A spherical balloon is being inflated at a rate of 8 cm³s-1. Find the rate of change of the surface area when the radius is 10 cm.
Answers
Answer:
1.6
Step-by-step explanation:
Firstly, we know the rate of change of volume \(v'=8\).
The equation for surface area is: \(A = 4\pi r^2\).
The derivative (rate of change) is then: \(A'=8\pi r*r'\)
The equation of the volume of a sphere is: \(V=\frac{4}{3}\pi r^3\).
The derivative (rate of change) is then: \(V' = 4\pi r^2 * r'\).
This means that \(r'=\frac{V'}{4\pi r^2}\).
We can then plug that into our equation for \(A'\) and get:
\(A'=8\pi r*\frac{V'}{4\pi r^2}=2*\frac{V'}{r}\)
After that, we can just plug in:
\(2*\frac{8}{10}=1.6\)
Related Questions
Consider the probability statements regarding events A and
B below.
P(A or B) = 0.3
P(A and B) = 0.2
P(AB) =0.8
What is P(B)?
A) 0.1
B) 0.375
C) 0.25
D) 0.667
Answers
The calculated value of the probability of B is (c) 0.25
How to calculate the probability of BFrom the question, we have the following parameters that can be used in our computation:
P(A or B) = 0.3
P(A and B) = 0.2
P(A/B) =0.8
First, we have
P(A/B) = P(A and B)/P(B)
Substitute the known values in the above equation, so, we have the following representation
0.2/P(B) = 0.8
So, we have
P(B) = 0.2/0.8
Evaluate
P(B) = 0.25
Hence, the probability of B is 0.25
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a truck with a gross weight of 30,000 pounds is parked at a slope of 5 degrees. calculate the force required to keep the truck from rolling down the hill
Answers
Answer:
The force required is 6000
Step-by-step explanation:
rewrite the function f(x)=-3(x+3)^2-13
in the form f(x)=ax^2+bx+c
Answers
Answer:
-3x^2-18x-40
Step-by-step explanation:
(x+3)^2: x^2+6x+9
= -3(x^2+6x+9)-13
Expand:
-3(x^2+6x+9): -3x^2-18x-27
= -3x^2-18x-27-13
Final Answer: -3x^2-18x-40
Answer:
-3x^2-18x-40
Step-by-step explanation:
-3(x+3)^2-13
-3(x^2+6x+9)-13
-3x^2-18x-27-13
-3x^2-18x-40
Americans are stressed out!
A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a
significant source of stress for me." To help form an estimate, the psychologist randomly selected 664
Americans and found that 69.6% of the sample agreed with the statement "the future of the nation is a
significant source of stress for me."
Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the true
proportion of all Americans that say the "the future of the nation is a significant source of stress for me."
Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.
The margin of error is given by E:
A 99% confidence interval is given by:
Answers
To find the margin of error, we can use the formula: E = z√((p(1-p))/n)
How is margin of error determined?where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.
From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.
Plugging in the values, we get:
E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385
So the margin of error is 0.0385.
To find the confidence interval, we can use the formula:
p ± E
where p is the sample proportion and E is the margin of error.
Plugging in the values, we get:
0.696 ± 0.0385
So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].
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brainliest to correct answer, please hurry
Answers
Start at 3, subtract 5 and you get -2
find the maximum and minumum of f(x) =\(f(x) =2\sqrt{x} -3\sqrt[3]{x}\) on interval [0,4]
this is math pls dont take it down
Answers
Answer:
1/27 at (x.y)= (1/3, 1,3)
Step-by-step explanation:
Hope this helps:)
Represent "sum of a number and five" algebraically? (Use n to represent "a number")
Answers
The algebraic representation of "sum of a number and five" can be written as
n + 5
Where n represents the "number".
In mathematics, an algebraic representation is a way of expressing a mathematical relationship or equation using symbols, letters, and mathematical operations. It is a symbolic representation of a mathematical expression or equation that allows us to work with abstract concepts and manipulate them according to certain rules.
For example, the equation y = 2x + 1 is an algebraic representation of a linear function, where y and x represent variables and 2x + 1 is an expression that relates them. Algebraic representations are often used in algebra, calculus, and other areas of mathematics to describe relationships between quantities, solve equations, and make predictions based on mathematical models.
Hence, the algebraic representation of "sum of a number and five" can be written as
n + 5
Where n represents the "number".
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7a+1+3=18
Please answer quickly!
Answers
Answer:
2
Step-by-step explanation:
So we have the equation:
\(7a+1+3=18\)
Add 1 and 3:
\(7a+4=18\)
Subtract 4 from both sides:
\(7a=14\)
Divide both sides by 7:
\(a=2\)
And we're done!
combine like terms.
7a+4=18
subtract 4 from 18
7a=14
divide 14 by 7
a=2
Please answer quickly!
THIS IS DUE IN 10 MINUTES I WILL AWARD BRAINLIEST
fill in the chart
Answers
percent row: 120% 0.03% 15%
Decimal row: 1.2 0.0003 0.15
Fraction row: 12/ 10 3/10000 3/20
1) Three runners run 100 yards race. Sara runs the
race in 9.25 seconds. Alex runs the race in 8.625
Seconds and Tonya runs the race in 9.8 seconds. Who
has the winning time?
Answers
The person that has the winning time is Alex.
How to know the person with winning time?From the information given, three runners run 100 yards race. Sara runs the race in 9.25 seconds and Alex runs the race in 8.625 seconds and Tonya runs the race in 9.8 seconds.
It should be noted that in a race, the person that has the lowest time wins.
In this situation, the person with 8.625 seconds is the lowest.
Therefore, Alex wins.
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Evaluate x/y for x = 3/10 and = 4/5
A: 7/50
B: 7/15
C: 3/8
D: 12/50
Answers
Answer:The correct anserw is B.
Step-by-step explanation:
FOR 100 POINTS!!!!!!!!!!!
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 29 41
Does not like burritos 54 135
Total 110 205
Part A: What percentage of the survey respondents liked neither hamburgers nor burritos? Show all work. (3 points)
Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)
Part C: Is there an association between liking burritos and liking hamburgers? Use ratios of joint and marginal frequencies to support your answer. (4 points)
Answers
Answer:
Part A:
To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.
Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135
Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54
Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189
Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100
Percentage = (189 / 205) x 100 = 92.2%
Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.
Part B:
To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.
Frequency of "Likes hamburgers" = 110 (given)
Total respondents = 205 (given)
Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents
Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%
Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.
Part C:
To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.
Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)
Marginal frequency of "Likes hamburgers" = 110 (given)
Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)
To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:
Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")
Ratio = 29 / (110 x 70)
Ratio ≈ 0.037 (rounded to three decimal places)
I NEED ANSWER ASAP PLEASE WITH WORK PLEASE AND TY!!!!!! In the image the question is 32!! What is the factored form of x2 + 12x - 64?
A (x-4)(x + 16)
B. (x-2)(x + 32)
C. (x + 4)(x - 16)
D. (x-6)(x + 18)
Answers
Answer:
A) (x-4)(x+16)
Step-by-step explanation:
\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)
Determine the slope of the line passing through (-8,-5) and (-10,-9)
Answers
Answer:
2
Step-by-step explanation:
y1-y2/x1-x2
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
I thought of a number n I multiplied it by 6. I added 19. I got 29 more than my number. Equation
Answers
Answer:
6n + 19 = 29 + n
n = 2
Step-by-step explanation:
your number = n
multiplied by n by 6 (6 * n or 6n)
6n then add 19 (6n +19)
29 more than my number = 29 + n
add it all together:
6n + 19 = 29 + n
when you solve, n = 2
Given a total-revenue function R(x) = 700/x? - 0.2x and a total-cost function 1 3 C(x) = 1400(x² + 2) +600, both in thousands of dollars, find the rate at which total profit is changing when x items have been produced and sold. P'(x) =
Answers
Answer:
Step-by-step explanation:
abcdefghijklmnopqrstuvwxyz
For what value of y does 125=(1/25)^(y-1)?
Answers
Answer:
y = -1/2 is the answer to 125=(1/25)^(y-1)
Question 3(Multiple Choice Worth 3 points)
(01.04 LC)
Which of the following expressions is equivalent to 2x +4? (The x+4 is to the power of x)
A) 8(2) ^x
B) 2^x/8
C) 16(2)^x
D) 2^x/16
Answers
The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)
Which expression is equivalent to the expressionFrom the question, we have the following parameters that can be used in our computation:
2ˣ⁺⁴
The above expression is an exponential expression with the following properties
Base = 2Exponent = x + 4When the above expression is expanded, we have
2ˣ⁺⁴ = 2ˣ * 2⁴
Evaluate the expression 2 exponent 4
So, we have the following representation
2ˣ⁺⁴ = 2ˣ * 16
Rewrite as follows
2ˣ⁺⁴ = 16 * 2ˣ
This gives
2ˣ⁺⁴ = 16(2ˣ)
Hence, the expression that is equivalent to the expression is 16(2ˣ)
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pls helppppp with my math
Answers
Answer:
\(\frac{1}{6}\)
Step-by-step explanation:
Answer:
Step-by-step explanation:
\(\frac{5}{6}-\frac{2}{3}=\frac{5}{6}-\frac{2*2}{3*2}\\\\=\frac{5}{6}-\frac{4}{6}\\\\=\frac{5-4}{6}\\\\=\frac{1}{6}\)
PLEASE HELP AND EXPLAIN HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST!!
Answers
The sequence of transformations that transform the the pre-image and the congruence of the pre-image and image are indicated by the option D.
D. Reflection, then rotation results in an image that is congruent to the original
What is a transformation of a geometric figure?A transformation is the performance of a rotation, reflection, translation, or dilation, that produces an image with a different size, location, orientation or shape.
The coordinates of the points on the triangle ABC are laterally equidistant from the vertical line in the middle between the triangles ABC and triangle DEF, such that the line in the middle is the line of reflection.
The vertical height of the coordinates of the triangle ABC and DEF, which are the same indicates that the transformation from triangle ABC to EFD is a reflection across the line in the middle between the two triangles. The side GH in triangle IGH corresponds to the side EF in the triangle EFD,
The length of GH = EF = 4 units
Similarly, IH = DE, and IG = DF, therefore;
Triangle EFD and triangle HGI are congruent by SSS congruence rule
The orientation of the side EF of the triangle EFD which is vertical and the side HG which is horizontal indicates a rotation of the triangle EFD by 90 degrees to obtain the triangle HGI
The correct option is therefore, the option D.
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The certain article reported that, in a study of a particular wafer inspection process, 150 dies were examined by an inspection probe and 85 of these passed the probe. Assuming a stable process, calculate a 95% confidence interval for the proportion of all dies that pass the probe.
Answers
Answer:
95% of confidence intervals for the proportion of all dies that pass the probe.
(0.4867 , 0.6453)
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 150
The sample proportion
\(p = \frac{x}{n} = \frac{85}{150} = 0.566\)
Level of significance = 0.05
The critical value Z₀.₀₅ = 1.96
Step(ii):-
95% of confidence intervals for the proportion of all dies that pass the probe.
\((p^{-} - Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p^{-} + Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} })\)
\((0.566 - 1.96\frac{\sqrt{0.566(1-0.566)} }{\sqrt{150} } , 0.566 + 1.96\frac{\sqrt{0.566(1-0.566)} }{\sqrt{150} })\)
( 0.566 - 0.0793 , 0.566 + 0.0793)
(0.4867 , 0.6453)
Conclusion:-
95% of confidence intervals for the proportion of all dies that pass the probe.
(0.4867 , 0.6453)
The length of a rectangle is 5 cm more than its width. If the perimeter is 58cm, calculate:
(a) Write an equation to show the perimeter of the rectangle ?
(b) calculate:
I.width
II.length
III. the area of the rectangle
Answers
The equation to show the perimeter of the rectangle is P = 2(2w + 5)
Writing an equation to show the perimeter of the rectangleFrom the question, we have the following parameters that can be used in our computation:
Length = 5 more than the width
Also, we have
Perimeter = 58
This means that
P = 2(w + 5 + w)
P = 2(2w + 5)
Calculating the dimensions and the areaIn (a), we have
P = 2(2w + 5)
This gives
2(2w + 5) = 58
So, we have
2w + 5 = 29
2w = 24
w = 12
Next, we have
l = 12 + 5
l = 17
Lastly, we have
Area = 17 * 12
Area = 204
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Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count.
Imari saw 42 sparrows.
How many birds did he count in all?
Enter your answer in the box.
Answers
Step-by-step explanation:
step 1. 42 represents 35% of the birds.
step 2. 42/.35 = all of the birds counted.
step 3. 42/.35 = 120.
step 4. There are 120 total.
Answer:
120
Step-by-step explanation:
Find the length of side AB. Round to the nearest hundredth inch.
Answers
The value of length of side AB is,
⇒ AB = 5 units
We have to given that;
The figure is shown a trapezoid.
Hence, By using Pythagoras theorem we get;
⇒ AB² = 4² + (5.25 - 2.25)²
⇒ AB² = 16 + 3²
⇒ AB² = 16 + 9
⇒ AB² = 25
⇒ AB = √25
⇒ AB = 5 units
Therefore, The value of length of AB is,
⇒ AB = 5 units
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Solve for x: 3(x + 1) = −2(x − 1) + 6. (1 point)
1
4
5
25
Answers
Answer: 1
Step-by-step explanation:
You are welcome :)
20 + 60 ÷ 5 + (9 - 4)2
Answers
Answer:
42
Step-by-step explanation:
20 + 60 ÷ 5 + (9-4)2
Use PEMDAS to solve this equation, so first solve what is in the parentheses
20 + 60 ÷ 5 + (5)2
Since there are no exponents, next solve the multiplication
20 + 60 ÷ 5 + 10
Next is division
20 + 12 + 10
Finally, addition
42
Could you please help me solve this question?
Answers
(g) Every student of class IV donated as much money as their number to make a fund for landslide, If there are 68 students in class IV how much money did they collect?
Answers
Answer:$2346
Step-by-step explanation: Assuming that the students' numbers start at 1, we have 1+2+3+4.....+65+66+67+68 as the total amount of money raised. We can see that 1+68 = 69 and 2+67 also equals 69. So, we can use this method to figure out how many 69s are in the sum. Since 68 divided by 2 is 34, there are 34 69s in the sum. 34x69 = 2346.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.
(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.
(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.
(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
The triangle similarity criteria are:
AA (Angle-Angle)SSS (Side-Side-Side)SAS (Side-Angle-Side)(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.
12/8 = 9/6
1.5 = 1.5
(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.
(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.
14/10 = 21/15
1.4 =
(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.
SMK = 90⁰, 60⁰, 30⁰
QTR = 90⁰, 30⁰, 60⁰
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x(x-4) if x =4 what is the answer
Answers
We plug the value on the expression, then:
\(4(4-4)=4(0)=0\)Therefore the answer is 0.
Answer:
0
Step-by-step explanation:
replace every x with 4
4(4-4)
4(0)
0