21 miles per hour is the speed of boat still in water and 9 miles per hour is the speed of current.
What is downstream speed and upstream speed?Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream.
Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The term "upstream speed" in this context refers to the boat's net speed.
13) Given that, a boat traveled 280 miles downstream and back.
Time taken by boat in downstream is 7 hours and in upstream is 14 hours.
Let the speed of a boat be x miles per hour and the speed of a current be y miles per hour.
So, the total speed in downstream is x+y miles per hour and the total speed in upstream is x-y miles per hour.
We know that, Distance = Speed × Time
Now, 280=(x+y)×7
⇒ x+y=40 ------(I)
Here, 280=(x-y)×14
⇒ x-y=20 ------(II)
Add equation (I) and (II), we get
x+y+x-y=40+20
⇒ 2x=60
⇒ x=30 miles per hour
So, x+y=40
⇒ y=10 miles per hour
14) Given that, a boat traveled 252 miles downstream and back.
Time taken by boat in downstream is 12 hours and in upstream is 84 hours.
Let the speed of a boat be p miles per hour and the speed of a current be q miles per hour.
So, the total speed in downstream is p+q miles per hour and the total speed in upstream is p-q miles per hour.
We know that, Distance = Speed × Time
Now, 252=(p+q)×12
⇒ x+y=21 ------(I)
Here, 252=(p-q)×84
⇒ p-q=3 ------(II)
Add equation (I) and (II), we get
p+q+p-q=21+3
⇒ 2p=24
⇒ p=12 miles per hour
So, p+q=21
⇒ q=9 miles per hour
Therefore, the speed of boat still in water is 21 miles per hour and the speed of current is 9 miles per hour.
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An hour before show time, only 170 people are seated for a movie. According to ticket sales, 95% of the people have yet to arrive. How many tickets were sold for the movie? Explain your thinking.
Answer:
Let's call the total number of people who will attend the movie "x". We know that 95% of these people have yet to arrive, which means that only 5% have already arrived.
We can set up an equation to represent this situation:
5% of x = 170
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 5% (or 0.05, which is the decimal equivalent of 5%):
5% of x / 5% = 170 / 5%
Simplifying the left side of the equation gives:
x = 170 / 0.05
Evaluating the right side of the equation gives:
x = 3400
Therefore, there were 3400 tickets sold for the movie.
Faizah is paid $11 per hour for her work at a factory. She works 9 hours a day and 24 days a month. She saves $594 a month. Express the amount she saves as a percentage of her income.
Answer:
The amount she saves is 25% of her income
Step-by-step explanation:
She is paid $11 per hour
She works 9 hours per day
and for 24 days per month
So, she works 9(24) hours per month
= 216 hours per month
Now, she is paid $11 hourly, so for 216 hours,
she will have 11(216) = $2376
Total income = $2376 per month
Saving = $594 per month
As a percentage, we divide the savings by the total income,
savings/(total income) = 594/2376 = 1/4 = 0.25
Hence we get 25%
delivered.
a. What is the constant rate of change? What does it represent?
b. What is the initial value? What might that represent?
The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.
The given problem can be solved as follows,
(a) The graph given is a straight line that passes through (0, 40) and (10, 240).
The constant rate of change is equivalent to the the slope of the line given as,
⇒ (240 - 40)/(10 - 0) = 20
(b) The initial value of the graph is given as the y-intercept of the line.
Which is given as 40.
It might represent the fixed cost.
Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.
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The missing graph is attached here.
in herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to what?
In Herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to behaviour.
THE MATCHING LAW
Herrnstein's Experiment Herrnstein (1961) conducted an experiment with pigeons in a room with two response buttons, red and white. Each key was assigned its own VI gain schedule. For example, under one condition, the left button pick was boosted on a VI 135 second schedule, and the right button pick was boosted on a VI 270 second schedule.
After the birds have learned as much as possible about this electoral situation, how do they distribute their responses? We trained them for days and then measured their reactions. As is often the case with VI schedules, birds returned many responses for each reinforcer received. Most interesting, however, is that in this condition, where two-thirds of the reinforcers came from the left button, the birds performed about two-thirds of the responses with the left button. That is, the proportion of left button responses equaled or matched the proportion of reinforcers delivered by the left button. In another condition, two birds received only about 15% of reinforcers from the left key and responded about 15% to that key.
Based on these results, Herrnstein proposed the following general principle for individual behavior when presented with alternative sequences. So, what you think makes sense rather than other options available at that particular moment.
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first to get it right gets brainliest
What kind of room has no doors or windows
PLEASE HELP 5. Find the distance of the line segment joining the two points: (2,0) (0,-2)
Answer:
I would think 2 for my answer
100m world record was completed at an average speed of 37.6 km/h. work out this speed in meters per second?
Step-by-step explanation:
1 km = 1000 m
1 hour = 3600 s
so,
37.6 km = 37,600 m (still per hour or per 3600 s).
in 1 second now that is
37600/3600 = 10.44444444... m/s
any list of five real numbers is a vector in set of real numbers r superscript 5ℝ5.
Yes, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.
A vector is a mathematical object that represents a quantity with both magnitude and direction. In the case of ℝ5, this set includes all possible lists of five real numbers, which can be thought of as five-dimensional vectors. Each number in the list represents a component or coordinate of the vector, indicating how far it extends in each of the five dimensions.
Therefore, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.
In mathematics, a vector is an element of a vector space, which is a set of objects that can be added together and multiplied by scalars (real numbers). The set ℝ⁵ is a vector space consisting of all 5-tuples (lists) of real numbers, written as (a₁, a₂, a₃, a₄, a₅), where each element aᵢ is a real number. Any list of five real numbers forms a vector in ℝ⁵ because it satisfies the required conditions to be an element of the vector space.
A list of five real numbers is indeed a vector in the set of real numbers ℝ⁵, as it meets the necessary criteria to be a part of the vector space.
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Find the value of x for which the function below is maximum
Answer:
x = \(\frac{1}{2}\)
Step-by-step explanation:
Given function;
y = 5 + x - x²
To find the maximum value, follow these steps
(i) Find the first derivative (which is the slope) of the given function with respect to x. i.e;
\(y^{'}\) = \(\frac{dy}{dx}\) = \(\frac{d(5 + x - x^2)}{dx}\)
\(y^{'}\) = \(1 - 2x\)
(ii) From the result in (i) determine the value of x for which the slope is zero. i.e.
x for which
1 - 2x = 0
=> 1 = 2x
=> x = \(\frac{1}{2}\)
Therefore, the value of x for which the function is maximum is \(\frac{1}{2}\)
Answer:
x = 1/2
Step-by-step explanation:
The standard equation of a quadratic function is given by:
y = ax² + bx + c, If a > 0 then the graph has a minimum but if a < 0, then the graph has a maximum. To find the maximum or minimum, we differentiate the function with respect to x and equate to zero that is y'(x) = 0.
For the function y = 5 + x - x², a = -1 < 0, therefore it has a maximum.
Differentiating with respect to x:
y'(x) = 1 - 2x
Equating to zero
-2x + 1 = 0
-2x = -1
x = -1/ -2
x = 1/2
The function has a maximum at x = 1/2
9(18) using disributive property.
Answer:
162
Step-by-step explanation:
9 * 18 = 162
Answer:
162
Step-by-step explanation:
HELP PLEASEEEI’ll
Make you brainlist
Answer:
Step-by-step explanation:
0,5 0.6 and 0.5 again? sorry i might be wrong if i am my apologies
Fitness mania charges 20$ to join their gym and then 15$ per month.
1. Write an equation in slope intercept form.
2. How much will it cost to belong to Fitness Mania for one year?
3. If a different gym LVAC, charges 0$ to join and 20$ a month, which gym would be the cheaper choice for one year?
Fitness mania is cheaper as $200 < $240
Rewrite each of the following expressions without using absolute value.
a) |a| if a>0
b) |2b| if b<0
c) |c| if c <0
d) |3c| if c≥0
Answer:
a) answer is "a"
b) answer is "-2b"
c) answer is "-c"
d) answer is "3c"
Step-by-step explanation:
Absolute value is positive value of something.
a>0 then a must be positive so absolute value means nothing if a is already positive. Therefore answer is a.
b<0, so b must be negative. absolute value makes 2b positive but you know b is negative so answer is -2b.
c<0 same as a except sign is flipped so answer is negative instead of positive.
c>=0, C is either 0 or positive so absolute value does nothing yet again so answer is just 3c.
Sorry is explanation wasn't through i'm only in middle school
a. | a | > 0, a is greater than and less than zero.
b. | 2b | if b < 0, b is not less than zero not greater than zero.
c. | c | if c < 0, c is not less than zero not greater than zero.
d. | 3c | if c ≥ 0, c is greater than zero and less than zero.
What is an absolute value function?We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.
In piecewise terms | x | = x for x ≥ 0 and | x | = - x for x < 0.
Given,
| a | > 0
∴ a is greater than and less than zero.
| 2b | if b < 0
b is not less than zero not greater than zero.
| c | if c < 0
c is not less than zero not greater than zero.
| 3c | if c ≥ 0.
c is greater than zero and less than zero.
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suppose you are allowed to choose four numbers from 1 to 5. if repetitions are allowed, what is the largest possible result for the standard deviation?
If repetitions are allowed, the largest possible result for the standard deviation would occur when we choose the same number four times. In other words, if we choose 4 four times, the standard deviation would be 0 because all of the numbers are the same and there is no deviation from the mean.
However, if we want to choose four different numbers, the largest possible standard deviation would occur if we choose one number twice and two other numbers once each. For example, if we choose 1, 2, 2, and 3, the standard deviation would be approximately 0.829. This is because the formula for standard deviation takes into account the differences between each number and the mean of all the numbers chosen.
In general, the larger the range of numbers to choose from, the larger the possible standard deviation. This is because there are more potential combinations of numbers that could have a high deviation from the mean. Additionally, allowing repetitions also increases the potential for deviation since the same number can be chosen multiple times.
Overall, the largest possible standard deviation when choosing four numbers from 1 to 5 with repetitions allowed would be 0 if we choose the same number four times, or approximately 0.829 if we choose two numbers twice and two other numbers once each.
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8) Given m∠ABC is 124 and m∠ABD IS 37, find m∠DBC.
To obtain the measure of the missing angle, subtract the measure of ∠ABD from the measure of ∠ABC. Note that m∠ABD + m∠DBC = m∠ABC.
\(m\angle DBC=m\angle ABC-m\angle ABD\)Thus, we have:
\(m\angle DBC=124\degree-37\degree=87\degree\)Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write
12/32
in simplest form. You must show your work to receive all possible points.
Answer:
3/8 might me ans
Step-by-step explanation:
12/33
6/16
3/8
A class trip to a beach has been planned for your senior trip. the resort only allows swimming when the temperature is between 75 degrees and 110 degrees. there is room for 50 people on your trip. write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip. 0 < x ≤ 50 and 75 < y < 110 x > 75 and y < 110 75 < x < 110 and 0 < y ≤ 50 x < 110 and y > 75
This real-world problem has the limitations 75< x <110 and 0< y\(\leq\) 50, hence:
option (C) is the best choice.
What is Inequality ?The term "inequality" refers to a mathematical expression in which both sides have mathematical signs that are either less than or greater than one another, and the expression is one where the two sides are not on equal footing.
We have:
Your senior vacation is scheduled to include a class trip to a beach. Only when it's between 75 and 110 degrees do guests at the resort get access to the pool. 50 passengers can go with you.
Let y be the number of passengers and x be the temperature
75 to 110 degrees are the range of the temperature.
75 < x < 110
50 passengers can go with you.
0 < y ≤ 50
In order to illustrate this real-world issue, the limitations are 75 <x <110 and 0< y \(\leq\)50.
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A triangle has side lengths of 10 inches, 11 inches, and 12 inches. What kind of triangle is it?
Answer:
Acute scalene triangle.
More Information:
Sides: a = 10 b = 11 c = 12
Area: T = 51.521
Perimeter: p = 33
Semiperimeter: s = 16.5
Angle ∠ A = α = 51.318° = 51°19'4″ = 0.896 rad
Angle ∠ B = β = 59.17° = 59°10'10″ = 1.033 rad
Angle ∠ C = γ = 69.513° = 69°30'46″ = 1.213 rad
Height: ha = 10.304
Height: hb = 9.367
Height: hc = 8.587
Median: ma = 10.368
Median: mb = 9.579
Median: mc = 8.631
Inradius: r = 3.122
Circumradius: R = 6.405
Vertex coordinates: A[12; 0] B[0; 0] C[5.125; 8.587]
Centroid: CG[5.708; 2.862]
Coordinates of the circumscribed circle: U[6; 2.242]
Coordinates of the inscribed circle: I[5.5; 3.122]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 128.682° = 128°40'56″ = 0.896 rad
∠ B' = β' = 120.83° = 120°49'50″ = 1.033 rad
∠ C' = γ' = 110.487° = 110°29'14″ = 1.213 rad
How to Solve:
The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).
1. Input data entered: sides a, b, and c.
a=10
b=11
c=12
We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.
a=10
b=11
c=12
2. The triangle perimeter is the sum of the lengths of its three sides
3. Semiperimeter of the triangle
The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.
4. The triangle area using Heron's formula
Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.
5. Calculate the heights of the triangle from its area.
There are many ways to find the height of the triangle. The easiest way is from the area and base length. The triangle area is half of the product of the base's length and height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.
6. Calculation of the inner angles of the triangle using a Law of Cosines
The Law of Cosines is useful for finding a triangle's angles when we know all three sides. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. Pythagorean theorem works only in a right triangle. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. It is best to find the angle opposite the longest side first. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. We also use inverse cosine called arccosine to determine the angle from the cosine value.
7. Inradius
An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.
8. Circumradius
The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.
9. Calculation of medians
A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.
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The area of a trapezoid can be found using the expression
1/2h(b1+b2)
where h is the height and b1 and b2 are the lengths of the bases
a trapezoid has a height of 12 units and bases or (2x+3) and (3x+1).
which expression represents the area of the trapezoid?
answer options:
5x+4
6x+3
30x+42
60x+48
The area of the trapezoid is 30x + 42. Option C
How to determine the expressionThe formula for calculating the area of a trapezoid is expressed as;
A = 1/2h(b1+b2)
Such that the parameters are enumerated as;
A is the areab1 and b2 are the bases of the trapezoidh is the height of the trapezoidNow, substitute the values, we get;
Area = 1/2 × 12(2x + 3 + 3x + 4)
collect the like terms, we have;
Area = 6(5x + 7)
Expand the bracket, we get;
Area = 30x + 42
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There are a total of 18 monkeys and orangutans in a primate habitat. The monkeys each eat 5 bananas a day, and the orangutans eat 8 bananas a day. Each day the monkeys and orangutans together eat 111 bananas. How many monkeys and orangutans are in the habitat?
Answer:
18
Step-by-step explanation:
Which number d forces a row exchange, and what is the triangular system (not singular) for that d? Which d makes this system singular (no third pivot)? 2x + 5y + z = 0 4x + dy + z = 2 y -z = 3.
The number d that forces a row exchange is 10, and the triangular system for that d is:
2x + 5y + z = 0
y - z = 3
4x + 20y + 4z = 8
This system is not singular because it has a third pivot.
The number d that makes this system singular (no third pivot) is 10, as shown below:
2x + 5y + z = 0
4x + 10y + z = 2
y - z = 3
In this case, the third row can be obtained by subtracting the first row from the second row, so there is no third pivot. This means that the system is singular and there are infinitely many solutions.
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if my avg is a 96 and my final exam is a 75 which is 25% of my whole grade what will my final grade be
Step-by-step explanation:
That means the 96 is 75% of your grade
96 (.75) + 75 (.25) = 90.75 final grade
what is 4 and 3/4 minus 1/3
Answer:
4.41666666667
Step-by-step explanation:
The table shows the postal charges for sending letters to Country Y.
How much does it cost to send a letter weighing 60 grams to
Country Y?
PLS HELP ASAP!!!!
Answer:
$01.70
Step-by-step explanation:
Answer:
it will cost 170 $ total ....
If you were to rotate ABCD 180degrees about the origin, what would the coordinate of A' be?
Answer:
5,5
Step-by-step explanation:
The tower of hanoi is traditionally seen with three
pegs. how would adding more pegs affect the
minimum number of moves required to solve for n
disks? why is this the case?
Adding more pegs to the Tower of Hanoi puzzle does not affect the minimum number of moves required to solve for n disks. The minimum number of moves remains the same regardless of the number of pegs.
The Tower of Hanoi puzzle is a classic mathematical problem that involves moving a stack of disks from one peg to another, using a third peg as an intermediate step. The goal is to move all the disks from the starting peg to the destination peg, following specific rules that only allow smaller disks to be placed on top of larger ones.
The minimum number of moves required to solve the Tower of Hanoi puzzle with n disks is always 2^n - 1, regardless of the number of pegs. This means that even if additional pegs are added to the puzzle, the minimum number of moves to solve it remains the same.
This is because the optimal strategy for solving the Tower of Hanoi puzzle involves recursively moving the disks from one peg to another, using the spare pegs as intermediate steps. The number of spare pegs does not affect the number of moves required for each individual disk. Each disk still needs to be moved once, following the same sequence of moves, until the entire stack is transferred to the destination peg. Therefore, the minimum number of moves remains constant regardless of the number of pegs in the puzzle.
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NEED HELP!!!!!!!!!!!
Answer:
6
Step-by-step explanation:
do you want an explanation?
btw, plz brainliest :)
Express the confidence interval 0.039 < p < 0.479 in the form p± E. A. 0.22 ±0.5 B. 0.259 ±0.5 C. 0.259 ±0.44
D. 0.259 ±0.22
Answer:
Step-by-step explanation:
To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.
The midpoint of the interval is the average of the lower and upper bounds:
Midpoint = (0.039 + 0.479) / 2 = 0.259
The width of the interval is the difference between the upper and lower bounds:
Width = 0.479 - 0.039 = 0.44
Half of the width is obtained by dividing the width by 2:
Half Width = 0.44 / 2 = 0.22
Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:
p ± E = 0.259 ± 0.22
So, the correct option is:
D. 0.259 ± 0.22
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an older apartment building is having water quality problems, in order to determine if there have been any adverse health outcomes in the building, you are going to collect information on the residents of the building: 1. if you have collected data on all persons living in the apartment building, is this a census or a sample? 2. if you have collected data on people that were home during your visits to that building, is that a census or a sample? if it is a sample, what type of sample is this? 3. if you asked people to give their age and you collected it as <5, 6-10, 11-15, 16- 20, 21-25, 26 and older, what type of variable is this? 4. if you asked people to give their age in years, what type of variable is this? 5. if you found that those apartments with older hot water heaters had worse health, what type of evidence is this? 6. if you went to the building and observed that health was getting worse over the course of your visits, what type of evidence is this? 7. if you found differences in health outcomes by age, what type of evidence is this? 8. if you found that younger people in the building had worse outcomes and offered an intervention to help improve their health, what type of evidence supported this decision?
1. If you have collected data on all persons living in the apartment building, it is considered a census. A census is a complete collection of data from every individual or unit in a population.
2. If you have collected data only on people who were home during your visits to the building, it is considered a sample. A sample is a subset of the population from which data is collected. In this case, it would be a convenience sample, as you are only collecting data from those who happened to be present during your visits.
3. If you asked people to give their age and collected it as age categories (e.g., <5, 6-10, 11-15, etc.), this is an example of a categorical variable. Categorical variables are qualitative and represent characteristics or attributes that fall into distinct categories or groups.
4. If you asked people to give their ages in years, this is an example of a continuous variable. Continuous variables are quantitative and can take any numerical value within a certain range. Age in years can be measured on a continuous scale.
5. If you found that apartments with older water heaters had worse health outcomes, this would be considered observational evidence. It suggests a correlation between the age of water heaters and health outcomes, but it does not prove a causal relationship. Further research would be needed to establish causality.
6. If you observed that health was getting worse throughout your visits, this would also be considered observational evidence. It indicates a trend or pattern, but again, it does not prove causation. Other factors could be influencing the observed change in health.
7. If you found differences in health outcomes by age, this would be considered associative evidence. It suggests a relationship between age and health outcomes, but it does not imply causality. Other factors could be influencing the observed differences.
8. If you found that younger people in the building had worse outcomes and offered an intervention to help improve their health, the decision would be supported by associative evidence. The observed association between age and health outcomes suggests that targeting younger individuals with interventions may be beneficial. However, further research would be needed to confirm the effectiveness of the intervention.
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Solve this system of 3 variables with elimination. Once you eliminate 1 variable to get down to only 2, you can use Desmos but show all work/steps first.
3x − 4y + z = 2
−9x + 12y − 3z = − 6
4x − 2y − z = -16
The solution of the system of the equations are; x = -2/3, y = -1/2 and z = 1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The system of equation is given by;
3x − 4y + z = 2 ---- (1)
−9x + 12y − 3z = − 6 -------(2)
4x − 2y − z = -16 -----(3)
Now we add equations 1 from equation 3;
(3x − 4y + z ) + (4x − 2y − z ) = 2 -16
7x - 6y = -14 -----(4)
Further we multiply equation 3 by 3 and subtract from equation 2;
3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6
12x - 6y - 3z + 9x - 12y + 3z = 42
21x - 18y = 42-----(5)
Now we multiply equation 4 by 3 and add it to equation 4
3(-3x + 3z) + (9x + 4z) = 5×3 - 2
-9x + 9z + 9x + 4z = 15 -2
13z = 13
z = 1
Now we put z = 1 in equation number 5
-3x + 3×1 = 5
-3x + 3 = 5
-3x = 5 - 3
-3x = 2
x = -2/3
y = -1/2
Therefore, the solution of the system of the equations are; x = -2/3, y = -1/2 and z = 1.
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