The function f(x,y) has only minimum value at (1,0) is -1 and maximum value does not exist.
The given function is f(x,y)=x²+y²-2x
First find the partial derivative with respect to x and y
f'(x)=2x-2
f'(y)=2y
f'(x)=0=f'(y)
2x-2=0
x=1
and y=0
Now we will cheak maxima and minima at (1,0)
f''(x,y)=2 and f"(x,y)=2 and f"(x,y)=0( derivative of first order of x with respect to y)
We know that
rt-s²≥0 and r positive then f is minimum and r negative maximum
r=2 , t=2 and s=0
rt-s²≥0 and r is positive so f(x,y) is minimum at (1,0)
f(1,0)=1-2=-1
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12. Reason A data set is represented by the box plot shown. Between which two values would the middle 50% of the data be found? Explain.
The middle 50% data of the boxplot will be calculated between the value of 7 to 14.
Explain about the box plot?The variation in information is shown using a boxplot, which is a standardized method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum"). It can reveal information about your outliers' values. Boxplots can also show you exactly securely your data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.The data set ranges are:
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Divide the given data in 4 quartiles Qs;
Q1 = 4 - 6
Q2 = 7 - 10
Q3 = 11 - 14
Q4 = 15 - 17
Thus, 50% data will be lying in Q2 and Q3.
Range - 7 - 14
Thus, the middle 50% data of the box plot will be calculated between the value of 7 to 14.
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Twelve of the workers received the following salaries: three of them earn P12,500 a month, four of them earn P11,000; twoearn P10,500 and the rest earn P9,000 a month. What is the median salary of the workers?
The median salary of the workers is P11,000.
What is median?In statistics, the median is a measure of central tendency that represents the middle value of a data set when the data set is ordered from least to greatest (or vice versa). If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. The median is used as a measure of central tendency when the data set has outliers or is not normally distributed.
How to calculate median?To calculate the median of a set of numbers:
Put the numbers in order from lowest to highest.If the number of items in the list is odd, the median is the middle number. For example, if the list is 3, 5, 7, 9, 11, the median is 7.If the number of items in the list is even, the median is the average of the two middle numbers. For example, if the list is 4, 6, 8, 10, the median is (6 + 8)/2 = 7.In the given question,
To find the median salary of the workers, we need to arrange the salaries in order from lowest to highest.
The salaries are:
P9,000, P9,000, P10,500, P10,500, P11,000, P11,000, P11,000, P11,000, P12,500, P12,500, P12,500, P12,500
There are 12 workers, so the median salary will be the average of the 6th and 7th salaries when arranged in order.
Median salary = (P11,000 + P11,000)/2
= P11,000
Therefore, the median salary of the workers is P11,000.
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Question 8 (2 points)
A survey asked 1,000 people if they invested in Stocks or Bonds for retirement. 700
said they invested in stocks, 400 said bonds, and 300 said both.
How many invested in just stocks?
Note: consider making a Venn Diagram to help solve this problem.
700
300
400
none
300 is the correct answer.
12. If zo 125°, what does zz equal in this figure?
A. 125°
B. 180°
C. 35°
D. 55°
Answer:
A
Step-by-step explanation:
∠ o and ∠ z are alternate exterior angles and are congruent, that is
∠ z = ∠ o = 125°
Cant figure out the surface area
Answer:
[tex]96 \: {m}^{2} [/tex]
The correct answer is B
Step-by-step explanation:
First, we have to find the area of one side of the cube:
[tex]a(side) = 4 \times 4 = 16[/tex]
Now multiply this number by 6 (since the cube has 6 sides in total):
[tex]a(surface) = 16 \times 6 = 96[/tex]
Answer: B - 96 sq m
Step-by-step explanation:
The surface area is the area of all the squares added up. To find the area of one square, you multiply 4 x 4, which equals 16. Then, count the number of sides on the cube. There are 6 sides on this cube. So, you multiply 16 x 6. 96 is your total. And you can eliminate C because it says meters instead of square meters.
(√3 + √3)²=
F) 12
G) 9
H) 6
J) 3
K) None of these
Answer:
F) 12
Step-by-step explanation:
To answer, we use the perfect square formula:
(a + b)² = a² + 2ab + b²
(√3 + √3)² = (√3)² + 2(√3)(√3) + (√3)²
Simplify:
√3² = 3
2(√3)(√3) = 2 x (√3)² = 2 x 3 = 6
Plug in:
(√3 + √3)² = 3 + 6 + 3 = 12
If 107 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $3.5 and total receipts for the concert was $391.25, how many of each went to the concert?
Answer:
Step-by-step explanation:
Let's assume that 'a' adults and 'c' children attended the concert.
From the problem statement, we know that:
a + c = 107 ---(1) (The total number of people who attended the concert is 107)
3.75a + 3.5c = 391.25 ---(2) (The total revenue generated from the concert is $391.25)
Now, we need to solve these two simultaneous equations to find the values of 'a' and 'c'.
To do this, we can use the elimination method to solve these equations.
First, we will multiply equation (1) by 3.5 to eliminate 'c':
3.5a + 3.5c = 374.5 ---(3)
Next, we will subtract equation (3) from equation (2):
3.75a + 3.5c - (3.5a + 3.5c) = 391.25 - 374.5
0.25a = 16.75
a = 67
Now that we know the value of 'a', we can substitute it into either equation (1) or (2) to find the value of 'c':
a + c = 107
67 + c = 107
c = 40
Therefore, there were 67 adults and 40 children at the concert.
PLEASE PLEASE HELP
The vertices of quadrilateral LMNP are L(-1 , 7), M(4,9), N(8, -1), and P(3,-3). Using the distance formula, determine the most precise classification of LMNP.
So, the most precise classification of quadrilateral LMNP is a kite.
What is equation?In mathematics, an equation is a statement that two mathematical expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in many areas of mathematics, science, and engineering to model relationships between quantities and to solve problems.
Here,
To classify the quadrilateral LMNP, we need to calculate the length of all four sides using the distance formula and then use those values to determine the shape of the quadrilateral.
The distance formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Using this formula, we can calculate the length of each side of the quadrilateral as follows:
LM = √[(4 - (-1))² + (9 - 7)²] = √[5² + 2²] = √29
MN = √[(8 - 4)² + (-1 - 9)²] = √[4² + (-10)²] = √116
NP = √[(3 - 8)² + (-3 - (-1))²] = √[(-5)² + (-2)²] = √29
PL = √[(-1 - 3)² + (7 - (-3))²] = √[(-4)² + 10²] = √116
Now, we can use the values we have calculated to determine the shape of the quadrilateral. We can see that LM = NP and MN = PL, which means that opposite sides are congruent. Also, LM and MN are not equal to PL and NP, which means that opposite sides are not parallel. Therefore, LMNP is a kite.
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find surface area of cilinder with the radius of 9 and height of 14. make sure to put the correct exponents with answer.
The surface area is 1305. 96 square units
How to determine the surface areaIt is important to note that the formula for calculating the surface area of a cylinder is expressed with the equation;
SA = 2πrh + 2πr²
Given that the parameters are;
SA represents the surface area.r represents the radius of the cylinderh represents the height of the cylinderπ takes the value of 3.14Now, substitute the values, we have;
Surface area = 2 × 3.14 × 9 ×14 + 2 × 3.14 × 9²
Multiply the values
Surface area = 791. 28 + 508. 68
add the values
Surface area = 1305. 96 square units
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g (40 points) suppose that x follows a binomial(n,p) distribution. assume that x1 , . . . , xn is a random sample of size n from this distribution.
The MLE of σ^2 for a random sample X1, X2, ..., Xn from a normal distribution with known mean μ is s^2/(n-1), and the MLE of σ is the square root of s^2.
Given a random sample X1, X2, ..., Xn from a normal distribution with mean μ and unknown variance σ^2, the likelihood function is:
L(σ^2) = (1/(2πσ^2)^(n/2)) * exp[-(1/(2σ^2)) * ∑(Xi - μ)^2]
To find the maximum likelihood estimator (MLE) of σ^2, we need to find the value of σ^2 that maximizes the likelihood function.
To do this, we take the natural logarithm of the likelihood function, since the logarithm is a monotonically increasing function and thus does not change the location of the maximum:
ln L(σ^2) = (-n/2) ln(2πσ^2) - (1/(2σ^2)) * ∑(Xi - μ)^2
To maximize this expression, we take the derivative with respect to σ^2 and set it equal to zero:
d/d(σ^2) ln L(σ^2) = (-n/2σ^2) + (1/(2(σ^2)^2)) * ∑(Xi - μ)^2 = 0
Solving for σ^2, we get:
σ^2 = (∑(Xi - μ)^2) / n
This means that the MLE of σ^2 is the sample variance, s^2 = (∑(Xi - μ)^2) / (n-1), since we usually use the sample variance to estimate the population variance when the population mean is known.
Therefore, the MLE of σ is the square root of the sample variance:
σ(hat) = sqrt(s^2)
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____the given question is incomplete, the complete question is given below:
Suppose that X1, . . . , Xn form a random sample from a Normal distribution for which mean μ is known, but the variance σ
2
is unknown. Find the MLE (maximum likelihood estimation) of σ.
8. for each of the given sample data sets below, calculate the mean, variance, and standard deviation. (a) 79, 52, 64, 99, 75, 48, 52, 24, 76 mean
The value for mean, variance, and standard deviation for the given set of data is 63.22, 794.04, and 28.17, respectively.
The method to calculate the various operations are:
Mean:
= (79 + 52 + 64 + 99 + 75 + 48 + 52 + 24 + 76) / 9 = 63.22
Mean is a measure of central tendency found by adding all the observations and dividing the result by the number of frequency or the total number of data set values.
Variance:
= ((79 - 63.22)² + (52 - 63.22)² + (64 - 63.22)² + (99 - 63.22)² + (75 - 63.22)² + (48 - 63.22)² + (52 - 63.22)² + (24 - 63.22)² + (76 - 63.22)² / (9-1) = 794.04
(Here, 63.22 is the mean calculated earlier)
Standard deviation:
= √(Variance)
=√(794.04) = 28.17
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Complete question is:
For each of the given sample data sets below, calculate the mean, variance, and standard deviation. (a) 79, 52, 64, 99, 75, 48, 52, 24, 76 mean =_______
variance = __________
standard deviation =_________
What is the maximum number of students to whom 48 apples, 60 bananas and and 96 guavas can be distributed equally? Also find the shares of each fruit.
Answer:
The maximum number of students to whom 48 apples, 60 bananas, and 96 guavas can be distributed equally is 20. Each student will receive 2 apples, 3 bananas, and 4 guavas.
please indicate which is the best answer to complete the figure bellow
Answer:
B
Step-by-step explanation:
The pattern is white black white. This eliminates options A and D
We then look at the patterns of the shapes. We can eliminate option F from this. Now, all we have left are options B and E. We see that the middle shape pattern is 3 of each. So, we have 3 stars, 3 diamonds, and 3 squares. This leaves the only option of B left.
The Student body of a large university consists of 30% Business majors. A random sample of 20 students is selected.
a. What is the probability that among the students in the sample at least 10 are Business majors?
b. What is the probability that at least 16 are not Business majors?
c. What is the probability that exactly 10 are Business majors?
d. What is the probability that exactly 12 are not Business majors? Show work please so I understand
The probability that at least 10 students in a random sample of 20 are Business majors is 0.139. The probability that at least 16 students in the sample are not Business majors is 0.147.
a. To find the probability that at least 10 students in a random sample of 20 are Business majors, we can use the binomial distribution with parameters n = 20 and p = 0.3 (the probability of success, i.e. being a Business major). Using a calculator or software, we can find this probability as:
P(X >= 10) = 1 - P(X < 10) = 1 - binomcdf(20, 0.3, 9) = 0.139
b. To find the probability that at least 16 students in the sample are not Business majors, we can use the same approach, but with q = 0.7 (the probability of failure, i.e. not being a Business major):
P(X >= 16) = 1 - P(X < 16) = 1 - binomcdf(20, 0.7, 15) = 0.147
c. To find the probability that exactly 10 students in the sample are Business majors, we can use the binomial probability formula:
P(X = 10) = (20 choose 10) * (0.3)^10 * (0.7)^10 = 0.201
d. To find the probability that exactly 12 students in the sample are not Business majors, we can use a similar formula:
P(X = 12) = (20 choose 12) * (0.7)^12 * (0.3)^8 = 0.200
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You need 1 1/4 cups of sugar to make cookies. To make 16 cookies you will need how many cups
of sugar
If you need 1 1/4 cups of sugar to make cookies, that is the amount of sugar needed for one batch of cookies. To find out how much sugar is needed to make 16 cookies, we can set up a proportion:
1 1/4 cups sugar is needed to make 1 batch of cookies
x cups sugar is needed to make 16 cookies
We can solve for x by cross-multiplying:
1 1/4 * 16 = x
20/4 = x
5 = x
Therefore, you will need 5 cups of sugar to make 16 cookies.
What is the probability that someone who does not take vitamins is a female? Round to three decimal places.
Female
Male
Total
(1 point)
O 0.374
O 0.139
O 0.080
O 0.626
Takes vitamins
248
145
193
Does not take vitamins
40
67
107
Total
288
212
500
Answer:
A) 0.374
Step-by-step explanation:
Let event A be that the person is female.
Let event B be that the person does not take vitamins.
[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
Therefore, from the given table:
[tex]\sf P(A) = \dfrac{288}{500}=0.576[/tex]
[tex]\sf P(B) = \dfrac{107}{500}=0.214[/tex]
[tex]\sf P(A \cap B)=\dfrac{40}{500}=0.08[/tex]
To calculate the probability that someone is female (Event A), given that they do not take vitamins (Event B), use the conditional probability formula for A given B:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Conditional Probability formula}\\\\A given B:\\\\$\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}$\\\end{minipage}}[/tex]
[tex]\sf \implies P(A|B)=\dfrac{0.08}{0.214}=0.374\;(3\;s.f.)[/tex]
The price of a mortgage is calculated using the present value of future cash flows, which includes an interest payment, CC, a principal payment, PrinPrin, the number of periods until the mortgage is to be paid off, tt, and a required rate of return, kk.
Mathematically, the general price movement of mortgages can be modeled as which of the following?
ΔPM=f(k)ΔPM=f(k)
ΔPM=f(Δk,ΔPrin)ΔPM=f(Δk,ΔPrin)
ΔPM=f(Δk,ΔC)ΔPM=f(Δk,ΔC)
ΔPM=f(Δk)
What are the type of securities that are issued to financial institutions where the funds are used to increase liquidity in the secondary mortgage market by financing the origination of mortgages? Check all that apply.
Private-label pass-through securities
Government National Mortgage Association (Ginnie Mae) mortgage-backed securities
Federal Home Loan Mortgage Association (Freddie Mac) participation certificates
Federal National Mortgage Association (Fannie Mae) mortgage-backed securities
The mathematical model that represents the general price movement of mortgages is: ΔPM = f(Δk, ΔPrin, ΔC)
Where ΔPM is the change in the price of the mortgage, Δk is the change in the required rate of return, ΔPrin is the change in the principal payment, and ΔC is the change in the interest payment.
This means that the change in the price of a mortgage is a function of the change in the required rate of return, the change in the principal payment, and the change in the interest payment.
The securities that are issued to financial institutions to increase liquidity in the secondary mortgage market by financing the origination of mortgages are:
Government National Mortgage Association (Ginnie Mae) mortgage-backed securitiesFederal Home Loan Mortgage Association (Freddie Mac) participation certificatesFederal National Mortgage Association (Fannie Mae) mortgage-backed securitiesFinancial institutions may also receive private-label pass-through securities, although these are not guaranteed by government entities like Ginnie Mae, Freddie Mac, or Fannie Mae.
They are not backed by the government, but by private institutions, which can make them riskier.
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Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released into the air in a laboratory. If the resulting radiation level is 40% above the safe level, how long should the laboratory remain vacated? (Hint: To start with, determine what fraction of the "resulting radiation level" is the maximum safe level.)
The laboratory should remain vacated for days.
In response to the stated question, we may respond that As a result, the expressions laboratory should be closed for 5.19 days to allow the radon gas to decline to a safe level.
what is expression ?An expression in mathematics is a combination of numbers, elements, and mathematical (like addition, reduction, multiplication, division, algebraic, and so on) that expresses an amount or value. Expressions may well be simple, such as [tex]"3 + 4"[/tex], or complicated, such as [tex]"(3x2 - 2) / (x + 1)"[/tex]. They might additionally contain functions like "sin(x)" or "log(y)". Expressions can be assessed by substituting variables with their values and performing the arithmetic operations in the specified sequence. For example, if x = 2, the ratio [tex]"3x + 5" equals 3(2) + 5 = 11.[/tex]Expressions are commonly used in mathematics to describe real-world situations, generate equations, and simplify complicated mathematical concerns.
We must apply the notion of radioactive decay and the half-life of radon gas to address this dilemma.
Begin by calculating the percentage of the safe radiation level that corresponds to the 40% increase. This can be written as:
[tex]1 + 0.4 = 1.4[/tex]
As a result, the resultant radiation level is 1.4 times that of the safe threshold.
To compute the proportion of the original amount of radon gas that remains after a certain period t, we may use the following formula:
[tex]N/NO = (1/2) t/T1/2)1/2 t/3.8) = 1/1.42 t/3.8) 1.4t / 3.8 = log(2) * (1.4)(1.4)t = 3.8x * log(2) * (1.4)t = 5.19[/tex]
As a result, the laboratory should be closed for 5.19 days to allow the radon gas to decline to a safe level.
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A group of people were asked if they had run a red light in the last year. 131 responded "yes", and 452 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year. Give your answer as a fraction or decimal accurate to at least 3 decimal places Submit QuestionQuestion 9
Answer:
.224 or 224/1000 or 28/125
Step-by-step explanation:
The probability of a person chosen at random having run a red light in the last year is:
P(run a red light) = Number of people who said "yes" / Total number of people surveyed
P(run a red light) = 131 / (131 + 452)
P(run a red light) ≈ 0.224 (rounded to 3 decimal places)
So the probability is approximately 0.224 or 224/1000 or 28/125.
Answer:
131/583
Step-by-step explanation:
Probability is the measure of likelihood or chance that an event will occur.
[tex]\text{Probability} = \frac{\text{Possible outcome of event}}{\text{Total outcome}}[/tex]
Total number of people asked if they had run a red light = number of people that responded 'yes' + number of people that responded 'no'
[tex]\text{Total outcome} = 131+452[/tex]
[tex]\text{Total outcome} = 583[/tex]
[tex]\text{Possible outcome} = \ \text{number of people that responded yes} = 131[/tex]
Probability that if a person is chosen at chosen at random, they have run a red light in the last year will be 131/583.
Given a regular pentagon, what is the value of p?
A) 54º
B) 13º
C) 27º
Pls help! Due tmrrww!!
Answer:
1. basement: 1,4,7,10,13
middle : 2,5,8,11,14
top: 3,6,9,12,15
2. you just need to skip count ten times then we will have 30. so she lives in apartment 30.
Step-by-step explanation:
how do you find the total surface area of a pyramid
Answer:
To find the total surface area of a pyramid you do SURFACE AREA =B+12(P×l)
Part B
Draw
parallel to
. You can draw
any length and place it anywhere on the coordinate plane, but not on top of
.
Find and record the ratio, n, of the length of
to the length of
. Then, multiply the lengths of
and
by n and record the resulting lengths.
In a diagram,
Then,
[tex]\dfrac{DE}{BC}=n[/tex]
For example, suppose that n=2; thus,
[tex]DE=2BC\longrightarrow2\times CA[/tex]
We can form a new triangle DEF whose side EF is parallel to CA; therefore,
[tex]\longrightarrow EF=2CA[/tex]
We can use the formula =rS12.6 to relate a ball's surface area S (in square centimeters) to its radius r (in centimeters). Suppose a ball has a radius of 12.04 centimeters. What is its surface area?
Carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.
The surface area of the sphere ball is 1817.74 square centimeters.
What is surface area?Every geometric shape has a different surface area formula, but the goal of all of them is to determine the total area occupied by all of the objects' faces. While the lateral surface area is calculated to determine the area occupied by the shape's curved surface, the total surface area takes into account all faces of the 3D shape, including the flat and curved surfaces. The area of the bases is excluded. One 3D shape called a sphere has just one round surface and no flat base.
Given that the surface area is related using the relation r = √(S/12.6).
Also, the value of r = 12.04, substituting the value we have:
(12.04) = √(S/12.6)
Squaring on both sides:
Hence. the surface area of the ball is approximately 1817.74 square centimeters.
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The complete question is:
A survey of 500 music lovers showed that 350 like rock, 300 like country, and 200 like both. How many of the 500 music lovers surveyed dislike both rock and country?
Answer:
50
Step-by-step explanation:
A Venn diagram is very helpful for this picture and I've included one in the attached.
If we look at the numbers we're given, we see that the numbers do not add up to 500 as 350 + 300 + 200 = 850.
However, we can work through the numbers to find the exact values and eventually the number of people that liked neither rock nor country.
Since 200 people like both rock and country, these people are part of the 350 people that like rock.
We can find the number of people who like rock only by subtracting 200 from 350:
350 - 200 = 150 (Rock only)
Using the same logic from above, we know that the 200 people who like both rock and country are a part of the 300 people who like country.
We can find the number of people who like country only by subtracting 200 from 300:
300 - 200 = 100 (Country only)
Currently, we have 450/500 as 150 + 200 + 100 = 450.
Now, we can find the number of people who like neither rock nor country by subtracting 450 from 500:
500 - 450 = 50 (Neither rock nor country)
We can check that the numbers we found equal 500:
Rock only + Both rock and country + Country only + Neither rock nor country = Total amount of music lovers surveyed
150 + 200 + 100 + 50 = 500
500 = 500
(**In the attached Venn diagram, M stands for the total set of music lovers, R stands for rock only, B stands for both, C stands for country only, and N stands for neither)
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If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (_____, _____) such that f'(c)>_______
If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (1, 2) such that f'(c)> 0.
How do we know?Applying the Mean Value Theorem for derivatives, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the interval (a, b) such that:
f'(c) = (f(b) - f(a)) / (b - a)
In the scenario above, we have that f is differentiable, and that f(1) < f(2).
choosing a = 1 and b = 2.
Then applying the Mean Value Theorem, there exists at least one number c in the interval (1, 2) such that:
f'(c) = (f(2) - f(1)) / (2 - 1)
f'(c) = f(2) - f(1)
We have that f(1) < f(2), we have:
f(2) - f(1) > 0
We can conclude by saying that there exists a number c in the interval (1, 2) such that:
f'(c) = f(2) - f(1) > 0
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-3+b> 7 OR b +9 <17.
The solution to the compound inequality -3+b> 7 OR b +9 <17 is given as follows:
b < 8 or b > 10.
How to solve the compound inequality?The inequality for this problem is defined as follows:
-3+b> 7 OR b +9 <17.
The or operation means that the we must solve each operation separately, and then the solution set to the compound inequality is given by the union of the solution set of each of the inequalities.
The solution set for the first inequality is given as follows:
-3+b> 7
b > 10.
The solution set for the second inequality is given as follows:
b + 9 < 17
b < 8.
Hence the solution for the entire inequality is of:
b < 8 or b > 10.
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It is known that a certain kind of algae in the Dead Sea can double in population every 4 days. Suppose that the population of algae grows exponentially, beginning now with a population of 1,000,000.
(a) How long it will take for the population to quadruple in size?
days
(b) How long it will take for the population to triple in size?
days
a. it will take 8 days for the population to quadruple in size.
b. t will take 6.34 days for the population to triple in size.
What is algae population?Organisms οf a species living tοgether in a grοup at a particular place are called a “pοpulatiοn” in Biοlοgy. A pοpulatiοn is an assοrtment οf οrganisms in a given lοcatiοn. These οrganisms, since they belοng tο the same species, can interbreed and prοduce mοre οf their kinds.
We have to use the following formula
P(t) = P0(b)t
⇒ 6000000 = 3000000(b)4
⇒ b4 = 2
⇒ b = 21/4
a. 12000000 = 3000000(2)t/4
⇒ 4 = 2t/4
⇒ 22 = 2t/4
⇒ 2 = t/4
⇒ t = 8 days
Thus, it will take 8 days for the population to quadruple in size.
b. 9000000=3000000(2)t/4
⇒ 3 = 2t/4
⇒ log 3 = (t/4)log 2
⇒ t = 6.34 days
Thus, it will take 6.34 days for the population to triple in size.
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16) Critique the sample method and the survey used by the guild. You’ll want to use some of the following words in your critique: sample, bias, random, response-bias, undercoverage, non-response, voluntary response.
Answer:
The critique of the sample method and survey used by the guild is as follows:
Sample: The sample used in the survey is not representative of the entire population. The survey was conducted only among the guild members, and hence it does not represent the views of non-members. This type of bias is called undercoverage bias.Bias: The survey seems to suffer from selection bias, where the participants who responded may not represent the entire population. This type of bias is known as response bias. It is possible that the members who chose to participate in the survey have different views from those who did not respond. Furthermore, the survey did not specify how the participants were selected, and hence there may be other types of bias present in the survey.Randomness: The survey did not use random sampling, which is a fundamental principle of survey research. A random sample ensures that every member of the population has an equal chance of being selected, which increases the representativeness of the sample.Non-Response: The survey did not address the issue of non-response bias, where participants who choose not to respond may have different views from those who respond. The survey did not specify the response rate, and hence it is unclear how many members chose to participate in the survey.Voluntary response: The survey seems to be a voluntary response survey, where members chose to participate voluntarily. This type of survey is known to suffer from bias because participants who respond are usually more motivated or have stronger opinions than those who do not respond.In summary, the survey used by the guild suffers from various types of bias, which may affect the validity and generalizability of the results. To improve the validity and reliability of the survey, the guild should use random sampling and address issues such as non-response and response bias.
When 1.00 g potassium chlorate is dissolved in 50.0 g water in a Styrofoam calorimeter of negligible heat capacity, the temperature decreases from 25.00°C to 23.36°C. Calculate q for the water and ?H° for the process.The specific heat of water is .
The specific heat of water is [tex]+41840J . mol^{-1}[/tex].
The following formula is used to determine how much heat a substance absorbs or releases during a heat exchange between two bodies, Calculate the value of q.
Q = m.s.t
Where,
Q is equal to how much heat is received or emitted.
m = The substance's mass
t = Temperature change
s = The substance's specific heat
The starting temperature in this dissolve is,
[tex]T_{i}[/tex] = 25.00°C
(25.00 + 273.00) K
= 298.00 K
Final temperature in this dissolving is,
[tex]T_{f}[/tex] = 23.36°C
= (23.36 + 273.00) K
Specific Water's heat is, [tex]4.184\frac{J}{g.K}[/tex]
In this issue, the heat that water releases are,
[tex]Q_{released} = 50.0g*4.184\frac{J}{g.K} * (298.00 - 296.36)K[/tex]
= 343.088J
2) Molar Mass of KClO₃ is [tex]122.55g mol^{-1}[/tex]
As a result, number of moles of KClO₃ present in 1g sample is,
[tex]\frac{1.00g}{122,55g/mol} = 0.0082mols[/tex]
Hence, the standard enthalpy change of the dissolving process is determined as follows:
Δ[tex]H^{o} = +\frac{343.088J}{0.0082mol} \\= +41840J . mol^{-1}[/tex]
The plus symbol (+) denotes the absorption of heat during the dissolving phase.
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Complete Question:
When 1.00 g potassium chlorate (KCIO₃) is dissolved in 50.0 g water in a Styrofoam calorimeter of negligible heat capacity, the temperature decreases from 25.00°C to 23.36°C. Calculate q for the water and AH° for the process. KCIO: (s) → K* (aq) + CIO (aq) The specific heat of water is 4.184 J K-1 g¯!.