The lateral surface of a cone is the curved surface that connects the base of a cone to the apex of the cone.
The lateral surface of a cone refers to the curved surface area that connects the base of the cone to its apex (the pointed top).
It forms the sloping sides of the cone.
In a cone shape, the base is a circle, and the lateral surface is the part that wraps around the sides to meet at the apex.
This surface does not include the base or the tip of the cone. It is only the curved part that connects the two.
The lateral surface area of a cone can be calculated using the formula A = πrl, where A represents the lateral surface area, r is the radius of the base of the cone, and l is the slant height, which is the distance from the apex to any point on the edge of the base.
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What is the largest rectangular area that can be enclosed with 400 feet of fencing?
Sterday, a movie theater sold 262 bags of popcorn. a large bag of popcorn costs $3. a small bag of popcorn costs $1. in all, the movie theater made $412 from popcorn sales. write and solve a system of equations to find how many bags of each size of popcorn were sold.
PLEASE PLEASE HELP IM LITERALLY CRYING.
Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down.
What is the equation for g(x)?
Enter your answer in the box.
g(x)= ????
Answer:
g(x) = 32x-7
Step-by-step explanation:
A vertical stretch is shown in an equation by multiplying the equation by a factor greater than 1. Since we are stretching by a factor of 4, we multiply the equation by 4:
g(x) = 4(8x) = 32x
A vertical translation is performed by subtracting a value from a function. To translate the function 7 units down, we will subtract 7 from the equation:
g(x) = 32x-7
The equation for g(x) = 32x - 7.
Given that,
Let f(x) = 8x,The graph of f(x) should be transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down.Based on the above information, the calculation is as follows:
g(x) = 4(8x)
= 32x
Now here we subtract 7 from the equation.
So, it is g(x) = 32x-7
Therefore we can conclude that the equation for g(x) = 32x - 7.
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A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A? 50 ≤ x ≤ 58 x ≥ 50 or x ≤ 58 x ≥ 52 or x ≤ 56 52 ≤ x ≤ 56
The inequality that represents the predicted possible percent of votes is 50 ≤ x ≤ 58
The margin of error (E) shows by how much the measured value can differ from the mean value.
Given that the probability of winning the election is 54% and there is a margin of error of 4%, hence:
Let x represent the predicted possible percent of votes.
x = 54% ± 4%
x = (54% - 4%, 54% + 4%)
x = (50%, 58%)
The inequality that represents the predicted possible percent of votes is 50 ≤ x ≤ 58
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The inequality representing the predicted possible percent of votes for candidate A is [tex]\( 50 \leq x \leq 58 \)[/tex].
The predicted possible percent of votes, x, for candidate A considering the margin of error can be represented as follows:
Given:
- Predicted percentage of votes for candidate A = 54%
- Margin of error = ±4%
The predicted range of percentages for candidate A can be expressed as:
[tex]\[ 54\% \pm 4\% \][/tex]
This translates to:
[tex]\[ 54\% - 4\% \leq x \leq 54\% + 4\% \][/tex]
Calculate the lower and upper bounds:
[tex]\[ 50\% \leq x \leq 58\% \][/tex]
Therefore, the inequality that represents the predicted possible percent of votes x for candidate A is [tex]\( \boxed{50 \leq x \leq 58} \)[/tex].
Complete question:- A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A?
50≤ x≤ 58
x≥ 50 or x≤ 58
x≥ 52 or x≤ 56
52≤ x≤ 56
Please explain your answer thanks
What is the value of 5^4 over 5^6
Fran graphs the equations y = 2x2 – 2 and y = –0.5x + 4. Her graph is shown below.
Which value is an approximate solution of 2x2 – 2 = –0.5x + 4?
Answer:
A
Step-by-step explanation:
I just took the test
What is the sum of the geometric sequence 1, 3, 9, … if there are 10 terms?
Answer: 29524
Step-by-step explanation:
Given geometric sequence : 1, 3, 9, …........................
First term of G.P. [tex]a = 1[/tex]
Second term of G.P.[tex]a_2=3[/tex]
Common ratio =[tex]r=\frac{a_2}{a}=\frac{3}{1}=3[/tex]
We know that the sum of the geometric sequence with n terms is given by :-
[tex]S=\frac{a(r^n-1)}{r-1}[/tex] for |r|>1
Substitute a = 1 , r =3 and n=10 , we get
[tex]S=\frac{1(3^(10)-1)}{3-1}\\\\=\frac{59049-1}{2}\\\\=-\frac{59048}{2}\\\\\Rightrrow\ S=29524[/tex]
Mr. Malone used 40 pounds of insecticide to cover 1,760 square feet of lawn and 60 pounds to cover an additional 2,640 square feet. how many pounds of insecticide would Mr. Malone need to cover his whole lawn of 4,480 square feet?
Answer:
101.8182 pounds.
Step-by-step explanation:
He used 40 pounds of insecticide to cover 1760 square feet of lawn and 60 pounds to cover an additional 2640 square feet. So,
1760 + 2640 = 4400 square feet of lawn with 40+60 = 100 pounds of insecticide. Then, his whole lawn is 4480 square feet andn he already covered 4400, so he need to cover 4480 - 4400 = 80 square feet more.
Now, one of the data given we can do a proportion:
40 pounds to 1760 square feet = [tex]\frac{40pounds}{1760ft^2}[/tex]
x pounds to 80 square feet = [tex]\frac{xpounds}{80ft^2}[/tex]
[tex]\frac{40pounds}{1760ft^2}=\frac{xpounds}{80ft^2}[/tex]
[tex]xpounds*1760ft^2 = 80ft^2*40pounds[/tex]
[tex]xpounds = \frac{80ft^2*40pounds}{1760ft^2}[/tex]
[tex]xpounds = \frac{3200pounds}{1760}[/tex]
[tex]x = 1.8182 pounds.[/tex]
Then, to cover his whole lawn of 4480 square feet he needs 100+1.8182 = 101.8182 pounds of insecticide.
find the value in this equation 16y=164
16y = 164
divide both sides by 16
y = 164 / 16 = 10.25
y = 10.25
Answer:
Step-by-step explanation:
16y=164
16/16=1 164/16= 10 1/4
164 divided by 16 is 10 1/4 when your dividing it step by step on paper.
419% of what number is 33.52 ? Find the answer in proportions
To solve the problem, '419% of what number equals 33.52?', one sets up a proportion and solves for the unknown. The calculated result equates to approximately 7.99.
Explanation:This question is asking for the base number where 419% of it equals 33.52.
Proportions play a crucial part in the calculation. Think of percentages as fractions with a denominator of 100. So, 419% can be written as 419/100. Now, let's set up a proportion to find our unknown number:
Let the unknown number be x.Set the proportions as follows: (419/100) / x = 33.52 / 1. This is because 419% of x equals 33.52.Now, cross-multiply and solving for x gives you the equation 419 * 1 = 100 * 33.52.Finally, solving for x gives x = (100 * 33.52) / 419. This results in approximately 7.99.Learn more about Percent Proportions here:https://brainly.com/question/31487888
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The midpoint of EF is M (4,10) one endpoint is E (2,6). Find the coordinates of the of the other endpoints F.
6,14
6,17
10,17
14,8
By applying this formula and solving for the unknown coordinates, the coordinates of endpoint F are determined to be (6, 14).
The student is asking to find the coordinates of the other endpoint F of a line segment EF given that the midpoint M is (4,10) and one endpoint E is (2,6). To find the coordinates of F, we can use the midpoint formula which states that the midpoint's coordinates are the averages of the endpoints' coordinates:
Midpoint Formula
Mx = (Ex + Fx) / 2
My = (Ey + Fy) / 2
Knowing the coordinates of endpoint E (2, 6) and midpoint M (4, 10), we can set up two equations to solve for the coordinates of F.
Finding Fx
4 = (2 + Fx) / 2
=> Fx = 4 * 2 - 2
=> Fx = 6
Finding Fy
10 = (6 + Fy) / 2
=> Fy = 10 * 2 - 6
=> Fy = 14
Therefore, the coordinates of the other endpoint F are (6, 14).
graph and solve the system
Y=-3x+3
Y=2x-7
I need this question answered asap! Thank you advance!!
The population in Rochester, New York, was 219,773 people in 2000 and 210,565 people in 2010. By about what percent did the population change? Did the population grow or shrink? Write the percent as a decimal.
Answer:
The population changed by 4.19%. The population shrank.
0.0419.
Step-by-step explanation:
We have been given that the population in Rochester, New York, was 219,773 people in 2000 and 210,565 people in 2010.
[tex]\text{Percent change}=\frac{\text{Final}-\text{Initial}}{\text{Initial}}\times 100[/tex]
[tex]\text{Percent change}=\frac{210,565-219,773}{219,773}\times 100[/tex]
[tex]\text{Percent change}=\frac{-9,208}{219,773}\times 100[/tex]
[tex]\text{Percent change}=-0.04189777\times 100[/tex]
[tex]\text{Percent change}=-4.189777\%[/tex]
[tex]\text{Percent change}\approx-4.19\%[/tex]
Therefore, the population changed by 4.19%.
Since the percent change is negative, therefore, the population decreased or shrank over the given period.
[tex]4.19\%=\frac{4.19}{100}=0.0419[/tex]
Which property of multiplication is used to rename 5/6 to 10/12?
The property of scaling or multiplying by a fraction is used to rename 5/6 to 10/12.
Explanation:The property of multiplication used to rename 5/6 to 10/12 is the property of scaling or multiplying by a fraction. To rename a fraction, you can multiply both the numerator and denominator by the same number. In this case, we can multiply both 5 and 6 by 2 to get 10 and 12 respectively. Therefore, 5/6 = 10/12.
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what is the domain of the following parabola
Answer:
C. All real numbers.
Step-by-step explanation:
We have been given an image of a parabola. We are asked to find the domain of given parabola.
We know that domain of a function is all real values of x for which function has a defined value.
We know that domain of a quadratic function is all real numbers, therefore, option C is the correct choice.
Answer: R
Step-by-step explanation: The domain of a function is the set of all x-values of the function.
The x-values on a coordinate system are the left-and-right values and
we can see that the parabola is expanding infinitely to the left and
to the right so the domain of the function is all real numbers.
Although there is an all real numbers option, you can also represent
this idea using a capital R like I have done below.
How many squares with side length 1/4 inch will fit into 1 square inch?
How many squares with side length 1/4 inch will fit into 1 square inch?
A) 1
B) 16
C) 4
D) 25
The number of squares with side length 1/4 inch that would fit into a 1-square inch is 4
A square to a four-sided quadrilateral that has four equal sides. A square has four right angles. The sum of angles in a square add up to 360 degrees.
Area of a square = length²
Perimeter of a square = 4 x length
In order to determine how many squares would fit into the a 1 inch square, divide the length of the square by the 1/4
Number of squares = 1 ÷ 1 / 4
1 x 4 = 4 squares
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The point R is halfway between the integers on the number line below and represents the number ____. (Use the hyphen for negative numbers and write the answer as a decimal, such as -6.4).
The value of point R is -2.5 if point R is halfway between the integers on the number line; the answer is -2.5.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
The number line is shown in the picture.
Let the number is R which is halfway between the integers on the number line.
A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
R is between the integers -3 and -2:
R = (-3 + (-2))/2 = -5/2
R = -2.5
Thus, the value of point R is -2.5 if point R is halfway between the integers on the number line; the answer is -2.5.
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One number is 3 more than another. Their sum is -13. Find the numbers
Find an expression in terms of n for the number of grey tiles in pattern n?
Write the ratio as a fraction in simplest form. 213213 feet : 412412 feet the ratio as a fraction in simplest form is .
Find the average rate of change for f(x) = x2 + 9x + 18 from x = −10 to x = 10.
a.3
b.7
c.9
d.11
The average rate of change of the given function is 9.
Given that, a function f(x) = x²+9x+18, we need to find the average rate of change for the function given,
So, the average rate of change = f(b)-f(a) / b-a
Here, a and b are -10 and 10,
So, f(-10) = 100-90+18 = 28
f(10) = 100+90+18 = 208
So, the average rate of change = 208-28 / 10+10
= 180 / 20 = 9
Hence, the average rate of change of the given function is 9.
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in parallelogram ABCD, angle D is a right angle. determine whether the parallelogram is a rectangle. If so, by what property
Which is a rational function?
A. y=sqrt x-3
B. y=5
C. y=x^2-3x+5
D. y=x-5/x
Help with number 6 and 7! Extra points and brainliest!!
For many hotels, including the Grand Hotel Toplice, the price of a room will fluctuate depending on _____
a.
the time of day
b.
the time of year
c.
the gender of the person
d.
the nationality of the person
Answer:
b.
the time of year
Step-by-step explanation:
The question is to select a suitable option from the given four option to find out the factor that affects the price of room most
a) Time of day is immaterial as hotels charge 24 hours at whatever time they enter.
b) time of year -- this is a correct factor as prices of rooms depend upon demand and demand increases due to seasons, holidays, festivals, etc.
c) the gender of the person is irrelevant in determining the price of the room as equal prices for both genders.
d) nationality of the person cannot differentiate the prices charged
Hence the suitable option is
b.
the time of year
If h(x) = 3x −7, find h(4). Show all work for credit!
What is the solution to the system of equation?
-3x-4y-32= -7
2x-6y+2=3
5x-2y+5z=9
Answer:
[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]
Step-by-step explanation:
we are given three equation of variable x, y and z.
-3x-4y-3z= -7 ------------- (1)
2x-6y+z=3 ------------- (2)
5x-2y+5z=9 ------------- (3)
Using elimination method to eliminate z from equation (1) and (2)Make the coefficient of z same in both equation.
Multiply equation (2) by 3
-3x - 4y - 3z = -7
6x - 18y + 3z = 9
Add above equation to eliminate z
3x - 22y = 2 ---------------(4)
Using elimination method to eliminate z from equation (2) and (3)Make the coefficient of z same in both equation.
Multiply equation (2) by -5
-10x + 30y - 5z = -15
5x - 2y + 5z = 9
Add above equation to eliminate z
-5x + 28y = -6 ---------------(5)
Using elimination method to eliminate x from equation (4) and (5)Make the coefficient of x same in both equation.
Multiply equation (4) by 5 and equation (5) by 3
15x - 110y = 10
-15x + 84y = -18
Add above equation to eliminate x
-26y = -8
[tex]y=\dfrac{4}{13}[/tex]
Substitute y into equation (5) to get x
So, [tex]-5x+28(\frac{4}{13})=-6[/tex]
[tex]x=\dfrac{38}{13}[/tex]
Substitute x and y into equation (1)
[tex]-3\cdot \frac{38}{13}-4\cdot \frac{4}{13}-3z=-7[/tex]
[tex]z=-1[/tex]
Solution:
[tex]x=\dfrac{38}{13},y=\dfrac{4}{13}\text{ and }z=-1[/tex]
An angle measuring 22 degrees is bisected what is the measure of he angle that are formed?
What is the solution of the system?
Use the elimination method.
−4x−2y=−12
2x+4y=−12
(?,?)
Please Help!
Answer:
The solution of the equation −4x−2y=−12 , 2x+4y=−12 are (6 , -6) .
Step-by-step explanation:
As given the equations are
−4x−2y = −12
Simplify the equation
-2(2x + y) = -12
2x + y = 6
Another equation
2x+4y=−12
2(x+2y) = −12
x + 2y = -6
Two equation becomes
2x + y = 6
x + 2y = -6
Multiply x + 2y = -6 by 2 and subtracted from 2x + y = 6 .
2x - 2x + y - 4y = 6 + 12
-3y = 18
[tex]y = \frac{-18}{3}[/tex]
y = -6
Putting the value of y in the equation
2x + -6 = 6
2x = 12
[tex]x = \frac{12}{2}[/tex]
x = 6
Therefore the solution of the equation −4x−2y=−12 , 2x+4y=−12 are (6 , -6) .