random sample has been taken from a normal population and two confidence intervals constructed using exactly the same data. The two CIs are (38.02, 61.98) and (39.95, 60.05). (a) What is the value of the sample mean

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]

Answer:

3. is your correct answer ok

Answer:x=-3.5

Step-by-step explanation:

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

Answer:

what's the question...?

Step-by-step explanation:

Leave a comment?

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:

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).

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

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!

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]

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?

Answer:

ninth grade teacher is going   skipping 30  to each class

Step-by-step explanation:

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!

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}}

bouquet of roses were made for sale : 648/8 = 81

ok done. Thank to me :>

Answer

Find the amount of money Khairul had initially

money with Khairul initially = 6x = 6(60) = 360

Step-by-step explanation:

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.

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.

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

Answer is A. 101°

Step-by-step explanation:

Step-by-step explanation:

Avg = 20 + 14 + 28 + 18 /4

Avg = 80/4 = 20

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.

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:

brainly.com/question/11897796

#SPJ1

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]

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]

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