To calculate the volume of a cylinder with a diameter of 28 units and a height of 28 units, use the formula V = πr²h. The calculated volume is approximately 17240.896 cubic units.
To find the volume of a cylinder, we use the formula:
V = πr²h
Here, the diameter of the cylinder is 28 units. To find the radius, we divide the diameter by 2:
r = 28 / 2 = 14 units
The height of the cylinder is given as 28 units. Substituting the values into the formula, we get:
V = π × (14)² × 28
V = π × 196 × 28
V = 5488π
Using the approximation π ≈ 3.142,
V ≈ 5488 × 3.142 ≈ 17240.896 cubic units
Therefore, the volume of the cylinder is approximately 17240.896 cubic units.
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You are traveling to Chicago for a job interview. You leave Toledo, Ohio, at 5:45 A.M. and arrive in Elkhart, Indiana, at 8:15 A.M.. The distance from Toledo to Elkhart is 136 miles; the distance from Toledo to Chicago is 244 miles. The speed limit is 65 mph. What is the minimum speed you must maintain in order to arrive in Chicago before 10:30 A.M.
which equation is shown in the graph?
y = [[x]]
y = [[x + 3]]
y = [[x]] - 3
y = |x - 3|
Find m/AEB
A.
10
B.
70
C.
110
D.
170
in a class of 32 students 11 are men what fraction of the students are men
11 - men 32 - students
So, 11/32 is the fraction.
The answer couldn't be simplified because 11 is a prime number.
If f(x)=4x-6 and g(x) =2x find f(x) •g(x)
Quan Le needs $203 to pay for the cost of an evening class. He has $37 and plans to borrow the rest from his brother. Round each amount to determine about how much he needs to borrow? Check your answer using the inverse operation.
if the surface area of two smilar spheres is 256 feet and 576 feet, what is the ratio of the volume of the smaller sphere to the volume of the largee sphere
The ratio of the volume of the smaller sphere to the volume of the larger sphere, given their surface areas are 256 ft² and 576 ft², is 8:27.
The student has asked about finding the ratio of the volumes of two similar spheres given their surface areas. The surface areas are 256 ft² and 576 ft². To find the volume ratio, we need to use the fact that the ratio of the surface areas of similar spheres is the square of the ratio of their radii, and thus the ratio of the volumes will be the cube of the ratio of their radii.
Let's denote the surface areas as S₁ and S₂, and the volumes as V₁ and V₂. Then, S₁:S₂ = (radius of smaller sphere)² : (radius of larger sphere)² and V₁:V₂ = (radius of smaller sphere)³ : (radius of larger sphere)³.
First, we find the square root of the surface area ratios: [tex]\sqrt{\frac{256}{576} }[/tex] = [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex]. Then, taking the cube of [tex]\frac{2}{3}[/tex] gives us the volume ratio V₁:V₂ = [tex](\frac{2}{3} )^3[/tex] = [tex]\frac{8}{27}[/tex].
Therefore, the ratio of the volume of the smaller sphere to the volume of the larger sphere is 8:27.
Circle 1 is centered at (5,8) and has a radius of 8 cm. Circle 2 is centered at (1,-2) and has a radius of 4cm. The circles are similar because you can translate circle 1using the transformation rule (___,___) and then dialate it using a scale factor of (___).
Find the number of ways that an organization consisting of 15 members can elect a president, a treasurer, and q secretary. (assuming no person is elected to more than one position)
Total Members = 15
For electing present number of members = 15
For electing treasurer the numbers of members =14
For electing secretary the numbers of members =13
Find the numbers of possible ways for election of members= ?
Possible ways for election =15*14*13
=2730
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Select the graph of the equation below.
y=3/2x^2 + 4x - 2
which of the following statements is false?
A. 2 is greater than or equal to 8
B. 2 is less than or equal to 8
c. 8 is less than or equal to 8
Hey can you please help me posted picture of question
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When designing a building, you must be sure that the building can withstand hurricane-force winds, which have a velocity of 73 mi/h or more. The formula f=0.004av^2 gives the force F in pounds exerted by a wind blowing against a flat surface. A is the area of the surface in square feet, and v is the wind velocity in miles per hour. How much force is exerted by a wind blowing at 81 mi/h against the side of the building shown?
The first step is calculate the surface area of the flat surface shown
Surface area of the rectangle = length * width = 25*12.9 = 322.5 square feet
Surface area of the triangle = 1/2 *base*height = 1/2*25*7.2 = 90 square feet
Total surface area = 322.5 +90 = 412.5 square feet
Total force = 0.004*a*v^2 = 0.004*412.5*81^2 = 10,825.65 pounds
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You have a box of chocolates that contains 59 pieces of which 37 are solid chocolate, 15 are filled with cashews, and 7 are filled with cherries. All the candies look exactly alike. You select a piece, eat it, select a second piece, eat it, and finally eat one last piece. Find the probability of selecting a solid chocolate piece followed by two cherry-filled chocolates. Round your answer to three decimal places.
The probability of selecting a solid chocolate piece followed by two cherry-filled chocolates in sequence is approximately 0.00407.
The question asks for the probability of selecting a solid chocolate piece followed by two cherry-filled chocolates. There are 59 pieces total in the box, with 37 solid chocolates, 15 filled with cashews, and 7 filled with cherries. To calculate the probability, we use the concept of dependent events since each chocolate is eaten before selecting the next, which changes the total number of chocolates available. The probability of choosing a solid chocolate first is 37/59. After eating it, there are 58 pieces left and still 7 cherry-filled chocolates, so the probability of then picking a cherry-filled chocolate is 7/58. Then there would be 57 pieces left and 6 cherry-filled chocolates, so the probability of finally picking a cherry-filled chocolate would be 6/57. To find the total probability of all events happening in sequence, we multiply the individual probabilities together:
Probability = (37/59) * (7/58) *(6/57)
Calculating this gives us the probability, to three decimal places:
Probability = 0.00407
shorty's gross pay last week was $251.20.if her hourly rate was $7.85,how many hours did she works?
A pattern on a quilt is made up of pieces of fabric in the shape of parallelograms. One piece of fabric is shown. What is the area of one piece of fabric? Enter your answer in the box.
Suppose the number of calls per hour to an answering service follows a poisson process with rate 4.
a.what is the probability that fewer than 2 calls came in the first hour?
Given that (-3,7) is on the graph of f(x), find the corresponding point for the function f(x + 5).
Answer: (-8,7)
Step-by-step explanation: It;s right
PLEASE PLEASE HELP ME?!?!!? PLEASSEE I ONLY HAVE 2 QUESTIONS!!!
When the function f(x) = 6(9)x is changed to f(x) = 6(9)x + 1, what is the effect?
Select one:
a. There is no change to the graph because the exponential portion of the function remains the same.
b. All input values are moved 1 space to the right.
c. The x-intercept is 1 space higher.
d. The y-intercept is 1 space higher.
Evaluate fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5 . (5 points)
Select one:
a. 9 to the power of negative 1 over 2
b. 9 to the power of negative 1 over 4
c. 9
d. 92
1. Changing f(x) to f(x) + 1 adds 1 to every output value of the function, moving that value "1 space higher". This is true for the y-intercept, too.
___
2. The rules of exponents apply:
a^b · a^c = a^(b+c)1/a^b = a^-bYou apparently want to simplify ...
... 9^(1/4) × 9^(1/2) / 9^(5/4)
... = 9^(1/4 + 1/2 - 5/4)
... = 9^((1+2-5)/4)
... = 9^(-2/4) = 9^(-1/2)
find the measure of the requested angle. find the complement of 41*
Find the measure of the requested angle. find the complement of 41°.
Solution:
The Sum of Complementary Angles is 90°.
So, Sum of Requested Angle and Given Angle =90°
So,Requested Angle+Given angle=90°
So,Requested Angle+41°=90°
To find, Requested Angle we subtract 41° from both sides,
Requested Angle+41°-41°=90°-41°
Requested Angle+0°=49°
So, Requested Angle=49°
Answer:49°
witch of the following expression is equivalent to the logarithmic expression below. log(3)5/x^2
A)log(3) 5+2 log(3)x
B)log(3) 5-2 log(3)x
C)2 log(3) 5-log(3)x
D)log(3) 5+log(3)x
Answer: The correct option is
(B) [tex]\log_35-2\log_3x.[/tex]
Step-by-step explanation: We are given to select the expression that is equivalent to the following logarithmic expression :
[tex]E=\log_3\dfrac{5}{x^2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following properties of logarithms :
[tex](i)~\log_a\dfrac{b}{c}=\log_ab-\log_ac,\\\\(ii)~\log_ab^c=c\log_ab.[/tex]
From (i), we get
[tex]E\\\\=\log_3\dfrac{5}{x^2}\\\\\\=\log_35-\log_3x^2~~~~~~~~~~~~~~~~~~~~[\textup{Using property (i)}]\\\\\\=\log_35-2\log_3x.~~~~~~~~~~~~~~~~~~~~[\textup{Using property (ii)}][/tex]
Thus, the required equivalent expression is [tex]\log_35-2\log_3x.[/tex]
Option (B) is CORRECT.
for a bake sale violet wants to use the recipe at the right. If she wants to double the recipe, how much flour will she need
Where is the second derivative of y = 4xex equal to 0?
Final answer:
The second derivative of the function y = 4x[tex]e^x[/tex] is equal to zero when x = -2. This is determined by differentiating the function twice, setting the second derivative equal to zero, and then solving for x.
Explanation:
The question is asking for the value of x at which the second derivative of the function y = 4xex is equal to zero. To solve this, we first find the first derivative, which is y'(x) = 4ex + 4x[tex]e^x[/tex] (applying the product rule). Next, we find the second derivative, y''(x) = 4[tex]e^x[/tex] + 4[tex]e^x[/tex] + 4x[tex]e^x[/tex], which simplifies to y''(x) = 8[tex]e^x[/tex] + 4x[tex]e^x[/tex]. Setting this equal to zero to solve for x:
0 = 8[tex]e^x[/tex] + 4x[tex]e^x[/tex]
We factor out ex:
0 = [tex]e^x[/tex](8 + 4x)
The exponential function ex is never zero, so we set the remaining factor equal to zero:
0 = 8 + 4x
By solving for x, we find:
x = -2
Therefore, the second derivative of the function y = 4x[tex]e^x[/tex] is equal to zero when x = -2.
since (3/4)^2=3/4•3/4=9/16 what is the value of 2/5^2
Is writing an equation this way ( 4 x 5 )-9-6 correct? If not why?
These tables of values represent continuous functions. In which table do the values represent an exponential function?
A.
x y
1 3
2 6
3 9
4 12
5 15
B.
x y
1 2
2 6
3 18
4 54
5 162
C.
x y
1 10
2 22
3 34
4 46
5 58
D.
x y
1 7
2 8
3 9
4 10
5 11
Answer:
The correct option is B.
Step-by-step explanation:
A function is called an exponential function if it has common ratio.
A function is called an linear function if it has common difference.
In option A.
[tex]\frac{f(2)}{f(1)}=\frac{6}{3}=2[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]
[tex]2\neq \frac{3}{2}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option A is incorrect.
In option B.
[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=3[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=3[/tex]
[tex]3=3[/tex]
Since the given table has common ratio, therefore it is an exponential function. Option B is correct.
In option C.
[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]
[tex]\frac{11}{5}\neq \frac{17}{11}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option C is incorrect.
In option D.
[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]
[tex]\frac{8}{7}\neq \frac{9}{8}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option D is incorrect.
Answer:
Table B represents an exponential function.
Step-by-step explanation:
An exponential function is a function which has common ratio. Using this fact we will evaluate the functions given in the form of a table.
Table A.
f(1) = 3
f(2) = 6
f(3) = 9
Now [tex]\frac{f(2)}{f(1)}=\frac{6}{3}=\frac{2}{1}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]
Ratios are not equal so it's not an exponential function.
Table B.
f(1) = 2
f(2) = 6
f(3) = 18
[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=\frac{3}{1}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=\frac{3}{1}[/tex]
Here ratios are same therefore it's an exponential function.
Table C.
f(1) = 10
f(2) = 22
f(3) = 34
[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]
Ratios are not equal therefore it's not an exponential function.
Table D.
f(1) = 7
f(2) = 8
f(3) = 9
[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]
Ratios are not equal so it's not an exponential function.
Therefore Table B is the correct option.
*. suppose that there are 5 dollar bills in a box: three 1 dollar bills, one 5 dollar bill and one 10 dollar bill. you are allowed to pick up two bills at the same time from the box randomly. let x denote the money you get from this game. (a) what's the p.m.f. of x?
To determine the probability mass function (PMF) for the game, one must calculate the probability of each possible sum of money resulting from drawing two bills, with the outcomes being 2, 6, 11, and 15 dollars.
To find the probability mass function (PMF) of the variable X, which represents the money you get from the game, we first identify all possible pairs of dollar bills you could draw from the box and then calculate the probability of drawing each pair. As there are three 1 dollar bills, one 5 dollar bill, and one 10 dollar bill, the possible sums of money (X) we can get by drawing two bills are 2 dollars, 6 dollars, 11 dollars, and 15 dollars.
To calculate the PMF of X, consider:
Picking two 1 dollar bills: The probability is C(3,2)/C(5,2) = 3/10.
Picking one 1 dollar bill and the 5 dollar bill: The probability is (C(3,1) imes C(1,1))/C(5,2) = 3/10.
Picking one 1 dollar bill and the 10 dollar bill: The probability is (C(3,1) imes C(1,1))/C(5,2) = 3/10.
Picking the 5 dollar bill and the 10 dollar bill: The probability is (C(1,1) imes C(1,1))/C(5,2) = 1/10
Therefore, the PMF of X is:
P(X = 2) = 3/10
P(X = 6) = 3/10
P(X = 11) = 3/10
P(X = 15) = 1/10