Answer:
Option C. 3077.2 mm³
Step-by-step explanation:
Data obtained from the question include the following:
Diameter (d) = 17 mm
Height (h) = 60 mm
Pi (π) = 3.14
Volume =?
Next, we shall determine the radius of the cone. This is illustrated below:
Diameter (d) = 17 mm
Radius (r) =.?
Radius (r) = diameter (d)/2
r = d/2
r = 14/2
r = 7 mm.
The radius therefore, is 7 mm.
To know how much frozen water
is in the icicle, we shall calculate the volume of the icicle using the formula for calculating the volume of a cone. This is illustrated below:
Height (h) = 60 mm
Pi (π) = 3.14
Radius (r) = 7 mm
Volume =..?
V = ⅓πr²h
V = ⅓ × 3.14 × 7² × 60
V = 3.14 × 49 × 20
V = 3077.2 mm³
Therefore, the amount of frozen water in the icicle is 3077.2 mm³
Answer:
C 3,077.2 mm
Step-by-step explanation:
Can anyone else not see the answers?
Answer: no I cannot it hasn't been working since this late afternoon I believe
Step-by-step explanation:
Jordon will play a triangle at his school’s music program. As its name suggests, the musical instrument is shaped like a triangle. Jordon has customized the dimensions to produce a unique melody, which is played when the shortest side is hanging down, parallel to the ground. Which side of the musical instrument should be parallel to the ground if its dimensions are as shown in the diagram?
Answer:
A. AB
Step-by-step explanation:
Given that the musical instrument has a shape of ∆ABC, we can determine the shortest side that would be parallel to the ground by comparison of the 3 angles of the triangle corresponding to each side that is opposite each of them.
What this means is that, the larger angle would have the largest side opposite it. The medium angle will have medium length side opposite it, while the smallest angle will have the smallest side opposite it.
m < A = 59°
m < C = 57°
m < C = 180 - (59+57) (sum of angles in a triangle)
m < C = 64°
The smallest angle out of the three angles is angle C = 57°.
The side opposite it, is side AB.
Side AB is the shortest side of ∆ABC.
Therefore, AB should be parallel to the ground.
The
side
of the musical instrument that should be parallel to the ground if the
dimensions
are as given is side AB, which is option A.
Given that:
Jordon will play a
triangle
in his school’s music program.
When playing, the shortest side
is hanging down,
parallel
to the ground.
From the figure:
m∠A = 59°
m∠C = 57°
By the
angle sum
property,
m∠A + m∠B + m∠C = 180°
59° + m∠B + 57° = 180°
m∠B + 116° = 180°
m∠B = 180° - 116°
= 64°
The
shortest side
will be the side that is opposite to the smallest angle.
So, the smallest side is the side opposite to C.
So, the side is AB.
Hence, the side is AB, which is option A.
Learn more about
Triangles
here :
https://brainly.com/question/2773823
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Simplify completely quantity 3 x plus 18 over 18
Answer:
(x+6) / 6
Step-by-step explanation:
(3x+18) /18
Factor out 3 from the numerator
3(x+6) /18
Cancel a 3 from the numerator and denominator
(x+6) / 6
Of his take-home pay each month, Jerry spends 1/6 on car payment and 1/4 on food. What fraction of his take-home pay is left after paying for these two items?
Answer:
The fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.
Step-by-step explanation:
Consider that the total take-home pay each month Jerry receives is, $x.
It is provided that:
Jerry spends 1/6 on car payment, i.e. Car Payment = [tex]\frac{1}{6}x[/tex].Jerry spends 1/4 on food, i.e. Food = [tex]\frac{1}{4}x[/tex].The remaining amount can be computed by subtracting the amount spent from the total amount.
Compute the amount Jerry has spent so far:
Amount Spent = Car Payment + Food
[tex]=\frac{1}{6}x+\frac{1}{4}x\\\\=[\frac{1}{6}+\frac{1}{4}]x\\\\=[\frac{2+3}{12}]x\\\\=\frac{5}{12}x[/tex]
Compute the remaining amount as follows:
Remaining Amount = Total Amount - Amount Spent
[tex]=x-\frac{5}{12}x\\\\=[1-\frac{5}{12}]x\\\\=[\frac{12-5}{12}]x\\\\=\frac{7}{12}x[/tex]
Thus, the fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.
factor the equation. x2-15x+54=0
Answer:
I hope it will help you...
Answer:
(x-9)(x-6)
x= 9, x= 6
Step-by-step explanation:
x² - 15x + 54 = 0x² - 9x - 6x + 54 = 0x(x-9) - 6(x-9)= 0(x-9)(x-6)= 0Factored, and roots are:
x-9=0 ⇒ x= 9x- 6 =0 ⇒ x= 6Which of the following are identities? Check all that apply.
Answer:
The true answers:
A
B
C
Step-by-step explanation:
A P E X
Algebra 2 help needed
Answer:
D
Step-by-step explanation:
From the graph, the y-intercept of f(x) is 2 and since the y-intercept is when x = 0, it would fall into the x ≤ 1 category so the y-intercept of g(x) is 0 - 4 = -4. Since 2 > -4, the answer is D.
factorise 8a^3+b^3+12a^2b+6ab^2
Answer:
(2a+b)^3
Step-by-step explanation:
8a^3+b^3+12a^2b+6ab^2
(2a)^3 + 3. (2a)^2 b + 3 (2a) b^2 + b^3
the above equation compare to (a+b)^3 = a^3 + 3a^2b+3ab^2 +b^3
when we compare both the equations
our a= 2a and b=b
so, our answer is (2a + b)^3
Pls answer will make brainlist
Answer:
D. 48 in.^2
Step-by-step explanation:
Sides DE and AB are corresponding, and the triangles are similar.
linear scale factor = k = AB/DE = 12/60 = 1/5
area square factor = k^2 = (1/5)^2 = 1/25
area of ABC = area of DEF * area scale factor = 1200 sq in * 1/25
area of ABC = 48 sq in
Answer: D. 48 in.^2
What is the slope of the following line? Be sure to scroll down first to see all answer options. (-2, 11) (2, -3)
Answer:
-7/2
Step-by-step explanation:
We can find the slope by using the slope formula
m = (y2-y1)/(x2-x1)
= ( -3 -11)/( 2- -2)
= ( -14)/ ( 2+2)
= -14/4
= -7/2
Volume of a Triangular Prism
Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Answer:
Volume of prism = 240 ft²
Step-by-step explanation:
Given:
Base of prism (B) = 10 ft
Length of prism (L) = 8 ft
Height of prism (H) = 6 ft
Find:
Volume of prism
Computation:
Volume of prism = [BHL] / 2
Volume of prism = [(10)(8)(6)] / 2
Volume of prism = [480] / 2
Volume of prism = 240 ft²
Find the dimensions of a deck which will have railings on only three sides. There is 28 m of railing available and the deck must be as large as possible.
Answer:
2x2x7
Step-by-step explanation:
Mr. Sanchez's students were asked to add two positive integers. Juan subtracted by mistake and got 2. Maria mistakenly multiplied and got 120. What was the correct answer?
Answer:
22
Step-by-step explanation:
Given
From Juan's calculation,
Difference of two positive integers = 2
From Maria's calculation,
Product of same integers = 120
Required
Find the sum of the two numbers
Let the two integers be represented by a and b
a - b = 2 ------- (1)
a * b = 120 ------- (2)
Make a the subject of formula in (1)
a = 2 + b
Substitute 2 + b for a in (2)
(2 + b) * b = 120
Open bracket
2 * b + b * b = 120
2b + b² = 120
Rearrange
b² + 2b = 120
Subtract 120 from both sides
b² + 2b - 120 = 120 - 120
b² + 2b - 120 = 0
At this point, we have a quadratic equation.
We start by expanding the expression
b² + 12b - 10b - 120 = 0
Factorize
b(b + 12) - 10(b + 12) = 0
(b - 10)(b + 12) = 0
This implies that
b - 10 = 0 or b + 12 = 0
Make b the subject of formula in both cases
b = 10 or b = -12
From the question, we understand that both numbers are positive.
This means that
b = -12 will be discarded.
Hence, b = 10
Recall that a = 2 + b
Substitute 10 for b
a = 2 + 10
a = 12
This implies that the two numbers are 12 and 10.
Their sum = 12 + 10
Sum = 22
The correct answer is 22
He length of an alligator in a zoo is 14 5/8 feet. The everglades national park lists the longest alligator ever recorded in florida at 17 5/12 feet. Which is the difference in their lengths?
Answer:
2 and 1/6 feet
Step-by-step explanation:
To do this you would just put aside 17 and 14 and you would subtract 5/12 by 5/8. To subtract these you would just find the lcm which is 48 and that would be denominator and to make the top the same as the bottom you would just multiply how much it took the denominator and multiply the numerator. So to subtract them you would get 20/48 for 5/12 and 30/48 for 5/8. When you subtract them you get -10/12 so then you will subtract 17 and 14 which is 3 then you will subtract 3 - 10/12 and you would get 2 and 2/12 which can simplify to 2 1/6 feet
The difference in the lengths of alligators in zoos and Florida is 2.79 feet.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
Given that
The length of an alligator in a Zoo = 14 5/8 feet.
The length of an alligator in Florida = 17 5/12 feet.
Convert fractions into decimals, and we get
The length of an alligator in a Zoo = 14.625 feet.
The length of an alligator in Florida = 17.416 feet.
So the difference in their lengths = 17.416 - 14.625
So the difference in their lengths = 2.79 feet
Therefore, the difference in the lengths of alligators in zoos and Florida is 2.79 feet.
Learn more about Arithmetic operations here:
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please help me :) Which of these numbers is the greatest? A. 3,213,213 B. 7.8 x 10 to the 5 power C. 6.3 x 10 to the 6 power D. 11,014,114
Answer:
Choice C : [tex]6.3*10^{6}[/tex]
Step-by-step explanation:
Choice A won't be it because it's only 3 million.
Choice B won't work because it's 83 million.
Choice C WILL WORK because it's 98 million.
Choice D won't work because it's only 11 million.
how to do this question plz
Answer:
17.7 percent
Step-by-step explanation
You find the area of the trapezoid and rectangle. You divide the area of the trapezoid by the rectangle. then move the decimal 2 places to the right.
Write a rule for the linear function in the table.
f(x) = 4x + 3
f(x) = -4x - 3
1
f(x) = x + 3
Answer:
I guess that you want to know the transformations:
We start with:
f(x) = y = 4*x + 3
a)the transformed function is:
f(x) = y = -4*x - 3
So the sign changed.
This means that we go from (x, y) to (x, - y)
This is a reflection over the x-axis which changes the sin of the y component.
b) Now we go to f(x) = 4*x + 3
So the coefficient in the leading term changed.
This is a horizontal contraction:
A horizontal contraction of factor K for the function g(x) is: g(K*x)
In our case, we have:
f(K*x) = 4*(k*x) + 3 = x + 3
4*k*x = x
4*k = 1
k = 1/4
Then the transformation is an horizontal contraction of scale factor 1/4.
Please answer the following questions
Answer:
4a) 110 square centimetres
4b) 127 square centimetres
6) 292 square centimetres
8) 800 tiles
Step-by-step explanation:
4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:
a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:
A = 12 * 15 = 180 square centimetres
The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:
a = 10 * 7 = 70 square centimetres
Therefore, the area of the shaded part is:
A - a = 180 - 70 = 110 square centimetres
b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:
A = 13 * 11 = 143 square centimetres
The unshaded part has dimensions 8 cm by 2 cm. Its area is:
a = 8 * 2 = 16 square centimetres
Therefore, the area of the shaded part is:
A - a = 143 - 16 = 127 square centimetres
6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.
The frame has dimensions 24 cm by 18 cm. Therefore, its area is:
A = 24 * 18 = 432 square centimetres
The photograph has dimensions 14 cm by 10 cm. Therefore, its area is:
a = 14 * 10 = 140 square centimetres
Therefore, the background area of the space not covered by the photograph is:
A - a = 432 - 140 = 292 square centimetres
8) The floor has dimensions 8 m by 4 m. The area of the floor is:
A = 8 * 4 = 32 square centimetres
Each square tile has dimensions 20 cm by 20 cm. In metres, that is 0.2 m by 0.2 m. The area of each tile is:
a = 0.2 * 0.2 = 0.04 square metres
The number of tiles that are needed is the area of the floor divided by the area of each tile:
A / a = 32 / 0.04 = 800 tiles
I have no clue how to do this please help
Answer:
Max = (6,0); min = (-2, 4)
Step-by-step explanation:
1. Summarize the constraints
[tex]\text{Constraints} = \begin{cases}(a)\qquad 2x - y & \leq 12\\(b)\qquad 4x+ 2y & \geq 0\\(c) \qquad x + 2y & \leq 6\\ \end{cases}[/tex]
2. Optimization equation
z = 5x + 2y
3. Graph the constraints to identify the feasible region
See the figure below.
The "TRUE" regions for each graph are the shaded areas to the side of the line indicated by the arrows.
The "feasibility region" is the dark green area where all three areas overlap and all three conditions are satisfied.
5. Determine the points of intersection among the constraints
(i) Constraints (a) and (b)
[tex]\begin{array}{rcr}2x - y & = & 12\\4x + 2y & = & 0\\4x - 2y & = & 24\\8x&=&24\\x & = & \mathbf{3}\\6 - y & = & 12\\-y & = &6\\y & = & \mathbf{-6}\\\end{array}\\[/tex]
The lines intersect at (3,-6).
(ii) Constraints (a) and (c)
[tex]\begin{array}{rcr}2x - y & = & 12\\x + 2y & = & 6\\4x - 2y & = &24\\5x & = & 30\\x & = & \mathbf{6}\\6 + 2y & = & 6\\2y & = &0\\y & = & \mathbf{0}\\\end{array}[/tex]
The lines intersect at (6,0).
(iii) Constraints (b) and (c)
[tex]\begin{array}{rcr}4x+ 2y &= & 0\\x + 2y &=& 6\\3x & = & -6\\x & = & \mathbf{-2}\\-2 +2y & = & 6\\2y & = &8\\y & = & \mathbf{4}\\\end{array}[/tex]
The lines intersect at (-2,4).
6. Determine the x- and y-intercepts of the feasible region
The five black dots at (3,-6), (6,0), and (-2,4) are the vertices of the polygon that represents the feasible region.
Each vertex is a possible maximum or minimum of z.
7. Calculate the maxima and minima
Calculate z at each of the vertices.
(i) At (-2,4)
z = 5x + 2y = 5(-2) + 2(4) = -10 + 8 = 2
(ii) At (3,-6)
z = 5(3) + 2(-6) = 15 - 12 = 3
(iii) At (6,0)
z = 5(6)+ 2(0) = 30 + 0 = 30
The maximum of z occurs at (6,0).
The minimum of z occurs at (-2, 4).
Agrid shows the positions of a subway stop and your house. The
subway stop is located at (-7,8) and your house is located at (6,4).
What is the distance, to the nearest unit, between your house and
the subway stop?
Answer: about 13u
Step-by-step explanation:
Distance can be calculated as [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\sqrt{(6-(-7))^2+(4-8)^2}\\\\\\\sqrt{(13)^2+(-4)^2}\\\\\\\sqrt{185}\\\\13[/tex]
Hope it helps <3
Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. The vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. The first time it reaches its highest point is after 1.31.31, point, 3 seconds. Its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. Find the formula of the trigonometric function that models the vertical height HHH between the dock and the boat's mast ttt seconds after Antonio starts his stopwatch. Define the function using radians.
Answer:
Step-by-step explanation:
Since we're given a time at which the height is maximum, we can use a cosine function for the model.
The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.
The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.
The period is given as 3 seconds, and the right shift is given as 1.31 seconds.
This gives us enough information to write the function as ...
H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)
H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm
What number on the number line represents ground level?
0
-1
-2
-3
-4
-5
-6
Answer:
0 represents ground level.
Step-by-step explanation:
0 on the number line represents ground level. Based on the photo, the 0 is in between the underground and the space above. The answer cannot be one of the negative numbers because those are all shown to be underground in the photo.
The incorrect work of a student to solve an equation 2(y + 4) = 4y is shown below: Step 1: 2(y + 4) = 4y Step 2: 2y + 6 = 4y Step 3: 2y = 6 Step 4: y = 3 Which of the following explains how to correct Step 2 and shows the correct value of y? The equation should be y + 4 = 4y after division by 2; y = 5 The equation should be y + 4 = 4y after division by 2; y = 2 2 should be distributed as 2y + 8; y = 4 2 should be distributed as 2y + 8; y = 2
Answer:
2 should be distributed as 2y + 8; y = 4
Step-by-step explanation:
Step 2 is wrong.
2(y + 4) = 4y
The step to solve is to expand brackets or distribute 2, not divide both sides by 2.
2y + 8 = 4y
Subtract both sides by 2y.
8 = 2y
Divide both sides by 2.
4 = y
45^2 can be found out by 4 x ____ x 100 + ____ = ____
A certain ferry moves up and down a river between Town A and B. It takes the ferry two hours to travel to Town A and only an hour and thirty minutes to return to Town B. If the current is 5mph how far apart are the two cities?
Answer:
The distance between two cities is 60 miles.
Step-by-step explanation:
Time taken to travel from B to A = 2 hours
Time taken to travel from A to B = 1.5 hours
Current speed = 5 mph
Let the speed of ferry in still water = u mph
When the ferry moves with the current, it will taken lesser time (i.e. A to B) and when it moves against the current it will take more time (i.e. B to A).
Let the distance between the two cities A and B = D miles
While moving with the current, speed = [tex](u+5)\ mph[/tex]
While moving against the current, speed = [tex](u-5)\ mph[/tex]
Formula for Distance = Speed [tex]\times[/tex] Time
Distance traveled in each case is same i.e. D.
So,
[tex]D = (u+5) \times 1.5 = (u-5) \times 2\\\Rightarrow 1.5u+7.5=2u-10\\\Rightarrow 0.5u =17.5\\\Rightarrow u = \dfrac{175}{5}\\\Rightarrow u = 35 \ mph[/tex]
Now,
[tex]D = (u+5) \times 1.5\\\Rightarrow D =(35+5) \times 1.5\\\Rightarrow D =(40) \times 1.5\\\Rightarrow \bold{D =60\ miles}[/tex]
So, the distance between two cities is 60 miles.
Answer:
I believe that the answer is 60 miles
Step-by-step explanation:
5
Write 2 -% as a decimal (not
8
as a
percentage).
Answer: 0.4
Step-by-step explanation:
i think
Trigonometry.... plzzz helllppp
Answer:
Hey there!
We can write this equation:
cosine xyz=6/15, or 0.4
arc cosine 0.4= 66.4
Thus, angle xyz is 66.4 degrees
Hope this helps :)
Question 21 of 31
What is the length of AC?
Answer:
C. 126
Step-by-step explanation:
We can use ratios to solve for corresponding side lengths.
[tex]\frac{140-x}{81} =\frac{x}{9}[/tex]
Cross multiply.
[tex]9(140-x)=81x[/tex]
[tex]140-x=9x[/tex]
[tex]140=10x[/tex]
[tex]14=x[/tex]
Plug x as 14.
[tex]140-14=126[/tex]
HELPP PLEASE
2. At Math Camp, students can either pack their own lunch every day or buy lunch at camp. If they want to buy lunch there are 3 options: Option A: they pay an initial fee of $30 and lunches cost $2 each Option B: shown on the graph Option C: they pay a flat fee of $70 which includes all lunches Write an equation for each option. (3 marks) Option A: Option B: Option C: b) Describe under what conditions, a student should choose each option. (Hint: you may want to graph all 3 lines on the same axes) (4 marks) Choose Option A if: Choose Option B if: Choose Option C if: 3. 4. A Campbell’s Soup can is 15cm tall and has a radius of 5 cm. How much paper is needed to make the label (think about what the label covers)? (3 marks) How much soup can this hold? (1 cm3 = 1 mL) (3 marks)
Answer:
3.
A. Y = 2x + 30 (red line)
B. Y=5x (blue line)
C. Y=70 (green line)
From 0 to 10 days, choose option B (shown on graph)
From 10 to 20 days, choose option A (first option)
From 20 days and more, choose option C.
4.
surface area of label = 471.2 cm^2
Step-by-step explanation:
Q1718436 Math Camp
2. At Math Camp, students can either pack their own lunch every day or buy lunch at camp. If they want to buy lunch there are 3 options:
Option A: they pay an initial fee of $30 and lunches cost $2 each
Option B: shown on the graph
Option C: they pay a flat fee of $70 which includes all lunches
Write an equation for each option. (3 marks) Option A: Option B: Option C:
A. Y = 2x + 30 (red line)
B. Y=5x (blue line)
C. Y=70 (green line)
b) Describe under what conditions, a student should choose each option. (Hint: you may want to graph all 3 lines on the same axes) (4 marks)
Choose Option A if: Choose Option B if: Choose Option C if:
Least cost is what is below the lowest possible line for the number of days stayed.
From 0 to 10 days, choose option B (shown on graph)
From 10 to 20 days, choose option A (first option)
From 20 days and more, choose option C.
Note that for days 10 and 20, there are two choices each.
3.
4. A Campbell’s Soup can is 15cm tall and has a radius of 5 cm. How much paper is needed to make the label (think about what the label covers)? (3 marks) How much soup can this hold? (1 cm3 = 1 mL) (3 marks)
The label only covers the curved surface.
Curved surface area
= 2 pi * r * h
= 2 pi (5) * 15
= 150 pi
= 471.2 cm^2
Darion saved the amount shown from his weekly allowance Calculate
the total amount he save 20$ 10$ 5$ 25$ 25$
Answer:
$20 i think
Step-by-step explanation: have a good day bye bye yup yup