Answer:
[tex]\displaystyle \frac{4r^2\pi }{9} \text{ cm}^3[/tex]
Step-by-step explanation:
We will write an expression for the second cone's volume. Let r be equal to the radius of the first cone.
The volume of a cone can be found with the following formula. Here, h is the height, r is the radius, and V is the volume.
[tex]\displaystyle V=\frac{1}{3} \pi r^2h[/tex]
We will substitute our given values and simplify.
[tex]\displaystyle V=\frac{1}{3} \pi (\frac{1}{3}*r )^2(12)[/tex]
Square.
[tex]\displaystyle V=\frac{1}{3} \pi \frac{r^2}{9} (12)[/tex]
Divide 12 by 3.
[tex]\displaystyle V=\pi \frac{4r^2}{9}[/tex]
Move π to the numerator.
[tex]\displaystyle V=\frac{4r^2\pi }{9}[/tex]
The volume of the new cone, with the same height but one-third of the original radius, is represented by the expression (4 / 9)πr².
The volume of a cone is given by the formula V = (1/3)πr²h.
For a cone with a radius r and height 12 cm, its volume can be expressed as:
[tex]V = (\frac{1}{3})\pi r^2(12) = 4\pi r^2[/tex]
Now, consider a cone with the same height, but with 1/3 of the original radius. Let the new radius be (1/3)r. Using the volume formula again:
[tex]V = (\frac{1}{3})\pi (\frac{1}{3}r)^2(12) = (\frac{1}{3})\pi(\frac{1}{9}r^2)(12) = (\frac{12}{27})\pi r^2 = \frac{4}{9}\pi r^2.[/tex]
Thus, the expression for the volume of the new cone is (4 / 9) πr².
Write the point-slope form of the equation of the line that passes through the point (1, 3) and has a slope of 2. Include your work in your final answer. Type your answer in the box provided to submit your solution.
Answer:
y - 3 = 2(x - 1).
Step-by-step explanation:
Point-slope form is
y - y1 =m(x - x1)
Here m (slope) = 2 , x1 = 1 and y1 = 3:
y - 3 = 2(x - 1).
Evaluate f(2) for f(x) = 3^x
Answer:
9
Step-by-step explanation:
3^2 = 9
Answer:
f(2) = 9
Step-by-step explanation:
Step 1: Substitute 2 for x in the function
f(x) = 3^x
f(2) = 3^2
f(2) = 3*3
f(2) = 9
Answer: f(2) = 9
Which expression is equivalent to Negative 12 (3 x minus three-fourths)?
Answer:
[tex]-36x+9[/tex]
Step-by-step explanation:
In the given problem options are missing.
The given expression is
[tex]-12\left(3x-\dfrac{3}{4}\right)[/tex]
We need to find the equivalent expression.
Using distributive property we get
[tex]-12(3x)-12(-\dfrac{3}{4})[/tex]
[tex]-36x+9[/tex]
Hence, the expression [tex]-36x+9[/tex] is equivalent to given expression.
Answer:
-36x + 9
Step-by-step explanation:
To find the answer, simplify by multiplying within the parentheses. -12×3x= -36x. -12×-¾=9. The expression then becomes -36x + 9, which is the answer.
Hope this helps. I got it right on Edgen.
Calculate the circumference of the inscribed circle. [Use π = 3.14]
A) 18.84 ft
B) 37.68 ft
C) 48 ft
D) 75.36 ft
Answer:
B) 37.68 ft
Step-by-step explanation:
The diameter is 12 because the square's side is 12. The circumference is diameter * pi. 12 * 3.14 = 37.68.
Hope I Helped
Bill made some purchases that totalled $18.75 and paid for them with a twenty-dollar bill. The cash register has only quarters, dimes and nickels.
In how many different ways can the cashier make change
Answer:
42
Step-by-step explanation:
The $1.25 in change can be made ...
5 quarters (1 way)4 quarters and any of 2, 1, 0 dimes (3 ways)3 quarters and any of 5, 4, 3, 2, 1, 0 dimes (6 ways)2 quarters and any of 7--0 dimes (8 ways)1 quarter and any of 10--0 dimes (11 ways)0 quarters and any of 12--0 dimes (13 ways)Change can be made a total of 1+3+6+8+11+13 = 42 ways.
Which figure is similar to the parallelogram? (Figures may not be drawn to scale.) A parallelogram has side lengths of 8 and 5.8. Angles are 68 degrees and 112 degrees. A parallelogram has side lengths of 4 and 4.8. Angles are 68 degrees and 112 degrees. A rectangle has a length of 6 and width of 4.8. All angles are 90 degrees. A parallelogram has side lengths of 4 and 2.9. Angles are 48 degrees and 132 degrees. A parallelogram has side lengths of 4 and 2.9. Angles are 68 degrees and 112 degrees.
Answer:
d
Step-by-step explanation:
HELP!!!! WILL MARK BRAINLEST IF CORRECT!
How is the distributive property used when finding the product of two polynomials? How are polynomials closed under multiplication?
Answer:
When you multiply the first number of each polynomial by the second. Then you add the products together and combine like terms to simplify.
Step-by-step explanation:
I don't really know how to explain this, lol.
24 decreased by the quotient of a number and 6 is -5
Answer: X/6 -24 = -5
Step-by-step explanation:
How many minutes will it take the school bus to complete the 52-km trip back to the school at an average speed of 1.0 km/min?
If the school bus travels at an average speed of 1.0 km/min, it will take 52 minutes to complete the 52 km trip back to the school.
It is given in the question that the school bus is traveling at an average speed = 1.0 km/min
The total distance the school bus will cover on the trip back to the school is = 52 km
According to the formula of speed,
Speed = Distance/Time
So, Time = Distance/Speed
Substituting the given values of distance and speed, we get
Time = 52 km/1.0 km/min
= 52 minutes
Therefore, the time being taken by the school bus to complete the 52 km trip back to the school (average speed = 1.0 km/min) = 52 minutes
To know more about speed,
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Find the surface area of number 4, last one!
Answer:
3,060 ft^2
Step-by-step explanation:
Shape 1:
Base: 36 × 10 = 360 (×2 = 720)
Large faces: 36 × 20 = 720 (×2 = 1,440)
Smaller face: 20 × 10 = 200
Add: 720 + 1,440 + 200 = 2,360
Shape 2:
Base: 15 × 10 = 150
Top face: 25 × 10 = 250
Triangular faces: 20 × 15 = 300
Add: 150 + 250 + 300 = 700
Add both shapes:
2,360 + 700 = 3,060
What is the degree measure of v?.
A) 31°
B) 34°
C) 58°
D) 74°
Answer:
B) 34°
Step-by-step explanation:
149 - 115 = 34°
Exterior angle = sum of other interior angles
Answer:
B) 34°
Step-by-step explanation:
The sum of the two opposite interior angles is equal to the exterior angle in a triangle
v+115 = 149
Subtract 115 from each side
v+115-115 =149-115
v =34
the area is 28 square cm, and 4 width
Answer:
High is 7
Step-by-step explanation:
If the area is 28 square cm, and 4 width Then the High is 7
Because 28/4=7
And 7*4=28
The 1997 a value of an object was $5000. In 2012, it was worth $9500. The annual percent growth has been constant. What is the annual percent growth?
Solution:
The increasing function is given as:
[tex]y = a(1+r)^t[/tex]
Where,
y is future value
a is initial value
r is growth rate
t is number of years
From given,
a = 5000
y = 9500
t = 1997 to 2012 = 15 years
r = ?
Substituting the values we get,
[tex]9500 = 5000(1+r)^{15}\\\\(1+r)^{15} = 1.9\\\\Take\ \frac{1}{15}th\ power\ on\ both\ sides\\\\1+r = (1.9)^{\frac{1}{15}}\\\\1+r = 1.04367\\\\r = 1.04367 - 1\\\\r = 0.04367\\\\In\ percentage,\\\\r = 0.04367 \times 100 \%\\\\r = 4.367 \% \approx 4.37 \%[/tex]
Thus annual percent growth is 4.37 %
Logan and Claudia want to split a bag of fun-sized candy, and decide to use the divider-chooser method. The bag contains 100 Snickers, 100 Milky Ways, and 100 Reese's, which Logan values at $4, $1, and $2 respectively. (This means Logan values the 100 Snickers together at $4, or $0.04 for 1 Snickers)
If Claudia is the divider, and in one half puts: 35 Snickers 30 Milky Ways 55 Reese's What is the value of this half in Logan's eyes?
Answer:
$2.80
Step-by-step explanation:
35 Snickers = $1.40
30 Milky Ways = $0.30
55 Reese's = $1.10
Value of bag:
$2.80
1/9 + x = 1/2
What fraction is X?
Final answer:
The equation 1/9 + x = 1/2 is solved by finding a common denominator and subtracting the fractions, which results in x = 7/18.
Explanation:
To solve the equation 1/9 + x = 1/2, we need to find the value of x.
First, we'll align the equation to isolate x:
1/9 + x = 1/2x = 1/2 - 1/9Next, we must have a common denominator to subtract the fractions. The least common denominator (LCD) for 9 and 2 is 18. We convert both fractions to have this common denominator:
x = (9/18) - (2/18)Now we subtract the numerators:
x = 9/18 - 2/18x = (9 - 2)/18x = 7/18Thus, the value of x is 7/18.
What is the answer to -3x+2y=5
3x+y=7
Answer:
x=1
y=4
(1, 4)
Step-by-step explanation:
To solve simultaneous equation, we can use either of these three methods. Substitution method, elimination method or graphical method. But for the purpose of this question, we would be using the elimination method.
-3x+2y=5 Equation 1
3x+y=7. Equation 2
Since in the two equations, x has the same coefficient, we can eliminate x by adding both equations together
-3x+3x=0
2y+y=3y
5+7=12
We now have 3y=12
Divide both sides by 3
y=12/3
y=4
Substitute y for 4 in equation 2.
3x+4=7
3x=7-4
3x=3
Divide both sides by 3
x=3/3
x=1
x=1 and y=4
2 Points
The value 4 is an upper bound for the zeros of the function shown below.
f(x) = 4x2 - 12x2 – x+15
O A. True
O. B. False
SUBMIT
Answer:
Step-by-step explanation:
A true true
Answer:
T
Step-by-step explanation:
Ellen Fowler stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Ellen receives a bunch of fan mail. She splits all the letters into 3 equal stacks to open with her mom and her sister. Each stack contains 21 letters.
Which equation can you use to find the number of letters n Ellen receives?
Answer:
Ellen receives a bunch of fan mail. She splits them all into 3 equal stacks to open up with her mom and sister and each stack contains 21 letters.
To find the total number of letters that Ellen has recieved we have to add up all the letters in the 3 piles.
Your equation would be 21*3=n
You would times 21 by 3 because there are 21 letters in each stack.
Where n would represent the number of letter that Ellen has recieved.
To solve for n you would simply go 21*3=63.
Ellen has revieved a total of 63 letters.
Hope this helps ;)
Answer:
7 letters
Step-by-step explanation:
Please write step by step of how you got the answer. Thankyou
Answer:
The solution in the attached figure
Step-by-step explanation:
step 1
Place the numbers -4, 4, 0, and -3 in the left side
Adds the numbers
[tex]-4+4+0-3=-3[/tex] ----> is correct
step 2
Place the numbers 3, -1, and -2 in the right side
Adds the numbers
[tex]-3+3-1-2=-3[/tex] ----> is correct
step 3
Place the numbers 1 and 2 in the base side
Adds the numbers
[tex]-4+1+2-2=-3[/tex] ----> is correct
The solution in the attached figure
An architect build a scale model of a sports stadium that was 12 inches. The actual height of the building was 180 feet.
Which scale did the architect use to create the scale of the sports stadium?
Answer:
Scale did the architect use to create the scale of the sports stadium is 1 inch = 15 feet.
Step-by-step explanation:
Given : An architect build a scale model of a sports stadium that was 12 inches. The actual height of the building was 180 feet.
To find : Which scale did the architect use to create the scale of the sports stadium?
Solution :
An architect build a scale model of a sports stadium that was 12 inches.
The actual height of the building was 180 feet.
The scale is determined by number of feet used in 1 inch.
i.e. For 12 inches it is 180 feet
For 1 inch = [tex]\frac{180}{12}[/tex] feet
1 inch = 15 feet
Therefore, scale did the architect use to create the scale of the sports stadium is 1 inch = 15 feet.
Estimate the square root of 51
Answer:
7.14
Step-by-step explanation:
Just use a calculator and type in the [tex]\sqrt{51}[/tex]
Solve for r write the answer in simplified form
7 = - 7r
Answer:
r = -1
Step-by-step explanation:
To get r isolated, you have to divide each side by -7
7 divided by -7 is -1, therefore r = -1
What is the slope of the line.
Step-by-step explanation:
Two points on the line are (1,4) and(-4,-4)
slope of the line =
[tex] \frac{ y2 - y1}{x2 - x1} [/tex]
[tex] \frac{ - 4 - 4}{ - 4 - 1} [/tex]
[tex] \frac{ - 8}{ - 5} [/tex]
[tex] \frac{8}{5} [/tex]
Help pls I dunno how to do it ): explanation would be nice
Kelly is reading a 1056-page book. During the past 8 days she has read 384 pages. At this rate, how many more days will it take her to complete the book?
Answer:
14.75 days
Step-by-step explanation:
number of pages she reads a day :
384/8 = 48
remaining of the book
1056-348= 708
708/48= 14.75 days
Micah recorded the amount of time his mom and dad spend reading bedtime stories. He plotted the data in the box plot below.
Which is an accurate comparison of the two data sets?
The lengths of time that his mom reads are typically longer and have less variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically shorter and have less variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically shorter and have more variability than the lengths of time that his dad reads.
Answer:
The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
Step-by-step explanation:
This is because the range is greater and the minimum and maximum are higher numbers.
The solution to the box plot is is the lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
What is box plot?A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.
A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.
It is used when showing the distribution of data points across a selected measure and if the box in a box plot is stretched in one direction or the other, then the data is skewed in that direction.
Given data ,
Let the box plots be represented as A and B
Now , the box plot A represents the minutes Mom used to spend during reading
And , the box plot B represents the minutes Dad used to spend during reading
From the box plots , we can see that the range is greater in the box plot A and the minimum and maximum are higher value numbers when Mom is reading the bedtime stories
Hence , from the box plots lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads
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An antique store is getting ready for their annual show in mark up all the prices by 25% if their most expensive item they have to markup is originally $840 what will be the show price be
Answer:
$1050
Step-by-step explanation:
The show price will be 25% of $840 and the result added to $840.
Therefore
25% of $840
25% /100% x $840
0.25 x $840
$210
Show price = $840 + $210
= $1050
The show price will be $1050
Final answer:
The show price of the most expensive item after the 25% markup will be $1050.
Explanation:
To determine the show price, we need to calculate a 25% markup on the original price of $840. This markup represents the additional amount added to the original price to determine the final selling price.
To calculate the markup amount, we multiply $840 by 0.25. This gives us $210, which represents the 25% of the original price.
Next, we add the markup amount to the original price. $840 plus $210 equals $1050. This means that the final show price of the most expensive item, after applying a 25% markup, will be $1050.
Therefore, the show price of the most expensive item after the 25% markup will be $1050.
PLEASE HELP ME I NEED HELP YOU WILL BE BRAINIEST
Answer:
533 sq in
Step-by-step explanation:
13x29=377. that is the area of the rectangle.
then, the side of the triangle will be 13+11= 24in
area of a triangle is bxh/2 so 13x24 is 312 then divided by 2 is 156.
Add the two areas together 377+156 to get 533.
Answer:
533 sq inch
Step-by-step explanation:
Area for rectangle is Length time with
29x13 = 377
area of triangle is base time hieght / 2
24 x 13 = 312 / 2 =156
add them
Jenna is filling containers of beans. Each container holds
1
3
of a kilogram of beans. If Jenna has 8 kilograms of beans, how many containers can she fill?
A) 21
B) 23
C) 24
D) 28
Answer:
C)24
Step-by-step explanation:
Answer:
24 or c
Step-by-step explanation:
its on usatestprep
WUIZ
9. The length of a rectangle is 4 inches greater than the width. The perimeter of the
rectangle is 24 inches. What are the dimensions of the rectangle?
O
A length = 12 in.; width = 8 in.
B length = 8 in.; width = 4 in
c length = 8 in.; width – 6 in.
D length = 6 in.; width = 2 in.
Answer:
B length = 8 in.; width = 4 in
Step-by-step explanation:
Given
the length L = w + 4
Perimeter = 24 inches
Perimeter of a rectangle
= 2(L + W)
We now have two equations.
Equation 1: L = w + 4
Equation 2: P = 2(L + W)
Substitute L as w + 4 into equation 1. And 24 for p
Therefore
24 = 2(w + 4 + w)
24 = 2(2w + 4)
Distribute 2 into (2w + 4)
We have
24 = 2 x 2w + 2 x 4
24 = 4w + 8
Subtract 8 from both sides
24 - 8 = 4w + 8 - 8
16 = 4w
Divide both sides by 4
16/4 = 4w/4
4 = w
w = 4 inches
Now substitute 4 for w into either of the equations to get
L.
Using equation 1 , we have
L = w + 4
L = 4 + 4
L = 8 inches
Answer:
12 oak as best value
Step-by-step explanation: