The WW2 era helped tp deliver several prosperity to the whites in the forms of college education funding, It gave them unemployment insurances in the nation and also helped them with housing benefits.
How did WW2 help the US?This bill, commonly known as the G.I. Bill, was passed by President Franklin D. Roosevelt on June 22, 1944, and it gave World War II veterans money for housing, unemployment insurance, and college tuition. Millions of WWII and post-World War II military veterans now have access to higher education.
It made it possible for hundreds of thousands of men and women to pursue higher education, many of whom would not have been able to do so without its assistance. Although it left many minority veterans behind, the bill also contributed to the growth of the middle class in America.
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Which graph represents the solution set of the system of inequalities?
y < -3x-2
y ≤ x-2
The graph that represents the solution to the system of inequalities is graph (a).
What is system of inequality?
A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem requires a variety of solutions and those solutions must satisfy multiple constraints, systems of inequalities are used.
The given system of inequalities is,
y < -3x - 2
y ≤ x - 2
y < -3x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a dotted line.
y ≤ x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a closed line.
The above highlights means that the shaded region that represent the solution to the system of inequalities will be at the left-hand side
Hence, graph (a) represents the system of inequalities.
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3 less than the difference of 15 and a number h
Answer: 15 - h - 3
Step-by-step explanation:
Let a, b, and c be real numbers where a ≠ b ≠ c ≠ 0. Which of the following functions could represent the graph below?
f(x) = x²(x-a)²(x-b)4(x-c)
f(x) = x³(x-a)³(x-b)(x-c)²
f(x) = x²(x-a)(x-b)³(x-c)³
f(x) = (x-a)^2(x-b)(x-c)^6
The characteristics of polynomial graphs' intercepts reveal the multiplicity's characteristics. The function is a potential representation of the graph; f(x) = x²·(x - a) (x - a) , ²·(x - b) (x - b),⁴·(x - c) (x - c).
How to find the calculation?The alternative provides a function that can represent a graph;
f(x) = x²·(x - a) (x - a)
²·(x - b) (x - b)
⁴·(x - c) (x - c)
Reason:
The graph's description is as follows:
Three points on the graph deviate from the x-axis.
Therefore;
The first equation is satisfied by the graph's even multiplicity at three places, such as x2, (x - a)2, and (x - b)4.
The graph once almost linearly crosses the x-axis.
Therefore;
The first equation's function contains a single zero or component, such as (x - c), so;
The function is a potential representation of the graph;
f(x) = x²·(x - a) (x - a)
²·(x - b) (x - b)
⁴·(x - c) (x - c).
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A distribution of values is normal with a mean of 200 and a standard deviation of 19. From this distribution, you are drawing samples of size 33. Find the interval containing the middle-most 86% of sample means: Enter your answer using interval notation. In this context, either inclusive [] or exclusive () intervals are acceptable. Your numbers should be accurate to 1 decimal places.
The interval containing the middle-most 86% of sample mean in the interval notation is is (196.4, 203.5)
The 50 +/- 86/2 percentile will make up the center 86% of the sample means' distribution.
The 86th percentile's z-score is 1.08
sample mean population mean = 200
standard deviation from mean = 19
sample size = 33.
Standard error (SE) is equal to 19 / sqrt(33) = 3.3077.
86th percentile x can be located using the formula z = (x - population mean)/sample error.
1.08 = (x - 200)/3.3077
x = 3.3077* 1.08 + 200 = 203.57
that is the interval's upper bound.
it is 3.5721 over the population mean (203.57 - 200).
Due to the symmetry of the normal distribution, the interval's bottom bound will be 1.66 standard deviations below the population mean (200 - 3.572 = 196.428).
then the interval is (196.4, 203.5).
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5400 dollars is placed in an account with an annual interest rate of 9%. To the
nearest tenth of a year, how long will it take for the account value to reach 15500
dollars?
Answer:
12.2 years
Step-by-step explanation:
To solve, use the exponential growth formula:
[tex]A_t=A_0(1+r)^x[/tex]
where
[tex]A_t[/tex] = Amount as a function of time ($15500)
[tex]A_0[/tex] = Original amount ($5400)
[tex]r[/tex] = rate (.09)
[tex]x[/tex] = time in years
So,
[tex]15500=5400(1+.09)^x\\15500(\frac{1}{5400})=5400(1.09)^x(\frac{1}{5400})\\2.87=1.09^x\\\log_{1.09}2.87=\log_{1.09}1.09^x[/tex]
Use the logarithmic rules that state [tex]\log_{a}a=1[/tex] and [tex]\log_{a}a^b=b\log_{a}a[/tex]:
So,
[tex]\log_{1.09}2.87=x\\12.24\ years=x[/tex]
The analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measures ANOVA.TrueFalse
The given statement ,the analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measure ANOVA is true.
The first stage of the repeated-measures ANOVA is identical to the independent-measures analysis and splits the overall variability into two components: between-treatments and within-treatments
Measurements that are repeated ANOVA is the extension of the dependent t-test and is the equivalent of one-way ANOVA for related, rather than independent, groups.
A repeated measures ANOVA is often referred to as a within-subjects ANOVA or ANOVA for correlated samples. The term "responsibility" refers to the act of determining whether or not a person is responsible for his or her own actions.
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Evaluate the function
f(n) = 4x + 5; Find f(2)
Answer: 13
Step-by-step explanation: To find f(2), you can put 2 into all of the x spots, thus making the equation 4(2)+5. From there you can do PEMDAS and multiply 4 and 2 to get 8, and then add 5 to get 13.
HEPPPP ASPP!!! PLEASE I BEG YOU !!
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours john’s brother works, and c, the total cost of the project ?
According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.
What are time and work?A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.
What is work time problem in math?The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.
Briefing:Given that John paid $485 to build a deck.
And he will pay $25 per hour to his brother for building the deck.
one hour of work costs John $25 + $485 .
Total cost of building deck = $25 × h number of hours + $485
3 hour of work costs $25 × 3 = $75 + $485 = $560
8 hour of work costs = $25 × 8 = $200 + $485 = $685
12 hour of work costs = $25 × 12 = $300 + $485 = $785
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The complete question is-
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?
h c
0 485
3 510
8 535
12 560
h c
0 510
3 535
8 560
12 585
h c
0 485
3 560
8 685
12 785
h c
0 510
3 585
8 710
12 810
The Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course. In analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours. Consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed: i. At the 5% level, BAOI can infer that the average time to complete exceeds 60 hours. ii. At the 1% level, BAOI can infer that the average time to complete exceeds 60 hours. What is true about i. and it: O Only (l) is true O There is insufficient information to determine which of the other answers shown here is correct. O Neither (1) nor (ii) is true O Both (1) and (ii) are true O Only ) is true
As per the given standard deviation, only (i) is true.
The term standard deviation refers the measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Here have given that the Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course.
Here by analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours.
So, let us consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed:
i. For the 5% level, BAOI can infer that the average time to complete exceeds 60 hours.
ii. For the 1% level, BAOI can infer that the average time to complete exceeds 60 hours.
Here we are trying to determine if they should spend at least 480 minutes a day studying.
Now, our knoll is that the mean is 480 and then we are looking for evidence that they are studying less than 480.
Here we don't know the population standard deviation so we're going to use a distribution.
In the given, critical values are going to be a distribution with degrees of freedom.
So, if we look at a chart 11 of freedom, we can see our critical value. I'm going to center to zero if I draw our T.
Therefore, the tail probability of.05 and the rest of it is.95%.
Based on these value we have conform that option (1) is correct.
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On a 3 section math test a student correctly answered 17/20 11/15 20/25 what percentage of questions on the entire test did the student answer correctly
Step-by-step explanation:
17 of 20
11 of 15
20 of 25
that is in total
17+11+20 = 48
of
20+15+25 = 60
so, he answered 48 of 60 correctly
48/60 = 4/5 = 0.8 = 80%
Answer:
79.44%
Step-by-step explanation:
We are given that there are 3 sections to this test and how the student scored in each of those sections. Let us add all of these fractions together.
[tex]\frac{17}{20} +\frac{11}{15} +\frac{20}{25} =\frac{143}{60} \\[/tex]
We must now divide this amount by 3 to find the average of the three sections. This gives us [tex]\frac{143}{180}[/tex].
These means that the student answered [tex]\frac{143}{180}[/tex] of the questions correctly, or 79.44%.
Frank bought two pork roasts. One roast weighed five and seven-eighths pounds and the other roast weighed nine and five-sixths pounds. What is the total weight of the pork roasts?
Answer:
15[tex]\frac{17}{24}[/tex]
Step-by-step explanation:
5 [tex]\frac{7}{8}[/tex] + 9 [tex]\frac{5}{6}[/tex] We can write the fractions as equivalent fractions with a common denominator of 24
[tex]\frac{7}{8}[/tex] x[tex]\frac{3}{3}[/tex] = [tex]\frac{21}{24}[/tex]
[tex]\frac{5}{6}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{20}{24}[/tex]
5[tex]\frac{21}{24}[/tex] + 9[tex]\frac{20}{24}[/tex]
5 + 9 + [tex]\frac{21}{24}[/tex] + [tex]\frac{20}{24}[/tex]
14 + [tex]\frac{41}{24}[/tex]
14 + [tex]\frac{24}{24}[/tex] + [tex]\frac{17}{24}[/tex] I broke up [tex]\frac{41}{24}[/tex] because [tex]\frac{24}{24}[/tex] is another name for 1
14+1 + [tex]\frac{17}{24}[/tex]
15[tex]\frac{17}{24}[/tex]
Properties of Definite Integrals A definite integral is a function that assigns a value to the area under a curve on a given interval.
Properties of Definite Integrals A definite integral is a function that assigns a value to the area under a curve on a given interval are additive , linearity , continuity , monotonicity and upper and lowersums.
1. Additivity: The definite integral of a sum is equal to the sum of the definite integrals.
2. Linearity: The definite integral of a linear function is equal to the product of the function's slope and the length of the interval.
3. Continuity: The definite integral of a continuous function is equal to the area under the curve between two points.
4. Monotonicity: If a function is increasing or decreasing on a given interval, then the definite integral of the function is also increasing or decreasing.
5. Upper and Lower Sums: The upper and lower sums of a function are the sums of the areas of rectangles constructed under or over the curve between two points. The definite integral of the function is equal to the difference between the upper and lower sums.
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Decide whether the random variable x is discrete or continuous. x represents the number of dependent children in a household
Time is represented by the variable. Since a person's speed, which can take on nearly any value, determines how long it takes them to complete a mile, this variable is continuous.
Define Continuous variable?If a quantitative variable is often obtained through measuring or counting, it can either be continuous or discrete. If a variable can take on any two particular real values and all other real values in between, it is said to be continuous over a range of real values.
First, when is a variable continuous and when is it discrete?
A variable is continuous if it can take any value (or at least a dense set of values) inside a certain interval as opposed to discrete if it can only take a few specific values on that interval.
For instance, the only possible values for the numbers one can roll on a dice are 1, 2, 3, 4, 5, and 6, to provide one example.
The variable in this instance now stands for time. Time is nearly always a continuous variable; in this instance, the time refers to the duration of a mile run. Therefore, that variable is capable of practically any value (depends on the speed of the person).
Therefore,
Time is represented by the variable. Since a person's speed, which can take on nearly any value, determines how long it takes them to complete a mile, this variable is continuous.
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1. Which equation describes the line with
slope -4 and y-intercept 2?
A y=-4x+2
B y=-4x-2
C y=4x-2
D y = 4x + 2
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.
Caleb's school is five blocks due north of his home, and is the closest to the straight-line distance from Caleb's s
A) 389 f t
B) 825 f t
C) 1,260 ft
(D) 1,481 ft
If Caleb's school is five blocks due north of his home, the figure that is closest to the straight-line distance from Caleb's s is (D) 1,481 ft.
What is distance?Distance can be defined as how far an object is from another object.
Using Pythagoreans theorem
Hypotenuse =√Perpendicular² + Base²
Where:
Perpendicular = 275 feet ×5 = 1375ft
Base = 275 feet × 2 = 550ft
Let plug in the formula
Hypotenuse =√ 1375 ft² + 550ft
Hypotenuse =√1,890,625 + 302,500
Hypotenuse =√2,193,128
Hypotenuse = 1,480.9ft
Hypotenuse = 1,481ft (Approximately)
Therefore the correct option is D.
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Lisa read 2/5 of her book over the weekend and 1/3 of it on monday. What fraction of the book is left?
Answer:
4/15
Step-by-step explanation:
To answer this question, we're gonna want to convert the fractions so that they have the same denominator (the number on the bottom of the fraction) and it's easy for us to visualize what's going on. AKA, we need to find the least common denominator (LCD).
We're going to multiply 2/5 and 1/3 by a number so they have the same denominator. In this case, that would mean multiplying them by the other fractions denominator. So multiplying 2/5 by 3 and 1/3 by 5.
2/5x3= 6/15. 1/3x5=5/15.
Now we're viewing the book in 15ths instead of both 5ths and 3rds.
6+5=11, so we know that 11/15 of the book has been read.
15/15-11/15=4/15
4/15 of the book is left to read.
Hope this explanation helped!
A box contains 2 red marbles and 3 black marbles. Two marbles are drawn in succession without replacement. Find the following: a. Find the probability the second marble is red? b. Find the probability that both marbles are the same color? c. Find the probability that the second marble is black given the first marble is red? d. Find the probability that first marble red given that the second marble is red?
a. The probability that the second marble is red is 2/5, since there are 2 red marbles and a total of 5 marbles.
b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.
c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.
d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.
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A customer spends a total of $52.25 at an amusement park. The customer buys a $30.25 ticket to enter the park and 4 game tickets.
If each game ticket costs the same amount, x, which statement is true?
Responses
An equation that can be used to find x is 4(x+30.25)=52.25, and each game ticket costs $5.50.
An equation that can be used to find x is 4 ( x + 30.25 ) = 52.25 , and each game ticket costs $ $ 5.50 .
An equation that can be used to find x is 4(x+30.25)=52.25, and each game ticket costs $18.00.
An equation that can be used to find x is 4 ( x + 30.25 ) = 52.25 , and each game ticket costs $ $ 18.00 .
An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $5.50.
An equation that can be used to find x is 4 x + 30.25 = 52.25 , and each game ticket costs $ $ 5.50 .
An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $18.00.
Answer: I believe its: An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $5.50.
Step-by-step explanation:
well, 52.25 - 30.25 is 22$
22 divided by 4 is 5.50
4 times x plus 30.25 is 52.25
so 4x+30.25= 52.25
simplify the expression: 6(1+9t)
Answer:
Hi!
The answer would be: 6 + 54t
I hope this helped you! :)
Step-by-step explanation:
Answer:
54t + 6
Step-by-step explanation:
Simplify the expression. Use the distributive property. The distributive property states that an expression which is given in form of a(b + c) can be solved into (ab) + (ac). Distribute and multiply 6 to all terms within the parenthesis. Then, simplify:
[tex]6(1 + 9t)\\\\=(6 * 1) + (6 * 9t)\\= (6) + (54t)\\ = 54t + 6[/tex]
54t + 6 is your answer.
~
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sort these items into the order that you would use them in order to calculate the confidence interval for the mean.
The order of calculate the confidence interval for the mean are as follows:
1. Select sample stat
2. select desired confidence
3. determine margin of error
4. specify upper and lower limits
Now, According to the question:
The order of calculate the confidence interval for the mean are as follows:
1. Select sample stat
2. select desired confidence
3. determine margin of error
4. specify upper and lower limits
Let's know:
What is Confidence Interval?
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.
The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.
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$80 at q $100 at qlet q represent the quantity of output and suppose the price of the good is $125 then the marginal revenue is
For the given diagram 1. d) all of them are correct, 2. d)none of them are correct and Total Revenue is 3. b. $90,125
1.
Marginal Revenue is
the change in Total Revenue/Change in units of output produced
In the given question the price of the output is fixed at $125.
Hence no matter what the quantity of output sold, every additional output produced will generate an additional revenue of $125.
hence option d) all of them are correct has to be chosen.
2.
Now we already know that if the price has been fixed at $125, the marginal revenue generated cannot be anything but $125.
Hence, option d) None of them are correct.
3.
Total Revenue = Price X Quantity
Here it is given that the Price is $175
Output is 515 units
Hence, the Total Revenue will be $(175 X 515)
= $90125
Hence, option b. $90125 is correct.
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Complete Question
(Image Attached)
Fully simplify.
(3x^2y^2)^3
(3x
2
y
2
)
3
Answer:
[tex]27x^6y^6[/tex]
Step-by-step explanation:
The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex]. So,
[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].
Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex]. So,
[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]
What is BC?
BC= units?
The value of BC = 25 using properties of triangle.
What are properties of triangle ?
Let us discuss here some of the properties of triangles.
1. A triangle has three sides and three angles.
2. The sum of the angles of a triangle is always 180 degrees.
3. The exterior angles of a triangle always add up to 360 degrees.
4. The sum of consecutive interior and exterior angle is supplementary.
Properties for isosceles:
Isosceles triangles are those triangles that have at least two sides of equal measure.
1. Two equal sides and two equal angles.
2. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.
3. The side opposite the vertex angle is called the base and base angles are equal.
Using 1st property,
in given triangle two angles are equal then opposite side will also be equal.
So, AB = AC
i.e. 4x+4 = 6x-14
4+14 = 6x-4x
18 = 2x
x = 9
Putting value of x in BC
BC = 2*9 +7
= 18+7
= 25.
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the manager of a store increases the price of a popular product the new price x+0.07x
Answer:
The new price of the product will be 1.07x, where x is the original price.
The manager has increased the price by 0.07x, which is 7% of the original price. This is equivalent to multiplying the original price by 1 + 0.07, or 1.07.
So, the new price of the product is 1.07 times the original price, or 1.07x.
The implicational rule of inference that permits us to derive a specific instance from a universal statement isa. Existential Generalization.b. Existential Instantiation.c. Universal Generalization.d. Universal Instantiation.
Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.
It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.
Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.
Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."
∀xA⇒A(x↔a}
for every formula A and every term a, where A(x↔a} is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of
∀xA.
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03 Multiple Choice
0/20
Select all of the expressions that are equivalent to (9x+6)-(8x-4).
M. 2(x + 1)
P. 2x + 6
R. 2x + 2
S. 2(x + 3)
T. 8x
the student government claims that 70% of all students favor an increase in student fees to buy indoor potted plants for the classrooms. a random sample of 12 students produced 2 in favor of the project.
(a) What is the probability that 2 or fewer in the sample will favor the project, assuming the student government's claim is correct? (Use 3 decimal places.) (b) Do the the data support the student government's claim, or does it seem that the percentage favoring the increase in fees is less than 70%? The data do not give us any indication that the percent favoring the increase in fees differs from 70%. The data seem to indicate that the percent favoring the increase in fees is greater than 70%. The data seem to indicate that the percent favoring the increase in fees is less than 70%. The data seem to indicate that the percent favoring the increase in fees is equal to 70%.
The probability that 2 or fewer in the sample will favor the project is 4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%
According to the question,
It is given that according to the student's government
The probability that number of students in favor of increment in fees : p = 0.70
The probability that number of students against the increment : q = 0.30
Sample Size : n = 12
Number of students follows Binomial distribution
(a) We have to find the probability that 2 or fewer in the sample will favor the project
P( x ≤ 2) = P(0) + P(1) + P(2)
As we know ,
P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾
=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰
=> P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹ + 12×11/2 × (0.70)²(0.30)¹⁰
=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]
=> P( x ≤ 2) = 5.9×10⁻⁶[0.78]
=> P( x ≤ 2) = 4.368 × 10⁻⁶
Which is very close to zero
(b) The data doesn't support the student government claim.
The data seem to indicate that the percent favoring the increase in fees is less than 70%.
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Given f(x) = 4x2 – 4x + 1 and g(x) = 2x – 1, which of the following are expression(s) for f · g? Select all that apply.
A. 6x3 + 6x2 – 6x + 1
B. (2x – 1)3
C. 8x3 – 12x2 + 6x – 1
D. 4x2 – 2x
The value for the expression, (f * g)(x) is calculated as: C. 8x³ - 12x² - 6x - 1.
How to Evaluate the Expressions of Functions?We are given the following functions,
f(x) = 4x² – 4x + 1 and g(x) = 2x – 1.
To find the value of the expression, (f * g)(x), it means we have to multiply the functions together. See the steps explained below.
(f * g)(x) = f(x) * g(x)
Plug in the values:
(f * g)(x) = f(x) * g(x) = (4x² – 4x + 1)(2x – 1)
(f * g)(x) = 4x²(2x – 1) - 4x(2x – 1) + 1(2x – 1)
Apply the distribution property of equality:
(f * g)(x) = 8x³ – 4x² - 8x² + 4x + 2x – 1
Combine like terms:
(f * g)(x) = 8x³ - 12x² - 6x - 1
Therefore, the answer is: C. 8x³ - 12x² - 6x - 1.
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u (x comma y )space equals space 5 (x plus y )u (x comma y )space equals space 5 y u (x comma y )space equals space 5 x u (x comma y )space equals space 5 x squared plus 5 y squared
To solve this system of differential equations using the series method, we can assume that the solution can be expressed as a power series in both x and y:
[tex]u(x,y) = a0 + a1x + a2y + a3xy + a4x^2 + a5y^2 + ...[/tex]
Substituting this expression into each of the differential equations and collecting the coefficients of each term gives us the following system of equations:
a0 + 5a0 = 0
a1 + 5a2 = 0
a2 + 5a1 = 0
a4 + 5a4 = 0
a5 + 5*a5 = 0
Solving this system of equations gives us the following values for the coefficients:
a0 = 0
a1 = 0
a2 = 0
a3 = 0
a4 = 0
a5 = 0
Therefore, the power series expansion of the solution is:
u(x,y) = 0
This means that the only solution to the differential equations is the trivial solution u(x,y) = 0.
Note that this method of solving differential equations using power series is only applicable if the differential equations are linear and homogeneous, which means that the coefficients of the terms in the differential equations do not depend on x and y, and the right-hand sides of the equations are all equal to 0. If the differential equations are nonlinear or inhomogeneous, other methods may be required to find their solutions.
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Find the rate of change of the line that contains the two points (-1, -4) and (5, 4). Be sure to show all calculations and reduce your slope to a fraction in simplest form.
The rate of change of the line that contains the two points (-1, -4) and (5, 4) is 4/3.
What is the rate of change of the line?The rate of change for a line is the slope, the rise over run, or the change in over the change in.
The slope of line can be calculated using the formula, slope =(y2-y1)/(x2-x1).
The given coordinate points are (-1, -4) and (5, 4).
Now, slope = (4-(-4))/(5-(-1))
= (4+4)/(5+1)
= 8/6
= 4/3
Therefore, the slope of a line is 4/3.
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