A recent study1 examines chocolate’s effects on blood vessel function in healthy people. In the randomized, double-blind, placebo-controlled study, 11 people received 46 grams (1.6 ounces) of dark chocolate (which is naturally flavonoid-rich) every day for two weeks, while a control group of 10 people received a placebo consisting of dark chocolate with low flavonoid content. Participants had their vascular health measured (by means of flow-mediated dilation) before and after the two-week study. The increase over the two-week period was measured, with larger numbers indicating greater vascular health. For the group getting the good dark chocolate, the mean increase was 1.3 with a standard deviation of 2.32, while the control group had a mean change of -0.96 with a standard deviation of 1.58.
Find a 90% confidence interval for the difference in means between the two groups MC-MN , where MC represents the mean increase in flow-mediated dilation for people eating dark chocolate every day and MN represents the mean increase in flow-mediated dilation for people eating a dark chocolate substitute each day. You may assume that neither sample shows significant departures from normality.
Round your answers to two decimal places.
Answer:
CI = (0.68, 3.84)
Step-by-step explanation:
We want to find the confidence interval for the difference in means between the two groups MC and MN.
where;
- MC represents the mean increase in flow-mediated dilation for people eating dark chocolate every day.
- MN represents the mean increase in flow-mediated dilation for people eating a dark chocolate substitute each day.
We are given;
Sample mean of C; x'c = 1.3
Sample mean of N; x'n = -0.96
Standard deviation of C; S_c = 2.32
Standard deviation of N; S_n = 1.58
Sample size of C; n_c = 11
Sample size of N; n_n = 10
Formula for the confidence interval for the difference in means is;
CI = (x'c - x'n) ± t√[(S_c²/n_c) + (S_n²/n_n)]
Where t is critical value at confidence level. From table attached, t at CL of 90% with DF = 10 - 1 = 9 is; t = 1.833
Thus;
CI = (1.3 - (-0.96)) ± 1.833√[(2.32²/11) + (1.58²/10)]
CI = [(1.3 + 0.96)) - 1.833√[(2.32²/11) + (1.58²/10)], [(1.3 + 0.96)) + 1.833√[(2.32²/11) + (1.58²/10)]
CI = (2.26 - 1.58), (2.26 + 1.58)
CI = (0.68, 3.84)
Right circular cylinder has volume and radius. Right circular cylinder is similar to cylinder and has volume. Find the radius of cylinder.
Answer: where’s the picture
Step-by-step explanation:
Hum
In Olongapo City, a bump car ride costs
Php 120 per person for the first 30 minutes
and Php 10.00 for every additional 10
minutes. If you spend Php 270.00 for a ride,
how long did you ride?
A pair of dice was rolled many times
and the results appear below. Based
upon these results, what is the
experimental probability of rolling a 2?
Outcome
2
3
3
4
5
6
7
8
9
10
11
12
Frequency
3
6
00
11
14
16
15 12
9
5
1
The percent probability is = [ ? ]%
Round to the nearest percent.
Enter
23/100 converted to a decimal
Can someone help me with this?
Answer:
I can help you via Watsapp
1
(b) If x= 1 - 2 then find the value of x-
x
Answer:
I think x - x = 0
FILLER FILLER
write 23/6 as an mixed number
Answer:
3 5/6
Step-by-step explanation:
18/6 = 3
23-18=5 (5/6 are left)
what value is needed to complete the square?
X²-2x + _______
Answer:
[tex]X^2-2x+1[/tex]
Step-by-step explanation:
Traditional pattern for a perfect square:
[tex]x^{2} +2ax+a^{2}[/tex]
Which factors into: [tex](x+a)^2[/tex]
We know becuase a is "missing" from the original equation that it must equal 1; therefore:
[tex]x^2+2x+1[/tex]
Which we know is correct because it factors into: [tex](x+1)^2[/tex]
Re write this expression 4(6 x +12)
Answer:
24 (x + 2)
24x + 48
these are two ways to rewrite the expression
Answer:
24x+48
Step-by-step explanation:
Calvin wrote inequalities to compare the heights, in feet, of rivers above or below flood stage.
Select all of the inequalities that are correct.
A. -10 > -9
B. 1> -18
C. -25 > -30
D. 3 < -5
E. -10 < 3
Answer:
I'm not 100% sure but I think its B. 1> -18
PLEASE HELP
A. 0
B. 2
C. -2
Answer:
B
Step-by-step explanation:
You can read this as "find g of f of 2"
Also written as g(f(2)).
What we're doing is is looking at the function f and getting the value when you input 2. f(2)
Since the function f is the curved one, you will find the coordinate where the input is 2. At input 2 or x=2, we get the value of 0.
Now back to g(f(2)) -- Because we have found the value of f when it is 2, we can replace this equation with:
g(0)
Now we find the value we get from g when we put 0 as the input. When 0 is our input, or when our x is 0, we see the point of g is (0,2) so our output is 2.
HELP WILL MARK BRAINLIEST
I need help on this please!
No links
Study guide for exam.
Find the LCD of the given rational equation: 9/x-1+-3x/x+6=4x/x^2-7x+6
Answer: the answer would be A.
(x-1)(x-6)(x+6)
Step-by-step explanation:
a p e x
The LCD of the given expression is (x-1)(x-6)(x+6).
What is LCD?
The least common denominator (LCD) is the smallest number or expression that can be a common denominator for a set of fractions.
What is the LCD in the given expression?
Factor the denominator of the right side of the equation.
[tex]\frac{9}{x-1}-\frac{3x}{x+6}=\frac{4x}{(x-1)(x-6)}[/tex]
From this, it is conclude that the common denominator will be [tex](x-1)(x-6)(x+1)[/tex].
Therefore, the LCD of the given expression is (x-1)(x-6)(x+6).
Learn more:https://brainly.com/question/2004756
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How much interest is to be paid at 1500 principal, 7% compounded annually, and for 3 years
Answer:
I = 337.56
Step-by-step explanation:
Given that,
Principal, P = 1500
Rate, R = 7%
Time, t = 3 years
We need to find the interest if it is compounded annually. We know that, the amount is given by :
[tex]A=P(1+\dfrac{r}{100})^n[/tex]
Put all the values,
[tex]A=1500\times (1+\dfrac{7}{100})^3\\\\A=1837.56[/tex]
We know that,
Interest = Amount - Principal
I = 1837.56 - 1500
I = 337.56
Hence, the interest is equal to 337.56.
Which of the following three-dimensional solids cannot be generated by rotating a two-dimensional figure around an axis?
sphere
pyramid
cylinder
cone
Answer:
Step-by-step explanation:
Sphere
. A point P is equidistant from R(-2, 4) and S(6,-4)
and its x-coordinate is twice its y-coordinate.
(0) Find the coordinates of P.
(ii) Hence, determine whether P, R and S are
collinear, showing your working clearly.
Answer:
I) coordinate of P is (11, 5.5)
II) Points are not collinear
Step-by-step explanation:
I) Let the coordinates of P be (a, b)
We are told that its x-coordinate is twice its y-coordinate. Thus, a = 2b
Now, P is equidistant from R(-2, 4) and S(6,-4). Thus;
PR = PS
Using the formula for distance between two coordinates, we have;
√((a - (-2))² + (b - 4)²) = √((a - 6)² + (b - (-4))²)
This gives;
(a + 2)² + (b - 4)² = (a - 6)² + (b + 4)²
Since a = 2b,then we have;
(2b + 2)² + (b - 4)² = (2b - 6)² + (b + 4)²
4b² + 8b + 4 + b² - 8b + 16 = 4b² - 12b + 36 + b² + 8b + 16
Simplifying this gives;
20 = 42 - 4b
42 - 20 = 4b
4b = 22
b = 22/4
b = 11/2
b = 5.5
Since a = 2b
Then a = 2 × 5.5
a = 11
Thus, coordinate of P is (11, 5.5)
II) Formula for area of triangle formed by three points is given as;
A = ½|(x1 - x2) (x2 - x3)|
|(y1 - y2) (y2 - y3)|
x1 - x2 = 11 - (-2) = 13
x2 - x3 = -2 - 6 = -8
y1 - y2 = 5.5 - 4 = 1.5
y2 - y3 = 4 - (-4) = 8
Thus;
A = ½|13 -8|
|1.5 8|
A = ½((13 × 8) - (1.5 × - 8))
A = ½(104 + 12)
A = 58
Since the area is not zero, then it means the points are not collinear.
A frozen yogurt shop charges $1.50 for a cone plus $0.35 for each scoop of
frozen yogurt. Rose paid $2.90 for her frozen yogurt. How many scoops did
she have?
Type your answer...
PLS HELP PLS PLS!!
A pyramid has a volume of 1,944 inches cubed and a rectangular base with the dimensions 18 inches by 9 inches. What is the height of the pyramid?
4 in.
12 in.
24 in.
36 in.
Answer:
36
Step-by-step explanation:
I used a triangle height calculator on G0ogle
If the base area is 162 square inches, then the height of the pyramid will be 36 inches. Then the correct option is D.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A pyramid has a volume of 1,944 inches cubed and a rectangular base with the dimensions of 18 inches by 9 inches.
Then the height of the pyramid will be
The volume of the pyramid will be
Volume = (Base area x height) / 3
Then the base area will be
Base area = 18 x 9
Base area = 162 square inches
Then the height of the pyramid will be
1944 = (162 h) / 3
5832 = 162 h
h = 36
More about the geometry link is given below.
https://brainly.com/question/7558603
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List the side lengths from shortest to longest. (20 points)
Answer:
b, a, c
Step-by-step explanation:'
The side opposite of the smallest angle(50) is always the smallest, which means b is the smallest
Hope this helps!
Answer:
b ,a ,c
Step-by-step explanation:
The side opposite the smallest angle is the shortest
The smallest
x = 180 - 70 -62 = 48
48 is the smallest angle so b is the smallest side
The side opposite the largest angle is the longest side
70 is the largest angle so c is the longest side
b ,a ,c
Find the distance between the points (-15, 3) and (-9, 8).
Answer:
61 units
Step-by-step explanation:
Plz help I've been crying about this question about number 8 plz help with number 8 I'll give brainiest.
Answer: I got ~17% (It's 17% as the problem asked for the answer to be rounded)
Step-by-step explanation:
I added the 12 possible chances from the spinner with the 6 sided die chances. This gets me 18. Since the problem is asking the probability of rolling an 8 or 10 alongside a 3, I did 3/18 and got 16.66% (repeating). I'm not entirely sure if I did this right, but I hope this helped somehow. Let me know if it's not the correct answer.
The knockoff Jersey store sold 6 more Leafs jerseys than Senators. Four times the number of Senators Jersey sold plus three times the number of Leafs jerseys sold is 102. How many Leaf Jerseys were sold?
Answer:
72
Step-by-step explanation:
6x4=24x3=72
SIMPLIFY
3(4x+4)-4=?
Answer:
12x+8
Step-by-step explanation:
3( 4x+4)-4 ( Remove the parentheses)
12x+12-4 Calculate
the answer would be 12x+8
HELP PLEASE PICTURE ABOVE. NO LINKS JUST HOW TO SOLVE STEP BY STEP AND THE ANSWER PLEASE
9514 1404 393
Answer:
4) -ln(2)/3
5) x = 9
6) x = 2
7) x = -6
Step-by-step explanation:
4) e^(-3x) = 2 . . . . given
-3x = ln(2) . . . . . take the natural log
x = -ln(2)/3 . . . . divide by the coefficient of x
__
5) ln(3x -5) = ln(11) +ln(2)
3x -5 = 11·2 . . . . . take antilogs
3x = 27 . . . . . . . . add 5
x = 9 . . . . . . . . . . divide by 3
__
6) log4(x -1) +log4(x +2) = 1
(x -1)(x +2) = 4 . . . . . take antilogs
x^2 +x -2 = 4 . . . . . . eliminate parentheses
x^2 +x +1/4 = 6 1/4 . . . add 2 1/4 to complete the square
(x +0.5)^2 = 6.25 . . . . write as a square
x +0.5 = ±2.5 . . . . . . . take the square root
x = -0.5 ± 2.5 = {-3, +2} . . . . . . x = -3 is an extraneous solution
x = 2
__
7) 8^x = 4^(x -3)
2^(3x) = 2^(2(x -3)) . . . . write using a common base of 2
3x = 2(x -3) . . . . . . . . . . take logarithms base 2
x = -6 . . . . . . . . . . . . . . .subtract 2x
The mean weight of cherry tomatoes on a farm is about 57 grams. The farmer is interested in testing a new type of fertilizer. They use the fertilizer on a particular patch and after the harvest, the mean weight of the tomatoes is 62 grams. They perform a t-test, with the null hypothesis being that the mean of all tomatoes grown with the new fertilizer is equal to 57 grams, and the alternative is that the mean is greater than 57 grams. There is a chance that they will mistakenly conclude the fertilizer improves the size of tomatoes when, in fact, it does not and they just got lucky with this particular crop. They wish to make sure the probability of making this mistake is no more than 8%. Below are four different p-values that they might get from their analysis. For which p-value should they reject the null hypothesis?
a. 0.10
b. 1.00
c. 0.15
d. 0.07
Answer:
The weight of a tomato depends on the variety of tomato. There are cherry, plum, grape, roma, and beef tomatoes of various sizes. The following tables shows different types of tomatoes, along with the average weight (in grams and ounces), the number of tomatoes per kilogram, and the number of tomatoes per pound.
Step-by-step explanation:
The hypotenuse of a right triangle is 13 m long. The shorter leg is 7 m shorter than the longer leg. Find the side lengths of the triangle. Length of the shorter leg: m Length of the longer leg: m Length of the hypotenuse: m
Answer: Shorter: 5 m Longer: 12m Hypotenuse: 13 m
Step-by-step explanation:
Write the following inequality in slope-intercept form. 6x+2y≤46
Answer:
y ≤ -3x + 23
Step-by-step explanation:
1. 6x + 2y ≤ 46
•subtract “6x” from both sides to isolate the “y” variable
2. 2y ≤ 46 -6x
•divide both sides by “2”
3. y ≤ 23 -3x
•reorder the terms so it fits the “y = mx + b” slope-intercept format
4. y ≤ -3x + 23
When Natalie runs the 400 meter dash, her finishing times are normally distributed with a mean of 71 seconds and a standard deviation of 2.5 seconds. What percentage of races will her finishing time be between 71 and 77 seconds, to the nearest tenth?
Answer:
49.2%
Step-by-step explanation: