How fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
To solve the question, we need to know the volume of a sphere
Volume of a sphereThe volume of a sphere V = 4πr³/3 where r = radius of sphere.
How fast the volume of the sphere is changingTo find the how fast the volume of the sphere is changing, we find rate of change of volume of the sphere. Thus, we differentiate its volume with respect to time.
So, dV/dt = d(4πr³/3)/dt
= d(4πr³/3)/dr × dr/dt
= 4πr²dr/dt where
dr/dt = rate of change of radius of sphere and 4πr² = surface area of sphereGiven that
dr/dt = + 3 cm/s (positive since it is increasing) and 4πr² = surface area of sphere = 10 cm²,Substituting the values of the variables into the equation, we have
dV/dt = 4πr²dr/dt
dV/dt = 10 cm² × 3 cm/s
dV/dt = 30 cm³/s
So, how fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
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Professor Mallory determines the distribution of students on five variables in her target population. She then uses nonprobability sampling to select students who fill the pre-established proportions of people in each combination of variables. Which sampling strategy did she use
The sampling strategy she use was a quota.
Quotas are meant to establish boundaries on the number of specific goods that are allowed to be lawfully imported into the country throughout a distinct period of time. In that, quotas are similar embargoes, except quotas don´t have explicit political purposes as embargoes do.
A Fixed quota would be a maximum amount not to be surpassed, while a tariff rate surcharge allows it, but with a higher duty.
Chloe gave out a survey to some students in her school about their favorite color. 219 of those surveyed said their favorite color was purple. If 73% of the students surveyed said their favorite color was purple, how many students were surveyed in total?
If 73% of the students surveyed said their favorite color was purple, 1,000 students were surveyed in total.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Let the total number of persons surveyed be x. However, the question tells us that 350 respondents, or 35% of this x, make up the total.
Hence, mathematically, we have;
73% of x = 219
(73/100) × x = 219
73x = 100×219
73x = 219,000
x = 219,000/219
x = 1,000 students
Thus, if 73% of the students surveyed said their favorite color was purple, 1,000 students were surveyed in total.
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How many arrangements are there of the letters in the word "greet?"
Sonja is spinning a spinner with 15 equal sectors labeled 1 through 15.
What is P(multiple of 6)?
2/15
4/15
2/5
3/5
Answer:
2/15
Step-by-step explanation:
there are only 2 numbers which are multiples of 6, which are both 6 and 12. That means it would be a 2/15 probability. You cannot simplify it more, so it will remain the same.
Answer:
2/15
Step-by-step explanation:
:)
Find the measure of angle A.
Angle 1. x+59
Angle 2. 84
Angle 3. x+51
I already know x= -7 But the measure of angle A is on the outside of the triangle
Ans: The measure of exterior angle i.e angle A is -52⁰.
You meant to say that the measure of an angle A is on exterior angle so let me elaborate it you clearly,
[tex]x + 59 \\ = - 7 + 59 \\= - 52[/tex]
At a football stadium, 2% of the fans in attendance were teenagers. If there were 240 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
12000
Step-by-step explanation:
240÷2=120
120=1%
120×100=12000
12000=100%
Answer: 12,000
Step-by-step explanation:
2% is = 240
1% is 240/2
100% is 240/2 × 100/1
Without buying points, a monthly mortgage payment will be $958. buying 1 point at closing would reduce the payment to $948.75. if each point costs $1000.00, rounded to the nearest year, how long would it take to break even by buying 1 point? a. 7 years b. 8 years c. 9 years d. 10 years please select the best answer from the choices provided a b c d
If each point costs $1000.00. how long would it take to break even by buying is:9 years.
TimeFirst step
Monthly savings=$958-$948.75
Monthly savings=$9.25
Second step
Time=(Cost of points/Mothly savings)/ 12 months
Time=($1,000/$9.25)/12 months
Time=108/12 months
Time=9 years
Therefore how long would it take to break even by buying is:9 years.
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Two trains leave a station going in opposite directions. The northbound train averages 87 miles per hour. The southbound train averages 113 miles per hour. How long will it take for the trains to be 600 miles apart?
Answer:
It takes 3 hours for the train to be 600 Miles apart
What's the answer to this question? 4*(5t+1)/5
Answer:
[tex]\boxed{\sf{4t+\dfrac{4}{5} }}[/tex]Step-by-step explanation:
In order to solve this, you must use the distributive property.
[tex]\sf{\dfrac{4\left(5t+1\right)}{5}}[/tex]
Distributive property:
⇒ A(B+C)=AB+AC
⇒ 4(5t+1)
Multiply by expand.
4*5t=20t
4*1=4
Rewrite the problem down.
20t+4
20t+4/5
[tex]\text{FRACTION RULES: }\\\\\\\Longrightarrow: \sf{\dfrac{A\pm \:B}{C}=\dfrac{A}{C}\pm \dfrac{A}{C}}[/tex]
[tex]\Longrightarrow: \sf{\dfrac{20t+4}{5}=\dfrac{20t}{5}+\dfrac{4}{5}}[/tex]
You have to divide the numbers from left to right.
⇒ 20/5=4
[tex]\Longrightarrow: \boxed{\sf{4t+\dfrac{4}{5} }}[/tex]
Therefore, the correct answer is 4t+4/5.Answer:
[tex]4t + \frac{4}{5}[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]\frac{4(5t + 1)}{5}[/tex]
[tex]\frac{(4 * 5t) + (4 * 1)}{5}[/tex]
[tex]\frac{20t + 4}{5}[/tex]
Step 2: Isolate the numerator into two fractions
[tex]\frac{20t +4}{5}[/tex]
[tex]\frac{20t}{5} + \frac{4}{5}[/tex]
[tex]4t + \frac{4}{5}[/tex]
Answer: [tex]4t + \frac{4}{5}[/tex]
I need help because I dont quiet understand pls explain?
Explain how to create a graph to model the relationship between the 2 quantities in the table.
Answer:
For every hour they work (x), they are being paid $25. (d)
Step-by-step explanation:
So, D=25x
the sum of six interior angles of a regular octagon is 800 the other two angles are equal find the size of each angle
An octagon is a polygon with 8 sides and angles. The two equal angles are 140 degrees each
How to calculate the sum of an interior angle of a polygon?An octagon is a polygon with 8 sides and angles
The formula for calculating the sum of interior angle of a regular polygon is expressed as:
S = (n-2) * 180
If the sum of six interior angles of a regular octagon is 800 the other two angles are equal, then;
800 + 2x = (8-2)*180
800 + 2x = 1080
2x = 1080 - 800
2x = 280
x = 140
The two equal angles are 140 degrees each
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Find the volume of the figure. Round answer to nearest hundredths place.
Answer: 540 nearest hundred is 500
Step-by-step explanation:
I multiplyed them together to get the answer.
Answer:
4834.9
Step-by-step explanation:
1) Split the Figure into a Cone and a Cylinder
2) Cylinder Formula V=πr²h And Cone V=1/3hπr²
3) π[tex]9^{2}[/tex]15 + 1/2(12)π([tex]9^{2}[/tex])
4) 3817.04+1017.88
5) 4834.9
The town of La Belle wants to build a soccer
field. They want it to be 50 yards wide and 80
yards long. What is the total area of the soccer
field? Show your process
Answer:
4000 yd^2
Step-by-step explanation:
50 yd * 80 yd = (50*80) ( yd * yd) = 4000 yd^2
Find the value of x
Answer: 11
Step-by-step explanation:
How would you solve this?
Answer:
the answer of the perimeter is B
Dilation is enlarging or shrinking a figure by using a scale factor.
Using a scale factor bigger than one, creates a
figure.
Using a scale factor between 0 and
creates a
figure.
Create your own
dilation examples or find 2 images of dilation examples. Be
sure the two examples are different by showing one getting larger and one
getting smaller.
Answer:
Step-by-step explanation:
scale factor bigger than one, in math greater than, the figure is larger than the object being used a figure smaller than 1 creates a figure smaller than the original
Luckily you can just use your web browser to scale a screen up or down in it's scale. try it.. top right ellipse for go ogle chrome lets you scale over 100 per cent or 1 and also under 100 per cent or less than 1 remember 100 per cent = 1.00
Exponential growth/decay problem 2
Answer:
a) decay
b) 2,950,000
c) 0.025
d) [tex]f(x)=2950000(0.975)^x[/tex]
e) 2,409,123
Step-by-step explanation:
Part (a)
Exponential DECAY, since the population was decreasing annually.
Part (b)
Initial amount = 2,950,000 people (in the year 2000)
Part (c)
Decay factor = 2.5% = 0.025 (in decimal form)
Part (d)
General form of exponential decay function:
[tex]f(x)=a(1-r)^x[/tex]
where:
a = initial amountr = rate of decay (in decimal form)x = time (in years)Given:
a = 2950000r = 0.025[tex]\implies f(x)=2950000(1-0.025)^x[/tex]
[tex]\implies f(x)=2950000(0.975)^x[/tex]
Part (e)
To determine the city's population in 2008:
[tex]x = 2008 - 2000 = 8[/tex]
[tex]\begin{aligned}\implies f(8) & =2950000(0.975)^8\\ & = 2409123\: \sf(nearest\:whole\:number)\end{aligned}[/tex]
15 is 60% of what number?
25
hope it helps...!!!!
Melissa will paint a jewelry box that is in the shape of a cube. The surface area of the cube can be determined using the formula A = 682 wheres represents the side length the cube Determine the surface area of the box that Melissa will paint to the nearest tenth of a square inch if x = 2.
The surface area of the box that Melissa will paint is 24 square units
Surface are of a cubeA cube is a solid figure with 6 faces. The formula for calculating the surface area of the cube is expressed as:
A = 6L^2
where
L is the side length of the cube
Given
L = 2units
Substitute
A = 6(2)^2
A = 6 * 4
A = 24 square units
Hence the surface area of the box that Melissa will paint is 24 square units
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What is the factored form of this expression? x9-1000
A. (x3-10)(x3+10)(x2-10x+100)
B. (x3+10)(x6-10x3+100)
C. (x-10)(x+10)(x3-10x2+100)
D. (x3-10)(x6+10x3+100)
Answer:
D. (x^3 - 10)(x^2 + 10x^3 + 100).
Step-by-step explanation:
Using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2):
We have x^9-1000 :
- here a = x^3 and b = 10 so:
x^9-1000 = (x^3 - 10)(x^2 + 10x^3 + 100)
give the answer
the areaaaaaa
Answer:
16
Step-by-step explanation:
The figure shown is a trapezoid
Area of a trapezoid = 1/2(bottom base length + top base length) × height
Bottom base length = 7 units
Top base length = 1 unit
Height = 4 units
So area = 1/2 ( 7 + 1 ) × 4
==> add 7 and 1
Area = 1/2 (8) × 4
==> multiply 1/2 and 8
Area = 4 × 4
==> multiply 4 and 4
Area = 16
HELpppppppppPPPPPPPPPPPPPPPpppppPPPPPPPP
Answer:
(a) mintutes, seconds
(b) Randomly pick 55 students to run a lap around the track and measure their times
Step-by-step explanation:
(a) When measuring distance like running you measure it in minutes and seconds
(b) When finding the average of a population you have to pick randomly and to get the best results you time them youself
Randomly pick 55 students to run a lap around the track and measure their times.
1.4.
Which scatter plot shows a negative linear association between x and y?
A.
B.
y
y
C.
D.
..
..
.
●
●
.
●
Answer:
need more details
Step-by-step explanation:
...
f(x) = x^2. What is g(x)?
A. g(x) = (4x)^2
B. g(x) = 2x^2
C. g(x) = (2x)^2
D. g(x) = (1/2x)^2
Answer:
C
Step-by-step explanation:
g(x) through the point (1,4) so its mean when x equal to 1, g(x) equal to 4 so you replace that point so you can choosse C
What will the equation be if f(x)= x^2 is translated 6 units left and 3 units up?
Answer:
(x+6)^2+3
Step-by-step explanation:
translate 6 left
left is negative
so (x+6)^2. it is + because the x goes in the opposite direction causing (x-6)^2 to go right
and 3 units up so add x by 3 to get (x+6)^2+3
Answer:
g(x) = (x + 6)² + 3
Step-by-step explanation:
To move horizontally replace each x with (x ± c)
if you move it to the right, you need x - c
if you move it to the left , you need x + c
Since we are moving to the left 6, we will have: g(x) = x² + 6
To move up or down, add or subtract the constant equal to the units moved, so to move it up 3 would give us:
g(x) = (x + 6)² + 3
A graph is below for further conformation.
hope this helps!
John, Britteny, Chloe, Kenji, Warner, and Juliette are in a race and are all considered equally fast what is the probability that John and Britteny would be the first two finishers
Detailed explanations are most welcome
Answer:
1/3
Step-by-step explanation:
There are 6 people partaking in this race.If John and Brittney are to be the first two finishers, then 2 out of the 6 people are the said first two finishers.That gives 2/6.By reducing the fraction, we have:(2÷2)/(6÷2) = 1/3.Hope this helps!
The classroom has 20 students and
1
10
of the students have blonde hair. How many students have blonde hair?
Answer:
2 students out of 20 have blonde hair.
Step-by-step explanation:
20 was the total number if u divide 20 ÷ by 10 = 2
so 2 is 1/10
because is only 1 out of 10
Answer:
2 students.
Step-by-step explanation:
20 divided by 10 = 2
The ratio of the measures if the sides of a triangle is 4:6:8, and its perimeter is 126 feet. What are the measures of the sides of the triangles
Answer:
56 feet.
Step-by-step explanation:
4k+6k+8k=18k=126⟹k=7
Therefore, the lengths are 4⋅7=28, 6⋅7=42 and 8⋅7=56 feet.
HELP ME FOR A BRAINLIEST BA3
Answer:
it should be -65. because I did this already
Answer:
x=3, y=-3
Step-by-step explanation:
pluging in y we get -3x+15=6, or -3x=-9
this means x is 3
Simply the expression.
4 (2m -6) - 3p - 2m + 8
Let's solve the equation.
4 (2m -6) - 3p - 2m + 8
= 8m - 24 - 3p - 2m + 8 (We simplified 4 (2m -6))
= 6m - 16 - 3p (We added the 8 to the 24)
= 6m - 3p - 16 (We organized the variables together so it matches an answer.)
The answer is A!
Answer: hii
The answer; 6m - 3p -16Step-by-step explanation:
How to solve your problem:
4 (2m -6) - 3p - 2m + 8
Simplify.
Distribute.
4 (2m -6) - 3p - 2m + 8
8m - 24 - 3p - 2m + 8
Add the numbers:
8m - 24 - 3p - 2m + 8
8m - 16 - 3p - 2m
Combine like terms:
8m - 16 - 3p - 2m
6m - 16 - 3p
Rearrange terms:
6m - 16 - 3p
6m - 3p - 16
Solution:
6m - 3p -16
Hopefully this helps you ~
- Matthew