High school students from track teams in the state participated in a training program to improve running times. Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds. After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds. Let X represent the running time of a randomly selected student before training, and let Y represent the running time of the same student after training. Which of the following is true about the distribution of X-Y?a. The variables X and Y are independent, therefore, the meanis 34 seconds and the standard deviation is 10 seconds.b. The v ales X and Y are independent therefore, the meanis 34 seconds and the standard deviation is 50 secondsc. The variables X and Y are not independent, therefore, the standard deviation is 50 seconds and the mean cannot be determined with the information given.d. The variables and are not independent, therefore, the meanis 3 seconds and the standard deviation cannot be determined with the information givene. The variables X and Y We not independent, therefore, neither the mean nor the standard deviation can be determined with the informantion given.
Answer:
b. The values X and Y are independent therefore, the mean is 34 seconds and the standard deviation is 50 seconds
Step-by-step explanation:
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.
Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds.
This means that [tex]\mu_X = 402, \sigma_X = 40[/tex]
After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds.
This means that [tex]\mu_Y = 368, \sigma_Y = 30[/tex]
Which of the following is true about the distribution of X-Y?
They are independent, so:
[tex]\mu = \mu_X - \mu_Y = 402 - 368 = 34[/tex]
[tex]\sigma = \sqrt{\sigma_X^2+\sigma_Y^2} = \sqrt{40^2+30^2} = 50[/tex]
This means that the correct answer is given by option b.
The values X and Y are independent therefore, the mean is 34 seconds and the standard deviation is 50 seconds.
What is the subtraction between normal variables?
The 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.
Before the training, the mean running mean time for the students to runing a mile was 402 seconds with standard deviation 40 seconds.
That is the [tex]\mu_x=402 , \sigma_x=40[/tex]
That is the after completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds.
That is [tex]\mu_y=368,\sigma_y=30[/tex]
which of the following is true about the distribution of X-Y?
They are independent
Therefore we get,
[tex]\mu=\mu_x-\mu_y=402-368=34[/tex]
[tex]\sigma=\sqrt{\sigma_x^2-\sigma_y^2}\\\sigma=\sqrt{40^2-30^2}\\\sigma =50[/tex]
Therefore the option b is correct.
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This means that the correct answer is given by option b.
What is the sum of the rational expressions below?
15/7x+12/7x
Answer:
27 / (7x)
Step-by-step explanation:
Since the denominators are the same, we can add the numerators
15 12
----- + ---------
7x 7x
27
----
7x
Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. They randomly survey 387 drivers and find that 298 claim to always buckle up. Construct a 84% confidence interval for the population proportion that claim to always buckle up.
Answer:
The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
They randomly survey 387 drivers and find that 298 claim to always buckle up.
This means that [tex]n = 387, \pi = \frac{298}{387} = 0.77[/tex]
84% confidence level
So [tex]\alpha = 0.16[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.16}{2} = 0.92[/tex], so [tex]Z = 1.405[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.74[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.8[/tex]
The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).
1st Coordinate Point: (1.4)
2nd Coordinate Point: ( 6 , 6)
(X,Y,) =
(X,Y)=
M = (Y-Y.) =(X-X)
given the number line which inequality has the solution shown below
0.4x + 7 < 1
0.5x + 6 > 3
0.3x + 8 < 3
0.2x + 5 > 2
Answer:
D
Step-by-step explanation:
When you simplify the expression you start by subtracting 5 from both sides. This gives you 0.2x > -3. Then to isolate "x" you divide both sides by 0.2. This gives you x > -15, which is shown in the number line.
What is the radius of a sphere with a volume of 62770 m, to the nearest tenth of a
meter?
Answer:
24.65
Step-by-step explanation:
Convert the equation into standard form 25x^2 -9y^2+200x +18y +166=0
Answer:
Step-by-step explanation:
You'd have to be really familiar with conic sections to know what to do with this. Good thing I am! ; )
Begin by grouping the x terms together and the y terms together, and getting the constant on the other side of the equals sign:
[tex]25x^2+200x-9y^2+18y=-166[/tex]
Now we need to complete the square on the x terms and the y terms. Do this by first factoring out the leading coefficient from each, the 25 from the x's and the 9 from the y's:
[tex]25(x^2+8x)-9(y^2+2y)=-166[/tex]
Now take half the linear term in each set of parenthesis, square it, and add it in to both sides, remembering the multiplier outside (the 25 and the 9). Our x linear term is 8. Half of 8 is 4, and 4 squared is 16, so we add a 16 into the parenthesis with the x's; our y linear term is 2. Half of 2 is 1 and 1 squared is 1, so we add a 1 into the parenthesis with the y's:
[tex]25(x^2+8x+16)-9(y^2+2y+1)=-166+400-9[/tex]
Note the 400 and -9 on the right side now. 25 times 16 is 400; we didn't just add in a 16, we have to multiply the scalar number into it before we know what we REALLY added in. And the -9 comes from multiplying the -9 times 1.
The reason we do this is to get the perfect square binomials on the left that we created while completing the square:
[tex]25(x+4)^2-9(y+1)^2=225[/tex]
Now, finally we will divide both sides by 225 to get this conic into standard form:
[tex]\frac{(x+4)^2}{9} -\frac{(y+1)^2}{25} =1[/tex]
This is a hyperbola with a horizontal transverse axis and a center of (-4, -1). The reason we know it's not an ellipse is because an ellipse will always have a + sign separating the x-squared from the y-squared whereas a hyperbola always has a - sign separating them. And we also know it's not a circle because the values of the leading coefficients weren't the same.
A pyramid and a cone are both 10 centimeters tall and have the same
volume. What statement must be true about the two solids?
A. The vertical cross-sections of the pyramid and cone at the same
width must have the same area.
B. The cross-sections of the pyramid and cone are the same shape.
C. The area of the cross-sections of the pyramid and cone are
multiples of each other.
D. The horizontal cross-sections of the pyramid and cone at the
same height must have the same area.
Answer:
D the horizontal cross-section of the pyramid and cone at the same height must have the same area
Use the angle relationship in the figure below to solve for x. Assume that lines a and b are parallel and the given angles are given in degrees.
9514 1404 393
Answer:
x = 5°
Step-by-step explanation:
The marked angles are "alternate exterior angles," hence congruent.
2x +90° = x +95°
x = 5° . . . . . . . . . . . . subtract (x+90°) from both sides
I have 3 pictures please check them out
Point C(6, 10) is dilated and end up at the image pointC C(10.5, 17.5) . What was the scale factor that was used for the dilation?
Answer:
Step-by-step explanation:xyyxxyduxuxifg icicuddididif uicidididciifificvidid idodididix ididididix ifidididix
what is 12.92÷10 to the power of five
than you
Answer:
0.0001292
Step-by-step explanation:
a raised to the power -m is 1/a raised to power m
The greatest power failure in the history of Dallas, Texas lasted
13 hours. How many minutes did this power failure last?
Answer:
its 780 minutes
Step-by-step explanation:
multiply 13 by 60
An airline promotion to business travelers is based on the assumption that no more than two-thirds of business travelers use a laptop computer on overnight business trips. a. State the hypotheses that can be used to test the assumption. H 0: p Select H a: p Select b. What is the sample proportion from an American Express-sponsored survey that found 359 of 535 business travelers use a laptop computer on overnight business trips (to 4 decimals)?
Answer:
a) The null hypothesis is [tex]H_0: p \leq \frac{2}{3}[/tex] and the alternate hypothesis is [tex]H_1: p > \frac{2}{3}[/tex].
b) The sample proportion is 0.6710.
Step-by-step explanation:
Question a:
An airline promotion to business travelers is based on the assumption that no more than two-thirds of business travelers use a laptop computer on overnight business trips.
At the null hypothesis, we test if the proportion is two-thirds or less, that is:
[tex]H_0: p \leq \frac{2}{3}[/tex]
At the alternate hypothesis, we test if the proportion is of more than two-thirds, that is:
[tex]H_1: p > \frac{2}{3}[/tex]
b. What is the sample proportion from an American Express-sponsored survey that found 359 of 535 business travelers use a laptop computer on overnight business trips (to 4 decimals)?
359 out of 535 is 359/535 = 0.6710.
The sample proportion is 0.6710.
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm
What is the volume of the sphere?
Answer:
12 cm³
Step-by-step explanation:
the volume of the sphere = 4/3 πr³
the volume of the cylinder (h=2r)= πr².2r
= 2πr³
the volume ratio of S : C =
4/3 πr³ : 2 πr³
= 4/3 : 2
= 4 : 6
= 2 : 3
so, the volume of the Sphere =
2/3 × 18 = 12 cm³
Answer:
Solution given:
radius [r]=height[h]
volume of cylinder=πr²h
18cm³=πr³
again
volume of sphere
=4/3 πr³
=4/3*18=24cm³
the volume of the sphere:24cm³
Joey, Mikey, and Anna each bought an equal number of comic books. If Anna
went home with six comic books, how many did the group buy?
Answer: 6, 2, 12, 18 I NEED HELP PLEASE
Answer:
the group bought 18 comic books.
Step-by-step explanation:
It says that Anna went home with 6 comic books and there are 3 people (Joey, Mikey, and Anna). So if Anna bought 6 comic books, Joey also bought 6 books and Mikey also bought 6 books. 6 + 6 + 6 = 18
Hope this is helpful
Interpret the results of the chi-square test.A die is rolled 180 times and the following data are obtained.Number Frequency 1 31 2 34 3 26 4 16 5 32 6 41A chi-square test was conducted to determine, at the 5% significance level, whether or not the die is loaded (i.e., that the six numbers are not equally likely).Carry out the hypothesis test.
Answer:
Step-by-step explanation:
From the given information:
Null and alternative hypothesis is:
[tex]\mathbf{H_o: \text{The die is not loaded i.e. six numbbers are equally alike}}[/tex]
[tex]\mathbf{H_a: \text{The die is loaded i.e. six numbbers are not equally alike}}[/tex]
Numbers Observed Expected (O - E) (O-E)^2 (O-E)^2/E
Frequency (O) Frequency (E)
1 31 30 1 1 0.03
2 34 30 4 16 0.53
3 26 30 -4 16 0.53
4 16 30 -14 196 6.53
5 32 30 2 4 0.13
6 41 30 11 121 4.03
Total 180 [tex]X^2= \sum (\dfrac{O-E}{E})^2=11.78[/tex]
degree of freedom = n - 1
= 6 - 1
= 5
Critical value at [tex]X^2_{0.05/2,5} =11.07[/tex]
Since the calculated [tex]X^2 \ is \ > X^2_{0.025/5}[/tex] , then we reject [tex]H_o[/tex]
Conclusion: Accept the alternative hypothesis.
The information provided gives sufficient evidence for us to conclude that the given die is loaded.
Jane and her friend Maria both invest in the stock market. The probability that Jane makes money in a given week is .6. The probability that Jane and Maria both make money in a given week is .48. What is the probability that Maria makes money in a given week if Jane also makes money in that same week
Answer:
.8
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that the probability that Jane makes money in a given week is .6 and the probability that Jane and Maria both make money in a given week is .48. Then the probability that Maria makes money in a given week...
Let the probability that Jane makes money in a given week be p(j) and that Maria makes money in a week be p(m) then
p(j) = .6 and
p(j) * p(m) = .48
.6 * p(m) = .48
p(m) = .48/.6
= .8
PLS HELP ASAP! WILL GIVE U BRAINLIEST
Valid or Invalid: If a number is even, then it is a multiple of 4.
A. Invalid
B. Valid
Answer:
valid
Step-by-step explanation:
it's valid because for example here are some even numbers, 0, 2, 4, 6, 8, they're are all multiples of four.
hope that helped :)
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100 POINTS IF YOU GUESS RIGHT PLEASE HELP
Answer:
5 and 3Step-by-step explanation:
Let the numbers be x and y.
We have:
x + y = 8x - y = 2Sum the two and find x:
2x = 10x = 5Find y:
y = 5 - 2y = 3Let the numbers be a and b
a+b=8a-b=2Add both
2a=10a=5Put in first one
5+b=8b=3Which choices are equivalent to the fraction below? Check all that apply.
Answer:
Step-by-step explanation:
It's A and B happy learning
Simplify the expression. Write your answer as a power.
(3.8^3)^4
The simplified expression is
Two similar trapezoids have areas 225 and 400. If the height of the smaller trapezoid is 12, find the height of the larger trapezoid.
Answer:
Step-by-step explanation:
The owners of an amusement park selected a random sample of 200 days and recorded the number of park patrons with annual passes who visited the park on each selected day. They computed a 90% confidence interval for the number of patrons with annual passes who visit the park daily. How would you interpret the 90% confidence interval of (35, 51)? a. There is a 90% chance that the population mean number of patrons with annual passes who are in the park on any given day is between 35 and 51. b. The method used to calculate the confidence interval has a 90% chance of producing an interval that captures the population mean number of annual pass holders in the park on any given day. c. Ten percent of the population of annual pass holders visit the park on any given day. d. There is a 90% chance that the sample percentage of park patrons with annual passes is contained in the interval 35 to 51.
Answer:
b. The method used to calculate the confidence interval has a 90% chance of producing an interval that captures the population mean number of annual pass holders in the park on any given day.
Step-by-step explanation:
The confidence interval calculated from the sample at a particular confidence level, gives a certain percentage of confidence based on the confidence level that the true mean of the population exists within the confidence interval Calculated.
For the scenario above, we can say that there is a 90% chance that the population mean number of annual pass holders in the park on a given day is within the interval (35, 51)
You deposit $200 each year for 10 years into a sinking fund that pays 6% interest compounded annually what is the future value of your fund
Answer:
FV= $2,636.16
Step-by-step explanation:
Giving the following information:
Annual deposit (A)= $200
Number of periods (i)= 10 years
Interest rate (i)= 6%
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= annual deposit
FV= {200*[(1.06^10) - 1]} / 0.06
FV= $2,636.16
Can someone please help me on this work I really need help I will but you brainly
Answer:
-3 1/4 is the answer for this question
HELP ME WITH THIS QUESTION PLEASE!!
Answer:
give me a heart first and then ill answer
Step-by-step explanation:
IF YOU HELP ME ILL give U 2$ AFTER UR DONE
Triangle ABC is defined by the points A(-2, 4), B(6,2), and C(1,-1). Using what you know about the distance formula, what type of triangle would ABC be?
Answer:
LOL i dont need money jus mark me brainliest :P
Step-by-step explanation:
[tex]distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]AB = \sqrt{(6--2)^2 + (2-4)^2} = \sqrt{8^2 + 2^2} = \sqrt{68}\\\\BC = \sqrt{(1-6)^2 + (-1-2)^2} = \sqrt{5^2 + 3^2} = \sqrt{34}\\\\AC= \sqrt{(1--2)^2 + (-1-4)^2}} = \sqrt{3^2 + 5^2 } = \sqrt{34}[/tex]
[tex]Clearly, this\ satisfies \ the\ Pythagoras\ theorem : AC^2 = AB^2 + BC^2[/tex]
[tex](\sqrt{68})^2 = (\sqrt{34} )^2 + (\sqrt{34} )^2\\\\68 = 34 + 34 \\68 = 68\\Hence\ satisfies .[/tex]
Therefore, the triangle ABC is a right angle triangle.
is (0,0) a solution to this system
is (0,0) a solution to what system?
Simplify 5√-32
a.-2
b.-4
c.2
d.16
There are______
Pairs of integers satisfying a÷b = -2
Answer:
There are only 1
Pairs of integers satisfying a÷b = -2
Step-by-step explanation:
Answer:
[tex]all \: positive \: integers \: in cluding \: 1[/tex]
so I dont really know how many
Step-by-step explanation:
eg
[tex] \frac{ - 2}{1} \\ \frac{ - 4}{2} \\ \frac{6}{ - 3} \\ = - 2[/tex]
they are all equal to negative 2