Answer:
The point estimate for the true difference between the population means is 0.13.
The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.
Step-by-step explanation:
To solve this question, before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
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.
Subtraction between normal variables:
When we subtract two normal variables, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
A sample of 263 cars owned by students had an average age of 7.25 years. The population standard deviation for cars owned by students is 3.77 years.
This means that:
[tex]\mu_s = 7.25, \sigma_s = 3.77, n = 263, s_s = \frac{3.77}{\sqrt{263}} = 0.2325[/tex]
A sample of 291 cars owned by faculty had an average age of 7.12 years. The population standard deviation for cars owned by faculty is 2.99 years.
This means that:
[tex]\mu_f = 7.12, \sigma_f = 2.99, n = 291, s_f = \frac{2.99}{\sqrt{291}} = 0.1753[/tex]
Difference between the true mean ages for cars owned by students and faculty.
Distribution s - f. So
[tex]\mu = \mu_s - \mu_f = 7.25 - 7.12 = 0.13[/tex]
This is also the point estimate for the true difference between the population means.
[tex]s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2325^2+0.1753^2} = 0.2912[/tex]
90% confidence interval for the difference:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs = 1.645*0.2912 = 0.48[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.13 - 0.48 = -0.35 years
The upper end of the interval is the sample mean added to M. So it is 0.13 + 0.48 = 0.61 years.
The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.
a water wheel has a radius of 15 feet. the wheel is rotating at 6 revolutions per minute. find the linear speed of the water. express your answer in terms of n and using units feet per second
Answer:
25.1333 per second
Step-by-step explanation:
1508 per min
Amare is building a rectangular fence. Originally, he plans to build an 18 ft by 14 ft fence but later decides to increase each dimension by x feet.
Which equation represents the new perimeter of the fence?
P = (18 + x ) + (14 + x )
P = (18 + 2x ) + (14 + 2x )
P = 2(18 + x ) + 2(14 + x )
P = 2(18 + 2x ) + 2(14 + 2x )
Answer:
P = 2(18 + x ) + 2(14 + x )Step-by-step explanation:
Given,
Dimensions of the fence = 18 ft and 14 ft
Then x ft is increased in both dimensions ,
New dimensions of the fence = (18 + x)ft and (14 + x)ft
Therefore,
Perimeter of the fence = 2 ( l + b)
= 2 l + 2 b
= 2(18 + x) + 2(14 + x) (Ans)
Hence,
Option C is correct.
A square has an area of 100 square meters.
What is the perimeter of the square?
Answer:
40 square meters
Step-by-step explanation:
Perimeter means to add up all sides.
area means one side times one side
10 times 10 makes 100 so i am guessing each side is 10
10 + 10 + 10 + 10 = 40
Does each equation have no solution, one solution, or infinitely many solutions? Place a check in the correct column.
One Solution
No Solution
Infinitely Many Solutions
3(4x - 2) = 12x - 6
3(4x - 2) = -12x - 6
-3(4x - 2) = -12x - 2
Taxi fare in Tampa cost a base fee of $4 plus an additional $0.85 for each mile traveled how much would a person pay to taxi fare in Tampa cost a base fee of $4 plus an additional $0.85 for each mile traveled how much would a person pay to take a taxi from work to home if the distance is 17 miles
Answer:
18.45
Step-by-step explanation:
Rectangle JKLM is shown. To the nearest tenth of a centimeter, what is the distance from J to M?
Answer:
10.2
Step-by-step explanation:
Answer:10.2
Step-by-step explanation:
In 1.8 s, a smart and swift dachshund caught his prey that was 8.5 m away what was the dogs speed?
Figure A ~ Figure B
Figure A
R = 4 ft
Figure B
R = 2 ft
V = 352 cu ft
Find the volume of Figure B.
Help please!!
The volume of figure B that is similar to figure A is: 44 cu. ft.
How to Find the Volume of Similar Figures?If the volumes of two figures are A and B respectively, and their radius is a and b respectively, then, Volume of A/volume of B = a³/b³.
Given that figures A and B are similar, we would have the following ratio:
352/volume of B = 4³/2³
352/volume of B = 64/8
352/volume of B = 8
Volume of B = 352/8
Volume of B = 44 cu. ft.
Learn more about the volume of similar figures on:
https://brainly.com/question/4315286
#SPJ1
Help with this one? Thanks
Answer:
I think the answer of this question is b
Use context clues to choose the correct meaning of the italicized word.
Mother asked Mary Jo to care for the baby.
be worried about
pay attention
to take charge of
Answer:
A.
Step-by-step explanation:
Privacy issues: In a Fall 2014 Pew Research survey, 25% of American adults say they are "not at all confident" that the records of their activity maintained by credit card companies will remain private and secure. With numerous data breaches since then, a consumer group is interested in determining whether the proportion has increased this year. They select a random sample of 300 adults and find that 30% state they are not at all confident. After conducting the hypothesis test for p = 0.25 compared to p > 0.25 . we obtain a -value of 0.023. Which of the following interpretations of the -value is correct? There is a % chance that 25% of American adults say they are not at all conħdent that the records of their activity maintained by credit companies will remain private and secure. There is a 2.3% chance that 30% or more of a sample of 300 American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure it 25% of Americans are not at all confident this year. There is a % chance that 30% or more of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if assume 25% of American adults are not at all confident in 2014. There is a 2.3% chance that 30% of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secur
There is a 2.3% chance that 30% or more of a sample of 300 American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if 25% of Americans are not at all confident this year. Answer:
Step-by-step explanation:
The null hypothesis is “the percentage of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure is 25%. If this is true, there is a 2.3% chance that a sample of 300 American adults will have 30% or more who say they are not at all confident.
Find the exact value of x
Answer:
Step-by-step explanation:
"x" is geometric mean
x² = 4 × 16
x² = 64
x = 8
What is the profit percent of a shopkeeper buys a footballer of $12 and sells it for $15
Answer:
25%
Explanation:
the profit made by the shopkeeper would be the difference between the selling price and cost price, which can be found using the equation $15 - $12 = $3.
now, we can find the profit percent using the difference ($3) and the cost price ($12):
$3 ÷ $12 × 100% = 25% (since $3 is 25% of $12, so the $3 increase in price is a 25% increase)
i hope this helps! :D
A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the shaded region.
11 yd
13 yd
4 yd
6 yd
Answer:
34 yd²
Step-by-step explanation:
Area of the shaded region = area of the outer rectangle - area of the inner rectangle
Area of outer rectangle = L*W = 13*6 = 78 yd²
Area of inner rectangle = L*W = 11*4 = 44 yd²
Area of the shaded region = 78 - 44 = 34 yd²
A regular ice cream cone is 5 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.75 inches.
(a)
Find the volume (in cubic inches) of the regular ice cream cone to the nearest tenth.
cu. in
(b)
Find the volume (in cubic inches) of the waffle cone to the nearest tenth.
cu. in
(c)
How much more ice cream (in cubic inches) fits in the waffle cone compared to the regular cone? Round your answer to the nearest tenth.
cu. in
Answer:
a) 8.2 in^3 b) 25.8 in^3 c) 17.6 in^3
Step-by-step explanation:
volume of cone=(1/3)π(r^2)*h
a) 8.2 in^3
regular ice cream cone=(1/3)π(1.25^2)*5=8.18=8.2 in^3
b) 25.8 in^3
waffle cone=(1/3)π(1.875^2)*7=25.77=25.8 in^3
c) 17.6 in^3
waffle cone-regular ice cream cone= 25.8-8.2=17.6 in^3
Use the laws of Sines and law of cosines to find missing dimensions
9514 1404 393
Answer:
11. inconsistent information
12. 26°
Step-by-step explanation:
11. The given numbers are inconsistent. (The first attachment shows one of the 4 possible solutions.)
__
12. In order to find angle C, we need to know side AC. We can find that using the Law of Cosines.
b = √(a² +c² -2ac·cos(B)) = √(19² +15² -2(19)(15)cos(120°)) = √871
b ≈ 29.513
Then angle C is found from the Law of Sines.
C = arcsin(c/b·sin(B)) = arcsin(15/29.513·sin(120°)) ≈ 26.11°
Angle C is about 26°.
The second attachment shows the output of a triangle solver.
What is 5/4 minus 1/3?
Answer:
11/12
Step-by-step explanation:
5/4 ---- 15/12
1/3------ 4/12
11/12
Answer:
11/12
Step-by-step explanation:
Hello! The answer to this question is 11/12. In this case, we want to make the denominator the same. To make the denominator the same we need to find the lowest common multiple. In this case the lowest common multiple is 12, (because 12 is the smallest number that 3 and 4 are both factors for.) 4x3=12 so now the denominator in 5/4 is 12 but whatever we do the bottom we do to the top. So since we multiplied the bottom (denominator) by 3 we have to multiply the top (numerator) by 3 as well. 5x3=15. Therefore, we now changed 5/4 to 15/12. Now, we have to do the same to the 1/3. 3x4= 12. 1x4=4. Now we have the two numbers, 15/12 and 4/12. 15/12-4/12=11/12! Therefore, your answer is 11/12. Hope this explanation helps! Happy learning!
The dot plot below shows how many campsites have each number of campers.
What is the mean absolute deviation of the data set shown?
Plezz help :(
Answer:
1
Step-by-step explanation:
The answer is 1.
Answer: The answer is 1 100%
Step-by-step explanation: i took the test
"All congruent triangles are similar, but all similar triangles are not congruent". Justify please!
Answer:
True similar triangles don't have to be the same size
Step-by-step explanation:
Answer:
Congruent means that the triangles are exactly the same in size and shape whereas similar means that the triangles have the same shape, but not the same size. Hope this helps!
What is the area of the figure on the coordinate plane below?
Answer:
-79
Step-by-step explanation:
A rocket is launched vertically from the ground with an initial velocity of 64 ft/sec. A) Write a quadratic function h(t) that shows the height, in feet, of the rocket t seconds after it was launched. B) Graph h (t) on the coordinate plane. C) Use your graph from Part 3 (b) to determine the rocket's maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air. ( Answer options A,B,C) Please don't answer if you don't know how to) Will Mark Brainliest.
The calculated quadratic function for the height of the rocket is "[tex]h = 64t - 16.085t^2[/tex]" and the further calculation of the given points can be defined as follows:
For point A):
Calculation of the quadratic function:Rocket Initial velocity (u) [tex]= 64 \ \frac{feet}{sec}[/tex]
Considering gravity's acceleration of 32.17 feet/sec2
The rocket's height can be expressed as follows:
[tex]h = ut - \frac{1}{2} \times 32.17 \times t^2 \\\\h = 64 - 16.085 \times t^2 \\\\h = 64t - 16.085t^2[/tex]
For point B):
A y-axis indicates its rocket's height in feet, whereas the x-axis represents the duration in seconds.
Please find the attached file.
For point C):
As seen in the graph, after t = 1.989 seconds, the rocket reaches its highest height of 63.662 feet.maximum height = 63.66 feet, time t = 2 seconds. After 3.979 seconds, the rocket's height returned to zero.It would be in the air for 3.979 seconds. The rocket lingered in the air for 4 seconds.
Find out more information about the velocity here:
brainly.com/question/25749514
433.54 in terms of pi
Answer:
138.0700636942675[tex]\pi[/tex]
Step-by-step explanation:
When you solve x^2 - 8x + 7 = 0 what is the last step of the equation
before you simplify to get the two answers? *
O x = -4 13
O x = 3 + 4
O x = 4 + 3
Answer:
x = 1 and x = 7
Step-by-step explanation:
The given equation is [tex]x^2 - 8x + 7 = 0[/tex].
We need to solve the equation.
It is a quadratic equation whose solution is given by :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Here, a = 1, b = -8 and c = 7
Put values,
[tex]x=\dfrac{-(-8)\pm \sqrt{(-8)^2-4(1)(7)} }{2(1)}\\\\=\dfrac{8\pm \sqrt{64-28}}{2}\\\\=\dfrac{8\pm 6}{2}\\\\=\dfrac{8+6}{2},\dfrac{8-6}{2}\\\\=7,1[/tex]
So, the values of x are x = 1 and x = 7.
Its me I told u to look for my username to help me with this questions
Answer:
96
Once again, apologies for the chicken scratch
Answer:
$96
Step-by-step explanation:
→ Work out the discount multiplier
( 100 - 20 ) ÷ 100 = 0.8
→ Multiply answer by price
0.8 × 120 = $96
A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 23 feet less than the height of the pole. If the wire is to be 9 feet longer than the height of the pole, what is the height of the pole?
9514 1404 393
Answer:
56 feet
Step-by-step explanation:
Let x represent the height of the pole. Then the distance to the anchor point is (x-23), and the length of the wire is (x+9). The Pythagorean theorem tells you the relation between these values is ...
(x+9)² = x² +(x -23)²
0 = x² -64x +448 . . . . . subtract the left side, put in standard form
0 = (x -8)(x -56) . . . . . . factor
The solutions to the quadratic are x=8 and x=56. For our purposes, we require x > 23 so the distances are positive. That means x=56 is the solution of interest.
The pole is 56 feet tall.
how many five-miute segments are in 3\4 of an houre
i need help and fast is 23 points good
Answer: 9
Step-by-step explanation: because 3/4 of an hour is 45 minutes and 45/5 is 9 and it’s in 5 min segments that’s why you divide 45 by 5
sorry for the first one i read the question wrong
Brennan ate 2 1/4 apples.Then he ate another 1 2/4 apples the next day.How many apples did Brennan eat altogether?Write in simplest.
Answer:
UwU your welcome!
Step-by-step explanation:
Convert the mixed fractions to a decimal. 2 1/4 is 2.25 1 2/4 is 1.5 2. Add them up. 3. 3.75 as a decimal or 3 3/4 as a mixed fraction or 15/4 as a improper fraction.
PLZ ANSWER, 8 POINTS
The radius of a circular clock is 13 centimeters. What is the
area of the clock?
Use 3.14 for pi
Answer:
452.16
Step-by-step explanation:
A = (3.14)r^2
A=(3.14)12^2
A=452.16
Answer:
530.66 cm
Step-by-step explanation:
A= π r 2
input known values
A= (3.14) (13^2)
Simplify
A= (3.14) 169
A= 530.66
A 12-sided sold has faces numbered 1 to 12. The table shows the results of rolling the solid 200
times Find the experimental probability of rolling a number greater than 10
Results
Number
1 2 3 4 5 6 7 8 9 10 11 12 Total
rolled
Frequency 17 13 15 15 17 14 15 32 16 14 15 17 200
The experimental probability of rolling a number greater than 10 [#/#] is
(Simplity your abswer)
Answer:
4/25 maybe?
Step-by-step explanation:
