Answer:
d. 72 in³
Step-by-step explanation:
To find the volume of a cylinder that a cone of volume 24 cubic inches fits in exactly inside of, we will follow the steps below:
From the question volume of the cone = 24 cubic inches
volume of a cone = [tex]\frac{1}{3}[/tex] πr²h
and volume of a cylinder = πr²h
This implies
volume of a cone = [tex]\frac{1}{3}[/tex] πr²h
= [tex]\frac{1}{3}[/tex] (volume of a cylinder)
volume of a cone = [tex]\frac{1}{3}[/tex] (volume of a cylinder)
24 = [tex]\frac{1}{3}[/tex] (volume of a cylinder)
multiply both-side of the equation by 3
24×3 = [tex]\frac{1}{3}[/tex] (volume of a cylinder)
72 =volume of a cylinder
Therefore volume of the cylinder that the cone fits exactly inside of is 72 cubic inches
What is the slope of the line shown on the graph? A)3 B)1/3 C)−3 D)−1/3
Answer:
1/3
Step-by-step explanation:
The slope of the line is found by
m = (y2-y1)/(x2-x1)
we have two point ( 0,0) and ( 3,1)
= ( 1-0)/( 3-0)
= 1/3
PLEASE HURRY! ANSWER ASAP
Which two grids can be combined to get 140%?
Square A) A grid model with 100 squares with 1 square shaded.
Square B) A grid model with 100 squares with 15 squares shaded.
Square C) A grid model with 100 squares with 40 squares shaded.
Square D) A grid model with 100 squares with 100 squares shaded
A and B
A and C
B and D
C and D
Line
A.
C.
D.
B.
Defined
Postulates
Theorems
Undefined
Terms
Answer: Undefined
Step-by-step explanation:
In geometry there are three undefined terms that we use to define other terms:
Point → In geometry a point has a location but no dimension.Plane → A plane extends is a 2-dimensional surface that extends infinitely on both sides. Line → A line is a one-dimensional undefined figure that extends infinitely in both the directions. It has length but has no width.Hence, the correct option is "Undefined".
In the diagram, AC and PR are vertical lines, while CB is a horizontal line segment. If CR : RB = 2 : 3, what are the coordinates of point Q? A. (-2, -4) B. (-1, -5) C. (-3, -3) D. (0, -6)
Answer:
A. (-2,-4)
Step-by-step explanation:
If CR:RB is 2:3, and C is (-4,-7), then R is (-2,-7)
You can stop here because only A has the x value as -2.
If you want to look at the y value also, -4 is 2/5 of the way between -2 and -7, which has the same 2:3 proportion.
How to find constant M ? did I do anything wrong here ?
Answer:
M=-1, N=7
Step-by-step explanation:
Something went wrong on the 4th line.
From the third line, it should read
2x^2-x+6Mx-3M+4
=x(2x-1+6M) - 3M+4
Equating with the RHS,
2x-1+6M = 2x-7
6M = -7+1 = -6
M = -1
Therefore
N = -3M+4 = -3(-1)+4 = 7
or
M=-1, N=7
The formula for any arithmetic sequence is an = a1 + d(n - 1), where an represents the value of the nth term, a1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the sequence -15, -11, -7, ...? an = -15 + (-4)(n - 1) an = -15 + (n - 1) an = 4 + (-15)(n - 1) an = -15 + 4(n - 1)
Answer:
4n
Step-by-step explanation:
Answer:
The 4th choice
Step-by-step explanation:
To figure this out you would have to just lug in all of the numbers into the equation to find the correct answer.
So first we would plug in the first number for a1 which will be -15. Then we would put in d or the common difference (the number of numbers in between the 2 numbers). So d in this case would be positive 4 since every single time the number is being added to 4.
Now we can solve, so we would just find all of the choices that do not have +4 because that will be wrong. Automatically you can see that choices 1 and 2 are wrong and 3 also looks wrong and the only one that matched our formula is 4 and 4 is the correct answer.
FIRST GETS BRAINLLEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter.
Answer:
8110
Step-by-step explanation:
80+80+50+50=260
3.14(50)²=7810
7810+260=8110
Anton bought a picnic cooler. His total bill, with tax, was $7.95.
He paid 6 percent sales tax. How much did he pay for the cooler
alone without the tax?
Answer:
$ 7.50
Step-by-step explanation:
The cost of the picnic cooler would be 100%.
With the 6% sales tax, Anton would pay 106% of the cost if the picnic cooler.
(since 100% +6%= 106%)
106%(picnic cooler)= $7.95
Cost of picnic cooler= 100%(picnic cooler).
Cost of picnic cooler
[tex] = \frac{7.95}{106} \times 100 \\ = 7.50[/tex]
Thus, he paid $7.50 for the cooler alone.
Find the zeros of y = x2 - 8x - 3 by completing the square.
O A. x=3+√7
B. X = +3
C. X = 4 + 119
O D. X= -4 + 119
Answer:
Assuming that you meant 4+√19 is C.
Step-by-step explanation:
[tex]x^2-8x-3=x^2-2(4)x-3=x^2-2(4)x+16-3-16\\(x-4)^2-19\\(x-4)^2-19=0\\(x+4)^2=19\\x+4=\sqrt{19} \\x=-4+-\sqrt{19}[/tex]
help please. Find the length of x.
Answer:
x=10
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
6.5 (6.5+6.5)
------ = -----------------------
5 x
6.5 (13)
------ = -----------------------
5 x
Using cross products
6.5x = 65
Divide by 6.5
6.5x/6.5 = 65/6.5
x = 10
Given: Circumscribed △XYZ XY=7, YZ=8. ZX=5 Find: AX, BY, CZ
Answer:
AX=2 BY=5 CZ=3
Step-by-step explanation:
Lets call AX (x). Once you do so, one can tell that AZ=5-x. CZ is also 5-x. BX is also x. Therefore you can say that BY=7-x which makes CY 7-x. Now for side YZ, CZ is 5-x and CY is 7-x.
5-x+7-x=8
solving that you get x=2
AX=2
BY=7-x=5
CZ=5-x=3
Hope this explains some more than the other answer. Please ask any questions.
These dot plots show the ages (in years) for a sample of sea turtles and a
sample of koi fish.
Age (in years)
What are the differences between the centers and spreads of these
distributions?
Select two choices: one for the centers and one for the spreads.
a A. Centers: The sea turtles have a lower median age than the koi.
3. B. Centers: The sea turtles have a greater median age than the koi.
c. Spreads: The ages of the sea turtles are more spread out.
D D. Spreads: The ages of the koi are more spread out.
*see attachment below for the dot plots that completes the question.
Answer:
B. Centers: The sea turtles have a greater median age than the koi.
D. Spreads: The ages of the koi are more spread out.
Step-by-step explanation:
The measure of center that can be used for comparison is the median, while the spread can simply be visualised by mere looking at how spread out the dots on the number line are. The spread of both can also be compared using their range. The greater the range, the more spread a data is.
=>Median Differences:
The median age for turtle = the middle value = 55
The median age for koi = 30
Therefore, sea turtles have a greater median age than the koi.
=>Spread Differences:
Range for turtle = the highest age - the least age represented on the dot plot = 65 - 45 = 20
Range for koi = 55 - 10 = 45
Koi has a greater range value than koi. Therefore, the ages of the koi are more spread out.
Is my answer correct. If not, what is the answer ? Thank you
Answer:
P = 3
Q = -4
R = 22
Step-by-step explanation:
Expand both sides and compare coefficients.
5Px^2 -PQx +10x -2Q = 15x^2 + Rx +8
Compare coefficients of x^2
5P = 15 => P = 3
Compare constant terms
-2Q = 8
Q = -4
Compare coefficients of x
-PQ + 10 = R
-(3)(-4) + 10 = R
R = 10 + 12 =22
AssAssessment captures blank growth
An eraser is in the shape of a triangular prism. Its dimensions are shown in the diagram. What is surface area of the
eraser?
50 mm
40 mm
40 mm
30 mm
3,600 square millimeters
4.800 square millimeters
5,400 square millimeters
6,000 square millimeters
Answer:
6000 square millimeters
Step-by-step explanation:
Side length of the slanting side can be calculated using the Pythagorean theorem,
L = sqrt(30^2+40^2) = 50
sufrace area of a triangular prism
= surface area of the end sections + the surface area of the three side faces
= 2*(30*40/2) + 40*(30+40+50)
= 1200 + 4800
= 6000 mm^2
Answer:
D) 6,000 square mm
Step-by-step explanation:
To find the surface area of the triangular prism, find the are of each face.
40 × 30 ÷ 2 = 600 × 2 sides = 120040 × 50 = 200040 × 30 = 120040 × 40 = 1600After adding all the sides' together, you get 6,000 square mm.
I need help doing this can anyone help?
You posted a lot of questions. I'll do the first four problems to get you started.
============================
Problem 1
This sequence is arithmetic because we add the same amount (4) each time to get the next term. The first term is -2. The first five terms are: -2, 2, 6, 10, 14
============================
Problem 2
This sequence is geometric. We multiply each term by 1/4 to get the next term. We start with 8 as the first term. The first five terms are 8, 2, 1/2, 1/8, 1/32.
============================
Problem 3
Similar to problem 1. This time we're adding -19 to each term to get the next one. The starting term is -6. This sequence is arithmetic and the first five terms are -6, -25, -44, -63, -82
============================
Problem 4
Similar to problem 2. This sequence is geometric with common ratio 2/3. First term is 6. The first five terms are 6, 4, 8/3, 16/9, 32/27
Tim wants to build a rectangular fence around his yard. He has feet of fencing. If he wants the length to be twice the width, what is the largest possible length? Write an equation and solve.
Answer:
how many feet of fencing does he have?
\
Step-by-step explanation:
What is the middle term of the product of (x - 4)(x - 3)?
Answer:
- 7x
Step-by-step explanation:
Given
(x - 4)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) - 4(x - 3) ← distribute both parenthesis
= x² - 3x - 4x + 12 ← collect like terms
= x² - 7x + 12
with middle term = - 7x
Answer:
Step-by-step explanation:
= x(x-3) - 4(x-3)
= x²-3x - 4x + 12
= x² -7x +12
So -7x is the middle term
Which function would represent the absolute value function that is equivalent to this piecewise function?
Answer:
5|x+2|-1
Step-by-step explanation:
Evidence is included
PLEASE HELLLLLLP MEEE
Answer:
None of the above
Step-by-step explanation:
In my opinion, I believe the answer is none of the above because
answer A says it has a peak from 10 to 15 km but the graph goes higher than 15 km
answer B says it has a gap from 25 to 30 km but the graph doesn't go that high.
Hope did helps:)
A swim team must be chosen from 12 candidates. What is the greatest number of different 3-person teams that can be chosen?
==========================================
Explanation:
We have 12*11*10 = 1320 permutations possible. This is where order matters. However, order does not matter with swim teams as there are no positions or ranks. All that matters is the group overall (rather than any individual in the group).
Consider the set {A,B,C}. We have 3*2*1 = 6 ways to arrange this set of letters. When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC. Therefore, we divide 1320 over 6 to get the final answer of 1320/6 = 220.
---------
You can use the combination formula with n = 12 and r = 3. Doing so will give the following:
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{12} C _3 = \frac{12!}{3!*(12-3)!}\\\\_{12} C _3 = \frac{12!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10*9!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10}{3!}\\\\_{12} C _3 = \frac{12*11*10}{3*2*1}\\\\_{12} C _3 = \frac{1320}{6}\\\\_{12} C _3 = 220\\\\[/tex]
As you can see, we get the same result and note how 1320/6 is also present as well.
The greatest number of different 3-person teams that can be chosen is 220.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
The Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Consider the set {A,B,C}.
3*2*1 = 6 ways to arrange this set of letters.
When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC.
We can use the combination formula with n = 12 and r = 3.
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.\\\\^{12}C_3= \dfrac{12!}{3! \times (12-3)!} ways.\\\\\\^{12}C_3= \dfrac{12!}{3! \times (9)!} ways.\\\\^{12}C_3= \dfrac{12 \times 11 \times 10 \times 9}{3! \times (9)!} ways.[/tex]
1320/6 = 220
Thus, the greatest number of different 3-person teams that can be chosen is 220.
Learn more about combinations and permutations here:
https://brainly.com/question/16107928
#SPJ2
In the given diagram, find the values of x, y, and z.
Oax = 20°, y = 21°, z = 20°
Ob.x = 64°, y = 21°, z = 64°
Oox = 64°, y = 21°, z = 20°
Odx = 115°, y = 115°, z = 64
Answer:
B) x=64, y=21, z=64
Step-by-step explanation:
X=180-116=64
Y cannot equal 115, and one angle is already 95, and that would put it over 180. The only remaining choice for y=21
z=180-95-21=64
What is the length of the short leg in the 30-60-90 triangle shown below?
Answer:
it is D. 5
Step-by-step explanation:
The long side (B) will always be (A root 3) meaning, if you just take away the square root of 3, then you get the short side A
Answer:
[tex]\boxed{Shortest\ Leg = 5}[/tex]
Step-by-step explanation:
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Where θ = 60 , opposite = [tex]5\sqrt{3}[/tex] and adjacent = shortest leg
=> Tan 60 = [tex]5\sqrt{3}[/tex] / shortest leg (Tan 60 = √3)
=> Shortest Leg = [tex]\frac{5\sqrt{3} }{\sqrt{3} }[/tex]
=> Shortest Leg = 5
Find m∠CBD,,,,,,,,,,
Answer:
angle CBD=125
Step-by-step explanation:
(8x-41)+(9x+17)=180
17x -24 = 180
17x=204
x=12
9(12)+17=125
Answer:
125
Step-by-step explanation:
The two angles from a straight line so they add to 180
ABC + CBD = 180
8x -41+ 9x+17 = 180
Combine like terms
17x -24 = 180
Add 24 to each side
17x -24+24 = 180 +24
17x = 204
Divide by 17
17x/17 = 204/17
x =12
We want angle CBD
CBD = 9x+17
= 9*12+17
=108+17
= 125
Can someone help with this please thanks!
Answer:
150 I believe but don't quote me on that
can you draw a quadrilateral with no parallel lines and at least one right angle?
Answer:
Yes
Step-by-step explanation:
We can draw a quadrilateral with no parallel lines and at least one right angle
Answer:
Yes
Step-by-step explanation:
It's possible to draw a quadrilateral with no parallel lines and with 1 right angle
I really hope this helps I know how you feel (:-D)
Amanda is ordering an ice cream dessert. She must order a size, a flavor of ice cream, and a topping. There are 2 sizes, 1 flavor, and 6 toppings to choose from. How many different ice cream desserts could she order?
Answer: 12
Step-by-step explanation:
Order requirement:
Size ; flavor and topping
Available variety:
Size = 2
Flavor = 1
Toppings = 6
Number of different ice-cream desserts which can be ordered :
Since one of each of size, topping and flavor must be selected :
(Number of available flavors * number of Toppings available * number of sizes available)
1 * 6 different Toppings = 6 varieties
6 varieties * 2 different sizes = 12 varieties
Therefore, there are 12 different variety of ice-cream dessert she can order.
What value, written as a decimal, should Lena use as the common ratio?
Answer:
an=1*2.5^(n-1)
=2.5^(n-1)
Step-by-step explanation:
Complete question below:
What value, written as a decimal, should Lena use as the common ratio? Lena is asked to write an explicit formula for the graphed geometric sequence. On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).
Solution
Point (1, 1), (2, 2.5), (3, 6.25).
a=1
ar=2.5
ar^2=6.25
From ar and ar^2
r=6.25/2.5
=2.5
r=2.5
an=ar^(n-1)
Therefore, the explicit formula is
an=1*2.5^(n-1)
=2.5^(n-1)
In the circle below, O is the center and mĞ= 128° What is the measure of angle HIG?
Answer:
26 degrees.
Step-by-step explanation:
From the figure it is clear that HI is the diameter and [tex]acr(GI)=128^{\circ}[/tex]. So,
[tex]\angle GOI=128^{\circ}[/tex]
[tex]\angle GOI+\angle GOH=180^{\circ}[/tex] (linear pair)
[tex]128^{\circ}+\angle GOH=180^{\circ}[/tex]
[tex]\angle GOH=180^{\circ}-128^{\circ}[/tex]
[tex]\angle GOH=52^{\circ}[/tex]
Using central angle theorem of a circle, we get
[tex]\angle HIG=\dfrac{\angle GOH}{2}[/tex]
[tex]\angle HIG=\dfrac{52^{\circ}}{2}[/tex]
[tex]\angle HIG=26^{\circ}[/tex]
Therefore, the measure of angle HIG is 26 degrees.
what is the smallest number by which 2408 should be multiplied to get a perfect cube
Answer:
90601
Step-by-step explanation:
we have to find smallest number by which 2408 should be multiplied to get a perfect cube.
First lets find prime factor of 2408 and power these prime factors have
2408 = 2*1204 = 2*2*602 = 2*2*2*301= 2*2*2*7*43
thus,
2408 = 2^3*7*31
we know that a cube is a number raised to the power three
in 2408
2 has a power of three
but 7 and 31 and there is power of one,
thus we need to make
power of 7 and 31 three by multiplying
7 with 7*7
and 31 with 31*31
thus,
2^3*7*31*7*7*31*31 is the minimum cube value for this number
2^3*7*31*7*7*31*31 = 2^3*7^3*31^3 = 2408 * 7^2*31^2 = 2408*90601
Thus, smallest number which should be multiplied with 2408 to make it a perfect cube is 90601