Answer:
a. (3.83952, 5.16049)
b. (7.32, 8.88)
c. The difference in the range of the confidence intervals suggest that taking the zinc loz-enges reduces the overall duration of cold symptoms
d. The assumptions required for the validity validity of a t-test include that the data is sampled from a source that have data that are normally distributed
Step-by-step explanation:
The given parameters are;
The number of participants that took zinc lozenges, n₁ = 25
The number of participants that took a placebo, n₂ = 23
The mean duration of the symptoms for the zinc lozenge group, [tex]\overline x_1[/tex] = 4.5 days
The standard deviation of overall duration, s₁ = 1.6 days
The mean duration of the symptoms for the placebo group, [tex]\overline x_2[/tex] = 8.1 days
The standard deviation, s₂ = 1.8 days
a. The 95% confidence interval if everyone in the population were to take zinc lozenges is given as follows;
[tex]CI=\bar{x}_1\pm t_{\alpha/2} \times \dfrac{s_1}{\sqrt{n_1}}[/tex]
n₁ = 25, the degrees of freedom (df) = n₁ - 1 = 24
The t-value for 95% confidence interval, with df = 24, with t = 2.064
Therefore, we have;
[tex]CI_{zl}=4.5 \pm 2.064 \times \dfrac{1.6}{\sqrt{25}}[/tex]
[tex]CI_{zl}[/tex] = 4.5 ± 0.66048
[tex]CI_{zl}[/tex] = (3.83952, 5.16049)
b. The 95% confidence interval if everyone in the population were to take the placebo is given as follows;
[tex]CI_p=\bar{x_2}\pm t_{\alpha/2} \times \dfrac{s_2}{\sqrt{n_2}}[/tex]
n₂ = 23, the degrees of freedom (df) = n₂ - 1 = 22
The t-value for 95% confidence interval, with df = 22, with t = 2.074
Therefore, we have;
[tex]CI_p =8.1 \pm 2.074 \times \dfrac{1.8}{\sqrt{23}}[/tex]
[tex]CI_p[/tex] = 8.1 ± 0.7784
[tex]CI_p[/tex] = (7.32, 8.88)
c. Based on the difference in the range of the 95% confidence interval for the mean duration of cold symptoms of the group that take zinc lozenges, (3.83952, 5.16049), and the mean of the group that are on a placebo, (7.32, 8.88), there is sufficient statistical evidence to suggest that there is a difference between the mean and taking zinc lozenges reduces the overall duration of cold symptoms more than if taking placebo
d. The assumptions required for validity when carrying out a t-test include;
i) The measurement scale is ordinal or continuous
ii) The sample is a simple random sample
iii) The data gives a normal distribution curve
iv) The sample size is reasonably large
v) The variance are homogeneous
Among these assumptions, the data must be randomly sampled from the population of interest and that the data variables follow a normal distribution
The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size and equality of variance in standard deviation
I need to know what this is? Can someone tell me… Honestly. What is the value of x?
Answer:
98º
Step-by-step explanation:
The sum of angles in a triangle is 180
---------------------
The missing angle in the triangle
180 - 45 - 53 = 82º
-------------------------
x is supplementary to 82º
x = 180 - 82
x = 98º
Find the angle for this problem
Answer:
ans: 31°
Step-by-step explanation:
<EFG = <EFH + <HFG
2x+52= 21 + ( x+31)
2x-x= 21 +31 -52
x= 0
so our question is to find <HFG so,
x+31°= 31°
I’m stuck on this question plz help
Answer:
3(n-8)
Step-by-step explanation:
Given the inequality, select all the values of x that make that inequality true 3(2k-1)<9 0 1 2 3 4
Answer:
We have the inequality:
3*(2*x - 1) < 9
Where the given options are:
0, 1, 2, 3, 4
(you wrote k instead of x, but before you wrote "select all the values of x that make that inequality true", then I assume that the variable is x instead of k).
Again, let's start with the inequality:
3*(2*x - 1) < 9
and let's isolate the variable x.
(2*x - 1) < 9/3 = 3
(2*x - 1) < 3
2*x < 3 + 1 = 4
2*x < 4
x < 4/2
x < 2
Then all the values of x that are strictly smaller than 2 make the inequality true.
From the given options (0, 1, 2, 3, 4) the two that make the inequality true are:
x = 0
and
x = 1.
the mean of three number is 15. if 2 of the numbers are 18 and 16 what is the third number
Answer:
The third number is 11
Step-by-step explanation:
First, you multiply 15 by 3 to get the sum(45) and then you add 18 and 16 to get 34. Lastly, you will minus 45 and 34 and your answer will be 11.
Point slope form equations can be converted into slope intercept form. Distinguish whether the following
equations are the equations of the same line. Prove and explain your answer. Show your work for your
teacher to review.
y+ 1 = 5(x + 2) and y = 5x + 10
PLEASE HELP IM LITERALLY DYING
Please help I will give brainlist
Answer:
they are NOT the same
Step-by-step explanation:
y+ 1 = 5(x + 2) is y = 5x + 9
distribute the 5 and get 5x + 10
when you subtract the 1 from both sides the 10 becomes a 9
The Park Protectors is a group of elementary students and teachers from 3232 schools who pick up trash at local parks. The line plot shows the tons of trash they picked up this year.
Answer:
[tex]Each = \frac{15}{128}[/tex]
Step-by-step explanation:
Given
See attachment for line plot
Required
Determine the total trash picked
The data on the line plot can be represented as:
[tex]Trash \to Schools[/tex]
[tex]\frac{1}{8} \to 6[/tex]
[tex]\frac{1}{4} \to 8[/tex]
[tex]\frac{1}{2} \to 2[/tex]
[tex]1 \to 0[/tex]
The total trash picked is:
[tex]Total = \frac{1}{8} * 6 + \frac{1}{4} * 8 + \frac{1}{2} * 2 + 1 * 0[/tex]
[tex]Total = \frac{3}{4} + \frac{8}{4} + 1+0[/tex]
Take LCM
[tex]Total = \frac{3+8+4+0}{4}[/tex]
[tex]Total = \frac{15}{4}[/tex]
The total picked by each school is:
[tex]Each = \frac{Total}{32}[/tex]
[tex]Each = \frac{15/4}{32}[/tex]
Rewrite as:
[tex]Each = \frac{15}{4*32}[/tex]
[tex]Each = \frac{15}{128}[/tex]
Kevin drew a diagonal inside a quadrilateral. He realizes the it always make 2 congruent isosceles triangleso. What kind of quadrilateral did Kevin use to draw the triangles ?
Answer:
The square is the quadrilateral.
Step-by-step explanation:
A quadrilateral is a 2 dimensional geometric shape. It has four sides which may be or may not be equal.
If a quadrilateral is a square and we make its diagonal so that we get two triangles.
These two triangles are isosceles triangle as the two sides are equal and the square has four equal sides and the triangles are congruent to each other.
here, the triangles ABC and ADC are congruent and isosceles.
A function has the points (1,5), (3,6), (4, 10), and (2, y).
Which point, (2, y), would keep this a function?
(4,11)
(4,5)
(3,8)
(6,3)
Answer:
sorry I don't know the answer
Please help!
The graphs of f(x)=−2x and g(x)=(12)x are shown.
What are the solutions to the equation −2x=(12)x ?
Select each correct answer.
-2
-1
2
4
Answer:
-1 and -2
Step-by-step explanation:
The function 2 represented by the equation f(x) = -(x - 2)² + 5 has the larger maximum.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
The functions are given as:
Function 1
f(x) = -(x - 4)² + 1
Function 2:
f(x) = -(x - 2)² + 5
A quadratic function is represented as a (x - h)² + k, when a is negative then, the vertex of the function is a maximum. In both functions, the value of a is -1. This means that both functions are at a maximum
The values of k in both functions are k = 1 and k = 5. By comparison, 5 is greater than 1. Therefore, function 2 has larger maximum.
Read more about quadratic functions at:
brainly.com/question/4140287
#SPJ3
complete question;
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. Function 1 graph of function f of x equals negative x squared plus 8 multiplied by x minus 15 Function 2 f(x) = −x2 + 2x − 15 Function 1 has the larger maximum at (4, 1). Function 1 has the larger maximum at (1, 4). Function 2 has the larger maximum at (−14, 1).
pls need help... brainliest :))
Answer:
I am not the best in this type of math, the best thing I can do is help you.
You see that there is a pattern in the chart? X adds 2 every column, and Y adds 4 every column.
I believe the slope simplified is 2/1, if you are following y/x. If not, then the other way around.
Unfortunately, I can't help you with the rest of the problem, but I hope you can get a good idea of what your supposed to do.
Have a good day.
Bab needs help with mafs
Answer:
The 4th option
Use sin -1, cos -1 or tan -1 to find the measure of
what is the answer to 7m-6,m=8
Answer:
50
Step-by-step explanation:
When given the following equation, and information,
7m - 6
m = 8
One must substitute the value of (m) into the equaiton. Then simplify and solve to evaluate the equation,
7m - 6
7(8) - 6
56 - 6
50
Answer:
50
Step-by-step explanation:
7m-6
Let m= 8
7(8) -6
Multiply first
56-6
Then subtract
50
26. Find the volume of a ball with a radius of 7 cm.
Answer:
Step-by-step explanation:
The formula for the volume of a sphere is
v= 4/3πr³
the radius is given as 7, so the volume is 4/3 × π × 7³
v= 4/3 × π × 343
= 1436.76 cm³
Segments BD and CE are axes of the ellipse below.
Which of the following reflective symmetries apply to the ellipse below?
Answer:
Yes and Yes
Step-by-step explanation:
If you fold them over on both sides then they overlap perfectly, therefore they are reflective.
-2 1/4 divided by (3 1/3) =
How much of a radioactive kind of xenon will be left after 15 days if the half-life is 5 days and
you start with 96 grams
Answer:
12 grams
Step-by-step explanation:
15/5 = 3 half lives
(1/2)³ = 1/8 of the original amount will remain
96 * 1/8 = 12 grams
Answer:
Step-by-step explanation:
Radioactive decay problems are very similar to compound interest formulas, except the rate is subtracted from one, instead of adding to one.
I.e.
mass at time t, m(t) = M (1 - r)^(t/h)
where
M = initial mass (grams)
m (t) mass left at time t (grams)
h = half-life in number of days
r = 0.5 from "half-life"
t = time lapse in number of days
Here
M = 96
h = 5
t = 15
m(15) = 96(1-0.5)^(15/5)
= 96 (1/2)^3
= 12 grams
11..
Solve the equation using the zero-product property.
-n(5n-4)=0
A. n= -1 or n= 4/5
B. n= 0 or n= -4/5
C. n= -1 or n= -4/5
D. n= 0 or n= 4/5
Answer:
D. n= 0 or n= 4/5
Step-by-step explanation:
Factor and set each factor equal to zero.
n
=
0
,
4
5
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
n
=
0
,
4
5
Decimal Form:
n
=
0
,
0.8
Question and choices are in the photo please explain the answer
Answer:
The answer is option C
Step-by-step explanation:
Product means that we have to multiply
So we multiply (3x - 4y) by (-2x + 5y - 6)
So the solution will be
3x(-2x + 5y - 6) - 4y(-2x + 5y - 6)
Note: don't forget that there are positive signs and negative signs in the equation
-6x² + 15xy - 18x + 8xy - 20y² - 24y
Group like terms
The like terms here are 15xy and 8xy so we group them
-6x² + 15xy + 8xy - 18x - 20y² - 24y
-6x² + 23xy + 8xy - 18x - 20y² - 24y
And that's your answer
You borrow $3,897 for a loan for college expenses with a 2.5% interest rate. How much interest is charged on the loan
Answer:
Amount of interest pay per year = $97.5 (Approx.)
Step-by-step explanation:
Given:
Amount borrow for college expenses = $3,897
Rate of interest = 2.5%
Find:
Amount of interest pay per year
Computation:
Using Simple interest formula;
Simple interest = Amount borrow x Rate of interest x number of year
Amount of interest pay per year = 3,897 x 2.5% x 1
Amount of interest pay per year = 3,897 x 0.025
Amount of interest pay per year = 97.425
Amount of interest pay per year = $97.5 (Approx.)
NEED ASAP NOWWWWWW TY
Answer:
subtract 8 from both sides
Step-by-step explanation:
Find the volume of the cone. round your answer to the nearest tenth.
Answer:
18 and if I round it off to the nearest tenth it will be 20
just so you know I'm not that good at maths
El 60% de los discos son de música clásica y el 10% es música para bailar si Fabián tiene 90 discos cuántos son de cada uno
Respuesta:
54 discos son de música clásica
9 discos son de música para bailar
:)
The following is a parallelogram solve for the variables
Answer:
x = 51, y = 17
Step-by-step explanation:
Consecutive angles sum to 180° , so
x + 129 = 180 ( subtract 129 from both sides )
x = 51
-------------------------------------
Opposite angles are congruent, so
3y = x = 51 ( divide both sides by 3 )
y = 17
Step-by-step explanation:
x + 129° = 180°
x = 180°- 129°
x = 51°
3y + 129° = 180°
3y = 180° - 129°
3y = 51°
y = 51°/3
y = 17°
A proportional relationship is shown in the table below: what is the slope and what numbers do i graph. ty besties
Answer:
The slope of the line is [tex]m = \frac{3}{5}[/tex] and the equation of the line is [tex]y = \frac{3}{5}\cdot x[/tex].
Step-by-step explanation:
From table we understand that slope of the line is constant, that is, for each change of [tex]x[/tex] there is one and only change in [tex]y[/tex], fulfilling the main characteristic of a line and we can determine the slope for every point of the line by means of the following expression:
[tex]m = \frac{y_{f}-y_{o}}{x_{f}-x_{o}}[/tex] (1)
Where:
[tex]x_{o}, x_{f}[/tex] - Initial and final x-coordinates of the line.
[tex]y_{o}, y_{f}[/tex] - Initial and final y-coordinates of the line.
If we know that [tex](x_{o}, y_{o}) = (0,0)[/tex] and [tex](x_{f},y_{f}) = (8,4.8)[/tex], then the slope of the line is:
[tex]m = \frac{4.8-0}{8-0}[/tex]
[tex]m = \frac{3}{5}[/tex]
From graph we conclude that x-intercept of the line is [tex]b = 0[/tex]. Hence, the equation of the line is [tex]y = \frac{3}{5}\cdot x[/tex] and we proceed to plot the expression with the help of a graphing tool.
please help me!!!! i really need help!!! THANK YOU
explain how you got your answer = brainliest
Answer:
8.481 ft² . I don't know if this is simplest form or not, but hopefully it is.
Step-by-step explanation:
How im going to do it is crafty, if i get it wrong im sorry.
Area circle = πr²
Area circle = 3.14 * 9 ≈ 28.27
28.27 / 360 = 0.07852777777
0.07852.777777 x 108 = 8.481
Answer = 8.481 ft²
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Simplify: {36 ÷ (-9)} ÷ {(-24) ÷ 6)
Answer:
1
Step-by-step explanation:
{36 ÷ (-9)} ÷ {(-24) ÷ 6}
= (-4) ÷ (-4)
= 1
Answer:
1
Step-by-step explanation:
{36 ÷(-9)} ÷ {(-24) ÷ 6)
{36 ÷ -9} ÷ {-24 ÷ 6}
(-4) ÷ (-4)
1
using BODMAS rule (Bracket 0f Division , Multiplication and Addition , Subtraction)
Rule
first small bracket ( ) must be solved
then curly bracket { }
then only big bracket [ ]
remebere while dividing -4 and -4 along with the numbers - signs also gets cancel. So ur answer is positive.
what is the bast estimation of mean for this data set
Answer:
mean = adding up all the numbers then divid by number of numbers
Step-by-step explanation:
I.e 2 5 7 9 7 add up = 30
30 ÷ 5 = 6 so 6 is the mode
Darcy harvests 8.3/4 acres of corn every 5/6 end fraction of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?
Given:
Darcy harvests [tex]8\dfrac{3}{4}[/tex] acres of corn every [tex]\dfrac{5}{6}[/tex] of an hour.
Darcy harvests corn at a constant rate.
To find:
How many acres does she harvest per hour?
Solution:
We have,
Acres harvest in [tex]\dfrac{5}{6}[/tex] of an hours = [tex]8\dfrac{3}{4}[/tex]
Acres harvest in 1 hour = [tex]8\dfrac{3}{4}\times \dfrac{6}{5}[/tex]
= [tex]\dfrac{32+3}{4}\times \dfrac{6}{5}[/tex]
= [tex]\dfrac{35}{4}\times \dfrac{6}{5}[/tex]
Cancel out the common factors, we get
Acres harvest in 1 hour = [tex]\dfrac{7}{2}\times \dfrac{3}{1}[/tex]
= [tex]\dfrac{21}{2}[/tex]
= [tex]10\dfrac{1}{2}[/tex]
Therefore, she can harvest [tex]10\dfrac{1}{2}[/tex] acres of corn per hour.