Answer:
9.8 cm
Step-by-step explanation:
Volume of a cylinder can be gotten with this formula
V=πr2h
h = height of the oil.
We were told that 3 litres of oil was removed, then, there is a falling in the level of oil by 10 cm, hence the height of the oil is now
h° =( h) - (0.1)
Then the new volume can be calculated as
V°= V - (3×10^-3)
But
volume= (π r2h°)
Then substitute we have
πr2h - 0.003 = π r2 (h-0.1)
If we open the bracket we have
0.003 = (πr2 ×0.1)
πr2=0.003/0.1
Then r=√ (0.03/0.1π)
=9.8 cm
Note that 1L = 10-3 m3
In a survey of adults aged 57 through 85 years, it was found that 86.6% of them used at least one prescription medication. Complete parts (a) through (c) below.
a. How many of the 3149 subjects used at least one prescription medication?
(Round to the nearest integer as needed.)
b. Construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.
(Round to one decimal place as needed.)
Answer:
a) 272 used at least one prescription medication.
b) The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).
Step-by-step explanation:
Question a:
86.6% out of 3149, so:
0.866*3149 = 2727.
272 used at least one prescription medication.
Question b:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 3149, \pi = 0.866[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 - 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.856[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 + 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.876[/tex]
For the percentage:
0.856*100% = 85.6%
0.876*100% = 87.6%.
The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).
The number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is: [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%
How to construct confidence interval for population proportion based on the sample proportion?Suppose that we have:
n = sample size[tex]\hat{p}[/tex] = sample proportion[tex]\alpha[/tex] = level of significance = 1 - confidence interval = 100 - confidence interval in percentageThen, we get:
[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
where [tex]Z_{\alpha/2}[/tex] is the critical value of Z at specified level of significance and is obtainable from its critical value table(available online or in some books)
For this case, we have:
n = 3149confidence interval is of 90%[tex]\alpha[/tex] = level of significance = 100 - 90% = 10% = 0..10[tex]\hat{p}[/tex] = sample proportion = ratio of 86.6% of n to n (at the least)Part (a):
The number of subjects used at least one prescription medication is:
[tex]\dfrac{3149}{100} \times 86.6 \approx 2727[/tex]
Thus, the sample proportion we get is:
[tex]\hat{p} = \dfrac{2727}{3149} \approx 0.8659[/tex]
For level of significance 0.10, we get: [tex]Z_{\alpha/2} = 1.645[/tex]
Thus, the confidence interval needed is:
[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\CI \approx 0.8659\pm 1.645 \times \sqrt{\dfrac{0.8659(1-0.8659)}{3149}}\\\\\\CI \approx 0.8659 \pm 0.0099[/tex]
Thus, CI is [0.8659 - 0.0099, 0.8659 + 0.0099] = [0.8560, 0.8758]
Thus, the number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is: [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%
Learn more about population proportion here:
https://brainly.com/question/7204089
Find the circumference and area of a circle with a diameter of 12 cm. (Use the approximation of 3.14 for )
Anyone good at Ks3 math?
Answer:
210 Km
Step-by-step explanation:
Distance travelled is calculated as
distance = speed × time ( time is in hours )
= 90 × 2 [tex]\frac{1}{3}[/tex]
= 90 × [tex]\frac{7}{3}[/tex]
= 30 × 7
= 210 Km
Determine the equations of the vertical and horizontal asymptotes, if any, for
Given:
The function is:
[tex]f(x)=\dfrac{2x}{x+4}[/tex]
To find:
The vertical and horizontal asymptotes of the given function.
Solution:
We have,
[tex]f(x)=\dfrac{2x}{x+4}[/tex]
For vertical asymptotes, equate the denominator and 0.
[tex]x+4=0[/tex]
[tex]x+4-4=0-4[/tex]
[tex]x=-4[/tex]
So, the vertical asymptote of the given function is [tex]x=-4[/tex].
The degree of the numerator is 1 and the degree of the denominator is also 1.
Since the degrees of numerator and denominator are equal, therefore the horizontal asymptote is:
[tex]y=\dfrac{a}{b}[/tex]
Where, a is the leading coefficient of numerator and b is the leading coefficient of denominator.
Leading coefficient of numerator is 2 and the leading coefficient of denominator is 1, so the horizontal asymptote is:
[tex]y=\dfrac{2}{1}[/tex]
[tex]y=2[/tex]
Therefore, the correct option is C.
Explain why ac is equal to
Bc
Answer:
because length is same I hope it will help you please follow me
which proportion would you use to find 8% of 75?
A: 8/100 = 75/n
B: 8/100 = n/75
C: 75/100 = 8/n
D: 75/100 = n/8
Answer:
B: 8/100 = n/75
Step-by-step explanation:
OPTION B is the correct answer.
What is the measure of ∠
A. 60°
B. 6°
C. 42°
D. 49°
Please help solve this for me I couldn’t take a picture of the whole thing but I also need to find the domain & range
Answer:
The vertex appears to be (-1,-5) (The lowest point of line)
Axis of symmetry is x = -1 (Notice that the x value of the vertex is same)
y-intercept is (0, -3) (where the line crosses the y-axis)
How many square millimeters are covered with paint? Express the answer in terms of π.
336π square millimeters
400π square millimeters
416π square millimeters
464π square millimeters
Answer:
336π square millimeters
Answer:
A
Step-by-step explanation:
Find the area of the triangle.
A. 73.6ft^2
B. 65.8 ft^2
C. 69.1 ft^2
D. 70.8 ft^2
The area of the triangle is (A) [tex]73.6ft^{2}[/tex].
What is trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.Trigonometric area of a triangle:Area = [tex]\frac{1}{2}[/tex] × [tex]a[/tex] × [tex]b[/tex] × [tex]sin[/tex] (θ)
Solution -Now, out the values in the formula for the solution.
[tex]A=\frac{1}{2} (16)(10)sin(67^{o} )\\A= 80sin(67^{o} )\\[/tex]
[tex]A=73.6ft^{2}[/tex]
Therefore, the area of the given triangle is (A) [tex]73.6ft^{2}[/tex].
Know more about the area of triangles here:
https://brainly.com/question/17335144
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I need b and c full problems!
Answer:
b: [tex]\frac{5-\sqrt{11} }{2}[/tex]< x < [tex]\frac{5+\sqrt{11} }{2}[/tex]
c: x < -5 , x > 7
Step-by-step explanation:
the degree of non zero constant polynomial is a. 1 b.4 c. a d.0
Answer:
please mark me as brainlist
Suku kedua belas dari barisan bilangan 8, 15, 24, 35, .... adalah ...
find the distance between (-1,-5) and (4,3)
Answer:
[tex]\sqrt{89}[/tex] = 9.83
Step-by-step explanation:
[tex]\sqrt{89}[/tex]
[tex]\sqrt{25 + 64} \\\sqrt{5^2 + 8^2}[/tex]
Answer: 89
Step-by-step explanation:
1) 18,27 – 9,756 =
2) 6 – 2,407 =
3) 18 – 5,432 =
4) 10 – 7,602 =
5) 13,013 – 12,5 =
6) 972,5 – 247,451 =
7) 83,12 – 90,2 + 12,3 =
8) 46,75 – 60,13 + 32,50 =
9) 254,0187 – 29,34682 =
10)1.015,568 – 123,712 =
no entiendo me ayudan
Answer:
1) -7929
2) -2401
3)-5414
4) -7592
5) 12888
6)-237726
7) 7287
8)-4588
9)-394495
10) 891856
3. What is the length of MA to the nearest tenth?
a) 0.1 cm
b) 3.5 cm
c) 17.0 cm
d) 7.7 cm
7.7cm
the rest is vastly (a and d) off or just enough off (can't be less then 5.2, because that's already the shortest side), to solve this by looking at it
Graph the first six terms of a sequence where a_1=4 and r=2
Step-by-step explanation: The standard formula for geometric sequence is an = a1 * r^(n-1) where r is the geometric factor and n is an integer. In this problem, upon substitution, an = 4*2^(n-1).
QUICK PLS!
Which question is best modeled with a division expression?
How much does it cost to buy 3 and one-half pounds of apples at $2 per pound?
How many apples are needed for 2 pies if the recipe uses 3 and one-half apples per pie?
How many more apples are needed if a recipe uses 3 and one-half apples and you only have 2 apples?
How many apples are in each pie if a total of 3 and one-half apples were used to bake 2 pies?
How many apples are in each pie if a total of 3 and one-half apples were used to bake 2 pies?
Here you will have to divide the data.
I need help ASAP !! Thanks
What addition sentence helps you find 5 – 4?
Answer:
4 + x =5
Step-by-step explanation:
By adding a variable you can set up an addition sentence
Sarah had 25 candies. Sarah gave 25 of the candies to her sister. Of the amount left, she gave 2/3 to her friend. How many candies does Sarah have left for herself?
Answer:
She has 5 candles left.
Step-by-step explanation:
Total of candy Sarah has = 25candies
If Sarah gave 2/5 of the candies to her sister, the total amount she gave her sister will be 2/5 of 25
2/5 of 25 = 10
The remaining candy left will be 25-10 which is 15.
If she gave 2/3 of the amount left to her friend, the amount she gave her friend will be 2/3×15 = 10candies.
A boardwalk game of chance costs 2 dollars to play. You have a 20% chance of winning 1 dollar, a 25% chance of winning back your entire 2 dollars, and a 35% chance to win 5 dollars. What is the expected value of playing the game if you lose your bet 20% of the time?
Answer:
For a give event with outcomes:
{x₁, x₂, ..., xₙ}
Each with probabilities:
{p₁, p₂, ..., pₙ}
The expected value is:
Ev = x₁*p₁ + ... + xₙ*pₙ
Here we have the outcomes and probabilities:
win $1, with a probability 20%/100% = 0.2
win $2, with a probability 25%/100% = 0.25
win $5, with a probability of 35%/100% = 0.35
do not win, with a probability of 20%/100% = 0.2
Then the expected value of the game is:
Ev = $1*0.2 + $2*0.25 + $5*0.35 + $0*0.2 = $2.45
And if we know that the game costs $2, then the expected value is:
Ev = $2.45 - $2 = $0.45
The expected value is $0.45
hi i just need a simple explanation for this question!
Answer:
5/3
Step-by-step explanation:
3^5 = 27 ^x
Rewrite 27 and 3^3
3^5 = 3^3^x
We know that a^b^c = a^(b*c)
3^5 = 3^(3x)
The bases are the same so the exponents are the same
5 = 3x
Divide by 3
5/3 =x
Answer:
x = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
[tex]3^{5} = 27^{x}[/tex]
These problems are getting you ready to work with exponential functions,
and ultimately with logarithms. The point here is that with variable exponents (notice the exponent is an x (on the right one) and not a number. Variable exponents can not be solved with regular algebra "rules" you need new ones.
The new ones will be Logs....
For now (until you learn logs) , you have to use some "tricks"
the "trick" in this problem is that you have to realize that 27 = [tex]3^{3}[/tex]...
with "common bases" this problem becomes trivial
[tex]3^{5} =(3^{3} ) ^{x}[/tex]
so now the bases are the same and the equals sign suggests that
3x = 5
thus x = [tex]\frac{5}{3}[/tex]
Not really understanding this, thanks for help in advance
Answer:
102
Step-by-step explanation:
Exterior angle is sum of interior angles.
∠1 = 51 + 51
∠1 = 102
Answer: m∠1 = 102°
Step-by-step explanation:
The inside angles of a triangle always add up to 180°
so get the 3rd inside angle with
[tex]180-51-51=78[/tex]
And we know that a straight line in 180° on each side
So we take 180° and subtract 78° to get our answer 102°
giving brainliest
2 variable table
Answer:
41
136
155
193
Step-by-step explanation:
use the equation 19*d+22=h
19 represents the number of hats knitted per day
22 represents the already made hats
Answer:
hhhhhhhhhhhhhhhhhhu
Step-by-step explanation:
Help quick!! I'll mark your answer as the brainliest if it's correct! Identify the function shown in this graph.
A. y= -1/5x + 3
B. y= 5x - 3
C. y= -5x + 3
D, y= -5x - 3
Answer:
C
Step-by-step explanation:
We see that the y-intercept is 3. So it is either A of B.
Plug in the point that is on the line (1, -2), we see that the point works for C.
What is the area of the parallelogram ?
Answer:
Step-by-step explanation:
[tex]Sin \ 30 = \frac{opposite \ side}{hypotenuse}\\\\\frac{1}{2}=\frac{h}{6}\\\\\frac{1}{2}*6=h\\\\3 = h[/tex]
h = 3 cm
Area of parallelogram = b * h
= 6 * 3
= 18 sq.cm
if -2 is a zero the polynomial 3x^2+2x+k, find the value of k
Answer:
value of K =16
I hope it's helps you
Please help me anyone
Answer:
115
Step-by-step explanation:
When x = -11, x^2 = 121. y = 121 - 6 = 115.
Hope this helped,
~cloud
Answer:
115
Step-by-step explanation:
y = x^2 - 6
Let x = -11
y = (-11)^2 - 6
y = (121) -6
= 115
Find the size of the angles marked by letters in the following diagram.
a=132°
b=20°
Answer:
Solution given:
a=132°[exterior angle of a cyclic quadrilateral is equal to the opposite interior angle]
again
In ∆ BCO is similar to ∆ BOE
so
b=20°[corresponding angle of similar triangle are equal]