Answer:
The volume of the given cylinder is 1607.7 in³ to the nearest tenth.
Step-by-step explanation:
The formula for the volume of a cylinder is:
\(\boxed{\textsf{Volume of a cylinder} = \pi r^2 h}\)
where r is the radius of the circular base, and h is the height of the cylinder.
From inspection of the given diagram:
r = 8 inh = 8 inπ = 3.14Substitute these values into the formula and solve:
\(\begin{aligned}\implies \sf Volume&=\pi r^2 h\\&=3.14 \cdot 8^2 \cdot 8\\&=3.14 \cdot 64\cdot 8\\&=200.96\cdot 8\\&=1607.68\\&=1607.7\; \sf in^3\;\;(nearest \; tenth)\end{aligned}\)
Therefore, the volume of the given cylinder is 1607.7 in³ to the nearest tenth.
Answer: 1607.7 in³
Step-by-step explanation:
In order to find the volume of a cylinder, you must find the area of its circle on the top or bottom and multiply that by the height.
The area of a circle is \(\pi r^{2}\), meaning you must multiply pi by the radius squared. In this problem, you are given the radius, which is 8 inches. When you square 8, you get 64. 64 is your radius squared.
Now, you multiply your radius squared with pi. This question tells you to use 3.14 as pi. So, you multiply 3.14 by the 64 you got earlier.
64 inches²· 3.14 = 200.96 inches²
200.96 is the area of the circle on the top and on the bottom of the cylinder (both of these circles have the same area).
Now, all that's left to do is to multiply 200.96 by your height, which is 8.
200.96 inches² · 8 inches = 1607.7 inches³
Therefore, your volume is 1607.7 inches³.
Find y ′ (???????????????????????????????????????? o???? y). Write your answer in terms of variable ???? only. (NOTE: (???????????? x) function is exponent of (x) function. HINT: Start by taking ????????( ) of both sides).
y = x tanx
The derivative y' of the function y = x * tan(x) is y' = tan(x) + x * sec^2(x). This is the final answer, expressed in terms of the variable x.
You find the derivative of y with respect to x (y') for the given function y = x * tan(x). Since you want the answer in terms of the variable x, I'll only use x as the variable.
To find the derivative, we need to apply the product rule since we have a product of two functions: x and tan(x). The product rule states that if we have a function y = u * v, then its derivative y' = u' * v + u * v', where u' and v' are the derivatives of u and v, respectively.
In our case, u = x, and v = tan(x). Now, we need to find the derivatives of u and v:
1. The derivative of u (u') with respect to x:
u' = d(x)/dx = 1
2. The derivative of v (v') with respect to x:
v' = d(tan(x))/dx = sec^2(x)
Now, we can apply the product rule:
y' = u' * v + u * v'
y' = (1) * tan(x) + x * sec^2(x)
So, the derivative y' of the function y = x * tan(x) is given by:
y' = tan(x) + x * sec^2(x)
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will give brainiest + 40 points
Which graph represents the function p(x) = |x – 1|?
Answer:
I think it's the second I e at the top
HELP PLSSS THIS IS HARD SOMEONE
Answer:
(-2,-1) i am pretty sure this is the answer because the 1/3 gives a big hint
PLS ANSWER I HAVE 5MIN!!
What is the slope of the following equation: 5x-10y=35
A. -10
B. 35
C. 5
D. 1/2 or 0.5
Answer:
d
Step-by-step explanation:
Does the following relationship represent a function?
a stick is broken at two points, chosen at random. if the length of the stick is $6,$ then what is the probability that all three resulting pieces are shorter than $5$ units?
The probability of all three resultant pieces being shorter than $5 units is 4 / 5.
Let's call the two random breakpoints on the stick A and B. We want to find the probability that both A and B are such that the lengths of all three pieces (AA, AB, and BB) are shorter than 5 units.
Since the length of the stick is 6 units, the maximum length of a single piece is 6 units, so we want to find the probability that both A and B are such that 0 < A < B < 5.
To find the probability of this occurring, we need to find the total number of possible combinations of A and B such that 0 < A < B < 5 and divide that by the total number of possible combinations of A and B.
The total number of possible combinations of A and B is simply 6 * 5 / 2 = 15, because there are 6 possible positions for A and 5 possible positions for B, and each combination is counted twice because the order of A and B doesn't matter.
The number of combinations such that 0 < A < B < 5 can be found by dividing the interval (0,5) into 4 sub intervals, each with length 1. There are 4 choices for A and 3 choices for B, so there are 4 * 3 = 12 combinations that satisfy the conditions.
The desired probability is 12 / 15 = 4 / 5.
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What is the difference between the median number of turkey sandwiches sold and the median number of ham sandwiches
sold?
The difference between the median number of turkey sandwiches sold and the median number of ham sandwiches sold can be determined using the given data about the number of sandwiches sold.
It is not mentioned in the question stem, but it is necessary to have the data in order to calculate the median and find the difference between the two
.Here's how you can calculate the median and find the difference:1. List the number of turkey sandwiches sold and ham sandwiches sold in ascending order. For example, if the data is as follows:
Turkey: 10, 20, 30, 40, 50 Ham: 5, 10, 20, 25, 30, 35, 40, 452.
Calculate the median of the two lists separately. The median is the middle value when the list is in ascending order. If the list has an odd number of values, the median is the middle number. If the list has an even number of values, the median is the average of the two middle numbers.
For example, for the turkey list:
Median = (30 + 40) / 2
= 35
For the ham list: Median = (20 + 25) / 2
= 223.
Find the difference between the median number of turkey sandwiches sold and the median number of ham sandwiches sold.
Difference = 35 - 22
= 13
Therefore, the difference between the median number of turkey sandwiches sold and the median number of ham sandwiches sold is 13.
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x = -5y + 4 3x + 15y = -1
Answer: UNDEFINED
Step-by-step explanation:
x=-5y+4 5y=-x+4 y=-1/5x+4/5
3x+15y= -1 15y=-3x-1 y=-1/5x-1/15
COMBINED: -1/5x+4/5=-1/5x-1/15 FIND COMMON DENOMINATOR=15
-3/15x=-3/15x-13/15
0=-13/15 UNDEFINED
An ecologist measures a group of saplings (young trees) and finds that they have an average circumference of 30 inches, with an SD of 5 inches. A histogram of the circumference values approximately follows the normal curve. A particular sapling has a 22 inch circumference. What percent of the trees have a circumference that is even smaller than this one's
Approximately 5.48% of the trees have a circumference smaller than 22 inches given that the mean is 30 inches.
To find the percentage of trees with a circumference smaller than 22 inches, we can use the concept of z-scores.
A z-score measures how many standard deviations a value is from the mean.
First, we calculate the z-score for the 22-inch circumference sapling using the formula:
z = (x - mean) / SD.
In this case, the mean is 30 inches and the standard deviation (SD) is 5 inches.
Plugging in the values, we get z = (22 - 30) / 5
= -1.6.
Next, we find the area under the normal curve to the left of the z-score using a z-table or a calculator.
A z-score of -1.6 corresponds to an area of approximately 0.0548.
To convert this to a percentage, we multiply by 100:
0.0548 * 100 = 5.48%.
Therefore, approximately 5.48% of the trees have a circumference smaller than 22 inches.
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An investor purchases a stock for $14.72 per share on April 21, 2015. The investor sells the stock for $15.15 per share on October 6, 2022. The investor receives a dividend of $.59 per share. The investor's tax rate is 28%. What is the investor's capital gain yield?
The investor's capital gain yield is 2.92%. This indicates the percentage increase in value from the initial investment to the selling price, taking into account the dividend received and the tax on the capital gain.
To calculate the capital gain yield, we need to determine the capital gain and the initial investment. The initial investment is the purchase price per share ($14.72), and the capital gain is the difference between the selling price per share ($15.15) and the purchase price per share. This gives us a capital gain of $0.43 per share.
Next, we calculate the tax on the capital gain by multiplying the capital gain by the tax rate (28%). The tax on the capital gain is $0.12 per share. Finally, we calculate the net capital gain by subtracting the tax on the capital gain from the capital gain.
The net capital gain is $0.31 per share. The capital gain yield is then calculated by dividing the net capital gain by the initial investment and multiplying by 100, resulting in a yield of 2.92%.
Based on the given information and calculations, the investor's capital gain yield for the stock is determined to be 2.92%. This indicates the percentage increase in value from the initial investment to the selling price, taking into account the dividend received and the tax on the capital gain.
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ILL GIVE YOU BRAINLEST PLEASE THIS IS THE ONLY QUESTION I HAVENT ANSWER!
A and B
Both A and B, when simplified get -(1/6), because the others have either 0 or 2 negative signs, denoting a positive end result.
The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s? s = StartFraction 3 Over 10 EndFraction m s = StartFraction 10 Over 3 EndFraction m m = StartFraction 3 Over 10 EndFraction s m = StartFraction 1 Over 30 EndFraction s. ⇔ HELP!!! I AM IN A DILEMMA!!!!
Answer:
\(s = \frac{3}{10}m\)
Step-by-step explanation:
Given
Mass = 30g
Spring Stretch = 9cm
Variation: Direct Variation
Required
Equation that relates the mass of the object, m, and the length of the spring, s
Let m represents mass and s represents length of the spring
Given that s varies directly to m;
This implies that
\(s\ \alpha\ m\)
Convert the above to an equation
\(s = km\); where k is the constant of variation;
The next step is to solve for k
Divide both sides by m
\(\frac{s}{m} = \frac{km}{m}\)
\(\frac{s}{m} = k\)
\(k = \frac{s}{m}\)
From the given parameters;
when m = 30; s = 9.
\(k = \frac{9}{30}\)
Divide the numerator and denominator by 3
\(k = \frac{3}{10}\)
To get the equation that relates the mass of the object to the length of the spring
Substitute \(k = \frac{3}{10}\) in \(s = km\)
This becomes
\(s = \frac{3}{10}m\)
Hence, the equation that relates the mass and length is \(s = \frac{3}{10}m\)
Answer:
s=3/10m
Step-by-step explanation:
option a) on edge
Carla attempted 12 free throw shots on a basketball court. She made 9 out of the shots. What is the experimental probability of Carla making a shot?
Answer:
75%
Step-by-step explanation:
9 ÷ 12 = 0.75
0.75 x 100 = 75 = 75%
Answer:
3/4
Step-by-step explanation:
Experimental probability, is the probability determined according to the results of an "experiment" or a trial. In Carla's "experiment", she attempted 12 total shots and made 9 shots. The probability that she made a shot would be 9/12, or 3/4.
Need help with two of these! Thank you
Step-by-step explanation:
17) 3x+5-12+4x+2x
3x+4x+2x +5-12
8x-7
if x =6
8*6-7 =48-7
= 41
18.) 9(3x-4y+8)
27x-36y+72
What is the value of x ??
F. 180
G. 90
H. 40
I. 8
Consider a hypothetical planet where the gravitational acceleration at the surface is found to be 15.3 m/s2. Calculate the gravitational acceleration at an altitude equal to the planet's diameter.
By considering the planet's diameter as the distance from its center, we can determine the gravitational acceleration at that altitude. At an altitude equal to the planet's diameter, the gravitational acceleration would be 3.825 m/s² on this hypothetical planet.
The inverse square law of gravity states that the gravitational force decreases as the square of the distance from the center of mass increases.
Since the diameter of the planet is equal to twice the radius, the altitude equal to the planet's diameter is equivalent to being at a distance twice the radius away from the center of mass.
Let's denote the planet's surface gravitational acceleration as "g" and the radius as "R".
Using the inverse square law, we can calculate the gravitational acceleration at an altitude equal to the planet's diameter as follows:
g_altitude = g * (R / (2R))²
= g * (1/4)
= g/4
= 15.3 m/s² / 4
= 3.825 m/s²
Therefore, at an altitude equal to the planet's diameter, the gravitational acceleration would be 3.825 m/s² on this hypothetical planet.
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6. (4 points) is 3 a generator for the group of multiplication modulo 11? show why this is or is not the case.
The order of 3 is 10, which means that 3 is a generator for the group of multiplication modulo 11.
The group of multiplication modulo 11 is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
To verify whether 3 is a generator for this group or not, let us use the following theorem:
For a finite group of order n, g is a generator if and only if its order is equal to n, which means that g has the power to reach all the elements in the group.
The order of the group of multiplication modulo 11 is 10. To determine whether 3 is a generator or not, we need to find out the orders of its powers.
Using the table below, we can determine the orders of 3, 3², 3³, and 3⁴.
power 3¹ 3² 3³ 3⁴
result 3 9 5 4
order 10 5 10 5
As seen from the table, the order of 3 is 10, which means that 3 is a generator for the group of multiplication modulo 11. Therefore, any other element in the group can be written as a power of 3.
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If the equation F(x,y,z)=0
determines z as a differentiable function of x and y, then, at the points where Fz≠0, the following equations are true.
∂z/∂x=−Fx/Fz and ∂z/∂y=−Fy/Fz.
Use these equations to find the values of ∂z/∂x and ∂z/∂y at the given point. 3z^3 − 3xy − 5yz + y^3 −9 = 0 , ( 2 , 3 , 3 )
The point (2, 3, 3), we have:
∂z/∂x = 1/8
∂z/∂y = -1/6
To use the equations given in the problem, we first need to check if Fz is not equal to zero at the point (2, 3, 3) in the equation 3z^3 − 3xy − 5yz + y^3 −9 = 0.
We can find Fz by taking the partial derivative of F with respect to z:
Fz = 9z^2 - 5y
At (2, 3, 3), we have:
Fz(2, 3, 3) = 9(3)^2 - 5(3) = 72
Since Fz is not equal to zero at the point (2, 3, 3), we can use the equations given in the problem to find ∂z/∂x and ∂z/∂y.
∂z/∂x = −Fx/Fz
To find Fx, we take the partial derivative of F with respect to x:
Fx = -3y
Therefore,
∂z/∂x = −Fx/Fz = -(-3y)/72 = 3y/72 = y/24
At the point (2, 3, 3), we have:
∂z/∂x (2, 3, 3) = 3/24 = 1/8
∂z/∂y = −Fy/Fz
To find Fy, we take the partial derivative of F with respect to y:
Fy = -5z + 3y^2
Therefore,
∂z/∂y = −Fy/Fz = -(-5z + 3y^2)/72 = (5z - 3y^2)/72
At the point (2, 3, 3), we have:
∂z/∂y (2, 3, 3) = (5(3) - 3(3)^2)/72 = -4/24 = -1/6
Therefore, at the point (2, 3, 3), we have:
∂z/∂x = 1/8
∂z/∂y = -1/6
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what is the answer for -31-8+31
Answer:
your answer is -8
31 -31 = 0
-8 is left
Answer:
8
Step-by-step explanation:
Add 31 + 8 then subtract 31 because it’s a negative number
For what values of x and y are the two triangles congruent by HL?
Answer:
y = 4 and x = 11
Step-by-step explanation:
x = y + 7 Substitute the first equation into the second equation and
solve for y
x + 1 = 3y
y + 7 + 1 = 3y
8 = 2y
4 = y x = y + 7
x = 4 + 7
x = 11
CAFFEINE Suppose an 8-ounce cup of coffee contains 100 milligrams of caffeine. The rate at which caffeine is eliminated from an adult's body is 11% per hour. The function f(x) = 100(0.89)* can be used to model the amount of caffeine left in a person's bloodstream after x hours of consuming the cup of coffee. Suppose the function g(x) = 25(0.89)* represents the amount of caffeine left in a person's bloodstream after x hours of consuming an 8-ounce cup of green tea. Describe g(x) as a transformation of f(x).
The function g (x) can be described as a transformation of f (x) in the sense that; it is dilation of f (x) about the origin by a scale factor of; 1 / 4.
What is the description of g (x) as a function of f (x)?As evident in the task content; it follows that the description of the function g (x) is to be determined as a transformation of the function f (x).
On this note, it is noteworthy to observe the two functions as follows;
f (x) / g (x) = 100 (0.89)* / 25 (0.89)*
f (x) / g (x) = 4
Therefore, when g (x) is expressed in terms of f (x); the result is; g (x) = f (x) / x.
Consequently, it can be inferred that the correct description of the function g (x) as a transformation of f(x) is that; g (x) is a dilation of f (x) about the origin by a scale factor of; 1 / 4.
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simplify -6x+7+x-3-2x-11
Answer:
−7-7
Step-by-step explanation:
Add the numbers
Combine like terms
Answer:
This it the right answer −7x−7
Step-by-step explanation:
if f(x)=x^2-4 find f(6)
Answer:
f(6) = 32
Step-by-step explanation:
Substitute x = 6 into f(x) , that is
f(6) = 6² - 4 = 36 - 4 = 32
the distance from city a to city b is 256.8 miles. the distance from city a to city c is 739.4 miles how much farther is the trip to city c than the trip to city b
Taking a difference, we can see that the trip to city C is 482.6 mi longer.
How much farther is the trip to city c than the trip to city b?
Here we know that the distance from city a to city b is 256.8 miles, and the distance from city a to city c is 739.4 miles
To find how much farther is the trip to city c than the trip to city b, we just need to take the difference between the two distances above.
That means that we need to take the distance to city c and subtract the distance to city b.
We will get:
739.4 mi - 256.8 mi = 482.6 mi
The trip to city C is 482.6 mi more than the trip to city B.
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Determine the intercepts of the line.
Do not round your answers.
3x + 2y = 5
Answer:
for x =
\(x = 5 - 2y \div 3\)
for y =
\(5 - 3x \div 2\)
Please help I’ll give brainliest
Answer:
B. $1650
Step-by-step explanation:
the middle share = 3/(2+3+5) × $5500
= 3/10 × $5500 = $1650
Find the distance between points E and W.
Answer:
0.8
Step-by-step explanation:
E is .5 units from 0 and 0 is .3 units from w. .5+.3=.8 units
Find the function (x, y) that is harmonic in the upper half plane Im(z) > 0 and has the boundary values (x, 0) = 1 for −1 1.
The required function that is harmonic in the upper half plane Im(z) > 0 and has the boundary values (x, 0) = 1 for
−1 < x < 1 is u(x, y) = -ay + 1, where a < 0.
The function (x, y) is said to be harmonic if it satisfies the Laplace equation,
∂²u/∂x² + ∂²u/∂y² = 0. The given boundary conditions are (x, 0) = 1 for −1 < x < 1 and u → 0 as |z| → ∞.
Now, let's break down the problem into different steps:
Let u(x, y) be the required harmonic function in the upper half-plane. Im(z) > 0
=>Thee upper half plane lies above the real axis. As per the boundary condition, u(x, 0) = 1 for −1 < x < 1. Therefore, we can write u(x, y) = v(y) + 1, where v(y) is a function of y only. Thus, we get the new boundary condition v(0) = 0.
As per the Laplace equation,
∂²u/∂x² + ∂²u/∂y² = 0, we get ∂²v/∂y² = 0. Hence, v(y) = ay + b, where a and b are constants. Since v(0) = 0, we get
b = 0. Therefore, v(y) = ay.
We must use the condition that u → 0 as |z| → ∞. As y → ∞, v(y) → ∞, which means u(x, y) → ∞. Hence, a < 0.
Thus, v(y) = -ay.
Therefore, u(x, y) = -ay + 1 is the required harmonic function in the upper half plane with the given boundary conditions. Thus, we can say that the required function that is harmonic in the upper half plane Im(z) > 0 and has the boundary values (x, 0) = 1 for −1 < x < 1 is u(x, y) = -ay + 1, where a < 0.
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D. Neither
I will give brianlest to whoever is right
Answer:
Negative Infinity
Step-by-step explanation:
It is a negative slope, therefore as x moves towards positive infinity, y will move towards negative infinity.
SURFACE AREA HELP ASAP!!
Answer:
Step-by-step explanation:
can you get a bigger picture pls