Answer:
The volume of the solid is 243[tex]\sqrt{2} \ \pi[/tex]
Step-by-step explanation:
From the information given:
BY applying sphere coordinates:
0 ≤ x² + y² + z² ≤ 81
0 ≤ ρ² ≤ 81
0 ≤ ρ ≤ 9
The intersection that takes place in the sphere and the cone is:
[tex]x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81[/tex]
[tex]2(x^2 + y^2) =81[/tex]
[tex]x^2 +y^2 = \dfrac{81}{2}[/tex]
Thus; the region bounded is: 0 ≤ θ ≤ 2π
This implies that:
[tex]z = \sqrt{x^2+y^2}[/tex]
ρcosФ = ρsinФ
tanФ = 1
Ф = π/4
Similarly; in the X-Y plane;
z = 0
ρcosФ = 0
cosФ = 0
Ф = π/2
So here; [tex]\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}[/tex]
Thus, volume: [tex]V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi[/tex]
[tex]V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho[/tex]
[tex]V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}[/tex]
[tex]V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ][/tex]
V = 243[tex]\sqrt{2} \ \pi[/tex]
A snack-size bag of carrots has a mean weight of 1.75
ounces and a standard deviation of 0.1 ounce.
Kendra bought a snack-size bag of carrots to measure
and found that it weighed 1.68 ounces.
What is the Z-score for the snack-size bag of carrots
that Kendra measured?
A. -0.70
B. -0.07
C. 0.07
D. 0.70
Answer:
The person above is right,
the answer is (A) -.70
They deserve brainliest
30% of the cars in a parking lot are green. If there 21 green cars, how many cars are parked in the parking lot?
Answer:
70 cars
Step-by-step explanation:
Let x cars are parked in the parking lot.
[tex]30\% \: of \: x = 21 \\ \\ \frac{30}{100} \times x = 21 \\ \\ x = 21 \times \frac{100}{30} \\ \\ x = \frac{2100}{30} \\ \\ x = 70 \: [/tex]
70 cars are parked in the parking lot.
There are 4 trucks for every 5 cars in a parking lot. If there are 80 cars, how many trucks are in the parking lot?
Answer:
There are 64 trucks!
Step-by-step explanation:
Which product matches the shading on the grids?
Answer:
I believe it is D. not sure tho
What is the answer, I need one quick!
Answer:
13, 106 and 254
Step-by-step explanation:
the price of a video game was reduced by $60 to 45. By what percentage was the price of the video game reduced?
Answer:
25% reduced
Step-by-step explanation:
45/60= .75
1-.75=.25
A 30 foot cable is being cut into pieces that are 7 1/2 feet long
Answer:
Cool
Step-by-step explanation:
Do you mean a 30 foot cable is being cut into pieces that are 7 1/2 feet long, how many pieces is it cut into?
Answer:
goodluck
Step-by-step explanation:
What percentage of the eggs hatched?
Answer:
Is there supposed to be a picture or what??
Step-by-step explanation:
Divide. Express your answer in simplest form.
8/9 ÷ 8
○7 1/9
○1/9
○8/72
○9
Answer:
1/9
Step-by-step explanation:
8/9 ÷ 8/1
8/9 x 1/8 = 8/72
The GCF for 8 and 72 is 8
[tex]\frac{8}{72}[/tex]÷[tex]\frac{8}{8}[/tex]=[tex]\frac{1}{9}[/tex]
Answer: 1/9
see below for work ⤵
Given the point and slope write the equation of the line (6, -6); slope = 5/6
Answer:
y=5/6x-11
Step-by-step explanation:
Slope intercept form: y=mx+b
With slope: y=5/6x+b
Replace x with 6 and y with -6
[To figure out which one is x or y remember (x,y) so if you compare (6,-6) then you will find that 6 is x and -6 is y]
-6=5/6(6)+b
Simplify:
-6=5+b
Subtract 5 on both sides:
-11=b or b=-11
Answer:y=5/6x-11 (Replace the b in y=5/6x+b with -11 since -11 is equal to b)
Hope this helps!
Jacob answered 80% of the questions in a test correctly.
He answered 32 of the questions correctly.
Work out the total number of questions in the test.
I think the answer would be 40 questions I don't know if this is actually correct tho
A new basketball 20% off if it’s original price and is now selling for $36 what is the original price of the basketball before
the sale?
Given f(x) = 2x2 + 4x - 3 and g(x) = 5x – 2, find f(x) · g(x).
Must show all work to receive credit! Show your work in the box below.
Answer:
i don't have and idea
Step-by-step explanation:
4+ (-1 2/3) what’s the answer
Answer:
2 1/3
Step-by-step explanation:
Drag each expression to match each number with an expression.
Number. Expression.
34 34x10*0
3,400 34x10*3
34,000 34x100
340 34x10*1
Answer:
3,400
Step-by-step explanation:
This is statistics. Please answer fast
Answer:
This is a normal distribution and we can use the standard score to compute for probabilities. We compute the standard score of the given.
Step-by-step explanation:
z = (x - mu)/sd
z = (2625 - 2600)/50 = 25/50 = 0.5.
Consulting the z-table, P(z <= 0.5) = 0.6915.
P(z > 0.5) = 1 - P(z <= 0.5) = 1 - 0.6915 = 0.3085.
I hope this helped! <3
A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?
O 2y = 16x +14
O y = 8x - 7
O y = -8x + 7
O 2y = -16x - 14
The other equation could be y = 8x - 7
How to determine the other equation?The first equation is given as:
y = 8x + 7
For the system of equation to have no solution, then the equations in the system would have different constant values.
Take for instance:
y = 8x + b
Where:
b is a constant not equal to 7
From the options, we have:
y = 8x - 7
Notice that -7 and 7 are not the same
Hence, the other equation could be y = 8x - 7
Read more about system of equations at:
https://brainly.com/question/13729904
On his most recent math test, Jeremy answered 48 questions correct out of 80 total questions. Which statement can be made about Jeremy's math test?
Answer:
Jeremy has gotten more than half of the test's questions correctly.
Step-by-step explanation:
To get half of the questions correctly, Jeremy needed at least 40, and Jeremy got more than 40, meaning he got more than half.
Brita has a monthly budget of x dollars. She spends $1,425 on her mortgage every month. One-third of her remaining budget is spent on recreational activities. Which equation below can be used to determine the amount, in dollars, spent on recreational activities?
Answer:
y = ⅓(x - 1425)
Step-by-step explanation:
Given
Budget = x
Mortgage = 1425
Required
Determine the amount spent on recreational activities.
First, we need to get the balance after she pays her mortgage.
Balance = Budget - Mortgage
Balance = x - 1425
From the question, we understand that she spends ⅓ of the balance on recreational activities.
Represent this with y.
y is calculated as thus:
y = ⅓ of Balance
y = ⅓ * (x - 1425)
y = ⅓(x - 1425)
Hence, the above equation y = ⅓(x - 1425) can be used to calculate the amount spent on recreational activities
what is the slope of the line
Answer:
y-mx+b
Step-by-step explanation:
1+6 pls help me nowwwwwww
Answer:
7
Step-by-step explanation:
Calculate the volume
Please show the steps....
Answer:
4,800
Step-by-step explanation: 6 times 5 times 8 times 20=4800 :D
Answer:
probably
Step-by-step explanation:
v = [20.(8+6)/2].5
v = 20.7.5
v = 700cm³ (that's a 3 btw)
A company has Liabilities of $23,500 and Stockholders' Equity of $56,500. How much
does the company have in Assets?
What is the median for 6.74
Answer:
sorry i needed the points for school
Step-by-step explanation:
Answer:
Median normally is the middle figure in a set of numbers. not totally sure.
find the inverse of the function y equals x squared minus 12
Answer:
Step-by-step explanation:
y=x^2-12
The inverse is
√x+12, -√x+12
A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles. A marble is drawn from the bag at random . How many possible possible outcomes are there?
° 3
° 5
° 6
° 14
HELP ME ASAP PLZ
The anser is 14 I guess because there are 14 marbles in total giving you 14 outcomes
Jordan's net income for the year ended December 31, Year 2 was $200,000.
Answer:
good for her / him but uh whats the question
please answer if you can? (This is my math from 8th grade)
Answer:
40!
Step-by-step explanation:
3x+20+40=180
3x+60=180
3x=120
x=40
Answer:
b=40
Step-by-step explanation:
A poll commissioned by Friends of the Earth and conducted by the Mellman Group found that 72% of American voters are in favor a carbon tax. Suppose that six voters in the United States are randomly sampled and asked whether they favor a carbon tax. Determine the probability that the number answering in the affirmative is a. Exactly four. b. At least two
Answer:
a
[tex]P(X = 4) = 0.31599[/tex]
b
[tex]P(X \ge 2) = 0.9921 [/tex]
Step-by-step explanation:
From the question we are told that
The proportion in favor of carbon tax is [tex]p = 0.72[/tex]
The sample size is n = 6
Generally the distribution of poll follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability that the number answering in the affirmative is 4 is mathematically represented as
[tex]P(X = 4) = ^{6}C_4 * (0.72)^4 * (1- 0.72)^{6-4}[/tex]
=> [tex]P(X = 4) = 0.31599[/tex]
Generally the probability that the number answering in the affirmative is At least two is mathematically represented as
[tex]P(X \ge 2) = 1 - P( X < 2 ) [/tex]
[tex]P(X \ge 2) = 1- [ P(X = 0 ) + P( X = 1)] [/tex]
=> [tex]P(X \ge 2) = 1- [ [ 1 * 1 * 0.00048 ]+ [ 6 * 0.72 * 0.00172] [/tex]
=> [tex]P(X \ge 2) = 1- [ 0.00791 ] [/tex]
=> [tex]P(X \ge 2) = 0.9921 [/tex]
Aarti posted a comment on her blog. Each day the number of responses to her comment was 125% of the number she
received on the previous day. If there were 64 responses the first day, how many were there on the fourth day?
O 100
112
оооо
125
132
Mark this and return
Save and Exit
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Submit
Answer:
125
Step-by-step explanation:
Answer:
125
Step-by-step explanation: