Answer:
24 waffles
Step-by-step explanation:
16÷6=2.66 so she can make that many waffles per egg
9x2.66= 23.94 which would round up to 24 waffles
if there is sufficient evidence to reject the null hypothesis, we conclude that the alternate hypothesis is true
if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
If there is sufficient evidence to reject the null hypothesis, we conclude that the alternate hypothesis is true. if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
This statement is describing the process of hypothesis testing in statistics. In hypothesis testing, a null hypothesis is a statement that there is no significant difference between two sets of data or no relationship between two variables. An alternate hypothesis is a statement that there is a significant difference or relationship.
When conducting a hypothesis test, a researcher will collect data and use statistical methods to determine the likelihood that the null hypothesis is true given the data. If the likelihood is low, the researcher will reject the null hypothesis and conclude that the alternate hypothesis is true. If the likelihood is high, the researcher will fail to reject the null hypothesis, but this does not necessarily mean that the null hypothesis is true. It means that the data is not strong enough to reject the null hypothesis.
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( HELP ME PLS )
315% of 26.2 is what?
Answer:
Solution:
315 percent of 26.2=82.53
Step-by-step explanation:
To calculate 315 percent of the number 26.2, we must create a ratio from which we can easily determine the value we are looking for.
First we create two simple equations with data that we know.
26.2 equals 100%, so we can save it as 26.2 = 100%
The value we are looking for can be called x
Now we know that x is 315 of the output value, so we can write it as x = 315.
So we have two simple equations:
1) 26.2=100%
2) x=315%
When we compare these two equations, we get:
26.2/x=(100%)/(315%)
Now we just have to solve the simple equation.
We calculate 315 percent of 26.2 :
26.2/x=100/315
(26.2/x)*x=(100/315)*x
26.2=0.31746031746032*x
26.2/0.31746031746032=x
82.53=x
x=82.53
Solution:
315 percent of 26.2=82.53
segment vu is parallel to segment lm. find the missing length. segment vu is parallel to segment lm. find the missing length. 44 27 24 39
The missing length of segment VU is 33.49.
The formula for finding the missing length of two parallel lines is given below:
L = L1 + (L2 - L1) * (L3/L4)
Where L1 is the length of one line, L2 is the length of the other line, L3 is the known length of the first line, and L4 is the known length of the second line.
In this problem, L1 is the length of segment LM and L2 is the length of segment VU. We know that L3 is 24 and L4 is 39.
Using the formula, we can calculate the missing length of segment VU as follows:
L = 44 + (27 - 44) * (24/39)
L = 44 + (-17) * (0.61538)
L = 44 - 10.51
L = 33.49
Therefore, the missing length of segment VU is 33.49.
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Triangle A C B is cut by line segment E D. Line segment E D goes from side B C to side A C. The length of B A is 4 x minus 6 and the length of E D is x + 2. The length of B E is x. Sides B E and E C are congruent. Sides A D and D C are congruent.
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
D
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
The length of BC is 10.
What are similar triangles?When two triangles have some common corresponding properties, they are said to be similar. But they are no congruent.
In the given question, comparing triangles ABC and DEC. We have;
DE/ AB = EC/ BC
But,
BC = 2BE
= 2x
So that,
(x + 2)/ (4x - 6) = x/ 2x
(x + 2)/ (4x - 6) = 1/ 2
2(x + 2) = (4x - 6)
2x + 4 = 4x - 6
collect like terms
6 + 4 = 4x - 2
10 = 2x
x = 10/ 2
x = 5
Then,
BC = 2x
= 2*5
BC = 10
The length of BC is 10.
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What is 6 x 3/5 as a fraction
Answer:
18/5 or 3 3/5
Step-by-step explanation:
Turn 6 into a fraction -> 6/1
Hence, 6/1 × 3/5
Multiply the numerators and denominators.
(6×3)/(1×5) = 18/5
Simplify = 3 3/5
Answer:
= 18/5
Step-by-step explanation:
6 × 3 = 18
Then:
6 × 3/5
= 18/5
...
In a classroom, there are 18 boys and 22 girls. What is the ratio of girls to boys? Always simplify ratios!!
The ratio of girls to boys would be = 11:9
what is a ratio?A ratio is defined as the expression that is used to show the relationship between two different variables.
The number of boys represented = 18 boys
The number of girls represented = 22 girls
To calculate the ratio of girls to boys the following is done;
22 : 18 ( divide through by 2)
11. : 9
Therefore the ratio of girls to boys in the classroom = 11:9
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Paula who is 49 years old is seven times older than her son, Daniel.Daniel is two years younger than his sister, Leah. How old is Leah?
given the system of linear equations, written in column form as follows which of the following is the corresponding row form of this system?
The row form of the system is 5x = 2 and y – y = 0.
Column form:
3x + y = 5
2x – y = –3
Row form:
3x + 2x = 5 – 3
y – y = 0
The row form of this system is 3x + 2x = 5 – 3 and y – y = 0. To convert from column form to row form, the first step is to eliminate the y terms in the equations. To do this, we need to add the two equations together. This gives us:
3x + y = 5
2x – y = –3
3x + 2x = 5 + (–3)
y – y = 0
5x = 2
y – y = 0
Finally, we can solve for x and y.
5x = 2 ⇒ x = 2/5
y – y = 0 ⇒ y = 0
Therefore, the row form of the system is 5x = 2 and y – y = 0.
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A group of adult males has foot lengths with a mean of 28.02 cm and a standard deviation of 1.35 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 31.1 cm significantly low or significantly high? Explain.
The bounds of non-unusual measures are given as follows:
Lower bound: 25.32 cm.Upper bound: 30.72 cm.Hence an adult male foot length of 31.1 cm is significantly high, as it is greater than the upper bound.
What is the range rule of thumb?The range rule of thumb states that measures that are more than two standard deviations from the mean in a data-set are considered unusual.
Considering the mean and the standard deviation for this problem, the bounds are given as follows:
Lower bound: 28.02 - 2 x 1.35 = 25.32 cm.Upper bound: 28.02 + 2 x 1.35 = 30.72 cm.More can be learned about the range rule of thumb at https://brainly.com/question/15825971
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You go to the grocery store and purchase the items listed in the table. What is your total if
the sales tax is 7%?
Answer:
where is the table?
Step-by-step explanation:
repost it with a picture of the table so we can answer it or tell the details and I'll answer in the comments?
solve 5+2x+12=4x+17-2x
Answer:
2x-4x+2x=17-12-5
0x=0
Which of the following is most likely the next step in the series?
The geometric figure which is most likely the next step in the series include the following: C. heptagon.
What is a series?In Mathematics, a series can be defined as a sequence of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
By critically observing the given series, we can logically deduce that the first geometric figure represent a square with four (4) sides, the second geometric figure represent a pentagon with five (5) sides, the third geometric figure represent a hexagon with six (6) sides. This ultimately implies that, each of the sides of the geometric figure increases by one (1).
In this context, the next geometric figure in the series must be a heptagon with seven (7) sides.
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4. If a tablet PC had a net cost of $453.60 after a series discount of 20/10/10, what
was the list price of the PC?
The series discount of 20/10/10 means that there are three discounts given in sequence. The first discount is 20%, the second is 10%, and the third is 10%.
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Let's call the original price x.
x - (20/100x) = 0.8x
then
0.8x - (10/1000.8x) = 0.72x
and finally
0.72x - (10/100*0.72x) = 0.648x
So, the net cost of $453.60 is equal to 0.648x.
We can find the original price by dividing the net cost by 0.648:
x = $453.60 / 0.648 = $700
So, the list price of the PC was $700.
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declare double variables x1, x2, x3, and x4, and read each variable from input in that order. find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
The answer is x4 = input.nextDouble() and double avgnumber = (x1 + x2 + x3 + x4) / 4.
Declare the double variables x1, x2, x3, and x4.
double x1, x2, x3, x4;
Read each variable from input in that order.
Scanner input = new Scanner(System.in);
System.out.println("Enter x1:");
x1 = input.nextDouble();
System.out.println("Enter x2:");
x2 = input.nextDouble();
System.out.println("Enter x3:");
x3 = input.nextDouble();
System.out.println("Enter x4:");
x4 = input.nextDouble();
To Find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
double avgnumber = (x1 + x2 + x3 + x4) / 4;
//This code takes four double variables from input and calculates the average by adding the four numbers together and dividing by four. The result is stored in the double variable avgnumber.
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Bethany runs 3 days a week four miles each day. How many miles does she run in 16 weeks?
Answer:
48 miles in 16 weeks dtLewis is a famous author only if he knows how to write. But Lewis is not a famousauthor. Hence, Lewis does not know how to write.1.If A, then B.2.Not A.So, 3.Not B.
The formula used to explain this statement is known as Modus Tollens, which is a form of logical inference.
Modus Tollens states that if the antecedent (A) of a conditional statement is false, then the consequent (B) must also be false. This is expressed mathematically as ¬A ⟹ ¬B. The formula used to explain this statement is known as Modus Tollens, which is a form of logical inference.
In this particular example, A is the statement that Lewis is a famous author, and B is the statement that Lewis knows how to write. Since the statement A is false, the statement B must also be false. This can be represented mathematically as:
¬A ⟹ ¬B
¬(Lewis is a famous author) ⟹ ¬(Lewis knows how to write)
False ⟹ False
Therefore, Lewis does not know how to write.
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Find the intervals on which the given function is increasing and the intervals on which it is decreasing. (Enter your answers using interval notation.) h(x) = (x + 2)^2 x (x-7)^1/3
The intervals on which the function is increasing are: (-∞, -2) and (7, ∞), and the intervals on which the function is decreasing are: (-2, 7). In interval notation, this is written as (-∞, -2), (7, ∞) and (-2, 7).
The given function is h(x) = (x + 2)^2 x (x-7)^1/3. This is a polynomial function with two terms. The first term, (x + 2)^2, is a quadratic function, and the second term, (x-7)^1/3, is a cube root function.
We can use the derivative of the function to determine the intervals on which the function is increasing and decreasing. Taking the derivative of the function yields: h'(x) = 2(x + 2)(x - 7)^1/3 + (x + 2)^2 x (1/3)(x - 7)^-2/3. Setting the derivative equal to zero, we can solve for x and find where the function is not increasing or decreasing. Solving this equation yields x = -2 and x = 7, the points of inflection.
Therefore, the intervals on which the function is increasing are: (-∞, -2) and (7, ∞), and the intervals on which the function is decreasing are: (-2, 7). In interval notation, this is written as (-∞, -2), (7, ∞) and (-2, 7).
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Find the area
…………………………
Answer:
118
Step-by-step explanation:
18*4=72
8+3*2=22
8*3=24
72+22+24=118
What is the measurement of the angle shown below? O O 150° 60° ○ 30° 10 20 30 0 170 150 150 140 130 120 180° 249 848 60 90 100 110 120 130 140 150 80 70 60 50 $ ata
150°
Because it is not acute it cant be 30°
Liliana has $3.60 in nickels and quarters in her backpack. She has 18 more nickels than quarters. How many coins of each type does she have?
Answer: Liliana has 9 quarters and 27 nickels.
Step-by-step explanation:
Let's call the number of quarters Liliana has "q" and the number of nickels she has "n".
From the problem, we know that:
n = q + 18 (because she has 18 more nickels than quarters)
We also know that the total value of the coins is $3.60. We can use the following equation to find the total number of coins:
(0.25 * q) + (0.05 * n) = 3.60
Now we can substitute the first equation into the second equation to get:
(0.25 * q) + (0.05 * (q + 18)) = 3.60
Simplifying this equation:
0.25q + 0.05q + 0.90 = 3.60
0.30q = 2.70
q = 9
So Liliana has 9 quarters. We can use the first equation (n = q + 18) to find the number of nickels she has:
n = 9 + 18
n = 27
Which means, Liliana has 9 quarters and 27 nickels.
what is the converse of the following conditional statement? "if two angles form a linear pair, then they are supplementary angles." if two angles are supplementary angles, then they form a linear pair. if two angles do not form a linear pair, then they are not supplementary angles." if two angles are not supplementary angles, then they do not form a linear pair. two angles form a linear pair if and only if they are supplementary angles.'
If two angles form a linear pair, then they are supplementary.
This is because it is not necessary for angles to form a linear pair for them to be supplementary. Angles can be supplementary even if they do not form a linear pair.
if two angles do not form a linear pair, then they are not supplementary angles
Supplementary angles do not have to be , whereas a linear pair must be adjacent and create a straight line. So, if two angles do not form a linear pair, then they are not supplementary .
if two angles are not supplementary angles, then they do not form a linear pair. Supplementary angles do not have to be adjacent, whereas a linear pair must be adjacent and create a straight line. So, , supplementary angles are not always linear pair . However, linear pairs are always supplementary.
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If two angles form a linear pair, then they are supplementary.
This is because it is not necessary for angles to form a linear pair for them to be supplementary. Angles can be supplementary even if they do not form a linear pair.
if two angles do not form a linear pair, then they are not supplementary angles
Supplementary angles do not have to be , whereas a linear pair must be adjacent and create a straight line. So, if two angles do not form a linear pair, then they are not supplementary .
if two angles are not supplementary angles, then they do not form a linear pair. Supplementary angles do not have to be adjacent, whereas a linear pair must be adjacent and create a straight line. So, , supplementary angles are not always linear pair . However, linear pairs are always supplementary.
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suppose 83% of all students taking a beginning programming course fail to get their first program to run on first submission. consider a group of 7 such students,where each student's success is independent from the other and the chance each student fails on their first try is consistent. (round answers to three decimal places.)
The probability that all fail on their first submissions is 27.1%.
For each student, there are only two possible outcomes. Either their first program run will fail, or it wont. The probability of the first program run of a student failing is independent of the first program run of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The expected value of the binomial distribution is
The variance of the binomial distribution is
The standard deviation of the binomial distribution is
In this question, we have that:
83% of all students taking a beginning programming course fail to get their first program to run on first submission. Sample of 7 students. This means that
All fail on their first submissions
So,
0.271 = 27.1% probability that all ail on their first submissions
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In science class, Farah uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 marbles, the height is 10 mL. After dropping in 6 marbles, the height is 11 mL. How much does the height increase for each marble? 0.5 mL How much water was in the cylinder before any marbles were dropped in? mL wwwww Submit
The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.
Finding Volume by Water Displacement Method:The volume of an object is the amount of space occupied by the object within all boundaries. The volume of any geometrical shape can be calculated by the respective formula.
The Water Displacement Method is a method that is used to calculate the volume of any object without knowing the dimensions. If we drop the object into the water and the amount that can be displaced will be equal to the volume of the object.
Here we have
After dropping 4 marbles, the height of the water level is 10 ml
After dropping 6 marbles, the height of the water level is 11 ml
This means for 2 extra marbles the water level increase up to 1 ml
So, the Volume of the marble = 1 ml/2 = 0.5 ml
From the given data,
After dropping 4 marbles the water level is 10 ml
As we know the volume of 1 marble = 0.5ml
=> Volume of 4 marbles = 4 × 0.5ml = 2ml
The water level before dropping 4 marbles = 10 ml - 2 ml = 8 ml
Therefore,
The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.
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Consider a one-sample two-sided z-test for a population proportion. Given that conditions for inference are met, which of the following is closest to the P-value for a test statistic of -1.86 ? A. 0.0157 B. 0.0314 C. 0.0628 D. 0.9371 E. 0.9686
The closest value to the P-value for a test statistic of -1.86 is 0.0628. Hence, option C is the correct answer to this question.
The P-value for a test statistic of -1.86 in a one-sample two-sided z-test for a population proportion can be found using a standard normal table or a calculator with a built-in function for z-scores. It represents the probability of obtaining a test statistic as extreme or more extreme than the one observed, under the assumption that the null hypothesis is true.
In this case, the test statistic of -1.86 is on the left tail of the standard normal distribution, since it is negative and represents a deviation to the left of the mean. To find the P-value, we would need to look up the area under the standard normal curve to the left of -1.86.
Using a standard normal table, we can see that the area under the curve to the left of -1.86 is approximately 0.0314. However, since this is a two-sided test, we also need to consider the area in the right tail, which is also 0.0314. Therefore, the P-value for a test statistic of -1.86 in a one-sample two-sided z-test for a population proportion is approximately 0.0314 + 0.0314 = 0.0628.
Hence, the answer to the P-value is 0.0628.
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PLEASE HELP SOON! :)
Multiply and simplify. ( 4x - 7 ) ( x + 5 )
What is the answer? Fill in the blanks in standard form, from left to right.
4x^? + ?x-?
blank 1: enter number
blank 2: enter number
blank 3: enter number
Q. 2
Multiply and simplify. ( 6x - 5y ) ( 2x^2 - 7xy - 8y^2 ) What is the answer?
1. 12x^3 - 52x^2y - 13xy^2 + 40y^3
2. 12x^3 - 42x^2y - 48xy^2 + 40y^3
3. 12x^3 - 10x^2y - 35xy^2 + 40y^3
4. 12x^3 - 42x^2y - 35xy^2 + 40y^3
Answer:
The answer to your question is no 1 that is
12x^3 - 52x^2y - 13xy^2 + 40y^3
identify the correct unit fraction to multiply by the second term to create a common denominator for the rational expression below:
(2x^(2)-16)/(x^(2)-4)-(x 4)/(x-2)
The correct unit fraction to multiply by the second term to create a common denominator is [tex](x+2)/(x+2)[/tex]
To find a common denominator for the given rational expression, we need to identify a unit fraction that can multiply the second term so the denominators of both terms will be the same.
The denominators of the two terms are [tex]x^2-4[/tex] and [tex]x-2[/tex]. To find a common denominator for these terms, we can multiply the second term [tex](x+2)/(x+2)[/tex] which is a unit fraction because it is equal to 1.
Multiplying the second term by [tex](x+2)/(x+2)[/tex] gives us:
[tex](x 4)/(x-2) * (x+2)/(x+2) = (4x(x+2))/(x^2-4)[/tex]
Now both terms have a common denominator [tex]x^2-4[/tex]. Thus the correct unit fraction to multiply by the second term to create a common denominator is [tex](x+2)/(x+2)[/tex]
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How many integers greater than 5400 have both of the following properties :
a) the digits are distinct.
b) the digits 2 and 7 do not occur,
There are 94830 integers greater than 5400
At first, go it looks .like an infinite number but As digits are distinct
so a maximum 10 digits number is possible
but 2 & 7 can not be used so the maximum 8-digit number can be there
Total number = 4 digits numbers, 5 Digits numbers, 6 digits number, 7 digits numbers, 8 digits numbers
All the 5 - 8 digit numbers would be > 5400
Available number of Digits = 8 ( 0, 1, 3, 4, 5, 6, 8, 9)
for numbers greater than 4 digits (5 - 8 Digits), 1st digit can be 1, 3, 4, 5, 6, 8, 9 then from the 2nd digit onward 0 can also be a digit but the already used digit can not be used. and further one digit (already used) will keep reducing
5 Digits numbers = 7 * 7 * 6 * 5 * 4 = 5880
6 Digit Numbers = 7 * 7 * 6 * 5 * 4 *3 = 17640
7 Digits numbers = 7 * 7 * 6 * 5 * 4*2 = 35280
8 Digit Numbers = 7 * 7 * 6 * 5 * 4 *3*2*1 = 35280
Now in 4-digit numbers
Number starting with 6, 8, 9 > 5400 & number starting with 5
Number starting with 6 , 8 , 9 = 3 * 7 * 6 * 5 = 630
Number starting with 5, the second digit must be 4, 6, 8, 9
Number starting with 5 = 1 * 4* 6 * 5 = 120
Total integers greater than 5400
=5880 + 17640 + 35280 + 35280 + 630 + 120
= 94830
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PLEASEHELP WITH PROBLEMS
In order to maximize profit the firm should produce 4 or 5 units.
The marginal revenue and the marginal cost are the same at quantity 6.
The marginal revenue curve and the marginal cost curve cross at a quantity 6.
The firm loses in a competitive industry because marginal revenue is decreasing as quantity increases.
The industry is in a long-run equilibrium.
True.
The graph is given below.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Marginal cost = Change in cost / Change in Quantity
Marginal Revenue = Change in Revenue / Change in Quantity
Profit = Marginal revenue - Marginal cost
Now,
Quantity Total cost Marginal cost Total revenue Marginal revenue Profit
0 5 0
(6 - 5)/(1 - 0) = 1 (6 - 0)/(1 - 0) = 6 (6 - 5) = 1
1 6 6
(8 - 6)/(2 - 1) = 2 (12 - 6)/(2 - 1) = 6 (6 - 2) = 4
2 8 12
(11 - 8)/(3 - 2) = 3 (18 - 12)/(3 - 2) = 6 (6 - 3) = 3
3 11 18
(15 - 11)/(4 - 3) = 4 6 (6 - 4) = 2
4 15 24
(20 - 15)/(5 - 4) = 5 6 (6 - 5) = 1
5 20 30
(26 - 20)/(6 - 5) = 6 6 (6 - 6) = 0
6 26 36
(35 - 26)/(7 - 6) = 9 6 (6 - 9) = -3
7 35 42
We see from the table,
There is no profit when the quantity is 6 and 7.
So,
In order to maximize profit the firm should produce 4 or 5 units.
Now,
From the table,
The marginal revenue and the marginal cost are the same at quantity 6.
The marginal revenue curve and the marginal cost curve cross at a quantity 6.
Now,
The firm loses in a competitive industry because marginal revenue is decreasing as quantity increases.
Now,
Since the marginal cost is the same.
The industry is in a long-run equilibrium.
True.
Now,
The marginal cost equation.
y = x + 0.5
i.e
(0.5, 1) and (1.5, 2)
y = mx + c
m = (2 - 1)/(1.5 - 0.5) = 1/1 = 1
1 = 1 x 0.5 + c
c = 1 - 0.5
c = 0.5
The marginal revenue equation.
y = 6
i.e
(0.5, 6) and (1.5, 6)
m = 0
6 = 0 x 0.5 + c
c = 6
The graph is given below.
Thus,
The statement is given above.
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a p-value of 0.04 obtained from a two-tailed t-test means that there is a % chance that the obtained results are due to . given the conventional significance level, you would reject the hypothesis.
A p-value of 0.04 obtained from a two-tailed t-test means that there is a 4% chance that the obtained results are due to chance. Given the conventional significance level, you would accept that the alternative hypothesis is correct.
If the null hypothesis is correct and the study is conducted several times and exactly as it was intended to be done, the P=0.04 indicates that.
In statistical hypothesis testing, it is necessary to state the alternative hypothesis, which is the statistical difference, and the null hypothesis, which is the absence of any statistical difference between the groups.
The test statistic, which is a uniformly scaled quantitative measure of the group difference, is then calculated.
The test statistic result is expected to be modest under the null hypothesis, but there is a small risk that it could accidentally be large. Once we get the test statistic, we use the test statistic to compute the p-value.
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The complete question is:
A p-value of 0.04 obtained from a two-tailed t-test means that there is a ____ % chance that the obtained results are due to _______. Given the conventional significance level, you would accept that the _________ hypothesis is correct.
find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (if not possible, enter impossible.) x y
The solution of the system of linear equations has infinitely many solutions.
Linear equation is defined as an algebraic equation of the form y=mx + b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.
Here we have given that the following linear equations are given then are listed as follows:
x + y = 4
y + z = 4
x + z = 4
ax + by + cz = 0
Here we have know that the sub-system consisting of 3 first equations has a unique solution x = y = z = 2.
While we add the fourth equation, then it becomes look like as follows:
=> 2a + 2b + 2c = 0
When we simplify this one then we get,
=> a + b + c = 0.
Which means that if a + b + c = 0, then the system of 4 equations has a unique solution otherwise it is IMPOSSIBLE to this system to have infinitely many solutions.
Complete Question:
Try to find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
x + y = 4
y + z = 4
x + z = 4
ax + by + cz = 0
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