The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph of the function.
Initially, as xxx increases, yyy
.
The slope of the graph is equal to
for all xxx between x=0x=0x, equals, 0 and x=3x=3x, equals, 3.
Starting at x=3x=3x, equals, 3, the function value yyy
as xxx increases.
The slope of the graph is equal to
for xxx between x=3x=3x, equals, 3 and x=5x=5x, equals, 5.
For xxx between x=0x=0x, equals, 0 and x=4x=4x, equals, 4, the function value yyy
000.
For xxx between x=4x=4x, equals, 4 and x=8x=8x, equals, 8, the function value yyy
000.
Answers
Related Questions
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
Answers
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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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.
Answers
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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A high school. Asket ball team is selling 10$ dollar raffle tickets as part of a fund raising program the first prize is a trip to the bahamas find the average amount per game
Answers
The Expected Value to the player for one play of the game is - 7.784.
Define Expected Value.In probability theory, the weighted average is expanded upon by the expected value. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the anticipated value.
Price of raffle ticket= $10
First price= $5460
Second prize= $496
Remaining 18 prize= $100
$0 for the remaining tickets= 3500-20=3480 tickets
When winning the 1st prize, the winnings = $5460−$10=$5450.
When winning the 2nd prize, the profit= $496−$10=$486.
When winning the other 18 prizes, the profit= $100−$10=$90.
When there is no winning, the loss= $0
The probability is calculated by dividing the number of likely outcomes by the total number of outcomes:
P(X=5450)= 1/3500
P(X= 486)= 1/3500
P(X= 90)= 18/3500
P(X= -10)= 3480/3500
The product of each alternative and its probability equals the expected value, which is added up:
E(X)= ∑ xP(x)
= 5450 * [tex]\frac{1}{3500}[/tex] + 486 * [tex]\frac{1}{3500}[/tex] + 90 * [tex]\frac{18}{3500}[/tex] + (-10) * [tex]\frac{3480}{3500}[/tex]
= [tex]\frac{-27224}{3500}[/tex]
= - 7.784
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Solve using substitution.
y = 6x + 2
y = 6x 10
Answers
Answer:
Step-by-step explanation:
1/27,20/9
HELP PLEASE In MNO, M≈ O, NO = 10 and OM= 8. Find MN.
Answers
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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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.)
Answers
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.
Morgan has an investment worth $13000 after 20 years if his original investment was for $15000 what must the interest rate have been
Answers
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!
describe the sampling distribution for the sample mean by naming the model and telling its mean and standard deviation.
Answers
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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y=-7x-1
Can you help me please, I need to graph it
thank you in advance
Answers
Answer:
The dots shown in the graph are the answers.
Step-by-step explanation:
Answer: (-0.25, .75)
automobile repair costs continue to rise with the average cost now at $367 per repair.† assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. answer the following questions about the cost of automobile repairs. what is the probability that the cost will be between $250 and $470?
Answers
The probability that the cost will be between $250 and $470 is 0.7354.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
Automobile repair costs continue to rise with the average cost now at $367 per repair.†
Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88.
We have to find the probability that the cost will be between $250 and $470.
P( 250 < x < 470 ) = P( x <470 ) - P( x < 250 )
P( x < 470 ) = NORMDIST( 470 , 367, 88, 1 ) = 0.8272
P( x < 250 ) = NORMDIST( 250 , 367, 88, 1 ) = 0.09183
P( 250 < x < 470 ) = 0.8272 - 0.09183 = 0.7354
P( 250 < x < 470 ) = 0.7354
Hence, the probability that the cost will be between $250 and $470 is 0.7354.
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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?
Answers
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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need help quickly its due in 30
Answers
Answer: Alternate exterior angles --> 1,8 and 2,7
Vertical angles --> 2,3 and 5,8
Corresponding angles --> 1,5 and 2,6
Alternate interior angles --> 3,6 and 4,5
a jury pool consists of 30 people, 16 men and 14 women. compute the probability that a randomly selected jury of 12 people is all male.
Answers
The probability that a randomly selected jury of 12 people is all male is 2.01 × 10⁻⁵ .
In the question ,
it is given that ,
total number of people in the jury pool is 30 people ,
the total number of men in the jury pool is = 16 ,
total number of women in the jury pool is = 14 ,
So , 12 members can be selected from 30 people in ³⁰C₁₂ ways ,
So , total number of ways = ³⁰C₁₂ = 86493225 ways
and 12 male can be selected from 16 men in ¹⁶C₁₂ ways
= ¹⁶C₁₂ = 1820.
So , the probability of selecting 12 men is = 1820/86493225
= 0.00002104211
≈ 2.01 × 10⁻⁵
Therefore , the required probability is 2.01 × 10⁻⁵ .
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type 1500 words in 30 minutes __ words per minute
Answers
Answer:
50
Step-by-step explanation:
1500/30=50
Answer:
50 words per minute
brainliest plss
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?
Answers
30% was the discount recived
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)
Answers
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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decrease £16855.21 by 3.5% rounded to 2 dp
Answers
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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#3 Mia has $50 on a gift card to her favorite *
coffee shop. Each time she visits the coffee
shop she spends $3.75 on her favorite drink.
Write an equation to represent the relationship
between n, the number of times she visits the
coffee shop, and b, the total balance on her
gift card
Answers
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.
Answers
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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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?
Answers
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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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
Answers
[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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Plot the points (6, 4) and (3, 2) and find the slope.
Answers
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.
A rectangular pan has a length that is the width. The total area of the pan is 432 in. 2. What is the width of the cake pan?.
Answers
Using the area formula, we know that the width of the pan is 18 inches.
What is the area?An area is a unit of measurement used to describe a region's size on a flat or curved surface.
While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.
So, the width of the pan will be:
We know that:
The length of a rectangular pan is exactly 4/3 the width.
The pan's total surface area is 432in².
Formula: Area = 432 = length*width = w*4w/3
Now, calculate the width as follows:
Formula: Area = 432 = length*width = w*4w/3
4w^2/3 = 432
w^2 = 432*3/4 = 324
w = 18
Therefore, using the area formula, we know that the width of the pan is 18 inches.
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Complete question:
A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.2. What is the width of the cake pan
Answer: B. 18 in
Step-by-step explanation:
You will get this answer using the Area formula, which is A-lw
If f(x)=x/3 and g(x)=6x+9 which is equal to f(g(x))
Answers
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]
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.
Answers
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 :)
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
Answers
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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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)
Answers
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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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 =
Answers
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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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)?.
Answers
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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let x represent the sum of the first 25 positive odd integers. let $y$ represent the sum of the next 25 positive odd integers. what is the value of y-x?
Answers
By using the concept of arithmetic series, it can be calculated that
y - x = 1250
What is arithmetic series?
Arithmetic series are those series whose difference between two consecutive terms are same.
The odd integers forms an arithmetic series
For the sum of first 25 odd integer
First odd integer = 1
25th odd integer = 49
Sum of first 25 odd integers = [tex]\frac{25}{2}(1 + 49)[/tex] = 625
x = 625
For the sum of first 50 odd integers
First odd integer = 1
50th odd integer = 99
Sum of first 50 odd integers = [tex]\frac{50}{2}(1 + 99)[/tex] = 2500
Sum of next 25 odd integers = 2500 - 625 = 1875
y = 1875
y - x = 1875 - 625 = 1250
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