Answers
Answer:
a. height: 36 units
b. radius: 4 units
Step-by-step explanation:
The volume of a cone is given by the formula ...
V = 1/3πr²h . . . . . for radius r and height h
This tells you the volume is jointly proportional to the height and the square of the radius. This means that for a given volume, the height is inversely proportional to the square of the radius. We can use this proportionality to answer the questions here.
__
a.The radius of Cone B is 2 units. Compared to Cone A, the radius of Cone B is 2/6 = 1/3 of the radius of cone A. The square of this ratio is (1/3)² = 1/9, and the inverse of that square is 9/1. This means the height of Cone B is 9 times the height of Cone A, so is ...
Cone B height = 9 × 4 units = 36 units
__
b.The height of this Cone B is 9 units, whereas the height of Cone A is 4 units. This means the height of Cone B is 9/4 times the height of Cone A. This is the inverse of the square of the ratio of radii of Cone B to Cone A. Inverting the height ratio, we get 4/9. Taking the square root of that, we get √(4/9) = 2/3. This means the radius of Cone B is 2/3 the radius of Cone A:
Cone B radius = 2/3 × 6 units = 4 units
_____
Additional comment
We can check the above dimensions using the volume formula.
a. V = 1/3π(2 units)²(36 units) = 48π units³
b. V = 1/3π(4 units)²(9 units) = 48π units³
These are the expected volume, so the answers check OK.
Related Questions
the line y=ax-1 is parallel to the line by-(a+1)x=2. These two lines have the same distance to the origin. find a and b
Answers
By using the parallel condition and the fact that the distance to the origin is the same, we will see that a = 1 and b = 2.
How to find the values of a and b?First, remember that two lines are parallel if have the same slope and different y-intercept.
In this case, we know that
y = a*x - 1
b*y - (a + 1)*x = 2
Are parallel, if we write both of them in the slope-intercept form, we get:
y = a*x - 1
y = (a + 1)*x/b + 2/b
Note that because both of the lines are parallel, the slopes must be equal, then we have that:
(a + 1)/b = a
Then if we know that the distance of both lines to the origin is the same, we have that:
|-1/(√(a^2 + 1))| = | (2/b)/(√(((a + 1)/b)^2 + 1))|
Because the slopes are equal the denominators are equal, this means that:
|-1| = |2/b|
And the y-intercepts must be different, this means that:
b = 2
now we can solve:
(a + 1)/b = a
(a + 1)/2 = a
a + 1 = 2a
1 = 2a - a = a
a = 1 and b = 2.
If you want to learn more about linear equations, you can read:
https://brainly.com/question/1884491
Damon has $200 in a savings account that earns 4% annually. The interest is not compounded. How much will he have in total in 1 year?
Answers
Explanation:
200 x (1+4%)
200 x (1+0.04)
200 x 1.04= 208
Andre drinks 15 ounces of water, which is 3/5 of the bottle. How much does the bottle hold? Use x for the number of ounces the bottle holds.
Answers
Step-by-step explanation:
15 = 3/5 x = 3x/5
75 = 3x
x = 25 ounces
The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. Round answer to the nearest cent. P = $11,000.00, r = 9%, t = 150 days
Answers
well, if take a year to be 365 days so hmmm 150 days is really just 150/365 of a year, so let's use that.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$11000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\to \frac{150}{365}\dotfill &\frac{30}{73} \end{cases} \\\\\\ A=11000[1+(0.09)(\frac{30}{73})]\implies A=11000\left( \frac{757}{730} \right)\implies A\approx 11406.85[/tex]
Joan has made four mistakes in her diagram. write down any three of them.
Answers
Answer:
dude
Step-by-step explanation:
how are you supposed to know but you are smart hopefully you will answer
3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations described below. a. The account pays 3% annual interest compounded monthly. b. The account pays 4% annual interest compounded continuously.
Answers
Answer:
Part A)
About $3767.34.
Part B)
About $3692.47.
Step-by-step explanation:
Part A)
Recall that compound interest is given by the formula:
[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
To obtain $4000 after two years, let A = 4000 and t = 2.
Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.
Substitute and solve for P:
[tex]\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}[/tex]
In concluion, about $3767.34 should be deposited.
Part B)
Recall the formula for continuous compound:
[tex]\displaystyle A = Pe^{rt}[/tex]
Where e is Euler's number.
Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:
[tex]\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}[/tex]
In conclusion, about $3692.47 should be deposited.
100 points! need done asap
An unfair spinner has sections labeled 1 2 or 3 that are all twice as large as each of the sections labeled 4 5 or 6 Develop a probability model to describe all possible outcomes of one spin of the spinner
Answers
Answer:
look at the pic and stay safe!! hope it helps
What is the length of BC?
24
36
48
30
Answers
Answer:
48/24
Step-by-step explanation:
You didn't say which one is line BC so I'm going to give you the answer 48 for the entire line but if you are asking for the middle point to end point then it is 24.
A group of friends go out for a meal and the meal costs £148.
They are given a discount of 25% because of a mix-up on their orders.
How much discount did the group of friends receive?
£
Answers
you would multiply by the percent off they get.
The Length Of A Room is two time its breadth and breadth is two time its height If The volume of room is 512m2 what is the cost of plastering its wall at rs 5.50 per m2
Answers
Answer:
Rs 2464
Step-by-step explanation:
Given:
The length of a room is 2 times its breadth and breadth is 2 times its height. The volume of the room is 512 cubic metre.To find:
The cost of plastering it's wall at Rs 5.50 per square metre.Solution : A/C to given data;
[tex]Length = 2 * Breadth\\L = 2 * B[/tex]---> (1) and [tex]Breadth = 2 * Height\\B = 2 * H[/tex]----> (2)
A/C to given data let, structure of room is cuboidal.
Now, we have to find out the height of the room, so we use formula of volume of the cuboid.
[tex]Volume of the room = L * B * H[from given data, and eq. {1} and eq. {2}][/tex]
[tex]512 = 2B * 2H * H[/tex]
[tex]512 = 2 * 2H * 2H * H[/tex]
[tex]512 = 4H * 2H^{2}[/tex]
[tex]512 = 8H^{3}[/tex]
[tex]H^{3} = \frac{512}{8}[/tex]
[tex]H^{3} = 64[/tex]
[tex]H = \sqrt[3]{64}[/tex]
[tex]H = 4 m[/tex]
[tex]Now, put\\ value\\ of \\H \\in \\eq. {2}[/tex]
[tex]B = 2 * H[/tex]
[tex]B = 2 * 4[/tex]
[tex]B = 8 m[/tex]
[tex]\\[/tex]Now, put value of B in eq. {1}
[tex]L = 2 * B[/tex]
[tex]L = 2 * 8[/tex]
[tex]L = 16 m[/tex]
Now, we have to find out area of the room, so we use formula of total surface area of cuboid.
[tex]Area of the room = 2*L*B + 2*L*H + 2*H*B[/tex]
[tex]Area of the room = 2 * 16 * 8 + 2 * 16 * 4 + 2 * 4 * 8[/tex]
[tex]Area of the room = 32 * 8 + 32 * 4 + 8 * 8[/tex]
[tex]Area of the room = 256 + 128 + 64[/tex]
[tex]Area of the room = 384 + 64[/tex]
[tex]Area of the room = 448 m^{2}[/tex]
Now, to find out room wall plastering cost
[tex]Room wall plastering cost = Area of the room * cost of plastering per ^{2}[/tex]
[tex]Room wall plastering cost = 448 * 5.50[/tex]
[tex]Room wall plastering cost = Rs 2464[/tex]
[tex]ence, the room wall plastering cost is Rs 2464.[/tex]
Find the measure of ∠ABC.
Answers
Answer:
170°
Step-by-step explanation:
There is a total of 180° and the angle is 10° less...
So, 180°-10° = 170°
Please 5 stars if correct!!!
I hope this helps!!!
Help picture below problem 11
Answers
Answer:
48
Step-by-step explanation:
vertical angles are equal
Answer:
48
Step-by-step explanation:
This is because vertical angles (which is opposite of each other when the two lines cross) are congruent, meaning they have the same angles.
three subtracted from 5 x a number is -128. what is that number
A) translate the statement above into an equation that you can solve to answer this question.
do not solve it yet use x as your variable.
the equation is :
B)solve your equation [A} for x
answer for x
Answers
5-3x=-128
LHS = RHS
(5 - 3) x A = -128
( 2 ) x A = -128
2A / 2 = -128 / 2
A = -64
At Garland School,
3/5 of the 490 students are boys.
At Bowood School, 5/7
of the 945 students are girls.
Which school has the greater number of girls and by how many?
You must show your working.
Answers
490 x 2/5 = 980/5 = 196 girls at Garland
945 x 5/7 = 4725/7 = 675 girls at Bowood
Bowood has more girls:
675-196 = 479 more
When spinning a penny, Claire believes the proportion of times the penny lands on heads is higher than 0.5. She spins a penny 50 times and it lands on heads 32 times. The P-value for the test of the hypotheses, H 0: p = 0.5, and H alpha: p greater-than 0.5, is 0.02, What is the correct interpretation of this value?
Answers
It depends on what the level of significance (alpha) is.
Since alpha is not stated, I'll assume that alpha = 0.05 by default.
Because the p-value is smaller than alpha, we reject the null hypothesis.
Therefore, we conclude that the alternative hypothesis is correct and the proportion of heads is greater than 0.5
Antonio weighs four pounds more than twice his brother weight. If Antonio weighs 97 pounds, how much does his brother weigh? Write and solve equation.
Answers
Answer:
The bother's weight is 46.5 lb.
Step-by-step explanation:
Let the brother's weight be b.
Antonio's weight is 2b + 4.
Antonio's weight is 97 lb.
2b + 4 = 97
2b = 93
b = 46.5 lb
Answer: The bother's weight is 46.5 lb.
find the rule to complete the pyramid.
Answers
Answer:
add two side by side values
Step-by-step explanation:
there are 5 values at the base of the pyramid.
4, 6, 3, 7 and 2
let's look at 6 and 3 first. when you add them together, you will get 9, which make up the upper layer of the pyramid. we can also support this statement when you add 7 with 2, which is also 9. so when you take 4 and add with 6, you will get 10, when you add 3 and 7, you will get 10.
now, let's see the second bottom layer. we get the answers as 10 in both blanks. so, add 10 with 9 and you will get 19, repeat with the other. so, the third layer will be 19, 19 and 19. to make the third layer complete, add 19 with 19, which will be 38. so, the fourth layer will be 38 and 38. add 38 with 38 and you will get 76 at the top of the pyramid.
Help picture below problem 15
Answers
Formula for Pythagorean theorem is a squared plus b squared equals c squared. The longest side is c and the rest is a and bb. Since we already have c we use formula a squared equals c squared minus b squared. AsquaredsquaredsquaredsquaredAsquaredsquaredsquaredsquared my thing is broken so I can't continuecontinue. Hope this helpshelps though
Solve the equation b(b+12) = 0. Check your solutions.
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \:b(b + 12) = 0[/tex]
Here, we have two cases :
Case 1[tex]\qquad \sf \dashrightarrow \:b = 0[/tex]
Case 2[tex]\qquad \sf \dashrightarrow \:b + 12 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \:b = - 12[/tex]
Hence, 0 and -12 are the only possible solutions for given equation.
can someone please help me
Answers
Like the given triangle is an isosceles triangle, the value of ∠ABC is 72°.
Types of TrianglesThere are 3 main classifications for triangles refer to its sides.
Equilateral triangle - This triangle presents all sides with the same dimensions and the all angles equal to 60°.Isosceles triangle - This triangle presents two sides with the same dimensions and it has two angles with equal size.Scalene triangle - This triangle presents all sides with different dimensions and it has all angles no equal size.The figure shows that the given triangle is an isosceles triangle because it has two equal sides (AB=AC). If it is an isosceles triangle, this triangle presents two sides with the same dimensions (AB=AC). and it has two angles with equal size(∠ACB=∠ABC).
Knowing the sum internal angles of triangle is 180°. You can write:
3x+6x+6x=180
15x=180
x=12
Like ∠ABC=6x, then ∠ABC=6*12=72°.
Read more about the types of triangles here:
https://brainly.com/question/24265179
In a parallelogram ABCD, angle a=70, find 2angle d
Answers
Answer:
D = 110
Step-by-step explanation:
Given,
In a parallelogram ABCD,
∠A =70∘
∠A + ∠B = 180∘.. (supplementary angles)
∠B = 180∘ – 70∘ = 110∘
∠A = ∠C and ∠B = ∠D.. (Opposite angles of parallelogram)
∠A = 70∘, ∠B = 110∘, ∠C = 70∘, ∠D = 110
Maria has 25 dollars. She has to buy a gallon of milk which costs $3.50. She wants to spend the rest of her money on cereal. If each box of cereal costs $4.50, how many can she purchase?
Answers
Step-by-step explanation:
total money she has = $25
she bought a gallon of milk for $3.50
amount remaining = 25-3.50 = $21.50
number of cereal she can buy with the remaining amount =21.50/4.50 = 4.77 boxes
she can buy 5 boxes (approximately)
BRAINLIEST AND 100 POINTS!
The equation yˆ=−5.131x2+31.821x−3.333 approximates the number of people standing in line to catch a commuter train x hour after 5 a.m.
What is the best estimate for the number of people in line at 7 a.m.?
23
27
32
40
Answers
Answer:
The answer is 40. I'm 100% sure.
Answer:
D.40
Step-by-step explanation:
Answer:the largest angle has a measure of ____degrees.
Answers
Angle 2= 3x
Angle3= x+40
5x+40= 180
180-40=140 140/5=28 =x
Angle 1= 28
Angle2=84
Angle 3=68
Largest =angle2: 84degrees
The length of the base of an isosceles triangle is x. The length of a leg is 3x−6. The perimeter of the triangle is 65. Find x.
Answers
Answer:
x = 11
Step-by-step explanation:
Hello!
In an isosceles triangle, the two legs are congruent by the property Base angle Theorem. It is isosceles when both angles on the base are congruent.
So, since the base is x, and the measure of one leg is 3x - 6, we know that the other leg is also 3x - 6 in length.
The equation for perimeter is : leg + leg + base = Perimeter
We can plug in 65 for the perimeter because it's given
Solve for x:
x + 3x - 6 + 3x - 6 = 657x - 12 = 657x = 77x = 11The value of x is 11.
X + 2x + 8 = X = 10 + 6
Answers
Answer:
x = 8/3
Decimal form: 2.66666666667
Step-by-step explanation:
Given:
[tex]x+2x+8=10+6[/tex]
Solution:
[tex]\mathrm{Add\:similar\:terms:}\:x+2x=3[/tex]
[tex]3x+8=10+6[/tex]
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
[tex]3x+8-8=16-8[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]3x=8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3x}{3}=\frac{8}{3}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=\frac{8}{3}[/tex]
[tex]x=2.66666666667[/tex]
~lenvy~
Answer/Step-by-step explanation:
Base on the given we are..
Solving for x:
Solve:
X + 2x + 8 = X = 10 + 6 {x+2x= 3x}
3x + 8 = 10 + 6 {10+6=16}
3x + 8-8=16-8 {16-8=8}
3x = 8 {divide both sides by same term}
3x/3 = 8/3
Therefore,
x = 8/3
Decimal form = 2.66666666667
[RevyBreeze]
The total cost f(x), in dollars, for renting a bowling lane for x hours is shown:
f(x) = 2x + 12
What does f(14) represent?
A. The number of dollars it costs to rent the bowling lane for 14 hours
B. The number of games you can bowl for a cost of $14
ting
C. The number of games you can bowl in 14 hours
D. The number of hours the bowling lane can be rented for a cost of $14
Answers
PLEASE HELP ME MATH IS HARD
Use the rectangle shown in the coordinate plane to answer each question.
1. Rotate rectangle KLMN 90º counter-clockwise about the origin. List the ordered pairs for each vertex of K'L'M'N'.
2. What do you notice about the ordered pairs of the original figure and the ordered pairs of the rotation about the origin?
Answers
Answer:
See below ↓
Step-by-step explanation:
1)
On rotating KLMN by 90° counterclockwise,the new coordinates are :K' = (-3, -6)L' = (-5, -4)M' = (-2, -1)N' = (0, -3)2)
What do we notice here?We notice that on rotating from Quadrant II to Quadrant III, we find that all the x and y values become negative (other than N' which changes intercepts from x to y)Answer:
Step-by-step explanation:
Rotate counter-clockwise = from right towards left
Rotate 90° about the origin = We can think that our rectangle is a flag and that we added a pole to it. The pole is rotated counter-clockwise about the origin until we have the 90°. Where is the flag now positioned?
(Draw a line from origin to one of the rectangle's points; draw another line from origin that is ⊥ to the previous one. You rotate that point 90° from right to left and will lend on the new line.)
1. K (-6, 3) L (-4, 5) M (-1, 2) N (-3, 0) → K' (-3,-6) L'(-5, -4) M'(-2, -1) N'(0, -3)
2. We notice that the rule for rotating 90° about the origin is (x, y)→(-y, x)
HELP PLEASEEEEEEEEEEE
Answers
Answer:
the numbee from left to right :
-1.5
-0.25
0.75
1.25
2.25
Answer:
-3/2, -15%, 0.80, 143%, 2 1/4
Step-by-step explanation:
Convert the fractions into decimals:
2 1/4 = 2.25
-15% = -0.15
143% = 1.43
-3/2 = -1.5
0.80 = 0.80
The order from least to greatest is -3/2, -15%, 0.80, 143%, 2 1/4
Hope this helps :)
What is the area of this figure?
Answers
Answer:
35 cm²
Step-by-step explanation:
Area of the 2 triangles combined:
1/2 x 4 x 5 = 10
Area of the square:
5 x 5 = 25
10 + 25 = 35
4×4 or 4×5 perimeter times area