Six different​ second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings​ (in mmHg) are listed below. Find the​ range, variance, and standard deviation for the given sample data. If the​ subject's blood pressure remains constant and the medical students correctly apply the same measurement​ technique, what should be the value of the standard​ deviation?

Answers

Answer 1

Answer:

[tex]Range=14[/tex]

[tex]\sigma^2 =32.4[/tex]

[tex]\sigma = 5 .7[/tex]

The standard deviation will remain unchanged.

Step-by-step explanation:

Given

[tex]Data: 136, 129, 141, 139, 138, 127[/tex]

Solving (a): The range

This is calculated as:

[tex]Range = Highest - Least[/tex]

Where:

[tex]Highest = 141; Least = 127[/tex]

So:

[tex]Range=141-127[/tex]

[tex]Range=14[/tex]

Solving (b): The variance

First, we calculate the mean

[tex]\bar x = \frac{1}{n} \sum x[/tex]

[tex]\bar x = \frac{1}{6} (136+ 129+ 141+ 139+ 138+ 127)[/tex]

[tex]\bar x = \frac{1}{6} *810[/tex]

[tex]\bar x = 135[/tex]

The variance is calculated as:

[tex]\sigma^2 =\frac{1}{n-1}\sum(x - \bar x)^2[/tex]

So, we have:

[tex]\sigma^2 =\frac{1}{6-1}*[(136 - 135)^2 +(129 - 135)^2 +(141 - 135)^2 +(139 - 135)^2 +(138 - 135)^2 +(127 - 135)^2][/tex]

[tex]\sigma^2 =\frac{1}{5}*[162][/tex]

[tex]\sigma^2 =32.4[/tex]

Solving (c): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt {\sigma^2 }[/tex]

[tex]\sigma = \sqrt {32.4}[/tex]

[tex]\sigma = 5 .7[/tex] --- approximately

Solving (d): With the stated condition, the standard deviation will remain unchanged.


Related Questions

Which of the following functions is graphed below?

Answers

Answer:

there are no functions her pls add them for an answer:)

Step-by-step explanation:

Which ordered pair is a solution to the following linear system?

y= x + 1

y = -2x + 1

A) (-1,-2)
B) (2,1)
C) (0,1)
D) (0,0)

Answers

Answer:

C. (0,1)

Step-by-step explanation:

x + 1 = -2x + 1

3x = 0

x = 0

y = (0) + 1

y = 1

Please help I’ll give brainliest

Answers

Answer:

B

Step-by-step explanation:  6 21  9 45

49 × 17 + 49 × 3

49 × (17 + 3)

49 × 20

Solve the following:
4x-3=2x+7
Thanks :)

Answers

Answer:

6x+10 i think is right(sorry if its not)

Answer:

5

Step-by-step explanation:

4x-3=2x+7

-2x -2x

2x-3=7

+3 +3

2x=10

2x/2x = x

10/2=5

x=5

Can someone help me understand this? Given that triangle ABC =~ triangle DEF, which of the following must be true?

Answers

Answer:

since these triangles are the same these angle must be the same

A=D

B=E

C=F

so the answer is C

Hope This Helps!!!

Line A (y=4x+2) is transformed into Line B (y=x+5). Which best describes the new slope and y-intercept?

Answers

Answer:

The new slope is 1 and the line is shifted flatter.

Step-by-step explanation:

Line A slope is 4.

Line B slope is 1.

The y-intercept rose up 3

As far as slope, it became flatter because the line only rises 1 'square' for every 1 'square' it travels to the right. It was rising 4 'squares' for every 1 to the right.  

What is the reflection image of P(0, 0) after two reflections, first across x = −3 and then across y = 4?

Answers

Answer:

(-6, 8)

Draw the point, draw the lines of reflection, reflect, find coordinates.

The sum of a number and 3:

Answers

Answer:

x+3?

Step-by-step explanation:

honestly, there is not alot of information present here. so when a hear "a number" i think variable.... which would be set up as x+3

convert 25meter square into centimeter square

Answers

Answer:

250,000 cm squared

Step-by-step explanation:

Draw the graph of y = 3x – 2 for –3 ≤ x ≤ 3

Answers

Answer:

In this case, we have a linear equation:

y = 3*x - 2

And we want to graph this in the interval  –3 ≤ x ≤ 3

Because this is a linear equation, to graph it we can just evaluate the equation in both extremes of the interval to find the two extremes of the graph.

Then we just need to connect these points with a segment, and that will be the graph of our equation.

Because the symbols used are: ≤

We need to graph the extremes with a black dot, which means that the point is included in the graph (would be different if we had -3 < x < 3)

The first extreme is when we have x = -3

y = 3*(-3) - 2 = -9 - 2 = -11

Then we have one extreme at (-3, -11)

The other is when x = 3

y = 3*3 - 2 = 9 - 2 = 7

Then the other extreme is at (3, 7)

Now we just need to draw these two points and connect them, an example of this can be seen in the image below:

The owner of a produce stand is selling baskets of peaches, priced by the kilogram. She rounded each measurements to the nearest 2 1 ​ start fraction, 1, divided by, 2, end fraction of a kilogram.How much heavier is the heaviest basket than the second heaviest basket?

Answers

Answer:

[tex]1\frac{1}{2}kg[/tex]

Step-by-step explanation:

Given

[tex]a = 6\frac{1}{2}[/tex] --- heaviest

[tex]b = 5[/tex] --- second heaviest

Required

The difference (d)

This is calculated as:

[tex]d = 6\frac{1}{2} - 5[/tex]

[tex]d = 1\frac{1}{2}[/tex]

plsss help (on pic)
First will put brainliest

Answers

Answer:

7 over 2x-2

Step-by-step explanation:

Answer:

g^-1 •7

7g^-1

7•1/g

answer is 7/g

I hoped I helped!! :)

A school held a tennis tournament.After each round,one-forth of the players were eliminated.If there were 64 players at the start of the tournament,which equation models the number of players left after 6 rounds?​

Answers

Answer:

Option B

Step-by-step explanation:

After each round of the tournament one-fourth players are eliminated.

That means the process of elimination will represent the exponential decay.

Equation of exponential decay is given by the expression,

[tex]y=a(1-r)^n[/tex]

Here, a = Initial number of players

r = Fraction of reduction in the number of players

y = Final number of players

n = Number of rounds

In the given question,

Initial number of the players (a) = 64

Fraction of reduction in the number of players (r) = [tex]\frac{1}{4}[/tex]

                                                                             = 0.25

Number of rounds (n) = 6

By substituting these values in the expression,

[tex]y=64(1-0.25)^6[/tex]

Therefore, Option B is the answer.

What is the value of x to the nearest degree?





22



63



77



68

Answers

Answer:

I need help on this to anyone please

2+4 = 8 and ½ + ½ = 1 is an example of which type of statement?

Answers

Answer:

it is an example of conditional statement.

hope it helps

¿Cuál de los siguientes productos algebraicos es un Binomio Suma por Binomio Diferencia?


Seleccione una:
a. (a + b) (a - b)
b. (a - b) (a - b)
c. (a + b) (a + b)
d. (a + b) (c + d)

Answers

The answer is d hope that helps

I need help please!!!

Answers

Answer:

answer is line m........

Choose the correct simplification of the expression (x?y)?
Ох^4у^3
Ox^6y^6
Ох^4у^2
Oxy^4

Answers

C, multiply the powers in the parentheses by 2

The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.


After how many seconds does the object reach its maximum height?


2 seconds

3 seconds

6 seconds
9 seconds

Answers

Answer:

Step-by-step explanation:

This answer can be found in the h value for the vertex of a parabola, (h, k). The k value is the max height and we were already given that information. We need to solve for h. There's an easy way and a really complicated way...I'll show you the easy way because it's actually quite useful to know, especially when doing a lot of work with quadratics!

The formula to find h is

[tex]h=\frac{-b}{2a}[/tex] and in our quadratic, a = -16, b = 96 and c = 6. Filling in what we need:

[tex]h=\frac{-96}{2(-16)}[/tex] so

h = 3

At 3 seconds the max height of 150 feet is reached.

simplify  ( √ 5 ) ( 3 √ 5 )

Answers

Answer:

( √ 5 ) ( √ 5 ) 3

5*3

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

( √ 5 ) x ( 3 √ 5 )

=> 3  ( √ 5 x √5)

=> 3 x ( √25)

=> 3 x 5

=> 15

An earthquake with a rating of 7.6 is
known to be a great earthquake that can
cause damage that extends several
hundred kilometers.
Math

Answers

Answer:

39,810,717.06

Step-by-step explanation:

Question:

What is the value of x when the richter scale rating is 7.6? Round your answer to the nearest hundreth.

Mathematically, the rating of an earthquake typically refers to its magnitude on the Richter scale.

The Richter scale is a logarithmic scale that measures the amplitude of seismic waves produced by an earthquake. Each increase of one unit on the Richter scale represents a tenfold increase in the amplitude of the seismic waves and approximately 31.6 times more energy released.

A rating of 7.6 on the Richter scale indicates a significant and powerful earthquake. It is considered a "great" earthquake and can cause widespread damage over an extensive area. The extent of the damage can depend on various factors, including the depth of the earthquake, the distance from populated areas, and the local building infrastructure.

It's important to note that while the magnitude of an earthquake provides a measure of its energy release, it doesn't directly indicate the extent of the damage or the specific geographical area affected. The effects of an earthquake can vary depending on factors such as local geology, distance from the epicenter, and the population density of the area.

Mathematically, the Richter scale provides a standardized way to quantify and compare the magnitude of earthquakes, aiding in the understanding and analysis of seismic events.

To know more about Richter scale. here

https://brainly.com/question/24037139

#SPJ2

Compare the graph h(x)=1/4x^2 to the graph of f(x) = x2.

Answers

Answer:

h(x) is the image after f(x) is horizontally stretched by a scale factor of 4

Step-by-step explanation:

Given

[tex]h(x) = \frac{1}{4}x^2[/tex]

[tex]f(x) = x^2[/tex]

Required

Compare h(x) to f(x)

We have:

[tex]h(x) = \frac{1}{4}x^2[/tex]

Substitute [tex]f(x) = x^2[/tex]

[tex]h(x) = \frac{1}{4}f(x)[/tex]

This means that f(x) is stretched horizontally by a scale factor of 4 to get h(x)

Which of these is the algebraic expression for "4 times the sum of 2 and y?"
4 ⋅ 2 + y
4(2 + y)
2 + 4 ⋅ y
2(4 + y)

Answers

Answer:

[tex]4(2 + y)[/tex]

Step-by-step explanation:

"4 times the sum of 2 and y".

Hope it is helpful...

Answer:

The answer is 4(2+y)

Explanation: No 1 is 4 times two and add 1

No 3 is 2 plus 4 and multiply y

No 4 is 2 times 4 and adds 2 y

Find the image of NPQ under the translation of (x, y) + (x + 8, y + 1).

АВС

DEF

KLM

GHJ

Answers

Answer:

Triangle KLM

Step-by-step explanation:

Firstly, we need to write the coordinates of triangle NPQ

We have this as;

(-7,-6) for N

(-4,-3) for P

(-4,-6) for Q

Now, we are going to use the given translation formula;

(x + 8, y + 1)

N’ will be (-7+ 8, -6 + 1) = (1,-5)

P’ will be (-4+ 8, -3+1) = (4,-2)

Q’ will be (-4+ 8, -6+1) = (4,-5)

Now, we need to find the triangle with the exact given transformation coordinates calculated above;

We have the triangle as;

KLM

With K as (1,-5) ; L as (4,-2) and ; M as (4,-5)

CAN SOMEONE PLEASE HELP?!

Answers

Answer:

70in.

Step-by-step explanation:

Since the given formula for perimeter is [tex]2l + 2w[/tex], all that's needed is to fill in the blanks with the numbers they give us.

[tex]2l + 2w[/tex]                  (Fill in for given length and width)

[tex]2(20)+2(15)[/tex]         (Multiply)

[tex]40 + 30[/tex]                  (Add)

[tex]70[/tex]

It tells us that length ([tex]l[/tex]) is 20 and that width ([tex]w[/tex]) is 15. So all that we have to do is use the equation it gave us to solve the equation.

I hope this helped :)

Step-by-step explanation:

Hey there!

Here;

Length (l) = 20 in

Width (w) = 15 in

Perimeter(p) = ?

We have;

Perimeter of rectangle (p) = 2l + 2w

= 2(l+w)

= 2(20+15)

= 2*35

= 70 inches

Therefore, perimeter of rectangular picture is 70 inches.

Hope it helps!

What is the slope of the function?

Answers

Answer:

Write function:

y = 3x+4

The slope is what we time x by, 3!

Help please thanks! :)

Answers

Answer:

Option A = 1/15 cubic meters

Step-by-step explanation:

Formule to find volume of rectangular prism:

Volume = width × height × length

V = w×h×l

V = 1/3 × 1/4 × 4/5

V = 1/15 cubic meters

* Which expression ((7 ^ 2) ^ 5)/(7 ^ 6) I need help

Answers

Answer:

the answer is D / 7^16...

Hello! Verify the identity. Please show your work! Use trigonometric identities to verify each expression is equal.


Yes this is from edge.

Answers

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

[tex]\displaystyle \csc^2 x -2\csc x \cot x +\cot ^2 x = \tan^2\left(\frac{x}{2}\right)[/tex]

Note that the left-hand side is a perfect square trinomial pattern. Namely:

[tex]a^2-2ab+b^2=(a-b)^2[/tex]

If we let a = csc(x) and b = cot(x), we can factor it as such:

[tex]\displaystyle (\csc x - \cot x)^2 = \tan^2\left(\frac{x}{2}\right)[/tex]

Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):

[tex]\displaystyle \left(\frac{1}{\sin x}-\frac{\cos x }{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)[/tex]

Combine fractions:

[tex]\displaystyle \left(\frac{1-\cos x}{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)[/tex]

Square (but do not simplify yet):

[tex]\displaystyle \frac{(1-\cos x)^2}{\sin ^2x}=\tan^2\left(\frac{x}{2}\right)[/tex]

Now, we can make a substitution. Let u = x / 2. So, x = 2u. Substitute:

[tex]\displaystyle \frac{(1-\cos 2u)^2}{\sin ^22u}=\tan^2u[/tex]

Recall that cos(2u) = 1 - sin²(u). Hence:

[tex]\displaystyle \frac{(1-(1-2\sin^2u))^2}{\sin ^2 2u}=\tan^2u[/tex]

Simplify:

[tex]\displaystyle \frac{4\sin^4 u}{\sin ^2 2u}=\tan^2 u[/tex]

Recall that sin(2u) = 2sin(u)cos(u). Hence:

[tex]\displaystyle \frac{4\sin^4 u}{(2\sin u\cos u)^2}=\tan^2 u[/tex]

Square:

[tex]\displaystyle \frac{4\sin^4 u}{4\sin^2 u\cos ^2u}=\tan^2 u[/tex]

Cancel:

[tex]\displaystyle \frac{\sin ^2 u}{\cos ^2 u}=\tan ^2 u[/tex]

Since sin(u) / cos(u) = tan(u):

[tex]\displaystyle \left(\frac{\sin u}{\cos u}\right)^2=\tan^2u=\tan^2u[/tex]

We can substitute u back for x / 2:

[tex]\displaystyle \tan^2\left(\frac{x}{2}\right)= \tan^2\left(\frac{x}{2}\right)[/tex]

Hence proven.

help please, try to explain it in steps for me if u can't that's fine, ty!

Answers

Answer:

B

Step-by-step explanation:

We are given that Expression One is:

[tex]2\cdot 10^x[/tex]

And Expression Two is:

[tex]4\cdot 10^{x+y}[/tex]

We are given that the value of Expression Two is 20,000 times greater than the value of Expression One. And we want to find the value of y. In other words:

[tex]4\cdot 10^{x+y}=20000(2\cdot 10^x)[/tex]

We can divide both sides by four:

[tex]10^{x+y}=10000\cdot 10^x[/tex]

Recall that:

[tex]x^a\cdot x^b=x^{a+b}[/tex]

Therefore:

[tex]10^x\cdot 10^y=10000\cdot 10^x[/tex]

Divide both sides by 10ˣ:

[tex]10^y=10000[/tex]

Solve for y:

[tex]\displaystyle y = \log_{10}10000 = 4[/tex]

Our answer is B.

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