A company requires a password to access a data storage vault. The password must be 4 characters long and may
contain digits and lowercase letters only.
How many passwords are possible if characters can be repeated? Enter your answer as a number, like this: 425
Answers
Answer:
There are 36 possibilities per character (26 lower case letters + 10 numbers), so the total number of permutations are 36^4 = 1,679,616
Step-by-step explanation:
Related Questions
The 13-year $1,000 par bonds of Vail Inc. pay 13 percent interest. The market's required yield to maturity on a comparable-risk bond is 14 percent. The current market price for the bond is $870.
a. Determine the yield to maturity.
Answers
The current market price for the bond is $870 the yield to maturity is 14.13%
How is yield to maturity calculated?The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)
knowing that:
Face value (par value) of the bond (F) = $1,000Annual coupon rate (C) = 13% of the face value = 0.13 * $1,000 = $130Years to maturity (n) = 13 yearsCurrent market price of the bond (P) = $870the formula is:
\(P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n\)
Putting the values:
\($870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13\)
Using the math we find that the percentage is approximately 14.13%;
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Keisha, Miguel, and Ryan sent a total of 103 text messages during the weekend. Ryan sent 3 times as many messages as Miguel. Keisha sent 8 more
messages than Miguel. How many messages did they each send?
Number of text messages Keisha sent:
Number of text messages Miguel sent:
Number of text messages Ryan sent:
Answers
Answer:
only god knows
Step-by-step explanation:
because they didn't give us an answer on how many text messages anyone sent
2x - 6y = 6
6x - 4y = 2
Answers
Answer:
x = - 3/7
y = - 8/7
Step-by-step explanation:
(2x - 6y = 6)/2 =
x - 3y = 3
x = 3y + 3
Substitution:
6 (3y +3) - 4y = 2
18y + 18 - 4y = 2
14y = -18+2
y = -16/14
y = - 8/7
Substitution:
x = 3(-8/7)+3
x = -24/7 + 3
x = -3/7
9514 1404 393
Answer:
(x, y) = (-3/7, -1 1/7)
Step-by-step explanation:
We can divide each equation by 2 and subtract the constant to put them in general form.
x -3y -3 = 0
3x -2y -1 = 0
This form facilitates use of the "cross multiplication method" of solution. That method tells us ...
1/d1 = x/d2 = y/d3
where the differences d1, d2, d3 are the differences of cross-products:
d1 = 1(-2) -(3(-3)) = 7
d2 = -3(-1) -(-2(-3)) = -3
d3 = -3(3) -(-1(1)) = -8
Then the solutions are ...
x = d2/d1 = -3/7
y = d3/d1 = -8/7
(x, y) = (-3/7, -8/7)
_____
Additional comment
When the general form equations ax+by+c=0 and dx+ey+g=0 have their coefficients written in two rows: (note the repeated first coefficient)
a, b, c, ad, e, g, dThe pattern in the cross-differences is relatively easy to see:
d1 = ae -dbd2 = bg -ecd3 = cd -gaThe expressions for the solution values, (x, y) = (d2/d1, d3/d1), are substantially identical to those of Cramer's method.
Consider the following linear program.
Min 3A + 4B
s.t.
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
Answers
Answer:
Minimum z =22 at A =6, B=1
See the graph below variable A is on the horizontal axis and variable B on the vertical axis
Step-by-step explanation:
We can solve using the graphical method
Min z = 3A + 4B
s.t.
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
Draw two lines using the constraint equations
1A + 3B = 9
1A + 1B = 7
The feasible region for the inequality constraints is the region that satisfies all 4 constraints below
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0
This is the heavily shaded region in the graph. The minimum will be at one of the corner points
There are three corner points on the graph
(0,7), (6,1) and (9,0)
Plug in these coordinate values with A being the first and B being second in the parentheses and see which set of values makes the objective function the minimum
Point (7,0) ==> z = 3(0) + 4(7) = 28
Point (6,1) ==> z = 3(6) + 4(1) = 22
Point (9,0) ==> z = 3(9)+4(0) = 27
Which figure appears to show
parallel lines?
A
B
C
D
Answers
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
Someone please help with this question asap!
Answers
Answer:
Side b is the longest because the longer side always lie opposite the bigger angle. Angle B is the biggest angle, and since side b is opposite angle B, side b is the longest.
\( \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star\)
The side opposite to the largest angle is the longest side of a triangle.
\( \qquad \large \sf {Conclusion} : \)
hence, we can conclude that the longest side is b
( since it's opposite angle is the largest, i.e 91° )
Can anyone help please. Please show work too
Answers
The solutions to the system of equations are x = 2 and 4
How to determine the solution to the system of equationsFrom the question, we have the following parameters that can be used in our computation:
f(x) = x - 3
g(x) = 1/(x - 3)
The solution to the system of equations implies that
f(x) = g(x)
So, we have
x - 3 = 1/(x - 3)
Cross multiply the equation
This gives
(x - 3)² = 1
So, we have
x - 3 = ±1
Add 3 to both sides
x = 3 ± 1
So, we have
x = 2 and 4
Hence, the solutions to the system of equations are x = 2 and 4
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What does v equal? ;-;
Answers
Answer:
v=-3
Step-by-step explanation:
-1=1/3v
-1*3=v
-3=v
Answer:
Step-by-step explanation:
\(-1 = \frac{1}{3} v\)
Multiply by 3
\(-3 = v\)
on the 9th of february 2012, the heights of the water in the bristol channel in cardiff, uk were as follows. low tide was 1.2 m at 2:00 am and high tide was 12.4 m at 7:56 am. assuming sinusoid periodicity, estimate the height of the water at sunset (5:16 pm on that day). give your answer as a decimal (in metres) rounded to 1 decimal place.
Answers
It should be close to 7m at around 5pm. In fact, this is the time of day when the water rises the fastest, so perhaps 8m
What is the period of the sinusoidal signal?The interval between successive peaks in the sinusoidal signal graph, or period, is only the number of seconds needed for one cycle of the sinusoid.
Are all sinusoidal sequences periodic?Depending on the values of angular frequency (), discrete-time sinusoidal sequences may or may not be periodic. A discrete-time sinusoidal signal must have an angular frequency () that is a multiple of 2 to be considered periodic.
It takes roughly 6 hours from low tide to high tide, or 12 hours for the entire tide cycle. Since low tide was at 2 a.m., low tide will be at around 2 p.m. as well. Three hours later, or at around 5 p.m., the water should be at the average level, which should be at (12.4+1.2)/2=6.8 m. Therefore, it should be close to 7m around 5:45. Actually, this is when the water rises the fastest, so it's probably close to 8m. Your 5.5m is obviously too low, regardless of where it is.
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Please help answer my question
Answers
Answer:
x = 6
Step-by-step explanation:
This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:
(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²
From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.
3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²
3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²
Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:
8x - 20 = 5x - 2
Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.
8x - 20 = 5x - 2
8x - 20 - 5x = 5x - 2 - 5x
3x - 20 = -2
3x - 20 + 20 = -2 + 20
3x = 18
3x/3 = 18/3
x = 6
Hopefully that's helpful! Let me know if you need more help. :)
Happy Card Co. designs personalized cards which cost $1.10 per card. The fixed cost to make the cards is $264 per day. If the company charges $5.10 per card, how many cards must be delivered daily to make a profit of $52? Show work below.
Answers
Step-by-step explanation:
x = number of cards
the production costs (PC) per day are
PC(x) = 264 + 1.1x
the sales (S) are
S(x) = 5.1x
the profit (P) per day is sales minus costs
P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =
= 5.1x - 264 - 1.1x = 4x - 264
we need to find the value of x, so that P(x) = 52.
52 = 4x - 264
316 = 4x
x = 316/4 = 79
79 cards must be delivered daily to make a profit of $52.
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Answers
Based on the information in the fragment, it can be inferred that Josiah's mistake is that he did not multiply the numerator and denominator by the correct number to equal 1,500 (option B). So, the correct statements are A, C, and D.
How to find the ratio?To find the proportion in this problem we have to do the following procedure:
The first step is multiply both sides by 1500.The second step is to evaluate the expression on the right-hand side.The third step is multiply 10 by 1500 on the left-hand side.The fourth step is divide 15000 by 20 on the left-hand side.Once we have carried out the previous steps we must continue the procedure rewriting the equation with the data obtained previously. With this information we can conclude that Josian had the necessary information to discover how many songs of each genre were played during an hour on his MP3, however he performed the wrong procedure so his result was wrong.
According to the above, we can infer that the products are not well carried out. So, Josiah's mistake is no multiplying the numerator and denominator by the correct number to equal 1,500 (option B).
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Andrea collected this data: 5, 8, 9, 12 What is one value that she could add to the data so that the median would be 11?
Answers
Answer:
19
Step-by-step explanation:
Median= Middle number
12-5= 7
12+7=19
WILL GIVE 20 POINTS, NEED HELP! Match the description table or graph or equation with the correct type of function.
Answers
1, D /non linear function table/
2, F /linear function table/
3, C /linear function equation/
4, B /non linear function equation/
5, A /linear function graph/
6, E /non linear function graph/
1. = d. Non linear function table
the table is not the same rate of change. The x values are +1 but the y values are not constant.
2. = f. Linear function table
The table shows a constant rate of y=x+3 so it is linear.
3. = c. Linear function equation.
It is a single variable no exponents
4. = b. Non linear function equation
This equation has a variable exponent of ^2 so x has 2 solutions and is a parabola
5. = a. Linear function graph
This is a straight line so it is linear
6. = e. Non linear function graph
This is not a line, it is not linear, it is a curve and a parabola
See attachment
150% as a simplified fraction
Answers
Answer:
It would be 3/2 as 1/2 is 50%, 2/2 or 1 is 100% and 3/2 is 150%
Step-by-step explanation:
XZ.P Point P(-7, 2) is mapped onto P¹ (3, -11) by the reflection y=mx+c. find the values of the constants m and c.
Answers
The values of the constants m and c include the following:
m = -1.3
c = 7.1
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;
2 = -7m + c ...equation 1.
-11 = 3m + c ...equation 2.
By solving the system of equations simultaneously, we have:
2 = -7m - 3m - 11
11 + 2 = -10m
13 = -10m
m = -1.3
c = 7m + 2
c = 7(-1.3) + 2
c = -7.1
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find an equation that passes through (1 ,2) and is parallel y=3x-9
Answers
Answer:
A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point (1, 2)
Substituting the values we get:
y - 2 = 3(x - 1)
Simplifying the equation we get:
y - 2 = 3x - 3
y = 3x - 1
Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .
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Question 3: Mathematical proficiency and the construction of mathematics ideas. To answer this question, you need to understand paragraphs 2.12 and 2.13 in your study guide: Key to note the following concepts: constructivism and behaviourism. inductive and deductive thinking or reasoning. instrumental and relational understanding conceptual and procedural knowledge; and ● elements of mathematics proficiency. . e . (10 marks) ● 3.1 Create an activity where procedural and conceptual understanding co-exists. Revisit your content areas and choose a problem to solve and demonstrate how procedural and conceptual knowledge can be linked to the teaching and learning process. (6) 3.2 Provide an example to explain the difference between conceptual knowledge and procedural knowledge.
Answers
Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
3.1 Activity: Procedural and Conceptual Understanding in Action
Content Area: Fractions
Problem: Comparing Fractions
Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.
Activity Steps:
Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).
Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.
After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:
What does it mean for one fraction to be greater than or less than another?
Can you explain why we need a common denominator when comparing fractions?
How can you visually represent and compare fractions to better understand their relative sizes?
Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.
Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.
Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.
Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.
By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.
3.2 Example: Conceptual Knowledge vs. Procedural Knowledge
Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.
Example: Division of Fractions
Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.
Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.
In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
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Classwork Topic: Solve problems 25 May 2023 1. Jessica and Melissa shared 12 pieces of dried pears. Jessica ate = of the dried pears! Melissa ate . How Pieces did they eat in all? What fraction of the dried eat altogether? many pears did they 2. There were is children playing in the park. One third of the children went home. How many children stayed in the park?
Answers
Apologies, but your questions seem to have errors and incomplete information.
For the first question about Jessica and Melissa sharing 12 pieces of dried pears, it is unclear how much Jessica ate as the fraction is missing. Similarly, information about how many pears Melissa ate is also missing. To answer the question accurately, I need the missing information.
For the second question about the children playing in the park, you mentioned that one-third of the children returned home, but you didn't provide the total number of children initially in the park. Without that information, I cannot determine how many children stayed in the park.
Please provide complete and accurate information for a precise answer.
The price of chocolates increased from $12.99
per pound to $14.99 per pound. What is the
percent
increase? Round to the nearest tenth of
a percent.
Answers
Answer:
About 13.3 percent
To find the percent increase divide 12.99 by 14.99 and get .8666577 subtract one to find percent increase and get .13342228 turn into percent and round to the nearest tenths place and get - 13.3 percent.
Two households are saving money each month to go towards the shared costs of a vacation trip. One household has $700 saved and will continue saving $400 each month. The other household has $1,000 saved and will continue saving $300 each month.
Use the system of equations, where y represents total saved and x represents number of months, to answer the question.
y = 400x + 700
y = 300x + 1,000
At what point would the two lines intersect if graphed?
Answers
The two lines will intersect after 3 months.
How to explain the equationWe can set the two expressions for y equal to each other:
400x + 700 = 300x + 1,000
100x + 700 = 1,000
100x = 300
x = 3
So the two lines will intersect after 3 months. In this case, to find the corresponding value of y, we can substitute x = 3 into either of the equations:
y = 400x + 700
y = 400(3) + 700
y = 1,500
Therefore, the two lines will intersect after 3 months, at a point with coordinates (3, 1,500).
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• 6x – 15y = 15
y=2 x - 1
5
Answers
Answer:
Slope=
2.000
0.800
=0.400
x−intercept=
2 /5
=2.50000
y−intercept=
−5 /5
=
−1
1
=−1.00000
Step-by-step explanation:
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
6x - 15y - 15 = 3 • (2x - 5y - 5)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true
2.1 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve 2x-5y-5 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x-5y-5 = 0 and calculate its properties
AXYZ AMNL
X
XY =
33°
Y
LA
12
N
124°
N
8
M
Answers
Answer:
8
Step-by-step explanation:
You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.
Corresponding sidesSegment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.
Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.
XY = 8 units
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May someone please explain to me how these questions work? Thank you.
What is the sum of the following series of numbers?
1 + 2 + 3 + 4 + … + 498 + 499
Answers
This is an arithmetic sequence with a first term of 1, a common difference of 1, and a last term of 499. We can use the formula for the sum of an arithmetic series to find the sum of the numbers:
S = (n/2)(a1 + an)
where:
S = sum of the series
n = number of terms
a1 = first term
an = last term
Substituting the given values, we get:
S = (499/2)(1 + 499)
S = (249.5)(500)
S = 124,750
So the sum of the series 1 + 2 + 3 + 4 + ... + 498 + 499 is 124,750.
components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 87% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 26% of all defective components. what is the probability that the following occur?
Answers
The probability that a defective component will be detected only by the first inspector is 0.19
The probability that a defective component will be detected by exactly one of the two inspectors is 0.38
The probability that all three defective components in a batch escape detection by both inspectors is 0.
It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.
Therefore P(A)=P(B)=81%=0.81
At least one inspector does not detect a defect on 38% of all defective components.
Therefore, bar P(A∩B)=0.38
As we know:
bar P(A∩B)=1-P(A∩B)=0.38
P(A∩B)=1-0.38=0.62
A defective component will be detected only by the first inspector.
P(A∩barB)=P(A)-P(A∩B)
=0.81-0.62
P(A∩barB)=0.19
The probability that a defective component will be detected only by the first inspector is 0.19
Part (B) A defective component will be detected by exactly one of the two inspectors.
This can be written as: P(A∩barB)+P(barA∩B)
As we know:
P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)
Substitute the respective values we get:
P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)
=0.81+0.81-2(0.62)
=1.62-1.24
P(A∩ barB)+P(bar A∩B)=0.38
The probability that a defective component will be detected by exactly one of the two inspectors is 0.38
Part (C) All three defective components in a batch escape detection by both inspectors
This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)
As we know bar P(A∩B)=P(bar A∪ bar B)=0.38
From part (B): P(bar A∩B)+P(A∩bar B)=0.38
This can be written as:
P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0
The probability that all three defective components in a batch escape detection by both inspectors is 0
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Let A, B, C be three points with position vectors a, b, c respectively. You may assume that the three points A, B, C do not all lie on the same straight line. Let D, E, F be the midpoints of the line-segments BC, AC, AB respectively. What is the point with position vector 1/3 (a+b+c)?
Answers
The midpoint of three points with the position vector 1/3(a + b + c) is given by:
P = (b + c - B - C) / 2 + (1/3)(b + c)
The point with the position vector 1/3(a + b + c) is given by:
P = F - (2/3)D - (1/3)E + (1/3)(b + c)
To find the point with the position vector 1/3(a+b+c), we can use the fact that the position vector of a point that divides a line segment in a given ratio can be found by taking the weighted average of the position vectors of the endpoints.
Given that D, E, and F are the midpoints of line segments BC, AC, and AB, respectively, we know that:
D = (B + C) / 2
E = (A + C) / 2
F = (A + B) / 2
To find the point with the position vector 1/3(a+b+c), we can substitute a = 3F - 2D - E into the equation:
1/3(a + b + c) = 1/3((3F - 2D - E) + b + c)
Expanding the equation further:
1/3(a + b + c) = 1/3(3F - 2D - E + b + c)
= (F - (2/3)D - (1/3)E) + (1/3)(b + c)
Therefore, the point with the position vector 1/3(a + b + c) is given by:
P = F - (2/3)D - (1/3)E + (1/3)(b + c)
Substituting the midpoints:
P = (A + B) / 2 - (2/3)((B + C) / 2) - (1/3)((A + C) / 2) + (1/3)(b + c)
= (A + B - 2B - 2C - A - C + b + c) / 2 + (1/3)(b + c)
= (b + c - B - C) / 2 + (1/3)(b + c)
Therefore, the midpoint of three points with the position vector 1/3(a + b + c) is given by:
P = (b + c - B - C) / 2 + (1/3)(b + c)
The point with the position vector 1/3(a + b + c) is given by:
P = F - (2/3)D - (1/3)E + (1/3)(b + c)
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Fill in the missing values below one at a time to find the quotient when x^3 - x^2 - 3x + 2 is divided by x - 2.
Answers
Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.
To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:
Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²
Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.
Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.
Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.
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How do you write 100/100 as a percentage?
Answers
Answer:
100%
Step-by-step explanation:
100/100 is equal to 1
that means you got nothing wrong
Answer:
1%
Step-by-step explanation:
100/100=1 I'm totally probably incorrect
Alicia has 4 yards of ribbon.she needs 1/3 yard to make 1bow.how many bows can alicia make
Answers
Answer: 12 bows
Step-by-step explanation
12*1/3 yard = 4 yard
12 bows
Answer:
Let's break this down.
Step-by-step explanation:
4 yards of ribbons.
1/3 yard to break it down.
so 1/3x3=1
3 ribbons per 1 yards.
3x4(Number of yards of ribbons she owns)=
12 bows.