================================================
Explanation:
When we talk about "odds in favor", we will use a colon to separate two whole numbers. The first number represents the number of ways for Evelyn to be chosen treasurer (just one way) and the second number represents all the ways she doesn't get chosen (the four other people)
Put another way, writing "odds in favor are 1:4" basically means "there's 1 way to get Evelyn elected and 4 ways for her to not get elected"
Instead of writing 1:4 you could write "1 to 4"
-----------
Side note: Contrast this with "odds against" and the ratio would flip from 1:4 to 4:1. Same idea, but the number of failures is listed first because we're focusing on the "against" (instead of "favor") portion. We read "4:1" as "4 to 1".
The odds in favor of Evelyn becoming treasurer are 1:5 or 1/5.
To determine the odds in favor of Evelyn becoming treasurer, we need to know the total number of possible outcomes and the number of favorable outcomes.
There are five members in the club, so there are five possible outcomes for the treasurer position, one for each member. Since Evelyn is one of the five members, she has one favorable outcome.
Therefore, the odds in favor of Evelyn becoming treasurer are 1:5 or 1/5.
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A company sells eggs whose individual weights are normally distributed with a mean of 70\,\text{g}70g70, start text, g, end text and a standard deviation of 2\,\text{g}2g2, start text, g, end text. Suppose that these eggs are sold in packages that each contain 444 eggs that represent an SRS from the population. What is the probability that the mean weight of 444 eggs in a package \bar x x ˉ x, with, \bar, on top is less than 68.5\,\text{g}68.5g68, point, 5, start text, g, end text?
Answer:
6.68% probability that the mean weight is below 68.5g.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]
Probability that the mean weight is below 68.5g:
This is 1 subtracted by the pvalue of Z when X = 68.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68.5 - 70}{1}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% probability that the mean weight is below 68.5g.
Answer:
P(x ∠ 68.5) = 0.07
Step-by-step explanation:
Got it right on khan.
If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles
Answer:
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
Step-by-step explanation:
The question is incomplete:
Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24 25–34 35–55 55 and over Total
Liked Crunchicles 4 9 3 23 39
Disliked Crunchicles 5 27 28 64 124
No Preference 7 27 10 93 137
Total 16 63 41 180 300
One consumer from the survey is selected at random. If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles .
If the consumer is 70 years old is included in the category "55 and over" from this survey. There are 180 subjects in that category.
The number that likes Crunchicles and are 55 and over is 23.
If we calculate the probability as the relative frequency, we have:
[tex]P(\text{L }|\text{ 55+})=\dfrac{P(\text{L \& 55+})}{P(5\text{5+})}=\dfrac{23}{180}=0.1278[/tex]
L: Likes Crunchicles.
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
e
65. the perpendicular
bisector of the
segment with
endpoints (-5/2,-2)
and (3, 5)
HELP PLEASE! Picture included!
Answer:
44x +56y = 95
Step-by-step explanation:
To write the equation of the perpendicular bisector, we need to know the midpoint and we need to know the differences of the coordinates.
The midpoint is the average of the coordinate values:
((-2.5, -2) +(3, 5))/2 = (0.5, 3)/2 = (0.25, 1.5) = (h, k)
The differences of the coordinates are ...
(3, 5) -(-2.5, -2) = (3 -(-2.5), 5 -(-2)) = (5.5, 7) = (Δx, Δy)
Then the perpendicular bisector equation can be written ...
Δx(x -h) +Δy(y -k) = 0
5.5(x -0.25) +7(y -1.5) = 0
5.5x -1.375 +7y -10.5 = 0
Multiplying by 8 and subtracting the constant, we get ...
44x +56y = 95 . . . . equation of the perpendicular bisector
Select the action you would use to solve x/3=12. Then select the property that justifies that action
Answer:
To solve this I would multiply both sides by 3
Step-by-step explanation:
i would use the multiplication property of equality
The property that justifies that action x/3=12 is a linear question using reciprocal law.
What is a linear equation?A linear equation has one or two variables.
No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.explanation:-
x/3= 12
x = 12*3 ( using reciprocal)
hence x = 36
solving this we will get the valve of Y if x is given.
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If one angle equals 34”, then the measure of its complement angle is 56°.
True
OO
False
I need help
Answer:
True
Step-by-step explanation:
Complementary means they should sum to 90 degrees
34+56=90
Answer:
True
Step-by-step explanation:
Complementary angles are angles that add to 90 degrees, or a right angle.
If the two angles are complementary, then they will add to 90 degrees.
One angle is 34°, and it's complement is 56°.
Add the angles.
34°+56°
90°
Since they add to 90 degrees, they are complementary angles. Therefore, the statement is true.
5+7.(9-4)
5+7=11
11×5=55
Answer: itz 605
Step-by-step explanation:
What’s the correct answer for this? Select all that apply
Answer:
B and C
Step-by-step explanation:
The correct options are :
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
In both the cases the length and the width of the section are equal
A toy car is placed on the floor He moves in a straight line starting from rest and travels with a constant acceleration for three seconds reaching a velocity of 4 meters per second it then slows down with constant deceleration of 0.5 meters per second squared For four seconds before hitting the wall and stopping draw a velocity time graph for the toy car what is the total distance travelled by the toy car
Answer:
18 meters.
Step-by-step explanation:
There is a constant acceleration for 3 seconds, reaching 4 m/s. This, when drawn on a velocity/time graph, creates a diagonal line. The area underneath this line, which is the distance it travels, is found by the following: 0.5(l*h), the formula used to find the area of a triangle.
0.5(3*4)=6m
There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.
0.5(2*4)=4m
Now, all that remains is a rectangle of height 2 and a length of 4, so we find the area of it.
2*4=8m
Finally, we add each of these up.
6m+4m+8m=18m
Sorry if the step by step process was poorly explained, I'm not the best at explaining. Hope this helped, though. :^)
The total distance traveled by the toy car is 18 meters.
What is acceleration?Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.
For three seconds, there is a steady acceleration that reaches 4 m/s. This yields a diagonal line when drawn on a velocity/time graph. The following formula can be used to determine the region beneath this line, or the distance it travels:
The triangle area is calculated using the formula:-
A = 0.5(l x h).
A = 0.5(3 x 4)=6m
There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.
0.5(2 x 4)=4m
Now, all that remains is a rectangle of height 2 and a length of 4, so we find its area of it.
2 x 4 = 8m
Finally, we add each of these up.
6m+4m+8m=18m
Therefore, the total distance traveled by the toy car is 18 meters.
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Find values of a. b. and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
X + y = 6
y + z = 6
x + z = 6
ax + by + cz = 0
a) a unique solution (a. b .c)=([])
b) no solution (a. b .c)=([])
c) infinitely many solutions (a. b, c) = ([])
Answer:
Step-by-step explanation:
The given equations are
x + y = 6- - - - - - - - -1
y + z = 6- - - - - - - -2
x + z = 6- - - - - - - - - 3
From equation 2, y = 6 - z
Substituting y = 6 - z into equation 1, it becomes
x + 6 - z = 6
x - z = 6 - 6
x - z = 0
x = z
Substituting x = z into equation 3, it becomes
z + z = 6
2z = 6
z = 6/2
z = 3
x = 3
Substituting x = 3 into equation 1, it becomes
3 + y = 6
y = 6 - 3
y = 3
ax + by + cz = 0
3a + 3b + 3c = 0
3(a + b + c) = 0
Therefore, it is impossible
You have also been asked to set up the basket ball court what is the circumference of the circle
Answer: circumference of the circle is 11.31 meters
C=\pi d\\C=\pi (2r)\\C=2\pi r
Where radius (r) is half of diameter (d)
Since radius of the circle shown in 1.8m, we plug it in the formula and get:
C=2\pi r\\C=2\pi (1.8)\\C=11.31
So C = 11.31 meters
NFL player Gerald Sensabaugh recorded a 46 inch standing vertical jump at the 2005 NFL Combine, at that time the highest for any NFL player in the history of the Combine. Sensabaugh weighed about 200 lb when he set the record. Part A What was his speed as he left the floor
Answer:
His speed as he left the floor is 4.83 m/s.
Step-by-step explanation:
Given: 46 inches = 1.1684 m and mass = 200 lb = 90.7185 Kg.
From the third equation of motion under free fall,
[tex]V^{2}[/tex] = [tex]U^{2}[/tex] - 2gs
Where; V is the final velocity (0), U is the initial velocity (unknown), g is the value of gravity - 10 m/[tex]s^{2}[/tex] and s is the distance = 1.1684 m.
Then;
0 = [tex]U^{2}[/tex] - 2gs
[tex]U^{2}[/tex] = 2gs
= 2 × 10 × 1.1684
= 23.368
⇒ U = [tex]\sqrt{23.368}[/tex]
= 4.8340 m/s
The initial velocity, U = 4.83 m/s.
Therefore, his speed as he left the floor is 4.83 m/s.
Answer:
His speed as he left the floor is 4.83 m/s.
Step-by-step explanation:
The probability that a can of paint contains contamination is 3.23%, and the probability of a mixing error is 2.4%. The probability of both is 1.03%. What is the probability that a randomly selected can has contamination or a mixing error?
Answer:
4.6%.
Step-by-step explanation:
The probability that a can of paint contains contamination(C) is 3.23%
P(C)=3.23%
The probability of a mixing(M) error is 2.4%.
P(M)=2.4%
The probability of both is 1.03%.
[tex]P(C \cap M)=1.03\%[/tex]
We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e. [tex]P(C \cup M)[/tex]
In probability theory:
[tex]P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%[/tex]
The probability that a randomly selected can has contamination or a mixing error is 4.6%.
Pythagorean theorem please help
Answer:
4√73
Step-by-step explanation:
x^2= 12^2 + 32^2
x^2= 144+ 1024
x^2=1168
x= 4√73
0.2x + (-0.9) + 1.7 = 9.6
0.2x + 0.8 = 9.6
X=
WHAT DOES x =
Answer:
x =44
Step-by-step explanation:
0.2x + (-0.9) + 1.7 = 9.6
Combine like terms
.2x +.8 = 9.6
Subtract .8 from each side
.2x +.8 -.8 = 9.6 -.8
.2x = 8.8
Divide each side by .2
.2x/.2 = 8.8/.2
x =44
What’s the correct answer for this?
Answer:
B and C
Step-by-step explanation:
The correct option are
B) a cross section of rectangular pyramid perpendicular to the base
C) a cross section of a rectangular prism that is parallel to it's base
Which of the following measurements is more precise?
4.69 m or 8.99 m
Answer:
The measures represent the same precisionWhen we talk about precision in measurements, we need to mention the significant figures, because that determines the precision.
Specifically, the more significant figures there are, more precise will be the number.
In this case, you can observe that both numbers have the same number of significant figures, which is 3, which means both numbers are equal in precision.
Using propositional logic to prove that each argument is valid.If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed. Mr. Kraso was not in town. If a crime was committed, then Mr. Krasov was in town. Therefore Jose did not take the jewerly. Use letters J, L, C, T.So for this question, I am very confused and would appreciate any help offerd.
Answer:
Step-by-step explanation:
We will first translate the situation to propositional logic. First, some notation is needed: [tex]\lor[/tex] is the or logical operation and [tex]\implies[/tex] is the symbol for logical implication. Define the following events:
J: Jose took the jewelry. L: Mrs Krasov lied, C: a crime was committed. T: Mr Krasov was in town.
We will symbol the propositions in logical symbols. Recall that [tex]\neg[/tex] means negation
If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed: [tex]J\lor L \implies C[/tex]
Mr. Krasov was not in town: [tex]\neg T[/tex]
If a crime was committed, then Mr. Krasov was in town: [tex]C\implies T[/tex]
We want to check if the conclusion Jose did not take the jewerly: [tex]\neg J[/tex] can be deduced from the premises.
First, recall the following:
- if [tex] a\implies b[/tex] and a is true, then b is true.
- [tex] a\implies b[/tex] is logically equivalent to [tex]\neg b \implies a[/tex]
Coming back to the problem, we have the following premises
[tex]J\lor L \implies C, \neg T, \neg T \implies \neg C, \neg C \implies \neg(J\lor L)[/tex]
where the equivalence for the logical implication was applied. REcall that the negation of an or statement is g iven by
[tex] \neg( a \lor b ) = \neg a \land \neg b [/tex] where [tex] \land[/tex] is the and logical operator.
USing this, we get the premises
[tex]J\lor L \implies C, \neg T, \neg T \implies \neg C, \neg C \implies \neg J\land \neg L[/tex]
Since [tex]\neg T[/tex], by having [tex]\neg T \implies \neg C[/tex], then it must be true that [tex]\neg C[/tex]. Since [tex]\neg C \implies \neg J\land \neg L[/tex], then it must be true that [tex] \neg J\land \neg L[/tex]. This final conclusion implies that it is true that [tex]\neg J[/tex] which is the statement that Jose did not take the jewelry.
A, B, and C are collinear points C is the midpoint of AB AC = 5x - 6 CB = 2x Find AB
Answer:
AB = 8
Step-by-step explanation:
Since C is the midpoint, ...
AC = CB
5x -6 = 2x
3x = 6 . . . . . . . add 6-2x
x = 2
Then the length of AB is ...
AB = 2(CB) = 2(2x) = 4(2)
AB = 8
For many years "working full-time" was 40 hours per week. A business researcher gathers data on the hours that corporate employees work each week. She wants to determine if corporations now require a longer work week. Group of answer choices Testing a claim about a single population proportion. Testing a claim about a single population mean. Testing a claim about two population proportions. Testing a claim about two population means.
Answer:
Correct option is: Testing a claim about two population means.
Step-by-step explanation:
In this provided scenario, a researchers wants to determine if corporations require a longer work week for the employees "working full-time".
It is given that for many years "working full-time" was 40 hours per week.
The researchers researcher gathers data on the hours that corporate employees work each week.
It is quite clear that the researcher wants to determine whether the number of hours worked per week must be increased from 40 hours or not.
A test for the difference between two population means would help the researcher to reach the conclusion.
Thus, the correct option is: Testing a claim about two population means.
2. A manufacturer produces light bulbs at a Poisson rate of 300 per hour. The probability that a light bulb is defective is 0.012. During production, the light bulbs are tested, one by one, and the defective ones are put in a special can that holds up to a maximum of 50 light bulbs. On average, how long does it take until the can is lled
Answer:
On average it will take 13 hrs 53 minutes before the van is filled
Step-by-step explanation:
The first thing we need to do here is to find find the number of defective light bulbs
Using the poisson process, that would be;
λ * p
where λ is the poisson rate of production which is 300 per hour
and p is the probability that the produced bulb is defective = 0.012
So the number of defective bulbs produced within the hour = 0.012 * 300 = 3.6 light bulbs per hour
Now, let X be the time until 50 light bulbs are produced. Then X is a random variable with the parameter (r, λ) = (50, 3.6)
What we need to find however is E(X)
Thus, the expected value of a gamma random variable X with the parameter (x, λ) is;
E(X) = r/λ = 50/3.6 = 13.89
Thus the amount of time it will take before the Can will be filled is 13 hrs 53 minutes
WILL GIVE BRAINLIEST! HURRY
Answer:
-1/2 =x
Step-by-step explanation:
4x - 6 = 10x -3
Subtract 4x from each side
4x-4x - 6 = 10x-4x -3
-6 = 6x-3
Add 3 to each side
-6+3 = 6x
-3 = 6x
Divide each side by 6
-3/6 = 6x/6
-1/2 =x
[tex]answer \\ - \frac{1}{2} \\ solution \\ 4x - 6 = 10x - 3 \\ or \: 4x - 10x = - 3 + 6 \\ or \: - 6x = 3 \\ or \: x = \frac{3}{ - 6} \\ x = - \frac{1}{2} \\ hope \: it \: helps[/tex]
Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢ 580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of GH¢2,358.60, how much was his total investment?
Answer:
GH¢2082.12
Step-by-step explanation:
Let "a" represent the amount invested at 12%. Then (a+580) is the amount invested at 14%. The total amount invested (t) is ...
t = (a) +(a +580) = 2a+580
Solving for a, we get
a = (t -580)/2
__
The accumulated amount from the investment at 12% is 1.12a. And the accumulated amount from the investment at 14% is 1.14(a+580). Together, these accumulated amounts total GH¢2358.60.
1.12(t -580)/2 +1.14((t -580/2 +580) = 2358.60
0.56t -0.56(580) +0.57t -0.57(580) +1.14(580) = 2358.60 . . . remove parens
1.13t + 5.8 = 2358.60 . . . . . . . . . simplify
1.13t = 2352.80 . . . . . . . . . . . . . . subtract 5.8
t = 2352.80/1.13 = 2082.12 . . . . divide by the coefficient of t
Mr. Azu's total investment was GH¢2082.12.
What is the slope-intercept equation of the line below?
Answer:D
Step-by-step explanation:
-2=4/5(0)-2
-2=0-2
-2=-2
-6/5=4/5(1)-2
-6/5=4/5-10/5
-6/5=4/5-10/5
-6/5=-6/5
A sample of 1100 computer chips revealed that 77% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 76% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.77 -0.76}{\sqrt{\frac{0.76(1-0.76)}{1100}}}=0.778[/tex]
Step-by-step explanation:
Information given
n=1100 represent the random sample taken
[tex]\hat p=0.77[/tex] estimated proportion of chips that fall in the first 1000 hours of their use
[tex]p_o=0.76[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Solution
We need to conduct a hypothesis in order to check if the true proportion is equal to 0.76.:
Null hypothesis:[tex]p=0.76[/tex]
Alternative hypothesis:[tex]p \neq 0.76[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.77 -0.76}{\sqrt{\frac{0.76(1-0.76)}{1100}}}=0.778[/tex]
Help! Best Answer = brainiest!
Answer:
30 or younger
Step-by-step explanation:
The top tree broke and fell over.the remaining tree teunk is 3 feet tall.the tip of the tree rests on the ground 14 feet from the base of the trunk.what is the lenght of the broken part of the tree to the nearest tenth of a foot
Answer:
14.3 feet.
14.3 feet
Step-by-step explanation:
The problem forms a right triangle in which:
The Vertical Leg of the Right Triangle = 3 feet
The Horizontal Leg of the Right Triangle =14 feet
We are to determine the length of the broken part of the tree. This is the Hypotenuse of the Right Triangle,
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\Hypotenuse^2=14^2+3^2\\Hypotenuse^2=205\\Hypotenuse=\sqrt{205}\\Hypotenuse=14.32\\ \approx 14.3 feet $(to the nearest tenth of a foot).\\Therefore, the lenght of the broken part of the tree to the nearest tenth of a foot is 14.3 feet.[/tex]
The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 5 in, what is the length of the chalkboard? A. 6.67 in B. 9.33 in C. 12 in D. 14 in
Answer:
A. 6.67 in
Step-by-step explanation:
length/width = 4/3 = x/5
Multiply by 5:
5(4/3) = x = 20/3 = 6 2/3
The length of the chalkboard is 6.67 inches.
work out the length of the container. Giver your answer to the nearest whole centimetre.
Dennis is making a container for tomato plant. The container will be in the shape of a cuboid.
missing length ? 40cm by 55cm.
The capacity of the container will be 180 litres.
1 Litre =1000cm cuboid.
Answer:
Length of the container = 82 cm
Step-by-step explanation:
Given:
Breadth of the container is 40 cm and height of the container is 55 cm
Volume of the container is 180 litres
To find: length of the container
Solution:
A container is in the shape of the cuboid.
Volume of cuboid = length × breadth × height
Put breadth = 40 cm , height = 55 cm and volume = 180 litres = 180000 [tex]cm^3[/tex]
(as 1 litre = 1000 [tex]cm^3[/tex] )
Therefore,
[tex]180000=length\,\times \,40\times 55\\length = \frac{180000}{40\times 55}=81.82\approx 82\,\,cm[/tex]
Which of the following sequence of transformations takes point J(9, 1) to J'(-3, 7)?
Answer:
Translate point J 12 units down and 6 units right.
THIS QUESTION IS KILLING ME
Calculate the volume of the object by using the triple integral.
The volume of the solid (call it S) in Cartesian coordinates is
[tex]\displaystyle\iiint_S\mathrm dV=\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{(x^2+y^2)^2-1}^{4-4(x^2+y^2)}\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
but I suspect converting to cylindrical coordinates would make the integral much more tractable.
Take
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=z\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]
Then
[tex]4-4(x^2+y^2)=4-4r^2=4(1-r^2)[/tex]
[tex](x^2+y^2)^2-1=(r^2)^2-1=r^4-1[/tex]
and the integral becomes
[tex]\displaystyle\iiint_S\mathrm dV=\int_0^{2\pi}\int_0^1\int_{r^4-1}^{4(1-r^2)}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\pi\int_0^1r(4(1-r^2)-(r^4-1))\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^1r(5-4r^2-r^4)\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^15r-4r^3-r^5\,\mathrm dr[/tex]
[tex]=2\pi\left(\dfrac52-1-\dfrac16\right)=\boxed{\dfrac{8\pi}3}[/tex]
