The radioactive compound 14CO2 may be used as a tracer to study metabolism in plants. Suppose that a compound isolated from a plant exhibited 28, 32, 27, 39 and 40 counts of radioactive decays per minute. A blank sample used to measure the background counts of the radiation counter gave 28,21, 28 and 20 counts per minute. It appears that the isolated compound gives more counts than those from background. Can we be 95% confident that the compound is indeed radioactive?
Answers
Using the t-distribution, it is found that since the test statistic is more than the critical value for the right-tailed test, it can be conclude that the isolated compound gives more counts than those from background, and hence, we can be 95% confident that the compound is indeed radioactive.
At the null hypothesis, it is tested if isolated compounds do not give more counts than those from background, that is:
[tex]H_0: \mu_1 - \mu_2 \leq 0[/tex]
At the alternative hypothesis, it is tested if the give more counts, that is:
[tex]H_1: \mu_1 - \mu_2 > 0[/tex]
Using a calculator, the mean and the standard deviation for each sample are given by:
[tex]\mu_1 = 33.2, s_1 = 6.058[/tex]
[tex]\mu_2 = 24.25, s_2 = 4.35[/tex]
Considering the sample sizes of 5 and 4, respectively, the standard errors are given by:
[tex]s_1 = \frac{6.058}{\sqrt{5}} = 2.71[/tex]
[tex]s_2 = \frac{4.35}{\sqrt{4}} = 2.175[/tex]
For the distribution of differences, the mean and standard error are given by:
[tex]\overline{x} = \mu_1 - \mu_2 = 33.2 - 24.25 = 8.95[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.71^2 + 2.175^2} = 3.4749[/tex]
The standard error was found from the standard deviation for each sample, hence, the t-distribution is used.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{8.95 - 0}{3.4749}[/tex]
[tex]t = 2.58[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with 5 + 4 - 2 = 7 df and a 0.05 significance level is of [tex]t^{\ast} = 1.895[/tex]
Since the test statistic is more than the critical value for the right-tailed test, it can be conclude that the isolated compound gives more counts than those from background, and hence, we can be 95% confident that the compound is indeed radioactive.
A similar problem is given at brainly.com/question/24826023
Related Questions
simplify (√(π -√17)^2)
Answers
Answer: The answer is Iπ + √17|.
please answer the file question
Answers
Answer:
x = 15
Step-by-step explanation:
Corresponding sides have the same ratio:
UV/PR = TV/QR
(x +6)/14 = (x -3)/8
4(x +6) = 7(x -3) . . . . . . multiply by 56
4x +24 = 7x -21 . . . . . . eliminate parentheses
45 = 3x . . . . . . . . . . . add 21-4x
15 = x . . . . . . . . . . . .divide by 3
_____
Alternate solution
The long-side : short-side ratios for the two triangles are ...
14 : 8 = (x +6) : (x -3)
If we look at the differences between the ratio numbers we see ...
14 -8 = 6
(x +6) -(x -3) = 9
That is, the numbers in the second ratio must be 9/6 = 3/2 times the numbers in the first ratio. In other words, ...
x -3 = (3/2)(8) = 12
x = 15
Check: x +6 = 3/2(14) ; 15 +6 = 21
The cost of providing water bottles at a high school football game is $35 for the rental of the coolers and $0.50 per bottle
Answers
The cost function is an illustration of a linear function
The equation of the cost function is C(x) = 35 + 0.5x
The given parameters are:
[tex]Rentals = 35[/tex] -- the cost of renting a cooler
[tex]Rate = 0.5[/tex] --- the rate per bottle
Assume the number of bottles in a cooler is x.
The cost function for the bottles in a cooler would be:
[tex]C(x) = Rentals + Rate \times x[/tex]
So, we have:
[tex]C(x) = 35 + 0.5\times x[/tex]
Evaluate the products
[tex]C(x) = 35 + 0.5x[/tex]
Hence, the equation is [tex]C(x) = 35 + 0.5x[/tex]
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Research workshop: Generating Research questions and evaluating sources.
Take notes for two sources
Take notes on your second source
Answers
Based on the information, the best research question that Juan should choose will be "How does playing a team sport affect a child's development?"
A research question simply means a question that a researcher wants to answer. It should be noted that choosing a research question is an important element in research.
From the complete question, it should be noted that since Juan is writing a paper about children who play team sports, and he has different research questions, he should choose the one that conveys the research appropriately.
In this case, the best option will be "How does playing a team sport affect a child's development?"
Learn more about research questions on:
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The constraints of a problem are listed below. What are the vertices of the feasible region?
x+3y<=6
4x+6y>=9
x>=0
y>=0
Answers
The vertices of the feasible region of the constraints is (0,2.5)
How to determine the vertices?The constraints are given as:
x + 3y ≤ 6
4x + 6y ≥ 9
x ≥ 0, y ≥ 0
Express the inequalities as equations
x + 3y = 6
4x + 6y = 9
Make x the subject in x + 3y = 6
x = 6 - 3y
Substitute x = 6 - 3y in 4x + 6y = 9
4(6 - 3y) + 6y = 9
Expand
24 - 12y + 6y = 9
Evaluate the like terms
-6y = -15
Divide by 6
y = 2.5
Substitute y = 2.5 in x = 6 - 3y
x = 6 - 3 * 2.5
Evaluate
x = -1.5
So, we have:
(x,y) = (-1.5, 2.5)
Recall that: x ≥ 0, y ≥ 0
This means that the feasible region must have positive coordinates or zero
So, we set x = 0
(x,y) = (0, 2.5)
Hence, the vertices of the feasible region of the constraints is (0,2.5)
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(2+√3)+(4-√3)
[tex] [/tex]
Answers
Explanation :
________________________________
Given:
(2+√3)+(4-√3)
To Find:
Evaluate the expression
Solution:
⇨Step 1:
Remove the parentheses
(2+√3)+(4-√3)
When there is + or no sign in front of an expression in parentheses, the expression remains the same
= 2 + √3+ 4-√3
⇨Step 2:
Cancel the opposite terms √3 and -√3
"Two numbers are opposites if they have the same absolute value but different signs"
= 2 + 4
⇨Step 3:
Add the numbers
= 6
Hence (2+√3)+(4-√3) = 6.
x squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?
Answers
Answer:
[tex]x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}[/tex] and [tex]y=-1,\frac{1}{2}[/tex]
The ordered pair solutions are [tex](-\sqrt{\frac{7}{4}},0.5)[/tex], [tex](\sqrt{\frac{7}{4}},0.5)[/tex], [tex](-1,-1)[/tex], and [tex](1,-1)[/tex].
Step-by-step explanation:
I'm assuming the system is [tex]\left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.[/tex]:
[tex]x^2+y^2=2[/tex]
[tex]x^2+(2x^2-3)^2=2[/tex]
[tex]x^2+(4x^4-12x^2+9)=2[/tex]
[tex]x^2+4x^4-12x^2+9=2[/tex]
[tex]4x^4-11x^2+9=2[/tex]
[tex]4x^4-11x^2+7=0[/tex]
[tex]x^4-11x^2+28=0[/tex]
[tex](x^2-7)(x^2-4)=0[/tex]
[tex](4x^2-7)(x^2-1)=0[/tex]
[tex]4x^2-7=0[/tex]
[tex]4x^2=7[/tex]
[tex]x^2=\frac{7}{4}[/tex]
[tex]x=\pm\sqrt{\frac{7}{4}}[/tex]
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]x=\pm1[/tex]
[tex]y=2x^2-3[/tex]
[tex]y=2(\pm\sqrt{\frac{7}{4}})^2-3[/tex]
[tex]y=2({\frac{7}{4}})-3[/tex]
[tex]y=\frac{7}{2}-3[/tex]
[tex]y=\frac{1}{2}[/tex]
[tex]y=2x^2-3[/tex]
[tex]y=2(\pm1)^2-3[/tex]
[tex]y=2(1)-3[/tex]
[tex]y=2-3[/tex]
[tex]y=-1[/tex]
Therefore, [tex]x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}[/tex] and [tex]y=-1,\frac{1}{2}[/tex]
The ordered pair solutions are [tex](-\sqrt{\frac{7}{4}},0.5)[/tex], [tex](\sqrt{\frac{7}{4}},0.5)[/tex], [tex](-1,-1)[/tex], and [tex](1,-1)[/tex].
Help help help help math math
Answers
Answer:
Yes, it is a function
Step-by-step explanation:
Each x value in the domain has its own output, and it does not have more than 1
what is the percent change of
30 to 90?
what is what is the percent change of 30 to 90?
Answers
Answer:
200% increase
Step-by-step explanation:
What is 10% of 75? Use the double number line below to label your work and answer.
Answers
Answer: the answer is 7.5
Step-by-step explanation:
What are the coordinates of the point (-4, 2) after a translation 2 units left and 2 units up?
A (-2, 0)
B (-6,0)
C (-2, 4)
D (-6, 4)
Answers
Answer:
the answer you're looking for is D. when you move to the left the -4 becomes -6 and when you move up 2 becomes 4.
Question
Bill needs to mow his yard which has the dimensions in the shape below. What is the area of yard he needs to mow?
Note: Round your answer to one decimal place.
12 m
5 m
15 m
Answers
Answer:
Step-by-step explanation:
imagine you chop off a right triangle from the left side
now you have a rectangle and a right triangle
the rectangle
height 5
width 12
5 x 12 = 60
triangle
height 5
width 3
3 x 5 = 15
15 / 2 = 7.5
60 + 7.5 = 67.5 m^2
Answer: 67.5 m^2
Step-by-step explanation:
To find out the area of the yard, we split the shape up into a triangle and rectangle. The area of the triangle is,
A = 1 × b × h/2 = 1 × 3 × 5/2 = 7.5 m^2.
And the area of the rectangle is,
A = 12 × 5 = 60 m^2.
We then add the area of the triangle and the area of the rectangle.
A = 7.5 + 60 =67.5 m^2
Rounded to one decimal place, the area of the yard is 67.5 square meters.
Determine the slope from the given graph below:
A ➼ The slope is -7
B ➼ The slope is−16
C ➼ The slope is 6
D ➼ The slope is -6
(Please help me! I'll mark brainliest and give five stars.<3)
Answers
Step-by-step explanation:
again (I just answered the same question), the slope is the ratio "y coordinate change / x coordinate change".
I see e.g the points
(-1, -1) and (0, -7) on the line.
x changes by +1 (from -1 to 0).
y changes by -6 (from -1 to -7).
so, the slope is -6/1 = -6.
so, D is the right answer.
Evaluate 4x^2 y^-3 for x=3 and y=-2
Answers
Answer:
36 and -1/8
Step-by-step explanation:
x^2 = 3^2 = 9 * 4 = 36
y^-3 = (-2)^-3 = -1/8
Answer:
-4.5.
Step-by-step explanation:
4x^2 y^-3
= 4x^2 / y^3
When x = 3 and y = -2
it is 4(3)^2 / (-2)^3
= 36 / -8
= -4.5.
Evaluate the expression when c=4. c^4 + 6
Answers
Answer:
262
Step-by-step explanation:
4x4x4x4+6
256+6
262
Select the interval where g(2) < 0.
(graphed on khan academy)
Answers
Answer:
the number 0 Originally called finding the vertical asymptote.
For n = 10 and 1 = 0.59, what is P(X = 8)?
P(X = 8) =
(Round to four decimal places as needed.)
Answers
nCx⋅px⋅(1−p)n−x
llllllllllllllllllllllllllllllllllllll
Give an expression for f + g.
A. 12x3 + 16x2 - 6x -8
B. 4x2 + 3x + 2
C. 4x2 + 3x - 8
D. 12x3 + 16x2 - 6x
Answers
Answer:
A)62x-8
B)11x+2
C)11x-8
D)62x
Step-by-step explanation:
12×3=36
16×2=32
36+32-6=62x-8
HELP ASAP Match each division expression to its quotient.
Answers
Answer:
2=-12.2/(-6.1
-2=16/(-8)
-3= -2 2/5/4/5
3= 3 3/7 / 1 1/7
Step-by-step explanation:
Little help? Ill give 5 stars and brainly (If correct)
Answers
Answer:
C
Step-by-step explanation:
Slope is rise over run. Pick two points and then count the rise and run. The rise in this case is one and the run is 2 and one over 2 is 1/2
[tex]Hiya![/tex]
Sokka is here to help!
ANSWER:[tex]C.[/tex]
Because, All you need to do is.. Find the slope of proportional graph, by y and x, Which the line is [tex]\frac{4}{2}[/tex].
[tex]And, \frac{4}{2} =\frac{1}{2} .[/tex]
Hopefully, this helps you!!
[tex]Sokka[/tex]
From a hot-air balloon, Guadalupe measures a 31^{\circ} ∘ angle of depression to a landmark that’s 316 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground?
Answers
Check the picture below.
Find the area of the figure.
7cm
8cm
11cm
Area is ___ square cm?
Answers
Answer:
616cm³
Step-by-step explanation:
you just need to multiply those numbers
7 x 8 x 11= 616
[tex]\text{Perimeter of the triangle,}\\\\ 2s = 7 + 8 +11 =26}\\\\\\\implies s = \dfrac{26}2 = 13\\\\\\\text{Apply Heron's formula to find the area of the triangle,}\\\\A = \sqrt{s(s-8)(s-7)(s-11)}\\\\\implies A = \sqrt{13(13-8)(13-7)(13-11)}\\\\\implies A = \sqrt{780} \\\\\implies A = 27.93~~ \text{cm}^2[/tex]
1 1/5- 1/3
AS FRACTION
Answers
Answer:
-2/15
this should work
Step-by-step explanation:
Answer:
13/15
Step-by-step explanation:
1 1/5 - 1/3 =
= 1 + 1/5 - 1/3
= 5/5 + 1/5 - 1/3
= 6/5 - 1/3
= 18/15 - 5/15
= 13/15
A bag with 6 marbles has 2 blue marbles, 1 red marble, and 3 yellow marbles. A marble is chosen from the bag at random. What is the probability that it
is not blue?
Answers
There are 2 blue marbles out of 6 total marbles.
6-2 = 4 marbles are not blue.
Probability of not being blue = 4/6 which reduces to 2/3
Answer: 2/3
Given that f(x) = ax – 5 and f(4) = 15, determine the value of a.
Answers
Given that f(x) = ax – 5 and f(4) = 15, then the value of a is 5
The given function is:
f(x) = ax - 5
If f(4) = 15, then x = 4
Substitute x = 4 into f(x) = ax - 5
f(4) = a(4) - 5
15 = 4a - 5
Solve for a by adding 5 to both sides
15 + 5 = 4a - 5 + 5
20 = 4a
Divide both sides by 4
4a/4 = 20/4
a = 5
Given that f(x) = ax – 5 and f(4) = 15, then the value of a is 5
Learn more on linear functions here: https://brainly.com/question/15602982
Wheel Fun offers rentals of paddle boats that can be enjoyed by 2 or 3 riders. The price for renting a paddle boat is $15 for each hour. Customers must also pay a $20 deposit on the rental. Write an equation that can be used to determine the price, y for renting a paddle boat for x, hours?
Answers
Answer:
15+20=35+15 And then add an additional plus 15 for each hour
Step-by-step explanation:
I don’t understand this please help
Answers
Answer:
i think BC = 8.5
Step-by-step explanation:
19-(2+6.5+2)
19-10.5
8.5
Pls help stuck on it
Answers
Answer:
4,-1
Step-by-step explanation:
Please like!♥
At a local movie theatre, sodas cost$4.50 and bags of popcorn cost &1.50. Kirk buys three times as many bags of popcorn as sodas and pays a total of $36. Write a system of equations and solve it using any method to determine how many of each item Kirk bought.
Answers
Answer:
this might help
Step-by-step explanation:
this might be kinda similar
Chickens and rabbits
In the yard were chickens and rabbits. Together they had 18 heads and 56 legs. How many chickens and how many rabbits were in the yard?
Correct answer:
chickens: 8
rabbits: 10
Step-by-step explanation:
a+b=18
2a+4b=56
a=8
b=10
a+b = 18
2•a+4•b=56
a+b = 18
2a+4b = 56
a = 8
b = 10
two piers, a and b, are located s km away from each other along a river. a motorboat, with a speed of v km/hour in still water, is cruising between the two piers. How much time t (in hours) will the motorboat need to get from pier a to pier b and back, if the speed of the current is 5km/hour? find t if: s=105 v=40
Answers
Answer:
speed in still water is v=40 speed of current