Calculate the population of a spherical cloud of locusts which lies in the ball x2 + y2 + (z – 1)2 < 1 if the population density is 1(x, y, z) = 10022, in locusts/mº. (d) Calculate the volume of the portion of the sphere x2 + y2 + x2 = 4 which lies in the region where z < 1. (Hint: How much of the sphere is removed?)
Answers
The volume of the portion of the sphere x² + y² + z² = 4 which lies in the region where z < 1 is (4π - 4)/3.
To calculate the volume of the portion of the sphere x² + y² + z² = 4 which lies in the region where z < 1, we first need to find the limits of integration.
The sphere x² + y² + z² = 4 has a radius of 2 and is centered at the origin. The region where z < 1 is the lower half of the sphere. We can find the equation of the plane that passes through the point (0,0,1) and is perpendicular to the z-axis by using the point-normal form of the equation of a plane:
z - 1 = 0
Solving for z,
z = 1
So the region where z < 1 is the portion of the sphere below the plane z = 1. To find the volume of this region, we can use spherical coordinates. The limits of integration for ρ are 0 to 2, for θ are 0 to 2π, and for φ are 0 to π/2.
The equation of the sphere in spherical coordinates is:
ρ^2 = 4
So we have:
\($V = \iiint_E dV = \int_0^2 \int_0^{2\pi} \int_0^{\frac{\pi}{2}} \rho^2 \sin\phi , d\phi , d\theta , d\rho$\)
Solving the integral, we get:
V = 4π/3 - 4/3
= (4π - 4)/3
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Related Questions
Negative solution for Multi-step equations
Answers
Answer:
\(\frac{1}{2}(4x+6)+3x=7x+9\)
\(\frac{1}{2}(4x+8)+3x=7x+9\)
Step-by-step explanation:
By putting the numbers in the given equation,
\(\frac{1}{2}(4x+6)+3x=7x+9\)
2x + 3 + 3x = 7x + 9
5x + 3 = 7x + 9
(5x + 3) - 7x = (7x + 9) - 7x
(5x - 7x) + 3 = 9
-2x + 3 = 9
(-2x + 3) - 3 = 9 - 3
-2x = 6
\(-\frac{2x}{2}=\frac{6}{2}\)
-x = 3
x = -3
Therefore, our equation is correct which has a negative result.
In place of 6 if we use 8, value of x will be negative again.
What is the equation of the line passing through the point (-2,-1) and perpendicular to the line y = 1/2x+5?
Plss help
Answers
Step-by-step explanation:
the slope of a line is always the factor of x.
here : 1/2
it is the ratio y/x indicating how many units y changes, when x changes a certain angina amount of units when going from one point to another.
a perpendicular slope puts x and y upside-down and flips the sign.
here : -2/1 = -2
so, the equation looks like
y = -2x + b
b is the y-intercept, and we get this by putting the x and y coordinates of the given point into this equation and solve for b :
-1 = -2×-2 + b
-1 = 4 + b
b = -5
the full equation is therefore
y = -2x - 5
according to the bureau of labor statistics it takes an average of 20 weeks for young workers to find a new job. assume that the probability distribution is normal and that the standard deviation is two weeks. what is the probability that 24 young workers average less than 19 weeks to find a job?
Answers
The required probability representing the 24 young workers average less than 19 weeks is given by approximately 0.0071.
Use the Central Limit Theorem to approximate the distribution of sample means from a normal population.
Sample mean X,
Sample size = n
Mean of the population = μ
And Standard deviation of the population =σ
X = 19 weeks
μ = 20 weeks
σ = 2 weeks
And n = 24.
Standardize the sample mean using the formula,
z = (X - μ) / (σ / √n)
Substituting these values, we get,
z = (19 - 20) / (2 / √24)
= -2.45
Use a standard normal distribution table
Probability that a standard normal variable is less than -2.45.
Probability is approximately 0.0071.
Therefore, the probability that 24 young workers have an average of less than 19 weeks to find a job is approximately 0.0071.
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HELP ASAP!! Find the total area of the figure below. Round your answer to the nearest tenth
Answers
Answer:
area = 88 mi²
Step-by-step explanation:
all vertical dimensions = 8/2 = 4 mi
area = (4 x 11.9) +(4 x 6.1) + (4 x 4) = 88 mi²
7 1/2 Divided by 3/4
Answers
Answer: the answer would be six sixtieths 6/60 or simplified one tenth 1/10
Step-by-step explanation:
take seven times two plus one, which is fifteen, and put it over two(15/2), then flip it so it is two over fifteen 2/15. then multiply two fifteenths times three fourths. two times three is six, so that would go on top, and fifteen times four is sixty, so that is the bottom. So, six over sixty 6/60. now, to simplify, both six and sixty are divisible by six, so six divided by six is one, and sixty divided by six is ten, so you would have one tenth 1/10. i have also included a image showing how i worked it out below.
Please answer smartly or you will be reported
Thankyou:)
Answers
Answer: The answer is B
Step-by-step explanation:
A restaurant chef wants to install a new floor in her kitchen. The kitchen measures 8 meters wide and 12 meters long, and the flooring costs $8.00 per square meter. How much will the chef's new floor cost?
Answers
Answer:
$768
Step-by-step explanation:
8 x 12 = 96 m²
1 m² = $8.00
96m² x $8.00 = $768
Team Jacob for question correct. You think session 7X - 32 find he injects total points
Answers
Answer:
-224
Step-by-step explanation:
hope it helps
if there is an 84% chance of an event happening in an hour, what is the probability that it happens in half an hour?
Answers
The probability of an event happening in half an hour cannot be determined simply by multiplying or dividing the probability of the event happening in an hour by a factor of 2.
Probabilities are not linear in that way. The probability of an event happening in half an hour would depend on the specific details of the event and the underlying probability distribution.
The probability of an event happening in half an hour, given an 84% chance of it happening in an hour, cannot be determined without additional information. The probability of an event occurring in half an hour would depend on the specific circumstances of the event and how the 84% probability was determined.
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if there is an 84% chance of an event happening in an hour, then the probability that it happens in half an hour will be 84% = 0.84.
One cannot easily calculate the likelihood of an event occurring in half an hour by multiplying or dividing the chance of the event occurring in an hour by a factor of 2.
In that sense, probabilities are not linear. The likelihood of an event occurring in half an hour is determined by the event's specifics and the underlying probability distribution.
Without further information, the likelihood of an event occurring in half an hour given an 84% chance of occurring in an hour cannot be computed. The likelihood of an event occurring in half an hour is influenced on the event's unique circumstances and how the 84% probability was calculated.
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Bookmarks Return Submit 1 3.3 Financing with Simple Interest Brittany's car purchasing decisions 1 erd Brittany has decided to get a new car. She has picked out a make and model but doesn't care if she buys new or 5 points What is the total cost of financing the new vehicle? O $32,000 O $163,840 O $31,100 O $33,638.40 s ar 1 pre-owned. The vehicle she has chosen is offering 0% financing for new and 5.12% APR simple interest on pre- 1 2. . owned. The new vehicle is $32,000 and the pre-owned is 2 $31 100. 3 5 points What is the total cost of financing the pre-owned car for 60 months (5 years)? y 4 Type your answer... 5 OM
Answers
5.12% means
5.12/100 = 0.0512 (each year)
PreOwned Vehicle Cost = 31,100
For 5 years simple interest, the value would be:
31100 * 0.0512 * 5 = $7961.6
Total have to pay: 31,100 + 7961.6 = $39,061.6
12.7 larson geometry of two solids are similar with a scale factor of p:q, then corresponding areas have a ratio of and corresponding volumes have a ratio of
Answers
When two solids are similar with a scale factor of p:q, their corresponding areas have a ratio of (p/q)^2 and their corresponding volumes have a ratio of (p/q)^3.
This means that if you were to take two similar solids and enlarge one by a factor of p and the other by a factor of q, the ratio of their areas would be (p/q)^2 and the ratio of their volumes would be (p/q)^3. This property is very useful in geometry and can be used to solve many problems involving similar solids. If two solids are similar with a scale factor of p:q, then their corresponding areas have a ratio of p²:q², and their corresponding volumes have a ratio of p³:q³.
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Here is Dan's recipe for breakfast.200ml of milk,50g of oats,30g of barley,40g of raisins.If he uses 100g of oats,how many grans of barley does he need
Answers
Answer:60g
Step-by-step explanation:
Hope this the answer
Determine if given table represents a function. Explain
your answer.
domain
range
-1
2
3
2
5
5
1
9
2
the table is a function because the domain values are
different.
the table is not a function because of the same domain and
different range values.
the table is not a function because of the same range and
different domain values.
the table is a function because the range values are the
same.
Answers
Answer:
The table is not a function because of the same range and different domain values.
When a range of values is used to estimate a population parameter, it is calledA. a point estimateB. a statistical parameterC. a range estimateD. an interval estimate
Answers
When a range of values is used to estimate a population parameter, it is called an interval estimate. The correct answer is option D.
What is interval estimate?An interval estimation is the evaluation of a parameter of a population by computing an interval, or range of values, within which the parameter is most likely to be located. An interval estimate gives you a range of values where the parameter is expected to lie. In other words, an interval estimate is a range in which the population parameter probably falls for a given level of confidence. We have to establish a level of confidence because we can never be 100 percent sure that the population mean falls within our confidence interval. A confidence interval is the most common type of interval estimate.
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I WILL GIVE CORRECT ANSWER BRAINLIEST
Start with the equation 6•0= 0 to explain why 6•-10 must equal -60.
Drag descriptions and equations to the table to complete the explanation.
please look at picture attached,
thank you
Answers
Answer:
Given = 6 x 0 = 0
Step 2 = Substitute. Any number plus its opposite equals 0 (10 +-10)
Step 3 = Use the distributive property
Step 5 = Subtract 60 from both sides
Step 6 = Simplify to solve for 6 x -10
Given = 6 x 0 = 0
Step 2 = Substitute. Any number plus its opposite equals 0 (10 +-10)
Step 3 = Use the distributive property
Step 5 = Subtract 60 from both sides
Step 6 = Simplify to solve for 6 x -10
a coin having probability p of coming up heads is successively flipped until two of the most recent three flips are heads. let n denote the number of flips. (note that if the first two flips are heads, then n
Answers
Let's analyze the scenario of flipping a coin with a probability 'p' of coming up heads successively until two of the most recent three flips are heads.
If the first two flips are heads, then 'n' would be equal to 2. This is because we have already achieved the condition of two heads in the most recent three flips.
Now, let's consider the case where the first two flips are not heads. In this situation, we need to continue flipping the coin until we get two heads in the most recent three flips. This means that the previous two flips could be either heads or tails.
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a coin having probability p of coming up heads is successively flipped until two of the most recent three flips are heads. let n denote the number of flips. Then N = ?.
-5n=4m+8: n = -1,0,1
Answers
Answer:
False
Step-by-step explanation:
Answer:
Solving for M
−2x=3
x−5=−3
√x+3=8
Step-by-step explanation:
marble middle school paid $500 for 16 graphing calculator
Answers
Answer:
31.25 I believe
Answer:
$31.25 per graphing calculator
Step-by-step explanation:
The question isn't there so I'm going to guess that it is asking for what is the cost of one calculator
$500/16=
$31.25 per graphing calculator
Why does the test for homogeneity follow the same procedures as the test for independence?
Answers
Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.
The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.
The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.
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a bus stops 5 people get off. then 11 people get on a bus now there are 19 people on the bus
Answers
Answer:
13 people
Step-by-step explanation:
If you're looking for how many people were on the bus before the most recent stop.
19-11 = 8
8 + 5 = 13
Write the six step in division
Answers
Answer:
Divide the tens column dividend by the divisor. Multiply the divisor by the quotient in the tens place column. Subtract the product from the divisor
Step-by-step explanation:
Equations
1. Billy Banjo is trying to save money for a new banjo. The banjo costs $300. Mr. Banjo
makes $6 an hour.
a. How many hours will he need to work in order to pay for his banjo?
b. Write an equation for the situation and explain what each variable means.
Answers
Step-by-step explanation:
a. To find out how many hours Billy Banjo needs to work to pay for his banjo, we can set up the following equation:
$$ 6h = 300 $$
where "h" represents the number of hours Billy Banjo needs to work and 6 represents the amount of money he earns per hour.
We can solve this equation by dividing both sides by 6, giving us:
$$ h = \frac{300}{6} $$
$$ h = 50 $$
Therefore, Billy Banjo needs to work 50 hours in order to pay for his $300 banjo.
b. The equation $6h = 300$ represents the situation where Billy Banjo is trying to save money for a new banjo that costs $300, and he earns $6 per hour. The variable "h" represents the number of hours Billy Banjo needs to work in order to pay for the banjo. The left side of the equation, $6h$, represents the amount of money Billy Banjo earns in "h" hours, while the right side of the equation, 300, represents the cost of the banjo he is trying to save up for. By setting these two expressions equal to each other, we are able to solve for the value of "h," which represents the number of hours Billy Banjo needs to work in order to pay for his banjo.
I need help with this
Answers
Answer:
Step-by-step explanation:
1- angle JZF
supplementary angle or straight angle =180 degree
HZJ+JZF=HZF straight angle
2- JZA
complementary angle or right angle =90 degree
HZJ+JZA=HZA ( right angle)
if angle HZJ=38 degrees
HZJ+FZJ=180
FZJ=180-38
FZJ=142 degreesHZG+HZJ=180
HZG=180-38=142 degrees ( which is vertical angle to FZJ and equal to it)
HZG=142 degrees
AZJ+HZJ=90 degrees
AZJ=90-38
AZJ=52 degrees
What is the solution to the system below?
x + y = 5
x - y = 3
Answers
( x, y ) = ( 4, 1 )
hope it helps!
Answer:
x= 4
y= 1
Step-by-step explanation:
by adding 2 equations
2x = 8
x= 4
by sub. in Equation 1
4+y=5
y = 5-4
y= 1
If a line has a slope of -4 and a y-intercept of 1, which of the following is its graph?
Answers
Answer: Yes its b
Step-by-step explanation:
Answer:
The answer is B I just finish doing that. Can I get a Brainlist please
Step-by-step explanation:
Use the Product Rule or Quotient Rule to find the derivative. \[ f(x)=\frac{3 x^{8}+x^{2}}{4 x^{8}-4} \]
Answers
Using Quotient rule, the derivative of the function is expressed as:
\(\frac{-x(3x^{8} + 12x^{6} + 1)}{(2x^{8} - 1)^{2}}\)
How to find the Derivative of the Function?The function that we want to differentiate is:
\(\[ f(x)=\frac{3 x^{8}+x^{2}}{4 x^{8}-4} \]\)
The quotient rule is expressed as:
\([\frac{u(x)}{v(x)}]' = \frac{[u'(x) * v(x) - u(x) * v'(x)]}{v(x)^{2} }\)
From our given function, applying the quotient rule:
Let u(x) = 3x⁸ + x²
v(x) = 4x⁸ − 4
Their derivatives are:
u'(x) = 24x⁷ + 2x
v'(x) = 32x⁷
Thus, we have the expression as:
dy/dx = \(\frac{[(24x^{7} + 2x)*(4x^{8} - 4)] - [32x^{7}*(3x^{8} + x^{2})] }{(4x^{8} - 4)^{2} }\)
This can be further simplified to get:
dy/dx = \(\frac{-x(3x^{8} + 12x^{6} + 1)}{(2x^{8} - 1)^{2}}\)
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Complete question is:
Use the Product Rule or Quotient Rule to find the derivative. \(\[ f(x)=\frac{3 x^{8}+x^{2}}{4 x^{8}-4} \]\)
Aubrey claims that if the dimensions of the parallelogram shown are doubled, then the area of the larger parallelogram will be 4 times more than the original. Which statement about her claim is completely true? A parallelogram with a base of 6 inches and height of 3 inches. A side has a length of 5 inches.
Answers
Answer:
Aubrey is correct because the area of the new parallelogram is 12 (6) = 72 square inches. The original area is 18 square inches. Since 4 (18) = 72, the new parallelogram has 4 times the area of the original.
Step-by-step explanation:
A parallelogram with a base of 6 inches and height of 3 inches. A side has a length of 5 inches.
Aubrey is correct because the area of the new parallelogram is 12 (6) = 72 square inches. The original area is 18 square inches. Since 4 (18) = 72, the new parallelogram has 4 times the area of the original.
Aubrey is correct because the area of the new parallelogram is 10 (7) = 70 square inches. The original area is 18 square inches. Since 4 (18) = 72, it is about 4 times larger than the original.
Aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. The original area is 18 square inches so the new parallelogram will have an area of 2 (18) = 36, or two times more than the original.
Aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. The original area is 30 square inches so the new parallelogram will have an area of 2 (30) = 60, or 2 times more than the original.
Workings
Area of a parallelogram=base×height
Original parallelogram
Base=6 inches
Height=3 inches
Area=base×height
=6×3
=18 square inches
New parallelogram with doubled dimensions
Base=6 inches doubled=12 inches
Height=3 inches doubled=6 inches
Area=base×height
=12×6
=72 square inches
New area=4 times original area
New area=4×18
New area=72 square inches
Answer:
the answer is A
Step-by-step explanation:
i wan to make this easy and fast
For each ordered pair, determine whether it is a solution to the system of equations. -18x+2y=8 and y=9x+4
Answers
For the given system of equations, no solution is possible.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
Given:
The system of equations,
-18x + 2y = 8 {equation 1}
y = 9x + 4 {equation 2}
Substitute the value of y from equation 2 to equation 1,
we get,
-18x + 18x + 8 = 8
0 = 0
That means, the lines of the equation are parallel to each other.
Therefore, no solution is possible for the system.
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Find the mean of the given frequency distribution table
Answers
Answer:
Mean = 32.8
Step-by-step Explanation:
Mean is given as Mean = (Σfx)/Σf
First, find the mid-point, x, of each class, and multiply by the frequency (f) of the class to get fx:
Class ==> f ==> x ==> fx
0-10 => 3 => 5 => 15
10-20 => 8 => 15 => 120
20-30 => 10 => 25 => 250
30-40 => 15 => 35 => 525
40-50 => 7 => 45 => 315
50-60 => 4 => 55 => 220
60-70 => 3 => 65 => 195
Sum the fx of all classes together to get Σfx:
Σfx = 15 + 120 + 250 + 525 + 315 + 220 + 195 = 1,640
Σf = 3 + 8 + 10 + 15 + 7 + 4 + 3 = 50
(Σfx)/Σf = \( \frac{1,640}{50} \)
(Σfx)/Σf = \( 32.8 \)
Mean = 32.8
a triangle's base and height are changing. (a) if the base is growing at a rate of 1 cm per second and the height is growing at a rate of 2 cm per second at what rate is the area changing the moment that the base is 4 cm and the height is 7 cm?
Answers
The rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.
What is the rate of change?The rate at which a variable alters over a predetermined amount of time. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.We know that,
The Base is growing at the rate of 1 cm per sec.
Height is growing at the rate of 2 cm per sec.
Area of triangle: 1/2 × b × h
The rate of change will be:
1/2 × b × h
1/2 × 4/1 × 7/2
28/4
7 cm per sec
Therefore, the rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.
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