Answer:
a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c) the required probability is 0.2000
Step-by-step explanation:
Given the data in the question;
During a specific ten-hour period, one defective circuit board was found.
Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.
Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.
f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex]; ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]
= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
Now,
a) the probability that it was produced during the first hour of operation during that period;
P( Y < 1 ) = [tex]\int\limits^1_0 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^1_0[/tex]
= [tex]\frac{1}{10} [ 1 - 0 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) The probability that it was produced during the last hour of operation during that period.
P( Y > 9 ) = [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^{10}_9[/tex]
= [tex]\frac{1}{10} [ 10 - 9 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c)
no defective circuit boards were produced during the first five hours of operation.
probability that the defective board was manufactured during the sixth hour will be;
P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )
= P( 5 < Y < 6 ) / P( Y > 5 )
we substitute
[tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]
[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]
= ( 6-5 ) / ( 10 - 5 )
= 0.2000
Therefore, the required probability is 0.2000
Which equation is modeled on the number line below?
Answer:
A
Step-by-step explanation:
You have two increments of -5, so you know that 2 x -5 = -10. You know it is negative 10 because it is going to the left.
Hope this helps!
Which equation below compares the amount of medicine, S, in Sofia’s system with the amount of medicine, L, in Lexi’s system? L = 16 x S S = 16 x L L = 4 + S S = 4 + L
Answer:
L=16xS
Step-by-step explanation:
Which expression is equivalent to 6(7x - 9)?
Answer:
42x - 54 I think
Step-by-step explanation:
Just simplify it
Solve for x. Round to the nearest tenth, if necessary.
Answer:
9.81925> rounding up, final answer is x= 9.8
PLEASE HELP!!!
True or false
3(x-2) and 3x-6 are
equivalent
Answer:
true!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
True.
Step-by-step explanation:
They are equivalent expression because if you distribute the 3 in 3(x-2), you will get the same expression as 3x-6.
3(x-2) =
(3*x) - (3*2) =
3x - 6
Hope this helps.
A bakery sells two kinds of baked goods: cookies and pie slices. A cookie costs 12 ani a pe sites $4. In one day, the store sold 34 baked goods for a total of $114. How many cookies die itey sele? How many pie slices did they sell? Write a system of equations and solve.
Answer:
uhhhhhhhhhhhh what does this say?
Write each quotient as a single power.
[tex]a)\frac{-3^4}{3^4} = -3^{4-4} = -1[/tex]
[tex]b)\frac{(-9)^{10}}{(-9)^5} = (-9)^{10-5}= (-9)^5[/tex]
[tex]c)\frac{11^9}{11^6} = 11^{9-6} =11^3[/tex]
ok done. Thank to me :>
A 2ft-by-2ft square is divided into smaller squares and portions are shaded. What is the area of the shaded portion?
Answer:
1.5 ft^2
Step-by-step explanation:
Since the length is divided into 4 parts,
Length of a small square = 2/4
= 0.5 ft
Hence,
Area of 1 small square = (0.5)(0.5)
= 0.25 ft^2
Area of shaded portion = Area of 6 small squares
= 6(0.25)
= 1.5 ft^2
Step-by-step explanation:
The area of the shaded cubes is 3 square feet.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given side²
We have,
Since the 2 ft-by-2 ft square is divided into 16 smaller squares, each smaller square has an area of:
(2/4)ft = 0.5ft.
Now,
Out of the 16 smaller squares, 6 smaller cubes are shaded.
Since each smaller cube occupies the space of one of the smaller squares, the total area of the shaded cubes is 6 times the area of one of the smaller squares.
The area of the shaded cubes is:
6 x 0.5ft² = 3ft²
Thus,
The area of the shaded cubes is 3 square feet.
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Express as a trinomial.
(x + 6) (2x + 8)
Answer:
2x² + 20x + 48
Step-by-step explanation:
(x+6)(2x+8)
(x)(2x) + (x)(8) + (6)(2x) + (6)(8)
2x² + 8x + 12x + 48
2x² + 20x + 48
how many units is -3 2/3 from zero on the number line
Answer:
It is 3 2/3 away from zero or 3.7 (3.66666666667) away from zero.
Step-by-step explanation:
It is 3 2/3 away from zero or 3.7 (3.66666666667) away from zero.
The two lines graphed below are not parallel. How many solutions are there to the system of equations?
○ A. Zero
○ B. Two
○ C. Infinity many
○ D. One
Question 6
You have been asked to set up chairs for the school concert.
The first row will have 10 seats, and each additional row has 4
seats more than the previous row. /(10 pts)
What is the total number of chairs needed to set up 25 rows?
Answer:
1500
Step-by-step explanation:
we can do simple triangle numbers to do this. 4 more seats per row. we take 10 which is the first row and add the last row which 110 because 4*25 rows is 100 more. now we can half the rows to 12.5 and multiply that by the 120 and we get 1500 and we are done
A movie theater charges $7.00 for adults and $2.00 for senior citizens. On a day when people paid for admission, the total receipts were $1225. How many who paid were adults? How many were seniors?
Answer:
7.00+2.00=9.00
2.00-7.00=5.00
The map shows the location of four places in a city:
Coordinate grid shown from negative 6 to positive 6 on the x-axis and negative 6 to positive 6 on the y-axis. A point labeled School is shown on ordered pair 2, 4. A point labeled Library is shown on ordered pair negative 3, 5. A point labeled City Park is shown on ordered pair negative 3, negative 4. A point labeled Museum is shown on ordered pair 2, negative 5.
Anna's house is in the same quadrant as the museum. Which of the following could be the coordinates of Anna's house?
(1, 4)
(−1, 4)
(1, −4)
(−1, −4)
Using quadrant concepts, it is found that the coordinates of Anna's house could be at (1,-4).
The signal rules for the quadrants of a point (x,y) are as follows:
First quadrant: x > 0, y > 0.Second quadrant: x < 0, y > 0.Third quadrant: x < 0, y < 0.Fourth quadrant: x > 0, y < 0.In this problem, the museum is in the fourth quadrant, which is the same as Anna's house, hence, since it is needed x positive and y negative, the coordinates of Anna's house could be at (1,-4).
You can learn more about quadrants at https://brainly.com/question/25900520
two cards from an ordinary deck of 52 cards are lost at random. what is the probability that a random card from the resulting deck is a spade
Answer:
so theirs 4 suits so 1/4 but since you have 2 cards
its 1/2 or 50%
Hope This Helps!!!
someone please help me!
GIVING BRAINLIST TO FIRST RIGHT ANSWER
Answer:
A. The mean is increased by 3
Step-by-step explanation:
2 + 9 + 11 + 10 + 3 + 5 + 4 + 12 = 56/8 = 7
2 + 9 + 11 + 10 + 3 + 5 + 4 + 12 + 34 = 90/9 = 10
10 - 7 = 3
help me out please
and i need a step by step explanation
Answer: 1 + (-1) + (-4) = -4
Step-by-step explanation:
By counting how many chips there are, you can get the following:
1 positive chip + 1 negative chip + 4 negative chips, which is
+1 + -1 + 4 x -1
= 1 -1 -4
= -4
Please Help I am giving many points!
Answer:
D
Step-by-step explanation:
n = 5
an = 176
an = a1*x^(n -1)
a5 = a1 * x^4 = 176
a7 = a1 * x^6 = 704
a7/a6 = a1 * x^6 / a1*x^4 = 704 / 176
Cancel out a1
x^6/x^4 = 704/176 Divide numerator and denominator by 176
x^2 = 4 Take the square root of both sides
x = 2 or - 2
176 = a1 * x^4
176 = a1 * 16
a1 = 11
a1 is going to be 11 whether x is 2 or minus 2.
hi mallllll. hehehe
once again its [tex]a_{1} = -11[/tex]
11. A bank teller has a total of 124 bills in five-dollar bills and ten-dollar bills. The total value of the
money is $840. How many ten-dollar bills does she have
Answer:
44 ten-dollar bills
Step-by-step explanation:
Assume that all 124 bills are ten-dollar bills,
124 x $10 = $1240
Total Value of Money : $840
$1240 - $840 = $400
There are $400 worth of five-dollar bills,
$400 / 5 = 80 (The number of five-dollar bills)
Therfore the number of ten-dollar bills,
124 - 80 = 44
Let's check:
44 x $10 = $440
80 x $5 = $400
Total = $440 + $400
= $840
Help pllsssssss to find the vAlue of a
Answer:
a = 11
Step-by-step explanation:
As all angles on a straight line must add up to 180°:
(9a + 6) + 75 = 180
9a + 6 + 75 = 180
9a + 81 = 180
Subtract 81 from both sides of the equation:
9a + 81 - 81 = 180 - 81
9a = 99
Divide both sides by 9 to isolate a:
9a ÷ 9 = 99 ÷ 9
a = 11
Hope this helps!
Answer:
[tex]a=11[/tex]
Step-by-step explanation:
These are supplementary angles, meaning they together make up the whole measure of the angle of a straight line. A straight line is 180°, so the sum of these has to be 180° too:
[tex](9a+6)+75=180[/tex]
Then just solve for a:
[tex]9a+6+75=180\\9a+81=180\\9a=99\\a=11[/tex]
Solve -2/3x > 8 or -2/3x < 4.
{x | x > -12 or x < -6}
{x | -12 < x < -6}
{x | x < -12 or x > -6}
{x | x < -12 or x > -6}
=========================================================
Explanation:
Let's solve the first inequality for x.
(-2/3)x > 8
-2x > 8*3
-2x > 24
x < 24/(-2)
x < -12
The inequality sign flips when we divide both sides by a negative value.
Let's do the same for the second inequality.
(-2/3)x < 4
-2x < 4*3
-2x < 12
x > 12/(-2)
x > -6
The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.
Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.
Factor
3x2- 2x - 5
*(3xpower of 2 -2x-5)**
Answer:
16
Step-by-step explanation:
3×2-2×-5=
6-(-10)=
6+10=
16
2/8 and 1/2 write < or >
Answer:
0.5 > 0.25
Step-by-step explanation:
2/8 = 1/4 = 0.25
1/2 = 0.5
Answer:
<
Step-by-step explanation:
1/2 equals more than 2/8.
Because if u simplify 2/8 it would equal 1/4 which is less than 1/2.
A card is fresh from an ordinary deck. Find the probability that it did a diamond given that it is a jack
Answer:
1/52
Step-by-step explanation:
A deck has 52 cards and the probability of picking a specific one is 1/52, or 1.92%
If you are looking for the probability of a diamond, it is 1/4, or 25%
In 2000, the moose population in a park was measured to be 650. By 2010, the population was measured to be 750. Assume the population continues to change exponentially. Find a formula for the moose population, P(x), where x is the number of years after 2000
Answer:
650 * (1.01)ˣ = P(x)
Step-by-step explanation:
One formula for exponential growth is
a*bˣ, where x represents time, a represents the initial amount, and b represents the growth rate. We have 650 as our initial amount because x is the number of years after 2000, and there are 650 moose in 2000. Then, we have
650 * b¹⁰ = 750 because, after 10 years, the moose population is 750. Solving for b, we have
750/650 = b¹⁰
(750/650)^(1/10) = b
= 1.01441296377 (can round this to 1.01)
Therefore, after x years, the moose population can be represented by the equation
650 * (1.01)ˣ
subtract the sum of h and 6 from 4
Sumas y restas de polinomios
I need help with a quiz
A rectangular prism has a volume of 960 cubic units. The area of the base is 80 square units. What is the height of the prism?
Answer: the area of the base will be multiplied by 4, since it will be changed from LW to
(2L)(2W) = 4LW
So, apply that to finding the new volume.
If the rectangular prism has a volume of 960 cubic units. Then the height of the prism will be 12 units.
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
A rectangular crystal has a volume of 960 cubic units. The region of the base is 80 square units.
The height of the prism will be given as,
960 = 80 x H
H = 960 / 80
H = 12 units
If the rectangular prism has a volume of 960 cubic units. Then the height of the prism will be 12 units.
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3. The lacrosse team is raising money by selling cheesecakes. The players plan to sell an entire cheesecake for $24.00 each and slices of cheesecake for $3.50 each. If they want to raise at least $700, how many of each could they sell?
Part A: List three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal of raising at least $700.
Part B: Write an inequality to represent the situation.
Part C: Graph the inequality and shade where the solutions are. y X
Part D: What is the difference in the amount of money raised for ordered pairs falling on the line and the ones that fall in the shaded area?
Part E: What do the x- and y-intercepts represent?
To reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.
To determine, if they want to raise at least $ 700, how many of each could they sell, listing three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal, the following calculation must be performed:
C + S = 700 24 x 20 = 480 700 - 480 = 220 / 3.5 = 62.85 24 x 10 = 240 700 - 240 = 460 / 3.5 = 131.42 24 x 15 = 360 700 - 360 = 340 / 3.5 = 97.14Therefore, to reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.
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help please i made it worth a lot of points
Answer:
[tex] \dfrac{4m^2n}{3p} [/tex]
second choice
Step-by-step explanation:
Deal with the numbers first, then with each set of equal variables.
Use the rule a^m/a^n = a^(m - n)
4/3 cannot be reduced, so the number part remains 4/3.
m^4/m^2 = m^2
n^3/n^2 = n^1 = n
p^3/p^4 = p^-1 = 1/p
Now put it all together:
[tex] \dfrac{4m^2n}{3p} [/tex]
second choice
[tex]\\ \sf{:}\longrightarrow \dfrac{4m^4n^3p^3}{3m^2n^2p^4}[/tex]
a^m/a^n=a^m-n[tex]\\ \sf{:}\longrightarrow \dfrac{4}{3}m^{4-2}n^{3-2}p^{3-4}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{4m^2np^{-1}}3}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{4m^2n}{3p}[/tex]
