A researcher examines 27 water samples for mercury concentration. The mean mercury concentration for the sample data is 0.097 cc/cubic meter with a standard deviation of 0.0074. Determine the 90% confidence interval for the population mean mercury concentration. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 0.0074
n = number of samples = 27
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 27 - 1 = 26
Since confidence level = 90% = 0.90, α = 1 - CL = 1 – 0.9 = 0.1
α/2 = 0.1/2 = 0.05
the area to the right of z0.05 is 0.05 and the area to the left of z0.05 is 1 - 0.05 = 0.95
Looking at the t distribution table,
z = 1.706
The critical value is 1.706
Margin of error = 1.706 × 0.0074√27
= 0.0024
The 90% confidence interval is
0.097 ± 0.0024
Related Questions
Choose the equation that represents the solutions of 0 = 0.25x² - 8x. 0.25± √(0.25)² - (4)(1)(-8) 2(1) O O X = X = X = X = -0.25± √√(0.25)² – (4)(1)(-8) 2(1) 8± √(-8)²-(4)(0.25) (0) 2(0.25) -8± √(-8)²-(4)(0.25)(0) 2(0.25)
Answers
The given equations represent the solutions of 0 = 0.25x² - 8x
What is an equation?An equation is a mathematical statement that shows the equality of two expressions, typically separated by an equal sign. Equations are used to solve problems and model real-world situations in many fields, including physics, engineering, and finance.
Redirecting to answer:
The equation 0 = 0.25x² - 8x can be rewritten as:
0.25x² - 8x = 0
Factoring out x gives:
x(0.25x - 8) = 0
So the solutions are x = 0 and 0.25x - 8 = 0, which gives x = 32.
Therefore, none of the given equations represent the solutions of 0 = 0.25x² - 8x
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A sequence has the nth term rule T(n) = 32 - 3n
What is the value of the first negative term in this sequence?
Answers
\(T(11) = -1\) represents the initial negative term inside the series.
What do the concepts positive and negative in logic mean?A phrase that acknowledges a characteristic or trait in anything is said to be positive. Negative terms are those that downplay some aspect or characteristic of something. The positive or negativizes of a phrase is termed its quality.
What does "positive" and "negative" mean?Positive simply denotes excellent or the polar opposite of negative. For instance, you're less likely to receive favorable feedback on your scorecard if you've a good mindset toward your assignments. It might be difficult to keep track of all the different definitions of the word positive.
T(n) is negative when \(32 - 3n < 0\), which can be rearranged as:
\(3n > 32\)
\(n > 32/3\)
Since \(n\) is an integer, the smallest value of n that satisfies this inequality is \(n = 11\).
Therefore, the \(11th\) term of the sequence is:
\(T(11) = 32 - 3(11) = -1\)
So the first negative term in the sequence is \(T(11) = -1.\)
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4 gallons times 17.5 mi/gal
Answers
Answer:
70
Step-by-step explanation:
I dont know if I'm right but Im sure you were asking the price for the total gallons? But if you were it would be 70 dollars.
Hope this helps! Good luck :)
Which function has a greater maximum?
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A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens down. The function increases through negative four, negative five and negative three, negative two. It has a maximum at negative two, one, then the function decreases through negative one, negative two and zero, negative five.
Answers
The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.
1. The given function is f(x) = \(-2(x+4)^2\) + 1.
2. To find the maximum of the function, we need to determine the vertex of the parabola.
3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.
4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.
5. The x-coordinate of the vertex is given by h = -4.
6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.
7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.
8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).
9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.
10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.
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Find the midpoint of CD.
M = (¹2
X1+X2 Y1+Y2
Y₁+Y2)
2 1
C = (10,-1) and D = (-6,3)
([? ],[ ])
Answers
Answer:
Step-by-step explanation:
C=(10,-1)
D=(-6,3)
\(mid~point~x=\frac{10+(-6)}{2} =\frac{10-6}{2} =\frac{4}{2} =2\\y=\frac{-1+3}{2} =\frac{2}{2} =1\)
mid point=(2,1)
The midpoint of line segment CD is M = (2, 1).
We have,
To find the midpoint of the line segment CD, we can use the midpoint formula:
M = ((X₁ + X₂)/2, (Y₁ + Y₂)/2)
Given C = (10, -1) and D = (-6, 3), we can substitute the values into the formula:
M = ((10 + (-6))/2, (-1 + 3)/2)
= (4/2, 2/2)
= (2, 1)
Therefore,
The midpoint of line segment CD is M = (2, 1).
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Find a polynomial in factored form of the shaded area.
Answers
Answer:
Below in bold.
Step-by-step explanation:
Area of shaded part
= 5*10 - x(x + 5)
= 50 - (x^2 + 5x)
= -x^2 - 5x + 50
= -(x^2 + 5x - 50)
= -(x + 10)x - 5).
The area of a square is s2, where s is the side length of the square. Jack has a square-shaped flower garden in his yard. Each side of the garden is 8 feet. What is the area of the flower garden?
Answers
Answer:
64 square feet
Step-by-step explanation:
A = s² = 8² = 8*8 = 64
In terms of geometric shapes, a slice of pizza closely resembles what?
Answers
Answer:
triangle
Step-by-step explanation:
It looks like a traingle
Is. She analyzes
st.
Martha graphs the data for the number of bracelets made, a, and the number of beads used,
y, and draws a line through the points.
Number of Beads Used
600
500
400
300
200
100
0
Bracelets Made
versus Beads Used
(31, 651)
(23, 483).
(10, 210)
5 10 15 20 25 30 35
Number of Bracelets Made
Write an equation that represents the relationship between the number of bracelets made
and the number of beads used. Show or explain how you found the slope and y-intercept.
Enter your equation and your work or explanation in the space provided.
You may use the drawing box to add a drawing to help explain your answer.
A
7
44
▶
Exhibits
P
Answers
The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.
First, the rate of change
= (483 - 210) / (23 - 10)
= 273 / 13
= 21
So, the equation for the relationship between the number of bracelets made and the number of beads used.
(y - 210) = 21 (x- 10)
y - 210 = 21x - 210
y = 21x
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A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 15% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.
Answers
Answer:
0.1198 < p < 0.1802
Step-by-step explanation:
Percentage who had, or intended to cheat (p) = 15% = 0.15.
1 - p = 1 - 0.15 = 0.85
Confidence interval = 95%, z = 1.96 = 2
number of observation= 560
p ± z * √(p * (1 -p)/n)
Lower limit:
0.15 - 2 * √0.15 * 0.85/560
0.15 - 0.0301780 = 0.119822
= 0.1198
Upper limit:
0.15 + 2 * √0.15 * 0.85/560
0.15 + 0.0301780 = 0.180178
= 0.1802
0.1198 < p < 0.1802
what is this answer h – 6.5 = 15
Answers
Answer:
h=43/2 = 21 1/2 = 21.5
Step-by-step explanation:
h−6.5=15
Add 6.5 to both sides.
h=15+6.5
Add 15 and 6.5 to get 21.5.
h=21.5
Simplify: 1. 4x−(1−2x)+(2x−7) 2. (3−0.4a)−(10−0.8a)
Answers
Answer:1.8(x -1)
2.0.4a -7
Step-by-step explanation:
Pls Solve my peoblem
2 × 100 ÷ 2
Answers
Answer: it = 100 thats your answer
Steps:
2 * 100 = 200
200/2 = 100
Answer: 100
Find the annual interest rate.
I= $562.50, P=$1500, t= 5 years
The annual interest rate is_____%
Answers
The annual interest rate is 7.5%.
What is Simple interest?
Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.
The formula for simple interest is:
I = P × r × t
where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.
In this case, we know I = $562.50, P = $1500, and t = 5 years.
we ca substitute values into the formula,
562.50 = 1500× r ×5
Simplifying, we get:
r = 562.50 / (1500 ×5)
r = 0.075
r = 7.5%
Therefore, the annual interest rate is 7.5%.
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GEOMETRY PROBLEMS PLEASE HELP ME
Answers
Answer:
12) The measure of PQR is 36 since both angles MQP (25) and PQR should add up to MQR (61)
13) The graph shows that both angles are congruent so that means:
2x+8= x+22
2x= x+14
x=14
14) angle ADB and angle BDC since it shows that both angles sum up to 90 degrees (also known as complementary angles)
15) Angles ADE and angle FDE are supplementary because they both add up to 180 degrees (supplementary angles)
16) Angles ADC and FDE are vertical because they are opposite of each other
17) Angles ADE and FDE are also linear pairs because both of them are adjacent (they both have a common side as well as a common vertex)
Hope this helps! ;)
The constant in 2x+8
The constant in 2x-8
The coefficient in 2x+8
The variable in 2x+8
The coefficient in -x+9
The constant in -x+9
What would be the answers for all of these?
Answers
2. -8
3. 2
4. X
5. -1
6. 9
fraction math kids picked 124 strawberries gave 1/4 of strawberries to their neighbor and their mother used f 2/4 of the strawberries in a pie rest was saved for snack how many does the family have to snack on
Answers
Answer:
The family has 1/4 of the strawberries left to snack on, or 31 left to snack on.
Step-by-step explanation:
Since they gave away 1/4 of the strawberries to their neighbor, and the others were used in a pie, that means that 1/4 of the strawberries remain. You do 124/4 in which 1/4 of that is 31, since 31x4 is equal to 124.
Two candidates for governor of a state differ in their accounts of the state's economy during the incumbent's term. The incumbent claims that during his four year term the economy has improved, citing a rise in the median household income from $33,000 to $34,500. The challenger claims that the economy has declined, citing that the buying power of families in the state has declined during the four years. Which of the following best explains how both candidates can be right?
Answers
The two candidates, who differ in their accounts of the state's economy, can be right if B. Though the median household income increased ...
The argument of the incumbent governor is that the rise in the median household income in the state by $1,500 (5% increase) shows that the state's economy has improved during his first tenure.The challenger is evaluating the purchasing power of families in the state, which according to him, has declined more because of the increase in the prices of goods and services, perhaps above 5%.The other three options do not support both candidates:A. It is not possible ...
C. The incumbent is ...
D. Only those in the middle ...
Data and Calculations:
Median household income 4 years before = $33,000
Median household income 4 years after = $34,500
Change (increase) in household income after 4 years = $1,500 ($34,500 - $33,000)
Thus, the only true statement for the two candidates to be right in their arguments is statement B.
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What is 6 1/4% of 95?
What is 3/10% of 115?
Answers
1.) 95/16
2.) 69/200
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer: (A) independent or (D) not mutually excusive
Step-by-step explanation: Just think about it, what card you draw from a deck doesn't depend on anything. Not mutually exculisve means the same as indendent.
The result of which expression will best estimate the actual product of (Negative four-fifths) (three-fifths) (Negative StartFraction 6 over 7 EndFraction) (five-sixths)?
(Negative 1) (one-fourth) (Negative 1) (negative 1)
(Negative 1) (one-half) (Negative 1) (1)
(Negative StartFraction 4 over 2 EndFraction) (Three-halves) (Negative two-fifths) (Five-halves)
(Negative three-fourths) (Negative three-fourths) (Negative one-fifth) (One-half)
Answers
Answer:
The Answer Is B
Step-by-step explanation:
-4/5 = -1 (Rounded)
3/5 = 1/2 (Rounded)
-6/7 = -1 (Rounded)
5/6 = 1 (Rounded)
If your looking for the whole thing it would be:
(-1)[1/2](-1)(1) = x
Your Welcome! <3
The result of which expression B will best estimate the actual product of (-4/5) × (3/5) × (-6/7) × (5/6).
What are arithmetic operations?The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.
It is given that the expression is, a product of Negative four-fifths) (three-fifths) (Negative StartFraction 6 over 7 EndFraction) (five-sixths),
= (-4/5) × (3/5) × (-6/7) × (5/6)
The final result of the given expression is,
= 360/1050
=0.34
The product of the given values in the expression B is obtained as the equivalent expression to the given values.
Thus, the result of which expression B will best estimate the actual product of (-4/5) × (3/5) × (-6/7) × (5/6).
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Joy has 60 basketball cards she has six times as many basketball cards as Laura how many basketball cards does Laura have
Answers
Answer:
probably 10 since you devide 60 by 6 and you get 10
Step-by-step explanation:
A wool suit, discounted by 75% for a clearance sale, has a price tag of $165. What was the suit's original price?
Answers
Answer:
$1,100
Step-by-step explanation:
Since we that 75% less than the original price, or 15% of the original price*, is equal to $165, we can set up an equation like this, where \(x\) represents the original price:
\(.15x=165\)
Now, just solve for \(x\) by dividing both sides by .15, the equivalent of 15%:
\(x=\frac{165}{.15}\\x=1100\)
Therefore, the original price of the suit was $1,100.
*The reason that we use .15 instead of .75 is that when something is on sale with 75% of the original price cut off, 15% of the original price remains. That's why \(.15x=165\).
Find the 36th term.
5, 8, 11, 14, 17, ...
36th term = [?
Answers
Answer:
110
Step-by-step explanation:
nth term = 3n + 2
3 (36) + 2
108 + 2 = 110
Answer:
The 36th term in the sequence is 104.
Here's how to find it:
- Start with the first number in the sequence: 5.
- Add the common difference, which is 3, to get the second number in the sequence: 8.
- Add the common difference to the second number to get the third number: 11.
- Continue adding the common difference to each subsequent number to find the next term in the sequence.
- The 36th term is three less than 37 times the common difference added to the first term.
- Using that formula, we can calculate the 36th term as: 5 + (36 - 1) * 3 = 5 + 105 = 110.
- Therefore, the 36th term in the sequence is 104.
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), what are the
coordinates of B?
Answers
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).
To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).
Using the midpoint formula, we can set up the following equations:
(x1 + x2) / 2 = -4
(y1 + y2) / 2 = 2
Substituting the coordinates of point A (-7, 3), we have:
(-7 + x2) / 2 = -4
(3 + y2) / 2 = 2
Simplifying the equations:
-7 + x2 = -8
3 + y2 = 4
Solving for x2 and y2:
x2 = -8 + 7 = -1
y2 = 4 - 3 = 1
Therefore, the coordinates of point B are (-1, 1).
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WILL GIVE BRAINLIEST TO THE RIGHT ANSWER
Tabitha and Paco are in a video game room that consists of 10 games. How many different ways can they play all 10 games if they play each game once?
A.362,880
B.20
C.3,628,800
D.55
Answers
Answer:
Its C
Step-by-step explanation:
????!! Someone please explain this
Answers
Answer:
$24
Step-by-step explanation:
First, find the cost to cover one pair of shoes.
Cost to cover one pair of shoes = surface area of the shoe box × cost per square inch
= 2(LW + LH + HW) × 0.02
L = 14 in.
W = 8 in.
H = 4 in.
Plug in the values
Cost to cover one pair of shoes = 2(14*8 + 14*4 + 4*8) × 0.02
= 2(112 + 56 + 32) × 0.02
= 2(200) × 0.02
= 400 × 0.02 = 8
Cost to cover one pair of shoes = $8
Cost to cover 3 pairs of shoes = 3*8 = $24
Which of the following is equivalent to
2/3 divided by 5/6
Answers
Answer:
2/3*6/5
Step-by-step explanation:
They both equal 4/5 once simplified
(2/3) / (5/6) -> 2/3 * 6/5 because when one divides by a fraction, that fraction will be flipped and multiplied by the once numerator.
This is called the Reciprocal Property.
Good luck!
You want to buy some rice. A 7-ounce package costs $2.59. A 16-ounce package costs $5.60. A 24-ounce package costs$9.36. Which package is the best buy?
Answers
Answer:
Thanks
Step-by-step explanation:
Thanks
A store accidentally priced an item at $20 instead of $30 and honored the mispricing.
Where should the store attribute the $10 difference?
Is it considered a loss or operating expense?
Thanks
Answers
Answer:
Sales
Step-by-step explanation:
Since it is mentioned that the store mistakenly priced an item at $20 instead of $30 so there is a difference of $10 so the price of sales is increased by $10 due to mispricing the value of the item so that it would be recorded at $30 rather than $20
Therefore in the given case neither it is considered as a loss nor an operating expense but as a sales and the same is to be relevant
Hence, the given options are incorrect