According to a study published in the New England Journal of Medicine, overweight people on low-carbohydrate and Mediterranean diets lost more weight and got greater cardiovascular benefits than people on a conventional low-fat diet (The Boston Globe, July 17, 2008). A nutritionist wishes to verify these results and follows 30 dieters on the low-carbohydrate and Mediterranean diets and 30 dieters on the low-fat diet. These data (measured in pounds) can be found on the text website, labeled Different Diets. Let Low-carb or Mediterranean and Low-fat diets represent populations 1 and 2, respectively. Use Table 2.
Low-carb Low-carb/
Mediterrean Diets Low- Fat diet Mediterreand diet Low-fat Diet
9.5 6.5 6.8 5.9
8.1 5.8 9.1 6.9
10.4 9.9 9.4 9.1
11.9 5.1 10.2 8.0
11.8 8.0 9.5 8.9
12.6 6.3 9.5 3.4
6.7 6.3 9.4 4.6
9.6 4.4 12.0 6.2
11.6 5.7 9.9 4.6
8.4 5.9 9.7 6.7
9.0 6.8 9.2 4.6
7.5 5.1 13.0 7.1
7.2 6.3 11.3 11.0
8.5 5.5 13.6 4.5
8.8 5.5 9.0 3.9
a.Set up the hypotheses to test the claim that the mean weight loss for those on low-carbohydrate or Mediterranean diets is greater than the mean weight loss for those on a conventional low-fat diet.
H0: ?1 ? ?2 ? 0; HA: ?1 ? ?2 > 0
H0: ?1 ? ?2 = 0; HA: ?1 ? ?2 ? 0
H0: ?1 ? ?2 ? 0; HA: ?1 ? ?2 < 0
b-1.Using the appropriate commands in Excel, find the value of the test statistic. Assume that the population variances are equal and that the test is conducted at the 5% significance level. (Round your answer to 2 decimal places.)
Test statistic
b-2. What is the critical value and the rejection rule?
Reject H0 if tdf < -1.672.
Reject H0 if tdf < -2.002.
Reject H0 if tdf > 2.002.
Reject H0 if tdf > 1.672.
c. At the 5% significance level, can the nutritionist conclude that overweight people on low-carbohydrate or Mediterranean diets lost more weight than people on a conventional low-fat diet?
No
Yes
Low-carb/Mediterrean Diets Low-fat Diet
9.5 6.5
8.1 5.8
10.4 9.9
11.9 5.1
11.8 8
12.6 6.3
6.7 6.3
9.6 4.4
11.6 5.7
8.4 5.9
9 6.8
7.5 5.1
7.2 6.3
8.5 5.5
8.8 5.5
6.8 5.9
9.1 6.9
9.4 9.1
10. 2 8
9.5 8.9
9.5 3.4
9.4 4.6
12 6.2
9.9 4.6
9.7 6.7
9.2 4.6
13 7.1
11.3 11
13.6 4.5
9 3.9
Answers
Answer:
Explained below.
Step-by-step explanation:
A two-sample test is to be performed to determine whether the mean weight loss for those on low-carbohydrate or Mediterranean diets is greater than the mean weight loss for those on a conventional low-fat diet.
(a)
The hypothesis can be defined as follows:
H₀: μ₁ - μ₂ ≤ 0 vs. Hₐ: μ₁ - μ₂ > 0
(b-1)
Use Excel to perform the t test for independent samples.
The output is attached below.
The test statistic value is, t = 7.58.
(b-2)
The degrees of freedom is, df = 58.
The critical value is, t₅₈ = 1.672.
The rejection region is:
Rejected H₀ if t > t₅₈ = 1.672.
(c)
Decision:
t = 7.58 > t₅₈ = 1.672
The null hypothesis will be rejected at 5% level of significance.
Thus, the nutritionist can conclude that overweight people on low-carbohydrate or Mediterranean diets lost more weight than people on a conventional low-fat diet.
The correct option is Yes.
Related Questions
3x² + 2x + 2 + 4x2 + 5 simplify
Answers
Answer:
3x^2+2x+15
Step-by-step explanation:
3x^2+2x+2+(4x2)+5
use pemdas
Answer:
smhhh
Step-by-step explanation:
What is the slope, y-intercept, and x-intercept of (7,-6) and (10,9)
Answers
Answer:
Slope: 5
X Intercept: (8.2,0)
Y Intercept: (0, -41)
Step-by-step explanation:
Slope:
y2-y1/x2-x1=9-(-6)/10-7=9+6/10-7=15/3=5
y=5x-41 - the slope intercept form
X Intercept:
if y=0
0=5x-41
+41 +41
41=5x
8.2=x
(8.2,0)
Y Intercept:
if x=0
y=-41
(0,-41)
hope this helps
brainliest?
The sales in thousands of dollars that Terrific Toys makes during one month can be approximated by the functions S(x)=2x³-2x²+4x, where x represents the number of days after the first day of the month. About how many days will it take the store to make $50,000?
Answers
Answer:
The days will it take the store to make $50,000 in a whole number are:
30 days.Step-by-step explanation:
Remember that x represents the number of days, so, you must replace different values in the formula until you obtain a value of $50,000, in this form:
S(x)= 2x³-2x²+4xS(1)= 2*1³-2*1²+4*1S(1)= 4 ($4).So, I'll show you that the value that you need is 30 in a whole number.
S(30)= 2*30³-2*30²+4*30S(30)= 52,320 ($52,320)I know that the value exceeds the amount of $50,000, but if you use just a day before:
S(29)= 2*29³-2*29²+4*29S(29)= 47,212 ($47,212)How you can see, if you use 29 days, the value doesn't reach $50,000, by this reason, you must use 30 days to reach it.
21π
Rational
Irrational
Answers
Answer: Rational
Step-by-step explanation:
21[tex]\pi[/tex] is rational because it is [tex]\pi[/tex] times 21 which is 65.9734457254 and numbers that terminate or repeat are rational.
If [tex]\sf x^{(x^4)} = 4,[/tex] then find the value of [tex]\sf x^{(x^2)} + x^{(x^8)}.[/tex]
Answers
By inspection, we can see that x = ±√2, since (±√2)⁴ = 2² = 4.
In particular, if [tex]x^n=n[/tex], which means [tex]x=n^{\frac1n}[/tex], then [tex]x^{x^n}=x^n=n[/tex].
Let x = √2. Then
[tex]x^{x^2}+x^{x^8}=(\sqrt2)^{(\sqrt2)^2}+(\sqrt2)^{(\sqrt2)^8}[/tex]
[tex]x^{x^2}+x^{x^8}=(\sqrt2)^2+(\sqrt2)^{16}[/tex]
[tex]x^{x^2}+x^{x^8}=2+256[/tex]
[tex]x^{x^2}+x^{x^8}=\boxed{258}[/tex]
Use the formula p=le^kt. A bacterial culture has an initial population of 500. If its population grows to 7000 in 2 hours, what will it be at the end of 4 hours
Answers
Answer:
98,000 bacteria.
Step-by-step explanation:
We are given the formula:
[tex]P=le^{kt}[/tex]
Where l is the initial population, k is the rate of growth, and t is the time ( in hours).
We know that it has an initial population of 500. So, l is 500.
We also know that the population grows to 7000 after 2 hours.
And we want to find the population after 4 hours.
First, since we know that the population grows to 7000 after 2 hours, let's substitute 2 for t and 7000 for P. Let's also substitute 500 for l. This yields:
[tex]7000=500e^{2k}[/tex]
Divide both sides by 500:
[tex]e^{2k}=14[/tex]
We can solve for the rate k here, but this is not necessary. In fact, when can find our solution with just this.
Let's go back to our original equation. We want to find the population after 4 hours. So, substitute 4 for t:
[tex]P=500e^{4k}[/tex]
We want to find the total population, P. Notice that we can rewrite our exponent as:
[tex]P=500(e^{2k})^2[/tex]
This is the exact same thing we acquired earlier. So, we know that the expression within the parentheses is 14. Substitute:
[tex]P=500(14)^2[/tex]
Square and multiply:
[tex]P=500(196)=98000[/tex]
So, after 4 hours, there will be 98,000 bacteria.
And we're done!
IS THE FRACTION 37/8 A RATIONAL NUMBER AND WHY
Answers
Option A)
Yes, Fraction 37/8 is a rational number because the decimal form of the number is terminal.
.
A Rational Number is any number that can be expressed as a fraction or ratio of two integers.
For example, 3/4, 8.75, 2, and -6 are all considered rational numbers.
Note that integers, or "whole numbers", are rational numbers. This is because they can be expressed as fractions.
For example, 2 can be rewritten as 2/1, or 200/100. -6 can be rewritten as -6/1, 6/-1, or -12/2.
Many non-integer, or decimal numbers, are also rational numbers.
For instance, 8.75 can be rewritten as 8 3/4, 875/100, or 1750/200. This also includes repeating decimal numbers like 0.3333333..., which can be rewritten as 1/3.
Fraction = 37 /8
Numerator = 37
Denominator = 8
Both are integer
The fraction of 37 divided by 8 = 37/8 is a Rational Number because both the numerator and denominator are integers.
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What is factorise 5y - 10
Answers
Answer:
5(y - 2)
Step-by-step explanation:
What is the GCF (Greatest Common Factor) for 5y and -10? It is 5 so you take 5 out of 5y and 5 out of -10. You put the 5 outside of the parentheses and put y - 2 inside of the parentheses. That is how you factorize 5y - 10
The factorized form of 5y - 10 is 5(y - 2).
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
When we are asked to factorize an expression, we are essentially trying to write the expression as a product of simpler expressions. In this case, we want to write 5y - 10 as a product of simpler expressions.
One way to approach this is to look for a common factor that is present in both terms of the expression.
In this case, we can see that both 5y and 10 are divisible by 5. Therefore, we can factor out the greatest common factor of the two terms, which is 5.
When we factor out 5 from 5y and -10, we are left with:
5y - 10 = 5(y - 2).
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Rewrite 38/7 as a mixed number. 5 3/7 3 8/7 3 7/8 5 4/7
Answers
Answer:
5 3/7
Step-by-step explanation:
Answer:
let's see what to do
Step-by-step explanation:
[tex] \frac{38}{7} = \frac{35 + 3}{7} = \frac{35}{7} + \frac{3}{7} = 5 + \frac{3}{7} \\ [/tex]
End....
thanks for watching ♥️♥️♥️♥️♥️.
The table below shows the illuminated percentage of the moon on a lunar cycle of 28 days. The relationship can be described using a cosine function.
A 2-column table with 5 rows. Column 1 is labeled d with entries 0, 7, 14, 21, 28. Column 2 is labeled percent with entries 0, 48, 96, 48, 0.
Use the drop-down menus to complete each statement.
The amplitude of the function is
.
The period of the function is
.
The graph has a vertical shift of
units.
Answers
Answer:
Use the drop-down menus to complete each statement.
The amplitude of the function is
✔ 48
.
The period of the function is
✔ 28
.
The graph has a vertical shift of
✔ 48
units.
Step-by-step explanation:
i got the question wrong for you homies, these were the correct ones on edge2020
blake ran laps around the gym
Answers
Please help with this two part question (Calculus)^^
Answers
Answer:
1) -0.016 pounds per square inch per cubic inch.
2) [tex]\displaystyle V'(P)=-\frac{800}{P^2}[/tex]
Step-by-step explanation:
We are given the equation [tex]PV=800[/tex].
Part A)
We want to determine the average rate of change of P as V increases from 200 cubic inches to 250 cubic inches.
To find the average rate of change between two points, we find the slope between them.
Rewrite the given equation as a function of V:
[tex]\displaystyle P(V)=\frac{800}{V}[/tex]
Hence, the average rate of change for V = 200 and V = 250 is:
[tex]\displaystyle \begin{aligned} m &= \frac{P(250) - P(200)}{250 - 200} \\ \\ & = \frac{3.2 - 4}{250 - 200} \\ \\ & = -0.016\end{aligned}[/tex]
Therefore, the average rate of change is -0.016 pounds per square inch per cubic inch.
Part B)
We want to express V as a function of P. This can be done through simple division:
[tex]\displaystyle V(P)=\frac{800}{P}[/tex]
We want to show that the instantaneous change of V with respect to P is inversely proportional to the square of P. So, let's take the derivative of both sides with respect to P:
[tex]\displaystyle \frac{d}{dP}\left[V(P)\right]=\frac{d}{dP}\left[\frac{800}{P}\right][/tex]
Differentiate. Note that 1/P is equivalent to P⁻¹. This allows for a simple Power Rule:
[tex]\displaystyle \begin{aligned} V'(P) & = 800\frac{d}{dP}\left[ P^{-1}\right] \\ \\ & = -800(P^{-2}) \\ \\ & = -\frac{800}{P^2}\end{aligned}[/tex]
Therefore, the instantaneous change of V is indeed inversely proportional to the square of P.
There are 3 students in the class and 27 apples. If the apples are divided equally among the students, how many does each student get?
Answers
Answer:
9 apples.
Step-by-step explanation:
27/3=9
What is the difference?
-6-[11)
-17
5
5
17
Answers
Answer:
-17
Step-by-step explanation:
You have to simplify the expression!
Answer:
-17
Step-by-step explanation:
A teacher keeps track of the number of students that participate at least three times in an optional study session each year. He models the attendance over the last nine years with this function.
n(t) = 3.53t^2 - 33.04t + 117.56
Which graph would most likely be associated with the given model?
Answers
Regression equations can be linear, quadratic or exponential
The graph that would most likely be associated with the given model is (b)
The regression equation is given as:
[tex]n(t) = 3.53t^2 - 33.04t + 117.56[/tex]
The above regression equation is a quadratic function (and non-linear).
So, the graph must represent a non-linear relationship.
From the given graphs, only graph (b) represents a quadratic function.
Other options are either linear models or exponential.
Hence, the graph that would most likely be associated with the given model is (b)
Read more about regression models at:
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Answer:
Its B
Step-by-step explanation:
4. What is the slope of the line that contains the points (-6,1) and (4,-4)? A. 2 B. -2 C. 1 2 a 1 D. 2
Answers
Answer:
It would be -[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Use the slope formula to find the slope m.
Lisa Company uses the periodic inventory system to account for inventories. Information related to Lisa Company's inventory at October 31 is given below:
October
1
Beginning inventory
390 units x $9.80 = $3,822
8
Purchase
790 units x $10.50 = 8,295
16
Purchase
590 units x $10.60 = 6,254
24
Purchase
195 units x $11.60 = 2,262
Total units and cost
1,965 units $20,633
Answers
Answer:
The value of ending inventory will be items of latest purchase.
Step-by-step explanation:
Given that,
Lisa Company uses the periodic inventory system to account for inventories.
Information related to Lisa Company's inventory at October 31 is given,
Suppose, find the value of ending inventory using the FIFO cost assumption if 500 units remains on hand at october 31
We need to calculate the value of ending inventory
Using FIFO method
[tex]value\ of\ ending\ inventory =305\ units\times\$10.6+195\ units\times\$11.60[/tex]
[tex]value\ of\ ending\ inventory = 3233+2262[/tex]
[tex]value\ of\ ending\ inventory =\$5495[/tex]
Hence, The value of ending inventory will be items of latest purchase.
Help help help help help Select the equivalent expression (3^2x5^3
Answers
Answer:
D
Step-by-step explanation:
(3^2x5)^3=91125
3^6x5^3=91125
The answer is 9 3⁶ x 5³
(3² x 5)³= 91125
3⁶ x 5³ = 91125
What is the solution to this equation?
3(4x + 3) = 2x - 5(3 - x) + 2
A.
o o
O
-
O
D.
-
Answers
Answer:
-0.86
Step-by-step explanation:
12x + 9 = 2x - 15 + 5x + 2
Combine
19x = -22
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 80 pounds. There were twice as many large boxes shipped as small boxes shipped and the total weight of all boxes was 1435. Determine the number of small boxes shipped and the number of large boxes shipped.
Answers
Answer:
There were 7 small boxes and 14 large boxes shipped.
Step-by-step explanation:
This problem may be solved by a system of equations:
I am going to say that:
x is the number of small boxes used
y is the number of large boxes used
There were twice as many large boxes shipped as small boxes shipped
This means that y = 2x
Each small box of paper weighs 45 pounds and each large box of paper weighs 80 pounds. The total weight of all boxes was 1435 pounds.
This means that 45x + 80y =1435
So we have to solve the following system:
y=2x
45x + 80y =1435
45x + 80 (2x) = 1435
205x = 1435
x= 1435/205
x=7
y=2x= 2(7) = 14
There were 7 small boxes and 14 large boxes shipped.
PLEASE HELP 40 POINTS!!! For what value of x is line a parallel to line b?
Enter your answer in the box.
x =
Answers
Answer: 22
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
Don't worry, don't worry child. Oh, geometry. How lucky are you: finally knowing this treasury of humanity. I'm jealous now. Haha.
In the annex, you can see what is happening :)
Look that, if a and b are paralels, 4x + 28 is External Alternate of the Opposite Vertex of 116, which is also 116. Then, they have the same value: 4x + 28 = 116.
If you don't remember those concepts, review the initial part of geometry. The proof of that is quite simply, moreover is easy to mentally deduce that.
62+(3·4)−24
PLS HELP MEEEEEEEE
Answers
Answer:
50
Step-by-step explanation:
62+(3·4)−24
62+12-24
Final Answer: 50
Answer:
50
Step-by-step explanation: :D
The sales tax on a pair of jeans is 7%. if juan paid $3.15 in tax, what was the cost of the jeans before tax?
Answers
Answer:
2.93
Step-by-step explanation:
3.15×7/100=0.2205
3.15-0.2205=2.9295
The cost of the jeans before tax $2.9295
What is percentage?"It is a number or ratio that can be expressed as a fraction of 100."
For given example,
Let 'a' be the original price of the jeans.
Let 'b' be the price of the jeans with tax.
then, b = a + tax
Juan paid $3.15 in tax for the jeans.
The sales tax on a pair of jeans is 7 percent.
First we find the tax on a pair of jeans.
⇒ tax = b × 7%
⇒ tax = 3.15 × (7/100)
⇒ tax = $0.2205
We need to find the cost of the jeans before tax.
Here, b = $3.15, tax amount = $0.2205
⇒ b = a + 0.2205
⇒ 3.15 = a + 0.2205
⇒ a = 3.15 - 0.2205
⇒ a = $2.9295
Therefore, the cost of the jeans before tax $2.9295
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Please help will give brainliest
Answers
Answer:
x=17
Step-by-step explanation:
These are corresponding angles, meaning they have the same measure. We must set them equal to each other.
Hope this helps :-)
Maggie purchased a 2-pound roast to fix for dinner. How many ounces does the roast weigh?
Answers
Answer:
32 ounces
Step-by-step explanation:
1 lb = 16 ounces
2 lbs = 2 * 16 = 32 ounces
URGENT!!!!! WILL MARK BRAINLIEST!!!!
Options:
AAS
SAS
AAA
ASA
Answers
V = 5x + 2y
X = 3
y = -4
a) Work out the value of V.
Answers
V= 15-8
V=7
A ball is thrown from a height of 70 meters with an initial downward velocity of 10/ms. The ball's height h (in meters) after t seconds is given by the following.
h=70-10t-5t^2
Answers
The time when the ball hit the ground, which is thrown from a height of 70 meters with an initial downward velocity of 10 m/s is 2.87.
What is a quadratic equation?A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
Here,(a,b, c) is the real numbers and (x) is the variable. To solve the equation for x, use the following formula,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The ball's height h (in meters) after t seconds is given by the following.
[tex]h=70-10t-5t^2[/tex]
The ball is thrown from a height of 70 meters with an initial downward velocity of 10 m/s. In this case,
Height h=70 metersVelocity v=10 m/s.The time when the ball hit the ground has to be find out. The value of the height when it hit the group is zero. Put the value of h=0 in the above equation,
[tex]h=70-10t-5t^2\\0=70-10t-5t^2\\5t^2+10t-70=0\\5t^2+10t-70=0\\[/tex]
Solve the quadratic equation using the following formula,
[tex]t=\dfrac{-10\pm \sqrt{10^2-4(10)(-70)}}{2\times5}\\t=-4.87, t=2.87[/tex]
Consider positive value. Thus, the time when the ball hit the ground, which is thrown from a height of 70 meters with an initial downward velocity of 10 m/s is 2.87.
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help please (: picture is included
Answers
PLEASE HELP!!! ILL GIVE BRAINLIEST THIS IS WORTH 20 POINTS PLEASE (ignore where it says 8 &2 points it’s how much the question adds up to in the grade book)
Answers
Answer:
x= -3 is the answer
UW=3 is the answer..
hope it helps you mate
please mark me as brainliast
Answer:
From the given figure, we can see that the 2 given line segments are equal in length
Hence,
11 + (x - 5) = 2x - 4
6 + 4 = x
x = 10
Now that we know the value of x, we can use it to get the length of the line segment UW
UW = 11 + (x - 5)
UW = 11 + (10 - 5)
UW = 11 + 5
UW = 16 units