The sample mean of the random sample is 50
The margin of error (E) is the amount of error allowed in the random sample.
The confidence interval (CI) is given by:
CI = μ ± E = (μ - E, μ + E)
Given a confidence interval of (38.02, 61.98), hence:
μ - E = 38.02 (1)
μ + E = 61.98 (2)
Hence solving equations 1 and 2 simultaneously gives:
μ = 50, E = 11.98
Hence the sample mean of the random sample is 50
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Rationalize the denominator and simplify the following expression:
fraction numerator 4 plus square root of 2 over denominator 2 space minus square root of 2 end fraction
let's recall that the conjugate of say a + b is simply the same thing with a different sign in between, namely a - b, so let's use the conjugate of the denominator and multiply top and bottom by it.
[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{4+\sqrt{2}}{2-\sqrt{2}}\cdot \cfrac{2+\sqrt{2}}{2+\sqrt{2}}\implies \cfrac{(4+\sqrt{2})(2+\sqrt{2})}{\underset{\textit{difference of squares}}{(2-\sqrt{2})(2+\sqrt{2})}}\implies \cfrac{(4+\sqrt{2})(2+\sqrt{2})}{2^2-(\sqrt{2})^2}[/tex]
[tex]\cfrac{8+4\sqrt{2}+2\sqrt{2}+(\sqrt{2})^2}{4-2}\implies \cfrac{8+4\sqrt{2}+2\sqrt{2}+2}{2}\implies \cfrac{10+6\sqrt{2}}{2} \\\\\\ \cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(5+3\sqrt{2})}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \boxed{5+3\sqrt{2}}[/tex]
Will give brainliest!
We know that a + b + c = 7 and [tex]\frac{1}{a+b} + \frac{1}{b+c} +\frac{1}{a+c} =\frac{7}{10}[/tex]. What is the value of [tex]\frac{10a}{b+c} +\frac{10b}{a+c} +\frac{10c}{a+b}[/tex]?
Answer:
19
Step-by-step explanation:
Note that
[tex]\dfrac{10a}{b+c} + \dfrac{10b}{a+c} + \dfrac{10c}{a+b} = 10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right)[/tex]
and
[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b}=\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]
from [tex]a+b+c=7 \implies a=7-bc; b = 7-a-c; c = 7-a-b[/tex]
and
[tex]\dfrac{7-b-c}{b+c}+\dfrac{7-a-c}{a+c}+\dfrac{7-a-b}{a+b} = 7\left(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{a+c}\right)-3[/tex]
because it is not difficult to note that
[tex]$\sum \dfrac a{b+c}=\dfrac a{b+c}+\dfrac b{c+a}+\dfrac c{a+b}$[/tex]
Therefore,
[tex]7\left(\dfrac{7}{10}\right)-3 = \dfrac{49}{10}-3 =\boxed{ \dfrac{19}{10}} = \dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b}[/tex]
Finally,
[tex]10\left(\dfrac{a}{b+c} + \dfrac{b}{a+c} + \dfrac{c}{a+b} \right) = 10 \cdot \dfrac{19}{10} = 19[/tex]
find the amount of money Khairul had initially
Answer
Find the amount of money Khairul had initially
money with Khairul initially = 6x = 6(60) = 360
Step-by-step explanation:
What is the average number of 20 14 28 18
Step-by-step explanation:
Avg = 20 + 14 + 28 + 18 /4
Avg = 80/4 = 20
what is the last number
lol
Answer:
Infinity probally. But there is a number called the god's number reported by Galileo in which he states a number in which the enitre universe fits.
If ACD and BAC are alternate interior angles and mACD=101°
Answer is A. 101°
Step-by-step explanation:
domain and range of y = x/(x+4)
Answer:
Step-by-step explanation:
[tex]y=\frac{x}{x+4}[/tex]
for domain x+4≠0
x≠-4
domain={R-{-4}}
R=all real numbers.
y(x+4)=x
yx+4y=x
yx-x=-4y
x(y-1)=-4y
[tex]x=-\frac{4y}{y+1} \\y+1\neq 0\\y\neq -1\\[/tex]
so Range ={R-{-1}}
Mrs. Sparks is a 9th-grade Algebra 1 teacher. She teaches three
Algebra 1 courses and all the classes recently took a chapter exam.
Below are the scores. PLZ HELP 100 POINTS
Answer:
ninth grade teacher is going skipping 30 to each class
Step-by-step explanation:
4-3/7. Can u pls help me out
Answer:
1/7
Step-by-step explanation:
4-3/7
1/7
Hope This Helps You.
Answer:
3 4/7
Step-by-step explanation:
Regroup 4 as 3 7/7.
Subtract 3 7/7 - 3/7 = 3 4/7
There's your answer!
please mark brainliest!
A rectangle has length 72 cm and width 56 cm. The other rectangle has the same area as this one, but its width is 21 cm. What is the length of the second rectangle?
Answer:
Step-by-step explanation:
As given, the other rectangle has the same area as this one, but its width is 21 cm. Hence, length is 192 cm.
which statement is true about the points located in quadrant IV on the coordinate plane
Answer:
B. The x-coordinate is positive, and the y-coordinate is negative
Step-by-step explanation:
Counting for the quadrants starts and the positive x-axis and then moves counterclockwise. This means that the IV quadrant will be the bottom right quadrant. The right axis is the positive x-axis and the bottom axis is the negative y-axis. This means that the coordinate for the IV quadrant must look like (x,-y).
patrick is thinking of a number. his number is twice as large as the smallest number that rounds to 30 when rounding to the nearest ten. what is patrick’s number?
Three classes at a junior high school raised money to buy a new computers.
Answer:
what's the question...?
Step-by-step explanation:
Leave a comment?
Solve for g.
16g–11g+g=6
g=
Expand and simplify.
(x + 1)(2-6)
g^x+1 =27 solve for x
Answer:x=-3.5
Step-by-step explanation:
which function is represented by the graph?
Answer:
[tex]y=-\sqrt{x+2}-1[/tex]
Step-by-step explanation:
Hi there!
Please take a look at the attached image. This is the parent function of the radical function.
[tex]y=\sqrt{x}[/tex]
This equation represents the transformations of the parent function:
[tex]y=a\sqrt{b(x-h)}+k[/tex]
a dictates vertical stretch.
b dictates horizontal stretch.
h dictates horizontal translation.
k dictates vertical translation.
If we take a look at the given graph, we can tell that the following transformations have been applied:
- reflection across x-axis (a = -1)
- translation 2 units to the left (h = -2)
- translation 1 unit down (k = -1)
Therefore, the function that represents the graph is:
[tex]y=-\sqrt{x+2}-1[/tex]
I hope this helps!
Myra ordered 648 roses for her flower shop. Her helpers made boquets for every 8 roses.How many bouquet of roses were made for sale?What is the solution
bouquet of roses were made for sale : 648/8 = 81
ok done. Thank to me :>
Help me ASAP now like really fast
Answer: I think the answer is C.. It looks like an 180 angle from my perspective.
I hope that is correct
Answer:
C
Step-by-step explanation:
Well, we know all the angles must sum up to 180º. From this, we can write the equation ' 3xº + 80º + 2xº = 180º ', which is answer choice C
What equation represents this sentence?
7 less than a number is 16.
7=16−n
7=n−16
7−n=16
n−7=16 100 ponits
Answer:
n - 7 = 16
Step-by-step explanation:
as it says "7 less than a number". If it was "a number less than 7" then it would be the 3rd one.
Answer: n - 7 = 16
Step-by-step explanation: i did quiz
What is 7.83 x10^6 in decimal form
Answer:
7830000.00
Step-By-Step Explanation:
78 - 783 - 7830 - 78300 - 783000 - 7830000
Answer: 7830000
Step-by-step explanation:
7.83*10^6=
------------->
7.83*10^6=7.83
since the exponent equals 6, lets move the decimal sign 6 places to the right.
7.83*10^6=7.8.3.0.0.0.0.
Result is 7 8 3 0 0 0 0
7.83*10^6=7830000
Which one is the correct answer ? Find the amplitude , period. Phase shift asymptotes domain range Use the fact that cos(x)=0 will be an asymptote
Answer:
3. is your correct answer ok
What is the inequality graphed below?
Answer:
y>=5/3x+5
Step-by-step explanation:
line is y=5/3x+5
shading is above the line
line is shaded
y>=5/3x+5
to convert 13 feet to yards you would use the ratio 1 yard / 3feet or true or false
Answer:
True
Explanation:
3 feet is 1 yard so 13/3 is 4.3 yards approximately
True
[tex] \frac{1 \: yard}{3 \: feet} = \frac{x \: yard}{13 \: feet} [/tex]
3x = 13
[tex]x = \frac{13}{3} yards[/tex]
The sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second. What are the numbers?
The numbers are 30, 22, and 66 if the sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the number are x, y and z
Then,
x + y + z = 118 ...(1)
y = x - 8 ...(2)
z = 3y ....(3)
After solving the above three equation by plugging the value of z in the equation (1) then solve this equation with (2) we will get:
x = 30
y = 22
Then z from the equation (3):
z = 3(22) = 66
Thus, the numbers are 30, 22, and 66 if the sum of three numbers is 118. The second number is 8 less than the first. The third number is 3 times the second.
Learn more about the linear equation here:
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It is impossible to solve this mixture problem: How many gallons of a 10% solution would need to be
added to a 20% solution to obtain a 30% solution.
True or False?
Answer:
false
Step-by-step explanation:
How many gallons of a 10% solution. Would need to be added to a 20% solution to obtain 50 gallons of a 30% solution?
2.How many gallons of milk containing 4% fat is mixed with milk containg 1% fat to obtain a 15 gallon mixture containing 2% fat?
The following statement is from the contract Peter signed with his Homeowner's Association (HOA).
"Overnight parking on community streets is prohibited. For the purpose of this contract, 'overnight' will be defined as the hours between 11:00 p.m. and 4:00 a.m. The HOA will monitor overnight parking not less than once every calendar week with nightly patrols by community security.
"In the event a car is found parked on community streets overnight and that ownership of the offending car can accurately be verified as a community homeowner, the homeowner will receive one (1) written warning asking him or her to correct the situation. A second and third infraction by the same homeowner, whether or not it is with the same car, will result in a monetary fine as permitted by CC&R guidelines and HOA bylaws. Further infractions (past 3) will result in monetary fines in addition to the towing of the car at the homeowner's expense."
Because of the extremely low ground effects and body profile on his racing car, Peter is unable to drive his car off of the street and onto the driveway. He has parked on the street overnight for the past five weeks. He has received one written warning and one monetary fine from the HOA. What consequences should Peter expect after this week's security check?
a.
His car will be towed.
b.
He will receive another monetary fine.
c.
He will receive a monetary fine and his car will be towed.
d.
A "boot" will be place on his car to prevent him from driving it.
Math
........................................................................
Answer:
i believe the and\swe is g because it is located within the boundaries of plane p but is on a line (not the green segments) that goes outside of plane p
Step-by-step explanation:
Write the equation's of the lines using the given information
m=-2, (3, -7)
Answer:
y = -2x-1
Step-by-step explanation:
The formula for a line is [tex]y-y_{1} = m(x-x_{1})[/tex].
Plug in the information given in the problem: y-(-7) = -2(x-3)
So you get y+7 = -2x+6.
The final form you want needs to be equal to y (that means you want y by itself on the left side of the equals), so subtract 7 from both sides.
You get y = -2x-1
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})~\hspace{10em} m = -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{-2}(x-\stackrel{x_1}{3}) \\\\\\ y+7=-2x+6\implies \blacktriangleright y=-2x-1 \blacktriangleleft[/tex]
Help me with questions please