Answer:
The volume of the cylinder is decreasing at a rate of 83629.2 m³/h.
Step-by-step explanation:
The volume of a is given by:
[tex] V = \pi r^{2}h [/tex]
Where:
r: is the radius = 55 m
h: is the height = 88 m
We can express the rate of change of the volume of the cylinder as follows:
[tex] \frac{dV}{dt} = \pi[h\frac{2rdr}{dt} + r^{2}\frac{dh}{dt}] [/tex]
If dr/dt = 11 m/h and dh/dt = -44m/h, we have:
[tex] \frac{dV}{dt} = \pi[88 m*2*55 m*11 m/h + (55 m)^{2}*(-44 m/h)] = -83629.2 m^{3}/h [/tex]
Therefore, the volume of the cylinder is decreasing at a rate of 83629.2 m³/h.
I hope it helps you!
Express your answer as a polynomial in standard form.
f(x) = x² – 3x + 9
g(x) = 5x – 9
Find: (gof)(x)
Answer:
Answer:
g(f(x)) = 5x^2 - 15x + 36
Step-by-step explanation:
f(x) = x² – 3x + 9
g(x) = 5x – 9
(g o f)(x)
g(f(x))
x = f(x) = x^2 - 3x + 9
g(x^2 - 3x + 9)
= 5(x^2 - 3x + 9) - 9
g(f(x)) = 5x^2 - 15x + 36
What is the slope of the line that contains these points?
Answer:
[tex]m=7[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Find points from chart.
Point (-7, -7)
Point (-4, 14)
Step 2: Find slope m
Substitute: [tex]m=\frac{14+7}{-4+7}[/tex]Add: [tex]m=\frac{21}{3}[/tex]Divide: [tex]m=7[/tex]Answer:
[tex]\boxed {\boxed {\sf m=7}}[/tex]
Step-by-step explanation:
To find the slope, we can use the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are points on the line.
We can pick any two points in the chart.
Let's use (-1, 35) and (2,56).
If we use these points, then the variables are:
[tex]x_1=-1 \\y_1=35 \\x_2=2 \\y_2=56[/tex]
Substitute the values into the formula.
[tex]m=\frac{56-35}{2--1}[/tex]
Solve the numerator.
56-35=21[tex]m=\frac{21}{2--1}[/tex]
Solve the denominator.
2--1= 2+1=3[tex]m=\frac{21}{3}[/tex]
Divide.
[tex]m=7[/tex]
The slope of the line is 7
What is the sales tax rate? *
Answer:
depends for each state
Step-by-step explanation:
How do I figure out the sales tax?
Calculating Total Cost. Multiply the cost of an item or service by the sales tax in order to find out the total cost. The equation looks like this: Item or service cost x sales tax (in decimal form) = total sales tax. Add the total sales tax to the Item or service cost to get your total cost.
NEED HELP ASAP PLS!!
(08.03) Consider the following pair of equations:
y = 3x + 3
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Answer:
(1,0)
Step-by-step explanation:
1. x - 1 =3x+3
2. 3x - x = 2x
3. -1+ 3 = 2
4. 2x = 2
5. 2/2 = 1
x = 1
6. 1-1 = 0
y = 0
(1,0)
Students from Texas, New York, Washington, Florida, and Utah identified their area of concentration at various universities. The results are listed in the table.
One of these students is selected at random. What is the probability that the student is from the state of Washington under the condition that the student studies history?
Enter a number in the box.
The probability of a random student who is from Washington and studies history is [tex]\frac{5}{33}[/tex].
What is probability?Probability is the chance of happening an incident or event. A probability is calculated by the ratio of the possible outcomes to total number of outcomes.
Given, the total number of students of History
= (30 + 17 + 20 + 32 + 33) = 132
The number of students from Washington who studies history = 20.
Therefore, the probability that the student is from the state of Washington under the condition that the student studies history is = [tex]\frac{20}{132} = \frac{5}{33}[/tex] .
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1. A statistician calculates that 8% of Americans are vegetarians. If the statistician is correct, what is the probability that the proportion of vegetarians in a sample of 569 Americans would be greater than 9%?2.The mean points obtained in an aptitude examination is 166 points with a standard deviation of 19 points. What is the probability that the mean of the sample would differ from the population mean by less than 1.1 points if 66 exams are sampled?
Answer:
1) the probability that the proportion of vegetarians in the sample would be greater than 9% is 0.1902
2) the probability that the mean of the sample would differ from the population mean by less than 1.1 points in the is 0.3616
p( /x" - u/ < 0.47 ) = 0.3616
Step-by-step explanation:
1)
Given that;
p = 8% = 0.08 and n = 569
what is the probability that the proportion of vegetarians in a sample of 569 Americans would be greater than 9% (0.09)
that is;
p( p" > 0.09) = ?
p( p" > 0.09) = p( z > [(0.09 - 0.08)/(√((0.08(1 - 0.08))/569))] )
= p( z > (0.01 / 0.0114))
= p ( z > 0.8772)
= 0.1902
Therefore the probability that the proportion of vegetarians in the sample would be greater than 9% is 0.1902
2)
Given that;
mean points obtained in an aptitude examination u = 166
standard deviation α = 19
sample size n = 66
x" - u = 1.1
first we say
x-score = (x" - u) / (α/√n) = 1.1 / (19/√66) = 1.1 / 2.3387 = 0.47
p( -0.47 < z < 0.47 )
= p( z < 0.47) - p( z < - 0.47)
= 0.6808 - 0.3192
= 0.3616
Therefore the probability that the mean of the sample would differ from the population mean by less than 1.1 points in the is 0.3616
p( /x" - u/ < 0.47 ) = 0.3616
On Friday, a local hamburger shop sold a combined total of 436 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number
of hamburgers sold. How many hamburgers were sold on Friday?
The ages of three teachers are consecutive even integers. Three times the age of the youngest teacher is 48 years more than the older teacher’s age. What is the age of the youngest teacher?A.14 B.18 C.22 D.26
Answer:
B
Step-by-step explanation:
The total number of carbohydrate grams per serving is missing from the nutrition label of Cade's box of cereal. However, the label indicates that a serving of cereal provides 7% of the recommended daily amount. Cade checked online and found that the recommended amount of carbohydrate is 300 grams. Based on this information how many grams of carbohydrates are in Cade's cereal?
Answer:
21 grams so the second answer choice
Step-by-step explanation:
300*.07=21
How many lines of symmetry does this figure have?
[Note: The black ball is part of the figure.]
A) 0
B) 1
C) 5
D) 10
Answer:
The answer is B) 1
Step-by-step explanation:
balls
remove it please......
what do you need removing? I'll try to help
4. Tom and Bina read 34 books in a month. Bina and Weiming read 58 books in the
same month. Weimning read twice as many books as Tom. How many books did
Bina read in that month?
Answer:
92
Step-by-step explanation:
the question is only asking how many books Bina read, so the amount of books Weimning read is irrelevant.
to get the answer, you have to add both the amount of books bina read in the month.
hope this helped :)
Explain the difference between a greatest common factor and a least common multpule
Answer:
The Greatest Common Factor, the GCF, is the biggest ("greatest") number that will divide into (that is, the largest number that is a factor of) both 2940 and 3150. On the other hand, the Least Common Multiple, the LCM, is the smallest ("least") number that both 2940 and 3150 will divide into.
Have a good day
A triangle with side lengths of 10, 18, and 30 inches is similar to another triangle. The shortest side of the other triangle has length 3 inches. What is the perimeter, in inches, of the smaller triangle?
Perimeter = 9.5
Perimeter = 10.6
Perimeter = 15.2
Perimeter = 17.4
Answer:
wo similar figures have a ratio of 3:5. If 1 side of the smaller figure is 9 ... 12 in. What is the length of LM? x. = 12. 24. A. 13 in. C. 16 in. A. 10 ft. B. 14.4 ft ... How long is the corresponding side of the larger polygon? A. 18 cm. B. 24 cm ... 2. 10. An equilateral triangle has side lengths of 14 inches. Find the altitude of the
Step-by-step explanation:
The perimeter of the smaller triangle will be 17.4. Then the correct option is D.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
A triangle with side lengths of 10, 18, and 30 inches is similar to another triangle.
The shortest side of the other triangle has a length of 3 inches.
Then the perimeter of the smaller triangle will be
Let the other two sides of the smaller triangle be x and y. Then we have
3/10 = x/18 = y/30
From the first two terms, we have
3/10 = x/18
x = 5.4 inches
Then from the first and third terms, we have
y/30 = 3/10
y = 9
Then the perimeter of the triangle will be
P = 3 + 5.4 + 9
P = 17.4 inches
More about the triangle link is given below.
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add on sc alawad2003
Answer:
Mkay?
Step-by-step explanation:
Numbers Of pizza to order
What is the slope of the line
Five friends want to share 1,000
comic books equally. Can you use mental math find how many
comic books each friend will get?
Answer:200
Step-by-step explanation:
Help plzz! 13 points and will give brainliest!
Answer: This is rly confusing
Step-by-step explanation:
if two dice are rolled one time, find the probability of getting a sum less than or equal to 4
Answer:
The probability of getting a sum less than or equal to 4 is 1/6.
Step-by-step explanation:
When two dices are rolled, the number of outcomes are: 6*6 = 36 which is written in ordered pairs consisting of outcome of both dices.
When two dices are rolled, the number of sample space elements is:
[tex]n(S) = 36[/tex]
Let A be the event that the sum of outcomes is less than or equal to 4:
[tex]A = \{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)\}[/tex]
That implies
[tex]n(A) = 6[/tex]
The probability of getting sum less than or equal to 4 will be:
[tex]P(A) = \frac{n(A)}{n(S)} = \frac{6}{36} = \frac{1}{6}[/tex]
Hence,
The probability of getting a sum less than or equal to 4 is 1/6
The probability of getting a sum less than as well as equivalent to 4 will be "[tex]\frac{1}{6}[/tex]".
Probability:The probability that may be an outcome will happen together in random experiment. The greater the likelihood of such an occurrence, the further probable it will materialize.
Let,
The event that the sum less than as well as equivalent to 4 be "A".
According to the question,
Whenever the 2 dices are rolled, the no. of outcomes will be:
= 6 × 6
= 36
and,
The no. of sample elements will be:
n(S) = 36
Now,
A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)}
The probability be:
→ P(A) = [tex]\frac{n(A)}{n(S)}[/tex]
= [tex]\frac{6}{36}[/tex]
= [tex]\frac{1}{6}[/tex]
Thus the response above is correct.
Find out more information about probability here:
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what is a correlation co-efficient?
Answer:
Correlation coefficients are used when you are doing statistics to find or measure how strong a relationship is between two variables.
Step-by-step explanation:
P(A) = 0.8, P(B) = 0.55 and P(A and B) = 0.35.
What is P(A or B)?
Work Shown:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.8 + 0.55 - 0.35
P(A or B) = 1.35 - 0.35
P(A or B) = 1
A probability of 1 means there is 100% certainty the event happens. This must mean that there are only possible outcomes are: either event A happens, or B happens, or possibly both A and B happen simultaneously.
What’s is the rate of change for the line that goes through the points (8,14) and (11,19.25)
Answer:
Rate of Change / Slope = 1.75 (or 7/4)
Step-by-step explanation:
Slope is Rise/Run which is (y2-y1)/(x2-x1). When we plug in both ordered pairs, we get (19.25-14)/(11-8)=5.25/3=1.75 as the slope.
The rate of change is the ratio of the rise and the run of the line. Hence, the rate of change of the line is 1.75
Rate of change = (Rise / Run)Rise = y2 - y1 = (19.25 - 14) = 5.25
Run = x2 - x1 = (11 - 8) = 3
Rate of change = (5.25 / 3) = 1.75
Therefore, the rate of change for the line is 1.75
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the point that doesn't lie to a straight line y=-4x+12 is
Answer:
12?
Step-by-step explanation:
Elizabeth spins each spinner once.
What is the probability the arrows will land on a consonant and the number 2?
20% is the answer
Hope this helps
Congo 2920 miles, yenisei 5512 kilometers, which is longer and by how much
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Answer:
yenisei is longer by 812.716 kilometers
Step-by-step explanation:
2920/.621371
=4699.284 kilometers
5512- 4699.284
= 812.716
yenisei is longer by 812.716 kilometers
Pls help with part b
Answer:
any number to the power of 0
Step-by-step explanation:
Any number to the power of 0 will be equal to 1.
[tex](1)^{0} (109)^{0} (-16.9)^{0\\}[/tex]
Any of those would work.
A rock is thrown upward with a velocity of 17 meters per second from the top of a 31 meter high cliff and it missies the cliff on the way back down when will the rock ve 8 meters from the ground level
Answer:
[tex]4.5\ \text{s}[/tex]
Step-by-step explanation:
t = Time taken
u = Initial velocity =17 m/s
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity = 9.81 m/s² = a
[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-17^2}{2\times -9.81}\\\Rightarrow s=14.73\ \text{m}[/tex]
Total height the rock is to fall when it is 8 meters from the ground is [tex]14.73+(31-8)=37.73\ \text{m}[/tex]
[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17}{-9.81}\\\Rightarrow t=1.73\ \text{s}[/tex]
Time taken to reach the maximum height is 1.73 s.
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 37.73=0+\dfrac{1}{2}\times 9.81t^2\\\Rightarrow t=\sqrt{\dfrac{37.76\times 2}{9.81}}\\\Rightarrow t=2.77\ \text{s}[/tex]
Time taken from the maximum height to the point which is 8 m from the ground is 2.77 s.
So, time taken from the moment of the throw to the point 8 m from the ground is [tex]1.73+2.77=4.5\ \text{s}[/tex].
A building is 1ft from an 11 ft fence that surrounds the property. A worker wants to wash a window in the building 14ft from the ground. He plans to place a ladder over the fence so it rests against the building. He decided he should place the ladder 11ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?
Answer:
L = 18,4 ft
Step-by-step explanation:
The building, the ground, and the ladder make up a right triangle, with legs:
The distance (a) between the bottom of the ladder and the building 12 ft
The distance (b) between the gound and the window 14 ft up
The hypothenuse is the length of the ladder (L)
According to Pythagoras theorem
L² = a² + b²
L = √ (12)² + (14)²
L = √ 144 + 196
L = √ 340
L = 18,4 ft
PLEASE HELP!!!!! PEOPLE ARE GETTING THEM WRONG FOR ME!!!
Answer:
18 lawns
Step-by-step explanation:
Lets take the number of lands that would be mow(ed) in 36 hours as x
Hence,
[tex]Thriugh\ the\ proportion\ method\ , we\ get\ \\\\3 : 6::x:36\\36*3=6x\\\frac{36*3}{6} =x\\\frac{108}{6}=x\\x=18[/tex]
4.9 divided by 3581.9
Just help me
Answer:
.00136799
Step-by-step explanation:
4.9/3581.9 into a calculator
Answer:
.00136798905
Step-by-step explanation:
Used a calculator!