Answer:
1/2
Step-by-step explanation:
1
3
−
1
2
(1)
2
=
1
3
−
1
2
2
=
1
3
−
1
4
=
1/12
You intend to estimate a population mean mu with the following sample. 45.3, 42.3, 53, 49, 15.2, 52.3, 45.6, 39.6, 39.4, 16.1, 54.4.You believe the population is normally distributed. Find the 99.9% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places (because the sample data are reported accurate to one decimal place).
Answer:
A 99.9% confidence interval for the population mean is [22.31, 59.91] .
Step-by-step explanation:
We are given the following sample values;
X = 45.3, 42.3, 53, 49, 15.2, 52.3, 45.6, 39.6, 39.4, 16.1, 54.4.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = 41.11
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex] = 13.59
n = sample size = 11
Here for constructing a 99.9% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 99.9% confidence interval for the population mean, [tex]\mu[/tex] is;
P(-4.587 < [tex]t_1_0[/tex] < 4.587) = 0.999 {As the critical value of t at 10 degrees of
freedom are -4.587 & 4.587 with P = 0.05%}
P(-4.587 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 4.587) = 0.999
P( [tex]-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}{[/tex] < [tex]4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.999
P( [tex]\bar X-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.999
99.9% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]41.11-4.587 \times {\frac{13.59}{\sqrt{11} } }[/tex] , [tex]41.11+4.587 \times {\frac{13.59}{\sqrt{11} } }[/tex] ]
= [22.31, 59.91]
Therefore, a 99.9% confidence interval for the population mean is [22.31, 59.91] .
Find the greatest common factor of 30p4q3, 45p6q5, 90p9q4
Answer:
no cule bro
Step-by-step explanation:
Answer:
15p4q3
Step-by-step explanation:
You have a bin full of the letters HGUSTWQ. If four letters are drawn at random, what is the probabilty the letters drawn will spell the word GUST ( in the order they are drawn )?
Answer:
see I need help for chemistry pls anyone here helps me I must submit before 10:30
Evaluate (5-3)^3+ -3^2(6-3)
Steps to solve:
(5 - 3)^3 + (-3)^2(6 - 3)
~Simplify
2^3 + (-3)^2(3)
2^3 + (-3)^6
~Solve exponents
8 + (-729)
~Subtract
-721
Best of Luck!
Find out the coordinates
100(z-0.2)=-10(5z+0.8)
Answer:
Z= 0.08
Or
Z= 2/25
Step-by-step explanation:
100(z-0.2)=-10(5z+0.8)
Opening all the bracket
100z - 20= -50z - 8
Collecting like terms, and at Same time adding up this like terms
100z +50z = -8+20
150z= 12
Dividing bith sides of the equation by 150 to look for the value of z
(150/150)(z)=12/150
Z= 0.08
Or
Z= 2/25
4x – 3y = 20
2x + y = 30
Using the two equations above, solve for y.
Answer:
4x-3y+20
Step-by-step explanation:
x=6.875
y=2.5
2x+y=30
x=12.5
y=-5
Help me please this is math
Answer:
c) none of the above
Step-by-step explanation:
this is because we should put the equation like:
1/3 - (-4/3) because the distance is 5 units and
1/3 + 4/3 = 5/3
this is because (-) × (-) = (+)
A domain consists of the values 1, 2, 3, and 2. A range consists of the values 5, 10, 15, and 20. The 1 in the domain corresponds to the 5 in the range, the first 2 in the domain corresponds to the 10 in the range, the 3 in the domain corresponds to the 15 in the range, and the second 2 in the domain corresponds to the 20 in the range. Does this relation represent a function? Explain.(1 point)
It does not represent a function. The domain value of 2 corresponds to two values within the range.
It does not represent a function. Each value in the domain corresponds to exactly one value in the range.
It does represent a function. Each value in the domain corresponds to exactly one value in the range.
It does represent a function. The domain value of 2 corresponds to two values within the range.
Answer:
It does not represent a function. The domain value of 2 corresponds to two values within the range.
Step-by-step explanation:
Given the function:
Domain : Range
1 => 5
2 => 10
3 => 15
2 => 20
For a relation to be considered a function, every domain value should have exactly 1 range value assigned to it or mapped to it.
In order words, a domain value should not have different range values.
In the relation given, domain value of 2, has more than 1 range value, 10 and 20, assigned to it. It does not have exactly 1 range value.
Therefore, the relation does not represent a function because the domain value of 2 corresponds to two values (10 and 20), within the range.
Answer:
It does not represent a function. The domain value of 2 corresponds to two values within the range.
Step-by-step explanation:
please help :)) ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
Find the triangle of the following figure: A. 30cm2 B: 36cm2 C. 18cm2 D. 15cm2
Answer:
D. 15cm2
Step-by-step explanation:
To find the area of a triangle, you multiply the base (10cm) and height of the triangle (3cm) and divide that by 2. So 10×3=30. Then, you need to divide this by 2. Since 30 is an even number, you won't get a decimal. So 30/2=15. And dont forget your units!
Julie travels 3 times as fast as Bill. Traveling in opposite directions, they are 190 miles apart after 2.5 hours. Find their rates of travel.
Answer:
Step-by-step explanation:
Let b
Bill's rate of travel = x
Let Julie's rate of travel = 3x
The time each travels is 2.5 hours
Together they travel a distance of 190 miles
d = r*t
Bill's distance covered is r * t = 2.5x
Julie's distance travel is 2.5 * 3x = 7.5x
The total distance = Bill + Julie
2.5x + 7.5x = 190
10x = 190
x = 190/10
x = 19
Bill's distance = 2.5 * 19 = 47.5
Julie's distance = 19 * 7.5 = 142.5
Rate = distance / time
Bill's rate = 47.5 / 2.5 = 19 miles per hour.
Julie's rate = 142.5/2.5 = 57 miles per hour
Is there an easier way?
You should notice that Bill's rate is just x which is 19 miles / hour
You can also notice that Julie is going 3 times as fast or 19*3 = 57
The three volumes of Lord of the Rings sit in order on a shelf. Each is 1 1/4 inches thick, comprising an inch of pages and 1/8 inch for each cover. A bookworm bores from page 1, volume I, to the last page of volume III. How far does it travel?
Answer:
4 2/4 (NOT SIMPLIFIED)
Step-by-step explanation:
Comprising means made of (aka including). You just add 1 1/4+1 1/4+1 1/4.
=3 3/4
The 1/8 is for the front and back cover. The bookworm ate through 3 volumes so there is 6 covers. So times 1/8 by 6. I turned the 6 into a fraction by putting it over 1. So now you have 1/8×6/1=6/8. Now you are going to add the 3 3/4 to the 6/8. You are going to turn the whole fraction to an improper. You are going to multiply the whole number(3) to the denominator(4), add that to the numerator(3) , and put it over the original denominator (4)= 15/4. Now you are going to set up the problem were you add the 6/8 to the 15/4. To add fractions the denominator have to be the same. With this problem you have two options: you can either do an equation to change the 6/8 denominator equal to 4 or an equation to change the 15/4 denominator equal to 8. Either one would work fine. I'm going to show you how to set the 6/8 denominator to 4.
1. Set it up as an equation 6/8=x/4
2. Find what gets the first denominator to the second in this case dividing by 2 6/8=x/4
3. What you do to the bottom is what you have to do with the top. So to find x, you need to divide 6 by 2= 3
So now your new equation is now 3/4+15/4. Adding this should give you 18/4, but most likely you have to write it as a proper fraction. To do this you are going to divide the 18 by 4. Your remainder will become your new numerator and the 4 will still be you denominator. The number times 4 fully goes into 18 will be your new whole number.
18/4=4.5
Martin's average score after 4 tests is 89. What score on the 5th test would bring Martin's average up to exactly 90?
Answer:
104
Step-by-step explanation:
89x4=356 90x5=450
450=356=104
Answer:
94
Step-by-step explanation:
((89x4)+94) divided by 5 = 90
y=1/4x + 6
that passes through the point (-4, 3) in slope-intercept form.
Answer:
The answer is
[tex]y = \frac{1}{4} x + 4[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line.
The equation is
y = 1/4x + 6
Comparing with the general equation above
Slope = 1/4
Since the lines are parallel their slope are also the same
That's
Slope of parallel line = 1/4
So the equation of the parallel line using point (-4 , 3) and slope 1/4 is
[tex]y - 3 = \frac{1}{4} (x + 4) \\ y - 3 = \frac{1}{4} x + 1 \\ y = \frac{1}{4} x + 1 + 3[/tex]We have the final answer as
[tex]y = \frac{1}{4} x + 4[/tex]Hope this helps you
The online program at a certain university had an enrollment of 580 students at its inception and an enrollment of 1725 students 3 years later
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
The online program at a certain university had an enrollment of 580 students at its inception and an enrollment of 1725 students 3 years later. Assume that the enrollment increases by the same percentage per year. a) Find the exponential function E that gives the enrollment t years after the online program's inception. b) Find E(11), and interpret the result. c) When will the program's enrollment reach 5500 students?
Let E0 be the number of students that enrolled at inception
E(t) be the number of students that enrolled at any time t
At inception i.e at t = 0, E0 = 580
The exponential function E that gives the enrollment at inception will be expressed as;
E(t) = E0e^kt (note that the exponential power is positive since number of students keep increasing yearly).
At inception:
E(0) = 580e^k(0)
E(0) = 580(1)
E(0) = 580
If after 3years, enrollment increases to 1725 students i.e at t = 3, E(t) = 1725. The equation becomes;
E(3) = P0e^kt
E(3) = 580e^3k
1725 = 580e^3k
Make k the subject of the formula:
e^3k = 1725/580
e^3k = 2.9741
Apply ln to both sides of the equation
ln(e^3k) = ln(2.9741)
3k = 1.08995
k = 1.08995/3
k = 0.3633
The exponential function E that gives the enrollment t years after the online program's inception will be expressed as;
E(t) = E0e^kt
Given E0 = 580 and k = 0.3633
E(t) = 580e^0.3633t
b) To get E(11), we will substitute t = 11 into the resulting expression in (a) above to have;
E(t) = 580e^0.3633t
E(11) = 580e^0.3633(11)
E(11) = 580e^3.9965
E(11) = 580×54.4074
E(11) = 31,556.287
E(11) ≈ 31,556 students
This means that about 31,556students enrolled 11years later.
c) To know when the program's enrollment reach 5500 students, we will set E(t) to 5500, E0 to 580 and k to 0.3633 and calculate the value of t
From the equation E(t) = 580e^0.3633t
5500 = 580e^0.3633t
e^0.3633t = 5500/580
e^0.3633t = 9.4828
Apply ln to both sides
ln(e^0.3633t) = ln(9.4828)
0.3633t = 2.2495
t = 2.2495/0.3633
t = 6.19
t ≈ 6years
This means that the program's enrollment will reach 5500 students 6 years later.
What if the perimeter of the table?
Step-by-step explanation:
13? i forgot all this math XD
Chris wonders whether the planes that fly over his house follow any sort of pattern. For two months, he
records whether each plane he sees follows a north-south route or an east-west route. He also records the
day of the week that he sees each plane.
Unfortunately, Chris dropped his data in the mud and can't read all of his numbers. The absolute and
relative frequency tables below show the numbers that Chris is able to read. Can you help him figure out
the rest?
Fill in the missing values from each table.
Answer:
Kindly check explanation
Step-by-step explanation:
From the relative frequency below:
For NORTH - SOUTH:
Monday - Thursday = 115 ; has a relative frequency of 75.16%,
Hence, we can obtain the row total since it amounts to 100% thus;
75.16% of row total = 115
0.7516× row total = 115
Row total = 115 / 0.7516 = 153.00
Hence, Friday - sunday:
Row total - (Monday-Thursday)
153 - 115 = 38
FOR EAST - WEST:
Monday - Thursday = 21 ; has a relative frequency of 25.30%,
Hence, we can obtain the row total since it amounts to 100% thus;
25.30% of row total = 21
0. 253 × row total = 21
Row total = 21 / 0.253 = 83.00
Hence, Friday - sunday:
Row total - (Monday-Thursday)
83 - 21 = 62
x = (38 / 100) × 100%
x = 0.38 × 100%
x = 38.00 %
Answer:
The basic explanation:
North - South/Friday - Sunday- 38 // Row total- 153
East - West/Friday - Sunday- 62 // Row total- 83
x- 38
what expression is equivalent
Answer:
-4x^2, -3x, -5
Step-by-step explanation:
-4x^2 + 2x - 5 (1 + x)
-4x^2 + 2x - 5 + 5x
-4x^2 - 3x - 5
WILL MARK BRAINLIEST
List all of the number sets that contain the number 15.
A. rational numbers and integers
B. rational numbers, integers, and natural numbers
C. rational numbers, integers, and whole numbers
D. rational numbers, integers, natural numbers, and whole numbers
Answer: D
Step-by-step explanation:
f(x) = x - 5, translated 6 units to the right.
Answer:
[tex]g(x) = x - 11[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 5[/tex]
Required
Translate to the right by 6 units
When a function is translated to the right, the resulting function becomes
[tex]g(x) = f(x - h)[/tex]
Where h is the number of units moved;
Since; h = 6
[tex]g(x) = f(x - h)[/tex]
becomes
[tex]g(x) = f(x - 6)[/tex]
Solving for f(x - 6);
[tex]f(x) = x - 5[/tex]
Substitute x - 6 for x
[tex]f(x - 6) = x - 6 - 5[/tex]
[tex]f(x - 6) = x - 11[/tex]
This implies that [tex]g(x) = x - 11[/tex] is the result of the translation
A doctor studying nutrition collected data on the weights (in kilograms) of infants in North Africa. The table below shows the mean weights for infants of different ages in the study. Plot the data in a scatter plot.
Answer:
Step-by-step explanation:
Got it correct on Khan Academy
The product of 6 and a is 30
Answer:
30 divided by 6=5
Step-by-step explanation:
a=5
5 times 6 is the product of 30
Which of the following is an example of a translation?
a) The preimage is twice the size as the image.
b) The preimage is moved 5 spaces up.
c) The preimage is rotated 90 degrees about the origin.
d) The image is a mirror reflection of the preimage.
Answer:
Step-by-step explanation:
a)the pre image us twice the same size as the image
ionic bonds occur between?
Answer:
Ionic bonds usually occur between metal and nonmetal ions. For example, sodium (Na), a metal, and chloride (Cl), a nonmetal, form an ionic bond to make NaCl. In a covalent bond, the atoms bond by sharing electrons. Covalent bonds usually occur between nonmetals.
An ionic bond is held together by the electrostatic attraction between ions that are near one another. Electrostatic attraction is the attraction between atoms that have opposite charge and holds the atoms together in ionic bonds.
What is the answer to x - 3 = -10
Answer:
x = -7
Step-by-step explanation:
x - 3 = -10
Add 3 to each side
x - 3+3 = -10+3
x = -7
Which of the following are dimensionally consistent? (Choose all that apply.)(a) a=v / t+xv2 / 2(b) x=3vt(c) xa2=x2v / t4(d) x=vt+vt2 / 2(e) v=x2 / at3(f) a3=x2v / t5(g) x=t(h) v=5at
Complete Question
The complete question is shown on the first uploaded image
Answer:
A
is dimensionally consistent
B
is not dimensionally consistent
C
is dimensionally consistent
D
is not dimensionally consistent
E
is not dimensionally consistent
F
is dimensionally consistent
G
is dimensionally consistent
H
is not dimensionally consistent
Step-by-step explanation:
From the question we are told that
The equation are
[tex]A) \ \ a^3 = \frac{x^2 v}{t^5}[/tex]
[tex]B) \ \ x = t [/tex]
[tex]C \ \ \ v = \frac{x^2}{at^3}[/tex]
[tex]D \ \ \ xa^2 = \frac{x^2v}{t^4}[/tex]
[tex]E \ \ \ x = vt+ \frac{vt^2}{2}[/tex]
[tex]F \ \ \ x = 3vt[/tex]
[tex]G \ \ \ v = 5at[/tex]
[tex]H \ \ \ a = \frac{v}{t} + \frac{xv^2}{2}[/tex]
Generally in dimension
x - length is represented as L
t - time is represented as T
m = mass is represented as M
Considering A
[tex]a^3 = (\frac{L}{T^2} )^3 = L^3\cdot T^{-6}[/tex]
and [tex]\frac{x^2v}{t^5 } = \frac{L^2 L T^{-1}}{T^5} = L^3 \cdot T^{-6}[/tex]
Hence
[tex]a^3 = \frac{x^2 v}{t^5}[/tex] is dimensionally consistent
Considering B
[tex]x = L[/tex]
and
[tex]t = T[/tex]
Hence
[tex]x = t[/tex] is not dimensionally consistent
Considering C
[tex]v = LT^{-1}[/tex]
and
[tex]\frac{x^2 }{at^3} = \frac{L^2}{LT^{-2} T^{3}} = LT^{-1}[/tex]
Hence
[tex]v = \frac{x^2}{at^3}[/tex] is dimensionally consistent
Considering D
[tex]xa^2 = L(LT^{-2})^2 = L^3T^{-4}[/tex]
and
[tex]\frac{x^2v}{t^4} = \frac{L^2(LT^{-1})}{ T^5} = L^3 T^{-5}[/tex]
Hence
[tex] xa^2 = \frac{x^2v}{t^4}[/tex] is not dimensionally consistent
Considering E
[tex]x = L[/tex]
;
[tex]vt = LT^{-1} T = L[/tex]
and
[tex]\frac{vt^2}{2} = LT^{-1}T^{2} = LT[/tex]
Hence
[tex]E \ \ \ x = vt+ \frac{vt^2}{2}[/tex] is not dimensionally consistent
Considering F
[tex]x = L[/tex]
and
[tex]3vt = LT^{-1}T = L[/tex] Note in dimensional analysis numbers are
not considered
Hence
[tex]F \ \ \ x = 3vt[/tex] is dimensionally consistent
Considering G
[tex]v = LT^{-1}[/tex]
and
[tex]at = LT^{-2}T = LT^{-1}[/tex]
Hence
[tex]G \ \ \ v = 5at[/tex] is dimensionally consistent
Considering H
[tex]a = LT^{-2}[/tex]
,
[tex]\frac{v}{t} = \frac{LT^{-1}}{T} = LT^{-2}[/tex]
and
[tex]\frac{xv^2}{2} = L(LT^{-1})^2 = L^3T^{-2}[/tex]
Hence
[tex]H \ \ \ a = \frac{v}{t} + \frac{xv^2}{2}[/tex] is not dimensionally consistent
We want to see which ones of the given expressions are dimensionally consistent. We will see that the correct options are:
a) x = 3*v*th) v = 5*a*tWhat means to be dimensionally consistent?
This means that we have the same units in the left and in the right side of the equation.
The units are:
a = [m/s^2]x = [m]v = [m/s]t = [s]Now we can analyze the expressions to see the units in each one, I will show you how to do it:
a) a = v/t + x*v^2
Replacing the units we have:
[m/s^2] = [m/s]/[s] + [m]*[m^2/s^2]
[m/s^2] = [m/s^2] + [m^3/s^2]
You can see that we have an m^3 in the right side, so these are not equivalent.
b) x = 3*v*t
Replacing the units we have:
[m] = 3*[m/s]*[s] = 3*[m]
So yes, the units are the same in both sides, so this is dimensionally consistent.
With the same procedure we can see that:
c) [m^3/s^2] = [m^3/s] not consistentd) [m] = [m] + [m*s] not consistente) [m/s] = [m^2] not consistentf) [m^3/s^6] = [m^3/s] not consistentg) [m] = [s] not consistenth) [m/s] = 5*[m/s] consistentSo the correct options are b and h.
If you want to learn more about dimensions, you can read:
https://brainly.com/question/20384972
What is the sum of Negative 1 + (negative 3)?
Answer:
[tex]\huge\boxed{-4}[/tex]
Step-by-step explanation:
=> [tex]\sf -1 + (-3)[/tex]
According to the rule [tex]\sf + * - = -[/tex]
=> [tex]\sf -1-3[/tex]
=> -4Answer:
-4
Step-by-step explanation:
-1 + (-3)
To add two negative numbers, add their absolute values, and make the answer negative.
The absolute values of -1 and -3 are 1 and 3. We add 1 + 3 and get 4.
Then we make the answer negative.
-1 + (-3) = -4
When two times a number is decreased by 3, the result is 11. What is the number?
Answer:
7
Step-by-step explanation:
let the unknown number be x
so x times 2 minus 3=11
it will now be 2x-3=11
the -3will cross the equal sign and change to +3
2x=11+3 which will be 2x=14
divide both sides by 2 and the final answer will be x=7
Perform the following operations and write the answers in radical form. Part A:√7+√3+√98−√18 Part B:3√5−3√11+2√121−3√90
Answer:
[tex]\sqrt{7}+\sqrt{3}+4\sqrt{2}[/tex] [tex]3\sqrt{5}-3\sqrt{11}+22-9\sqrt{10}[/tex]Step-by-step explanation:
Part A ;
[tex]\sqrt{7} +\sqrt{3} +\sqrt{98} -\sqrt{18} \\\\\sqrt{98}=7\sqrt{2}\\\sqrt{18}=3\sqrt{2}\\\\=\sqrt{7}+\sqrt{3}+7\sqrt{2}-3\sqrt{2}\\\\\mathrm{Add\:similar\:elements:}\:7\sqrt{2}-3\sqrt{2}=4\sqrt{2}\\\\=\sqrt{7}+\sqrt{3}+4\sqrt{2}[/tex]
Part B ;
[tex]3\sqrt{5} - 3\sqrt{11} + 2\sqrt{121} -3\sqrt{90} \\\\2\sqrt{121}=22\\3\sqrt{90}=9\sqrt{10}\\\\=3\sqrt{5}-3\sqrt{11}+22-9\sqrt{10}[/tex]