0.08 cm/min
Step-by-step explanation:
Given:
[tex]\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}[/tex]
Find [tex]\frac{dr}{dt}[/tex] when diameter D = 20 cm.
We know that the volume of a sphere is given by
[tex]V = \dfrac{4\pi}{3}r^3[/tex]
Taking the time derivative of V, we get
[tex]\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}[/tex]
Solving for [tex]\frac{dr}{dt}[/tex], we get
[tex]\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})[/tex]
[tex]\:\:\:\:\:\:\:= 0.08\:\text{cm/min}[/tex]
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week. a. Give a 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week. b. In the general population, 30% have 5 or more servings of soft drinks a week. Is there evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population
Answer:
a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Step-by-step explanation:
Question a:
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].
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.
This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/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}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]
The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
Question b:
30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Simplify to the extent possible:
(logx16)(log2 x)
Answer:
Step-by-step explanation:
Use the change-of-base rule.
Which equation is true?
f of negative 10 = 1
f of 2 = negative 10
f of 0 = 6
f of 1 = negative 10
Answer:
f(0) = 6
Step-by-step explanation:
Complete question:
The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y
From the pair of coordinates given, hence;
f(1) = 0
f(-10) = 2
f(0) = 6
f(3) = 17
f(-2) = -1
From the following options, this shows that f(0) = 6 is correct
Answer:
f(0) = 6
Step-by-step explanation:
EDGE
What is the m∠ACB?
10°
50°
90°
180°
Answer:
The total sum of angles in a triangle is 180, thus the value of ∠ACB will be obtained as follows:
Given that the triangle is a right triangle, the sum of angles will be:
(4x)°+(7x-20)°+90=180
simplifying and solving for x we get:
4x+7x-20+90=180
11x=180+20-90
11x=110
dividing both sides by 11 we get:
(11x)/11=110/11
this gives us
x=10°
Thus substituting the value of x in:
∠ACB=(7x-20)°
=(7*10-20)
=70-20
=50°
Answer: 50°
Answer:
50
Step-by-step explanation:
About 9% of the population has a particular genetic mutation. 400 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 400
Answer:
36 people
Step-by-step explanation:
The expected value E(X) = mean of sample = np
Where, p = population proportion, p = 9% = 0.09
n = sample size, = 400
The mean of the number of people with genetic mutation, E(X) = np = (400 * 0.09) = 36
36 people
Use the formula for nCr to evaluate the given expression.
27C2 = ___ (Type an integer or a simplified fraction.)
Answer:
351
Step-by-step explanation:
27C2 = 27! / 2! × (27-2)!
= 27×26×25! / 2×1 × 25!
= 27×26 /2
= 27×13
= 351
which of the following tables represents an inverse variation between x and y
Answer:
I think that d is the answer
Question 7(Multiple Choice Worth 1 points)
(07.02 MC)
Jason has two bags with 6 tiles each. The files in each bag are shown below
1
2
3
4
5
6
Without looking, Jason draws a file from the first bag and then a file from the second bag What is the probability of Jason drawing the file numbered 5 from the first bag and an odd file from the second bag?
0
영
o
Answer:a.3/6
Step-by-step explanation:
Because there’s a total of 12 files in each bag which is 6 in each
Which of the following answer choices correctly shows the graph of y=−2x+5?
The graph of the linear function y = -2x + 5 is attached below.
Graph of Linear FunctionA linear function is a type of function that describes a relationship between two variables in which the output of the function is directly proportional to the input. It is a type of function that follows a straight-line pattern when graphed. Linear functions can be expressed in the form of an equation, such as y = mx + b, where m is the slope of the line, and b is the y-intercept.
The linear function given is y = -2x + 5
In this function, the slope of the line is -2 and the y-intercept is 5
This shows that the graph will pass through the y-axis at 5 which is a straight line.
Kindly find attached graph below.
Learn more on graph of linear function here;
https://brainly.com/question/7807573
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Write the equation of the line that passes through
the points (-1, 2) and (6, 3) in slope-intercept form.
Answer:
[tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
1) Determine the slope (m)
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-1, 2) and (6, 3):
[tex]m=\frac{\displaystyle 3-2}{\displaystyle 6-(-1)}\\\\m=\frac{\displaystyle 3-2}{\displaystyle 6+1}\\\\\m=\frac{\displaystyle 1}{\displaystyle 7}[/tex]
Therefore, the slope of the line is [tex]\frac{\displaystyle 1}{\displaystyle 7}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+b[/tex]
Plug in one of the given points and solve for b:
[tex]2=\frac{\displaystyle 1}{\displaystyle 7}(-1)+b\\2=-\frac{\displaystyle 1}{\displaystyle 7}+b[/tex]
Add [tex]\frac{\displaystyle 1}{\displaystyle 7}[/tex] to both sides to isolate b:
[tex]2+\frac{\displaystyle 1}{\displaystyle 7}=-\frac{\displaystyle 1}{\displaystyle 7}+b+\frac{\displaystyle 1}{\displaystyle 7}\\\\\frac{\displaystyle15}{\displaystyle 7} =b[/tex]
Therefore, the y-intercept of the line is [tex]\frac{\displaystyle15}{\displaystyle 7}[/tex]. Plug this back into [tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+b[/tex]:
[tex]y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}[/tex]
I hope this helps!
A G.P is such that the 3rd term minus a first term is 48. The 4th term minus 2nd term 144. Find: (i) Common ratio ii) The first term (ii) 6th term of the sequence
Answer:
Step-by-step explanation:
r is the common ratio.
Third term minus first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
Fourth term minus second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
:::::
r²-1 = 48/a₁
a₁ = 6
:::::
a₆ = a₁r⁵ = 1458
(i) The common ratio for the given condition is 3.
ii) The first term of the sequence is 6.
iii) The 6th term of the sequence is 1458.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that a is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.
As the third term minus the first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
The fourth term minus the second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
r²-1 = 48/a₁
a₁ = 6
a₆ = a₁r⁵ = 1458
Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence is 1458.
Learn more about the sequence here:
brainly.com/question/21961097
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Which of the following describes an angle with a vertex at Z?
round 8 5/6 to the nearest whole number
Answer:
9
Step-by-step explanation:
8 5/6
5/6 is close to 1 so it will round up
8+1 = 9
8 5/6 rounds to 9
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Round [tex]8\frac{5}{6}[/tex] to the nearest whole number
In order to round up, the fraction needs to be either 1/2 or greater than 1/2. In our case, it is greater than half therefore we will round up to 9.
Answer: [tex]9[/tex]
The function above models hhh, the height of a flower pot in meters, ttt seconds after it falls from a fourth floor balcony. What is the height of the flower pot, in meters, 333 seconds after it falls
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the function is not given.
However, I will give a general rule.
From the question, we understand that the question requires the value of h(3)
Assume:
[tex]h(t) = 20 - 4t[/tex]
Then:
[tex]h(3) = 20 - 4*3[/tex]
[tex]h(3) = 20 - 12[/tex]
[tex]h(3) = 8[/tex]
This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.
Discrete
Continuous
Categorical
Qualitative
choose one
NO FAKE ANSWERS
FIRST MARKED BRAINLIST
qualitative
Step-by-step explanation:
b cos the question is in quality format
Answer:
cutee!
SUP???
Hiii friend :]
cuteee~!
prettyyy
The mean examination mark of a random sample of 1390 students is 67% with a standard deviation of 8.1%.
How many students scored above 80%? (Round to the nearest student)
Answer:
76 students scored above 80%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean examination mark of a random sample of 1390 students is 67% with a standard deviation of 8.1%.
This means that [tex]\mu = 67, \sigma = 8.1[/tex]
Proportion above 80:
1 subtracted by the p-value of Z when X = 80, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 67}{8.1}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a p-value of 0.9452.
1 - 0.9452 = 0.0548.
Out of 1390 students:
0.0548*1390 = 76
76 students scored above 80%.
A tank has the shape of an inverted circular cone with height 8 m andbase radius 2 m. It is filled with water to the top. Find the integralfor the work required to empty the tank by pumping all of the waterto the top of the tank. DoNOTcompute the integral. (The densityis 1000 kg/m3.)
Answer:
Step-by-step explanation:
I'll try to make this make as much sense as possible. If we have a cone with a liquid in it, this liquid takes up volume. Therefore, our main equation, at least at first, is to find the volume. This is because if we pump the liquid out of the tank, the thing that changes is the amount of liquid in the tank which is the tank's volume. The formula for the volume of a circular cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex] and here's what we know:
r = 2 and h = 8. The formula for volume has too many unknowns in it, so let's get the radius in terms of the height and sub that in so we only have one variable. The reason I'm getting rid of the radius is because in the problem we are being asked how much work is done by pumping the liquid to the top of the tank, which is a height thing. Solve for r in terms of h using proportions:
[tex]\frac{r}{2}=\frac{h}{8}[/tex] and solve for r:
[tex]r=\frac{2}{8}h =\frac{1}{4}h[/tex] so we will plug that in and rewrite the equation:
[tex]V=\frac{1}{3}\pi(\frac{1}{4}h)^2h[/tex] and simplify it til it's a simple as it can get.
[tex]V=\frac{1}{3}\pi(\frac{1}{16}h^2)h[/tex] and
[tex]V=\frac{\pi}{48}h^3[/tex] and since the volume is what is changing as we pump liquid out, we find the derivative of this equation.
[tex]\frac{dV}{dt}=\frac{\pi}{48}*3h^2\frac{dh}{dt}[/tex] and of course this simplifies as well:
[tex]\frac{dV}{dt}=\frac{\pi}{16}h^2\frac{dh}{dt}[/tex]
Work is equal to the amount of force it takes to move something times the distance it moves. In order to find the force it takes to move this liquid, we need to multiply the amount (volume) of liquid times the weight of it, given as 1000 kg/m³:
F = [tex]1000(\frac{\pi}{16}h^2\frac{dh}{dt})[/tex] and the distance it moves is 8 - h since the liquid has to move the whole height of the tank in order to move to the top of the 8-foot tank. That makes the whole integral become:
[tex]W=\int\limits^8_0 {1000(\frac{\pi}{16}h^2(8-h)) } \, dh[/tex] and we'll just simplify it down all the way:
[tex]W=62.5\pi\int\limits^8_0 {8h^2-h^3} \, dh[/tex] and you're done (except for solving it, which is actually the EASY part!!)
1. Which expression is equivalent to 9k + 16? Explain why.
A 4 + 5k + 10 +6
B 4 + 3k + 2k + 10 +6
C2k +7 + 10 + 6
D 3k + 4k + 2k + 10 +6
Answer:
D
Step-by-step explanation:
3k +4k+2k+10+6
Collect like terms
9k +16
Answred Gauthmath
Answer:
D 3k + 4k + 2k + 10 +6
Step-by-step explanation:
A 4 + 5k + 10 +6 Combine like terms
5k+ 20 not equal
B 4 + 3k + 2k + 10 +6 Combine like terms
5k +20
C 2k +7 + 10 + 6 Combine like terms
2k + 23
D 3k + 4k + 2k + 10 +6 Combine like terms
9k+ 16
I need help with this
Answer:
D. Rotation reflection is the right answer
Answer:
Rotation, reflection
Step-by-step explanation:
R and I are equal so if you rotate clockwise you'll see I is in the top left and R would be in the bottom left. By reflecting, it's like flipping a pancake. R will now be in the in the top left on top of I.
(It's kind of weird to explain) Sorry if that was confusing.
The temperature at 5 a.m. was −7.4°C. By 9 a.m., the temperature was −4.7°C. How much warmer was the temperature at 9 a.m.?
Answer:
2.7°C.
Step-by-step explanation:
If it was -7.4°C. at 5 am, then -4.7°C. at 9am, then the temperature rose by 2.7°C.
Proof:
-7.4
-4.7
--------
2.7
I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? Thank you!
Answer:
a)125/291
b) 48/73
Step-by-step explanation:
a) total of yes/total asked
b) total above average yes/ total above average (yes and no)
Answer:
See explanation. You didn't specify on whether the problem asks for a fraction or decimal, so I put both decimal and fraction.
Step-by-step explanation:
First we answer a:
Total amount of people polled is 291. Number of people who wear glasses is: [tex]48 + 51 + 26 = 125[/tex]
Divide to get the proportion: [tex]\frac{125}{291}[/tex] which is also equal to: 0.4295532646
Then we answer b:
b asks for the proportion of all above average readers who wear glasses, so the total number would be: [tex]48 + 25 = 73[/tex]. The number of above average readers who wear glasses is then 48.
We then get the proportion: [tex]\frac{48}{73}[/tex], which is also equal to 0.6575342466.
William's assembly unit has decided to use a p-Chart with 2-sigma control limits to monitor the proportion of defective castings produced by their production process. The quality control manager randomly samples 150 castings at 10 successively selected time periods and counts the number of defective castings in the sample.
Sample Defects
1 9
2 14
3 9
4 9
5 13
6 8
7 12
8 10
9 12
10 11
Required:
a. What is the Center Line of the control chart?
b. What value of z should be used to construct the control chart?
c. What is the Upper Control Limit?
d. What is the Lower Control Limit?
Answer: attached below is the missing p chart
a) 0.07133
b) 2
c) 0.098
d) 0.045
Step-by-step explanation:
sample size = 150 castings
number of periods = 10
a) Determine the center Line of the control chart
( 0.06 + 0.0933 + 0.06 + 0.06 + 0.0867 + 0.0533 + 0.08 + 0.067 + 0.08 + 0.073) / 10
mean = 0.07133
standard deviation = 0.01335
b) Determine the value of Z to be used
Given that we are using 2sigma limits .
the value of Z to be used = 2
c) Upper limit control
= mean value + z-value * std
= 0.0713 + 2*0.01335 = 0.098
d) Lower Control Limit
= mean value - z-value * std
= 0.0713 - 2*0.01335 = 0.045
Question 1 of 5
A community orchestra is losing money. They have always sold tickets for
$12, but they decide to increase the price by $3. For their next concert, they
sell 200 tickets at the increased price.
Select the expression representing the amount of money earned from ticket
sals.
A. 200(12-3)
B. 200(12) + 3
C. 200(12+3)
D. 200(12) - 3
Answer:
200 (12+3)
Step-by-step explanation:
They sold 200 tickets at a price of (12+3)
200 (12+3)
Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 640 to 680 nm. What is the mean and variance of the wavelength distribution for this radiation?
a money market fund advertises a simple interest rate of 9% find the total amount received on an investment of 5000 for 17 months
Answer:
Step-by-step explanation:
Formula: Simple interest = PRT
P= 5000
R= 9%
T= 17
So, 5000 x 9/100 x 17 = 7650
In another case, p and 2p are the first and second term respectively of an arithmetic progression. The nth term is 336 and the of the first n terms is 7224. Write down two equations in n and p and hence find the values of n and p
Consecutive terms in this sequence differ by p.
First term: p
Second term: p + p = 2p
Third term: 2p + p = 3p
and so on. It follows that the n-th term satisfies
np = 336
Presumably you meant to say the "sum of the first n terms" is 7224, which is to say
p + 2p + 3p + … + np = 7224
which can be rewritten as
p (1 + 2 + 3 + … + n) = 7224
p (n (n + 1)/2) = 7224
n (n + 1) p = 14,448
Substitute the first equation in the second one and solve for n :
336 (n + 1) = 14,448
n + 1 = 43
n = 42
Now solve for p :
42p = 336
p = 8
please help
Find the missing side of this right
triangle.
X
7
12
X
= [?]
Answer:
13.9 (if x is the Hypotenuse)
Step-by-step explanation:
which one is the Hypotenuse (the side opposite of the 90 degree angle) ?
because that determines the calculation.
if x is the Hypotenuse then Pythagoras looks like this
x² = 7² + 12² = 49 + 144 = 193
x = sqrt(193) = 13.9
if 12 is the Hypotenuse, then it looks like this
12² = 7² + x²
144 = 49 + x²
95 = x²
x = sqrt(95) = 9.75
What is the area of the triangle formed from (0,-3), (0,4), and (4,-3)?
A. 24 square units
B. 48 square units
C. 14 square units
O D. 6 square units
find the area of a semicircle whose radius is 2.4 cm
Answer:
15.072
Step-by-step explanation:
Pls Mark Brainiest okay
Answer:
2.88 pi or approximately 9.0432 cm^2
Step-by-step explanation:
The area of a semicircle is 1/2 the area of a circle
A = 1/2 pi r^2
A = 1/2 pi ( 2.4)^2
A = 2.88 pi cm^2
If we use 3.14 as an approximation for pi
A = 2.88 * 3.14
A =9.0432 cm^2
Couldn’t figure this out, please help
(A)
Step-by-step explanation:
This system of equations will no solution if they have the same slope and only differ in the y-intercept values. So let's rewrite the two equations into their slope-intercept forms:
[tex]y = \frac{3}{h-2}x + 5[/tex]
[tex]y = \frac{8}{h}x + \frac{5}{h}[/tex]
For them to have no solution, their slopes must equal each other:
[tex]\dfrac{3}{h-2} = \dfrac{8}{h} \Rightarrow 3h=8h-16[/tex]
or
[tex]h = \dfrac{16}{5}[/tex]
Putting this value into our system of equations, we get
[tex]y = \frac{5}{2}x + 5[/tex]
[tex]y = \frac{5}{2}x + \frac{25}{16}[/tex]
This is a system of equations consisting of two parallel lines and as such, do not intersect and so, no solution.
