Answer:
84π mm^2
Step-by-step explanation:
formula for circumference is 2πr where r is the radius of circle
Given,The circumference of the base of a cylinder is 24π mm
Thus,
2πr= 24π mm
=> r = 24π mm/2π = 12 mm
________________________________________
A similar cylinder has a base with circumference of 60π mm.
radius for this cylinder will be
2πr= 60π mm
r = 60π mm/2π = 30mm
______________________________________________
Given
The lateral area of the larger cylinder is 210π mm2
lateral area of cylinder is given by 2πrl
where l is the length of cylinder
thus,
r for larger cylinder = 30mm
2π*30*l = 210π mm^2
=> l = 210π mm^2/2π*30 = 3.5 mm
___________________________________________
the lateral area of the smaller cylinder
r = 12 mm
l = 3.5 mm as both larger and smaller cylinder are same
2πrl = 2π*12*3.5 mm^2 = 84π mm^2 answer
Answer:
33.6pi mm2 is the correct answer
edge 2021
Step-by-step explanation:
The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.
What is the lateral area of the smaller cylinder?
17.1π mm2
33.6π mm2
60π mm2
84π mm2
7. A large population of ALOHA users manages to generate 60 requests/s, including originals and retransmissions. Time is slotted in units of 50 ms. (Page 265 in the book may provide some help with this question.) (12 pts) a) What is the chance of success on the first attempt
Answer:
P(success at first attempt) = 0.1353
Step-by-step explanation:
This question follows poisson distribution. Thus, the formula is;
P(k) = (e^(-G) × (G)k)/k!
where;
G is number of frames generated in one frame transmission time(or frame slot time)
Let's find G.
To do this, we need to find number of frames generated in 1 slot time which is given as 50 ms.
Now, in 1000 ms, the number of frames generated = 50
Thus; number of frames generated in 50 ms is;
G = (50/1000) × 50
G = 2.5
To find the chance of success on the first attempt will be given by;
P(success at first attempt) = P(0) = e^(-G) = e^(-2) = 0.1353
Investment: Suppose you receive a gift of $1,000 and decide to open a CD (certificate of
deposit) as a low risk investment. The best CD rate you could find is 2.25%, which means that
your original investment will grow at a rate of 2.25% each year.
Assuming the rate of increase does not change, which of the following statements is TRUE
about your CD account balance?
It will no longer grow after several years.
It will triple in approximately 3 years.
O 4 years after the original investment, it is approximately $1,093.
O It will double in approximately 10 years.
Answer: 4 years after the original investment, it is approximately $1,093.
Step-by-step explanation:
Hi, to answer this question we have to apply the simple interest formula:
I = p x r x t
Where:
I = interest
P = Principal Amount
r = Interest Rate (decimal form)
t= years
Replacing with the values given
I = 1000x (2.25/100) x t
It will triple in approximately 3 years. FALSEI = 1000x (2.25/100) x 3 =67.5
1000+67.5 = 1067.5
It will no longer grow after several years: False, it will grow because it has a growth rate.4 years after the original investment, it is approximately $1,093. TRUEI = 1000x (2.25/100) x 4 =90
1000+90 = $1090
It will double in approximately 10 years.I = 1000x (2.25/100) x 10 =225
1000+90 = $1225
Feel free to ask for more if needed or if you did not understand something.
Find the 12th term of the following geometric sequence.
10, 30, 90, 270, ...
Answer:
r = 90/30
r = 3
T12 = 10 × 3¹¹
T12 = 1771470
helppppppppppp i give you brailienst
Answer:
5%
Step-by-step explanation:
Well let’s make a fraction 2/40.
So we have to simplify it to 1/20.
And we do 1 / 20.
So 1 / 20 is .05.
To make this a percent we put the seminal place 2 places to the right.
So the percent is 5%.
xdy+ydx= ? (a) d(x+y) (b) d(x/y) (c) d(x-y) (d) d(xy)
Answer:
d) d(x)
Step-by-step explanation:
Derivative Rules
Product Rule xy -> d(xy) = xdy + ydxSolve the system by the substitution method.
X-2y=6
Y=2x-21
Answer:
Hey there!
We have two equations, x-2y=6, and y=2x-21.
Thus, we can substitute all y's in the first equation for 2x-21.
x-2(2x-21)=6
x-4x+42=6
-3x+42=6
-3x=-36
3x=36
x=12
y=2(12)-21
y=24-21
y=3
x=12, and y=3.
Hope this helps :)
Answer:
[tex]\boxed{x=12, y=3}[/tex]
Step-by-step explanation:
[tex]x-2y=6\\y=2x-21[/tex]
Plug y as 2x-21 in the first equation.
[tex]x-2(2x-21)=6\\x-4x+42=6\\-3x+42=6\\-3x=-36\\x=12[/tex]
Plug x as 12 in the second equation.
[tex]y=2(12)-21\\y=24-21\\y=3[/tex]
For a certain bathtub, the cold water faucet can fill the tub in 9 minutes. The hot water faucet can fill the tub in 11 minutes. If both faucets
are used together, how long will it take to fill the tub?
Do not do any rounding.
Answer:
2 minutes
Step-by-step explanation:
You need to first subtract 9 from 11 and you get 2 minutes.
11 minutes will it take to fill the tub by both hot and cold water faucets.
What is Time?
Time as the progression of events from the past to the present into the future.
Given that,
the cold water faucet can fill the tub in 9 minutes
The hot water faucet can fill the tub in 11 minutes.
If both the faucets are used together then it takes 11 minutes to fill the tub because it takes longer time for hot water faucet to fill the tub.
Therefore it takes 11 min to fill the tub together.
To learn more on Time click:
https://brainly.com/question/28050940
#SPJ5
Which phrase best describes the graph of a proportional relationship?
A) a straight line passing
B) a straight line
C) a curve
D) not a straight line
Answer:
A. a straight line passing
Step-by-step explanation:
Answer:
a straight line passing
Step-by-step explanation:
Eli is making a party mix that contains pretzels and chex. For each cup of pretzels, he uses 3 cups of chex. He wants to make 12 cups of party mix.
Answer:
36 cups of Chex total.
Step-by-step explanation:
Well, he will obviously be using 12 cups of pretzels, so let's set that aside. For every cup of pretzels, there are 3 cups of chex. So, multiply 3x12. That will give you how much chex you will need.
A man is standing 20 feet away from the base of a tree and looking at the top of a tree wondering it’s height. If the man’s eyes are located 6 feet off the ground and the angle of elevation is 67°, how tall is the tree? Round to the nearest tenth of a foot.
Answer: 53.1ft
Step-by-step explanation:
We can draw a triangle rectangle.
Where the distance between the man and the tree is one cathetus, (the vertex is on the man's eyes)
The tree itself is the other cathetus, and the line that connects the man's eyes and the tip of the tree is the hypotenuse.
We know that:
The angle at the vertex of the man's eyes is 67°
And the adjacent cathetus, the distance between the man and the tree, is 20ft.
Then using the relation:
Tan(A) = (opposite cathetus)/(adjacent cathetus)
We can find the height of the treee:
Tan(67°) = X/20ft
Tan(67°)*20ft = X = 47.1ft
But remember that this is measured from the mans eye's, and the man's eyes are 6ft away from the ground.
Then the height of the tree is 47.1ft + 6ft = 53.1ft
Which equation shows a=bc^2+d solved for c
Answer:
[tex]\large \boxed{c=\pm \sqrt{\dfrac{a-d}{b}}}[/tex]
Step-by-step explanation:
Hello,
[tex]a=bc^2+d \\ \\ <=> a-d=bc^2+d-d=bc^2 \ \text{ subtract d }\\ \\ <=> c^2=\dfrac{a-d}{b} \ \text{ divide by b, assuming b is different from 0}\\ \\<=>\large \boxed{c=\pm \sqrt{\dfrac{a-d}{b}}} \ \ \text{ take the root of both parts}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the correct option? How to do this one
Answer:
Option C is the answer.
Step-by-step explanation:
here, given that;
angle XYZ=82°
we know, according to the inscribed angle theorem,
angle XYZ=1/2 of arc XZ.
or, arc XZ = 2×82°
Therefore, the value of arc XYZ is 164°.
hope it helps..
The drama club is selling T-shirts and caps to raise money for a spring trip. The caps sell for $5.00 each, and the T-shirts sell for $10.00 each. The drama club needs to raise at least $500.00 for the trip. The inequality that represents this situation is graphed, with x representing the number of caps sold and y representing the number of T-shirts sold. Which solution is valid within the context of the situation?
Answer:
The correct answer to this question is C: (72,24).
Step-by-step explanation:
We are given that:
The cost of 1 cap is $5 each
The cost of 1 t-shirt is $10 each
Let x be the number of caps sold
Let y be the number of t-shirt sold
In the context we are given that the drama club needs to raise at least $500 to go on the trip.
So based on this information we can create a inequality as:
the number of caps sold x (times) the cost of a single cap + the number of shirts x (times) the cost of a single t-shirt ≥ (greater than or equal to) 500
Inequality: 5x+10y ≥ 500 ( We used a greater than or equal to symbol because it said that the drama club need at least $500 for the trip.
Next we need to figure out how many caps and t-shirt were sold.
- We can already take out two of the options which are the two answer with negatives in them because we know that when you multiply a positive number with a negative number we get a negative number and we don't want that. (So Option A and Option D are out.)
Now all we do is plug x and y into our inequality equation ( 5x+10y ≥ 500 )
B) x=65 caps, y= 17.5 t-shirts ----> 5(65)+10(17.5) =500 which you get $500
YOU MAY THINK THIS IS THE ANSWER BUT! if you look closely at variable y it said they sold 17.5 t-shirt, but here there thing how do you sell 17 shirts and a half of shirt? Which means this option is also wrong!
C) x =72 caps, y =24 t-shirts ------> 5(72)+ 10(24)= $600 which is more than the original amount they were going for because it said at least $500.
So the correct option to this question is C, they sold 72 caps and 24 t-shirts and earned $600 dollars.
Answer: C
Step-by-step explanation: Each coordinate point is located within the solution set, as shown on the graph.
First, take out any solution that includes a negative number, since there cannot be a negative number of bags. So, (-2,10) and (9,-3) are not solutions.
Next, take out any solution that does not have all whole numbers because the bags are whole objects. So, (4.5,9) is not a solution.
So, (8,5) is a valid solution in the context of the situation.
How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? Which of the following represents a function
Answer: The required number of heads = 30
Step-by-step explanation:
Given, Total tosses = 50
The theoretical probability of getting head = [tex]\dfrac{1}{2}[/tex]
As per given,
Experimental probability = Theoretical probability + 20% of Theoretical probability
= [tex]\dfrac{1}{2}+\dfrac{20}{100}\times\dfrac{1}{2}[/tex]
= [tex]\dfrac{1}{2}+\dfrac{1}{10}=0.5+0.1=0.6[/tex]
Required number of heads = (Experimental probability) x (Total tosses )
= 0.6 x 50
= 30
Hence, the required number of heads = 30
A relation is said to be a function if each input value corresponds to a unique output value.For example: {(1,2), (3,4), (2,3), (4,1))}
Answer:
35 is the Answer
The probability density of a random variable X is given in the figure below.
From this density, the probability that X is between 0.68 and 1.44 is:
Find the probability that X is between 0.68 and 1.44.
Answer:
0.38
Step-by-step explanation:
The area under the probability density curve is equal to 1.
The width of the rectangle is 2, so the height of the rectangle must be ½.
The probability that X is between 0.68 and 1.44 is therefore:
P = ½ (1.44 − 0.68)
P = 0.38
Using the uniform distribution, it is found that there is a 0.38 = 38% probability that X is between 0.68 and 1.44.
-----------------------
Uniform probability distribution:
Has two bounds, a and b. The probability of finding a value between c and d is:[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
In this problem:
The bounds are 0 and 2, thus [tex]a = 0, b = 2[/tex].The probability that X is between 0.68 and 1.44 is:
[tex]P(0.68 \leq X \leq 1.44) = \frac{1.44 - 0.68}{2 - 0} = 0.38[/tex]
0.38 = 38% probability that X is between 0.68 and 1.44.
A similar problem is given at https://brainly.com/question/13547683
What the answer now fast
sine(X) = opposite side / hypotenuse
sine(X) = (2√11) / (4√11)
sine(X) = (2/4)
sine(X) = 0.5
X = arcsine(0.5)
X = 30°
Answer: m∠x = 30°
Step-by-step explanation:
In a right triangle, if the short side of the right angle is Half the length of the hypotenuse, the triangle has angles of 30°, 60° and 90°
∠x is the smallest one, so m∠x = 30°
It is possible to figure the sine and get the angle from that, but in this case it might not be necessary. ;-)
What is the equation of the parabola with focus (1, -3) and directrix y = 2?
Answer:
(x-1)²=-10(y-0.5)
Step-by-step explanation:
A random sample of 61 Foreign Language movies made in the last 10 years has a mean length of 135.7 minutes with a standard deviation of 13.7 minutes. Construct a 95% confidence interval.
Answer:
95% confidensce interval of the mean (two-tail) = [132.2, 139.2]
Step-by-step explanation:
Given:
N = size of sample = 61
m = sample mean = 135.7
s = sample standard deviation 13.7
Need 95% confidence interval
Solution.
alpha (95% confidence interval) = 0.05
(1-alpha/2) = 0.975 [two sided]
Equation for confidence interval of the mean
= m +/- t(1-alpha/2,N-1) * s / sqrt(N)
= 135.7 +/- 2.0003 * 13.7 / sqrt(60)
= [132.16, 139.24]
An epidemiologist wishes to know what proportion of adults living in a large metropolitan area have subtype ayr hepatitis B virus. Determine the sample size that would be required to estimate the true proportion to within 3% margin of error with 95 percent confidence.
Answer:
Sample size 'n' = 1067
Step-by-step explanation:
Explanation:-
Given margin of error of the true proportion
M.E = 0.03
The margin of error is determined by
[tex]M.E =Z_{\alpha } \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]
Level of significance = 0.95
The critical value Z₀.₀₅ = 1.96
The margin of error is
[tex]0.03 =1.96 \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]
we know that
[tex]\sqrt{p(1-p} \leq \frac{1}{2}[/tex]
[tex]0.03 =\frac{1.96 X\frac{1}{2} }{\sqrt{n} }[/tex]
on cross multiplication , we get
√n = 32.66
Squaring on both sides, we get
n = 1066.6≅1067
Solve for x: ex = 5.2
Answer:
x = ln (5.2)
Step-by-step explanation:
e^x = 5.2
Take the natural log of each side
ln ( e^x) = ln( 5.2)
x = ln (5.2)
Answer:
x ≈ 1.91, if e refers to 2.718281828...
x = 5.2/e, if e is simply another variable
Step-by-step explanation:
We are given:
ex = 5.2
Now, if e is referring to the irrational value of e that is about 2.718281828..., then when we divide both sides by e to solve for x, we get:
ex = 5.2
x = 5.2 / 2.718281828... ≈ 1.91
However, if e is simply another varialbe, then we just have:
ex = 5.2
x = 5.2/e
~ an aesthetics lover
Can someone pls help me! I'm stuck
Answer:
the parabola opens down
Step-by-step explanation:
The quadratic equation is
ax^2 + bx + c
When a < 0 the parabola opens down
a > 0 it opens up
since a = -2 the parabola opens down
800x87979 cuanto es?
800x87979 es 70, 383, 200
Espero que esto te ayude
Answer:
Step-by-step explanation:
800*87979 = 70,383,200
A= 63°
C = 7.75 inch
B = 47°
Oblique Triangle
4. Refer to the oblique triangle shown. What's the size of angle C?
O A. 60°
B. 125°
O C. 45°
O D. 70°
Answer:
Option D is correct.
Angle C = 70°
Step-by-step explanation:
The sum of angles in a triangle = 180°
So,
(Angle A) + (Angle B) + (Angle C) = 180°
(Angle A) = 67°
(Angle B) = 43°
(Angle C) = ?
67° + 43° + (Angle C) = 180°
Angle C = 180 - 67 - 43 = 70°
Angle C = 70°
Hope this Helps!!!
If the secant value is 37^ * , the cosine value to the hundredths degree is: A 0.80 B1.25 C0.60
Answer:
The value of the cosine function at 37º is 0.80. A. 0.80
Step-by-step explanation:
The correct statement is: "If the secant of 37º is 1.25, the cosine value to the hundredths degree is:"
Secant and cosine functions are related by the following trigonometric identity:
[tex]\sec 37^{\circ} = \frac{1}{\cos 37^{\circ}}[/tex]
[tex]\cos 37^{\circ} = \frac{1}{\sec 37^{\circ}}[/tex]
[tex]\cos 37^{\circ} =\frac{1}{1.25}[/tex]
[tex]\cos 37^{\circ} = 0.80[/tex]
The value of the cosine function at 37º is 0.80. The right answer is A.
Help !!! Need answer fast. Find the value of x.
Answer:
x=60
Step-by-step explanation:
We know that when two secant lines, or a secant line and a tangent line, intersect at a point outside the circle, the measure of the angle formed at the point of intersection is half the difference between measures of the intercepted arcs.
So, we can set up the equation [tex]55=\frac{1}{2} (170-x)[/tex], which will come out to [tex]x=60[/tex].
hope this helps!
In an episode of the old school version of the game show Family Feud, 43 out of a random sample of 100 people said they pick their noses at red lights. Find a 95% confidence interval of the proportion of all people who pick their noses at red lights.
Answer:
95% of confidence interval of the proportion of all people who pick their noses at red lights
(0.3342 , 0.5258)
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 100
Given data 43 out of a random sample of 100 people said they pick their noses at red lights.
sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{43}{100} = 0.43[/tex]
Level of significance = 0.05
Z₀.₀₅ = 1.96
Step(ii):-
95% of confidence interval of the proportion of all people who pick their noses at red lights
[tex](p^{-} -Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } ,p^{-} +Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.43 -1.96 \sqrt{\frac{0.43(1-0.43)}{100} } ,0.43 +1.96 \sqrt{\frac{0.43(1-0.43)}{100} })[/tex]
( 0.43 - 0.0958 , 0.43 + 0.0958)
(0.3342 , 0.5258)
Conclusion:-
95% of confidence interval of the proportion of all people who pick their noses at red lights
(0.3342 , 0.5258)
Helen’s age is a multiple of 4. Next year it’ll be a multiple of 3. Helen’s older brother is now 19. How old is Helen now?
Answer: Helen is 8 years old.
Step-by-step explanation:
Given: Helen’s age is a multiple of 4.
i.e. Choices for Helen’s age = 4, 8 , 16, ...
Helen’s older brother is now 19.
That means Helen's age < 19
Choices for Helen's age left = 4, 8, 16
Next year it’ll be a multiple of 3.
That is only possible if Helen's age = 8
Because next year her age = 8+1 = 9 years which is divisible by 3.
Hence, Helen is 8 years old.
Determine a differential equation that models the growth of a population of fish as a function of time in days under each of the following hypotheses:
a) The rate of population increase is proportional to the size of the population. The population increases by 2 percent per day. (Treat time in days as a continuous variable, i.e. the rate at which the population increases is .02 times the population size.) dP/dt =
b) The rate of population increase is again proportional to the size of the population with the same constant of proportionality but 4 percent of the population is harvested each day. dP/dt =
c) The rate of population increase is again proportional to the size of the population with the same constant of proportionality but 1000 fish are harvested each day. dP/dt =
d) The equation in part c) has a threshhold. What is it?
Step-by-step explanation:
a).
It is given that rate at which the population increases is directly proportional to size of the population. Thus we have,
[tex]\frac{dP}{dt}\propto P[/tex]
It is given in the question that the population increases by 2% in one day. Now we know that the time in days is a continuous variable, so we have
2% of P = [tex]$\frac{2}{100}\times P$[/tex]
[tex]$\therefore \frac{dP}{dt}=0.02 P $[/tex]
b).
It is given that the population is harvested by 4 % in one day
[tex]$\therefore \frac{dP}{dt} =0.02P-0.04P$[/tex]
(Since 4% of the P is harvested.)
[tex]$\therefore \frac{dP}{dt}=-0.02P$[/tex]
c).
It is given that 1000 fish are being harvested or removed in one day.
[tex]$\therefore \frac{dP}{dt}= 0.02 P-1000$[/tex]
d).
The threshold is given by
[tex]$0.02 P_{eq}-1000=0$[/tex]
[tex]$\therefore P_{eq}=\frac{1000}{0.02}$[/tex]
or [tex]$P_{eq}=5\times 10^4$[/tex]
Suppose a car depreciates linearly the second you drive it off the lot. If you purchased the car for $31,500 and after 5 years the car is worth $20,500, find the slope of the depreciation line.
Answer: m = - 2200
Step-by-step explanation: Slope of a line is a number which describes the steepness and direction of a linear graph. It is represented by the letter m.
The year a car is bought and its price means:
f(0) = 31,500
Five years later, the price is $20,500, i.e.:
f(5) = 20,500
With these two pairs of value, slope is calculated as:
[tex]m = \frac{y-y_{0}}{x-x_{0}}[/tex]
[tex]m = \frac{20500-31500}{5-0}[/tex]
[tex]m = \frac{- 1100}{5}[/tex]
m = - 2200
The slope of the depreciation line is m = -2200 and it is negative because the line decreases along time.
(a) Plot the following function ona Karnaugh map.(Do not expand to minterm form before plotting.)
F(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
(b) Find the minimum sum of products.
(c) Find the minimum product of sums
Answer:
a) the K-map is in the attachment
f = Σm(0,1,2,3,6,10,14,15)
b) from the k-map, the minimum sum of products is
F = A'B' + CD' + ABC
c) the minimum product of sums is
F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')
Step-by-step explanation:
A Karnaugh map (K-map) is a pictorial framework used to limit the Boolean expressions without utilizing Boolean algebra theorems and equation controls.
a) the given function is f(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
expanding the function as four variable terms
f(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
= A'B'(C + C')(D + D')+(A + A')(B + B")CD' + ABC(D + D') + A'B'CD' + ABCD'
= A'B'CD + A'B'CD' + A'B'C'D' + ABCD' +AB'CD' + A'BCD' + A'B'CD' + ABCD +ABCD' + A'B'CD' + ABCD'
=A'B'CD + A'B'CD' + A'B'C'D + A'B'C'D' + ABCD' + AB'CD' + A'BCD' +ABCD
f = Σm(0,1,2,3,6,10,14,15)
note: diagram is in the attachment
b) the minterms for the minimum sum of product are
f = Σm(0,1,2,3,6,10,14,15)
simplifying the K-map(done in the attachment)
from the k-map, the minimum sum of products is
F = A'B' + CD' + ABC
c) the maxterms for the minimum product of sums are
f = ПM(4,5,7,8,9,11,12,13)
plot the K-map to find minimum product of sums(done in the attachment)
the minimum product of sums is
F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')