The approximate amount of water that remains in the tub after the 6 spherical balls are placed in the tub are 3479.12 in³.
What is the approximate amount of water that remains in the tub?The first step is to determine the volume of the cylinder.
Volume of the tub = πr²h
Where:
r = radius = diameter / 2 = 18/2 = 9 inches h = height π = 3.143.14 x 9² x 20 = 5086.8 in³
The second step is to determine the volume of the 6 balls.
Volume of a sphere= 4/3πr³
r = diameter / 2 = 8/2 = 4 inches
6 x (3.14 x 4/3 x 4³) = 1607.68 in³
Volume that remains in the tub = 5086.8 in³ - 1607.68 in³ = 3479.12 in³
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find the value of each of the lettered angles in the diagram below
Answer:
Step-by-step explanation:
Remark
You have an isosceles triangle. That means that the angles opposite the marked sides are equal. So mark the angle on the lower left of the triangle as 50 degrees.
The solution to problem depends on the fact that the sum of the two inside angles of the triangle (each of which is marked as 50 degrees) not supplementary to the exterior angle, are still equal to the exterior angle.
Givens
<1 = 50 degrees
<2 = 50 degrees
Exterior angle = 15x + 25 Substitute the givens into the equation
Equation
<1 + <2 = 15x + 25
Solution
50 + 50 = 15x + 25 Combine the left side
100 = 15x + 25 Subtract 25 from both sides
100 - 25 = 15x + 25 - 25 Combine
75 = 15x Divide both sides by 15
75/15 = 15x/15
5 = x
Answer
<1 = 50 degrees
<2 = 50 degrees
15x + 25 = 75 + 25 = 100
help with applications of surface area and volume problems! will reward brainly, 10th grade geometry
Answer:
Question 1:
Rectangular prism requires [tex] 10.185\: in^2[/tex] more material to make than the cylinder.
Question 4:
The cylindrical container holds [tex]\bold{60.16\: in^3}[/tex] more than the rectangular prism.
Step-by-step explanation:
Question 1:
In order to select the correct answer, we should find the surface areas (SA) of both cylindrical as well as rectangular containers. Let us start...For cylindrical container:h = 10 in & r = 4.5 in[tex] SA (Cylindrical \:container) = 2\pi rh+2\pi r^2-\pi r^2[/tex] ([tex]\pi r^2[/tex] is subtracted because the container is open from the top)[tex] SA (Cylindrical \:container) = 2\pi rh+\pi r^2[/tex] [tex] SA (Cylindrical \:container) = 2(3.14)(4.5)(10)+3.14 (4.5)^2[/tex] [tex]\implies \red{\boxed{\bold{SA (Cylindrical \:container) =346.185\: in^2}}}[/tex] Next, we find the surface area of the rectangular container which has following dimensions.[tex] l = 8\: in,\: b = 8\: in,\: h= 8.5\: in[/tex][tex] SA ( rectangular\: container) = 2(lb+bh+lh)-lb[/tex] (lb is subtracted because container is open from the top)[tex] \implies SA ( rectangular\: container) = lb+2(bh+lh)[/tex][tex] \implies SA ( rectangular\: container) = 8*8+2(8*8.5+8*8.5)[/tex][tex] \implies \purple{\boxed{\bold{SA ( rectangular\: container) = 336\: in^2}}}[/tex]Here, SA (Cylindrical container) > SA (rectangular container)[tex] Difference = 346.185 - 336 = 10.185\: in^2[/tex][tex]\bigodot[/tex] This means: rectangular prism requires [tex]\bold{10.185\: in^2}[/tex] more material to make than the cylinder.Question 4:
[tex] V_{Cylinderical\: container}= \pi r^2 h [/tex][tex] \implies V_{Cylinderical\: container} =3.14 (4)^2 (9)[/tex][tex]\implies\red{\boxed{\bold{V_{Cylindrical\: container}=452.16\: in^3}}}[/tex][tex]V_{rectangular\: container}= l*b* h[/tex][tex] \implies V_{rectangular\: container}= 7*7* 8[/tex][tex] \implies \orange{\boxed{\bold{V_{rectangular\: container}= 392\: in^3}}}[/tex] Here, [tex] V_{Cylinder\: container}>V_{rectangular\: container}[/tex][tex] Difference = 452.16 - 392= 60.16\: in^3[/tex][tex]\bigodot[/tex] Thus, the cylindrical container holds [tex]\bold{60.16\: in^3}[/tex] more than the rectangular prism.Rectangle ABCD has vertex coordinates A(-1,-1), B(-1,-3), C(-4,-3), and
D(-4,-1). It is translated 3 units up and reflected across the yaxis. What are
the coordinates of A'B'C'D"?
A. AT1,2).B1.0).C'(4.0).D*(4,2)
B. A-1,2),B(-3,2).(-3,-1),-1,-1)
OC. A1.-1),B1,-3),C*(4,-3),D*(4,-1)
D. A12-1),B(2,-3),C(-1,-3), D-1,-1)
Step-by-step explanation:
A. AT1,2).B1.0).C'(4.0).D*(4,2)
your answer
The distance traveled by a car traveling at a constant speed is directly proportional to the time spent traveling. If the car went 910 miles in 13 hours, how far will it go in 14 hours
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"d" directly proportional to "t"}}{d=kt}\qquad \textit{we also know that} \begin{cases} d=910\\ t=13 \end{cases} \\\\\\ 910=k13\implies \cfrac{910}{13}=k\implies 70=k~\hfill \boxed{d=70t} \\\\\\ \textit{when t=14, what is "d"?}\qquad d=70(14)\implies d=980~miles[/tex]
12% of 59.7 is what number?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{12\% of 59.7}}{\left( \cfrac{12}{100} \right)59.7}\implies 7.164[/tex]
Which Stem-and-Leaf Plot matches the data set shown below?{11, 23, 13, 17, 13, 24, 22, 32, 12, 35} PLEASE HELP ME
Answer:
I am going to use a dot to represent a line:
1 . 1, 2, 3, 3, 7
2. 2, 3, 4
3. 2, 5
A teacher administers three different versions of a test to his students The two-way table shows the results.
Find the probability of the event below using the formula for conditional probability. Round your answer to the nearest tenth.
P(pass | Test A)
The probability is ____%
SHOW ALL WORK
The P(pass | Test A) is 31.81%, P(pass | Test B) is 29.87%
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Part A:
Total number of students = 154
Total number of students passed the test = 49
The probability:
P(pass | Test A) = 49/154 = 31.81%
Part B:
Total number of students = 154
Total number of students passed the test = 46
The probability:
P(pass | Test B) = 46/154 = 29.87%
Thus, the P(pass | Test A) is 31.81%, P(pass | Test B) is 29.87%.
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Answer:
87.5%
Step-by-step explanation:
add the number of students who took test A (49+7=56)
take the number of students who passed test A and divide it by the number of students who took the test A
49÷56=.875= 87.5%
Simplify: 10 - (16 ÷ 8)3 • 9 + 9
Answer:
-35
Step-by-step explanation:
Answer:
54(16÷8)-10?????
Step-by-step explanation:
I'm bad at this
what’s the answer to 4*100000
Answer:
400000
Step-by-step explanation:
your welcome
I need help, please and thank you
Answer:
It's -3.125
Step-by-step explanation:
1/8 in decimal is 0.125
the 3 is a whole number so just put it in front.
Remember it's a negative, so you get:
-3.125
Answer:
-3.125
Step-by-step explanation:
- Multiply 3 and 8 to get 24. [tex]-\frac{24+1}{8}[/tex]
- Add 24 and 1 to get 25. [tex]-\frac{25}{8}[/tex]
- Turn [tex]-\frac{25}{8}[/tex] into a decimal to get -3.125
pls help im confused
e + 20 ≥ 33
Please help me solve this!
( solving one-step inequalities )
Answer:
=> e is greater than Or equal to 13
Answer:
Hey I don't know if this helps but I your trying to see if the equality is true of false it would be false
The line passes through points A (6:0) and B(O:4). Write the equation of the line.
Answer:
y = (-2/3)x + 4 or
3y = -2x + 12
Step-by-step explanation:
Slope of line passing through (x₁, y₁) and (x₂, y₂) is given by
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
In this particular case where the points are (6,0) and (0,4) we get the slope as (4-0)/(0-6) = -2/3
Equation of a line with slope m and y intercept c is given by
y = mx + c
substituting for m we get the equation y = (-2/3)x + c
Substituting the first point (6,0) we get
0 = (-2/3)(6) + c or -4 + c = 0 or c =4
Therefore y = (-2/3)x + 4 or multiplying both sides by 3 we get
3y = -2x + 12
3 added to twice a number
Answer:
The equation is n2 + 3
Step-by-step explanation:
The n represents the number.
for example the number 10
if you put it in the equation it becomes
(10)(2) +3
10x2=20
20+3=23
Evaluate the integral, please help!!!
[tex]\int_{0}^{\pi}(1+cosx) dx[/tex]
Answer:
pi
Step-by-step explanation:
First solve the integral
[tex]\int\ {(1+ cos x} )\, dx[/tex]
[tex]\int\ {1} \, dx +\int\ {cos x} \, dx[/tex]
[tex]\int\ {1} \, dx = x[/tex] and [tex]\int\ {cos x} \, dx = sin x[/tex]
x + sin x
Now consider the limit from 0 to π
[tex]\lim_{0 \to \\pi } (x+sin x)[/tex]
(π +sin π) -(0 +sin 0)
sin π = 0 and sin 0 = 0
π-0
π
Answer:
[tex]\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx=\pi[/tex]
Step-by-step explanation:
[tex]\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx\\\\=x+\sin x\biggr|^{\pi}_0\\\\=[\pi+\sin\pi]-[0+\sin0]\\\\=\pi[/tex]
Remember your antiderivatives!
Julia is making a flag for a project. The design of one of the flags, composed of three triangles, is shown in the figure.
40 cm
9 cm
41 cm
18 cm
41 cm
9 cm
40 cm
What is the perimeter of the flag Julia made?
ОА.
180 centimeters
OB.
116 centimeters
O c.
280 centimeters
OD.
198 centimeters
Which term should be used in the box?
5(x – 2x + 6x + 10) = 5x – 10x + ? +50
A) 30x
B) 30
C) 11.3
D) 11
Answer:
A) 30x
Step-by-step explanation:
5(x - 2x + 6x + 10)
Distribute:
5(x) + 5(-2x) + 5(6x) + 5(10)
5x - 10x + 30x + 50
Therefore, 5(x - 2x + 6x + 10) is equivalent to 5x - 10x + 30x + 50
Hope this helps!
Answer:
A) 30x
Step-by-step explanation:
Given equation:
5(x – 2x + 6x + 10) = 5x – 10x + ? + 50
Let the "?" be represented as "a". Then,
⇒ 5(x – 2x + 6x + 10) = 5x – 10x + a + 50
[Right hand side] Put all the terms inside a parenthesis (except "a").
⇒ 5(x – 2x + 6x + 10) = 5x – 10x + a + 50
⇒ 5(x – 2x + 6x + 10) = (5x – 10x + 50) + a
Isolate the "a" on one side by subtracting the terms inside the parenthesis.
⇒ 5(x – 2x + 6x + 10) - (5x – 10x + 50) = (5x – 10x + 50) + a - (5x – 10x + 50)
⇒ 5(x – 2x + 6x + 10) - 5x + 10x - 50 = a
[Left hand side] Simplify the distributive property
⇒ 5(x – 2x + 6x + 10) - 5x + 10x - 50 = a
⇒ (5x – 10x + 30x + 50) - 5x + 10x - 50 = a
[Left hand side] Open the parentheses
⇒ (5x – 10x + 30x + 50) - 5x + 10x - 50 = a
⇒ 5x – 10x + 30x + 50 - 5x + 10x - 50 = a
[Left hand side] Combine like terms and simplify
⇒ 5x – 10x + 30x + 50 - 5x + 10x - 50 = a
⇒ x(5 – 10 + 30 - 5 + 10) + (50 - 50) = a
⇒ x(30) = a
[Left hand side] Open the parenthesis and simplify
⇒ x(30) = a
⇒ 30x = a = ?
Therefore, the correct option is A (30x).
If you are in a great deal of debt but want to save for an emergency fund, you should
Save for the fund while paying down your debt
pay down your debt first
consider getting a second job to pay down your debt first
consider getting a second job, and save that job's money, and then pay down your debt
Answer:
option number 4 seems sensible!
Fill in the Activity Log correctly
using the following
information.
Joey performed exercise and the following information needs to be logged in the log: He did a vigorous combination of
cardiovascular exercise and muscular exercise in the form of kickboxing for 20 minutes, and then he ended with a 10-
minute cool-down. He started with a 5-minute warm-up. He did these activities on 3/2/10.
Date: Warm-up: Cool-down:
Type of
Description of
Activity and Time
Activity:
(Cardiovascular,
Intensity Total
Level Time
(Moderate,
or
Muscular, or
Flexibility)
Vigorous)
march 2,2010 5 minutes 10 minutes
NEXT QUESTION
ASK FOR HELP
TURN IT IN
Answer:
The activity log can be filled up for any kind of activity including physical activity like exercise.
Step-by-step explanation:
Warmed up for 5 minutes.
Ran for 15 minutes across the street.
Sat to cool down for about 6 minutes.
How many helmets must the company make and sell to break even? helmets
The sale the company must make and sell to break even is;
B=600
How many helmets must the company make and sell to break even?Generally, the equation for the break even is mathematically given as
In conclusion
B=y vertex/price of each
Therefore
B=15600/26
B=600
In conclusion, the company's break even is
B=600
CQ
A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15,900). How many helmets must the company make and sell to break even?
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Answer:
600
Step-by-step explanation:
Hey, what it do? I need help i am in imense pain trying to answer this can someone help me?
Toby plans to enroll for 2 semesters per year of college. How can he calculate the extra amount he needs for expenses for each semester? What is the amount that he needs per semester?
simplify square root can you put the steps i would love if you helped me
1. √72
2. √144
3. √45
can anyone help me with this
Step-by-step explanation:
If 5x - 8 = 12 , then x = 4
5x - 8 = 12
5x = 12 + 8
5x = 20
x = 20/5
x = 4
If -2(3x + 5) = -17 + x , then x = 1
-2(3x + 5) = -17 + x
-6x - 10 = -17 + x
x + 6x = 17 - 10
7x = 7
x = 7/7
x = 1
MATHHH HELPPPPP I NEED TO FINISH THIS BUT IM STUCK
Answer:
10 I think but not sure. but It has to be an Evan number
please help me with this please.......asap
Answer:
B and D because I know that I think
identify the rational numbers represented by the letters on the number line.
[tex]\huge\rm\underline{Answer}[/tex]
✧ Rational numbers are represented on the number line by dividing a unit into as many divisions as the denominator of the rational number
Here , Each unit is divided into 7 equal parts . It means denominator of the rational number is 7.
A is on the 10th Mark to the left of 0.So , A represents -10/7
B is on the 6th mark to the left of 0 .So , B represents -6/7
C is on the 3rd mark to the right of 0.So , C represents 3/7
D is on the 15th mark to the right of 0.So , D represents 15/7
Hope it helps ~
Identify an equation in slope-intercept form for the line parallel to y = 4x - 9
that passes through (-5,3).
O A. y = 4x - 23
ОВу
O B. y - 1x+45
4x
O c. y = 4x+23
O D. y= - 4x + 7
Answer:
c. y=4x+24
Step-by-step explanation:
To identify the equation, the equation must satisfy the points (-5,3).
putting x as -5 should give us y=3
c. y = 4x + 23
y = 4 * (-5) + 23
y = -20 + 23
y = 3
[tex]\rule{300}{1}\\\dashrightarrow\large\textsf{\textbf{\underline{Given question:-}}}[/tex]
Identify an equation in slope-intercept form for the line parallel to y = 4x - 9
that passes through (-5,3).
[tex]\dashrightarrow\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
If lines are parallel to each other, they have the same slope.
If a line is parallel to [tex]\bold{y=4x-9}[/tex], and the slope of this line is 4, then the slope of the line that's parallel to [tex]\bold{y=4x-9}[/tex] also has a slope of 4.
All right, we know the slope, but that's part of the slope-intercept equation,
We also need to identify the y-intercept; one way to find it (the one I always use) is the point-slope form.
Point-slope form looks like so:-
[tex]\longmapsto\sf{y-y_1=m(x-x_1)}[/tex]
Replace y1 with 3, m with 4, and x1 with -5:-
[tex]\longmapsto\sf{y-3=4(x-(-5)}[/tex]
On simplification,
[tex]\longmapsto\sf{y-3=4(x+5)}[/tex]
On further simplification,
[tex]\longmapsto\sf{y-3=4x+20}[/tex]
On further simplification,
[tex]\longmapsto\sf{y=4x+20+3}[/tex]
Final equation:-
[tex]\longmapsto\sf{y=4x+23}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
1. Use the function f (x) to answer the questions:
f(x) = 2x^2 − 3x − 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
2. The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company: (picture of graph attached below)
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
I promise to give braInliest to the correct answer.
Answer:
A vertical shift is when the graph literally moves vertically, up or down. The movement is all based on what happens to the y-value of the graph. The y-axis of a coordinate plane is the vertical axis. When a function shifts vertically, the y-value changes.
Step-by-step explanation:
Aiden earned a score of 22 on exam a that had a mean of 40 and a standard
deviation of 10. he is about to take exam b that has a mean of 650 and a standard
deviation of 25. how well must aiden score on exam b in order to do equivalently
well as he did on exam a? assume that scores on each exam are normally distributed.
Using the normal distribution, it is found that he needs a score of 605 in exam b in order to do equivalently well as he did on exam a.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For the z-score for exam a, we have that the parameters are given as follows:
[tex]X = 22, \mu = 40, \sigma = 10[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 40}{10}[/tex]
Z = -1.8.
Then, for the equivalent grade X in exam B, we have that:
[tex]Z = -1.8, \mu = 650, \sigma = 25[/tex]
Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.8 = \frac{X - 650}{25}[/tex]
X - 650 = -1.8 x 25
X = 605.
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Which has the digit 6 in the tenths place?
82.56
65.28
56.82
28.65
Answer:
28.65
hope this helps!