Part I: Recalling the "Volume of cone" formula
Given:
Height of cone = 10 yardsRadius of cone = 9 yardsFormula (Volume of cone):
[tex]\text{Volume of cone:} \ \dfrac{1}{3} \times \pi \times r^{2} \times h[/tex]
[Where r and h are the radius and the height respectively.]
Part II: Determining the volume of the cone
Substitute their values into the formula to determine the volume of the cone.
[tex]\implies \text{Volume of cone:} \ \dfrac{1}{3} \times \pi \times (9)^{2} \times (10)[/tex]
∴ Let π be 3.14 ∴
[tex]\implies\text{Volume of cone:} \ \dfrac{1}{3} \times 3.14 \times (9)^{2} \times (10)[/tex]
Simplify the expression to determine the volume.
[tex]\implies\text{Volume of cone:} \ \dfrac{1}{3} \times 3.14 \times 81 \times 10[/tex]
[tex]\implies\text{Volume of cone:} \ 3.14 \times 27 \times 10[/tex]
[tex]\implies\text{Volume of cone:} \ 31.4 \times 27[/tex]
[tex]\implies\text{Volume of cone} = 847.8 \ \text{yd}^{3} = \boxed{847.80 \ \text{yd}^{3}} \ \ \ \ \ \ \ \ (\text{Nearest hundredth)}[/tex]
How do you find the other side lengths of a right triangle when only given the value of one of the sides?
Which statement is most likely to be true? the scores from mrs. jones’s class are the closest to the class mean. the scores from mrs. rijo’s class are the closest to the class mean. the scores from mr. phan’s class are the closest to the class mean. the scores from mrs. scott’s class are the closest to the class mean.
Answer:
The scores from Mrs. Rijo’s class are the closest to the class mean.
Step-by-step explanation:
Jus took the test
Answer:The scores from Mrs. Rijo’s class are the closest to the class mean.
Step-by-step explanation:
B
Plis help me with this one!!!!!!!
Answer: (0, 9) or x = 0, y = 9
Step-by-step explanation:
The solution is the point of intersection.
Here, the lines intersect at the point (0, 9) in the format of (x, y) so we can pull out the answers x = 0 and y = 9.
Answer:
(0, 9)
Step-by-step explanation:
First we need to find the equations of each line!What I'd do is use the equation:gradient (m) = change in y ÷ change in xStarting with the left line, let's pick two coordinates that are on the lineI've picked: (-2, 5), (-3, 3)gradient (m) = (3 - 5) ÷ (-3 - -2) = -2 ÷ -1 = 2We can then use the equation y = mx + c (m is gradient)y = 2x + cWe know we have the point (-3, 3) on this line(-3, 3) = (x, y) so x = -3 and y = 3y = 2x + c3 = 2 × -3 + c3 = -6 + cc = 9Finally, we can say y = 2x + 9Doing the exact same steps for the other line...
y = -3x + 9Since we now have two y = ... equationsWe can say y = yWhich is the same as2x + 9 = -3x + 9We rearrange to find x...5x = 0x = 0That gives us the x-coordinate of where the lines meet (the solution of the system of equations)We can then pick either equation to find the y-coordinate:y = -3x + 9y = -3 × 0 + 9 = 9So the solution we have is at the point (0, 9)!The $23 rd term in a certain geometric sequence is 16 and the $28th term in the sequence is 24. What is the $43 rd term?
Answer:
81
Step-by-step explanation:
Geometric sequence formula: [tex]a_n=ar^{n-1}[/tex]
Given:
[tex]a_{23}=ar^{22}=16[/tex][tex]a_{28}=ar^{27}=24[/tex]Find common ratio (r):
[tex]\begin{aligned}\implies \dfrac{a_{28}}{a_{23}} =\dfrac{ar^{27}}{ar^{22}} & =\dfrac{24}{16}\\ \implies r^5 & =\dfrac32\\ \implies r & = \sqrt[5]{\frac32} \end{aligned}[/tex]
Find initial term (a):
[tex]\implies ar^{22}=16[/tex]
[tex]\implies a(\sqrt[5]{\frac32} )^{22}=16[/tex]
[tex]\implies a(\frac32} )^{\frac{22}{5}}=16[/tex]
[tex]\implies a=\dfrac{16}{(\frac32)^{\frac{22}{5}}}[/tex]
Find the 43rd term:
[tex]\implies a_{43}=ar^{42}[/tex]
[tex]\implies a_{43}= \left(\dfrac{16}{(\frac32)^{\frac{22}{5}}}\right)(\sqrt[5]{\frac32} )^{42}[/tex]
[tex]\implies a_{43}=16 \cdot (\frac32)^{-\frac{22}{5}} \cdot (\frac32)^{\frac{42}{5}}[/tex]
[tex]\implies a_{43}=16 \cdot (\frac32)^4[/tex]
[tex]\implies a_{43}=16 \cdot \left(\dfrac{3^4}{2^4}\right)[/tex]
[tex]\implies a_{43}=16 \cdot \left(\dfrac{81}{16}\right)[/tex]
[tex]\implies a_{43}=81[/tex]
Jonah has a recipe that uses 1 ½ cups of brown sugar and 2 ⅓ cups of flour to make 24 muffins. He has a total of 7 cups of flour. Jonah wants to use all of his flour to make as many muffins as possible using the recipes. Part A: Exactly how many cups of brown sugar will Jonah use, if he uses all 7 cups of flour? Part B: Exactly how many muffins will Jonah make if he uses all 7 cups of flour?
Answer:
Part A: 4.5 cups
Part B: 3
Step-by-step explanation:
Part A:
We will have to find how many muffins he will make first if he uses all 7 cups.
# of muffins = 7/(2 + 1/3) = 3
Cups of sugar = 3 * (1 +1/2) = 4.5 cups
Part B:
We solved this in Part A
The number of muffins is 3
⚠️‼️ HELP PLEASE WILL GIVE POINTS
Answer:
48°
Step-by-step explanation:
Angles on a straight line sum to 180°Therefore [tex](7x-92)+(6x+12)=180[/tex]Combine like terms[tex]13x-80=180[/tex]Add 80 to both sides[tex]13x=260[/tex]Divide both sides by 13[tex]x=20[/tex]Insert this into 7x - 927 * 20 - 92 = 140 - 92 = 48What is the value of (3^0)^-3?
Answer:
1
Step-by-step explanation:
[tex](3^{0} )^{-3} =1^{-3} =\frac{1}{1^3} =1[/tex]
Anything to the power of 0 = 1
Negative exponents = inverse
Hope this helps!
HURRYYY
The diagram shows a cone of the height of 5 cm and a base radius of 12 cm
What is the total surface area of the side and base?
Use 3.14 as an approximation for IT
Answer:
radius r = 12 m
height h = 5 m
slant height s = 13 m
volume V = 753.982237 m ³
lateral surface area L = 490.088454 m²
base surface area B = 452.389342 m²
total surface area A = 942.477796 m²
The total surface area of cone is 942 cm².
What is Total surface area of Cone?Total surface area is the sum of the area of the circular base and the area of the curved part of the cone.
The total surface area of a cone is the sum of the area of the base and the lateral area:
SA = πr² + πrl
where, r is radius
l is slant height
Now, for finding the slant height of the given cone is
l² = r² + h²
l² = 12² + 5²
l² = 144 + 25
l² = 169
l = 13 cm
Now, SA = π X 12² + π X 12 X 13
= 144π + 156π
= 300π
= 300 X 3.14
= 942 cm²
Thus, the total surface area of cone is 942 cm².
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A college baseball team ordered 5,400 hats to sell at games. Each box holds 60 hats. How many boxes will the team get?
boxes
Answer:
90 boxes
Step-by-step explanation:
you will have to divide the total amount you have by the groups they will go into. in this case it is 5400/60 = 90
The probability that Aiko can drive to work without having to stop at a red light is 0.125. The odds against Aiko driving to work without seeing a red light are _[blank]_. What odds best complete the sentence?
The probability that Aiko drives without seeing a red light is the likelihood of not seeing the red light
The odds against Aiko driving to work without seeing a red light is 7 : 1
How to determine the odd against Aiko?The probability of not having to stop at a red light is given as:
P(Not Stop) = 0.125
The probability that he would stop at a traffic light is calculated using:
P(Stop) = 1 - 0.125
Evaluate
P(Stop) = 0.875
The odds against Aiko driving to work without seeing a red light is calculated using:
Odd = P(Stop) : P(Not stop)
So, we have:
Odd = 0.875 : 0.125
Simplify
Odd = 7 : 1
Hence, the odds against Aiko driving to work without seeing a red light is 7 : 1
Read more about probability at:
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5. Find the value of x to the nearest tenth. Volume of the prism
is 576 cm?
Volume: 576 cm3
the volume of the triangular prism will be, the area of the triangular face times its length
[tex]\stackrel{\textit{area of the triangle}}{\left[ \cfrac{1}{2}(\underset{b}{8})(\underset{h}{8}) \right]}~~ ~~\stackrel{length}{(x)}~~ = ~~\stackrel{volume}{576}\implies 32(x)=576 \\\\\\ 32x=576\implies x=\cfrac{576}{32}\implies x=18[/tex]
. Which is a true statement about the transformation?
Answer: The orientation of the vertices was changed.
(x, y) ---> (x + 8, y - 3)
Step-by-step explanation: The triangle translation isn't on quadrant II, it's on quadrant I, so that answer choice isn't correct. The triangle ABC translated 8 units right and 3 units down, not 8 units left and 3 units up. Whenever you dilate, translate, rotate, or reflect triangles like ABC, the next triangle becomes A'B'C because it shows you that it's a transformation of the original triangle. The orientation of the figure didn't change, because it didn't change shape, rotation, or size, so the orientation wasn't affected at all, just the vertices.
The transformation is (x, y) ---> (x + 8, y - 3), because think of it like this. I already said that the triangle translated 8 units to the right, which means that the triangle is translating 8 units in the positive direction to the right. The triangle going 3 units down is in the negative direction, and that's why it's (x, y) ---> (x + 8, y -3).
Let me know if this is right! :)
what is the translation from quadrilateral EFGH to quadrilateral E' F'G'H'
Answer:
transformation down 4, transformation right 1
Step-by-step explanation:
Answer:
Four down, 1 right so [tex](x+1,y-4)[/tex]
Step-by-step explanation:
Hope this helps! Have a good day! :)
(20 points and Brainliest)
Given the following graph, what is the x-coordinate of the vertex?
A)0
B)-1
C)8
D)7.5
Answer:
Since the vertex is the tallest or shortest point on the graph, the vertex would be 8 since 8 is the tallest point. So it would be B. 8
Step-by-step explanation:
find the solution to the system of equations by using either graphing and substitution y = 6 - x and y = x - 2
pls explain ur answer.
Answer:
x = 4, y = 2
Step-by-step explanation:
y = 6 - x
y = x - 2
Substitute the value for y in the first equation into the second.
So we get:
6 - x = x - 2
-x - x = -2 -6
-2x = -8
x = 4
Plug this into second equation:
y = 4 - 2 = 2.
Check these results in equation 1:
y = 6 - x
2 = 6 - 4 = 2
- so correct.
expand and simplify 2(5x+3)-2(2x-3)
Answer:
hopes this helps.
Step-by-step explanation:
Hey there!
2(5x + 3) - 2(2x - 3)
DISTRIBUTE
= 2(5x) + 2(3) - 2(2x) - 2(-3)
= 10x + 6 - 4x - 6
COMBINE the LIKE TERMS
= (10x - 4x) + (6 + 6)
= 10x - 4x + 6 + 6
= 6x + 12
Therefore, your answer is: 6x + 12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Some1 help pzl
Find the surface area 7m 15m 6m
Answer:
474 m²
Step-by-step explanation:
Surface area of a rectangular prism:
SA = 2(lw + lh + hw)
Given:
width (w) = 6 mlength (l) = 7 mheight (h) = 15 m⇒ SA = 2(7 · 6 + 7 · 15 + 15 · 6)
= 2(42 + 105 + 90)
= 2(237)
= 474 m²
Answer:
474 Sq m
Step-by-step explanation:
You have two sides that are 7m x 6m
(7*6)*2 = 84
You have two sides that are 15m x 6m
(15*6)*2 = 180
You have two sides that are 15m x 7m
(15*7)*2 = 210
84+180+210=474
Alex and Bev sat six tests, each with 50 marks.
The table shows their mean percentages after five tests.
Alex
60%
Bev
52%
After all six tests, their mean percentages were equal.
In the sixth test, Alex scored 24 out of 50
Work out Bev's score, out of 50, in the sixth test.
Answer:
44
Step-by-step explanation:
60 × 5 or 300
or
52 × 5 or 260
24
50
× 100 or 0.48 × 100
or 48
348 implies
60 × 5 +
24
50
× 100 – 52 × 5
or
300 + 48 – 260 or 88
You drop a ball off a 50ft roof to see how long it will bounce. Each bounce loses 10% of the height of its previous height
Answer answer answer answer
Answer:
the answer is option C
Step-by-step explanation:
45/4 = 45 divided by 4 = 11.25
-8 times 11.25 gives you -90
Answer: the answer is choice c . 45 divided by 4 = 11.25 .
negative 8 times 11.25 gives you negative 90 .
Step-by-step explanation: HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST .THANKS .
round 56709 to the nearest thousands
Answer:
57000
Step-by-step explanation:
56709 = 50000 + 6000 + 700 + 9
6709 is closer to 7000 that 6000
The answer is 57000
Hope this helps :)
Have a nice day!
The volume of a cylinder is 66 cubic meters and the radius is 2 meters. Find the height of the cylinder. Round to the nearest tenth.
Find the area of this figure
Step-by-step explanation:
well, I see one large rectangle (20×6), and 2 small triangles with their horizontal sides being (20-8-6)/2 = 3 m. and their vertical joined side being 10-6 = 4 m.
the total area is simply the sum of the rectangle and the 2 triangles.
the rectangle is
20×6 = 120 m²
each triangle is
4×3/2 = 2×3 = 6 m²
we have 2 of them, so their combined area is 2×6 = 12 m².
the total area is
120 + 12 = 132 m²
5x + 2y = 8
-4x + 10y = 40
Answer:
(0, 4 )
Step-by-step explanation:
5x + 2y = 8 → (1)
- 4x + 10y = 40 → (2)
multiplying (1) by - 5 and adding to (2) will eliminate y
- 25x - 10y = - 40 → (3)
add (2) and (3) term by term to eliminate y
- 29x = 0 , then
x = 0
substitute x = 0 into (1) and solve for y
5(0) + 2y = 8
0 + 2y = 8
2y = 8 ( divide both sides by 2 )
y = 4
solution is (0, 4 )
Need the Answer quickly
Look at the table below showing an example of a checkbook ledger. a 6-column table has 5 rows. the first column is labeled check number with entries blank, blank, 156, blank, blank. the second column is labeled date with entries 9/15, 9/16, 9/18, 9/18, 9/18. the third column is labeled description with entries pharmacy, paycheck, rent, dinner, movie tickets. the fourth column is labeled amount debited with entries (in dollars) 15.20, blank, 425, 22.30, 26.75. the fifth column is labeled amount credited with entries blank, 1,015.50 dollars, blank, blank, blank. the sixth column is labeled balance with entries 219.80 dollars, blank, blank, blank, blank. according to the table, what is omar’s bank balance? $761.25 $810.30 $814.75 $1,186.25
The total remaining bank balance in the account of Omar after reducing all the debit and adding the paycheck is $761.25.
What do you mean by debit and credit amount?The money which is paid from an account is called the debit amount and the money which is paid into an account is called the credit amount.
To know the remaining balance of the account, all the debit amount is subtracted from it and all the credit amount is added to it.
The data given in the table is,
Pharmacy - $15.20-Debited
Rent - $425.00-Debited
Dinner - $22.30-Debited
Movie Ticket - $26.70-Debited
Pay Check - $1015.50-Credited
Initial Balance- $219.80
The initial balance is $219.80, and a paycheck of $1015.50 is credited to his account. Thus, the total balance in his account without any debit is,
[tex]\rm A_i=1015.50+219.80\\\\A_i=1253.30[/tex]
The total amount debited from their account of Omar is,
[tex]\rm A_d=15.20+425+22.30+26.70\\\\A_d=474.05[/tex]
Thus, the total remaining amount in his account is,
[tex]\rm A= 1253.3-474.05\\\\A=761.25[/tex]
Hence, the total remaining bank balance in the account of Omar after reducing all the debit and adding the paycheck is $761.25.
Learn more about the debit and credit amounts here;
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Answer:
According to the table, what is Omar’s bank balance?
$761.25
I need help with my homework it’s a math question
3 divided by 1/8
A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 lower than in the first. The tax in the first city was 3. 5% and the tax in the second city was 7%. The total hotel tax paid for the two cities was $455. How much was the hotel charger in each city before tax?
By solving a system of equations we will see that the charge on the first city was $5,000, and on the second city, $4,000.
How much was the hotel charge in each city?
Let's define the variables:
C₁ = charge in the first city.C₂ = charge on the second city.We know that:
C₂ = C₁ - $1000
And we also know that the total tax is $455, then we can write:
0.035*C₁ + 0.07*C₂ = $455
(this says that the total tax is $455)
So we have a system of equations:
C₂ = C₁ - $1000
0.035*C₁ + 0.07*C₂ = $455
We can replace the first one into the second to get:
0.035*C₁ + 0.07*(C₁ - $1000) = $455
0.105*C₁ - $70 = $455
C₁ = ($455 + $70)/0.105 = $5,000
And:
C₂ = C₁ - $1000 = $5,000 - $1,000 = $4,000
The charge in the first city is $5,000 and in the second city was $4,000.
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Hurry need help!!!!!!1
Answer:
it would be 3
Step-by-step explanation:
you have to add both fracitons and you would add 3/4+1/4 and you would get 4/4 and that becomes a whole number thin you would add 2 and 1 and you would git 3 thats how i got the answer hope this helps if not please let me know
Answer:
I think the other person is correct and her answer is good
Step-by-step explanation:
Daniel owns a synall business selling used books. He knows that in the last week 60
customers paid cash, 4 customers used a debit card, and 23 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with a
credit card as a fraction in simplest form.
The probability that the next customer that comes into Daniel's business will pay with a credit card is 23 / 87.
What is the probability?Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the next customer will pay with a credit card = number of people who paid with a credit card / total number of customers
23 / (23 + 60 + 4)
23 / 87
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