Volume of a sphere:
V = 4/3 π r ³
Differentiate V with respect to time t :
dV/dt = 4π r ² dr/dt
Surface area of a sphere:
A = 4π r ²
Differentiate A with respect to t :
dA/dt = 8π r dr/dt
You're given that the volume is increasing at a constant rate, dV/dt = 10 cm³/s, so
10 cm³/s = 4π r ² dr/dt
Solve for dr/dt (the rate of change of the sphere's radius):
dr/dt = 5/(2π r ²) cm³/s
Substitute this into the equation for dA/dt :
dA/dt = 8π r (5/(2π r ²) cm³/s)
dA/dt = 20/r cm³/s
At the moment the radius is r = 5 cm, the surface area is increasing at a rate of
dA/dt = 20/(5 cm) cm³/s = 4 cm²/s
When the surface area is increasing at a rate of dA/dt = 2 cm²/s, the radius r is such that
2 cm²/s = 20/r cm³/s
which happens when the radius is
r = 20/2 (cm³/s) / (cm²/s) = 10 cm
Find the probability that when a couple has five children, at least one of them is a boy. (assume that boys and girls are equally likely.)
Answer:
The easiest way to figure this is to find P(no girls in 5 births) = (1/2)^5 = 1/32 -------------- The P(at least one girl in 5 births) = 1 - 1/32 = 31/32
The probability that when they have five children, at least one of them is a boy is 31/32
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome:
The probability that a couple will have a boy or girl among the five children = 1/2
If they gave birth to 5 children:
The probability that when they have five children, at least one of them is a boy = 1 - (1/2)^n where:
n is the total number of children
The probability that when they have five children, at least one of them is a boy = 1 - (1/2)ⁿ
The probability that when they have five children, at least one of them is a boy = 1 - (1/2)⁵
The probability that when they have five children, at least one of them is a boy = 1- 1/32 = 31/32
Hence the probability that when they have five children, at least one of them is a boy is 31/32
Learn more here: https://brainly.com/question/13604758
someone down to help...............
Containers A (6cm, 5cm, 4cm), B (5cm, 4cm, 3 cm) and C (3cm, 3cm, 2 cm) are three rectangular containers. At first, container A is filled with water to its brim while containers B and C are empty. Next, some water from container A is poured into containers B and C so that container B is completely full while container C is half full. Find the height of the water left in container A..
<><><><><><><><><><><><><><><>
the Sealy family attended a baseball game. They offered food from the attendant working in their area. The food bill came to $62.50. The sealys decided to give the attendant an 18% tip. How much did the family pay for the meal.
50% of 180 dancers said they prefer hip hop class over tap class. How many dancers prefer hip hop class?
Answer:
90
Step-by-step explanation:
50% of 180 = 90%
90% is the answer.
Create a stem-and-lead plot using the following data: 21 14 7 9 30 21 6 6 28 21 31 35 14 17 20 9 24 34 7 21 28
Step-by-step explanation:
stem and leaf
0 66779
1 447
2 0111148
3 0145
plss help me plsssssss I've been 24 hours studiyng right now soo please help me
Answer:
1)b 0.48
2) c 0.35
3) a 0.092
4) d 51.2
5) a 4
6) b0.6
7) d 3
8) a 3.33
9) a 37.125
10) c 9.1
workout the following divisions:
Answer:
I think this is the same as yesterday.
look at picture for question. will mark brainilest please
Answer:
b. 3 pounds
.............
please help
answer choices:
A:0.125
B:0.20
C:0.80
D:1.0
9514 1404 393
Answer:
B: 0.20
Step-by-step explanation:
Green was selected 8 of the 40 times. We expect its probability of selection to be about ...
8/40 = 1/5 = 0.20 . . . p(green)
Answer:
B 0.2
Step-by-step explanation:
First find out how many marbles are in total
16 + 8 + 6 + 9 + 1 = 40
Then simply divide the number of green marbles by the total.
8 / 40 = 0.2
What is 2 ½ divided by ½ equal too
Answer:
it woulb be 1.25
is 5/9 x 5/5 greater than, less than, or equal to 5/9
Answer:
Equal to
Step-by-step explanation:
5/5 is another way of saying 1
so you do 5/9 times 1
and you get 5/9
What is the remainder to the following polynomial division problem?
(x^2+ 6x + 5) / (x + 2)
Answer:
I think it is -3
Step-by-step explanation:
x+4-(3/x+2) is the answer I got
Part B: Which box-and-whisker plot displays
Mario's data?
Brainliest quick
Answer:
Step-by-step explanation:
i think it's D i have the same test today
Answer:
C cause it has to be 54 then the median is 58
Step-by-step explanation:
use the table to write a proportion.
Answer:
22
Step-by-step explanation:
Hey yall I really need some help; Image attached below
- 50 points
Answer:
YAY an answer got deleted so i can add mine!
Step-by-step explanation:
like i said the answer is 72m2
to find the area you multiply 48 by 1.5
48 x 1.5 = 72
Please find the area of of the shaded polygon
Answer:
8
Step-by-step explanation:
The Arc Electronic Company had an income of 7676 million dollars last year. Suppose the mean income of firms in the same industry as Arc for a year is 9090 million dollars with a standard deviation of 77 million dollars. If incomes for this industry are distributed normally, what is the probability that a randomly selected firm will earn more than Arc did last year
Answer:
0.9772 = 97.72% probability that a randomly selected firm will earn more than Arc did last year
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Suppose the mean income of firms in the same industry as Arc for a year is 90 million dollars with a standard deviation of 7 million dollars.
This means that [tex]\mu = 90, \sigma = 7[/tex]
What is the probability that a randomly selected firm will earn more than Arc did last year?
Arc earned 76 million, so this is 1 subtracted by the pvalue of Z when X = 76.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{76 - 90}{7}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
1 - 0.0228 = 0.9772
0.9772 = 97.72% probability that a randomly selected firm will earn more than Arc did last year
An amount of $41,000 is borrowed for 7 years at 7.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Fred buys 16 bags of tortilla chips and 28 jars of salsa dip. What is the ratio of salsa jars to bags of tortilla chips? Simplify your answer.
here's a graph of a linear function write the equation that describes that function
Answer:
y=3/4x+2
Step-by-step explanation:
The volume length and breadh of a
cuboid are 60cm3, 5cm, 4cm then it
height is
Answer:
3cm
Step-by-step explanation:
volume of cuboid =length × base × height
so height will be
volume divided length ×base
v=60cm^3
lenght=5cm
base=4cm
h= 60 ÷(5×4)
h= 60÷20
h= 3cm
remember that cm^3 will cancel one time with 5cm and second time 4cm and leave you with cm
A sports announcer states that there are 65,000 fans in the stadium. Estimate the maximum noise level. Is this estimate reasonable? Explain your reasoning.
Question:
The scatter plot shows the maximum noise level when different numbers of people are in a stadium. The linear model is given by the equation y=1.5x + 22.7 where y represents maximum noise level and x represents the number of people, in thousands, in the stadium.
A sports announcer states that there are 65,000 fans in the stadium. Estimate the maximum noise level. Is this estimate reasonable? Explain your reasoning.
Answer:
[tex]y = 97522.7[/tex]
Step-by-step explanation:
Given
[tex]y = 1.5x + 22.7[/tex]
[tex]x = 65000[/tex]
Required
Find y
Substitute 65000 for x in the given equation
[tex]y = 1.5 * 65000 + 22.7[/tex]
[tex]y = 97500 + 22.7[/tex]
[tex]y = 97522.7[/tex]
It is reasonable because as the population increases, the noise level also increases
PLEASE HELP!!!!!!!!!! Which list of numbers is ordered from smallest magnitude to largest magnitude?
3.0.1-10]. 1-221
0.3.1-101.1-221
|-221.1-10.30
1-221.1-10.0.3
Answer:
the second one, 0,3,|-10|,|-22|
Step-by-step explanation:
The question is asking for the order smallest to largest. When a number is placed in absolute value, | |, it automatically becomes a positive number.
With that said, 0 is the smallest and 22 is the greatest.
hi good day plss help me plssssssssss i need yoyre help now plss
Answer:
6.c 7.c 8. b 9. a 10. a
Step-by-step explanation:
6=c as 39.10-19.56
7. 89.2-78.6
8. 8.03-5.1
9. 40.98-15.6
10.55.6-47.5
What is the area of the triangle below?
20 square units
15 square units
7.5 square units
30 square units
Answer:
7.5 square units
Step-by-step explanation:
Base of the triangle = 5 units
Height of the triangle = 3 units
Area of the triangle
[tex] = \frac{1}{2} \times base \times height \\ \\ = \frac{1}{2} \times 5 \times 3 \\ \\ = \frac{1}{2} \times 15 \\ \\ = 7.5 \: {units}^{2} [/tex]
Answer:
7.5
Step-by-step explanation:
ok this is a math question if you don't know anything about this go away.
3. A volleyball coach plans her daily practices to include 10 minutes of stretching, 2/3 of the entire practice scrimmaging, and the remaining practice time working on drills of specific skills. On Wednesday, the coach planned 100 minutes of stretching and scrimmaging. How long, in hours, is the entire practice?
Answer:h
Step-by-step explanation:
F
convert 9,78 h to hours, minutes and seconds
In an arithmetic sequence (Sn=n^2 -2n) .USE formula (Tn=Sn-Sn-1) to determine Tn
Answer:
Tn=-1
Step-by-step explanation:
Please mark as brainliest
1. If you earn $15 an hour and you work 35 hours a week, how much do you earn in 4 weeks?
Answer:
$2100
Step-by-step expla35 x 4 = 140 140 x 15 = 2100