Convert to cylindrical coordinates:
[tex]x=x[/tex]
[tex]y=r\cos\theta[/tex]
[tex]z=r\sin\theta[/tex]
Then [tex]E[/tex] is the set of points [tex](r,\theta,x)[/tex] such that [tex]0\le r\le1[/tex], [tex]0\le\theta\le2\pi[/tex], and [tex]7y^2+7z^2\le x\le7[/tex] or [tex]7r^2\le x\le7[/tex].
Now
[tex]\displaystyle\iiint_E5x\,\mathrm dV=5\int_0^{2\pi}\int_0^1\int_{7r^2}^7xr\,\mathrm dx\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{245\pi}3}[/tex]
To evaluate the triple integral, convert to cylindrical coordinates and use the given bounds. Plug in the limits of integration and calculate the integral.
Explanation:To evaluate the triple integral ∫ 5x dv, where E is bounded by the paraboloid x = 7y^2 + 7z^2 and the plane x = 7, we can use cylindrical coordinates. Let's express x in terms of y and z:
x = 7y^2 + 7z^2
Substitute this expression for x in the integral:
∫5x dv = ∫35(y^2 + z^2) dv
Now, convert the integral to cylindrical coordinates:
∫35(r^2sin(θ)rdrdθdz
Since the region E is bounded by x = 7, the limits of integration for r and z are 0 to 7. For θ, the limits are 0 to 2π. Plug in these limits and evaluate the triple integral to find the answer.
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The last 30 times that Eric has played his video game he has scored over 100,000 points 40% of the time. What prediction can you make about the next 15 times Eric plays his video game?
Answer:
A)
He will score over 100,000 points 4 times.
B)
He will score over 100,000 points 6 times.
C)
He will score over 100,000 points 8 times.
D)
He will score over 100,000 points 12 times.
Step-by-step explanation:
Answer is B
Answer:
B) He will score over 100,000 points 6 times.
Step-by-step explanation:
I got it correct on USATP.
Hope this helps!
From: Aug1e
For the function below, state the x-coordinate of the x-intercept that is located to the fight of the origin.
[tex]f(x)=x^3-9x[/tex]
Answer:
x = 3
Step-by-step explanation:
It should NOT be "fight of the origin", rather "right of the origin".
Now let's move on to solve the question...
The x-intercept is found by setting the function equal to 0. Thus:
0 = x^3 - 9x
Let's solve this using algebra:
[tex]0=x^3-9x\\0=x(x^2-9)\\0=x(x-3)(x+3)[/tex]
Hence, x = -3 and x = 3
The coordinate that is to the right of the origin is the positive one, so x = 3 is the x-intercept we are looking for.
-1 3/7 x (-3 2/3)=?
64 POINTS AWARDED, PLEASE ANSWER ASAP!!!!!
What is the area of a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)?
Answer:
40 units^2
Step-by-step explanation:
This is because your figure has a height of 8 and a width of 5. 8*5=40 so there u go! Please mark brainliest
Answer:
Area of rectangle = 40 square units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x₁, y₁) and (x₂, y₂) is given by,
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Area of rectangle = Length * Breadth
To find the length and breadth
Here a rectangle with vertices at (7, 3), (12, 3), (12, 11), and (7, 11)
Length1 = √[(x₂ - x₁)² + (y₂ - y₁)²]
√[(12 - 7)² + (3 - 3)²] = √5² = 5
Length2 = √[(x₂ - x₁)² + (y₂ - y₁)²]
√[(12 - 12)² + (11 - 3)²] = √8² = 8 units
Therefore Length of rectangle = 8 and
Breadth of rectangle = 5 units
To find the area of rectangle
Area = Length * Breadth
= 8 * 5 = 40 square units
A fireworks company has two types of rockets called Zinger 1 and Zinger 2. The polynomial -16t^2 + 150t gives the height in feet of Zinger 1 at t seconds after launch. The polynomial -16t^2 + 165t gives the height of Zinger 2 at t seconds after launch. If the rockets are launched at the same time and both explode 6 seconds after launch, how much higher is Zinger 2 than Zinger 1 when they explode? 414 ft
90 ft
324 ft
990 ft
Answer:
90 feet
Step-by-step explanation:
If we put t = 6 into both the formulas, we will get the height of each.
Zinger 1:
Height = [tex]-16t^2 + 150t[/tex]
Putting t = 6,
[tex]-16(6)^2 + 150(6)=324[/tex]
Zinger 2:
Height = [tex]-16t^2 + 165t[/tex]
Putting t = 6,
[tex]-16(6)^2 + 165(6)=414[/tex]
The difference in height is 414 - 324 = 90 feet
The function F is defined by F(x)= 12 x + 1 2 . Use this formula to find the following values of the function:
F(3)
F(-12)
F(1/3)
F(3/4)
F(k)
F(a/2)
F(x-1)
F(x+h)
Just solving for one of these would be really helpful!
Answer:
Step-by-step explanation:
I will assume that you meant F(x)= 12x + 12. If you meant a fraction, write 1/2.
Then F(3) = 12(3) + 12 = 48
F(-12) = 12(-12) + 12 = -132.
F(1/3) = 12(1/3) + 12 = 4 + 12 = 16
Please verify what you meant. Then I will answer the remaining questions.
[tex]\(F(3) = 48\), \(F(-12) = -132\), \(F\left(\frac{1}{3}\right) = 16\), \(F\left(\frac{3}{4}\right) = 21\), \(F(x) = 12x + 12\).[/tex]
To find the values of the function [tex]\(F(x) = 12x + 12\)[/tex] for the given inputs:
1. F(3): Substitute x = 3 into the function: F(3) = 12(3) + 12 = 36 + 12 = 48.
2. F(-12): Substitute x = -12 into the function: F(-12) = 12(-12) + 12 = -144 + 12 = -132.
3. [tex]\(F\left(\frac{1}{3}\right)\)[/tex]: Substitute [tex]\(x = \frac{1}{3}\)[/tex] into the function: [tex]\(F\left(\frac{1}{3}\right) = 12\left(\frac{1}{3}\right) + 12 = 4 + 12 = 16\).[/tex]
4. [tex]\(F\left(\frac{3}{4}\right)\)[/tex]: Substitute [tex]\(x = \frac{3}{4}\)[/tex] into the function: [tex]\(F\left(\frac{3}{4}\right) = 12\left(\frac{3}{4}\right) + 12 = 9 + 12 = 21\).[/tex]
5. F(k): Substitute x = k into the function: F(k) = 12k + 12.
6. [tex]\(F\left(\frac{a}{2}\right)\)[/tex]: Substitute [tex]\(x = \frac{a}{2}\)[/tex] into the function: [tex]\(F\left(\frac{a}{2}\right) = 12\left(\frac{a}{2}\right) + 12 = 6a + 12\).[/tex]
7. F(x-1): Substitute x = x-1 into the function: F(x-1) = 12(x-1) + 12 = 12x - 12 + 12 = 12x.
8. F(x+h): Substitute x = x+h into the function: F(x+h) = 12(x+h) + 12 = 12x + 12h + 12.
These are the values of the function for the given inputs.
An organization consists of 8,684 employees. They decided to conduct a survey about their new vacation policies. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. Assuming a 95% confidence level, which of the following statements holds true?
A. As the sample size is appropriately large, the margin of error is ±0.032.
B. As the sample size is too small, the margin of error is ±0.032.
C. As the sample size is appropriately large, the margin of error is ±0.0265.
D. As the sample size is too small, the margin of error cannot be trusted..
I think the answer is A. am I correct?
A is the correct answer
Answer:
The correct option is A.
Step-by-step explanation:
An organization consists of 8,684 employees. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. It means
[tex]n=884[/tex]
[tex]p=\frac{36}{100}=0.36[/tex]
The value of z-score for 95% confidence level is 1.96.
The formula for margin of error is
[tex]ME=z\times \sqrt{\frac{p(1-p)}{n}}[/tex]
Where, z is z-score at given confidence level, p is sample proportion and n is number of samples.
[tex]ME=\pm 1.96\times \sqrt{\frac{0.36(1-0.36)}{884}}[/tex]
[tex]ME=\pm 0.0316425[/tex]
[tex]ME\approx \pm 0.032[/tex]
The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.
Solve using a proportion.
Answer:
t = 24 yards
Step-by-step explanation:
Since the trapezoids are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{t}{c}[/tex] = [tex]\frac{u}{d}[/tex]
Substitute in given values
[tex]\frac{t}{0.4}[/tex] = [tex]\frac{15}{0.25}[/tex] ( cross- multiply )
0.25t = 6 ( divide both sides by 0.25 )
t = 24
Cards numbered 1 through 20 are mixed up and placed in a bag. Milan chooses one of the cards without looking.
What is the probability that Milan chooses a card with a number 12 or greater?
3/5
4/5
9/10
9/20
Answer: 9/20
Step-by-step explanation:
Easy!!!
WILL GIVE BRAINIEST ANSWER!!
Question: a semi-regular tessellation may have:
A. gaps between shapes
B. overlapping shapes
C. three types of shapes
D. only one type of shape
I think it’s C. three types of shapes
because more than one repeating shape with no spaces or overlapping between shapes
A semi-regular tessellation may have three types of shapes. They do not have gaps between shapes, no overlapping shapes.
What are the semi-regular tessellations?The semi-regular tessellations are the different shapes occupied in a plane with the same behavior and same lengths of sides for each shape. The shapes may be triangles, hexagons, and squares.There are no gaps in between those shapes. So, there is no overlapping of shapes.These are formed by two or more types of regular shapes.Given options:A. Gaps between shapes - false
B. Overlapping shapes - false
C. Three types of shapes - true
D. Only one type of shape - false
Thus, a semi-regular tessellation may have three types of shapes.
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How do I find X for this problem? I’m stuck
Corresponding sides of the two triangles occur in a ratio with one another. In particular, you have the relationship
[tex]\dfrac6{6+x}=\dfrac{10}{15}=\dfrac y{y+4}[/tex]
We only need the first two parts to solve for [tex]x[/tex]:
[tex]\dfrac6{6+x}=\dfrac{10}{15}\implies6\cdot15=10(6+x)\implies90=60+10x\implies30=10x[/tex]
[tex]\implies\boxed{x=3}[/tex]
A rectangular prism has length 14 cm, width 3.4 cm, and height 11.6 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!
Answer:
552.16 cm^3
Step-by-step explanation:
Just multiply the lenght together.
The volume of the rectangular prism is approximately 552.16 cubic cm.
To find the volume of a rectangular prism, you need to multiply its length, width, and height.
Given that the length is 14 cm, the width is 3.4 cm, and the height is 11.6 cm, we can calculate the volume as follows:
Volume of a rectangular prism = Length × Width × Height
Volume of a rectangular prism = 14 cm × 3.4 cm × 11.6 cm
Volume of a rectangular prism ≈ 552.16 cm³ (rounded to the nearest tenth)
Therefore, the volume of the rectangular prism is approximately 552.16 cubic cm.
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Roberto's toy car travels at 40 centimeters per second (cm/sec) at high speed and 15 cm/sec at low speed. If the car travels for 25 seconds at high speed and then 45 seconds at low speed, what distance would the car have traveled?
Answer:
1675 cm
Step-by-step explanation:
distance = speed · time
total distance = speed1 · time1 + speed2 · time2
= (40 cm/s)(25 s) + (15 cm/s)(45 s) = 1000 cm + 675 cm = 1675 cm
Roberto's toy car travels 1000 cm at high speed (40 cm/sec for 25 sec) and 675 cm at low speed (15 cm/sec for 45 sec), totaling 1675 cm.
Explanation:To calculate the total distance traveled by Roberto’s toy car, we need to consider the two separate speeds at which the car travels and the time it spends at each speed.
First, we calculate the distance at high speed using the formula distance = speed × time. At high speed, the car travels at 40 cm/sec for 25 seconds, so we multiply these two values to get the distance:
Distance at high speed = 40 cm/sec × 25 sec = 1000 cm
Next, we calculate the distance at low speed, where the car travels at 15 cm/sec for 45 seconds:
Distance at low speed = 15 cm/sec × 45 sec = 675 cm
Finally, we add these two distances together to find the total distance traveled by the toy car:
Total distance = Distance at high speed + Distance at low speed = 1000 cm + 675 cm = 1675 cm
Therefore, Roberto’s toy car would have traveled 1675 centimeters in total.
HALP PLEASE NEED HALP, ASAP??
Answer:
5
Step-by-step explanation:
since -4 *-2 = 8 and -8+8=0
0*-2=0
0+5=5
Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 3, negative 2, and 2
Which of the following functions best represents the graph?
f(x) = x3 + x2 − 4x − 4
f(x) = x3 + x2 − x − 1
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 6x − 12
Answer:
f(x) = x3 + 3x2 − 4x − 12
Step-by-step explanation:
A polynomial which falls tot he left and rises to the right is a function with a positive leading coefficient. Its formed by the x-intercepts or zeros x = -3, -2 and 2. The zeros form the factors (x+3)(x+2)(x-2). Multiply the factors using the distributive property to find the function in standard form.
(x+3)(x+2)(x-2)
(x^2 + 3x + 2x + 6)(x-2)
(x^2 + 5x + 6)(x-2)
x^3 + 5x^2 + 6x -2x^2 - 10x - 12
x^3 + 3x^2 - 4x - 12
A bacteria culture is doubling in size of every day. If the bacteria culture starts at 5,200, write an equation for its population size,p, as a function of the number of days ,d, since it started
The answer is:
The equation is:
[tex]Total(t)=5200*(2)^{t}[/tex]
Why?It's an exponential growth problem, we can calculate the exponential growth using the following equation:
[tex]Total(t)=StartPopulation*(1+r)^{\frac{t}{2}}[/tex]
Where,
Total, is the total population after "t" time in days.
Start population, for this is equal to 5,200
r,is equal to the percent of growth, for this case it's 100% each day.
t, is the time elapsed.
So, rewriting the equation, we have:
[tex]Total(t)=5200*(1+\frac{100}{100})^{t}[/tex]
[tex]Total(t)=5200*(1+1)^{t}[/tex]
[tex]Total(t)=5200*(2)^{t}[/tex]
Have a nice day!
HELP ASAP PLEASE!!!!!
The answer is A. a=(-1) b=(7)
Answer: A
Step-by-step explanation: simple mafs
The weight of an object on a particular scale 155. 2lbs the measured weight May very from the actual weight by the most 0.4 lbs what is the actual weight of the objects
Answer:
154.8-155.6
Step-by-step explanation:
155.2-.4=154.8 or maybe its more in that case the most it could be is 155.2+.4=155.6
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Twenty percent of candies in a package are red. The rest are another color.
Simulate randomly checking 20 packages for red candies using these randomly generated digits. Let the digits 1 and 2 represent a red candy.
91027 18200 74536 83514
Approximately how many red candies will be in the packages?
Answer:
Step-by-step explanation:
The probability of picking a red candy from a full bag is 0.20.
But we also have experimental information represented by those 20 digits, each of which tells us how many red candies are in each package.
In the 2nd package there is 1 red candy. In the fourth there is 1 red candy (since 2 represents a red candy, just like 1 represents a red candy).
Next, in the 6th and 8th packages there is 1 red candy each. Finally, in the 19th package there is 1 red candy. Now add up these results: the number of red candies is 1 + 1 + 1 + 1 + 1, or 5. This seems to indicate that there will be 5 red candies in the entire 20 packages.
Caution: What I have shared here is MY personal interpretation of what we are being asked.
Joel is looking at cost for using a gym. He could pay $50 per month for unlimited use or he could pay $12 per month plus $4 visit. How many visits would he have to make each month to make each month to make the $50 per month unlimited use option the cheapest one?
He would have to make 10 visits at the ($12 per month + $4 each visit) gym to make the ($50 per month for unlimited visits) gym the cheapest option.
Explanation:
12 + (4 x 10) =
12 + (40) = $52
Answer:
He would have to use it more than 10 times in the month.
Step-by-step explanation:
4x+12>50
4x=38
x> 9.5
4(10)+12>50
52>50
To determine whether the inverse of a function is a function you can perform the horizontal line test.
true or false
Answer:
[tex]\boxed{\text{TRUE}}[/tex]
Step-by-step explanation:
If a horizontal line intersects the graph of a function in all places at exactly one point (the horizontal line test), the inverse of the function is also a function.
For example, the inverse of a hyperbola (like ƒ(x) =1/x) is a function, because every horizontal line intersects with the graph at exactly one point.
However, the inverse of a parabola (like ƒ(x) = x²) is not a function, because a horizontal line intersects with the graph at two points.
find the volume of the pyramid below.
A. 1200 units^3
B. 1300 units^3
C. 400 units^3
D. 433 units
Answer:
Hence correct choice is C. [tex]Volume=400[/tex] [tex]units^3[/tex]
Step-by-step explanation:
Given that length of the square base of the pyramid a = 10 units
Given that height of the pyramid is h = 12 units
Now question says to find the volume of the given cone.
So plug these values into formula of volume of the square pyramid.
[tex]Volume=\frac{1}{3} a^2h[/tex]
[tex]Volume=\frac{1}{3} (10)^2(12)[/tex]
[tex]Volume=\frac{1}{3} (100)(12)[/tex]
[tex]Volume=\frac{1}{3} (1200)[/tex]
[tex]Volume=400[/tex]
Hence correct choice is C.
Answer:
The correct answer is option C. 400 units³
Step-by-step explanation:
Formula:-
Volume of pyramid = (a²h)/3
Where a - side of base
h - height of pyramid
From the figure we can see a square pyramid
To find the volume of pyramid
here a = 10 units and h = 12 units
Volume = (a²h)/3 = (10² * 12)/3
= 400 units³
What is the r-value of the following data to three decimal places?
A. -0.811
B. 0.811
C. 0.901
D. -0.901
Answer:
-0.9007 it would be D. if I'm right
Step-by-step explanation:
X Values
∑ = 34
Mean = 6.8
∑(X - Mx)2 = SSx = 140.8
Y Values
∑ = 54
Mean = 10.8
∑(Y - My)2 = SSy = 164.8
X and Y Combined
N = 5
∑(X - Mx)(Y - My) = -137.2
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -137.2 / √((140.8)(164.8)) = -0.9007
Meta Numerics (cross-check)
r = -0.9007
Answer: Your answer is D. -0.901 !
If f(x) = x^2 I horizontally compressed to g(x) which could be the equation of g(x)?
A. [tex]g(x) =( \frac{1}{5} x)^2[/tex]
B. [tex]g(x) = x^2+5[/tex]
C. [tex]g(x) = (5x)^2[/tex]
D.[tex]g(x) = (x-5)^2[/tex]
Answer: Option C.
Step-by-step explanation:
For a parent function [tex]f(x)=x^2[/tex], you have these transformations:
If [tex]f(x)=c(x^2)[/tex] and [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor "c".
If [tex]f(x)=c(x^2)[/tex] and [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor "c"
If [tex]f(x)=(cx)^2[/tex] and [tex]0 <c <1[/tex] then the graph is stretched horizontally by a factor "c"
If [tex]f(x)=(cx)^2[/tex] and [tex]|c| > 1[/tex] then the graph is compressed horizontally by a factor "c"
In this problem we have the function [tex]f(x)=x^2[/tex] and we know that this is horizontally compressed to g(x), then the transformation is:
[tex]f(x)=(cx)^2[/tex] and the factor must be [tex]|c| > 1[/tex]
You can observe that the option that shows this form is the option C. Therefore, the equation of g(x) is:
[tex]g(x) = (5x)^2[/tex]
Where [tex]|5| > 1[/tex]
A horizontal compression of the function f(x) = x² is represented by the function g(x) = (5x)², where x is multiplied by a constant greater than 1, causing the function to be 'squeezed' together along the x-axis.
Explanation:The question is asking for a horizontal compression of the function f(x) = x². A horizontal compression occurs when we multiply the x by a constant greater than 1 inside the function parentheses. This affects the rate at which the function grows horizontally.
A good way to visualize this is by thinking of the x-axis being 'squeezed' together. Given the choices, the function that represents a horizontal compression of f(x) = x² is C: g(x) = (5x)². In this case, we are multiplying x by a constant (5), thus compressing the function horizontally compared to the original function.
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Please help ..........
Answer:
(a)
Step-by-step explanation:
Using Pythagoras' theorem
11² + 12² ? 16²
121 + 144 ? 256
265 > 256 ⇒ acute triangle
If the left side < right side then obtuse
If the left side = right side then right
Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
Answer:
(x,y) = (-2, 0)
and
(x,y) = (2.5, 2.25)
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equations.
Please see the attached image below, to find more information about the graph
s
The equations are:
y1 + 4 = x^2
y1 = x^2 - 4
y2 - x = 2
y2 = x +2
The intersection of the two graphs correspond to
(x,y) = (-2, 0)
and
(x,y) = (2.5, 2.25)
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Mike has a collection of 16 antique tin toys, including 2 airplanes. If Mike randomly selects a toy, what is the probability it will be an airplane? (Write the probability as a fraction in simplest form) A) 1 2 B) 1 4 C) 1 8 D) 1 16
Answer:
C. 1/8
Step-by-step explanation:
This is because the number two goes into sixteen eight times. This is the simplest form of the fraction.
In the playoffs, the Algenauts won their division playoff series 3 games to 1 and then beat their arch-rivals the Geometers in the League Championship series 4 games to 2. If the Algenauts won 80% of their home playoff games and 60% of their away playoff games, what percentage of their playoff games were at home?
Answer:
h = 48
Step-by-step explanation:
So they played 48 home games. They won 3/4, so they won 36 and lost 12.
They played 48 away games. They won 2/3, so they won 32 and lost 16.
All tolled, they won 36 + 32 = 68 games and lost 12 + 16 = 28 games.
To calculate the percentage of home playoff games played by the Algenauts, we use a system of equations with the known win rates and number of games played. Solving, we find that approximately 71.43% of their playoff games were at home.
The student is asking about the percentage of home playoff games played by the Algenauts. The Algenauts won 3 division playoff games and then beat their rivals, the Geometers, with a score of 4-2. Given their win rates of 80% for home games and 60% for away games, we can calculate the percentage of games played at home using a system of equations.
Let H be the number of home games and A be the number of away games. Since the Algenauts played a total of 3 + 4 = 7 games, and won 3 + 4 = 7 games, we have the following equations:
H + A = 7 (total games)
0.80H + 0.60A = 7 (total games won)
Solving the system of equations, we get H = 5 and A = 2, meaning 5 out of the 7 games were played at home. Therefore, the percentage of home games is (5/7) * 100, which equals approximately 71.43%.
What is the range of this data set? 43, 78, 12, 32, 97
Median:
Mean:
Range:
range: 85.
media: 12.
mean: about 52.4