Using the formula of volume of cone, the height of the cone is 3/8.
In the given question,
We have to find the missing dimension of the cone.
Volume of cone is 1/18 pi, radius is 2/3 ft.
As we know that volume of cone is one third of the product of pi, square of radius and height.
The formula of cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex]
where V=Volume of cone
r=radius of cone
h=height of the cone
We know V=1/18 π, r=2/3 ft.
We don't know the value of h. So we find the value of h.
putting the value in formula
[tex]\frac{1}{18}\pi=\frac{1}{3}\pi\times\frac{4}{9}\times h[/tex]
Simplifying
[tex]\frac{1}{18}\pi=\frac{4}{27}\pi\times h[/tex]
[tex]\frac{\pi}{18}=\frac{4\pi}{27}\times h[/tex]
Multiply by 4/27π on both side
[tex]\frac{\pi}{18}\times\frac{27}{4\pi}=\frac{4\pi}{27}\times\frac{27}{4\pi}\times h[/tex]
Simplifying
[tex]\frac{1}{2}\times\frac{3}{4}=h[/tex]
Simplifying
h = 3/8
Hence, the height of the cone is 3/8.
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The perimeter of a triangle is 51 meters.The second side is twice as long as the first. The third side is 3 meters less than three times the first. What is the length of the second side of the triangle?
The length of the second side of the triangle is 18 m
What is the perimeter of a Triangle?
The perimeter of a triangle is given by the formula
Perimeter of a triangle = Sum of all three sides
Let the sides of the triangle be a , b , c
Perimeter of a triangle = a + b + c
Given data ,
Perimeter of the triangle = 51 m
Let the first side , second side and third side of the triangle be a , b and c respectively
So , a + b + c = 51 m
And , The second side is twice as long as the first
So , b = 2a
And , The third side is 3 meters less than three times the first
So , c = 3a - 3
Substituting the values of a , b and c in the perimeter equation , we get
a + 2a + 3a - 3 = 51
6a - 3 = 51
Adding 3 on both sides , we get
6a = 54
Divide by 6 on both sides , we get
a = 9 m
Substituting the value of a , we get
b = 2a
b = 2 x 9
b = 18 m
c = 3a - 3
c = 3 x 9 - 3
c = 27 - 3
c = 24 m
So the length of the first side , second side and third side is 9m , 18 m and 24 m respectively
Hence , the length of the second side is 18 m
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Question 6 of 10
For what values of x is the expression below defined?
√3x²+√4x
OA. x< 1
OB. x > 0
OC. x = 0
OD. x<0
The given expression √3x²+√4x is defined for x > 0
By property |f(x)| < c
⇒ f(x) < 0 and - f(x) < 0
⇒√3x²+√4x < 0 and -(√3x²+√4x) < 0
⇒ x < -√4/3 and x < -√4/3
Therefore x should be greater than 0.
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Solve for x
7(x-2) < 2x +3
Give your answer as an improper fraction in its simplest form.
Answer:
[tex]x < \frac{17}{5}[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
Which descriptions from the list below accurately describe the relationship
between AQRS and ATUV? Check all that apply.
A. Congruent
B. Similar
c. Same size
D. Same sides
The two relationships between the two triangles QRS and TUV is that they are similar triangles.
Option b is correct.
What is a similar triangle?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
Similar figures are described as items with the same shape but varying sizes, such as two or more figures. The polygon with three sides is a triangle. The prerequisites for a triangle's resemblance are that the corresponding angles on both triangles must be identical, and the corresponding sides must be proportional to one another.
In the given question, we have:
The two triangles: QRS and TUV;
and we have the measure of the angles;
∠Q = 76°
∠R = 26°
∠S = 76°
∠T = 76°
∠U = 26°
∠V = 76°
and the sides measure:
RQ = 4cm;
RS = 2cm;
SR = 4cm;
UT = 12cm;
TV = 6cm;
UV = 12cm;
So, when we find the proportion of the corresponding sides, we get:
The ratio of sides is as [tex]\frac{1}{2}[/tex];
and all the corresponding angles are equal;
So, we can say that the two triangles are similar;
Hence, The two triangles are similar;
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Last week, a florist sold 715 roses. Of the
roses sold, 7 out of every 11 roses were
red. How many red roses did she sell?
The total number of red roses sold by the florist is 455.
A Fraction represents the parts of a whole or collection of objects. The first and most common form of representing a fraction is [tex]\frac{a}{b}[/tex].
Here, a is the numerator, and b is the denominator.
Number of Roses sold by The florist = 715
Fraction for the number of red roses sold = [tex]\frac{7}{11}[/tex] (7 out of 11 roses)
We have to find the number of red roses sold by the florist.
Now,
The number of red roses sold by the florist will be
[tex]\frac{7}{11} \ of\ 715[/tex]
[tex]=\frac{7}{11}*715[/tex]
[tex]=\frac{7*715}{11}[/tex]
[tex]=\frac{5005}{11}[/tex]
[tex]=455[/tex]
Hence, the total number of red roses sold by the florist is 455.
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IXL Help Fast Please !
Answer:9-0
Step-by-step explanation:sdwew
Answer:
x = 35 degrees
Step-by-step explanation:
3x-11+2x+16 = 180
5x +5 = 180
5x = 180 -5
5x = 175
5/5 x = 175/5
x = 35 degrees
Given the graph of f(x), find each of the following:
f(-1), f(0), f(1), f(2), f(3)
f(x) __________ Feedback _______________
The value of the function at x = -1, 0, 1, 2, and 3 will be -4, 3, 2, -1, and 0, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
From the graph of f(x), then the value of the function at x = -1, 0, 1, 2, and 3 will be given as,
x f(x) Feedback
-1 -4 Point is in the fourth quadrant
0 3 Point is in the y-axis
1 2 Point is in the first quadrant
2 -1 Point is in the second quadrant
3 0 Point is in the x-axis
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What is the image of ( − 8 , 7 ) after a dilation by a scale factor of 3 centered at the origin?
The image of (-8, 7) after dilation by a scale factor of 1/3 centered at the origin is : (-8/3, 7/3)
Given point P (-8, 7)
The point is dilated by a scale factor of 1/3 centered at the origin is equivalent to multiplying the point by 1/3 for both the co-ordinates.
Therefore, the new point is given by :
P' = (-8×(1/3), (7)×(1/3))
P' = (-8/3, 7/3)
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Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use.
How much of the 10% alcohol solution should Bruce use?
__ mL
How much of the 15% alcohol solution should Bruce use?
__mL
x = 10% solution
y = 15% solution
let's start at the beginning, without the equation just yet, so let's start off by making a table for the substances and let's use the decimal format for the percentages to get the actual amounts.
[tex]\begin{array}{lcccl} &\stackrel{mL}{quantity}&\stackrel{\textit{\% of mL that is}}{\textit{alcohol only}}&\stackrel{\textit{mL of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{10\% sol'n}&x&0.10&0.10x\\ \textit{15\% sol'n}&y&0.15&0.15y\\ \cline{2-4}&\\ mixture&50&12&6 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.10x+0.15y=6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies y=50-x}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.10x+0.15(\underset{y}{50-x})=6} \\\\\\ 0.10x+7.5-0.15x=6\implies -0.05x+7.5=6\implies -0.05x=-1.5 \\\\\\ x=\cfrac{-1.5}{-0.05}\implies \boxed{x=30}\hspace{15em}\stackrel{50~~ - ~~30}{\boxed{y=20}}[/tex]
What is the scale factor from JKL to MNO?
What is the scale factor from MNO to JKL?
What is the distance of line segment JL?
If line segment LK is 5cm, what is line segment ON?
Icm
Write the angle that corresponds to angle JLK? (please type using capital letters)
The scale factor from JKL to MNO is 1/2, and the scale factor from MNO to JKL is 2.
What is a scale factor?The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.
It is given that:
The scale factor from JKL to MNO:
The scale factor = JK/MN = 4/8 = 1/2
The scale factor from MNO to JKL:
The scale factor = MN/JK = 8/4 = 2
JL = 11/2 = 5.5 cm
LK = 5 cm
ON = 5x2 = 10 cm
Angle JLK = Angle MON
Thus, the scale factor from JKL to MNO is 1/2, and the scale factor from MNO to JKL is 2.
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What is the slope of the
function below?
(2,5)
(4,8)
Slope =
?
Answer:
y = 3/2x + 2
Step-by-step explanation:
The x axis runs by 2.
The y axis rises/drops (depends on which you are using) by 3.
The format is rise over run.
So its 3/2
O and R are the subsets of a Universal set, U, such that U={22,23,24,25,26,27,28,29,30} 0={ prime numbers } {R}={ even numbers } a) Draw a Venn diagram to represent this information.
b) List the elements of.
i) ( O U R )'
ii) ( O ∩ R)'
iii) O ∩ R
The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
O and R are the subsets of a Universal set, U, such that
U = {22,23,24,25,26,27,28,29,30}
O = {prime numbers} = {23, 29}
R = {even numbers} = {22, 24, 26, 28, 30}
The elements of (OUR)' will be given as,
(OUR)' = {23, 29}
The elements of (O∩R)' will be given as,
(O∩R)' = {22, 23, 24, 26, 28, 29, 30}
The elements of O∩R will be given as,
O∩R = 0
The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.
The Venn diagram is given below.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
A line representing the "rise" and the "run" of the line is shown in the image attached below. Also, a slope of this line in simplest form is equal to 1.27.
How to determine the slope (pitch) of a line?Mathematically, the slope (pitch) of a geometric figure or line can be calculated by using this formula:
Slope (pitch) = V/H
Where:
V represents the rising vertical distance (rise) of an object.
H represents the horizontal distance (run) an object runs through.
From the graph of this line, we would choose the following data points for the rise and run:
Rise (x, y) = (2.5, 2)
Run (x, y) = (8, 9)
Substituting the selected data points into the formula, we have;
Slope (pitch) = (9 - 2)/(8 - 2.5)
Slope (pitch) = 7/5.5
Slope (pitch) = 1.27
At point (2.5, 2), the equation of this line is given by:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the data points.y - 2 = 1.27(x - 2.5)
y - 2 = 1.27x - 3.175
y = 1.27x - 3.175 + 2
y = 1.27x - 1.175
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Ed has a card shop. Ed’s profit on “Good Luck” cards in 2018 was . This was a decrease of on his profit in 2017. Work out Ed’s profit on “Good Luck” cards in 2017.
Ed’s profit on “Good Luck” cards in 2017 is $450.
Given that, Ed's profit on “Good Luck” cards in 2018 was £360. This was a decrease of 20% on his profit in 2017.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Let x be the profit on "Goodluck" card in 2017.
Now, x - 20% of x=360
⇒ x - 20/100 × x = 360
⇒ x - 0.2x = 360
⇒ 0.8x = 360
⇒ x = 360/0.8
⇒ x = 450
Therefore, Ed’s profit on “Good Luck” cards in 2017 is $450.
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"Your question is incomplete, probably the complete question/missing part is:"
Ed's profit on “Good Luck” cards in 2018 was £360.This was a decrease of 20% on his profit in 2017.Work out Ed's profit on “Good Luck” cards in 2017.
Iris's checking account pays simple interest at 3% per year. She has $185 in her account. Write a linear function to model the amount of money in her checking account at any time t.
simplify the expression. 6q + 2 + 3q + 5
Answer:
9q+7
Step-by-step explanation:
1. Add 6q+3q, which is 9q
2. Then add 2+5, which is 7
3. Then combine those answers and you get a final answer of 9q+7
Answer:
9q+7
Step-by-step explanation:
1. Group all like terms: 6q+3q and 2+5
2. Add the like terms together. 6q+3q= 9q. 2+5=7
3. Rewrite the equation 9q+7
ANSWER : 9q+7
please help me (20pts)
Answer:
Step-by-step explanation:
Assuming that a linear function can be in all different directions, but remain straight. It might be B. Because the answer shows (0,-1) and the other solutions don't have a y-intercept with a 0 x-intercept...?
Find the length of the curve
y=e^x, 0≤x≤ 1.
The length of the curve is 2.0036.
The equation of the curve is y = e^(x). The interval is 0 ≤ x ≤ 1. A curve is a smoothly drawn figure or line in a plane that has a bend or twist in it. A curve is defined as a continuous and smooth flowing line with no sudden twists. A curve is an abstract concept in mathematics that describes the path of a continuously moving point. The arc length of a curve y = f(x) in the increasing interval from a to b is given below.
[tex]L = \int\limits^a_b {\sqrt[]{ 1 + (\frac{dy}{dx})^{2}} \, dx[/tex]
dy/dx = d(e^x)/dx = e^x
(dy/dx)² = e^(2x)
The length of the given curve is calculated below.
[tex]L = \int\limits^1_0 {\sqrt[]{ 1 + e^{2x}}, dx[/tex]
L = [√(1+e^2x) + (1/2)ln(√(1+e^2x) - 1) - (1/2)ln(1 + √(1+e^2x))] from limits 0 to 1.
L = [√(1+e²) + (1/2)ln(√(1+e²) - 1) - (1/2)ln(1 + √(1+e²))] - [√(1+1) + (1/2)ln(√(1+1) - 1) - (1/2)ln(1 + √(1+1))]
L = [√(1+e²) + (1/2)ln(√(1+e²) - 1) - (1/2)ln(1 + √(1+e²))] - [√2 + (1/2)ln(√2 - 1) - (1/2)ln(1 + √2)]
L ≈ 2.0036
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Please answer need to turn it in please help me answer
Answer: Sir in what way would you like me to explain this
Step-by-step explanation:
a whole number divided by a decimal number is a whole number
Answer:
This statement is False.
Step-by-step explanation:
It is not impossible, but on MOST occasions, you will get a decimal number.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
this is my homework and I dont understand please help me
find the unit vector
Answer:
Step-by-step explanation:
Vector:
AB = { 2 - 5; 7 - 3; -1 - (-1) } = { -3; 4; 0 }
Vector modulus:
| AB | = √ ( (-3)² + 4² + 0² ) = √ (9 + 16 + 0 ) = √ 25 = 5
Unit vector:
U = -(3/5)·i + (4/5)·j + 0/5·k
U = -(3/5)·i + (4/5)·j
A bin contains 400 colored erasers that fit on the ends of pencils. The
numbers of erasers of each color is as follows.
color Green Blue Red Yellow
Number 88 60 160 92
a) A random sample of 25 erasers is selected, with replacement,
from the bin, find the probability that:
(i) exactly 2 erasers are green;
(ii) at most 3 erasers are blue (4 decimal) ;(use excel and write
the function in answer sheet)
(iii) between 8 erasers and 12 erasers, inclusive, are red. ;(use
excel and write the function)
b) Erasers are selected at random, without replacement, from the bin
until 5 yellow erasers are obtained.
Give two reasons why a binomial distribution does not model
the number of erasers selected.
a) The probabilities are given as follows:
i) Exactly 2 green: 0.0479 = 4.79%.
ii) At most 3 blue: 0.2174 = 21.74%.
iii) Between 8 and 12 red: 0.6926 = 69.26%.
b) The binomial distribution is not used as there is not a fixed number of trials, and also the trials are not independent, as there is no replacement.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter n is dependent of the sample size of 25, hence:
n = 25.
For item i, the probability is of P(X = 2) with p = 88/400 = 0.22, hence, using the binomial distribution, it is of:
0.0479 = 4.79%.
For item ii, the probability is of P(X <= 3) with p = 60/400 = 0.15, hence, using the binomial distribution, it is of:
0.2174 = 21.74%.
For item iii, the probability is of P(8 <= X <= 12), with p = 160/400 = 0.4, hence the probability is of:
0.6926 = 69.26%.
For problem b, the binomial distribution cannot be used, as:
It can take 5, 6, ..., 400 trials to take 5 yellow erasers, there is not a fixed number of trials.There is no replacement, hence the probability of a success on differential trials are different.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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Which of the following is the correct graph of the linear equation below?
y-1= 1/5 (x+5)
The values for which the given equation satisfies are provided in main body.
What is linear equation?
An equation that has the highest degree of one is understood as a equation. this suggests that no variable in an exceedingly equation has an acquaintance over one. The graph of a equation continually forms a line.
Main body:
According to the question:
y-1= 1/5 (x+5)
To solve this , we need to let one value for x and find its value for y.
Let x= 0
y-1= 1/5 (0+5)
y-1= 1/5 (5)
y =2
for x = 0 , y =2
Let x = 5
y-1= 1/5 (5+5)
y-1= 1/5 (10)
y = 3
for x = 5 , y = 3
Hence the graph is straight line.
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How do you simplify ((-3)2)3.
Answer: -18
Step-by-step explanation:
((-3)2)3
((-3) x 2) x 3
Apply rule (-a) = - a
(-3) = -3
-3 x 2 x 3
-6 x 3
= -18
arch
Convert the following equation
into slope-intercept form.
-8x + y = -9
0
y = [? ] x + [
Slope-intercept form is −8x+9. One of the formulas used to get a line's equation is the slope-intercept formula.
What is Slope-intercept form ?Slope-intercept is a specific form of linear equations. The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = − 3 x + 5 , we see that the slope of the line is − 3 .
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is where the slope, or steepness, of the line is located.
-8x + y = -9
move y to right side
-8x = -9-y
Divide both sides by -8
-8x/-8x = -(9/-8) - (y/-8)
Simplify
-8x/-8x = -(9/-8) - (y/-8)
Simplify -8x/-8x : x
Simplify -(9/-8) - (y/-8) : -9 - y / 8
x = -(-9 - y / 8)
y = mx + b.
y = −8x+9
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y = f(x-5)+3 looking for a graph
If leonardo picks 5 buckets of blueberries an hour, and his piecework rate is $15 per bucket. How much many will he make in 4 weeks of blueberry picking? He works 5 days a week, 6 hours a day.
Answer:
30 every 5 days
Step-by-step explanation:
23. Meagan uses shipping boxes to mail
850 bags of glass beads. Each box can
hold 24 bags. If she fills each box, how
many bags of glass beads will be left
for the last box? (Should I add,subtract,multiply,or divide?)
5 candy bars with 12 sections split between 3 friends equally
Answer:
20 sections per friend
Step-by-step explanation:
First find the total number of sections
5 * 12 = 60 sections
Divide by 3 friends
60/3 = 20
20 sections per friend
