The volume [tex]V_c[/tex] of a cone with base radius [tex]r_c[/tex] and height [tex]h_c[/tex] is
[tex]V_c = \dfrac{1}{3}\pi r_c^2 h_c[/tex]
Similarly, the volume [tex]V_s[/tex] of a sphere with radius [tex]r_s[/tex] is
[tex]V_s = \dfrac{4}{3}\pi r_s^3[/tex]
We know that [tex]V_c=V_s[/tex] and that [tex]h_c=96[/tex]
So, we can set up the following equation:
[tex]\dfrac{96}{3}\pi r_c^2=\dfrac{4}{3}\pi r_s^3[/tex]
We can simplify the common denominator 3, and pi appearing on both sides:
[tex]96r_c^2=4r_s^3[/tex]
We can divide both sides by 4:
[tex]24r_c^2=r_s^3[/tex]
Without further information, this is all we can say: the cubed radius of the sphere is the same as 24 times the squared radius of the cone.
The values for the radius of the cone and the sphere is 24 units.
It is given that a cone and a sphere have the same volume.
It is required to find the radius of the cone and sphere if the height of the cone is 96.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
We know the volume of the cone:
[tex]\rm V_c = \pi R^2\frac{H}{3}[/tex]
Where R is the radius of the cone and H is the height of the cone.
And the volume of the sphere:
[tex]\rm V_s = \frac{4}{3} \pi r^3[/tex]
Where r is the radius of the sphere.
[tex]\rm V_c = V_s[/tex] (From the question)
[tex]\rm \pi R^2\frac{H}{3}=\rm \frac{4}{3} \pi r^3[/tex]
[tex]\rm \pi R^2\frac{96}{3}=\rm \frac{4}{3} \pi r^3[/tex] ( H = 96 units)
[tex]\rm 32R^2=\rm \frac{4}{3} r^3[/tex]
[tex]\rm 24R^2= r^3[/tex]
We are assuming that R = r
[tex]\rm 24r^2= r^3[/tex]
r = 24 units and
R = 24 units.
Thus, the values for the radius of the cone and the sphere is 24 units.
Learn more about the volume here:
https://brainly.com/question/16788902
10y^2+10y+3=0 use quadratic formula to solve each equation
Answer: [tex]\bold{-\dfrac{1}{2}\pm \dfrac{\sqrt5}{10}}i[/tex]
Step-by-step explanation:
[tex]10y^2+10y+3=0\qquad \rightarrow \quad a=10,\ b=10,\ c=3\\\\y=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\y=\dfrac{-10\pm \sqrt{10^2-4(10)(3)}}{2(10)}\\\\\\.\ =\dfrac{-10\pm \sqrt{100-120}}{2(10)}\\\\\\.\ =\dfrac{-10\pm \sqrt{-20}}{2(10)}\\\\\\.\ =\dfrac{-10\pm 2i\sqrt5}{2(10)}\\\\\\.\ =\dfrac{-5\pm i\sqrt5}{10}\\\\\\.\ =-\dfrac{1}{2}\pm \dfrac{\sqrt5}{10}i[/tex]
At the fair the ratio of male to females was 4:5. If there are 160 males at the fair, how many females are there? Show work.
Solve for x: −3|x − 3| = −6
Answer:
x = 5 x = 1
Step-by-step explanation:
−3|x − 3| = −6
Divide each side by -3
−3/-3|x − 3| = −6/-3
|x − 3| = 2
An absolute value is equal to a positive and negative solution
x-3 =2 and x-3 = -2
Add 3 to each side
x-3+3 = 2+3 x-3+3 = -2+3
x = 5 x = 1
if x/8 =5/4 then x=10 true false
Answer:
true
Step-by-step explanation:
given
[tex]\frac{x}{8}[/tex] = [tex]\frac{5}{4}[/tex] ( cross- multiply )
4x = 40 ( divide both sides by 4)
x = 10
Final answer:
The equation x/8 = 5/4 is solved by multiplying both sides by 8, resulting in the correct solution x = 10. Thus, the statement is indeed true.
Explanation:
To solve the equation x/8 = 5/4, we need to perform algebraic operations to solve for x. We multiply both sides of the equation by 8 to isolate x on one side, which gives us:
x = (5/4) × 8
Now, we simplify this further:
x = (5 × 2) = 10
Therefore, the statement 'if x/8 = 5/4 then x = 10' is true, since we have confirmed that multiplying 5/4 by 8 indeed equals 10. It is important to understand that multiplication and division are inverse operations, and we can solve for an unknown by isolating it on one side of the equation.
Which polynomial is a quintic binomial?
A: x^2+4x
B: 3x^5+2
C: x^4+2x^3-x^2+7x+11
D: 5x^2-2x+1
ANSWER :
Quintic binomial is a binomial having highest degree 5.So (B) 3x^5+2 is correct having highest degree .
Hope this helps
Thanks
Final answer:
The quintic binomial among the options given is B: 3[tex]x^5[/tex] + 2, as it has two terms and its highest degree is five.
Explanation:
The question asks to identify which polynomial is a quintic binomial.
A quintic polynomial is one where the highest degree of any term is five, and a binomial is a polynomial with exactly two terms.
Looking at the options provided, Option B: 3[tex]x^5[/tex] + 2 fits this description, as it has two terms and the highest degree is five.
Solve these equations. Show solutions on a number line.
|x+8|=x+8
Answer:
-8 < x < inf
[-8 , inf )
Step-by-step explanation:
set up a +/- |x + 8| = x + 8
the setup a number line and use test points
Answer:
x > -8
Step-by-step explanation:
ummmmmm so its not negative lol
Start time 7:59am,end time 2:33 pm elapsed time is
6:34 minutes Six hours thirty four minutes
Answer:
6 hours 34 minutes.
Step-by-step explanation:
12.00 pm - 7.59 am = 4 hours 1 minute.
2.33 pm - 12.00 pm = 2 hours 33 minutes.
Answer is 6 hours 34 minutes.
I need help please????
The one you have highlighted is correct
the first one is the right one
there are four students in each small reading group there are 24 students in all.
how many reading groups are there
Answer:
6
Step-by-step explanation:
24 / 4 = 6
Final answer:
The number of reading groups can be determined by dividing the total number of students, which is 24, by the number of students in each group, which is 4. The calculation is 24 ÷ 4, resulting in 6 reading groups.
Explanation:
To find the number of reading groups, we can use a simple division operation because we are dividing a larger group of items (students) into smaller equal-sized groups. In this case, we have 24 students and want to find out how many groups of 4 students we can create from that total.
Here's the step-by-step explanation:
Identify the total number of students, which is 24.
Identify the number of students in each reading group, which is 4.
Divide the total number of students by the number of students in each group: 24 ÷ 4 = 6.
Therefore, there are 6 reading groups.
How do you find the area of 12ft and 20ft and 18ft
Answer:
106.65
Step-by-step explanation:
its the same formula as the area of a triangle.... smallest number as base
Calculate the median of 5,10,12,4,6,11,13,15
Amélie runs a bakery. She wants to find out whether her cake sales are affected by the weather conditions. She recorded the daily temperature and the number of cakes she sold on different days of the year. The table shows the data she gathered.
Daily Temperature (°F) Cakes Sold
42 39
45 52
48 31
54 61
59 72
62 35
64 61
65 34
67 58
75 45
84 24
The correlation coefficient is close to .
Based on this information, we can conclude that Amélie's cake sales are affected by the daily temperature.
Answer:
the coeffiectans is 100
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that Amélie runs a bakery. She wants to find out whether her cake sales are affected by the weather conditions. She recorded the daily temperature and the number of cakes she sold on different days of the year
Let us find the correlation coefficient for the variables x, daily temperature and y, no of cakes sold.
x y
42 39
45 52
48 31
54 61
59 72
62 35
64 61
65 34
67 58
75 45
84 24
r -0.197481837
Since r is nearer to 0 than to 1, we find that there is a negative very moderate correlation between the two variables.
We cannot conclude that Amélie's cake sales are affected by the daily temperature.
A bike shop charges x dollars to rent a bike for half a day.it charges (x+40)dollars to rent for a full day.the table shows the shops bike rentals for one day.on that day the shop made a total of $600from bike rentals.how much does it cost to rent a bike for a full day?
The cost of full-day bike rental cannot be calculated because the information about how many half and full day rentals exist was not provided. This is needed to create an equation using the given variable and total revenue.
Explanation:
The question is about finding the cost of a full day bike rental. From the problem, we know that the total revenue from the rentals was $600. However, as the necessary information about the number of half-day and full-day rentals for the given day is not provided, we cannot provide a specific price. Usually, if we know the number of half-day and full-day rentals, we can set up an equation to determine the cost of a full day rental, denoted as (x+40) in the problem.
Learn more about Bike Rental Cost here:https://brainly.com/question/30303793
#SPJ3
what is the height and length of a rectangular box with a volume of 6x^2-600 with a width of 6
Answer:
(x+10) and (x-10)
Step-by-step explanation:
The volume of a rectangular box is defined as
Volume = width*height*length
In this case
Volume = 6x^2-600 = 6*(x^2 - 100)
And we also know,
Volume = (6)*height*length
So,
6*(x^2 - 100) = (6)*height*length
This means that
height*length = (x^2 - 100)
height*length = (x+10)*(x-10)
The table shows the daily temperatures for a city. What is the mean absolute deviation for this data?
A) 5.2
B) 6.1
C) 55
D) 57
Where is the picture
And I think the answer is 6.1
Answer:
A.) 5.2 is the deviation
Step-by-step explanation:
Allow me to explain!
The mean of the data is found by adding the four temperatures (5.2+6.1+55+57) and dividing by 4. This gives you 30.825. The number given that is furthest from this number is 5.2, making it your answer.
Juan and Rob are selling cookie dough for a school fundraiser . Juan has t cookie dough orders , and Rob has 40 cookie dough orders . They have a total of 75 cookie dough orders all together . Write a equation to describe this situation . How many cookie dough orders does Juan have?
Answer:
Juan has 35(t) cookie dough orders.
Step-by-step explanation:
75(Overall) - 40(Rob's) = 35(Juan's)
Hope this helps you. :)
Answer:
t+ 40 = 75; t = 35
Step-by-step explanation:
t + 40 = 75
Subtract 40 from each side.
t = 35
Juan has 35 cookie dough orders.
How do you find the area of a circle if you already have the diameter
Answer:
If you have the diameter of a circle, you can use it to find the area of that circle. Just plug that value into the formula for the area of a circle and solve. Hope this helps. :)
Answer:
The area of a circle is Pi * Radius^2 or Pi * diameter.
So do 3.14 * the diameter.
plz solve ASAP
solve the equation
-3(y-5)=24
y=?
Answer:
3
Step-by-step explanation:
Answer:
y=3
Step-by-step explanation:
-5 - 3 = -7
-8 * -3 = 24
bc a (-) plus a (-) equals a (+)
How many students participated in the survey
50 people answered the survey.
Please help solve this question.
Answer: OPTION A
Step-by-step explanation:
Descompose the number 20 into its prime factors:
[tex]20=2*2*5=2^2[/tex]
Because, by definition:
[tex]\sqrt[n]{a^n}=a[/tex]
Then, you must rewrite 2²*5 inside of the square root, as following;
[tex]\frac{3\sqrt{2^2*5}}{\sqrt{5}}[/tex]
Simplify as following:
Keeping on mind that [tex]\sqrt[n]{a^n}=a[/tex], then:
[tex]\frac{3*2\sqrt{5}}{\sqrt{5}}[/tex]
Note:
[tex]\frac{\sqrt{5}}{\sqrt{5}}=1[/tex]
Then:
[tex]\frac{6\sqrt{5}}{\sqrt{5}}=6(1)=6[/tex]
Therefore, as you can see the answer is the option A
Answer:
option A)
6
Step-by-step explanation:
Given in the question the expression
3√20 / √5
(3 x √20) / √5
√20 can be separated as 5x4
(3 x√5x4) / √5
square root rule
(3 x √5√4) / √5
cancelling √5 from both sides
3 x √4
3 x 2
6 answer
So simplified form of 3√20/√5 is 6a 12 inches by 12 inches by 12 inches container of water was placed in the freezer.Water expands 4% when it is frozen.What is the volume of the container when it is frozen?
2. Simplify 2(54−1)3 completely. Show as much work as possible for full credit.
[tex](2 \times 54 - 2)3 = 108 - 2 \times 3 = 106 \times 3 = 318[/tex]
Answer:
[tex]\boxed{\bold{318}}[/tex]
Step By Step Explanation:
Calculate Within Parenthesis: [tex]\bold{(54-1)}[/tex]
[tex]\bold{53}[/tex]
Rewrite Equation
[tex]\bold{2\cdot \:53\cdot \:3}[/tex]
Multiply: [tex]\bold{2\cdot \:53\cdot \:3}[/tex]
[tex]\bold{318}[/tex]
➤ [tex]\boxed{\bold{Mordancy}}[/tex]
Select the correct answer! Which point is the vertex of the graph defined by f(x) = 6|x − 2| − 5?
A. (6, 5)
B. (2, -5)
C. (0, 0)
D. (6, -2)
The Answer to your question is:
B: (2,-5)
Answer:
the vertex is (2,-5)
Step-by-step explanation:
f(x) = 6|x − 2| − 5
WE need to find out the vertex of the given absolute function
The vertex form of absolute function is
f(x) = a|x − h| +k
where (h,k) is the vertex
Now we compare the given f(x) with the vertex form
h= 2 and k = -5
so the vertex is (2,-5)
A box in the shape of a right rectangular prism has a length of 8 inches, a width of 4 inches, and a height of 3 inches. What is the volume, in cubic inches, of the box? Do not round your answer.
Answer:
V = 96 cubic inches
Step-by-step explanation:
Volume of a rectangular prism is V= LWH,
we are given W = 4, L = 8, and H = 3. Plug them in and find W...
V = (4)(8)(3)
V = 32(3)
V = 96 cubic inches
What is the product? 2y/y-3 multiplied by 4y-12/2y+6
The answer is 4y / y+3
Step-by-step explanation:See the attached figure
Answer:
D. 4y/y+3
thanks (:
this one is confusing
Answer:
see explanation
Step-by-step explanation:
given
2x ÷ 4 = 10 or
[tex]\frac{2x}{4}[/tex] = 10 ( multiply both sides by 4 )
2x = 40 ( divide both sides by 2 )
x = 20
-------------------------
(b)
He may have mistaken the ÷ for a - (subtraction sign )
2x - 4 = 10 ( add 4 to both sides )
2x = 14 ( divide both sides by 2 ), leading to
x = 7 ← the incorrect answer he obtained
Answer:
Step-by-step explanation:
What is the sum of an infinite geometric series if the first term is 8 and the common ratio is 1⁄2?
A. 16
B. 8
C. 32
D. 4
Answer:
A
Step-by-step explanation:
The sum to infinity of a geometric series is
S (∞ ) = [tex]\frac{a}{1-r}[/tex] ( - 1 < r < 1 )
where a is the first term 8 and r is the common ratio, hence
S(∞ ) = [tex]\frac{8}{1-\frac{1}{2} }[/tex] = [tex]\frac{8}{\frac{1}{2} }[/tex] = 16
This sum of the infinite geometric series is 16 since the correct option is (A) 16.
Definition of infinite geometric series:The sum of infinite geometric sequences is called an infinite geometric series. There would be no final term in this series. The infinite geometric series has the general form a1+a1r+a1r2+a1r3+..., where a1 is the first term and r is the common ratio. The sum of all finite geometric series can be found.
How to find the sum of the series?In terms of the first term a1 and the common ratio r, the sum is...[tex]S =\frac {a_1}{(1-r)}[/tex]
We discover... by substituting the given numbers and performing the arithmetic...[tex]S = 8/(1 -1/2) = 16[/tex]
The total number of items in the series is 16.
Learn more about infinite geometric series here, https://brainly.com/question/27350852
#SPJ2
A line has a slope of a and has a y intercept of (0,b).Which equation represents this libe
Answer:
y = ax + bStep-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
We have the slope m = a, and the y-intercept b.
Substitute:
y = ax + b
Find the square inches
Answer:
The area of the figure is 16
Step-by-step explanation:
If you look closely there are four squares inside the figure so you get the area of one square and times it by four for the area of 16.
Answer:
16 in^2
Step-by-step explanation:
Think of the entire shape as a rectangle above and a square below. The rectangle's length and width are 6 inches and 2 inches. The side of the square is 2 inches.
area of rectangle: Ar = length * width
area of square: As = side^2
total area = Ar + As
total area = 6 in * 2 in + (2 in)^2
total area = 12 in^2 + 4 in^2
total area = 16 in^2
**WILL MARK BRAINLIEST AND THANK YOU**
Solve the equation f(x)=g(x) by graphing the functions f(x)=3^x+1 and g(x)=4 on the same set of coordinate axes.
Which statements about the solution are true?
Select *EACH* correct answer.
A. The solution to the equation is x=1
B. The ordered pair that contains the solution to the equation lies in Quadrant I
C. The ordered pairs that contain the solutions to the equation like in Quadrants I and II.
D. There are 2 solutions to the equation.
E. The ordered pair that contains the solution to the equation lies in Quadrant II
See the graph below.
The answer is: B. The ordered pair that contains the solution to the equation lies in Quadrant I