Answer:
The answer is "[tex]\frac{324}{5}[/tex]"
Step-by-step explanation:
If the missing value is this [tex]z= 9-y-x^2[/tex] then:
[tex]\bold{z =9-y-x^2} \\\\\to x\leq 0 \\\\\to y < 0\\\\let: \ z= 0\ then\\\\ \to 9-y-x^2=0\\\\\to y=9-x^2\\\\if\ y=0 \\\\\to 0=9-x^2\\\\\to x=3\\\\\text{Calculate the volume: }\\[/tex]
[tex]\to \int \int z dz\ \ = \int \int_{R} (9-y-x^2) dz\\\\[/tex]
[tex]=\int_0^{3} \ \int_0^{9-x^2} (9-y-x^2) dy \ dx\\\\=\int_0^{3} (9y- \frac{y^2}{2}-x^2 y)^{9-x^2} _{y=0}\ dx\\\\=\int_0^{3} (9-x^2)^2- \frac{(9-x^2)^2}{2}\ dx\\\\=\frac{1}{2} \int_0^{3} (9-x^2)^2\ dx\\\\=\frac{1}{2} \int_0^{3} 81+x^4-18x^2 \ dx\\\\=\frac{1}{2} (81x +\frac{x^5}{5}-6x^3)^3_0 \\\\= \frac{1}{2} (\frac{648}{5}) \\\\=\frac{324}{5}[/tex]
In a certain assembly plant, three machines, B1, B2, B3, make 30%, 45%, and 25%, respectively, of the products. It is known from past experience that 2%, 3%, and 2% of the products made by each machine, respectively, are defective.
A. Suppose that a finished product is randomly selected. What is the probability that it is defective?
B. If a product were chosen randomly and found to be defective, what is the probability that it was made by machine B3.
Answer:
a. The probability that the finished product selected is defective is 2.45%.
b. The probability that product chosen randomly was defective and made by machine B3 is 20.41%.
Step-by-step explanation:
Let A represents the defective product.
We also have the following from the question:
P(B1) = Probability or percentage of the made by machine B1 = 30%, or 0.30
P(B2) = Probability or percentage of the made by machine B2 = 45%, or 0,45
P(B3) = Probability or percentage of the made by machine B3 = 25%, or 0.25
P(A/B1) = Probability or percentage of product B1 that is defective = 2%, or 0.02
P(A/B2) = Probability or percentage of product B2 that is defective = 3%, or 0.03
P(A/B3) = Probability or percentage of product B3 that is defective = 2%, or 0.02
We can therefore proceed as follows:
A. Suppose that a finished product is randomly selected. What is the probability that it is defective?
To determine this, the rules of elimination is applied and we have:
P(A) = (P(B1) * P(A/B1)) + (P(B2) * P(A/B2)) + (P(B3) * P(A/B3)) ………… (1)
Where;
P(A) = Probability that the selected product is defective = ?
Substitutes the values defined above into equation (1), we have:
P(A) = (0.30 * 0.02) + (0.45 * 0.03) + (0.25 * 0.02)
P(A) = 0.006 + 0.0135 + 0.005
P(A) = 0.0245, or 2.45%
Therefore, the probability that the finished product selected is defective is 2.45%.
B. If a product were chosen randomly and found to be defective, what is the probability that it was made by machine B3.
To calculate this, the Bayes’ rule is employed as follows:
P(B3/A) = (P(B3) * P(A/B3)) / [(P(B1) * P(A/B1)) + (P(B2) * P(A/B2)) + (P(B3) * P(A/B3))] = (P(B3) * P(A/B3)) / P(A) ………….... (2)
Where;
P(B3/A) = The probability that product chosen randomly was defective and made by machine B3 = ?
Also, from the values already defined and obtained in part A, we have:
P(B3) = 0.25
P(A/B3) = 0.002
P(A) = 0.0245
Substituting the values into equation (2), we have:
P(B3/A) = (0.25 * 0.02) / 0.0245
P(B3/A) = 0.005 / 0.0245
P(B3/A) = 0.2041, or 20.41%
Therefore, the probability that product chosen randomly was defective and made by machine B3 is 20.41%.
3y+6 divided by 2a:let y=4 and x=3
Answer:
3
Step-by-step explanation:
You first plug in the values for x and y into the equation
3(4)+6÷ 2(3)
Then Simplify each side
12+6÷6
18÷6
=3
What was Madame de Soto’s motive for intervening?
Answer:
On May 21, 1541, the Spaniards saw for the first time the Mississippi River, the “Father of the Water” south of Memphis, Tennessee. They crossed the river and made their way through Arkansas and Louisiana. Then, early in 1542, de Soto turned back to the Mississippi River
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Shonda painted 3 walls in her home. She used 34 of her paint. She used the same amount of paint on each wall.
How much of her paint was used on each wall?
Answer:
1/4
Step-by-step explanation:
For the triangles to be congruent by SSS, what must be the value of x? 1 3 6 8
Answer:
C
Step-by-step explanation:
6
Answer:
C
Step-by-step explanation:
It gib the funny check mark
A person is running fast and furious in 120 seconds at a rate of 20 m/s. What is the distance? help!!!!!!
9514 1404 393
Answer:
2400 m
Step-by-step explanation:
Distance is the product of speed and time:
d = (20 m/s)(120 s) = 2400 m
The person ran 2400 meters in 120 seconds.
A loaf of sandwich bread contains 24 slices. Which of these tables correctly shows the ratios of different numbers of loaves of bread to the numbers of total slices they contain?
Answer:
which table?
Step-by-step explanation:
im assuming it would look like this
1 24
2 48
3 72
4 96
5 120
6 144
7 168
8 192
9 216
10 240
just multiply the number of loaves to 24
Hope this helped :)
10 raise to power2 - 11 raise to power 2 + 4raise to power2
Answer:
-5
Step-by-step explanation:
100 - 121 + 16
Power of 2 just means to multiply the number by iteself. So 10×10, 11×11, 4×4.
please help need assistance
Answer:
18
Step-by-step explanation:
Keep in mind that anything with a subscript of 0 always comes out as a 1
16(1)+2(2)²(4⁻¹)
= 16+8(4⁻¹)
=16 + 8(1/4)
=16+2
=18
Hope this helps! :)
Problems 4 (a and b), 6 (a,b, and c), 7 (a,b, and c), 8, and 9 (a,b, and c) Thank you so much!
For real help on this, people will receive more points to prevent point stealing.
Answer:
no problem glad to help
please
help i’ve been stuck on
this all day
Answer:
CPB
Step-by-step explanation:
acute is less than 90 degrees and right is 90 degrees and obtuse is over 90 degrees
Answer: The answer is CPB
Yoooo who’s smart I need help in this ASAP
Answer:
3[tex]\sqrt[9]{Z}[/tex]²
Step-by-step explanation:
Expression -
(27[tex]\sqrt[3]{Z}[/tex]²) ^1/3
Transform the expression -
³[tex]\sqrt[3]{27}[/tex][tex]\sqrt[3]{Z}[/tex]²
Simplify - //Note: ignore the ' * '//
3[tex]\sqrt[3]{*}[/tex][tex]\sqrt[3]{z}[/tex]²
Simplify (Again) -
3[tex]\sqrt[9]{Z}[/tex]²
7. What is the equation of the line that passes through (-1, -4) and (0,5)?
A.) y = 9x + 5 B.) y = 5x + 9 C.) y = -9x + 5 D.) y = -5x + 9 E.) none of these
1
Answer:
A)y=9x+5
Step-by-step explanation:
If x=-1, y=-4,
y=9*-1+5=(-9)+5=-4
If x=0, y=5,
y=9*0+5=5
kelly flies a distance of 2,100 miles. The trip takes 4 2/3 hours.
What is the airplane's unit rate of speed in miles per hour?
Answer:
450 miles per hour
Step-by-step explanation:
Kelly flies at a distance of 2,100 miles
The time taken for the trip is 4 2/3 hours
Therefore the rate of speed can be calculated as follows
= 2,100 ÷ 4 2/3
= 2,100 ÷ 14/3
= 2100 × 3/14
= 150 × 3
= 450 miles per hour
Answer:
450
Step-by-step explanation:
A car that costs $14,000 without tax costs $14,700 with tax what is the sales tax percent (percent increase)?
Yo the car is.......................Step-by-step explanation:
Can someone help me find the area of the triangle
please!!!
Answer:
18
Step-by-step explanation:
Look at image please help me
Answer:
[tex](\frac{y^{2} }{x^{2} } )[/tex]^1/2
Answer:
the answer would be y/x
A random sample of 5 homes in Newberry, Florida had a mean of $169,900 and a standard deviation of $21,756. Construct a 95% confidence interval for the average home of this size in Newberry.
A. (144885.25, 194914.75).
B. (150440.842, 189359.16).
C. (150830, 188969.98).
D. (142886, 196914).
Answer:
D. (142886, 196914).
Step-by-step explanation:
To solve for this question, we would use t score instead of z score. The reason is because, our sample size is small.
The formula for Confidence Interval =
C.I = Mean ± t score × standard deviation/√n
n = 5 samples
Degrees of freedom = n - 1 = 5 - 1 = 4
The t score for a 95% confidence interval with degrees of freedom 5 is : 2.776
Hence,
Confidence Interval =
169,900 ± 2.776 × 21,756/√5
169,900 ± 2.776 × 9.7295789837
169, 900 ± 27009.311259
Confidence Interval
169,900 - 27009
= 142886
169, 900 + 27009.311259
= 196914
Hence, the confidence interval = (142886, 196914)
Option D is the correct answer
Using the t-distribution, it is found that the 95% confidence interval for the average price of a home of this size in Newberry is of (142886, 196914), given by option D.
In this problem, we have the standard deviation for the sample, thus, the t-distribution is used to solve this question.
The sample mean is [tex]\overline{x} = 169900[/tex].The sample standard deviation is [tex]s = 21756[/tex].The sample size is [tex]n = 5[/tex]First, we find the number of degrees of freedom, which is the sample size subtracted by 1, so df = 5 - 1 = 4.
Then, we find the critical value for the 95% confidence interval with 4 df, which looking at the t-table or using a calculator is given by t = 2.7765.
The margin of error is:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
In this case:
[tex]M = 2.7765\frac{21756}{\sqrt{5}} = 27014[/tex]
The confidence interval is:
[tex]\overline{x} \pm M[/tex]
Then
[tex]\overline{x} - M = 169900 - 27014 = 142,886[/tex].
[tex]\overline{x} + M = 169900 + 27014 = 196,914[/tex].
Thus, the correct option is D. (142886, 196914).
A similar problem is given at https://brainly.com/question/15180581
If December 6 falls on a Saturday, then January 19 of the next year falls on which day of the week?
January 19 would fall on a Tuesday
Inquality x=3 is a solution or x=-2is a solution for 7(2 -x)>5
Answer:
5
Step-by-step explanation:
Write an expression in simplest form that represents the area of the banner
Answer:
Can I have a picture so I can give you one
Step-by-step explanation:
thank you
Which of the following correctly represents the given data in the problem?
a = 24, g = 48, h = 22, i = 80
a = 22, c = 80, d = 24, i = 48
a = 24, b = 48, c = 22, i = 48
a = 24, c = 48, e = 22, i = 80
Answer:
D
Step-by-step explanation:
100% true
Answer:
It is D
Step-by-step explanation:
Marty worked 19.5 hours last week. He earns $8.50 per hour. What were Marty’s earnings last week?
Answer:
Step-by-step explanation:
Marty's earnings = 8.50 x 19.5 = 165.75
What is the slope of the line that passes through the points (8, 7)(8,7) and (4, 5) ?(4,5)? Write your answer in simplest form.
The slope of the line is 1 / 2. The equation of the line is y = 1/ 2 x + 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the line passes through points (8, 7) and (4, 5). The slope of the line will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 5 - 7 ) / ( 4 - 8 )
Slope = -2 / -4
Slope = 1 / 2
Calculate the y-intercept,
y = mx + c
5 = 1 / 2 x 4 + c
c = 5 - 2 = 3
The equation is written as,
y = mx + c
y = 1/2x + 3
Therefore, the slope of the line is 1 / 2. The equation of the line is y = 1/ 2 x + 3.
To know more about an equation of the line follow
https://brainly.com/question/18831322
#SPJ3
9
The rate shown represents the number of residents for each police officer in a city.
400 residents
1 police officer
Which rate is equivalent?
10,000 residents
25 police officers
O
4,000 residents
100 police officers
2 residents
800 police officers
500 residents
101 police officers
chart below
Answer:
A: 10,000 residents to 25 police officers
Step-by-step explanation:
400*25=10,000
The modified expression x^3(2x+5)-4(2x+5) has two terms with a common factor of
Answer:
( 2 x +5) ( x ^3 − 4 )
Step-by-step explanation:
I dont think this the answer your looking for, however, if you work backwards from here by expanding, you might get what you want. :)
5.
To make 1 pitcher of lemonade, Joel used 2 cups of lemon
juice and 5 cups of water. Which fraction shows the ratio
of cups of lemon juice to cups of water used in each
pitcher of lemonade?
Answer:
2/5
Step-by-step explanation:
2 cups of lemon juice to 5 cups of water.
another easy middle school question
Answer:
D
Step-by-step explanation:
Slope-intercept form is [ y = mx + b ] where m = slope and b = y-intercept. We are already given the slope and y-intercept so m = 2 and b = -4.
y = 2x - 4
Best of Luck!
Answer:
y = 2x - 4
Step-by-step explanation:
Add preposition ...The plane landed ____the ranway.
Answer:
On
The plane landed ON the runway.
Step-by-step explanation:
A preposition is a word that shows the relationship of a noun or pronoun with another word.
For example, in this sentence the noun is plane and we need to connect it with runway.
And on is the answer that makes the most sense.
Sylvio loaned a friend $1500 at a simple annual interest rate of 5%. How many years did it take Sylvio’s friend to repay him if Sylvio earned $225 in interest?
Answer:
Option B. 3 years.
Step-by-step explanation:
Sylvio loaned a friend $1,500 at a simple annual interest rate of 5%.
Formula of simple interest = I = P(rt)
I = Interest ($225)
P = Principal amount ( $1,500)
r = 5% = 0.05
t = time ( ? )
Now put the values to find the years.
225 = 1500( 0.05t)
225 = 75t
75t = 225
t =
t = 3
It will take 3 years to repay him if Sylvio earned $225 in interest.
