The value of a is zero from the given expression
Subject of formulaSubject of formula is a way of representing a variable with another variable.
Given the expression below;
5=5/ax+1
We are to make x the subject of the formula
1 =1/ax+1
Cross multiply
ax+1 = 1
ax = 1-1
ax = 0
Find the value of a
a = 0/x
a = 0
Hence the value of a is zero from the given expression
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3. la mamá de jordan compró 7 cajas de envases de jugo para después del entrenamiento del equipo. cada caja tenía 8 envases de jugo. después que el equipo bebió todo el jugo que quiso, quedaron 29 envases de jugo. el equipo abrió una nueva caja solo después de beber todo el jugo de la caja anterior. ¿cuántas cajas de jugo abrió el equipo?
Answer:
Step-by-step explanation:
The team drank a total of 7 x 8 = 56 juice boxes, and there were 29 remaining, so the team opened 56 - 29 = 27 juice boxes.
Since the team only opened a new box after finishing the previous one, the team opened 27 - 1 = 26 boxes of juice in total.
To explain this solution in more detail, we can use basic arithmetic. We know that the mom bought 7 boxes of juice, each containing 8 juice boxes,
so the total number of juice boxes is 7 x 8 = 56. After the team drank all the juice they wanted, there were 29 juice boxes remaining. This means that the team drank 56 - 29 = 27 juice boxes.
Since the team only opened a new box of juice after finishing the previous one, the number of boxes opened will be one less than the total number of juice boxes consumed.
Therefore, the team opened 27 - 1 = 26 boxes of juice in total. It is important to note that this assumes that the team opened all the boxes they consumed and did not drink any juice directly from the remaining boxes.
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The graphs below have the same shape. What is the equation of the red
graph?
A. g(x) = 1 x^2
B. g(x) = (1 - x)^2
C. g(x) = 7 - x^2
D. g(x) = (7 - x)^2
Answer:
the answer is g(x) = 1 - x²
Since the intercept of g(x) are :
for x intercept , g(x) =0 (1-x)×(1+x) =0
and for y intercept y= 1
hence then its should be g(x) = 1- x²
The equation of red graph that is g(x) = 1 - x²
Given,
f(x) = 4 - x²
g(x)
Now,
Since the intercept of g(x) are :
for x intercept , g(x) =0 (1-x)×(1+x) =0
and for y intercept y= 1
Thus the equation of graph will be :
g(x) = 1- x²
The coefficient of x² is negative which indicates that the graph is concave down in nature .
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use natural logarithms to solve the equation 3e^2x+5=27
The solution to the equation 3e^(2x) + 5 = 27 is x = 1.36.
To solve the equation 3e^(2x) + 5 = 27 using natural logarithms, we can follow these steps:
Step 1: Subtract 5 from both sides of the equation:
3e^(2x) = 22
Step 2: Divide both sides of the equation by 3:
e^(2x) = 22/3
Step 3: Take the natural logarithm (ln) of both sides of the equation:
ln(e^(2x)) = ln(22/3)
Step 4: Apply the property of logarithms that states ln(e^a) = a:
2x = ln(22/3)
Step 5: Divide both sides of the equation by 2:
x = ln(22/3)/2
Using a calculator, we can evaluate ln(22/3) to be approximately 2.72.
Therefore, x = 2.72/2 = 1.36.
So, the solution to the equation 3e^(2x) + 5 = 27 is x = 1.36.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5
Answer:
C
Step-by-step explanation:
I may be wrong...
Sooo sorry if I am
you flip a coin and get heads 11 times, so the chance of getting heads in 11/30. Is this an example of theoretical or expiremntal probabilty
two sides that form from the right angle of a right triangle are 6 inches and 4 inches
12. Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 8 and the 8th term is 18.
A. 7
B. 12
C. 15
D. 5
Answer:
12
Step-by-step explanation:
5 fewer than a number, k.
Answer:
k-5. The question seems incomplete though.
Answer:
k - 5
Step-by-step explanation:
5 fewer than a number, k can be written as 5 less than k, which is k - 5.
kareem the trainer has two solo workout plans that he offers his clients: plan a and plan b. each client does either one or the other (not both). on monday there were clients who did plan a and who did plan b. on tuesday there were clients who did plan a and who did plan b. kareem trained his monday clients for a total of hours and his tuesday clients for a total of hours. how long does each of the workout plans last?
The duration for the workout of Plan A is (total hours trained on Tuesday - total hours trained on Monday) / 2, and the duration of Plan B is (total hours trained on Monday - total hours trained on Tuesday) / 2.
Let's assume that Plan A lasts for x hours and Plan B lasts for y hours.
We can set up a system of two linear equations using the information provided:
x + y = hours trained with Plan A and Plan B on Monday
x + y = hours trained with Plan A and Plan B on Tuesday
Adding the two equations together:
2x + 2y = total hours trained on both days
Simplifying this equation, we get:
x + y = total hours trained on both days / 2
We can substitute this expression for x + y in one of the original equations, say the first one:
x + y = hours trained with Plan A and Plan B on Monday
(total hours trained on both days / 2) = hours trained with Plan A and Plan B on Monday
Similarly, we can substitute x + y in the second equation:
(total hours trained on both days / 2) = hours trained with Plan A and Plan B on Tuesday
Now we have two equations with two variables:
x + y = total hours trained on both days / 2
x + y = hours trained with Plan A and Plan B on Monday
Subtracting the second equation from the first, we get:
0 = (total hours trained on both days / 2) - (hours trained with Plan A and Plan B on Monday)
Therefore,
hours trained with Plan A and Plan B on Monday = total hours trained on both days / 2
We can use the same logic to find the hours trained with Plan A and Plan B on Tuesday:
hours trained with Plan A and Plan B on Tuesday = total hours trained on both days / 2
Since we know the total hours trained on both days and the hours trained with Plan A and Plan B on each day, so solving for x and y:
x = hours trained with Plan A and Plan B on Monday - hours trained with Plan A and Plan B on Tuesday
y = hours trained with Plan A and Plan B on Tuesday - hours trained with Plan A and Plan B on Monday
Substituting the expressions we found earlier, we get:
x = (total hours trained on both days / 2) - hours trained with Plan A and Plan B on Tuesday
y = (total hours trained on both days / 2) - hours trained with Plan A and Plan B on Monday
We can simplify these expressions to get:
x = (total hours trained on Tuesday - total hours trained on Monday) / 2
y = (total hours trained on Monday - total hours trained on Tuesday) / 2
Therefore, the duration of Plan A is (total hours trained on Tuesday - total hours trained on Monday) / 2, and the duration of Plan B is (total hours trained on Monday - total hours trained on Tuesday) / 2.
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Here is an issue to consider concerning internal validity. Sometimes a participant in this lab has a response time that is less than 100 milliseconds. How might you explain such very short responses? Suppose another experiment had participants say the word "now" as soon as they detected the green circle, and that the response times were between 100 and 200 milliseconds. What would you conclude about the cognitive tasks involved in these two versions of simple detection?
The response times observed in the two experiments suggest that the cognitive demands of the two tasks differ, with the second task being more cognitively demanding than the first.
The very short response times of less than 100 milliseconds observed in the lab might be due to several factors. One possibility is that the participant has developed a prepotent response that is initiated almost automatically upon presentation of the stimulus. This means that the participant has become so familiar with the task that their response is almost reflexive, requiring little cognitive processing. Another possibility is that the stimulus presented was so salient or intense that it elicited an immediate and involuntary response from the participant. In the second experiment where participants say the word "now" as soon as they detect the green circle, the response times were between 100 and 200 milliseconds. This suggests that the cognitive tasks involved in this version of simple detection may require more conscious effort and attention than the tasks in the first experiment. Participants in the second experiment had to actively detect the presence of the green circle and make a conscious decision to say "now", whereas in the first experiment their response may have been more automatic. Therefore, the response times observed in the two experiments suggest that the cognitive demands of the two tasks differ, with the second task being more cognitively demanding than the first.
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What is the correct rate of change of Bill and Kevin's trip
ss2−14s 49=f∣∣s−7 where f(s)= therefore f(t)=
The inverse Laplace transform of f(s) is f(t) = e^(7t) * u(t).We are given that:
s^2 - 14s + 49 = f(s) * (s - 7)
We can simplify the left-hand side of the equation as:
(s - 7)^2 = f(s) * (s - 7)
Dividing both sides by (s - 7), we get:
s - 7 = f(s)
Therefore, the Laplace transform of f(t) is f(s) = s - 7.
To find the inverse Laplace transform of f(s), we use the formula:
L^-1{f(s - a)} = e^(at) * L^-1{f(s)}
Applying this formula with a = 7 and f(s) = s, we get:
f(t) = e^(7t) * L^-1{s}
The inverse Laplace transform of s is a unit step function u(t), which is defined as:
u(t) = {
1 for t ≥ 0
0 for t < 0
}
Therefore, the inverse Laplace transform of f(s) = s is:
L^-1{s} = u(t)
Substituting this in our previous equation, we get:
f(t) = e^(7t) * u(t)
Hence, the inverse Laplace transform of f(s) is f(t) = e^(7t) * u(t).
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3) A particularly fast tortoise can run with a top speed of 10 centimeters per second. The tortoise's hare friend hare can run up to 20 times as fast as that. In a race between the two, the hare sits and rests for two minutes after the starting gun fires, but the tortoise moves right off at top speed. After its rest, the hare runs as fist as it can, but the tortoise still wins the race by a single shell length (which is about twenty centimeters). a. During the race, who nuns the greater distance? How do you know? b. Across the entire race, who has the greater average velocity? How do you know? c. At some point in the period during which both are running, who has the larger instantancous velocity? How do you know? 4)
∗+A
particularly fast tortoise can run with a top speed of v
r
. A hare can run with a speed v
μ
. In a race between the two, the hare sits and rests for a time Δt
0
after the starting gun fires, but the tortoise moves right off at top speed. After its rest, the hare runs as fast as it can, but the tortoise still wins the race by a single shell length (length of shell =s ). The length of the racetrack is represented by d. The race is considered over when the tortoise crosses the finish line. a. Using the symbols defined in the problem, write an equation for Δ
T
, the total amount of time that the tortoise ran during the race b. Using the symbols defined in the problem, write an equation for Afu. the total amount of time that the hare spent running. c. Find expressions for the length d of the racetrack and the times that the animals each ran ( Δt
T
and Δt
1
), in terms of only the other symbols defined in the problem ( v
f
,v
m
,s, and Δt
0
- the symbol d can't appear in your expressions for Δf
r
and Δt
i
this time!). 5) ** Oscillococcinum is a real homeopathic 'medicine' that is touted as a relief for flulike symptoms. Its key ingredients are duck liver and heart, which are diluted to ' 200c
’
within the pill material. Meaning: the duck organ is diluted to 1 part in 100, then the dilution is repeated 200 times. After two dilutions, the ratio of duck organ to pill material is 1 in 10
4
, after three, the ratio is 1 in 10
∘
, and so on all the way to 200.) Make an estimate of how many original duck organ molecules are in one Oscillococcinum pill. You may assume that each pill has a mass of about 1 g. Do not use a calculator! Perform all calculations roughly, in your head or on paper. Be sure to clearly state your assumptions and how you came to the numbers you estimated, since grading on this problem will be mostly based on your reasoning, not on your answer. We are not interested in whether you can "guess" a right answer, but in whether you can use your everyday experience to infer information about topics about which you may have little direct knowledge
a. During the race, the tortoise runs the greater distance. We know this because it is stated that the tortoise wins the race by a single shell length, which is about twenty centimeters. This means that the tortoise crosses the finish line before the hare, indicating that it has covered a greater distance.
b. Across the entire race, the tortoise has the greater average velocity. Average velocity is defined as the total distance traveled divided by the total time taken. Since the tortoise crosses the finish line first, it covers the entire race distance in less time compared to the hare. Therefore, the tortoise has a greater average velocity.
c. At some point during the race, the hare has a larger instantaneous velocity. Instantaneous velocity refers to the velocity of an object at a specific instant in time. The hare is capable of running up to 20 times faster than the tortoise's top speed. Therefore, when the hare is running at its maximum speed after the rest, it will have a larger instantaneous velocity compared to the tortoise.
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Which linear inequality represents the solution set graphed?
A. y≥4x+5
B. y>4x-5
C. y≥4x-5
D. y>-4x-5
The linear inequality (B) y>4x-5 represents the given solution set graph.
What is linear equality?A linear inequality in mathematics is an inequality involving a linear function. One of the symbols for inequality is found in linear inequality. It displays non-equal data in graph style. The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half. For > and, the border line is solid, and for and, it is dashed. Typically, the half-plane that resolves the inequality is shaded.So, the linear inequality that represents the graph:
Graph the inequation as follows:
(A) y≥4x+5 (Refer to attached Graph 1)(B) y>4x-5 (Refer to attached graph 2)(C) y>-4x-5 (Refer to attached graph 3)Now, we can easily notice that graph 2 which is of equation (B) y>4x-5 matches the given graph.
Therefore, the linear inequality (B) y>4x-5 represents the given solution set graph.
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The correct question is given below;
Which linear inequality represents the solution set graphed?
A. y≥4x+5
B. y>4x-5
C. y>-4x-5
john and jane go rock-climbing together. john climbs a height of $(x 5)$ miles in $(x-1)$ hours and jane climbs a height of $(x 11)$ miles in $(x 1)$ hours. if john and jane were climbing at the same speed, what must have been their speed, in miles per hour?
Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.
Distance covered by John = Distance covered by Jane
Therefore, \($(x + 5) = (x + 11)$\)
Thus, x = 6
Now, we need to find the speed of both, which is given by the formulae:
Speed = Distance / Time
So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph
Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)
Speed of Jane = \($17 / 7$\) mph
Since both have to be equal, Speed of John = Speed of Jane Therefore,
\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)
Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph
Speed of Jane = \($7 / 3$\) mph
Thus, their speed was \($7 / 3$\) mph.
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Introductory Statistics Course Withdrawals. A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. a. Compute the probability that 2 or fewer will withdraw. b. Compute the probability that exactly 4 will withdraw.
The probability that exactly 4 students will withdraw is approximately 0.2048.
The problem asks us to calculate the probabilities related to student withdrawals in an introductory statistics course. We are given that 20% of students withdraw from the course and that 20 students registered for the course.
a. To compute the probability that 2 or fewer students will withdraw, we need to calculate the cumulative probability of the binomial distribution. We can use the binomial probability formula:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Using the formula, the probability can be calculated as follows:
P(X = 0) = (20 choose 0) * (0.2^0) * (0.8^20) ≈ 0.0115
P(X = 1) = (20 choose 1) * (0.2^1) * (0.8^19) ≈ 0.0729
P(X = 2) = (20 choose 2) * (0.2^2) * (0.8^18) ≈ 0.1948
Therefore, P(X ≤ 2) ≈ 0.0115 + 0.0729 + 0.1948 ≈ 0.2792
b. To compute the probability that exactly 4 students will withdraw, we use the binomial probability formula:
P(X = 4) = (20 choose 4) * (0.2^4) * (0.8^16) ≈ 0.2048
Therefore, the probability that exactly 4 students will withdraw is approximately 0.2048.
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In the diagram below BD is parallel to XY what is the value of y ?
How many decimal places should we have in the product for this multiplication problem : 0.73 x 2.52
Answer:
4
Step-by-step explanation:
because the first number has 2 decimal places and the second 2. So, 2+2=4
Answer:
ksoslsmskksisosjzjsoslsndhsislsmndjddu
Step-by-step explanation:
yapamadım
hi i need help so how should I write the the 4x^3-3x^2+100x-75 as a product of linear factors?
Answer:
(4x - 3)(x^2 + 25)
Step-by-step explanation:
Step as below:
4x^3-3x^2+100x-75 =x^2*4x - x^2*3 + 25*4x - 25*3 = x^2(4x -3) + 25*(4x - 3) = (4x - 3)(x^2 + 25)One of the factors is linear, the second factor cannot be factored anymore
find the values of k for which the line y = 2x + k + 2 cuts the curve y = 2x^2 + (k + 2)x + 8 at two distinct points.
The values of k for which the line y = 2x + k + 2 cuts the curve y = 2x² + (k + 2) + 8 at two distinct points are; k > -12 or k < 4
What is the point of Intersection of the line and the curve?We are given the equation of the line as;
y = 2x + k + 2
Equation of the curve is;
y = 2x² + (k + 2) + 8
Now, to find the the values of k for which the line y = 2x + k + 2 cuts the curve y = 2x² + (k + 2) + 8 at two distinct points, we will just equate both equations to get;
2x + k + 2 = 2x² + (k + 2) + 8
2x + k + 2 = 2x² + kx + 2x + 8
2x² + kx + (-k + 6) = 0
Now, Two distinct solutions is the same as having a positive discriminant.
b² - 4ac > 0
k² - 4(2 * (-k + 6)) > 0
k² + 8k - 48 > 0
Solving using quadratic equation calculator gives;
k > -12 or k < 4
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Please help with part (b) and (c) of the question ((: Thank youuuu
B) Note that in the prompt above, you can use translation to map the line y= 2x -4 onto the line y = 2x + 4.
While you can use axial symmetry in the y - axis to map the line y = x onto the line y = -x.
What is the meaning of Translation and Axial Symmetry?Axial symmetry is symmetry around an axis; an item is axially symmetric if it retains its appearance when rotated around an axis.
A baseball bat with no brand or other design, or a plain white tea saucer, for example, looks the same when rotated by any angle around the line traveling longitudinally through its center, indicating that it is axially symmetric.
A transformation in which the coordinate system's origin is shifted but the orientation of each axis remains constant
So for B) you can use a translation to map the line y = 2x -4 onto the line y = 2x + 4 by shifting the first line 4 units upwards along the y - axis....
mathematically, that would be:
y = 2x - 4 + 4
y = 2x
For C) you can use axial symmetry on the y - axis to achhieve the mapping of y = x onto y = -x by reflection.
The polar opoppsite of y = x is y = -x.
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I dont know how to do this question someone help meeeee
Answer:
90
Step-by-step explanation:
First, let's make a line of separation to make a rectangle and triangle.
Now, we know the area of a rectangle is l × w, where l = length and w = width. The length and width of this rectangle is is 8 and 9, so 8 × 9 = 72.
Next, the area of a triangle is bh ÷ 2, where b = base and h = height. We're given the base of the triangle as 9 m. To find the height, we subtract 8 from 12 and get 4. 9 multiplied by 4 is 36, and 36 divided by 2 is 18.
Lastly, we combine the area of the rectangle and triangle. 72 + 18 = 90.
Therefore, the answer is 90 m^2.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
I need help asap please
Answer:
x = - 69
Step-by-step explanation:
if its wrong i can help u again
What are independent variables and dependent variables when
conducting a research design to investigate the impact of a school
nutrition program on grade performance of students at high
school?
Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.
The researcher would design and implement the program, and this variable would be under their control.
Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.
In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.
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Please provide Guidance ASAP on how to calculate the last question and answer this question.
How many years will it take to reach 50,000 pairs and what unrealistic assumptions were made in prediting the time it would take to reach 50,000 pairs?
Table 7. Analysis of Bald Eagle Recovery
What is the shape of the curve? J-shaped exponential curve
Doubling time from 1,000 to 2,000 4.73 years
Doubling time from 2,000 to 4,000 9.47 years
Doubling time from 4,000 to 8,000 18.94 years
Average doubling time 11.05 years
Doubling time increasing or decreasing? increasing
Starting number of breeding pairs 791 Year 1974
Theoretical prediction to reach 1,582 pairs Year 1979
Theoretical prediction to reach 3,164 pairs Year 1987
Theoretical prediction to reach 6,328 pairs Year 2002
Theoretical prediction to reach 12,636 pairs Year 2030
How many years to reach 50,000 pairs? 235 years
To calculate the time it would take to reach 50,000 pairs, we can use the average doubling time provided in the table. The shape of the curve is a J-shaped exponential curve.
which means that the number of pairs increases at an accelerating rate over time. Since the average doubling time is 11.05 years, we can determine the number of times we need to double the initial number of breeding pairs (791) to reach 50,000 pairs. By successively doubling the number of pairs and keeping track of the years passed, we reach 50,000 pairs in 235 years (as given in the table).
However, there are unrealistic assumptions made in predicting the time to reach 50,000 pairs. The main assumption is that the doubling time remains constant, while in reality, factors such as environmental limitations, availability of resources, and human intervention could cause the rate of growth to change over time.
Additionally, the model assumes that there are no significant negative events (such as disease outbreaks or natural disasters) that could negatively impact the bald eagle population during this period.
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which property is illustrated for all expressions a and b if a=b then b=a
Answer:
Symmetric property
–5(–3 + 5x) = simplify
Answer: -25x + 15
Step-by-step explanation:
Because you asked
Answer:
To simplify the expression, we can use the rules of order of operations, which dictate that we should perform operations in the following order:
Perform any calculations inside parentheses or other grouping symbols, working from the innermost set of parentheses to the outermost.
Perform any exponents or radicals.
Perform all multiplications and divisions, working from left to right.
Perform all additions and subtractions, working from left to right.
Applying these rules to the expression -5(-3 + 5x), we get:
Perform any calculations inside parentheses or other grouping symbols, working from the innermost set of parentheses to the outermost:
$-5(-3 + 5x)$
$-5(-3) + -5(5x)$
$15 + -5(5x)$
Perform any exponents or radicals:
$15 + -5(5x)$
Perform all multiplications and divisions, working from left to right:
$15 + -5(5x)$
$15 + -25x$
Perform all additions and subtractions, working from left to right:
$15 + -25x$
Therefore, the simplified expression is 15 + -25x.
Step-by-step explanation:
The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments: investigate further whether the proportions of furnished apartments differ be- tween apartments with different numbers of bedrooms, it is useful to test formally whether the number of bedrooms in an apartment and whether it is furnished or not are independent (a) State the null hypothesis the relevant form of the test statistic and the approximate distri- bution of the test statistic for carrying out this text (b) Provide cross-tabulation of the apartment data by these two factors (you should generate this table using R)
(c) Carry out a formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv. the resulting p-value for the test, or rejection region You should also ensure that you conclude your formal test by interpreting the p-value (or rejection region and your observed test statistic) in terms of the original question discussed above:'
The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000
formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv
500x + 900y + 1500z = 750,000 - - - (1)
x + y + z = 1000 - - - - (11)
x = 200 + y + z - - - - (111)
x + 2y + 3z = 1550 - - - (1V)
I bedroom = x
2 bedroom = y
3 bedroom = z
All the condition s gjvbbs'
500x + 900y + 1500z = 750,000 - - - (1)
x + y + z = 1000 - - - - (11)
x = 200 + y + z - - - - (111)
x + 2y + 3z = 1550 - - - (1V)
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Considering the triangle with exterior angles and interior angles as described. The statements that are true include
m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°How to determine the statements that are correctThe problem is solved considering this 3 theorems about triangles
exterior angle of a triangle theoremlinear pair theoremsum of angles in a triangleexterior angles theorem: m∠2 + m∠3 = m∠6
If a triangle side is created, the outside angle that results is equal to the sum of the two opposite internal angles.
Linear pair theorem: m∠5 + m∠6 =180°
Linear pairs are particular instances of supplementary angles that only involve two neighboring angles.
Sum of angles in a triangle is equal to 180 degrees:
m∠2 + m∠3 + m∠5 = 180°
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If the graph of y=|x| is compressed vertically by a factor of 1/3, reflected about the x-axis and translated 3 unit(s) left and 5 unit(s) up, what is the equation of the new graph?
Answer:
Y= -1/3 |x+3| +5
Step-by-step explanation:
An absolute value will always make a V line.
In your particular problem it wants you to reflect it over the x axis, and to do this you simply need to place a negative.
A negative in the beginning of the problem is only there to say whether you flip your line or not, and this means you don't have to worry about it any more.
What it looks like so far: Y= -
Next it wants you to compress the line vertically by 1/3
A number that causes your line to compress is always less than one
A number that stretches your line would be 1 or more
This number is always placed right next to the left of the parenthesis or absolute value.
What it looks like so far: Y= - 1/3
Now we want the line to move left 3 units.
We are now inside of the absolute value because this is where we move the line left or right. This can get a little confusing, but once you get it then you don't forget it.
Inside the line.. a -# moves right and a +# moves left.
This number should be placed inside the absolute value and to the right of the x.
What it should look like: Y= - 1/3 |x + 3|
Now they want us to move the line up by 5 points.
To the outer right side of the absolute value is where we move things up or down.
To move a number up you need to place a + sign with however many places it wants you to move to the right of the sign, but to move the line down you need to place a - sign with however many places it wants you to move to the right of the sign.
To move this up you simply need to place a +5 to the outer right side of the absolute value.
What you should end up with: Y= - 1/3 |x+3| +5