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
how would i plot this on a graph??
Answers
Step-by-step explanation:
This is in the form of
[tex]h(x) = y[/tex]
in this case, x is 1 and y is 7. So ourbpoint would be (1,7.)
Question 1: Four expressions are shown below:
A. 2(4x + 2)
B. 2(3x + 3)
C. 6x + 6
D. 8x + 4
Which two expressions are equivalent to 2(3x + 2 + x)? (5 points)
A and D
B and D
A and C
C and B
Question 2:
Which of the values in the set {3, 4, 5, 6} is a solution to the equation 4x + 2 = 22?
3
4
5
6
Answers
Answers;
Question 1 answer: The first and last option.
Question 1 explanation: 2(4x + 2) is 4x = 12 = 2 = 14 x 2 = 28 and 8x + 4 is 8 x 4 = 32 + 4 = 36 which is 8 more than 28 then, 3x = 9 + 2 + 3 x 2 = 28.
2(4x + 2) = 28 and 8x + 4 equals 36 which is 8 more and they're both equivalent to 2(3x + 2 + x) because 2(3x = 2 = x) equals 28.
Pleaseeeee heeeeelp!!!
Answers
A=35
B=14
C=5
Answer:
a=35 b=14 c=5
Step-by-step explanation:
a
180-55-90=35
b
b+6=20
b=14
c
4c-6=14
14+6=20
20/4=5
A boat is traveling at a constant speed. In 2 hours, the boat travels 180 miles. How many hours will it
take the boat to travel 225 miles?
Answers
Answer:
2 1/2 hours
Step-by-step explanation:
For 1 hour, it would travel 90 miles.
For half of 90 which is 45 it would travel 1/2 hr.
225-180 is 45 miles, which is another half hr.
2 hrs plus 1/2 hr is 2 1/2 hours.
Which coast less per bag 18 tea bags for 2.70 or 64 tea bags for 9.28
Answers
Answer:
64 tea bags for 9.28
Step-by-step explanation:
Hey mathematicians ! Can anyone help me with these problems please ! Will give brainly !
Answers
27) 115=5(5a-2)
115= 25a-10
125=25a
a=5
28) -72=-x-6(x+5)
-72=-7x-30
-42=-7x
x=6
i did two of them. now i gtg so won't do the rest
What are the coordinates of B
Answers
Answer:
(-4,-5)
Step-by-step explanation:
The coordinates of the midpoint for x = sum of x/2=2
The coordinates of the midpoint for y = sum of y/2=-2
firstly to work out x coordinate:
[tex] \frac{x + 8}{2} = 2[/tex]
rearrange to find x which is -4
work out y coordinate:
[tex]\frac{y + 1}{2} = - 2[/tex]
rearrange to find y which is -5
so coordinates are (-4,-5)
Students from CAMPA participated in a school fundraiser. The six graders raised $600. The seventh graders raised 35% more than the six graders. The eighth graders raised. 10% less than the seventh graders. What is the total amount the school raised?
Answers
Answer:
$2,139 was the total amount the school raised.
Step-by-step explanation:
35% of 600= 210
210+600 = $810
10% of 810= 81
810-81= $729
6th Graders= $600
7th Graders= $810
8th Graders= $729
9. The 10,000 seat stadium is 89% full. How many people are watching the game inside the stadium? with solution pls.
Answers
Giải phương trình vi phân sau
Y"=2y'+y=e^x
Answers
You likely mean to write the differential equation,
y'' - 2y' + y = exp(x)
The homogeneous part
y'' - 2y' + y = 0
has characteristic equation
r² - 2r + 1 = (r - 1)² = 0
with a root at r = 1 with multiplicity 2, so the characteristic solution is
y = C₁ exp(x) + C₂ x exp(x)
For the particular solution, we assume an ansatz
y = ax² exp(x)
where a is an unknown constant. Differentiating the ansatz twice:
y' = ax² exp(x) + 2ax exp(x) = (ax² + 2ax) exp(x)
y'' = (ax² + 2ax) exp(x) + (2ax + 2a) exp(x) = (ax² + 4ax + 2a) exp(x)
Substitute y and its derivatives into the DE:
(ax² + 4ax + 2a) exp(x) - 2 (ax² + 2ax) exp(x) + ax² exp(x) = exp(x)
Solve for a :
(ax² + 4ax + 2a) - 2 (ax² + 2ax) + ax² = 1
2a = 1
a = 1/2
Then the particular solution is
y = 1/2 x² exp(x)
The general solution is then
y = C₁ exp(x) + C₂ x exp(x) + 1/2 x² exp(x)
Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
Answers
The cost of each bag of apple is $6.35
Let the cost of a bag of apple be xIf Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount
The correct equation that represents the statement will be given as:
6.17 + 8x = 56.97Make x the subject of the formula
8x = 56.97 - 6.17
8x = 50.8
x = 50.8/8
x = 6.35
Hence the cost of each bag of apple is $6.35
Learn more on equations here: https://brainly.com/question/2972832
Which inequality below is true?
a. -2>4
b. -4< 2
C. -4> 4
d. -4> -2
Answers
Because 2 is greater than -4
Hope this helps!
Brainliest is much appreciated!
A 2-gallon bottle of fabric softener costs $16.64. What is the price per cup?
Answers
Answer:
each cup would cost $0.52
Step-by-step explanation:
there are 16 cups in 1 gallon so you multiply that by two. Then you have 32 so you divide 16.64 by 32 and you end up with 0.52. hope this helped :))
Tell me I got this wrong
A large community college has professors and lecturers. The total number of faculty members is 136. The school reported that they have 6 professors for every 11 lecturers. How many professors does the community college employ?
Answers
10. In a recent season, the San Francisco Giants
won 75 out of 162 games. What percent of their
games did they win? Round to the nearest tenth if
necessary.
Answers
Using the percentage concept, it is found that the San Francisco Giants won 46.3% of their games.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem:
The Giants played a total of 162 games, hence b = 162.They won 75 games, hence a = 75.Then:
[tex]P = \frac{75}{162} \times 100\% = 46.3\%[/tex]
The San Francisco Giants won 46.3% of their games.
You can learn more about the percentage concept at https://brainly.com/question/10491646
hello please help me
Answers
Answer:
I think it is 249 for the first one and the second one i dont know sorry
Step-by-step explanation:
Find a polynomial with the following zeros.
HELPPPP ASAPPP
Answers
Answer:
x³ - 4x² + 2x + 4 = 0
Here's how I solved this:
You start off by rewriting the zeros into factors:
1 - √3 → x = 1 - √3 → (x - 1 - √3)
2 → x = 2 → (x - 2)
1 + √3 → x = 1 + √3 → (x - 1 + √3)
Now you want to multiply the factors together:
(x - 1 - √3) · (x - 2) · (x - 1 + √3)
- Multiply the first two factors together -
(x - 1 - √3) · (x - 2)
↓
(x · x - x · 2 - √3 · x + √3 · 2 - x + 2)
- Combine like terms and simplify -
(x · x - x · 2 - √3 · x + √3 · 2 - x + 2)
↓
(x² - 3x - √3 · x + 2√3 + 2)
- Now multiply the third factor -
(x² - 3x - √3 · x + 2√3 + 2)(x - 1 + √3)
↓
(x² · x + x² · √3 - x² - 3x · x - 3x · √3 + 3x - √3 · xx - √3 · x · √3 +√3 · x + 2 · √3 · x + 2 · √3 · √3 - 2 · √3 + 2x + 2 · √3 - 2)
↓
(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)
- Combine like terms and simplify -
(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)
↓
x³ - 4x² + 2x + 4
--------------------------------------------------------------------------------------------------------------
And there we get our solution: x³ - 4x² + 2x + 4
using guassion elimination metheed x+2y-3y=11,3x+2y+z=1, 2x+y-5z=11
Answers
2y+4x+6z=23
True or false
Plz help
Answers
[tex]0 - (-\frac{31}{43})=0+ \frac{31}{43}=\frac{31}{43}[/tex]
ANSWER : true
ok done. Thank to me :>
Answer:
True
Step-by-step explanation:
[tex]0 - ( - \frac{31}{43} ) \\ 0 + \frac{31}{43} \\ = \frac{31}{43} [/tex]
Jocelyn gave the cashier $50 to pay for 3 shirts. The cashier gave her $5.03 in change. Each shirt cost the same amount. What is the cost in dollars and cents for each pair of shirts?
Answers
Answer:
14.9
Step-by-step explanation:
50-5.03 = 44.97
44.97 ÷ 3 = 14.99
Put the following capacities in order from smallest to largest. 0.1 l 0.5 l 1000 ml 10 ml 15 cl
Answers
Answer:
10 ml, 0.1 l, 15 cl, 0.5 l, 1000 ml
Step-by-step explanation:
m is an SI prefix for milli-, meaning 1/1000.
c is an SI prefix for centi-, meaning 1/100.
Expressed in liters, these volumes are ...
0.10 l
0.50 l
1000/1000 l = 1.00 l
10/1000 l = 0.01 l
15/100 l = 0.15 l
In order from smallest to largest, they are ...
0.01 l, 0.10 l, 0.15 l, 0.50 l, 1.00 l
In the original units, the order is ...
10 ml, 0.1 l, 15 cl, 0.5 l, 1000 ml
The area of the Mountain Island Educational State Forest in North Carolina is 3 square miles. What is the area, in square yards, of this forest
Answers
The area of the forest in square yards is [tex]9.3 \times 10^6[/tex]
The area of the forest in square miles is given as:
[tex]Area = 3mi^2[/tex]
To convert the area to square yards from square miles, we multiply the area by 3.098 * 10^6.
So, we have:
[tex]Area = 3 \times 3.098 \times 10^6yd^2[/tex]
Evaluate the product
[tex]Area = 9.294 \times 10^6yd^2[/tex]
Approximate
[tex]Area = 9.3 \times 10^6yd^2[/tex]
Hence, the area of the forest in square yards is [tex]9.3 \times 10^6[/tex]
Read more about areas at:
https://brainly.com/question/24487155
What is the diameter of circle 0?
Answers
Answer:
8
Step-by-step explanation:
diameter is the radius times 2
A basketball player made 80 out of 100 attempted free throws what percent of free throws was made ?
Answers
Answer:
8/10
Step-by-step explanation:
id hope your have a great day
Answer:
80%
Step-by-step explanation:
80÷100=.8 which is 80%
A line with a slope of 2 passes through the point (3,9).
Write an equation for this line in point-slope form.
Answers
Answer:
y-9=2(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-9=2(x-3)
There are 52 grams of carbs in 1/4 cup of syrup for a particular brand. How many carbs are in 1 tablespoons?
Round your answer to the nearest integer.
Answers
A 1/4 cup is 4 tbsp, and 52/4 = 13
There is a total of 52 grams of carbs in 1/4 cup, then 1 tablespoon will contain 208 grams of carbs.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given information in the question,
There are 52 grams of carbs in 1/4 cup of syrup
Let's assume that the amount of carbs in 1 tablespoon is x.
So,
x = (52 × 4)
x = 208 grams.
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The temperature is -8 degrees Fahrenheit. The height pressure front increases the temperature to 7 degrees Fahrenheit. By how many degrees did the temperature increase.
(Please show work and explanation)
Answers
Answer:
3 dregreess 5 degrees temperature
can anyone pls help?
Answers
Answer:
5x+12+x'
_______
2x'-2x-4
'=2
Solve and check answer 3(4-5x)=3(4x+3)
Answers
Hey there!
3(4 - 5x) = 3(4x + 3)
3(4) + 3(-5x) = 3(4x) + 3(3)
12 - 15x = 12x + 9
-15x + 12 = 12x + 9
SUBTRACT 12x to BOTH SIDES
-15x + 12 - 12x = 12x + 9 - 12
SIMPLIFY IT!
-27x + 12 = 9
SUBTRACT 12 to BOTH SIDES
-27x + 12 - 12 = 9 - 12
CANCEL out: 12 - 12 because it gives you 0
KEEP: 9 - 12 because it helps solve for the x-value
NEW EQUATION: -27x = 9 - 12
SIMPLIFY IT!
-27x = -3
DIVIDE -27 to BOTH SIDES
-27x/-27 = -3/-27
CANCEL -27/-27 because that gives you 1
KEEP: -3/-27 because it helps solve for the x -value
NEW EQUATION: x = -3/-27
SIMPLIFY IT/REDUCE the FRACTION!
x = 1/9
Therefore, your answer is: x = 1/9
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
which system of equation does the graph represent