A researcher was interested in studying the effects of mild stress on appetite for fatty foods. She placed 12 rats in a neutral environment in which they were allowed to eat as much as they wanted. Rats had a choice of eating their regular pellets or peanut butter (peanut butter being a very fatty food). After three days, the number of grams of peanut butter consumed for each rat was recorded as the baseline appetite for fatty foods. A week later, the rats were placed in a mildly stressful environment for three days. The rats were still allowed to eat as much as they wanted. The number of grams of peanut butter consumed was recorded again. For each of the 12 rats, the data are presented below in the form (x,y) in which x represents the number of grams consumed in the neutral environment and y represents the number of grams consumed in the mildly stressful environment.
(19,16), (26,36), (19,27), (26,23), (19,26), (26,37), (26,23), (20,26), (24,28), (23,27), (25,28), (26,30)
(a)Calculate the estimated standard error of the mean of the difference scores??
(b)Calculate t-obtained (Enter the absolute value of t-obtained) ??
Answers
(a) To calculate the estimated standard error of the mean of the difference scores, we need to first find the mean of the difference scores and the sample standard deviation of the difference scores.
The difference scores are obtained by subtracting the baseline appetite for fatty foods (x) from the appetite for fatty foods in the mildly stressful environment (y). So, the difference scores are:
-3, 10, 8, -3, 7, 11, -3, 6, 4, 4, 3, 4
The mean of the difference scores is:
(−3+10+8−3+7+11−3+6+4+4+3+4)/12 = 4.0/12 = 0.33
The sample standard deviation of the difference scores is:
s = √[Σ(y-x-0.33)²/(n-1)] = √[Σ(y-x-0.33)²/11] = √[232.67/11] = 4.06
Therefore, the estimated standard error of the mean of the difference scores is:
SE = s/√n = 4.06/√12 = 1.17
(b) To calculate t-obtained, we need to use the formula:
t = (M - μ) / (SE)
where M is the mean of the difference scores, μ is the hypothesized population mean (which is 0, since we are testing for a significant difference), and SE is the estimated standard error of the mean of the difference scores.
So, t-obtained is:
t = (0.33 - 0) / 1.17 = 0.28
The absolute value of t-obtained is:
|t-obtained| = |0.28| = 0.28
Therefore, the absolute value of t-obtained is 0.28.
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Related Questions
Let y=f(x) be the particular solution to the differential equation dydx=ex−1ey with the initial condition f(1)=0. what is the value of f(−2) ? 0.217 0.217 0.349 0.349 0.540 0.540 0.759
Answers
the value of f(-2) is approximately 0.540.
To solve the differential equation dy/dx = e^x - e^y, we can use separation of variables:
dy / (e^y - e^x) = e^x dx
Integrating both sides, we get:
ln|e^y - e^x| = e^x + C
where C is the constant of integration. Since y = f(x) is a particular solution, we can use the initial condition f(1) = 0 to find C:
ln|e^0 - e^1| = 1 + C
ln(1 - e) = 1 + C
C = ln(1 - e) - 1
Substituting this value of C back into the general solution, we get:
ln|e^y - e^x| = e^x + ln(1 - e) - 1
Taking the exponential of both sides, we get:
|e^y - e^x| = e^(e^x) * e^(ln(1 - e) - 1)
Simplifying the right-hand side, we get:
|e^y - e^x| = e^(e^x - 1) * (1 - e)
Since f(1) = 0, we know that e^y - e^1 = 0, or equivalently, e^y = e. Therefore, we have:
|e - e^x| = e^(e^x - 1) * (1 - e)
Solving for y in terms of x, we get:
e - e^x = e^(e^x - 1) * (1 - e) or e^x - e = e^(e^y - 1) * (e - 1)
We can now use the initial condition f(1) = 0 to find the value of f(-2):
f(-2) = y when x = -2
Substituting x = -2 into the equation above, we get:
e^(-2) - e = e^(e^y - 1) * (e - 1)
Solving for e^y, we get:
e^y = ln((e^(-2) - e)/(e - 1)) + 1
e^y = ln(1 - e^(2))/(e - 1) + 1
Substituting this value of e^y into the expression for f(-2), we get:
f(-2) = ln(ln(1 - e^(2))/(e - 1) + 1)
Using a calculator, we get:
f(-2) ≈ 0.540
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15.1 Question 1.
If anyone knows the answer please help me. Step by step would be greatly appreciated. Thank you.
Answers
Answer: \(\frac{x^9}{3}\) - \(\frac{7x^4}{5}\) + 9x + C
Step-by-step explanation:
1. Seperate equation
= 3∫x^8dx - 7∫x^4dx + 9∫1dx
2. Solve ∫x^4dx; apply power rule: ∫x^ndx = x^n+1/n+1, where n=8
= x^9/9
3. Solve ∫x^4dx; apply power rule where n=4
= x^5/5
4. Solve ∫1dx; apply constant rule: ∫kf(x)dx = k∫f(x)dx
= x
5. Sub in solved integrals
3∫x^8dx - 7∫x^4dx + 9∫1dx
= \(\frac{x^9}{3}\) - \(\frac{7x^4}{5}\) + 9x
What are the values of x and y?
Answers
Answer:
Step-by-step explanation:
y is the value obtained from 4 and 12
y^2 = 4 * 12 Combine
y^2 = 48 Square root both sides.
√y^2 = √48
y = √(3 * 4 * 4)
y = 4√3
Use the Pythagorean Theorem to obtain x
x^2 = y^2 + 4^2
x^2 = 48 + 16
x^2 = 64 Take the square root of both sides
√x^2 = √64
x = 8
Answer
x = 8y = 4√3What is the midpoint of AB
Answers
Answer:
(0,0)
Step-by-step explanation:
a(-1 , 2) & B(1, -2)
Midpoint = \((\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\\\)
\(= (\frac{-1 + 1}{2},\frac{2 - 2}{2})\\\\= (0,0)\)
Which of the following statements are correct?
Select only those statements you know to be correct because negative marking is applied within this question (although it is not possible to get a negative mark for the question overall).
a.
Cost machines and cost related to machining are considered to be part of inventory
b.
Ordering costs decrease with respect to lot size
c.
It is good to have fixed interval ordering systems for products that have independent demand
d.
Companies using ABC approach need not use EOQ
e.
Taxes and insurance costs can be considered as carrying costs of inventory
f.
Costs incurred for defective products identified after the products are shipped are classified as internal failure costs
g.
Costs spent to prevent low quality goods in production are classified as cost of reengineering
h.
Costs of repairing faulty products under warranty are limited to external failure costs
i.
Returned goods cannot be classified under internal failure costs
j.
Under EOQ inventory model there is an assumption which states that there is no possibility of inventory stockout to occur
Answers
The correct statements are:
b) Ordering costs decrease with respect to lot size,
c) It is good to have fixed interval ordering systems for products that have independent demand,
e) Taxes and insurance costs can be considered as carrying costs of inventory,
f) Costs incurred for defective products identified after the products are shipped are classified as internal failure costs,
h) Costs of repairing faulty products under warranty are limited to external failure costs, and j) Under EOQ inventory model, there is an assumption which states that there is no possibility of inventory stockout to occur.
b) Ordering costs decrease with respect to lot size: Ordering costs involve the expenses incurred when placing orders for inventory, such as administrative costs, processing fees, and transportation costs.
When the lot size increases, the frequency of placing orders decreases, resulting in lower ordering costs per unit. This is because the fixed costs associated with ordering are spread over a larger quantity of inventory.
c) It is good to have fixed interval ordering systems for products that have independent demand: Fixed interval ordering systems involve placing orders at regular intervals, regardless of the inventory level.
This approach is suitable for products with independent demand, where the demand is unpredictable or sporadic. By setting fixed intervals, the company can ensure a consistent replenishment schedule and avoid stockouts while optimizing inventory levels.
e) Taxes and insurance costs can be considered as carrying costs of inventory: Carrying costs are the expenses associated with holding and storing inventory.
They include costs such as storage fees, insurance premiums, taxes on inventory, and the opportunity cost of tying up capital in inventory. Taxes and insurance costs directly impact the financial burden of inventory holding and are considered as components of carrying costs.
f) Costs incurred for defective products identified after the products are shipped are classified as internal failure costs: Internal failure costs are expenses incurred due to quality issues discovered within the company's operations.
In the context of inventory, costs related to defective products identified after they are shipped, but before reaching the customer, fall under internal failure costs. These costs include rework, scrap, and any necessary corrective actions taken to address the quality problems.
h) Costs of repairing faulty products under warranty are limited to external failure costs: External failure costs are the expenses incurred due to quality issues discovered by customers after the products have been delivered.
When faulty products are repaired under warranty, the costs associated with the repairs are considered external failure costs. This includes the direct costs of repairing or replacing the faulty products and any associated customer service expenses.
j) Under EOQ inventory model, there is an assumption which states that there is no possibility of inventory stockout to occur: The Economic Order Quantity (EOQ) model is a widely used inventory management technique.
It assumes that demand for the product is constant and known with certainty, there are no quantity discounts or price variations, and there is no possibility of stockouts occurring.
The assumption of no stockouts simplifies the calculations and ensures that the optimal order quantity obtained from the model will meet the demand without interruptions.
However, in real-world scenarios, stockouts can occur due to unforeseen factors, variability in demand, or supply chain disruptions.
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What is formula of segment?
Answers
The formula for a line segment is:
segment = √((x2 - x1)^2 + (y2 - y1)^2)
1. Calculate the difference between the x-coordinates: x2 - x1
2. Square the result of step 1: (x2 - x1)^2
3. Calculate the difference between the y-coordinates: y2 - y1
4. Square the result of step 3: (y2 - y1)^2
5. Add the results of step 2 and step 4: (x2 - x1)^2 + (y2 - y1)^2
6. Calculate the square root of the result of step 5: √((x2 - x1)^2 + (y2 - y1)^2)
This final result is the length of the line segment.
The formula for a line segment is relatively straightforward. Begin by calculating the difference between the x-coordinates (x2 - x1) and square the result. Then find the difference between the y-coordinates (y2 - y1) and square the result. Add the two results together and take the square root of the sum. This final result is the length of the line segment. This formula can be used to calculate the length of any line segment, regardless of its size or shape.
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a smartphone was purposefully dropped from a height of 10 meters to test its durability from external physical impact. it will be damaged 100% of the time, but the damage can occur in different parts of the phone. it has been shown that 76% of the damages occur in the glass screen, while the other 24% occur in the battery. a number of smartphones were tested and the tests were independent. find the probability that the first time you observe a battery damage is during the third trial or later.
Answers
Answer:
what the quistion?
Step-by-step explanation:
sry i cant spell
The probability that the first time a battery damage is observed is during the third trial or later is 42.74%.
To solve this problem, we can use the geometric distribution, which models the number of trials until the first success in a sequence of independent trials. In this case, the probability of success is 0.24 (the probability of a battery damage) and the probability of failure is 0.76 (the probability of a glass screen damage).
The probability of observing a battery damage for the first time on the third trial or later can be calculated as the complement of the probability of observing a battery damage on the first or second trial.
The probability of observing a battery damage on the first trial is 0.24, and the probability of observing a battery damage on the second trial is (0.76)(0.24) = 0.1824 (the probability of no battery damage on the first trial times the probability of battery damage on the second trial). Therefore, the probability of observing a battery damage for the first time on the third trial or later is 1 - 0.24 - 0.1824 = 0.5776.
However, the question asks for the probability of observing a battery damage for the first time on the third trial or later, which means we need to take into account the fact that we may have observed a battery damage before the third trial. Therefore, we need to adjust our calculation by subtracting the probability of observing a battery damage for the first time on the first or second trial from our previous result.
The probability of observing a battery damage for the first time on the first or second trial is 0.24 + 0.1824 = 0.4224. Therefore, the probability of observing a battery damage for the first time on the third trial or later is 0.5776 - 0.4224 = 0.1552 or 15.52%.
Therefore, the probability that the first time a battery damage is observed is during the third trial or later is 42.74%
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A baseball is thrown into the air from a height of 5 feet. The ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. Which equation models the height of the baseball? Assume that acceleration due to gravity is –16 ft/s2.
Answers
Answer:
Step-by-step explanation:
Since we know that the max height is 43.5 feet, we can use that in the work form of a parabola to solve for the time it was at its max height. This time will serve as the h value in the vertex of the parabola. Then we can rewrite the parabola in terms of time.
The work form of a parabola is
\(y=-|a|(x-h)^2+k\) and believe it or not, we have everything we need to solve for h. We know the k of the vertex (43.5) and we also know that at time 0, before any time at all went by, the object started out at 5 feet. So we have a coordinate to use (0, 5) as x and y. We also know that a = 16. Plugging all that in to the work form:
\(-16(0-h)^2+43.5=5\) and
\(-16(h^2)=-38.5\) and
\(h^2=2.40625\) so
h = 1.551209206 sec
This gives us a vertex of (1.551209206, 43.5).
Now let's plug in and find the rest of the equation.
\(s(t)=-16(t-1.551209206)^2+43.5\) and expanding that binomial:
\(s(t)=-16(t^2-3.102418412t+2.406250001)+43.5\) and distributing the -16 in:
\(s(t)=-16t^2+49.63869459t-38.50000002+43.5\) and combining like terms:
\(s(t)=-16t^2+49.63869459t+4.9999999\)
so if we round to the nearest whole number, the quadratic will be
\(s(t)=-16t^2+50t+5\) which tells us that this object was lauched from an initial height of 5 feet and that it was launched at an upward velocity of 50 feet/sec.
A shopper at a clearance sale is pleased to discover some lamps on sale for $9 each. The original price tags read $30. What percentage is the discount?
Answers
Answer: 70% of a discount
Step-by-step explanation:
What value of w makes 19 – (–10) = w a true sentence?
Answers
19 + 10 = w Neg & neg = positive
w = 29
Please help and provide explanations!! Will mark as a brainliest !
Answers
The smallest possible value of x is 8.
Given:
LCM of x and 60 = 240
240 = 2*2*2*2*3*5
= \(2^{4} *3*5\)
60 = 2*2*5*3
= \(2^2*5*3\)
so x must have the same primes as 240.
x = \(2^i*3^j*5^k\)
i<=4 and j,k <= 1
so,
x = \(2^4\)
x = 8.
Therefore the smallest possible value of x is 8.
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esemate 5,840 x 25 i need help please
Answers
Answer:
146,000
Step-by-step explanation:
Simple math let me know if you need anymore help honey, have a nice day!
Felipe is working to find the quotient of 6 and
3
4
Answers
Answer:
8 is the answer
6/1 / 3/4
6/1 * 4/3
24/3
8
Step-by-step explanation:
2 in the coordinate plane, line p has slope 1 3 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r?.
Answers
The slope of the line r is 3 and the y intercept is (0,15) .
We know that coordinates of the point (x,y) after dilation by factor k centered at (a,b) is (k(x-a) + a , k(y-b) + b) .
In the question ,
it is given that
the slope of the line p \(=\) 3
and the intercept of the line p = (0,2)
So , the equation of the line p is y = 3x + 2 .
So , the coordinates of the point (0,2) after dilation by factor 3 centered at (0,0) is (3(0 - 0) + 0 , 3(5 - 0) + 0)
= (0 , 15)
Point (0,0) does not lie on the line, so the line r after dilation is parallel to the line p,
the slope of line r = 3 , the y intercept is 15 .
Therefore , The slope of the line r is 3 and the y intercept is (0,15) .
The given question is incomplete , the complete question is
In the coordinate plane, line p has slope 3 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r ?
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list two ways you can maximize a tax-sheltered retirement program
Answers
The ways that you can maximize a tax-sheltered retirement program include:
1. when the contributions made by the employer are not taxable
2. when the employee has started making contributions early in life,
What is a tax-sheltered retirement?A tax-sheltered is a retirement savings plan that enables self-employed individuals and workers of tax-exempt organizations to invest pretax money to create retirement income. A dependable source of income in retirement, tax-sheltered annuities are made to pay out consistently throughout time.
The fact that employer contributions are tax-free is one of the best features of retirement programs. Only when an employee takes money out of their retirement accounts do taxes need to be paid. If the employee starts making contributions early in life, the plans also allow the employee the chance to maximize returns, which is another benefit that the employee can get from them.
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James takes out a loan of 9000 euros which keeps on charging simple interest at a rate of 3% of the original amount per annum until it is cleared. James pays of 770 euros each year to reduce the loan. After how many years will James have fully cleared the loan?
Answers
James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.
To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.
The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.
In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.
In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.
This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.
Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.
Combining like terms, we have 9000 + 270 = 1.04x.
Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.
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rsti is a parallelogram. what is the value of x 2x+15 x+15
Answers
For x = 0, the sides of parallelogram are equal.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
There are six crucial parallelogram characteristics to be aware of:
Congruent sides are those when AB = DC.
Congruent opposite angels are D = B.
(A + D = 180°) Consecutive angles are supplementary.
All angles are correct if just one of them is.
A parallelogram's diagonals cut each other in half.
A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides.
As the sides of parallelogram are parallel and equal,
2x + 15 = x + 15
2x = x
x = 0
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?????????????????????????????????????????????
Answers
area of semi circle= (1/2).π.r²
(1/2)×3.14×14×14
307.72 cm²
solve the following addition x + 8 =23
Answers
Answer:
x= 15
Step-by-step explanation:
23-8= 15
x=15
Consider the function
f(x)=2x^2+4x−6
Over what interval is f(x) negative?
A. (0, 3)
B. (-3, 1)
C. (0, -8)
D. (-1, -8)
Answers
letter d I think that but I don't sure
Answer:
the answers d
Step-by-step explanation:
Connor is a 400m runner His median time is
Answers
Answer: 57.8
Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8
4y+18/5y= 2 what is the value of y?
Answers
Answer: 5/19
Step-by-step explanation:
4y + 18/5y = 2
20y + 18y = 10
38y = 10
y = 10/38
Using the number line below, determine which of the following expressions are equal to −9. Select all that apply.
A.
−12−(−3)
B.
−10−1
C.
−5−4
D.
−1−(−10)
E.
1−(−8)
F.
5−14
Answers
Answer:
-14
Step-by-step explanation:
An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations such as addition, subtraction, etc.
The expressions that give -9 are −12 − (−3), −5 − 4, and 5 − 14.
Option (A), (C), and (F) are the correct answer.
What is an expression?An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations such as addition, subtraction, etc.
We have,
A.
= −12 − (−3)
= -12 + 3
= -9
B.
= −10−1
= -11
C.
= −5 − 4
= -9
D.
= −1 − (−10)
= -1 + 10
= 9
E.
= 1 − (−8)
= 1 + 8
= 9
F.
= 5−14
= -9
We see that the expressions that give -9 are:
(A) −12 − (−3)
(C) −5 − 4
(F) 5−14
Thus,
The expressions that give -9 are:
Option (A), (C), and (F).
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For f(x) = -x + 8, which statement is true?
Answers
A triangle has a perimeter of 7x 8. the first side of the triangle has a length of 3x, and the second side has a length of 2x − 5. what is the length of the third side of the triangle? x 13 2x 13 5x − 5 12x 3
Answers
The length of the third side of the triangle with a perimeter of 7x + 8 is 2x + 3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
A triangle is a polygon that has three sides. The perimeter of a triangle is the sum of all the three sides.
Hence:
Perimeter of triangle = side 1 + side 2 + side 3
A triangle has a perimeter of 7x + 8. the first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.
Hence:
Perimeter of triangle = side 1 + side 2 + side 3
7x + 8 = 3x + (2x - 5) + side 3
7x + 8 = (5x - 5) + side 3
side 3 = 7x + 8 - (5x - 5)
side 3 = 2x + 13
The length of the third side is 2x + 3
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what is the nth term rule of the linear sequence below 15, 7, -1, -9, -17
Answers
Answer:
8n+7
Step-by-step explanation:
hi are u good at rational exponenets? good now help me out
Answers
Answer:
Step-by-step explanation:
nth root of a number 'a' is represented by the expression,
\(\sqrt[n]{a}\)
In this expression 'n' = Index of of the radical
\(\sqrt[4]{16}\) is called the 4th root of 16.
In \(\sqrt[4]{16}\), the index is 4 and the radicand is 16.
4th root of 16 can be represented by \(\sqrt[4]{16}\)
\(\sqrt[4]{16}=(16)^{\frac{1}{4}}\)
\(=(2^{4})^{\frac{1}{4}}\)
= 2
Guys please help me with this question
Answers
Answer:
Step-by-step explanation:
\(\frac{g}{f} (x)=\frac{g(x)}{f(x)} \\=\frac{3x^2+x}{4x} \\=\frac{x(3x+1)}{4x} \\=\frac{3x+1}{4}\)
what do i need to add to 31/6 to make 5
Answers
Step-by-step explanation:
31/6 + x = 5
x = 5 - 31/6
x = 30/6 - 31/6 = - 1/6
28 is 160% of what number?
Answers
Answer:
28 is 160% of 17.5
Step-by-step explanation:
The value of number is, 17.5
That is, 28 is 160% of 17.5.
We have to give that,
To find 28 is 160% of which number.
Let us assume that,
A number = x
Hence, We can write as,
28 = 160% of x
Solve for x,
28 = 160/100 × x
Multiply by 100,
28 × 100 = 160x
2800 = 160x
160x = 2800
Divide into both sides by 160,
x = 2800/160
x = 280/16
x = 140/8
x = 70/4
x = 35/2
x = 17.5
Hence, The solution of the number is, 17.5
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