Answer:
[tex]\dfrac{dV}{dt}=502.65\ mm^3/s[/tex]
Step-by-step explanation:
The volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
The rate of change of volume means,
[tex]\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}[/tex]
We have, [tex]\dfrac{dr}{dt}=2\ mm/s\ and\ r=40\ mm[/tex]
So,
[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s[/tex]
So, the volume is increasing at the rate of [tex]502.65\ mm^3/s[/tex].
-12(x - 3) - (2x - 6) = 60
Answer:
x=-9/7
Step-by-step explanation:
Answer:-12(x - 3) - (2x - 6) = 60
= -12 OJHORZHOEHFOSDHSKDKCDEZIAIFDNSQDKFFFFFFFFFFFFZIDJAZIFJOIJF
Step-by-step explanation:
EFKJNDOIDNOIEFJOAIZFOUJFNJBVJFNVJNZJCN
what is ( 5 x 1 ) + ( 5 x 1/3)
Answer:
The answer is 20/3
Step-by-step explanation:
(5 x 1 ) + ( 5 x 1/3)
5 + ( 5 × 1/3 )
5 + 5/3 = 20/3
If Robert buys a candy bar for 78 cents, how much
change does he get back from a one-dollar bill?
32 cents
23 cents
22 cents
33 cents
Answer this correctly I’ll give brainalist + 10 points
Find the slope of the line that passes through the two points. (0, 0), (3, 2)
Answer:
the slope is 2/3 bcoz u do 2-0/3-0
SOMEONE, PLEASE HELPP ME!!!
Ten hamburger values meals cost $60.
The area for the trapezoid is__in2.
Answer:
1204 in squared
Step-by-step explanation:
During a guided tour of Sindrow Castle, a group of tourists climbed to the top of Fineview Tower.
At the top, the guide asked the six children in the group to guess how many steps they had
climbed. Their guesses were 155, 157, 167, 168, 179 and 183.
The guide revealed that the closest guess was only 3 more or less than the correct number and
that two of the other guesses were no more than 10 away.
How many steps had they climbed?
A 160
B 164
C 171
D 176
Answer:
C
Step-by-step explanation:
A company makes fifty-six million, nine hundred two thousand, one hundred twenty six widgets each year. what is this number in stardard form?
A local anime fan club surveyed its members regarding their viewing habits last weekend, and the following information was obtained: 35 members had watched an episode of Naruto, 48 had watched an episode of Death Note, 24 had watched both an episode of Naruto and an episode of Death Note, and 12 had watched neither Naruto nor Death Note. (Round your answers to three decimal places.)
(a) What percent of the club members had watched Naruto or Death Note?
(b) What percent of the club members had watched only Naruto?
(c) What percent of the club members had watched only Death Note?
Answer:
a) 83.099% of the club members had watched Naruto or Death Note.
b) 15.493% of the club members had watched only Naruto
c) 33.803% of the club members had watched only Death Note.
Step-by-step explanation:
First we find the number of students which each habit, treating the habits as Venn sets.
I am going to say that:
Set A: Watched an episode of Naruto.
Set B: Watched an episode of Death Note.
24 had watched both an episode of Naruto and an episode of Death Note:
This means that [tex](A \cap B) = 24[/tex]
48 had watched an episode of Death Note
This means that [tex]B = 48[/tex].
We have that:
[tex]B = (B-A) + (A \cap B)[/tex]
In which B - A are those who watched only Death Note. So
[tex]48 = (B-A) + 24[/tex]
[tex](B-A) = 24[/tex]
35 members had watched an episode of Naruto
This means that [tex]A = 35[/tex].
[tex]A = (A-B) + (A \cap B)[/tex]
[tex]35 = (A-B) + 24[/tex]
[tex](A-B) = 11[/tex]
At least one:
This is
[tex](A \cup B) = A + B - (A \cap B)[/tex]
So
[tex](A \cup B) = 35 + 48 - 24[/tex]
[tex](A \cup B) = 59[/tex]
Total number of students:
59 at least one, 12 none, so 71 total.
(a) What percent of the club members had watched Naruto or Death Note?
At least one, so 59 out of 71
59*100/71 = 83.099
83.099% of the club members had watched Naruto or Death Note.
(b) What percent of the club members had watched only Naruto?
11 out of 71. So
11*100/71 = 15.493
15.493% of the club members had watched only Naruto.
(c) What percent of the club members had watched only Death Note?
24 out of 71. So
24*100/71 = 33.803
33.803% of the club members had watched only Death Note.
Answer:
i think it is (b) What percent of the club members had watched only Naruto?
Step-by-step explanation:
Find the length of the diameter of circle O. Round to the nearest tenth.
Answer:
Diameter = 19.33
Step-by-step explanation:
Imaging a radius line from O to the endpoints of the 7. call this line R.
Label the part of the vertical line from O to the 90 degree intersection y.
Now you have a right triangle.
Using the Pythagorean theorem:
R² = 7² + y²
also
y = R - 3
substitute for y:
R² = 49 + (R-3)²
R² = 49 + R² - 6R + 9
simplify:
0 = 58 - 6R
6R = 58
R = 9.6667
Diameter = 2(9.6667) = 19.33
↓⊂∩⊥ββ⊄⊃БНasdsxЫ
c=9 d=8
6d-2c
Answer:
im sorry what?
Step-by-step explanation:
Help please, what's the answer?
Question 7
Exponential functions have a variable degree.
Answer is 3^x + 6.
Question 8
Changing 15.3% to a decimal, we get 0.153.
Answer: Choice (4)
how do you make like terms? thank you
Answer:
Like terms are terms whose variables are the same. In other words, terms that are "like" each other. For example, 2x and 3x are like terms. Furthermore, 3y² and 4y² are also like terms. If two factors are like terms they can be combined.
Step-by-step explanation:
Hope this helps!
Answer:
Step-by-step explanation:
why is angle 3 congruent to angle 7?
Answer:
they are congruent because they are corresponding angles
Step-by-step explanation:
hi, if your looking for extra points (50+) and brainiest here is ur chance, answer this question correctly plz
Answer:
i will take company (a) because they are giving in less rate
Answer:
You would want to go with A
Step-by-step explanation:
If you do plan a it is 180 dollars a year when you spend 15 dollars per GB, B is cheaper on the other hand because it is 75 dollars a month so therefore 900 dollars a year
A is cheaper
If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t 0. Do the particles collide? If they collide find t. If not enter NONE.
r1(t) = t^2, 8t − 15, t^2
r2(t) = 11t − 30, t^2, 13t − 40
t=
Answer:
Step-by-step explanation:
[tex]r_1(t) = < t^2 , 8t-15,t^2> \\ \\ r_2(t) = < 11t-30, \ t^2 , \ 13t-40> \\ \\ at \ r_1 = r_2 \\ \\ t^2 = 11t - 30 , \ \ \ \ \ \ \ \ \ \ \ \ 8t - 15 = t^2 , \ \ \ \ \ \ \ \ \ t^2 = 13t -40 \\ \\ t^2 - 11t + 30\ \ \ \ \ \ \ \ \ \ \ \ t^2 -8t + 15 , \ \ \ \ \ \ \ \ \ \ \ \ t^2 -13t + 40 \\ \\ t^2 -8t-3t + 30=0 \ \ \ \ \ \ t^2 - 2t -4t + 15=0 \ \ \ \ \ \ t^2 - 1t - 13t + 40 =0[/tex]
[tex](t-6)(t-5) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-3) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-8)[/tex]
[tex]\mathbf{The \ common \ value \ of \ t \ = \ 5}[/tex]
Evaluate 150 - ( 2 +x)^ 3 when x - 2
Answer:
it's 86
Step-by-step explanation:
150-(2+x)^3=150-(2+2)^3
=150-4^3
=150-64
=86
The value of the expression 150 - (2 + x)³, when x = 2 is, 86.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 150 - (2 + x)³, when x = 2.
This can be obtained by replacing x = 2 in the expression.
Therefore, 150 - (2 + x)³.
= 150 - (2 + 2)³.
= 150 - 4³.
= 150 - 64.
= 86.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ5
Can you please help me
no xdxdxdxdxdxxdxdxdxdxdxdxdxdxddxd
Find the slope of line with the given points (- 6, 2)(3, 7)
Answer:
m = 5/9
Step-by-step explanation:
rise = 5
run = 9
m = rise/run
m = 5/9
Answer:
m = 5/9
Step-by-step explanation:
Use the slope formula to find the slope m.
[tex]m = \frac{5}{9}[/tex]
Before dividing, decompose 420 to make it easier to divide by 4.
Answer:
4/420=105
Step-by-step explanation:
decompose 42 and divide by 4 is 10 and is 20 divided by 4 is 5
Use the distributive property to write an equivalent expression. (6+8)⋅x *
Answer: 14*x
Step-by-step explanation: I am 99% sure
77006
75863
Subtract
Answer:
1143
Step-by-step explanation:
Please help please please plewse
Answer:
-1 and -5
Step-by-step explanation:
(1 point)
Find the area enclosed by the curve r=2 sin(0) + 3 sin(90).
If the 0's are indeed zeroes, then it would appear that you're using degrees, so that the equation
r(θ) = 2 sin(0°) + 3 sin(90°)
describes a circle r = 3 (since sin(0°) = 0 and sin(90°) = 1). In this case, the area would simply be π r ² = 9π.
But I suspect you meant to use θ, so the curve has the far more interesting equation,
r(θ) = 2 sin(θ) + 3 sin(9θ)
Since sin(9θ) has a period of 2π/9 and sin(θ) has a period of 2π, their sum has a period of 2π. (That is, 2π times the LCM of 1 and 1/9, which is 1.) But we observe r(θ) is odd, since
r(-θ) = 2 sin(-θ) + 3 sin(-9θ)
… = -2 sin(θ) - 3 sin(9θ)
… = - r(θ)
which tells us that the curve closes itself over a half-period. So the area bounded by the curve is given by the integral,
[tex]\displaystyle\int_0^\pi\int_0^{r(\theta)}r\,\mathrm dr\,\mathrm d\theta[/tex]
If you're not familiar with double integrals yet, all you need to know is that this reduces to the area formula you may/should be familiar with,
[tex]\displaystyle\frac12\int_0^\pi r(\theta)^2\,\mathrm d\theta[/tex]
Compute the integral:
[tex]=\displaystyle\frac12\int_0^\pi(2\sin(\theta)+3\sin(9\theta))^2\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac12\int_0^\pi(4\sin^2(\theta)+12\sin(\theta)\sin(9\theta)+9\sin^2(9\theta))\,\mathrm d\theta[/tex]
Apply some identities:
sin²(θ) = (1 - cos(2θ)) / 2
sin(θ) sin(9θ) = (cos(9θ - θ) - cos(9θ + θ)) / 2 = (cos(8θ) - cos(10θ)) / 2
sin²(9θ) = (1 - cos(18θ)) / 2
[tex]=\displaystyle\frac14\int_0^\pi(4(1-\cos(2\theta))+12(\cos(8\theta)-\cos(10\theta))+9(1-\cos(18\theta))\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac14\int_0^\pi(13 - 4\cos(2\theta) + 12\cos(8\theta) - 12\cos(10\theta) - 9\cos(18\theta))\,\mathrm d\theta[/tex]
[tex]=\dfrac14 \left(13\theta-2\sin(2\theta)+\dfrac32\sin(8\theta)-\dfrac65\sin(10\theta)-\dfrac12\sin(18\theta)\right)\bigg|_0^\pi[/tex]
[tex]=\dfrac1{40} \left(130\theta-20\sin(2\theta)+15\sin(8\theta)-12\sin(10\theta)-5\sin(18\theta)\right)\bigg|_0^\pi[/tex]
[tex]=\dfrac{130\pi-20\sin(2\pi)+15\sin(8\pi)-12\sin(10\pi)-5\sin(18\pi)}{40}[/tex]
= 13π/4
Floyd Electric is fabricating flanges for a new electrical motor. The flange is to be 25 millimeters in diameter with an upper tolerance limit of 26.5 millimeters and a lower tolerance limit of 23.5 millimeters. Bill Floyd took a sample consisting of ten flanges, measured the diameter and recorded the observations in the table. He has heard discussion of 6 sigma in the business news recently and would like to join the club. What percentage decrease in process standard deviation would be required for Floyd Electric to achieve 6-sigma process capability? Assume that his process mean remains where it is.
A) 36%
B) 40%
C) 46%
D) 58%
This question is incomplete, the missing table is uploaded along this answer below.
Answer:
percentage of age reduction is 40
Option B) 40% is the correct answer
Step-by-step explanation:
Given the data in the question;
from the table in the image below;
sample x = 25.69 , 25.58 , 24.78 , 24.94 , 24.87 , 24.63 , 25.70 , 25.52 , 24.95 , 24.91
mean = ∑x/n
where n is sample size
= (25.69 + 25.58 +24.78 + 24.94 + 24.87 + 24.63 + 25.70 + 25.52 +24.95 ) / 10
= 251.57 / 10
mean u = 25.157
so;
S/N Sample (X) Mean (u) (X-U)²
1 25.69 25.157 0.284089
2 25.58 25.157 0.178929
3 24.78 25.157 0.142129
4 24.94 25.157 0.047089
5 24.87 25.157 0.082369
6 24.63 25.157 0.277729
7 25.7 25.157 0.294849
8 25.52 25.157 0.131769
9 24.95 25.157 0.042849
10 24.91 25.157 0.061009
Total 251.57 1.54281
Mean 25.157
Sample Variance = ∑(x-u)²/n-1 = 1.54281 / (10 - 1) = 1.54281 / 9 = 0.1714
Standard deviation STD1 = √ (variance) = √0.1714 = 0.414
now, for 6-sigma capability, Cpk = 2
Cpk = min of ( USL - mean ) / 3×STD), (Mean - LSL) / 3×STD
since our mean is centered between USL and LSL;
Cpk = ( 26.5 - 25 ) / 3×STD2
we substitute
2 = ( 26.5 - 25 ) / 3×STD2
6STD2 = 1.5
STD2 = 1.5 / 6
STD2 = 0.25
so current standard deviation STD1 = 0.414
required standard deviation for 6-sigma process STD2 = 0.25
so percentage of age reduction will be;
⇒ ( 0.414 - 0.25 ) 0.414 = 0.164 / 0.414 = 0.396 ≈ 0.4
⇒ 0.4 × 100 = 40%
Therefore, percentage of age reduction is 40
Option B) 40% is the correct answer
A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% milk, steamed, and 0.5 cup of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of skim milk, frothed, and no whipped cream. The plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. The airline makes a profit of $1.58 on each regular latte and $1.65 on each low-fat latte. Assuming that all lattes that are made can be sold, what would be the ideal mix of regular and low-fat lattes to maximize the profit for the airline?
Answer:
To maximize profit, the amount of each type of coffees made are;
The number of regular latte made = 52 cups
The number of low-fat latte made = 48 cups
Step-by-step explanation:
The given parameters are;
The number of espresso in a regular latte = 1 shot
The number of cups of 2% milk in regular latte = 1 cup
The amount of whipped cream in a regular latte = 0.5 cup
The number of cups of skim milk in the low-fat latte = 1.25 cup
The number of espresso in a low-fat latte = 1 shot
The amount of whipped cream in a low-fat latte = 0 cup
The number of cups of espresso in the journey = 100 shots
The number of cups of skim milk in the journey = 60 cups
The number of cups of 2% milk in the journey = 60 cups
The amount of profit the airline makes on each regular latte = $1.58
The amount of profit the airline makes on each low-fat latte = $1.65
Let 'x' represent the number regular lattes made and let 'y' represent the number low-fat lattes made, we have;
x ≤ 30/0.5 = 60
x ≤ 60
y ≤ 60
y ≤ 60/1.25 = 48
∴ y ≤ 48
x + y ≤ 100
Therefore, the given that more profit is made from the sale of low-fat latte than for regular latte, the maximum number of low-fat latte should be made
Therefore, the number of low-fat latte made, y = 48
Therefore, the number of regular latte made, x ≤ 100 - 48 = 52
For maximum profit, the maximum number of low-fat latte, 'x', should be made
Therefore, x = 52
The ideal mix of regular and low-fat lattes to maximize profit is 52 cups of regular latte and 48 cups of low-fat latte
What is the equation of the line that passes through the point (4, -8) and has a
slope of -1/2?
Answer is y=-1/2x-6
:)
Answer:
yo sorry I'm dum need points
A directed line segment AB with A (1,3) and B (8,4) is partitioned by point C such that AC and CB form a 4:1 ratio. Find C
Write your answer as a coordinate point.
Do not include spaces in your answer.
Write your answer as a decimal if necessary.
Answer:
[tex]C = (\frac{33}{5},\frac{19}{5})[/tex]
Step-by-step explanation:
Given
[tex]A = (1,3)[/tex]
[tex]B = (8,4)[/tex]
[tex]AC : BC = 4 : 1[/tex]
Required
Determine the coordinates of C
To do this, we make use of:
[tex]C = (\frac{nx_1 + mx_2}{n+m},\frac{ny_1 + my_2}{n+m})[/tex]
Where:
[tex]A = (1,3)[/tex] ---- [tex](x_1,y_1)[/tex]
[tex]B = (8,4)[/tex] ---- [tex](x_2,y_2)[/tex]
[tex]m:n = 4 : 1[/tex]
So:
[tex]C = (\frac{1 * 1 + 4*8}{1+4},\frac{1*3 + 4*4}{1+4})[/tex]
[tex]C = (\frac{33}{5},\frac{19}{5})[/tex]
-2p-4=2 pls help me.
Answer:
p= -3
Step-by-step explanation:
-2p-4=2
+4 +4
-2p=6
/-2 /-2
p=-3