Absolute increase in population will be 2050
And percentage increase will be 56.94 %
We have given population in 2005 is 3600
And population in 2011 is 5650
So absolute increase in population = 5650-3600 = 2050
We have to find the percentage increase in population
So relative percentage increase in population will be 2050/3600 *100 = 56.94 %
So population will increase by 60 %
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decrease £16855.21 by 3.5% rounded to 2 dp
The lowered value will thus be £16265.28.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
Therefore, the decreased sum is: 16265.2777 = 16855.21 - (16855.21 3.5/100) = (16855.21 - 589.93235).
Next, we'll round the number to two decimal places: 16265.2777, 16265.278, and 16265.28
Hence, The lowered value will thus be £16265.28.
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One diagonal of a rhombus is decreasing at a rate of 777 centimeters per minute and the other diagonal of the rhombus is increasing at a rate of 101010 centimeters per minute. At a certain instant, the decreasing diagonal is 444 centimeters and the increasing diagonal is 666 centimeters. What is the rate of change of the area of the rhombus at that instant (in square centimeters per minute)?.
At that point, the area of the rhombus is changing at a rate of -1 cm²/min (measured in square centimeters per minute).
What is rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the form of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen. The graphic below illustrates some examples of rhombuses in everyday objects, like a diamond, a kite, an earring, etc.
Here,
The area of a rhombus is given in terms of its diagonal lengths x and y,
A = (1/2)xy
A' = (1/2)(x'y +xy')
A' = (1/2)((-7 cm/min)(6 cm) +(4 cm)(10 cm/min))
A' = (1/2)(-42 cm²/min +40 cm²/min)
A' = -1 cm²/min
The rate of change of the area of the rhombus at that instant (in square centimeters per minute) is -1 cm²/min.
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Madelyn is a high school basketball player. In a particular game, she made some free throws (worth one point each) and some two point shots. Madelyn made a total of 13 shots altogether and scored a total of 21 points. Determine the number of free throws Madelyn made and the number of two point shots she made.
The number of free throws = 5
The number of two point shots = 8
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of free throws be = x
Let the number of two point shots be = y
The total number of shots made by Madelyn is = 13
So , the equation is
x + y = 13 be equation (1)
The total number of points scored by Madelyn is = 21
So , the equation is
x + 2y = be equation (2)
On simplifying the equation , we get
Subtracting equation (1) from equation (2) , we get
2y - y = 8
y = 8
Therefore , the value of y is 8
And , The number of two points be = 8
Substituting the value for y in equation (1) , we get
x + y = 13
x + 8 = 13
Subtracting 8 on both sides of the equation , we get
x = 5
Therefore , the value of x is 5
And , the number of free throws is 5
Hence , The number of free throws = 5
The number of two point shots = 8
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Charlie went to purchase a new pair of
boots that were originally marked $89.
When he checked out they rang up $62.50.
What percent discount did Charlie
receive on the new boots?
30% was the discount recived
Morgan has an investment worth $13000 after 20 years if his original investment was for $15000 what must the interest rate have been
Answer:
8%
Step-by-step explanation:
pls mark brainliest
Answer : The interest rate have been 8 %
Step-by-step explanation :
First we have to calculate the simple interest.
As we know that:
Simple interest = Total amount - Principle
Simple interest = $130,000 - $50,000
Simple interest = $80,000
Now we have to calculate the interest rate.
Using simple interest formula:
where,
S.I = simple interest = $80,000
P = principle = $50,000
R = interest rate = ?
T = time = 20 years
Now put all the given values in the above formula, we get:
Therefore, the interest rate have been 8 %
Found answer from Alleei!
-7/8 is greater than or equal to m - 13/8
Answer:
Step-by-step explanation:
greater than
Answer: Greater than
describe the sampling distribution for the sample mean by naming the model and telling its mean and standard deviation.
Mean and standard deviation for the sample distribution is in the main body.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
sample Mean
Population mean =mu = ∑ xi /N
Mu represents pop mean
∑xi = the sum of all scores in the dataset
sample mean is the average score of a sample on a given variable and is represented by
x bar = ∑ xi /N
SE.M(Sample error of the Mean) is
=σ/√n
standard deviation is
σ = √∑(xi - υ)²/N
hence the formula for each of terms is as follows.
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Solve using substitution.
y = 6x + 2
y = 6x 10
Answer:
Step-by-step explanation:
1/27,20/9
The dimensions of a room with one window and one door are shown. Ivan wants to have the four walls painted. The painter says the area is 542.2 square feet.
PLEASE HELP ASAPPP!!! THX (multi-answer)
A reasonable estimation of the total area of the room to be painted is:
A. 2[(30+40) x 8] = 2(70 x 8) = 2 x 560 = 1,120 ft²E. [2(40) x 8] + [2(30) x 8] = 640 + 480 = 1,120 ft².What is an estimation?Estimation involves the approximation of values with number rounding.
Estimates make it easier to do some mathematical operations involving fractions or decimals.
What is the area?The area is the space occupied by a two-dimensional object.
The area is always the product of the length and width (height or depth).
Given the dimensions of the room:
Length of one side = 29¹/₂ ft
Height of the four sides = 8 ft
Length of the second side = 38³/₈ ft
Based on estimation, the dimensional values are approximated to:
Length of one side of the rectangular room = 30 ft
Height of the four sides = 8 ft
Length of the second side of the rectangular room = 40 ft
There are four walls for the room, and we can deduct the areas of the door and window, but these are not given, so we ignore them.
The area of the four walls can be computed as follows:
Area of two sides with same dimensions = 480 ft² [2(30 x 8)]
Area of two sides with same dimensions = 640ft² [2(40 x 8)]
Total area = 1,120 ft² (480 ft² + 640 ft²)
Thus, the options that satisfy the estimated area of the four walls of the room are Options A and E.
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the homework consists of 36 independent problems. if the time taken to answer each question is a random variable with mean 6 minutes and a standard deviation 3 minutes. suppose we want to find the probability that all 36 problems in the homework will be completed in less than 180 minutes. which of the following is incorrect?
the probability that all 36 problems in the homework will be completed in less than 180 minutes
P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)
given that
there are 36 independent problems
mean(μ) = 6minutes
standard deviation(σ) = 3 minutes
sample standard deviation = σ/[tex]\sqrt{n}[/tex]
= 3/[tex]\sqrt{36}[/tex]
=3/6
=0.5
the sample mean x of 36 questions answering time approximately follows a normal distribution with mean 6 minutes and sample standard deviation is 0.5 minutes
now we need to find the probability that all 36 problems in the homework will be completed in less than 180 minutes
P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)
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y=-7x-1
Can you help me please, I need to graph it
thank you in advance
Answer:
The dots shown in the graph are the answers.
Step-by-step explanation:
Answer: (-0.25, .75)
If f(x)=x/3 and g(x)=6x+9 which is equal to f(g(x))
Answer:
f(g(x)) = 2x + 3
Step-by-step explanation:
f(g(x)) is called a composite function
To compute f(g(x)) simply substitute whatever g(x) definition is wherever there is an x in f(x)
We have [tex]g(x) = 6x + 9[/tex]
[tex]f(x) = \dfrac{x}{ 3}[/tex]
So instead of x just use 6x + 9 to get
[tex]f(g(x)) = \dfrac{6x+9}{3} = 2x + 3[/tex]
Tim answered all the questions on the math test but got 10 wrong answers. He got 4 points for each correct answer, there were no penalty points for incorrect answers. His score was 76 points.
Write an equation to find the total number of questions (q) on Tim's math test
The equation to find the total number of questions (q) on Tim's math test is 76 = 4x + 0
How to write and solve equation?Number of wrong questions = 10
Points received for right question = 4 points
Points received for wrong question = 0 points
Total of Tim's score = 76%
Let
the number of questions right answered by Tim be x.
Total points gained by Tim for the right answer = number of questions right answered x Points received for a right answer
= x × 4
= 4x
Points gained by Tim for the wrong answer = number of questions wrong answered x Points received for a wrong answer
= 10 × 0
= 0
Total points scored by Tim = Points gained for the right answer + Points gained for the wrong answer
76 = 4x + 0
76 = 4x
divide both sides by 4
x = 76/4
x = 19
Hence, the number of question answered right by Tim are 19.
Total number of questions attempted by Tim
Total number of questions attempted by Tim
= number of questions answered right +number of questions answered Wrong
= 19 + 10
= 29
Hence, the total number of questions attempted by Tim is 29.
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students at a high school are asked to evaluate their experience in the class at the end of each school year. the courses are evaluated on a 1-4 scale – with 4 being the best experience possible. in the history department, the courses typically are evaluated at 10% 1's, 15% 2's, 34% 3's, and 41% 4's. mr. goodman sets a goal to outscore these numbers. at the end of the year he takes a random sample of his evaluations and finds 10 1's, 13 2's, 48 3's, and 52 4's. at the 0.05 level of significance, can mr. goodman claim that his evaluations are significantly different than the history department's?
No , as we fail to reject the null hypothesis Mr. Goodman claim that his evaluations are significantly different than the history department's.
What is null hypothesis?
Statistics is the study of research and surveys on numerical data in mathematics. In order to conduct surveys, the hypothesis must be established. There are typically two different kinds of hypotheses. A null hypothesis is one that holds true, whereas an alternate hypothesis is another.The null hypothesis is a broad assertion or default stance that there is zero happening or nothing happening in probability and statistics. For instance, there is no relationship between two measured occurrences or a connection between groups. Unless additional evidence has been presented to refute the theory, it is generally accepted that it is true in this context.Test statistic X2 =1.9196
p value =0.5893
No , as we fail to reject the null hypothesis Mr.Goodman claim that his evaluations are significantly different than the history department.
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HELP PLEASE In MNO, M≈ O, NO = 10 and OM= 8. Find MN.
In the given triangle MNO, the length of MN is 10
Calculating the length of a side in a triangleFrom the question, we are to determine the length of the unknown side in the triangle
The side is MN
From the given information, we have that
In ΔMNO,
∠M ≅ ∠O
Thus,
ΔMNO is an isosceles triangle
Since angle M is congruent to angle O, the sides facing the two angles will also be congruent.
That is,
NO ≅ MN
From the given information,
NO = 10
Therefore,
MN = 10
Hence, the length of MN is 10
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lacy draws a '10' from a standard deck of 52 cards. without replacing the first card, she then proceeds to draw a second card and gets a '4'. are these events independent? input yes or no
Determine the probability of drawing a spade and then a club without replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
The first two events are not independent, with a probability P = 0.00603
The second pair of events is independent, and the probability is P = 0.0625
First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.
A) Now, if Lacy first draws a spade card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.
The probability of drawing a 10 card at first is:
P = 4/52 (because there are 4 10's and a total of 52 cards).
The probability of drawing a 4's after is:
Q = (4/51)
The joint probability is the product of the individual probabilities, this will give: p = P*Q = (4/52)*(4/51) = 0.00603
B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).
The probability of drawing a spade is:
P = 13/52
Now we replace the spade card drawn.
The probability of drawing a club will be:
Q = 13/52
The joint probability is:
p = P×Q = (13/52)² = 0.0625
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in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees. find the length of w, to the nearest centimeter
The length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
Using cos law:
W = √(41² + 17² - 2×41×17 cos 134)
After solving:
W = 54.20 cm
Thus, the length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
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Find the value of x in the following equation:
2.5(5x + 2) = 12.5x + 5
A: x = 0
B: x = 1.5
C: No solution
D: Infinite solutions
[tex] \Large{\boxed{\sf Option \ D) \ \ Infinite \ solutions }} [/tex]
[tex] \\ [/tex]
Explanation:We will solve this equation by isolating x.
[tex] \\ [/tex]
Given equation:
[tex] \sf 2.5(5x + 2) = 12.5x + 5 [/tex]
[tex] \\ [/tex]
Expand the left side of the equation using the following distributive property:
[tex] \blue{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \green { \boxed{ \sf Distributive \: property \text{:}}} \\ \\ \sf A(B + C) = AB + BC \\ \end{array}}\\\end{gathered} \end{gathered}} [/tex]
[tex] \\ [/tex]
[tex] \sf \overbrace{\sf 2.5}^{A} (\underbrace{\sf 5x}_{B} + \overbrace{\sf 2}^{C}) = 12.5x + 5 \\ \\ \sf 2.5 \times 5x + 2.5 \times 2 = 12.5x + 5 \\ \\ \sf 12.5x + 5 = 12.5x + 5 [/tex]
[tex] \\ [/tex]
Now, subtract 5 from both sides of the equation:
[tex] \sf 12.5x +5 - 5 = 12.5x + 5 - 5 \\ \\ \sf 12.5x = 12.5x [/tex]
[tex] \\ [/tex]
Finally, divide both sides of the equation by 12.5:
[tex] \sf \dfrac{12.5x}{12.5} = \dfrac{12.5x}{12.5} \\ \\ \\ \boxed{\boxed{\sf x = x}} [/tex]
[tex] \\ [/tex]
Since any value is equal to itself, the equation has infinite solutions.
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
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Complete the following (use the straight-line method): Auto: $40,000 Residual: $4,000 Estimated life: 5 years Year Cost Depreciation Accumulated Book Expense Depreciation Value
After 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
Given,
Cost of auto =$40,000
Residual value =$4000
Estimated lifetime =5 years
Straight-line Method:-
Depreciation cost can be calculated by formula,
[tex]Depreciation=\frac{cost\ of\ assest-residual}{estimated\ lifetime}[/tex]
It is constant for every year.
Accumulated depreciation can be calculated by formula,
[tex]Accumulation\ Depreciation=\frac{cost\ of\ assets-residual}{estimated\ lifetime}*Number\ of\ years[/tex]
Book value at start of year is nothing the cost of asset at that year and Book value at end of year is difference between cost of asset at that year and depreciation cost.
Using the above formulas all the values for each year is caculated and formed into a table.
Year BookValue DepreciationCost Accumulation Book Value
Start End
1 $40,000 $7,200.00 $7,200 $32,800
2 $32,800 $7,200.00 $14,400 $25,600
3 $25,600 $7,200.00 $21,600 $18,400
4 $18,400 $7,200.00 $28,800 $11,200
5 $11,200 $7,200.00 $36,000 $4,000
Thus, after 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
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sampling on campus. you see a woman student standing in front of the student center, now and then stopping other students to ask them questions. she says that she is collecting student opinions for a class assignment. explain why this sampling method is almost certainly biased.
Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.
What do you mean by sampling?
Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.
According to the question,
A true sampling would be a mixed demographic group. A sampling from several like areas:
e.g. infront of the student store, infront of the regular store, infront if a food pantry, infront of ... or even better do a blind survey.
Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.
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type 1500 words in 30 minutes __ words per minute
Answer:
50
Step-by-step explanation:
1500/30=50
Answer:
50 words per minute
brainliest plss
PLEASE HELP
The variable y varies jointly with x and w when y = -42, x = 2, and w = -3.
1.) Find the constant of variation.
k =
2.) Find w when y = 3 and x = 1/14
w =
Answer:
1). The constant of variation is 7
2). w = 6 for the given values of x and y
Step-by-step explanation:
"Varies jointly" tells us that y is a direct result of a mathematic operation involving x and w. We will assume y is directly prorportional to x and w, in the sense that we can find a multiplicative relationship of the form y=Kxw, where K is the constant of variation.
We are given one data point: y=-42 where x is 2 and w is -3. Let's put those values into our trrial expression:
y=Kxw
-42=K(2)(-3)
-42 = -6K
K = 7
The expression becames y = 7xwThe constant of variation is 7.
The value of w for y=3 and x=(1/14) would be:
y=7xw
3 = 7*(1/14)*w
3 = (1/2)*w
w = 6Answer:
1) k = 7
2) w = 6
Step-by-step explanation:
Joint variation equation
If y varies jointly with x and w:
[tex]\boxed{y \propto xw \implies y=kxw}[/tex]
for some constant k.
Given:
y = -42x = 2w = -3Substitute the given values into the joint variation equation and solve for k:
[tex]\begin{aligned}y&=kxw\\\implies -42&=k \cdot 2 \cdot -3\\-42&=-6k\\k&=\dfrac{-42}{-6}\\k&=7\end{aligned}[/tex]
Therefore, the equation is:
[tex]\boxed{y=7xw}[/tex]
To find w when y = 3 and x = 1/14, substitute these values into the found equation and solve for w:
[tex]\begin{aligned}y&=7xw\\\implies 3&=7 \cdot \dfrac{1}{14} \cdot w\\3&=\dfrac{7}{14} \cdot w\\42&=7w\\w&=6\end{aligned}[/tex]
Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total. How many cows and how many chickens are on the farm?
a. Explain what 120 represents, and how it relates to the cows and chickens.
b. Explain what 48 represents, and how it relates to the cows and chickens.
c. Setup a system, of two equations, to help you solve this riddle.
d. Solve this system using either Elimination or Substitution, show your work, and state your answer as a complete sentence.
Answer:
a. 120 represents the total number of cow legs and chicken legs
b. 48 represents the total number of cow heads and chicken heads
c. System:
Let x = number of cows
Let y = number of chickens
1. 2x + 4y = 120
2. x + y = 48
d. I am going to use substitution for this problem
Step 1: Solve for y in the equation x + y = 48
1. x + y = 48 → y = -x + 48
Step 2: Substitute -x + 48 for y in 2x + 4y = 120
2. 2x + 4(-x + 48) = 120
Step 3: Solve for x
3. 2x - 4x + 184 = 120 → -2x + 184 = 120 → -2x = -64 → x = 32
Step 4: Sustitute 32 for x in x + y = 48
4. (32) + y = 48
Step 5: Solve for y
5. y = 16
Number of chickens on the farm (y) = 16
Number of cows on the farm (x) = 32
Step-by-step explanation:
All of it is above :)
water is pouring at a constant rate into a tank that is a 4-foot-high rectangular solid. if the warer was turned on at 11:00 and if at 11:25 the depth of the water in the tank was 4 inches, at what time was the pool full
The time at which the pool was full is 4:00 when the water is in the 4 inches tank .
What is multiplication?In mathematics, multiplication is one of the four basic arithmetic operations. It represents the basic idea of repeated addition of the same number.
Equating the time when pool be full :The height of the tank is 4 feet water pouring is turned on at 11:00 at 11:25 the depth of the water in the tank is 4 inches.
which means,
To fill 4 inches it takes = 25 min
To fill 1 inch it takes = 25/4 min 4 feet = 4×2.54 = 48 inches
To fill 48 inches it takes = 48 × 25/4
= 300 min
= 5 hours
So, 5 hours after 11:00 will be 4:00
Hence, the time at which the pool was full is 4:00
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A perfect square has length n if its last n digits (in base 10) are the same and non-zero. What is the longest possible length? What is the smallest square achieving this length?
The longest possible length is 3
The smallest square achieving this length : 38² = 1444.
Square:
A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. The complete length of a square's boundary is its perimeter. As a result, the length of each side can be added to determine the square's perimeter. Since a square has four sides, its perimeter may be calculated by adding all four of its sides. The space a square takes up is its area.
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a ship is off course. if the ship is traveling at 11 miles per hour, how far off course will it be after 3 hours?
Ship travels 33miles in 3 hours.
What is distance?
Distance is the actual distance that a body travels. Additionally known as path length. For instance, the path length for an item going from point O to point P will be distance OP = 360 m. It is a scalar quantity, the distance. It lacks direction and just possesses magnitude.
Ship travels in one hour = 11miles
Therefore, Ship travels in 3 hours = 11×3
= 33miles
Hence, Ship travels 33 miles in 3 hours.
*SHIP OFF COURSE IS NOT GIVEN IN THE QUESTION.
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3x+12=-5x+28 necesito ayuda para mi examen please
Answer:
x = 2
Step-by-step explanation:
3x + 12 = -5x + 28
3x + 12+ 5x = -5x + 28 + 5x
8x + 12 = 28
8x + 12 - 12 = 28 - 12
8x = 16
8x/8 = 16/8
x = 2
to log on to a certain computer account, the user must type in a -letter password. in such a password, no letter may be repeated, and only the lower case of a letter may be used. how many such -letter passwords are possible? (there are letters in the alphabet.)
There are 358,800 different ways that a 4-letter password might be used.
Explain the term permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.For the stated question-
To make a four-letter password with no repeating letters and just lowercase letters;Every letter from A -Z (or 26) can be used as the initial letter for the computer account.Apart from the first letter again for second letter, we can select any letter between A and Z.Whatever letter from A to Z is available for selection, with the exception of the first and second letters again for third letter.For the fourth letter, we might select any letter between A and Z besides the first, second, and third letters.
SO;
Number of possible combinations for 4-letter passwords
= 26 × 25 × 24 × 23
= 358,800
Thus, there are 358,800 different ways that a 4-letter password might be used.
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The complete question is-
To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible.
Plot the points (6, 4) and (3, 2) and find the slope.
Answer:
Slope is 2/3.
Step-by-step explanation:
I can't help you plot the points, but the slope formula is y2-y1/x2-x1.
2-4/3-6. -2/-3. This simplifies to 2/3.
Find the determinant of the following matrix A by *only* using the 3 basic properties in Treil section 3 paragraph 3.1 (page 79), the determinant formula for triangular and diagonal matrices, and row or column operations. Explain your work. A= (1 0 2 0 3 0 1 2 3 4 1 0 3 0 5
0 0 0 2 4
1 0 3 0 8)
We must first transform matrix A into a triangular or diagonal matrix in order to determine its determinant.
Using the row operations to change the matrix, having three rows and five columns, in a triangular matrix, having three rows and three columns.
combining the first and second rows, then the first and third rows:
(1 0 2 0 3 0 1 2 3 4 1 0 3 0 5 (1 0 0 2 4 (1 0 3 0 8 (3 0 5 2 11
0 0 0 2 4 + 0 0 0 2 4) + 1 0 3 0 8) = 0 0 0 2 4
1 0 3 0 8) 2 0 6 0 16)
subtracting the second and third rows from the first row
We get a triangular matrix
(3 0 5 2 11 (0 0 0 2 4 (2 0 6 0 16 (1 0 5 0 3
0 0 0 2 4 - 0 0 0 2 4) - 2 0 6 0 16) = 0 0 0 2 4
2 0 6 0 16) 0 0 0 0 0)
Now that the matrix is triangular, we can use the determinant formula for triangular matrices, which states that the determinant of a triangular matrix is equal to the product of the diagonal elements. The diagonal elements of matrix A are 1, 0, and 0, so the determinant of matrix A is 0.
Therefore, the determinant of matrix A is 0, and we can find it by only using the three basic properties in Treil section the determinant formula for triangular and diagonal matrices, and row or column operations.
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