Answer:
a) -6 mpg.
b) 2.77 mpg
c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
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.
Gas mileage A: Mean 36, standard deviation 6, sample of 50:
So
[tex]\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485[/tex]
Gas mileage B: Mean 42, standard deviation 8, sample of 50:
So
[tex]\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314[/tex]
Distribution of the difference:
Mean:
[tex]\mu = \mu_A - \mu_B = 36 - 42 = -6[/tex]
Standard error:
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142[/tex]
A. Find the point estimate.
This is the difference of means, that is, -6 mpg.
B. Find the margin of error
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 - 0.95}{2} = 0.025[/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 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = zs = 1.96*1.4142 = 2.77[/tex]
The margin of error is of 2.77 mpg
C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)
The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg
The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg
The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
One number is three less than another number. Their product is 40. Find the numbers.
Answer:8 and 5
Step-by-step explanation:8 times 5 is 40 and 5 is 3 less than 8
a car gets 30 miles per gallon of gas. at this rate, how many gallons would it take for the car to go 360 miles
Answer:
The car would need 12 gallons of gas to go 360 miles
Step-by-step explanation:
360÷30=12
Answer:
it would take 12 gallons of gas
Step-by-step explanation:
[tex]360 \div 30 = 12[/tex]
Solve 7x2 + 1 = 29.
A) x = +1.5
B) x= +1
C) x = +2.5
D) x = +2
Answer:
the answer is D.
Step-by-step explanation:
write in decimal form 7+3/100+9/1000
Answer:
7.039
Step-by-step explanation:
7 + 3/100 + 9/1000
7 + 0.03 + 0.009
7.039
Answer:
7.039
Step-by-step explanation:
7 = 7
3/100 = .03
9/1000 = .009
therefore
7 + 3/100 + 9/1000 = 7 + .03 + .009
7.039
Please help me with this problem
ln -3x + ln 4 = ln 58
9514 1404 393
Answer:
x = -29/6 = -4 5/6
Step-by-step explanation:
The equation simplifies to ...
ln(-3x·4) = ln(58)
Taking antilogs, the equation becomes ...
(-3x)(4) = 58
Dividing by -12 shows us the value of x.
x = -58/12
x = -29/6 = -4 5/6
__
The applicable rule of logarithms is ...
ln(ab) = ln(a) +ln(b)
Answer:
7x - 4x = 21
3x = 21
x = 21÷3
x = 7
find the alternative interior angles in each figure
Answer:
Step-by-step explanation:
Please help me ITS DUE PLEASE
Answer:
Step-by-step explanation:
its A
Answer:
Answer:
Step By Step:
Letter:A
I WILL GIVE BRAINILY PLSSSSS HELPLPPP
Which linear function is increasing at a greater
rate? Explain your reasoning.
Linear Function 1 has an x-intercept of (4, 0) and
a y-intercept at (0, 22)
Linear function 2 includes the points in the table
below
Answer:
Linear function 2
Step-by-step explanation:
If Linear function 1 has an x-intercept of 4,0 and a y-intercept of 0,22
It's a negative equation, Its not increasing Its decreasing.
So it must be Linear function 2
How much is 331 ft in meters?
it would be 100.889, darling. hope this helps. <3
Two lines intersect, and you know the measure of one angle. How can you determine the measures of the other three angles
Answer:
Opposite angles are the same measure.
Angles around a point = 360°
When you add all the angles, you get 360.
Angle a and b would measure the same and so would angle d and c. So you double the measure for one of those angles and subtract it from 360.
Then, you half that value( divide by 2) and this is to find the measure of the other angle
a. -3/2
b. 0
c. 3/2
d. DNE
solve each of the following systems, if possible. indicate whether the system has a unique solution, infinitely many solutions, or no solution.
a. 2x + 10y = 9
3x + 15y = 13
b. 2x + 8y = 5
3x + 12y = 7.5
c. y = 3-x
d. 5x -8y = -1
-5/2 x + 4y = 1/2
Answer:
(a) No solution
(b) Infinitely many solution
(c) No solution
(d) Infinitely many solution
Step-by-step explanation:
Solving (a):
[tex]2x + 10y = 9[/tex] --- (1)
[tex]3x + 15y = 13[/tex] --- (2)
Multiply (1) by 1.5
1.5 * [[tex]2x + 10y = 9[/tex]]
[tex]3x + 15y = 13.5[/tex] --- (3)
Subtract 2 and 3
[tex]3x - 3x + 15y - 15y = 13.5 - 13[/tex]
[tex]0 = 0.5[/tex]
The above is false; Hence, the system has no solution
Solving (b):
[tex]2x + 8y = 5[/tex] --- (1)
[tex]3x + 12y = 7.5[/tex] -- (2)
Multiply 1 by 1.5
1.5 * [[tex]2x + 8y = 5[/tex]]
[tex]3x + 12y = 7.5[/tex]
Subtract 2 and 3
[tex]3x - 3x + 12y - 12y = 7.5 - 7.5[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
Solving (c):
[tex]y = 3 - x[/tex]
A second equation is required to solve for (c)
Solving (d):
[tex]5x - 8y = -1[/tex] --- (1)
[tex]-\frac{5}{2}x+ 4y = \frac{1}{2}[/tex] --- (2)
Multiply (2) by 2
[tex]-5x + 8y = 1[/tex] --- (3)
Add 1 and 3
[tex]5x - 5x -8y + 8y = -1 + 1[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
Draw a picture of a line and a point that is not on the line. Draw in the shortest distance from the point to the line, What do you notice about the line connecting the point and the line to the original line?
Answer: The line connecting the point and the line is perpendicular to the original line.
Step-by-step explanation:
(Forgot the name but there is also a theorem stating that the shortest distance between a point and a line is the one that is perpendicular)
Solve for <2.
499
62 = [?]
44/42
Answer:
Solution given'
<2+90+49=180°[sum of interior angle of a triangle]
<2=180-139
<2=41°
ANSWER THIS ASAP NO FILE AT ATT!!
The answer would be A
Answer:
It would be A
Step-by-step explanation:
Once again the shape does not rotate or flip it stays the same but moves on the coordinate plane.
What is the product
2 1/3 times 3 1/4
Answer:
[tex]7\frac{7}{12}[/tex]
Step-by-step explanation:
I need the answer fast
Answer:
84
Step-by-step explanation:
Answer:
it would either be 2 or 26
Step-by-step explanation:
pls mark braainlieszt
Which measurement could be a surface area measure?
24 km2
18 m3
63 oz.
12 mm
Given
f(x) = 2x - 1 and g(x) = 4x + 6,
which operation completes the statement?
f(x) ___ g(x) = 8x^2 + 8x - 6
i need to determine what math sign i have to use on the ____ the options are *,+,-, and the divide symbol
this is operations on functions!!!
f(x) times g(x) = 8x^2+8x-6
(2x-1) times (4x+6) = 8x^2+8x-6
====================================================
Explanation:
The functions f(x) and g(x) are linear functions. The result of f(x) ___ g(x) is some quadratic function.
It's very likely that the answer is a multiplication sign because of the general template of
(linear)*(linear) = (quadratic)
For example, x*3x = 3x^2.
Let's see if the two functions multiply out to 8x^2+8x-6 or not.
-----------------------
f(x) * g(x) = ( f(x) ) * ( g(x) )
f(x) * g(x) = ( 2x-1 ) * ( 4x+6 )
f(x) * g(x) = y * ( 4x+6 ) ......... let y = 2x-1
f(x) * g(x) = 4xy + 6y ......... distribute
f(x) * g(x) = 4x( y ) + 6( y )
f(x) * g(x) = 4x( 2x-1 ) + 6( 2x-1 ) .... replace y with 2x-1
f(x) * g(x) = 8x^2-4x + 12x-6 .... distribute twice more
f(x) * g(x) = 8x^2+8x-6
We end up getting the correct result. So this confirms that a multiplication sign is needed to fill in the blank.
15 POINTS. EZ QUESTION.
The pentagon below has been reduced by a scale of 0.5.
A pentagon with an area of 120 inches squared.
What is the area of the reduced pentagon?
30 in.²
60 in.²
90 in.²
120 in.²
Answer:60 inches squared
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
bc i got it right on edg test/ exam 2021
NEED HELP ON MATH TEST ASAP!! Will give BRAINLY
Must show work on all problems!!
Parker Moore is single and pays into an HMO. The total cost is $8,550 annually and the employer pays 90 % of the total cost . Parker also pays 50% of the optional annual dental premium of $782. How much is deducted each week from his paycheck ?
Answer:23.96
Step-by-step explanation:
100-90=10%
10/100=0.10
0.10(8550)=855
100-50=50%
50/100=0.50
0.50(782)=391
855+391=1246
1246/52=23.96
Find the volume of a pyramid with a square base, where the perimeter of the base is 10.4\text{ in}10.4 in and the height of the pyramid is 9.6\text{ in}9.6 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
21.6in^3
Step-by-step explanation:
\text{Volume of Pyramid:}
Volume of Pyramid:
V=\frac{1}{3}Bh
V=
3
1
Bh
Where B is the area of the base
\text{Perimeter of base}:
Perimeter of base:
\,\,10.4
10.4
\text{Side length of base}:
Side length of base:
\,\,\frac{10.4}{4}=2.6
4
10.4
=2.6
Divide perimeter of square by 4 to get side length
\text{Area of base}:
Area of base:
\,\,2.6^2=6.76
2.6
2
=6.76
Area of a square is s^2
B=
B=
\,\,6.76
6.76
h=
h=
\,\,9.6
9.6
given
V=
V=
\,\,\frac{1}{3}Bh
3
1
Bh
V=
V=
\,\,\frac{1}{3}(6.76)(9.6)
3
1
(6.76)(9.6)
Plug in
V=
V=
\,\,21.632
21.632
V\approx
V≈
\,\,21.6\text{ in}^3
21.6 in
3
plz help 5th grade work
Answer:
81 , 24 AND 108
Step-by-step explanation:
The answer to the above question
Answer:
Step-by-step explanation:
Since our interval is given as it is, we are in QIII. That interval is equivalent to 270 degrees to 360 degrees, which is QIII. If we draw this right triangle in QIII and label it accordingly, the side adjacent to the reference angle is sqrt2 and the hypotenuse is 2. We know this because the cosine ratio is defined as the side adjacent to the reference angle over the hypotenuse of the right triangle. That means that we have to find the missing side in order to determine the other 2 main trig ratios. Using Pythagorean's Theorem, we have
[tex]2^2=\sqrt{2}^2+b^2[/tex] and
[tex]4=2+b^2[/tex] so
[tex]b=\sqrt{2}[/tex]. But since it is for a value that, in QIII is negative, it is [tex]-\sqrt{2}[/tex]
Now we can find the sin and tan of that reference angle. Sin is defined as the side opposite the reference angle over the hypotenuse, so
[tex]sin\theta=\frac{-\sqrt{2} }{2}[/tex] and tan, which is defined as side opposite the reference angle over the side adjacent to the reference angle, then
[tex]tan\theta=\frac{-\sqrt{2} }{\sqrt{2} }=-1[/tex]
HELP PLEASEEEEEEE!!!
Answer:
first one , I believe, sorry if incorrect
One radius of a circle is the same length as any other radius of the same
circle.
A. True
B. False
A. True
In a circle, all radii have the same length. The radius is the distance from the center of the circle to any point on its circumference. Since the center is equidistant from all points on the circumference, all radii will have the same length. Therefore, the statement is true.
4 × 7/8 = ? 4 × 6/8 =?
Answer:
4 × 7/8 = 3.5
Step-by-step explanation:
4 × 6/8 = 3
Answer:
3.5 and 3
Step-by-step explanation:
In this composite function, (f◦g)(x) where f(x)=(X-3) and g(x)=X^2 what is (f◦g)(x) when x=1?
Answer:
When x = 1, (f◦g)(x) is -2.
Step-by-step explanation:
Composite function:
The composite function of f and g is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this question:
[tex]f(x) = x - 3, g(x) = x^2[/tex]
Composite function:
The composite function is:
[tex]f(g(x)) = f(x^2) = x^2 - 3[/tex]
At x = 1
[tex](f \circ g)(1) = 1^2 - 3 = 1 - 3 = -2[/tex]
So
When x = 1, (f◦g)(x) is -2.
neeeeeeeeeeeeed help
Answer:
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[/tex]
D. 34 lakh