Step-by-step explanation:
We start with the formulas for the volumes of a cylinder and a cone.
Cylinder:
[tex] V_{cylinder} = \pi r^2 h [/tex]
Cone:
[tex] V_{cone} = \dfrac{1}{3} \pi r^2 h [/tex]
Now we calculate the two volumes.
Cylinder:
[tex] V_{cylinder} = \pi r^2 h [/tex]
[tex] V_{cylinder} = \pi \times (10~cm)^2 \times 9~cm [/tex]
[tex] V_{cylinder} = \pi \times 100~cm^2 \times 9~cm [/tex]
[tex] V_{cylinder} = 900 \pi~cm^3 [/tex]
Cone:
[tex] V_{cone} = \dfrac{1}{3} \pi \times (10~cm)^2 \times 9~cm [/tex]
[tex] V_{cone} = \dfrac{1}{3} \pi \times 100~cm^2 \times 9~cm [/tex]
[tex] V_{cone} = 300 \pi~cm^3 [/tex]
The volume of the cylinder is 900pi cm^3, and the volume of the cone is 300pi cm^3.
Now we divide the volume of the cylinder by the volume of the cone.
[tex] \dfrac{900 \pi~cm^3}{300 \pi~cm^3} = 3 [/tex]
Dividing the volume of the cylinder by the volume of the cone gives us 3, showing that the volume of the cylinder is 3 times the volume of the cone.
The volume of a cylinder is three times the volume of a cone.
Explanation:To show that the volume of a cylinder is three times the volume of a cone, we need to compare their formulas. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height.
Let's calculate the volume of the cylinder first. Given that the radius (r) is 10 cm and the height (h) is 9 cm, we can substitute these values into the formula: V = π(10 cm)²(9 cm) = 900π cm³.
Now let's calculate the volume of the cone. Again, substituting the values for r and h, we have V = (1/3)π(10 cm)²(9 cm) = 300π cm³.
Comparing the volumes, we have 900π cm³ for the cylinder and 300π cm³ for the cone. Dividing the volume of the cylinder by the volume of the cone, we get (900π cm³) / (300π cm³) = 3. This shows that the volume of the cylinder is three times the volume of the cone
What is the slope of the equation Y = 5/4x - 7/4
Answer:
The slope is 5/4
Step-by-step explanation:
This equation is written in slope intercept form
y = mx+b, where m is the slope and b is the y intercept
y = 5/4x -7/4
5/4 is the slope and -7/4 is the y intercept
I need to know how to find x
Answer:
x = [tex]\frac{20}{3}[/tex]
Step-by-step explanation:
ΔABC and ΔEDC are similar triangles ( AA ), hence the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{ED}[/tex] = [tex]\frac{BC}{DC}[/tex], substitute values
[tex]\frac{x}{4}[/tex] = [tex]\frac{5}{3}[/tex] ( cross- multiply )
3x = 20 ( divide both sides by 3 )
x = [tex]\frac{20}{3}[/tex]
How many times does 3 go into 100??
Final answer:
In mathematics, to find out how many times 3 goes into 100, we divide 100 by 3, resulting in 33 times with a remainder of 1.
Explanation:
The question posed is concerned with division, which falls under the subject area of mathematics. When we consider how many times 3 goes into 100, we are calculating the number of times the number 3 can be subtracted from 100 until we reach zero or a number less than 3. To solve this problem, we use division.
To divide 100 by 3, you would start by seeing how many groups of 3 are in 100. Performing the division gives us 33 with a remainder of 1, which means that 3 goes into 100 a total of 33 times with 1 left over. Therefore the quotient (the result of division) is 33 and the remainder is 1.
The concept being described in the reference material, which mentions exponents and their use to indicate repeated multiplication of a base number, is not directly related to this question, hence it will not be incorporated in the calculation of the division of 3 into 100.
The base edge of a square pyramid is 30 cm. The pyramid is 6 cm tall. Find the volume of the pyramid
Answer:
5400 cm^3
Step-by-step explanation:
Volume = Base Area * H
Base area is the area of a square with one side = 30 cm
H = 6cm
Base Area = s^2
Base Area = 30^2 = 900
Volume = 900 * 6
Volume = 5400 cm^3
Answer:
1800 cm³
Step-by-step explanation:
Recall that the formula for the area of a square is A = s², where s is the side length.
Here, that area is A = (30 cm)²2.
The formula for the volume of a square pyramid is:
V = (1/3)(base area)(height)
= (1/3)(30 cm)²2*(6 cm)
= (1/3)(900 cm²)(6 cm) = 1800 cm³
The volume of this pyramid is 1800 cm³.
f(x)= x^2 -16x+63 find the x-intercepts of this function
Answer:
The x-intercepts will be, x= 7 or x =9
Step-by-step explanation:
f(x)= x^2 -16x+63
At the x-intercept, f(x) is zero.
Therefore;
x² - 16x + 63 = 0
solving it quadratically;
product = 63
Sum = -16
x² - 9x - 7x + 63 = 0
x(x-9) - 7( x-9) = 0
(x-7) (x-9) = 0
x = 7 or x = 9
Therefore;
The x-intercepts will be, x= 7 or x =9
Answer:
(7, 0) and (9, 0)
Step-by-step explanation:
The x-intercepts refers to the points where the graph of the function crosses the x-axis, or simply the zeroes of the function. In this case, we can determine these points analytically or graphically. We simply graph the function;
y = x^2 -16x +63 then determine where the function crosses the x-axis; see the attachment below;
The x-intercepts of this function are;
(7, 0) and (9, 0)
A chair is on sale for $40, which includes an 80 percent discount. Ms Morrison thinks the original price of the book is $32. Explain ms Morrison’s mistake and determine the accurate original price of the chair. Plzzz I will give you 100 points
Answer:
she thought the chair's orginal price was fourty instead it is 72
Step-by-step explanation:
Help please!
What is the value of x?
picture below!
Answer: 8
[tex]{10}^{2} = 100 \\ {6}^{2} = 36 \\ 100 - 36 = 64 \\ \sqrt{64} = 8[/tex]
Answer:
8
Step-by-step explanation:
6² + x² = 10²
36 + x² = 100
x² = 64
x² = √64
x = 8
What’s the equation in vertex form?
Answer:
[tex]\large\boxed{y=(x+5)^2-64}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\\text{We have the equation:}\ y=x^2+10x-39\to x=1,\ b=10,\ c=-39.\\\\\text{Substitute:}\\\\h=\dfrac{-10}{2(1)}=\dfrac{-10}{2}=-5\\\\k=f(-5)=(-5)^2+10(-5)-39=25-50-39=-64\\\\\text{Finally:}\\\\y=1(x-(-5))^2-64=(x+5)^2-64[/tex]
The rectangular prism with volume 120 cm3, width 5 cm, and height 3cm. what is the length
Answer:
L = 8
Step-by-step explanation:
The volume of a rectangular prism is found by V = L*h*w. Substitute V = 120, w = 5 and h =3 then solve for the length.
120 = L*3*5
120 = 15L
8 = L
what is 3 billion divided by 24 simplified
Answer: one hundred and twenty five million
Answer:
125,000,000
Step-by-step explanation:
3 billion has 9 0's so you take that and divide it by 24 to get:
3,000,000,000/24=125,000,000 as your answer
Match each function
Answer:
* The degree of the function is 4 and the leading coefficient is positive
f(x) = (x + 6)(2x - 3)(x - 1)²
* The degree of the function is 5 and the leading coefficient is negative
f(x) = (x - 2)²(-2x - 1)²(-x + 1)
* The degree of the function is 6 and the leading coefficient is negative
f(x) = (-x + 1)³(x + 2)²(x - 3)
* The degree of the function is 5 and the leading coefficient is positive
f(x) = (-2x + 1)²(x - 3)²(x + 1)
Step-by-step explanation:
∵ f(x) = (x + 6)(2x - 3)(x - 1)²
∵ (x)(2x)(x²) = 2x^4
∴ The degree of the function is 4
∴ The leading coefficient is positive ⇒ (2)
∵ f(x) = (x - 2)²(-2x - 1)²(-x + 1)
∵ (x)²(-2x)²(-x) = (x²)(4x²)(-x) = -4x^5 ⇒ (neglect -ve with even power)
∴ The degree of the function is 5
∴ The leading coefficient is negative ⇒ (-4)
∵ f(x) = (-x + 1)³(x + 2)²(x - 3)
∵ (-x)³(x)²(x) = (-x³)(x²)(x) = -x^6
∴ The degree of the function is 6
∴ The leading coefficient is negative ⇒ (-1)
∵ f(x) = (-2x + 1)²(x - 3)²(x + 1)
∵ (-2x)²(x)²(x) = (4x²)(x²)(x) = 4x^5
∴ The degree of the function is 5
∴ The leading coefficient is positive ⇒ (4)
9,220,000,000 in scientific notation
Answer:
9.22×10^9
Step-by-step explanation:
The number must be written with
- a number between 1-10
- multiplied by a power of 10
The power of 10 tells you how many times you moved the decimal.
The angle of a triangle is 30 degrees 60 degrees and 90 degrees Is this a unique triangle
Yes it is called a right angled triangle
PLEASE HELP ASAP!!
A triangle with vertices A(2, -2), B(-1, 1) and C(0,2) is reflected across the y-axis and then dilated by a factor of 3 with the origin as the center of dilation.
What is the x-coordinate of the A’?
A. -6
B. 2
C. -2
D. -4
Answer:
A. -6
Step-by-step explanation:
(2,-2) reflected over X would be (-2,2). Then dilate by 3 which you multiply by 3. So -2 x 3 = -6.
PLEASE HELP, I’LL GIVE BRAINLIST IF NEEDED!
Answer:
i forgot to
Step-by-step explanation:
What is the total area of the polygon?
the area is 164. You multiply 6x4=24 and then u do 10x8=80 and then u add and get 164
Find AM in the parallelogram
Answer:
AM = 6
Step-by-step explanation:
Using the property of a parallelogram
• The diagonals bisect each other
MO is a diagonal, hence
AM = AO = 6
The following frequency table summarizes the number of children that dads in Dads Club have.
Based on this data, what is a reasonable estimate of the probability that the next dad to join Dads Club has fewer than 3 children?
Answer:
C
Step-by-step explanation:
Now there are 6+4+8+1+1=20 dads in the Dads Club.
Fewer than 3 children have
1 child - 6 dads2 children - 4 dads.So, 6+4=10 dads have fewer than 3 children.
The probability that the dad of Dads Club has fewer than 3 children is
[tex]Pr=\dfrac{10}{20}=0.5 \text{ or } 50\%.[/tex]
The probability that the next dad to join Dads Club has fewer than 3 children is reasonable to be 50%.
Option: C is the correct answer.
C. 50%
Step-by-step explanation:Let P denotes the probability of an event.
and A denote the event that the next dad has fewer than 3 children.
From the table the total number of dads are: 6+4+8+1+1=20
The number of dad who have less than 3 children are: 6+4=10
Hence, we have
[tex]P(A)=\dfrac{\text{Number\ of\ dad\ with\ less\ than\ 3\ children}}{\text{Total\ number\ of dad}}[/tex]
Hence, we have:
[tex]P(A)=\dfrac{10}{20}=\dfrac{1}{2}[/tex]
which in percentage is given by:
[tex]P(A)=50\%\\\\(Since,\\\\\dfrac{1}{2}\times 100=50\%)[/tex]
If Tina cuts a lawn by herself, she can finish in 5 hours. If bill cuts the same lawn by himself it takes him two hours longer than Tina. How long will it take them both working together?
Final answer:
Tina and Bill will take approximately 2 hours and 55 minutes to finish cutting the lawn when they work together, combining their individual rates of work.
Explanation:
If Tina cuts a lawn by herself, she can finish in 5 hours. If Bill cuts the same lawn by himself it takes him two hours longer than Tina, which means it takes Bill 7 hours. To determine how long it will take both of them working together, we can use the rates at which they work. Tina's rate of work is 1/5 of the lawn per hour, and Bill's rate is 1/7 of the lawn per hour. Working together, their combined rate is the sum of their individual rates, which is (1/5 + 1/7) of the lawn per hour.
To find the combined rate, we calculate:
(1/5) + (1/7) = (7/35) + (5/35) = 12/35 of the lawn per hour. To find out how long it will take them to finish the lawn together, we take the reciprocal of this combined rate. Therefore, 35/12 hours, or 2 hours and 55 minutes, is the amount of time they will need to finish cutting the lawn when working together.
Given: circle k(O),
ED
diameter,
m∠OEF=32°, m
EF
=(2x+10)°
Find: x
Answer:
[tex]x=53[/tex]
Step-by-step explanation:
step 1
Find the measure of arc DF
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<OEF=\frac{1}{2}(arc\ DF)[/tex]
we have
[tex]m<OEF=32\°[/tex]
substitute
[tex]32\°=\frac{1}{2}(arc\ DF)[/tex]
[tex]arc\ DF=64\°[/tex]
step 2
Find the measure of x
we know that
[tex]arc\ DF+arc\ EF=180\°[/tex] ---> is half the circle
we have
[tex]arc\ DF=64\°[/tex]
[tex]arc\ EF=(2x+10)\°[/tex]
substitute
[tex]64\°+(2x+10)\°=180\°[/tex]
[tex]2x\°=180\°-74\°[/tex]
[tex]2x\°=106\°[/tex]
[tex]x=53[/tex]
The value of x for the angles of the inscribed circle is gotten as; x = 53°
What is the value of the angle in the circle?
Let us first find the angle subtended by the arc DF
From inscribed angle theorem, we know that the measure of an inscribed angle is half the measure of the intercepted arc. Thus;
m∠EOF = ¹/₂(arc DF)
Thus;
¹/₂(arc DF) = 32°
arc DF = 64°
From half circle theorem, we can say that;
arc DF + arc EF = 180°
Thus;
64 + 2x + 10 = 180
2x = 180 - 74
2x = 106
x = 53°
Read more about inscribed angles at; https://brainly.com/question/13110384
How many radians is 60 °
Answer:
1.047
Step-by-step explanation:
60° × π/180 = 1.047rad
or
From the standard conversion factor
360∘ = 2 π r a d
we may use ratio and proportion to obtain that
60 ∘ = π 3 r a d
Answer:
pi/3
Step-by-step explanation:
To convert from degrees to radians, we multiply by pi/180
60 degress * pi/180 = pi/3
60 degrees is pi/3 radians
Larry and four friends each ate a half of a pizza, how many whole pizzas did they consume all together? A)5
B)2/5
C)5/2
D)5 1/2
total 5 friends ate 5 half pieces of pizza
so we will add all 5 pieces togther.
total pizza = 1/2 +1/2+1/2+1/2+1/2 = 5/2
so option C is answer
EASY QUESTION 20 POINTS& BRAINLIEST
Graph the system of equations. {3x+y=6 −3x−4y=12
please add a pic of the graph or give me the correct coordinates and explain.Thanks :)
Answer:
See explanation below, and see attached photo for graphs
Step-by-step explanation:
To graph 3x + y = 6, find the x and y intercepts.
We get the x intercept when y = 0, so plug in 0 for y and solve...
3x + 0 = 6
3x = 6
x = 2, so the x intercept is at (2, 0)
We get the y intercept when x = 0, so plug in 0 for x and solve...
3(0) + y = 6
y = 6, so the y intercept is at (0, 6)
Plot those two points and draw a line through them
To graph -3x - 4y = 12, find the x and y intercepts.
We get the x intercept when y = 0, so plug in 0 for y and solve...
-3x - 4(0) = 12
-3x = 12
x = -4, so the x intercept is at (-4, 0)
We get the y intercept when x = 0, so plug in 0 for x and solve...
-3(0) - 4y = 12
-4y = 12
y = -3, so the y intercept is at (0, -3)
Plot those two points and draw a line through them
The system of equations 3x + y = 6 and -3x - 4y = 12 is graphed by converting each to slope-intercept form, plotting points, and drawing lines. Intersection is found by solving the equations simultaneously, resulting in the intersecting point (4, -6).
Explanation:To graph the system of equations consisting of 3x + y = 6 and -3x - 4y = 12, we first need to solve each equation for y to get them into slope-intercept form (y = mx + b). Here are the steps:
For the first equation, 3x + y = 6, subtract 3x from both sides to get y = -3x + 6.For the second equation, -3x - 4y = 12, start by adding 3x to both sides to get -4y = 3x + 12, then divide everything by -4 to get y = -3/4x - 3.Next, we plot the lines on a coordinate plane by finding at least two points for each line based on the equations we've just derived:
For y = -3x + 6, we could use x = 0 (which gives us y = 6) and x = 2 (which gives us y = 0).For y = -3/4x - 3, we could use x = 0 (which gives us y = -3) and x = 4 (which gives us y = -6).After plotting these points for each line, draw straight lines through the points to complete the graph. The coordinates of the intersection of the two lines can be found by setting the two equations for y equal to each other and solving for x:
-3x + 6 = -3/4x - 3Multiplying every term by 4 to clear fractions: -12x + 24 = -3x - 12Add 12x to both sides: 24 = 9x - 12Add 12 to both sides and divide by 9: x = 4Substitute x = 4 into y = -3x + 6 to find y: y = -3(4) + 6 = -12 + 6 = -6Therefore, the intersection point is at (4, -6).
In 1995, Orlando, Florida, was about 175,000. At that time, the population was growing
at a rate of about 2000 per year.
i. Write an equation, in slope-intercept form to find Orlando’s population for any
year.
ii. What is Orlando’s population in 2010?
To model Orlando's population growth, an equation in slope-intercept form is y = 2000x + 175000. The year 2010 is 15 years after 1995, so substituting 15 in for x gives a population of approximately 205,000 residents for Orlando in 2010.
To answer the student's question, first we need to write an equation in slope-intercept form to find Orlando's population for any year. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the starting value when x=0). In this case, the variable y represents Orlando's population, m represents the annual growth rate (2000 people per year), and x represents the number of years since 1995.
Using these variables, our equation becomes y = 2000x + 175000, where x is the number of years since 1995. To find Orlando's population in 2010, we must substitute x with 15, since 2010 is 15 years after 1995.
The calculation would be: y = 2000(15) + 175000, which simplifies to y = 205000.
Therefore, Orlando's population in 2010 was approximately 205,000 residents.
5. What’s the answer to this question
Answer:
Graph 3
Step-by-step explanation:
julie,ellen, and jenny shared a pizza. julia ate 1/8 of the pizza Ellen and Jenny ate 3/8 of pizza Did they eat whole pizza
Julia ate 1/8
Ellen and Jenny ate 3/8
1/8 + 3/8 = 4/8
No they didn't eat the whole pizza, they only ate half of the pizza.
Julie, Ellen, and Jenny together ate [tex]\frac{1}{8}[/tex]+ [tex]\frac{3}{8}[/tex] = [tex]\frac{4}{8}[/tex] or [tex]\frac{1}{2}[/tex]of the pizza, which means they ate only half of it, not the entire pizza.
The question involves the mathematical concept of fractions and their addition. Julie ate [tex]\frac{1}{8}[/tex] of the pizza, while Ellen and Jenny together ate [tex]\frac{3}{8}[/tex]of the pizza. To determine if they ate the whole pizza, we need to add these fractions.
[tex]\frac{1}{8}[/tex] (Julie's portion) + [tex]\frac{3}{8}[/tex] (Ellen and Jenny's portion) = [tex]\frac{4}{8}[/tex]or [tex]\frac{1}{2}[/tex] after simplifying.
Since [tex]\frac{1}{2}[/tex] is less than a whole, Julie, Ellen, and Jenny did not eat the entire pizza. They ate only half of it.
WRITE AND SOLVE A DIVISON EQUATION TO FIND THE NUMBER OF 1/3 POUND HAMBURGER PATTIES THAT CAN BE MADE 4 POUNDS OF GROUND BEEF.
Answer:
12 patties
Step-by-step explanation:
4 ÷ 1/3 = 12
What is the result when you convert 7/8 to a percent?
Answer:
87.5%
Step-by-step explanation:
write the height of zak as a fraction of the height of fred
[tex]\bf \cfrac{Zak}{Fred}\qquad \cfrac{1.86}{1.6}\implies \cfrac{~~\frac{186}{100}~~}{\frac{16}{10}}\implies \cfrac{186}{100}\cdot \cfrac{10}{16}\implies \cfrac{186}{16}\cdot \cfrac{10}{100}\implies \cfrac{93}{8}\cdot \cfrac{1}{10} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{93}{80}~\hfill[/tex]
To express Zak's height as a fraction of Fred's, divide Zak's height by Fred's height. This will yield a fraction that represents how Zak's height compares to Fred's. The heights need to be provided to calculate the actual fraction.
Explanation:To write the height of Zak as a fraction of the height of Fred, we need to know both Zak's height and Fred's height. For instance, if Zak's height is 4 feet and Fred's height is 6 feet, the fraction representing Zak's height in relation to Fred's height would be ⅓ (Zak's height) over ⅔ (Fred's height). This is simplified by dividing both the numerator and the denominator by the GCD (Greatest Common Divisor) of Zak's and Fred's height if they are not already in simplest form.
If Zak is shorter than Fred, the fraction will be less than 1, indicating that Zak is shorter than Fred. Conversely, if Zak is taller than Fred, the fraction will be greater than 1, indicating Zak's greater height. In your specific question, it seems the heights are not provided, so please provide them in order to calculate the exact fraction.
What is the nth term of the arithmetic sequence 7,5,3,1?
Answer:
tn = 7 + (n - 1)*(-2) or
tn = 9 - 2n
Step-by-step explanation:
You are (beginning with 7) subtracting 2 from the term to the left.
a = 7
d = -2
tn = a1 + (n - 1)*d
tn = 7 + (n - 1)*(-2)
Try this out on n = 4
t4 = 7 + (4 - 1)*-2
t4 = 7 + (3) (-2)
t4 = 7 - 6
t4 = 1 just as it says.
More generally
tn = 7 + (n - 1)*-2
tn = 7 + (-2n) + 2
tn = 9 - 2n