The following measurements (in picocuries per liter) were recorded by a set of argon gas detectors installed in a research facility:

381.3,394.8,396.1,380
Using these measurements, construct a 95% confidence interval for the mean level of argon gas present in the facility. Assume the population is approximately normal.

Answers

Answer 1

Answer:

The 95% confidence interval for the mean level of argon gas present in the facility is (374.4, 401.7).

Step-by-step explanation:

Before building the confidence interval, we have to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{381.3+394.8+396.1+380}{4} = 388.05[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(381.3-388.05)^2+(394.8-388.05)^2+(396.1-388.05)^2+(380-388.05)^2}{3}} = 8.58[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 4 - 1 = 3

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{8.58}{\sqrt{4}} = 13.65[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 388.05 - 13.65 = 374.4

The upper end of the interval is the sample mean added to M. So it is 388.05 + 13.65 = 401.7

The 95% confidence interval for the mean level of argon gas present in the facility is (374.4, 401.7).


Related Questions

In the diagram, the perimeter of the rectangle is 56. What is its area?

Answers


l
=
15 yep this should be the answer

Driving 70 mph, it takes Alicia 3 hours to reach the airport to go on a vacation. It then takes her 3 hours to get to her destination with the jet traveling at a speed of 400 mph. How many miles does Alicia travel to get to her destination?

Answers

Answer:

Total distance covered= 910 miles

Step-by-step explanation:

Distance = speed x time

Distance covered from home to airport = 70 x 3= 210 miles

Distance covered from airport to destination= 350 x 2= 700 miles

Add them together to get the final answer.

Q: Solve for x: 8x-2-5x=8
A. OX=13
B. OX=2 1/2
C. OX=3 1/3
D. OX=7

Answers

Answer:

c. 3 1/3

Step-by-step explanation:

8x-2-5x=8

3x=10

x=10/3=3 1/3

Answer:

x=[tex]3\frac{1}{3}[/tex]

Step-by-step explanation:

Hi there!

We want to find the value of x in this expression:

8x-2-5x=8

Our goal is to isolate x on one side

Combine like terms on the left side (add the terms with x together)

3x-2=8

Add 2 to both sides (-2+2=0)

3x-2=8

   +2  +2

__________

3x=10

Divide both sides by 3

x=[tex]\frac{10}{3}[/tex]

Simplify the improper fraction

x=[tex]3\frac{1}{3}[/tex]

Hope this helps!

Coefficient and degree of the polynomial

Answers

Answer:

The leading coefficient is -8 as it is a mix of x and cardinal, if it was x alone then it wouldn't be the coefficient, we would use the next number shown.

If it was just a number and no x then it would still be the coefficient.

The degree is 9 as it is the highest power shown.

Step-by-step explanation:

See attachment for examples

Please help !!!!!!! Asap

Answers

Answer:

A, C, E, G

Step-by-step explanation:

Basic set operation

which is larger 1 1/2 or 1 15/16

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

1 (15/16)

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Converting the Fractions...}}\\\\\rightarrow \frac{1}{2}=\frac{1*8}{2*8}= \boxed{\frac{8}{16}}\\\\\text{We would only compare the fractions because we have the same whole number.}\\\\\frac{8}{16} <\frac{15}{16}\\\\\text{Therefore:}\\\\\boxed{1\frac{15}{16} >1\frac{1}{2}}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

The answer is 1 and 15/16

Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest. To decide if it's feasible to do this by investing In an account that compounds monthly, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places

Answers

Answer:

The annual interest rate would have to be of 0.1%.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest.

This means that:

[tex]A(4.9) = 1200 + 24000 = 25200[/tex]

[tex]t = 4.9[/tex]

[tex]P = 24000[/tex]

Compounded monthly:

This means that [tex]n = 12[/tex]

What would the annual rate of interest have to be?

We have to solve for r, so:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]25200 = 24000(1 + \frac{r}{12})^{12*4.9}[/tex]

[tex](1 + \frac{r}{12})^{12*4.9} = \frac{25200}{24000}[/tex]

[tex](1 + \frac{r}{12})^{58.8} = 1.05[/tex]

[tex]\sqrt[58.8]{(1 + \frac{r}{12})^{58.8}} = \sqrt[58.8]{1.05}[/tex]

[tex]1 + \frac{r}{12} = (1.05)^{\frac{1}{58.8}}[/tex]

[tex]1 + \frac{r}{12} = 1.00083[/tex]

[tex]\frac{r}{12} = 0.00083[/tex]

[tex]r = 12*0.00083[/tex]

[tex]r = 0.001 [/tex]

The annual interest rate would have to be of 0.1%.

Find the area of the shape shown below.

Answers

Answer:

28 units²

Step-by-step explanation:

Area of trapezoid =

2(8 + 4)/2 = 12

Area of rectangle =

2 x 8 = 16

16 + 12 = 28

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Determine if the statement is always, sometimes, or never true:

An equilateral triangle is an acute triangle.

never
always
sometimes

Answers

The answer is always your welcome

Answer:

always

Step-by-step explanatia;won:

Question 17 of 25
Solve the inequality. Enter the answer as an inequality that shows the value of
the variable; for example f>7, or 6 < w. Where necessary, use <= to write s
and use >= to write .
V-(-5) <-9
Answer here
I
SUBMIT

Answers

Answer:

v-(-5)<-9

v- remove brackets -5

v- -5= -4 +5 ( opposite operation)

v- = -4

v< -4

what is the area of the triangle ://

Answers

Answer:

The area of a triangle is:

Area = 1/2(bh)

Area = 1/2(70)

Area = 35 square inches

Let me know  if this helps!

Answer:

A = 35

Step-by-step explanation:

a^2 + b^2 = c^2

10^2 + b^2 = 12^2

100 + b^2 = 144

144 - 100 = b^2

b^2 = 44

b = 6.6

6.6 x 10 = 66/2 = 33

7 - 6.6 = 0.4

10 x 0.4 = 4/2 = 2

Area = 33 + 2

Area = 35

There is 3m wide path around a circular cricket ground having the diameter of 137 m. Find the area of the path.​

Answers

Answer:

1320 m^2

Step-by-step explanation:

area of ground = π r ^2

= (22/7) × (137/2)^2

= 14,747.0714286 m^2

area of ground and path

=( 22/7)(143/2)^2

= 16,067.0714286 m^2

area of path

=16,067.0714286 -14,747.0714286

= 1320 m^2

note :

r = radius = diameter /2

area of a circle = π r^2

diameter of circle created with path and ground = 137 + 2 × width of path

= 137 + 2× 3 = 143 m

Angelica’s bouquet of dozen roses contains 5 white roses. The rest of the roses. What fraction of the bouquet is pink? There are 12 roses in a dozen

Answers

Answer:

7/12

Step-by-step explanation:

total: 12 roses

white roses: 5

pink roses: 7

fraction of pink roses = 7/12

In a model, a submarine is located at point (0, 0) on the coordinate plane. The submarine’s radar range has an equation of 2x2 + 2y2 = 128

Draw the figure on a graph and label the location of the submarine. Make sure your name is on the paper, and label this activity Part 2.
Can the submarine’s radar detect a ship located at the point (6, 6) ? Mark that location on your graph, and explain how you know whether or not the ship will be detected in the space provided on the Circles Portfolio Worksheet.

Answers

Answer:

Remember that for a circle centered in the point (a, b) and with a radius R, the equation is:

(x - a)^2 + (y - b)^2 = R^2

Here we know that the submarine is located at the point (0, 0)

And the radar range has the equation:

2*x^2 + 2*y^2 = 128

You can see that this seems like a circle equation.

If we divide both sides by 2, we get:

x^2 + y^2 = 128/2

x^2 + y^2 = 64 = 8^2

This is the equation for a circle centered in the point (0, 0) (which is the position of the submarine) of radius R = 8 units.

The graph can be seen below, this is just a circle of radius 8.

We also want to see if the submarine's radar can detect a ship located in the point (6, 6)

In the graph, this point is graphed, and you can see that it is outside the circle.

This means that it is outside the range of the radar, thus the radar can not detect the ship.

What is the sum of the infinite geometric series?​

Answers

Answer:

-6

Step-by-step explanation:

a1= -3

r= -(3/2)/-3 = 0.5

r>-3

s= a1/1-r

= -3/1-0.5

=-6

Please Help!
What is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6.

Answers

The locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.

Given: A circle of radius 6 units

To find: The locus of the midpoint of all chords that can be drawn from a given point on the circle.

To find the required locus, we need to know the following:

Locus of a moving point is the trajectory of that point. It is the geometrical figure represented by the equation which is satisfied by the coordinates of the moving point.A chord of a circle is a line segment joining any points of a circle.Equation of a circle with center at origin and radius of [tex]r[/tex] units is [tex]x^{2} +y^{2} =r^{2}[/tex] According to the midpoint formula, the coordinates of the midpoint of the line segment joining the points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]

Let, without loss of generality, the given circle be centered at the origin. Even if it is not, we can shift the origin to the center of the given circle with coordinate transformation.

Then, the equation of the given circle is [tex]x^{2}+y^{2} =6^{2}[/tex], that is, [tex]x^{2}+y^{2} = 36[/tex]

Let the coordinates of the given fixed point be [tex](a,b)[/tex]

Let the coordinates of any point on the circle be [tex](p,q)[/tex] and let the coordinates of the midpoint of the chord joining the points [tex](a,b)[/tex] and [tex](p,q)[/tex] be [tex](h,k)[/tex]

We have to find the locus of [tex](h,k)[/tex]

Then, using the midpoint formula,

[tex](h,k)=(\frac{a+p}{2} ,\frac{b+q}{2})[/tex]

On solving, we get,

[tex]p=2h-a,q=2k-b[/tex]

Since [tex](a,b)[/tex] and [tex](p,q)[/tex] are both points on the given circle, they satisfy the equation of the circle, [tex]x^{2}+y^{2} = 36[/tex]

Then,

[tex]a^{2} +b^{2} =36[/tex]

[tex]p^{2} +q^{2} =36[/tex]

Substituting [tex]p=2h-a,q=2k-b[/tex] in [tex]p^{2} +q^{2} =36[/tex], we have,

[tex](2h-a)^{2} +(2k-b)^{2} =36[/tex]

[tex](2(h-\frac{a}{2}) )^{2} +(2(k-\frac{b}{2}))^{2} =36[/tex]

[tex]4(h-\frac{a}{2})^{2} +4(k-\frac{b}{2})^{2} =36[/tex]

[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =\frac{36}{4}[/tex]

[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =9[/tex]

[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =3^{2}[/tex]

This is the locus of the point [tex](h,k)[/tex]

Replace [tex](h,k)=(x,y)[/tex] to get,

[tex](x-\frac{a}{2})^{2} +(y-\frac{b}{2})^{2} =3^{2}[/tex]

This is the equation of a circle with center at [tex](\frac{a}{2} ,\frac{b}{2} )[/tex] and radius 3 units.

Thus, we can conclude that the locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.

Learn more about locus here:

https://brainly.com/question/23824483

Players A and B play a basketball game in which they take turns shooting the ball, and the first player to make their shot wins. Player A has probability 2/3 of making each of her shots. Player B has probability 1/2 of making each of his shots. If Player A shoots first, what is the probability that she will win

Answers

Answer:

Player A has a probability 2/3 of making each of her shots, then she has a probability 1/3 of missing each shot.

Player B has a probability 1/2 of making each of his shots, then he also has a probability 1/2 of missing each shot.

Let's separate each case.

Let's define:

P(x) = probability of winning at the "x" shot.

Player A wins on the first shot.

Because she has a probability 2/3 of making each of her shots, the probability of winning at the first shot is

P(1) = 2/3

Now let's see the next case, player A wins at her second shot.

This means that first, she misses her first shot, with a probability of:

p₁ = 1/3

Player B must miss his shot, the probability is:

p₂ = 1/2

Now player A must make her shot, so the probability is:

p₃ = 2/3

The joint probability is the product of the individual probabilities, so we have:

P(2) = (1/3)*(1/2)*(2/3) = 1/9

Now we can see the pattern, for P(3) we have

A misses: p₁ = 1/3    (first shot of A)

B misses: p₂ = 1/2

A misses: p₃ = 1/3   (Second shot of A)

B misses: p₄ = 1/2

A makes the shot: p₅ = 2/3

P(3) =  (1/3)*(1/2)*(1/3)*(1/2)*(2/3) = 1/54

We already can see the pattern.

P(n) = (1/3)^(n - 1)*(1/2)*(n - 1)*(2/3)

Player A has a probability P of winning, and we can write P as:

P = P(1) + P(2) + P(3) + ...

Then we will have:

P = 2/3 + 1/9 + 1/54 + 1/324 + ... ≈ 0.8

Triangle DEF contains right angle E. If angle D measures 40° and its adjacent side measures 7.6 units, what is the measure of side EF? Round your answer to the nearest hundredth.

Answers

[tex]\\ \rm\longmapsto cot40=\dfrac{7.6}{EF}[/tex]

[tex]\\ \rm\longmapsto EF=\dfrac{7.6}{cot40}[/tex]

[tex]\\ \rm\longmapsto EF=\dfrac{7.6}{1.19}[/tex]

[tex]\\ \rm\longmapsto EF=6.38units[/tex]

Answer:

[tex]\displaystyle 6,38\:units[/tex]

Step-by-step explanation:

You would set your proportion up like so:

[tex]\displaystyle \frac{7,6}{EF} = cot\:40° \\ \\ 7,6 = EFcot\:40° → 6,3771571969... = \frac{7,6}{cot\:40°} \\ \\ 6,38 ≈ EF[/tex]

I am joyous to assist you at any time.

Can someone explain this to me please

Answers

Answer:  Choice B

Explanation:

Everywhere you see an x, replace it with a+2.

[tex]f(x) = 3(x+5)+\frac{4}{x}\\\\f(a+2) = 3(a+2+5)+\frac{4}{a+2}\\\\f(a+2) = 3(a+7)+\frac{4}{a+2}\\\\[/tex]

Jack is 4 times as old as Lacy. 3 years from now the sum of their ages will be 71 . How old are they now?

Answers

Answer:

Lacy is 13 and Jack is 52

Step-by-step explanation:

In 3 years their ages will add up to 71 so you have to subtract 6 as there are two of them to get 65. Lacy's age is represented by x and since Jack is 4 times older his age is represented by 4x. So added together their age is 5x. So 5x=65. Then 65/5=13. So 13=x. So Lacy is 13 and Jack is 52 as 13x4 is 52.

Question 12 plz show ALL STEPS

Answers

9514 1404 393

Answer:

  θ = 1.5 radians ≈ 85.9°

Step-by-step explanation:

The arc length in terms of central angle and radius is ...

  s = rθ

where θ is the central angle in radians. Here, we want to find θ, so we have ...

  θ = s/r . . . . divide by r

For the given numbers, ...

  θ = (6 cm)/(4 cm) = 3/2 = 1.5 . . . radians

I radian is 180°/π, so 3/2 radians is ...

  (3/2)(180°/π) = 270°/π ≈ 85.9°

WILL GIVE BRAINLIST IF CORRECT Which function is represented by this graph

Answers

Answer:

Step-by-step explanation:

B; So this is a transformation problem from the parent function of f(x)=|x| so the function is is moved 3 units down giving it the -3 at the end and is moved to the right 7 units so it would be x-7

6+7=10
13+8=18
32+21=32
11+34=0
31+03=?​
process please

Answers

Answer:

6+7=13

13+8=21

32+21=52

11+34=46

31+03=34

Step-by-step explanation:

im not sure in the 31+03


Area and perimeter please?

Answers

Answer:

Area = 240 cm²

Perimeter = 80 cm

Step-by-step explanation:

✔️ Area of the triangle = ½*base*height

base of the triangle = 24 cm

height = 20 cm

Plug in the known values

Area = ½*24*20

= 12*20

Area = 240 cm²

✔️Perimeter of the triangle = sum of all the three sides that make up the triangle

Perimeter = 22 + 24 + 34

= 80 cm

What is the equation

Answers

Answer:

y=3x+1

Step-by-step explanation:

Determine slope with two coordinates and use it in the formula

the length of a rectangle is 4 meters longer than the width. if the area is 22 square meters , find the rectangle dimension

Answers

Let breadth be x

Length=x+4

We know

[tex]\boxed{\sf Area_{(Rectangle)}=Length\times Breadth}[/tex]

[tex]\\ \sf\longmapsto x(x+4)=22[/tex]

[tex]\\ \sf\longmapsto x^2+4x=22[/tex]

[tex]\\ \sf\longmapsto x^2+4x-22=0[/tex]

By solving

[tex]\\ \sf\longmapsto x=-2\pm\sqrt{26}[/tex]

It doesnot have any real roots

HELP HELP ASAP!!! ANYONE ANYONE

Answers

Answer:

Step-by-step explanation:

factor each total

27 = 3 x 3 x 3

18 = 3 x 3 x 2

45 = 3 x 3 x 5

The largest (and only) common factor is 3

however each factorization also contains the product 3 x 3 = 9

so the maximum each bag may have cost is $9 and if so, she sold 5 bags of sugar cookies.

another option would be that each bag cost $3 and she sold 15 bags of sugar cookies. However, the question asked for the maximum possible price.

Help please I’m not sure what the answer for this one is no need to explain

Answers

Answer:

b.  e^9.45 = x

see last example and this explains whole numbers and decimals.

Step-by-step explanation:

Another example we can Solve  100=20e^2t .

Solution

100 = 20e^2t

5 = 20e ^2t

in 5 = 2t

Therefore  t = in5/ 2

Step 1 was ; Divide by the coefficient of the power

Step 2 was ; Take ln of both sides. Use the fact that ln(x) and ex are inverse functions

Step 3 was; Divide by the coefficient of t

Another example;

Solve  e^2x−e^x = 56 .

Solution

Analysis

When we plan to use factoring to solve a problem, we always get zero on one side of the equation, because zero has the unique property that when a product is zero, one or both of the factors must be zero. We reject the equation  e^x=−7  because a positive number never equals a negative number. The solution  ln(−7)  is not a real number, and in the real number system this solution is rejected as an extraneous solution.

Another example is;

Solve  e^2x=e^x+2 .

Answer

Q&A: Does every logarithmic equation have a solution?

No. Keep in mind that we can only apply the logarithm to a positive number. Always check for extraneous solutions.

Last example determines decimals ;

Solve  lnx =3 .

Solution

lnx^x=3=e^3

Use the definition of the natural logarithm

 

Graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to  20 . In other words  e^3≈20 . A calculator gives a better approximation:  e^3≈20.0855 .

The graph below represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to  20 . In other words  e^3≈20 . A calculator gives a better approximation:  e^3≈20.0855 .

It shows values of graphs of  y=lnx  and  y=3  cross at the point  (e^3,3) , which is approximately  (20.0855,3) .

See graph below.

I need the help ASAP please

Answers

Answer:

Option B

Answered by GAUTHMATH

look at the image to see

Answers

Answer:

surface area = perimeter of base x slant height all of it divided by 2 and then add area of base

pb = 4(6)=24 x 9.5 = 228 /2 = 114 + 36 = 150

hope that answers your question :)

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