height s and angle t opposite the base. Find a formula for the base length b in terms of the angle t and the slant height s.Find a formula for the enclosed area A in terms of t and s.
OK, let's try with no figure. We have an isosceles triangle sides s,s, and b.
Opposite b is angle t.
Draw the altitude h to bisect t. We have two right triangles, legs b/2 and h, hypotenuse s. The angle opposite b/2 is t/2 so
sin(t/2) = (b/2)/s = b/2s
So we arrived at the first part,
b = 2s sin(t/2)
The area of a triangle with sides s,s and included angle t is
A = (1/2) s² sin t
Maggie had a 1/4 cup in a 1/2 cup measuring cup how could she have measured out 3 3/4 cups of flour? find at least two different ways
Answer:
Step-by-step explanation:
1.
1/4 cup x 13 and 1/2 cup x 1
2.
1/2 cup x 7 1/4 cup x 1
the area of a regular pentagon with a radius of 7 cm is
The area of a regular pentagon is 116.516 squared centimeters, if the pentagon has a radius of 7 cm.
Step-by-step explanation:
The given is,
Radius of pentagon - 7 cm
Step:1
Ref the attachment,
The pentagon contain 10 right angled triangle.
Angle of Right angle triangle = [tex]\frac{360}{10}[/tex] = 36°
From the right angle OPQ triangle,
sin ∅ = [tex]\frac{Opp}{Hyp}[/tex]
Where, ∅ = 36°
Radius = Hyp = 7 cm
Trigonometric ratio becomes,
sin 36° = [tex]\frac{b}{7}[/tex]
0.5878 = [tex]\frac{b}{7}[/tex] (∵ sin 36° = 0.5878 )
b = ( 0.5878 × 7 )
b = 4.115 cm
From the right angle OPQ triangle,
cos ∅ = [tex]\frac{Adj}{Hyp}[/tex]
Where, Adj = h
cos 36° = [tex]\frac{h}{7}[/tex]
0.809017 = [tex]\frac{h}{7}[/tex]
h = ( 0.809017 × 7 )
h = 5.663 cm
Step:2
Area of triangle OPR,
[tex]A = \frac{1}{2} (Height )(Base)[/tex]
Where, Height, h = 5.663 cm
Base = b + c = 4.115 + 4.115 = 8.23 cm
Area of OPQ becomes,
A = [tex]\frac{1}{2}[/tex] (8.23)(5.663)
= [tex]\frac{1}{2}[/tex] ( 46.6065)
A = 23.30324 squared centimeters
Step:3
Pentagon contain 5 triangles,
Area of pentagon = 5 × Area of triangle
= 5 × 23.30324
= 116.516 squared centimeters
Area of pentagon = 116.516 squared centimeters
Result:
The area of a regular pentagon is 116.516 squared centimeters, if the pentagon has a radius of 7 cm.
A survey of 2,254 American adults indicates that 17% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device.50 (a) According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones.51 Conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Answer:
We conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Step-by-step explanation:
We are given that a survey of 2,254 American adults indicates that 17% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones.
We have to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Let p = proportion of Americans who only use their cell phones to access the internet
SO, Null Hypothesis, [tex]H_0[/tex] : p = 38% {means that the proportion of Americans who only use their cell phones to access the internet is same as that of Chinese proportion of 38%}
Alternate Hypothesis, [tex]H_a[/tex] : p [tex]\neq[/tex] 38% {means that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = proportion of cell phone owners who browse the internet
exclusively on their phone in a survey of 2,254 adults = 17%
n = sample of adults = 2,254
So, test statistics = [tex]\frac{0.17-0.38}{\sqrt{\frac{0.17(1- 0.17)}{2,254} } }[/tex]
= -26.542
Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie in between the critical values of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Came someone help me please!!
Answer:
D
Step-by-step explanation:
if m increases n increases too and vice versa
please like and Mark as brainliest
The number of hours per week that high school seniors spend on computers is normally distributed, with a mean of 6 hours and a standard deviation of 2 hours. 80 students are chosen at random. Let y be the mean number of hours spent on the computer for this group.
Find the probability that y is between 6.2 and 6.9 hours.
To find the probability that y is between 6.2 and 6.9 hours, calculate the z-scores and use the standard normal distribution table.
Explanation:To find the probability that y is between 6.2 and 6.9 hours, we need to calculate the z-scores corresponding to these values and then use the standard normal distribution table. The formula to calculate the z-score is z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For 6.2 hours: z = (6.2 - 6) / 2 = 0.1
For 6.9 hours: z = (6.9 - 6) / 2 = 0.45
Using the standard normal distribution table, the probability that y is between 6.2 and 6.9 hours is P(0.1 ≤ z ≤ 0.45). Thus, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 4.02 and x = 0.89 in the z table which has an area of 0.99997 and 0.81327 respectively.}
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Write the polynomial in factored form as a product of linear factors f(r)=r^3-9r^2+17r-9
Answer:
f(r) = (x -1)(x -4+√7)(x -4-√7)
Step-by-step explanation:
The signs of the terms are + - + -. There are 3 changes in sign, so Descartes' rule of signs tells you there are 3 or 1 positive real roots.
The rational roots, if any, will be factors of 9, the constant term. The sum of coefficients is 1 -9 +17 -9 = 0, so you know that r=1 is one solution to f(r) = 0. That means (r -1) is a factor of the function.
Using polynomial long division, synthetic division (2nd attachment), or other means, you can find the remaining quadratic factor to be r^2 -8r +9. The roots of this can be found by various means, including completing the square:
r^2 -8r +9 = (r^2 -8r +16) +9 -16 = (r -4)^2 -7
This is zero when ...
(r -4)^2 = 7
r -4 = ±√7
r = 4±√7
Now, we know the zeros are {1, 4+√7, 4-√7), so we can write the linear factorization as ...
f(r) = (r -1)(r -4 -√7)(r -4 +√7)
_____
Comment on the graph
I like to find the roots of higher-degree polynomials using a graphing calculator. The red curve is the cubic. Its only rational root is r=1. By dividing the function by the known factor, we have a quadratic. The graphing calculator shows its vertex, so we know immediately what the vertex form of the quadratic factor is. The linear factors are easily found from that, as we show above. (This is the "other means" we used to find the quadratic roots.)
choose the equation with the lowest answer
10 - 0.01
10 × 0.01
10 ÷ 0.01
10 + 0.01
A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from the center of the circle. Find the volume of the torus.
Consider a circle with radius [tex]r[/tex] centered at some point [tex](R+r,0)[/tex] on the [tex]x[/tex]-axis. This circle has equation
[tex](x-(R+r))^2+y^2=r^2[/tex]
Revolve the region bounded by this circle across the [tex]y[/tex]-axis to get a torus. Using the shell method, the volume of the resulting torus is
[tex]\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx[/tex]
where [tex]2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}[/tex].
So the volume is
[tex]\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx[/tex]
Substitute
[tex]x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt[/tex]
and the integral becomes
[tex]\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt[/tex]
Notice that [tex]\sin t\cos^2t[/tex] is an odd function, so the integral over [tex]\left[-\frac\pi2,\frac\pi2\right][/tex] is 0. This leaves us with
[tex]\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt[/tex]
Write
[tex]\cos^2t=\dfrac{1+\cos(2t)}2[/tex]
so the volume is
[tex]\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}[/tex]
A botanist collected one leaf at random from each of 10 randomly selected mature maple trees of the same species. The mean and the standard deviation of the surface areas for the 10 leaves in the sample were computed.Assume the distribution of surface areas of maple leaves is normal. What is the appropriate method for constructing a one-sample confidence interval to estimate the population mean surface area of the species of maple leaves, and why is the method appropriate?
Answer:
One sample t-test for population mean would be the most appropriate method.
Step-by-step explanation:
Following is the data which botanist collected and can use:
Sample meanSample Standard DeviationSample size (Which is 10)Distribution is normalWe have to find the best approach to construct the confidence interval for one-sample population mean. Two tests are used for constructing the confidence interval for one-sample population mean. These are:
One-sample z test for population meanOne-sample t test for population meanOne sample z test is used when the distribution is normal and the population standard deviation is known to us. One sample t test is used when the distribution is normal, population standard deviation is unknown and sample standard deviation is known.
Considering the data botanist collected, One-sample t test would be the most appropriate method as we have all the required data for this test. Using any other test will result in flawed intervals and hence flawed conclusions.
Therefore, One-sample t-test for population mean would be the most appropriate method.
Jason has four dollars more than Robert while Nancy has triple Roberts money how much do they each have is some of their money totals to $67
Answer:
r = 12.6, j = 16.6, n = 37.8
Step-by-step explanation:
Set up your system of equations:
j = 4 +r
n = 3r
67 = j + n + r
Plug in the first two to get down to just r so that you can solve:
67 = (4 + r) + 3r + r
67 = 5r + 4
63 = 5r
12.6 = r
Plug in r value into the other two equations above to get j and n:
j = 4 + 12.6 = 16.6
n = 3(12.6) = 37.8
Hope this helps!
PLEASE HELP! D:
The expression on the left side of an equation is shown below. 3(x+1) +9=_
If the equation has no solution, which expression can be written in the box on the other side of the equation?
A) 3(x+4)
B) 2(x+6)+x
C) 4(x – 3) – x
D) 3(x+1)+9x
Answer:
C. 4(x-3)-xStep-by-step explanation:
All of the given expressions are equivalent to 3x+12 except selection C. Using that in your equation makes it be ...
... 3(x +1) +9 = 4(x -3) -x
... 3x +12 = 3x -12
... 12 = -12 . . . . . false
There is no value of x that will make this true, hence NO SOLUTION.
_____
Comment on the other choices
3x+12 = 3x+12 has an infinite number of solutions, as any value of x will make this true.
Answer:
C. 4(x-3)-xA new pair of basketball shoes costs $98.00 at the sporting goods store. If there is a 10% sales tax, what is the actual cost of the shoes?
$
Answer 98x1.10 =107.8
Step-by-step explanation:
Answer:
107.80
Step-by-step explanation:
98*.10+=107.80
The prior probabilities for events A1 and A2 are P(A1) = 0.30 and P(A2) = 0.55. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits.a) Are A1 and A2 mutually exclusive? b) Compute P(A1 ∩ B) and P(A2 ∩ B). c) Compute P(B). d) Apply Bayes’ theorem to compute P(A1 | B) and P(A2 | B).
We're given the following probabilities:
[tex]P(A_1)=0.30[/tex]
[tex]P(A_2)=0.55[/tex]
[tex]P(A_1\cap A_2)=0[/tex]
[tex]P(B\mid A_1)=0.20[/tex]
[tex]P(B\mid A_2)=0.05[/tex]
(a) Yes, [tex]A_1[/tex] and [tex]A_2[/tex] are mutually exclusive. This is exactly what zero probability of their intersection means. The two events cannot occur simultaneously.
(b) Use the definition of conditional probability to expand:
[tex]P(A_1\cap B)=P(A_1)P(B\mid A_1)=0.30\cdot0.20=0.06[/tex]
[tex]P(A_2\cap B)=P(A_2)P(B\mid A_2)=0.55\cdot0.05=0.0275[/tex]
(c) By the law of total probability,
[tex]P(B)=P(A_1\cap B)+P(A_2\cap B)=0.06+0.0275=0.0875[/tex]
(d) Bayes' theorem says
[tex]P(A_1\mid B)=\dfrac{P(A_1)P(B\mid A_1)}{P(B)}=\dfrac{0.30\cdot0.20}{0.0875}\approx0.686[/tex]
[tex]P(A_2\mid B)=\dfrac{P(A_2)P(B\mid A_2)}{P(B)}=\dfrac{0.55\cdot0.05}{0.0875}\approx0.314[/tex]
Using probability concepts, it is found that:
a) Since [tex]P(A1 \cap A2) = 0[/tex], events A1 and A2 are mutually exclusive.
b) P(A1 ∩ B) = 0.06, P(A2 ∩ B) = 0.0275.
c) P(B) = 0.0875.
d) P(A1|B) = 0.6857 and P(A2|B) = 0.3143.
-----------
Conditional Probability
[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.-----------
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which
P(B|A) is the probability of B happening when A has happened.P(A|B) is the probability of A happening when B has happened.-----------
Item a:
Two events A and B are mutually exclusive if they cannot happen together, that is, [tex]P(A \cap B) = 0[/tex].Since [tex]P(A1 \cap A2) = 0[/tex], events A1 and A2 are mutually exclusive.-----------
Item b:
To compute these probabilities, we use conditional probability.
A1 and B:
[tex]P(B|A1) = \frac{P(A1 \cap B)}{P(A1)}[/tex]
Since [tex]P(A1) = 0.3, P(B|A1) = 0.2[/tex]
[tex]0.2 = \frac{P(A1 \cap B)}{0.3}[/tex]
[tex]P(A1 \cap B) = 0.2(0.3) = 0.06[/tex]
Thus P(A1 ∩ B) = 0.06.
A2 and B:
[tex]P(B|A2) = \frac{P(A2 \cap B)}{P(A2)}[/tex]
Since [tex]P(A2) = 0.55, P(B|A1) = 0.05[/tex]
[tex]0.05 = \frac{P(A2 \cap B)}{0.55}[/tex]
[tex]P(A2 \cap B) = 0.05(0.55) = 0.0275[/tex]
Thus P(A2 ∩ B) = 0.0275.
-----------
Item c:
P(B) can be written as:
[tex]P(B) = P(A1)P(B|A1) + P(A2)P(B|A2) = 0.3(0.2) + 0.55(0.05) = 0.06 + 0.0275 = 0.0875[/tex]
Thus P(B) = 0.0875.
-----------
Item d:
Applying Bayes Theorem, first for A1 given B.
[tex]P(A1|B) = \frac{P(A1)P(B|A1)}{P(B)} = \frac{0.3(0.2)}{0.0875} = 0.6857[/tex]
Then for A2 given B.
[tex]P(A2|B) = \frac{P(A2)P(B|A2)}{P(B)} = \frac{0.55(0.05)}{0.0875} = 0.3143[/tex]
Thus P(A1|B) = 0.6857 and P(A2|B) = 0.3143.
A similar problem is given at https://brainly.com/question/22428992
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger? Round to four decimal places.
Answer:
[tex]P(X\geq 3.4)=0.0228[/tex]
Step-by-step explanation:
Given the mean is 3.2, standard deviation is 0.8 and the sample size is 64.
-We calculate the probability of a mean of 3.4 as follows:
#First determine the z-value:
[tex]z=\frac{\bar X -\mu}{\sigma/\sqrt{n}}\\\\=\frac{3.4-3.2}{0.8/\sqrt{64}}\\\\=2.000[/tex]
#We then determine the corresponding probability on the z tables:
[tex]Z(X\geq 3.4)=1-P(X<3.4)\\\\=1-0.97725\\\\=0.0228[/tex]
Hence, the probability of obtaining a sample mean this large or larger is 0.0228
To find the probability of obtaining a sample mean of 3.4 pounds or larger, calculate the z-score and find the corresponding probability using the standard normal distribution table.
Explanation:To find the probability of obtaining a sample mean of 3.4 pounds or larger, we need to calculate the z-score for the sample mean and then find the corresponding probability using the standard normal distribution table.
First, calculate the z-score using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we have: z = (3.4 - 3.2) / (0.8 / √64) = 0.2 / (0.8 / 8) = 0.2 / 0.1 = 2.
Next, we can find the probability by looking up the z-score of 2 in the standard normal distribution table. The probability of obtaining a sample mean of 3.4 pounds or larger is approximately 0.0228 or rounded to four decimal places.
Learn more about Calculating probability from z-score here:https://brainly.com/question/32538975
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Circle o is inscribed in triangle rst such that it is tangent at points m,n, and p. if rp is 7, rt is 17 and sm is 5, then what is the length of side st?
Answer:
15
Step-by-step explanation:
Tangents to the circle from the same point are the same length. Then rn = 7, and nt = 10. This means mt = 10, so ...
st = sm +mt = 5 +10
sm = 15
The Venn diagram shows three types of numbers: odd (O), even (E), and prime (P).
Circles O and P overlap, and circle P also overlaps with circle E.
Which is represented by Ø?
O ⋃ P
E ∩ P
O ⋃ E
E ∩ O
Answer:
E∩O is the correctStep-by-step explanation:
The set that represents the notation Ø is E ∩ O
What are Venn diagrams?Venn diagrams are used to represent sets and the relationship between them using diagrams
The sets are given as:
O = Odd
E = Even
P = Prime
The notation Ø represents an empty set.
In the number system, a number cannot be even and odd at the same time
Hence, the set that represents Ø is E ∩ O
Read more about Venn diagrams at:
https://brainly.com/question/2099071
please help if I get it wrong I cant go back (all I need is an answer)
Answer:
Subtract 9 I agree with the 1st question but can you help me back just comment if you wanna