Answer:
The point estimate is 5,617.
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
The 98% confidence interval for the difference between the two population means is (5163, 6071).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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 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.
Compound 1:
127 brakes, average brake life of 42,814 miles, population standard deviation of 1819 miles. This means that:
[tex]\mu_1 = 42814[/tex]
[tex]s_1 = \frac{1819}{\sqrt{127}} = 161.41[/tex]
Compound 2:
163 brakes, average brake life of 37,197 miles, population standard deviation of 1401 miles. This means that:
[tex]\mu_2 = 37197[/tex]
[tex]s_2 = \frac{1401}{\sqrt{163}} = 109.73[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 42814 - 37197 = 5617[/tex]
The point estimate is 5,617.
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{161.41^2 + 109.73^2} = 195.18[/tex]
Confidence interval
The confidence interval is:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = zs[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Margin of error:
[tex]M = zs = 195.18*2.327 = 454.18386 [/tex]
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
For the confidence interval, as we round to the nearest whole number, we round it 454. So
The lower bound of the interval is:
[tex]\mu - zs = \mu - M = 5617 - 454 = 5163[/tex]
The upper bound of the interval is:
[tex]\mu + zs = \mu + M = 5617 + 454 = 6071[/tex]
The 98% confidence interval for the difference between the two population means is (5163, 6071).
-5, 20, -80, 320, ... is a geometric
sequence.
What is the explicit rule
Answer:
Multiplied by -4
Step-by-step explanation:
-5 (-4) = 20
20 (-4) = -80
-80 (-4) = 320
Tracey paid $150 for an item that was originally priced at $510. What percent of the original price did Tracey pay?
Answer:
29.4118%
Step-by-step explanation
510 * x = 150
x = .2941176
multiply by 100 to get percent
29.4118
Erin spent half of her weekly allowance at the movies. To earn more money her parents let her wash the car for
$7. What is her weekly allowance if she ended with $12?
Write an equation to represent this situation
Help me with this question
Answer: The angle is a acute angle not obtuse angle.
Step-by-step explanation:
What is the slope of this line?
a.−23
b.−13
c.13
d.23
Answer:
D
Step-by-step explanation:
I think you meant to put the answers as a fraction
Answer:
if there were slashes in between every answer, the answer would be
D. 2/3
Step-by-step explanation:
m = y2-y1 / x2-x1 (slope formula) ⋅the two points i used were: (0,-3) and (3,-1)
m = -1-(-3) / 3-0 (plug in the points)
m = -1+3 / 3-0
m = 2/3 (Simplify to get your answer)
What is the number ten written in base 2?
Which shows two triangles that are congruent by AAS
Answer:
answer A is the correct option.
Step-by-step explanation:
The triangles ( A ) are congruent by AAS theorem
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔABD
Now , AB is the common side of both the triangles
And , measure of ∠ACB = measure of ∠ADB
And , the measure of ∠ABC = measure of ∠ABD = 90°
So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent
To learn more about congruent triangles click :
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help me please guys im being times and trying to get this done fast!
Answer:
C.
Step-by-step explanation:
You're trying to figure out how many more hours he needs to work in order to have worked for 240 hours.
State the postulate or theorem you would use to prove each pair of triangles congruent.
a) SSS
b) SAS
c) ASA
d) AAS
e) HL
f) Not possible
Answer:
f) Not possible
Step-by-step explanation:
The triangles can be shown to be similar by SAS, but the corresponding sides are not marked as congruent. With the given information, it is not possible to show the triangles are congruent.
Solve the following for x. Show all work. x+3/5 =2
Answer:
x+3/5=2
or,x+0.6=2
or,x=2-0.6
x=1.4
Monique mother is 23 years older than Monique. The product of their ages is 518. How old are Monique and her mother?
Answer:
14 and 37
Step-by-step explanation:
[tex]x-y =23\\xy=518[/tex]
x= mother's age
y= Monique's Age
[tex]y=\frac{518}{x}[/tex]
[tex]x=23+y[/tex]
[tex](23+y)y=518[/tex]
[tex]23y+y^{2} =518[/tex]
[tex]y^{2} +23y-518=0[/tex]
[tex](y-14)(y+37)=0[/tex]
[tex]y=14[/tex] monica is 14 years old
The mother: [tex]x-y=23\\x-14=23\\x=23+14 = 37[/tex]
Hope this helps
which expression is equal to 4-6
-1-1 or 2-4 or 3-5 or 6-8 or 7-9 or 8-10
What is the ratio of 1/2 to 6?
(A) 12
(B) 3
(C)1/3
(D)1/6
(E) 1/12
Answer:
e, 1/12
Step-by-step explanation:
1) turn the first fraction into a whole number, the closest whole number being 1.
what did you multiply 1/2 by to get 1? the answer would be 2.
whatever you do to oneside, do to the other. when you multiply 6 by 2, you get twelve.
therefore, the answer is 1/12
If f(x)=7e^x, find which is the value of f(−3) rounded to the nearest hundredth.
Answer:
[tex]f(-3)\approx0.35[/tex]
Step-by-step explanation:
[tex]f(x)=7e^x[/tex]
[tex]f(-3)=7e^{-3}\approx0.35[/tex]
t•t•t•t•t•t•t rewrite using exponents
Answer:
t^7
Step-by-step explanation:
there are 7 ts so it is t to the power of 7
solve for x . Help me solve them
[tex]\\(1).\\\\(1.7898)^{2x} = (1.7898)^6\\\\\implies \ln(1.7898)^{2x} = \ln(1.7898)^6\\\\\implies 2x \ln(1.7898) = 6 \ln(1.7898)\\\\\implies 2x =6\\\\\implies x = \dfrac 62 =3\\\\(3).\\\\2^{5x -6} = 4^{x+9}\\\\\implies 2^{5x -6} = (2^2)^{x+9}\\\\\implies 2^{5x-6} = 2^{2x+18}\\\\\implies \ln(2^{5x-6}) = \ln(2^{2x+18})\\\\\implies (5x -6) \ln 2 = (2x +18) \ln 2\\\\\implies 5x -6 = 2x +18\\\\\implies 5x -2x = 18 +6\\\\\implies 3x = 24\\\\\implies x = \dfrac{24}3 =8[/tex]
Simplify the expression 7h+(−8.3d)−13+6d−2.9h.
Answer:−2.3d+4.1h−13
Step-by-step explanation:
A total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rate if the annual interest is $430?
3,400 at 10%
600 at 15%
This is the answer.
Evan made a tower from 32 building blocks. Aisha made a tower using 5 times as many blocks. How many blocks did Aisha use to make her tower?
Answer:
160
Step-by-step explanation:
32×5 is 60 hope that helps
which expression represents 100 less than 3 times the sum of 18 and 2
Answer: 3 times (18+ 2) - 100
3 (18+2) - 100 = -40
Step-by-step explanation:
Michelle paid $3.00 per shirt. When she sells each shirt, she adds 150% markup to the price she paid for the shirt. What is the selling price for each shirt?
Answer:
$8.50 per shirt
Step-by-step explanation:
If the shirt was $3 originally, and they added 150% markup, 100% of 3 is 3.
so a 100% markup of a $3 shirt would be 6 dollars.
But since she marked it up 150%, you have to know 50% of $3.
50% of something is half, so
3 / 2 = 1.5
so ontop of the $3 extra, she adds $1.5, so
3 + 3 + 1.5 = 8.5
Michelle will sell the shirts for $8.50 each
Pls help my child has no clue and this math is too hard for me to understand!!
Answer: 160
Step-by-step explanation: The questions says that there are 144 which make up 90% of the total group.
What is the other 10%? To figure this out, we can set up a proportion which we can do in the following way:
144/t = 90/100
From here, you can cross multiply 144 x 100 = 14,400
90t = 14,400
t= 160
You can always check by plugging 160 into t to make sure the proportion is equal. I picked t as my varriable of choice which stands for team members. But you can pick an varriable (letter) to find an unknown.
In practice, is best that your child uses a calculator because in the real world, its a practical handy tool and one doesn't have time to memorize every detail by doing that long division. Once your child gets the hang of practicing setting up proportions, your child can solve a variety of problems without going back in circles.
Hope this explanation helps. Best of luck to you and your child.
the degree of the polynomial p³q²-6p²q⁵+p⁴q⁴
Answer:
idioet.
Step-by-step explanation:
Solve the equation logx = cosx to five decimal places by Newton Raphson method.
Answer:
OK okokokokokokokokokokokok
Function 1 is defined by the equation y=-1/4r-5
Function 2
Step-by-step explanation:
as just answered in the other question, the y-intercept is simply the y-value, when x=0.
it is -5 for function 1.
and function 2 clearly crosses the y-axis at y = -7, which is the y-intercept.
as -5 is greater than -7, function 1 had the greater y- intercept.
This year, a small business had a total revenue of $41,600 . If this is 28% more than their total revenue the previous year, what was their total revenue the previous year?
Answer:
Hey will you marry me? serious question
Y= (3x-4)3
Y=(2-4x)3
Y=(3x6-2x4)4
Answer:
y=24
Step-by-step explanation:
what is rational exponent of -(49)1/2?
[tex] {7}^{2( \frac{1}{2}) } \\ [/tex]
Cancel the common factor of 2.
[tex] {7}^{1} [/tex]
Evaluate the exponent[tex] \:= 7[/tex]
Which value of x makes the equation true? 1/5 (2x-10) + 4x = -3(1/5x+4)
A -1/5
B 1/5
C 2
D -2
Answer:
Step-by-step explanation:
1/5 (2x - 10) + 4x = -3(1/5x + 4)
a bit ambiguous, I'll ASSUME you mean
1/5 (2x - 10) + 4x = -3(x/5 + 4)
2x/5 - 2 + 4x = -3x/5 - 12
5x = -10
x = -2
My answer being one of your options makes me think my assumption was correct.
what is the rate of change for these data?
Answer:
-2 gallons per minute
Step-by-step explanation:
As we can clearly see, the water is continuously decreasing every 15 minutes by 30 gallons.
So, the rate of change is -30 gallons per 15 minutes
However, we can simplify this ratio by dividing both sides by 15, so we get
-2 gallons per minute
