The radius is 1.13 inches and the height of the cylinder is 4.52 inches.
How to calculate the value?From the information, it's important to use the volume of a cylinder to illustrate the information.
Use the volume of a cylinder.
V = πr²h
V = volume.
r = radius
h = height
where:
V = 18
h = 2(2r) = 4r
Plug in the values into the equation and solve for r.
18 = πr²(4r)
18 = 4πr³
Divide both sides of the equation by 4π.
9 / (2π) = r³
r³ = 1.43
r = 1.13 inches.
Finally, multiply the radius by 4 to get the height. This will be:
= 4 × 1.13
= 4.52 inches.
In conclusion, the height is 4.52 inches.
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13. Nick is five years older than Will. The sum of their ages is 21. How old is Nick? Solve algebraically.
Answer:
Nick = 13 years old.
Step-by-step explanation:
Define the variables:
Let n = the age of Nick (in years).Let w = the age of Will (in years).Given:
Nick is 5 years older than Will.The sum of their ages is 21.Create a system of equations with the given information and defined variables:
[tex]\begin{cases} w=n-5\\n+w=21\end{cases}[/tex]
Substitute the first equation into the second equation and solve for n:
[tex]\implies n+(n-5)=21[/tex]
[tex]\implies 2n-5=21[/tex]
[tex]\implies 2n-5+5=21+5[/tex]
[tex]\implies 2n=26[/tex]
[tex]\implies 2n \div 2=26 \div 2[/tex]
[tex]\implies n=13[/tex]
Therefore, Nick is 13 years old.
To find the age of Will, simply substitute the found value of n into the first equation and solve for w:
[tex]\implies w=13-5[/tex]
[tex]\implies w=8[/tex]
Therefore, Will is 8 years old.
Determine the values of m and n in the polynomial 2x* + mx -x + n such that the binomial (x - 1) is a factor and that the remainder when divided by (x + 2) is -18.
The remainder theorem of polynomials states: if a polynomial p(x) is divided by a binomial (x - a), the remainder obtained is p(a).
In this case, the polynomial is:
[tex]p(x)=2x^4+mx^3-x^2+n[/tex]Applying the remainder theorem p(-2) = -18, that is:
[tex]\begin{gathered} p(-2)=2\cdot(-2)^4+m\cdot(-2)^3-(-2)^2+n \\ -18=2\cdot16+m\cdot(-8)-4+n \\ -18=32-8m-4+n \\ -18-32+4=-8m+n \\ -46=-8m+n\text{ (eq. 1)} \end{gathered}[/tex]Given that (x - 1) is a factor, then p(1) = 0, that is:
[tex]\begin{gathered} p(1)=2\cdot1^4+m\cdot1^3-1^2+n \\ 0=2+m-1+n \\ -2+1=m+n \\ -1=m+n\text{ (eq. 2)} \end{gathered}[/tex]Now, we have a system of 2 equations and 2 variables: m and n. Subtracting equation 2 to equation 1, we get:
-8m + n = -46
-
m + n = -1
------------------------
-9m = -45
m = (-45)/(-9)
m = 5
Substituting this result into equation 2, we get:
5 + n = -1
n = -1 - 5
n = -6
What’s the correct answer answer asap for brainlist
Answer: Europe quit buying crops which left the united states with a surplus of crops
hope i helped
Step-by-step explanation:
Find the derivative of each function. Simplify each derivative and express all exponents as positive values.
Answer:
[tex]\boxed{f^{\prime}(x)=x^2^{}-\frac{1}{2}}[/tex]Explanation:
Step 1. The function we have is:
[tex]f(x)=\frac{x^3}{3}-\frac{x}{2}[/tex]And we are asked to find the derivative of the function. The rule to find the derivative for this type of function is:
[tex]\begin{gathered} \text{for a function }of\text{ the form} \\ f(x)=ax^n \\ \text{The derivative is:} \\ f^{\prime}(x)=a(n)x^{n-1} \end{gathered}[/tex]Step 2. Before we apply the derivative rule, remember the following:
[tex]\begin{gathered} \text{for a function } \\ f(x)=g(x)+h(x) \\ \text{The derivative is:} \\ f^{\prime}(x)=g^{\prime}(x)+h^{\prime}(x) \end{gathered}[/tex]This means that we need to derivate each part or term of the function and combine them for the total derivative.
Step 3. Apply the derivative rule from step 1 to the given function.
First we rewrite the function as follows:
[tex]\begin{gathered} f(x)=\frac{x^3}{3}-\frac{x}{2} \\ \downarrow \\ f(x)=\frac{1}{3}x^3-\frac{1}{2}x^1 \end{gathered}[/tex]Apply the derivative rule:
[tex]f^{\prime}(x)=\frac{1}{3}(3)x^{3-1}-\frac{1}{2}(1)x^{1-1}[/tex]Step 4. The last step is to simplify the expression:
[tex]\begin{gathered} f^{\prime}(x)=\frac{1}{3}(3)x^{3-1}-\frac{1}{2}(1)x^{1-1} \\ \downarrow \\ f^{\prime}(x)=\frac{1}{3}(3)x^2-\frac{1}{2}(1)x^0 \\ f^{\prime}(x)=x^2-\frac{1}{2}x^{^0} \\ \sin ce^{} \\ x^0=1 \\ \downarrow\text{ The result is }\downarrow \\ f^{\prime}(x)=x^2-\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]\boxed{f^{\prime}(x)=x^2^{}-\frac{1}{2}}[/tex]Complete the following statement.a0
ANSWER
x = 10
EXPLANATION
We want to find the missing box in the statement given.
Let the box be represented by x:
[tex]x\text{ + (-7) = 3}[/tex]To solve this, move (-7) to the other side, the sign changes:
[tex]\begin{gathered} x\text{ = 3 + (+7)} \\ x\text{ = 3 + 7} \\ x\text{ = 10} \end{gathered}[/tex]The box is 10.
Which of the following systems of equations can be used to find a, the number of adults attending, and s, the number of students attending the game?
The problem can be expressed in the following system of linear equations:
A total of 120 adults (a) and students (s) attended a school:
a + s = 120
Each adult paid $2.50, mathematically, that is 2.5a
Each student paid $1, mathematically, that is 1s
and the total paid by adults and students attending the game was $189
then, we have:
2.5a + 1s = 189
then, we can conclude that the problem can be expressed as follows:
a + s = 120
2.5a + 1s = 189
or equivalently:
a + s = 120
2.5a + s = 189
so, the correct answer is D.
During revision, you should _____.A set your first draft aside for awhileB work from typed or printed textC write down additional thoughtsD All of the above
You should jot down any new ideas you have while you revise.
Revision is the process of rearrangement, addition, or deletion of paragraphs, sentences, or words in writing. Writers are free to edit their work both during and after the writing process. Many of the techniques associated with editing are used in revision, but it can also require more significant changes to the goal, target audience, and content.
To ensure proper memorization, revise by reading or writing the material again. A must-do before each exam is revision. Additionally, it allows you to check for errors and reorganize your work.
During revision, you should write down additional thoughts.
The correct option is (c).
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Which of the following order satisfies a set of number
r-s for r=63 and s=9
54
Explanation
to figure out this, just replace the given values and evaluate
Step 1
[tex]r-s[/tex]let
r=63
s=9
now, replace
[tex]\begin{gathered} r-s \\ 63-9 \\ 54 \end{gathered}[/tex]so, the answer is 54
select the correct answer what is the simplified form of 45
The solution is option C.
????????????????????
we have
m=-2
point (1,2)
step 1
find the equation of the line in point slope form
y-3=-2(x-1)
convert to slope intercept form
y-3=-2x+2
y=-2x+2+3
y=-2x+5
To graph the line we need two points
Find the y-intercept (value of y when the value of x is equal to zero)
For x=0
y=5
so
the y-intercept is (0,5)
Find the x-intercept
Value of x when the value of y is equal to zero
For y=0
0=-2x+5
2x=5
x=2.5
the xintercept is (2.5,0)
Plot the points (0,5) and (2.5,0), join them and graph the line
using a graphing tool
see the attached figure
please wait a minute
Which of the following graphs shows a parabola with a vertex of (-4,4) and solutions of (-6,0) and (-2,0)?
Equation is -(x+4)² +4.
What is parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. The vertex form of a quadratic equation is y = a (x h) 2 + k as opposed to the regular quadratic form, which is an x 2 + b x + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.
Given Data
Solutions (-6, 0) and (-2,0)
y = a(x - (-6)) (x-(-2))
y = a(x+6) (x+2)
Vertex (-4,4)
at x = -4 and y = 4
4 = a(-4+6)(-4+2)
4 = a (2)(-2)
a = -1
y = -1(x+6)(x+2)
y = -(x²+8x+12)
y = =(x² + 3x +4x+4²-4²+12)
y = -(x+4)² +4
Equation is -(x+4)² +4.
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given the Venn diagram below what is the probability that both event A and B will occur
the probability of both is the one they share
[tex]0.2[/tex]An error has been made in subtracting the polynomials as shown in the student work. What error has the student made, (Ignore the response I wrote and write a new one).
In carrying out the subtraction:
[tex](6x^2-4x-5)-(3x^2-7x+2)[/tex]We observe that:
[tex]\begin{gathered} 6x^2-3x^2=3x^2 \\ -4x-(-7x)=3x\text{ and }-4x+(-7x)=-11x \\ -5-(2)=-7\text{ and }-5+(2)=-3 \\ \end{gathered}[/tex]We observe that the student added two of the terms instead of subtracting. This was the error in the students' work.
A jar contains 5 red marbles, 7 green marbles, and 6 blue marbles.
What is the probability that you draw 3 green marbles in a row if you do replace the marbles after each draw? =
What is the probability that you draw 7 blue marbles in a row if you don't replace the marbles after each draw? =
Probability of drawing 3 green marbles in a row with replacement is 0.059
The probability that you draw 7 blue marbles in a row without replacement is 0
What is the probability?
Probability is used to determine the odds in favor or against a random event happening. The probability that the random event happens lie between 0 and 1. The more likely it is that an event would happen the closer the probability value would be to 1.
Probability of drawing 3 green marbles in a row with replacement = (7/18) x (7/18) x (7/18) = 0.059
The probability that you draw 7 blue marbles in a row without replacement = (6/18) x (5/17) x (4/16) x (3/15) x (2/14) x (1/13) x 0 = 0
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three more than eight times a number is equal to 19. find the number.
Let that number be variable x
MATHEMATICALLY THE STATEMENT IS SAYING
[tex]8x + 3 = 19 \\ 8x = 19 - 3 \\ 8x = 16 \\ \frac{8x}{8} = \frac{16}{8} \\ x = 2 [/tex]
That number is 2ATTACHED IS THE SOLUTION
What is the y-value when the x-value is 18?
Answer: -11
Step-by-step explanation:
please help !!!!!!!!!!!!!!!!!!!!!
5⁶ is the simplified form of the expression ( 5⁶/5³ )².
What is the simplified form of the given expression?Given the expression in the question;
( 5⁶/5³ )²
To simplify the expression; us the law of indices.
xᵃ ÷ xᵇ = xᵃ⁻ᵇ
Hence, perform the operation inside the parenthesis
( 5⁶/5³ )²
( 5⁶ ÷ 5³ )²
( 5⁶⁻³ )²
( 5³ )²
To remove the parenthesis, apply the law of indices.
( xᵃ )ᵇ = xᵃ ˣ ᵇ
( 5³ )²
5³ ˣ ²
5⁶
Therefore, the simplified form of the expression is 5⁶.
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Use the order of operations to simplify - +4(4.50 – 1.50).O A. 122/2B. 24/1/2c. 23/1/D. 11/1/SUBMIT
SOLUTION
This becomes
[tex]\begin{gathered} -\frac{1}{2}+4(4.5-1.50) \\ opening\text{ the bracket we have } \\ -\frac{1}{2}+(4\times4.5)+(4\times(-1.50) \\ -\frac{1}{2}+18-6 \\ -\frac{1}{2}+12 \\ 12-\frac{1}{2} \\ =11\frac{1}{2} \end{gathered}[/tex]Hence the answer is option D
An architect is standing 250 feet from the base of a building and would like to know the height of the building. If he measures the angle of elevation to be 55°, what is the approximate height of the building? Round any intermediate calculations if needed to know less than six decimal places and round the final answer to the nearest 10th of a foot
see the figure below to better understand the problem
we have that
[tex]\begin{gathered} tan55^o=\frac{h}{250}---->\text{ by TOA} \\ \\ solve\text{ for h} \\ h=250*tan55^o \\ h=357.0\text{ ft} \end{gathered}[/tex]The answer is 357.0 feetDetermine whether the relation defines a function, and give the domain and range.{(-8, 7),(4.7).(-9, 1);
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define when a relation defines a function
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
The domain is the set of all first elements of the ordered pairs. The range on the other hand is the set of all second elements of the ordered pairs.
Since every x-values of the given relation is associated with only one y-value, therefore it defines a function.
The domain is given as:
[tex]\lbrace-8,4,-9\rbrace[/tex]The range is given as:
[tex]\lbrace7,7,1\rbrace[/tex]how long will it take $600 to earn $72 at the rate of 0.03 percent annual?
It takes 400 years for $600 to earn $72 at the rate of 0.03 percent annual
What is Simple Interest?"Simple" interest refers to the straightforward crediting of cash flows associated with some investment or deposit.
The formula for calculating Simple interest
I=PRT
Where I is the Interest
P=Principle amount
I is interest Amount
R is rate of interest per year as a percent
T is time period involved
P=600
I=72
r=0.03%
t=?
I=PRT
Plug in the values P, R and I
72=600×(0.03%)×T
72=600×0.0003×T
72=0.18×T
400=T
Hence it takes 400 years, for amount $600 to earn $72 at the rate of 0.03 percent annual.
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6 more than a number is the same as the
number times 4.
Answer:
2
Step-by-step explanation:
Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money, AAA, in dollars, that he receives from the first donor given that he walks ddd kilometers is given by the formula A(d)=10dA(d)=10dA, left parenthesis, d, right parenthesis, equals, 10, d. The money, BBB, in dollars, that he receives from the second donor given that he walks ddd kilometers is given by the formula B(d)=2d+d^2B(d)=2d+d
2
B, left parenthesis, d, right parenthesis, equals, 2, d, plus, d, squared.
Let TTT be the total money that Onur raises from those donors by walking ddd kilometers in the walkathon.
Write a formula for T(d)T(d)T, left parenthesis, d, right parenthesis in terms of A(d)A(d)A, left parenthesis, d, right parenthesis and B(d)B(d)B, left parenthesis, d, right parenthesis.
The function of the total money raised from both donors after walking d kilometers is T(d) = 12d + d^2
How to determine the composite function of the total amount?From the question, the given parameters are:
First donor at d kilometers, A(d)=10dSecond donor at d kilometers, B(d) = 2d + d^2Also, from the question, T is the total money raised from both donors at d kilometers
This means that the equation of the total money can be represented a
T(d) = A(d) + B(d)
Substitute the known values in the above equation
So, we have the following equation
So, we have
T(d) = 10d + 2d + d^2
Evaluate the like terms in the above equation
T(d) = 12d + d^2
The equation cannot be further simplified
Hence, the composite function is T(d) = 12d + d^2
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Complete question
Onur is participating in a walkathon fundraiser. Two donors promised to donate money based on the total distance he walks. The money, A, in dollars, that he receives from the first donor given that he walks d kilometers is given by the formula A(d)=10d
The money, B, in dollars, that he receives from the second donor given that he walks d kilometers is given by the formula B(d)=2d+d^2
Let T be the total money that Onur raises from those donors by walking d kilometers in the walkathon.
Write a formula for T(d) in terms of A(d) and B(d)
AlgebraName1. If f(x) = 2x - 4, find each valdea)(3)b) f(x) = 9
Answer:
Step-by-step explanation:
Comment
The question is since f(x) really means y, then when y = 9 what's x?
Solution
y = 2x - 4
y = 9
9 = 2x - 4 Add 4 to both sides
9+4 = 2x Combine
13 = 2x Divide both sides by 2
13/2 = 2x/2
6.5 = x
Do you mean what is f(X) when x is 3. f(3) = 2x - 4. So what is y when x = 3
y = 2x - 4 Substitute 3 for x
y = 2*3 - 4 Combine
y = 6 - 4
y = 2
Tim needs to be at work at 8:00 A.M. It takes him 30 minutes to get ready in the morningand 15 minutes to drive to work. What is the latest time Tim can get up in the morningwithout being late for work?
The given information is:
- Tim needs to be at work at 8:00 A.M.
- He needs 30 minutes to get ready in the morning
- It takes him 15 minutes to drive to the work
The total time Tim needs to get ready and drive to work is:
[tex]30min+15min=45min[/tex]So, he needs at least 45 minutes to be on time at work. So, the latest time Tim can get up in the morning is 45 minutes earlier than 8:00 A.M., and it is equal to:
[tex]\begin{gathered} 8:00\text{ is equal to 7 hours and 60 min, so:} \\ 60min-45min=15min \\ \\ The\text{ latest time is: }7:15A.M. \end{gathered}[/tex]The answer is 7:15 A.M.
What was the most common button length? Write your answer on the line below.Answer inches
Answer:
3/4 inches
Explanation:
The most number of cross symbols (vertical line) is on the length 6/8 inches, that is, 3/4 inches.
So, the most common button is of length 3/4 inches.
y = x ^ 2 + 2x - 24 i need to know the points at the x-intercept ( , ) and ( , ) points at the y intercept: ( , )and i’d it’s a min or max
Question : the function in the question is given below as
[tex]y=x^2+2x-24[/tex]Step 1: Calculate the x-intercept
The x-intercept for any curve is the value of the x coordinate of the point where the graph cuts the x-axis, or we can say that the x-intercept is the value of the x coordinate of a point where the value of the y coordinate is equal to zero.
Equating the equation above to zero (0)
[tex]\begin{gathered} y=x^2+2x-24 \\ x^2+2x-24=0 \end{gathered}[/tex]Solving using the quadratic formula below,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The general formula of a quadratic equation is given below
[tex]ax^2+bx+c=0[/tex]By comparing the coefficient, we will have the values to be
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-24 \end{gathered}[/tex]Step 2: Substitute the values into the quadratic formula to get the values of x
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{2^2-(4\times1\times-24)}}{2\times1} \\ x=\frac{-2\pm\sqrt[]{4^{}+96}}{2} \\ x=\frac{-2\pm\sqrt[]{100}}{2} \\ x=\frac{-2\pm10}{2} \\ x=\frac{-2+10}{2}\text{ or }x=\frac{-2-10}{2} \\ x=\frac{8}{2}\text{ or x=}\frac{\text{-12}}{2} \\ x=4\text{ or x=-6} \end{gathered}[/tex]Hence,
The x-intercepts are
[tex](-6,0)\text{ and }(4,0)[/tex]x-intercepts are (-6,0) and (4,0)
Step 3: Calculate the coordinate of the y-intercept
The point where a line or curve crosses the y-axis of a graph.
In other words: find the value when x equals 0
[tex]\begin{gathered} y=x^2+2x-24 \\ y=(0)^2+2(0)-24 \\ y=0+0-24 \\ y=-24 \end{gathered}[/tex]Hence,
The y-intercept is
[tex](0,-24)[/tex]The y-intercept is (0,-24)
Below is the graph of the function on the question with its x-intercepts and y-intercepts
Step 4: Determine if the graph is minimum or maximum
The first step is to determine whether your equation gives a maximum or minimum. This can be done by looking at the x^2 term. If this term is positive, the vertex point will be a minimum; if it is negative, the vertex will be a maximum.
The coefficient of the x^2 term is a positive 1
Hence,
The equation
[tex]y=x^2+2x-24\text{ }[/tex]is a minimum quadratic graph
In this figure, lines a and B are intersected by Line T. Which of these statements proves that lines A and B are parallel
Correct answer is C, For the given figure, ∠2 = ∠3, as they are corresponding angles of parallel lines.
What are corresponding angles?The angles created when a transversal intersects two parallel lines are known as corresponding angles.
Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.
Two congruent or identical triangles' corresponding angles are those of a congruent pair of their sides in a triangle. As a result, these angles are equivalent or have the same value.
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Complete Question -
In the figure, lines a and b are intersected by line t. Which of these statements proves that lines a and
b are parallel?
∠1 and ∠2 are supplementary∠1 and ∠3 are supplementary∠2 = ∠3∠1 = ∠2Suppose you deposit $10,000 in an account for 8 years at the annual interest rate 3%.
a. What would be the ending account balance if the interest is compounded by monthly?
b. What would be the ending account balance if the interest is compounded daily?
c. What would be the ending account balance if the interest is continuously compounded?
d. What are the graphs of (a), (b) and (c)?
e. Are these three answers similar? Why or not why?
For the ending account balances, these are the solution
a. The ending account if it is compounded monthly is $12,708.68
b. If it is compounded daily = $12712.374
c. If it is continuous = $12712.49
d. The graphs are in the attachment
e. The answers are not similar
How to solve for the ending account balancesThis is the data that we can use to solve the problem
Principal = $10000
Time = 8 years
Rate = 3 percent
The ending balance when compounded monthly
= number of months n
= 12
A = P (1 + r/n)^nt
= 10000 (1 + 0.03/12)⁸*¹²
= 10000 (1.0025)⁹⁶
= 100000 X 1.270868
= 12,708.68
The amount that would be the ending account if it is compounded monthly is $12,708.68
b. If it is compounded daily
total number of days in a year n = 365
10000 (1 + 0.03/365)⁸*³⁶⁵
10000 x 1.2712374
= $12712.374
c. The endind account if the interest is compounding continuously
[tex]A = Pe^r^t\\\\A = 10000 *e ^0^.^0^3^*^8[/tex]
= $12712.49
e. The answers are not similar here due to the fact that all of the accounting periods that we used are not the same for the problems that we have here.
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