When weighing the alternatives, the suitability of each alternative can be expressed using a scoring system. The scoring system assigns scores to each alternative based on how well they fulfill the variables to consider.
The following rating scale is used:
+2: Very suitable
+1: Quite suitable
0: Neither suitable nor unsuitable
-1: Not quite suitable
-2: Not suitable at all
These scores reflect the extent to which each alternative meets the criteria or variables being evaluated. A higher positive score (+2 or +1) indicates that the alternative is highly suitable and fulfills the variables well. A score of 0 suggests that the alternative does not strongly align with the variables, neither positively nor negatively. Negative scores (-1 or -2) indicate that the alternative is not suitable and fails to fulfill the variables effectively.
By assigning scores to each alternative, decision-makers can compare and evaluate the different options based on their suitability and alignment with the desired criteria. This helps in making informed decisions and selecting the most appropriate alternative that best meets the desired objectives or requirements.
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Let f(x) be any integrable, periodic function with period I such that its integral over any interval of length I
(i.e., over a period) is A for some A E R. Define fn(x) := f(nx), and prove that f(x) converges to f(x) = + (the
average) in the sense of distributions.
We have shown that for any test function φ(x), the integral of fn(x)φ(x) converges to the integral of f(x)φ(x) as n approaches infinity.
Since the convergence holds for any test function φ(x), we conclude that fn(x) converges to f(x) = A/I in the sense of distributions.
To prove that the sequence of functions fn(x) = f(nx) converges to the constant function f(x) = A/I in the sense of distributions, we need to show that for any test function φ(x), the integral of fn(x)φ(x) converges to the integral of f(x)φ(x) as n approaches infinity.
Let's begin the proof:
Start with the definition of convergence in the sense of distributions:
We need to show that for any test function φ(x), the integral of fn(x)φ(x) converges to the integral of f(x)φ(x) as n approaches infinity.
Consider the integral of fn(x)φ(x):
∫[0, I] fn(x)φ(x) dx
Substitute fn(x) = f(nx):
∫[0, I] f(nx)φ(x) dx
Make a change of variable:
Let u = nx, then du = n dx.
The integral becomes:
∫[0, I] f(u)φ(u/n) du/n
Note that as n approaches infinity, u/n approaches infinity as well, so we can replace φ(u/n) with φ(0) in the integral.
Rewrite the integral with the substitution u = nv:
∫[0, I] f(nv)φ(0) dv
Since f(v) is periodic with period I, we can substitute nv with v:
∫[0, I] f(v)φ(0) dv
Simplify the integral:
f(v)φ(0) ∫[0, I] dv = f(v)φ(0) I
Finally, take the limit as n approaches infinity:
lim(n→∞) ∫[0, I] fn(x)φ(x) dx = lim(n→∞) f(v)φ(0) I
The limit on the right-hand side does not depend on n and equals f(v)φ(0) I.
Therefore, we have shown that for any test function φ(x), the integral of fn(x)φ(x) converges to the integral of f(x)φ(x) as n approaches infinity.
Since the convergence holds for any test function φ(x), we conclude that fn(x) converges to f(x) = A/I in the sense of distributions.
Thus, we have proven that the sequence of functions fn(x) = f(nx) converges to the constant function f(x) = A/I in the sense of distributions.
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ocal park is in the shape of a square. A mop of the local park
Eh the scale 1 inch to 200 feet
If the park is shown as a square on the map, each o f which
one foot long, how long is each side of the square park
If a straight path in the park is 900 feet long, how long would
be when represented on the map?
The scale is 1 inch to 200 feet, theta means if the length of a line segment on the map is 1 inch than the actual length on the ground is 200 feet and vice versa.
i.e. if the actual length on the ground is 200 feet than the scaled length on the map is 1 inch.
So, by using the elementary method, if the actual length on the ground is 1 foot than the scaled length on the map is [tex]\frac{1}{200}[/tex] inch.
Here, on the map, the side of the square park is 1 foot=12 inch.
So, the actual length of each of the sides of the park is
[tex]12\times 200=2400[/tex] feet.
In another case, the actual length of the straight path in the park is 900 feet.
So, the scaled length on the map is
[tex]900\times \frac{1}{200}=4.5[/tex] inch.
Hence, 900 feet long straight path will be represented by 4.5 inch line segment on the map.
3x + 2y = -9
4x - 2y = -26
please help I have to solve this with the elimination method
Answer:
x = - 5, y = 3
Step-by-step explanation:
Given the 2 equations
3x + 2y = - 9 → (1)
4x - 2y = - 26 → (2)
Adding (1) and (2) term by term eliminates the y- term, that is
7x = - 35 ( divide both sides by 7 )
x = - 5
Substitute x = - 5 into either of the 2 equations and solve for y
Substituting into (1)
3(- 5) + 2y = - 9
- 15 + 2y = - 9 ( add 15 to both sides )
2y = 6 ( divide both sides by 2 )
y = 3
Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meter was found to be 10.8.
Find the probability of no dandelions in an area of 1 m². P(X=0)=P(X=0)= Find the probability of at least one dandelion in an area of 1 m².
P(at least one) = Find the probability of at most two dandelions in an area of 1 m². P(X≤2)=P(X≤2)=
The probability of no dandelions in an area of 1 m² is approximately 0.00034.
Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meter was found to be 10.8. Given this, we can find the probabilities of different numbers of dandelions in an area of 1 m².
Let X be the number of dandelions in a square meter. We can assume that X follows a Poisson distribution.
Using Poisson distribution, the probability of no dandelions in an area of 1 m² is:
P(X = 0) = e-10.8 × 10.8^0/0! ≈ 0.00034
In conclusion, the probability of no dandelions in an area of 1 m² is approximately 0.00034. This means that the occurrence of no dandelions in an area of 1 m² is very rare. The Poisson distribution is used when we are dealing with counts and the occurrence of events over a fixed interval or region. It is used when the occurrence of an event is rare, and it follows the assumption that the events occur independently of each other.
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What is a x-coordinate
Answer:
The horizontal line on a graph.
Step-by-step explanation:
Answer:
The horizontal value in a pair of coordinates: how far along the point is.
The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5).
I hope this help you out
(20x + 18) = 4x - 9. Helppp
Answer:
x=− 1.6875
:)))))))))))))))))))))))))
Answer:
[tex]x=-\frac{27}{16}\\\\x =- 1\frac{11}{16}[/tex]
Step-by-step explanation:
[tex](20x + 18) = 4x - 9\\\\20x+18=4x-9\\\\\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}\\\\20x+18-18=4x-9-18\\\\Simplify\\\\20x=4x-27\\\\\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\20x-4x=4x-27-4x\\\\Simplify\\16x=-27\\\\\mathrm{Divide\:both\:sides\:by\:}16\\\frac{16x}{16}=\frac{-27}{16}\\\\Simplify\\x=-\frac{27}{16}\\\\x =- 1\frac{11}{16}[/tex]
the diffrence of twice a number and 9 is -21
Answer:
- 6
Step-by-step explanation:
Step 1:
2x - 9 = - 21 Equation
Step 2:
2x = - 12 Add 9 on both sides
Step 3:
- 12 ÷ 2 Divide
Answer:
x = - 6
Hope This Helps :)
Answer:
x = -6
Step-by-step explanation:
Let x = unknown number
2x -9 = -21
Add 9 to each side
2x -9+9 = -21+9
2x = -12
Divide by 2
2x/2= -12/2
x = -6
A bike travels a distance of 575 meters in 10 minutes. What is its speed in meters per second.Please help
Answer:
57.5 meters per second
distance÷time= speed
I Need help on this please
Answer:
it would be 10.
Step-by-step explanation:
you have to reflect the quadrilateral to Q over x-axis then the Y-axis, and you would see that 10 is on the same side of ST.
n how many ways can the digits in the number 7,440,000 be arranged?
Answer:
7!/(4! × 2!× 1!) = 105 ways
What is an equation for the line perpendicular to y = 3x – 1 that passes through (-9, -2)?
Answer:
y = -1/3x - 5Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes, so the line is:
y = -1/3x + bFinding the value of b, using the given point (-9, -2)
-2 = -1/3*(-9) + b-2 = 3 + bb = -2 - 3b = -5The line is
y = -1/3x - 510. Prove that, for every positive integer n, there exist two regular polygons with the property that the ratio of the measure of an interior angle of one of the polygons to the measure of an interior n+1 angle of the other equals n + 1/ n.
It's given to prove that, for every positive integer n, there exist two regular polygons with the property that the ratio of the measure of an interior angle of one of the polygons to the measure of an interior n + 1 angle of the other equals n + 1/ n.
We know that for a regular polygon with n sides, the measure of each interior angle is given by:
(n-2)×180°/n
That is to say, each interior angle of a regular polygon with n sides is equal to (n-2)×180/n degrees.
Suppose P and Q are two regular polygons with P having n sides and Q having n+1 sides. Then, measure of each interior angle of polygon P is given by: (n-2)×180/n degrees
Similarly, the measure of each interior angle of polygon Q is given by: (n-1)×180/(n+1) degrees
Thus, the ratio of the measure of an interior angle of one of the polygons (say P) to the measure of an interior n+1 angle of the other (say Q) is given by:
(n-2)×180/n ÷ (n-1)×180/(n+1) = (n+1)/n
Therefore, we can conclude that for every positive integer n, there exist two regular polygons with the property that the ratio of the measure of an interior angle of one of the polygons to the measure of an interior n+1 angle of the other equals n+1/n.
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When Kenneth woke up the temperature was
3°F. By lunchtime, the temperature was eight
times warmer. What was the temperature at
lunchtime? Write your answer as an integer.
Answer:24
Step-by-step explanation:
3 times 8 is 24
Answer:
24°F
Step-by-step explanation:
It's pretty simple. All you need to know is simple math.
First of all take away the °F. Then do the multiplcation.
3 x 8 = 24
Then add the °F back and that's your answer.
Which inequality goes with “at least” ?
A. X >
B. X <
C. X <_
D. X >_
Answer:
C because ≤ means less than or equal to.
function: y = 2(x + 3)² +1
Answer:
10x
Step-by-step explanation:
Which algebraic expression is a polynomial with a degree of 4?
Answer:
for ponits
Step-by-step explanation:
Suppose that, in 1997, China produced 12.672 million pounds of wheat. The total world production that year totaled 106 million pounds of wheat. What percent of the world's total production of pounds of wheat is contributed by China? Round your answer to the nearest tenth.
Answer:
use a calculator and u got this
Step-by-step explanation:
the percent of the world's total population is 12%
in 1997 China produced 12.672 million pounds of wheat
the total pounds is 106 millions of pounds of wheat
the total production of wheat can be calculated as follows
= 12.672/106 × 100
= 0.119 × 100
= 11.9
= 12%
hence the percent of the world's total production of pounds of wheat is contributed by China by 12%
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Suppose R and S are relations on {a, b, c, d}, where R = {(a, b),
(a, d), (b, c), (c, c), (d, a) } and S = {(a, c), (b, d), (d, a) }. Find the
followings. [20 pts.] a. R3 b. $3 c. ROS d. RUS e. S - R
a. R3 = {(a, a), (a, b), (a, c), (a, d), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, a), (d, b), (d, d)}.
b. S3 = {(a, a), (a, c), (a, d), (b, a), (b, c), (b, d), (d, a), (d, c)}.
c. R ∪ S = {(a, b), (a, d), (a, c), (b, c), (c, c), (d, a), (b, d)}
d. S - R = {(a, c), (b, d)}
To find the given operations on relations R and S, let's start with the definitions of each operation:
a. R3: This represents the composition of relation R with itself three times.
To find R3, we need to perform the composition operation on R three times:
R3 = R ∘ R ∘ R
Calculating R ∘ R:
R ∘ R = {(a, c), (a, a), (b, a), (c, c), (d, b), (d, d)}
Now, let's calculate R ∘ R ∘ R:
R ∘ R ∘ R = R ∘ (R ∘ R)
= R ∘ {(a, c), (a, a), (b, a), (c, c), (d, b), (d, d)}
= {(a, a), (a, b), (a, c), (a, d), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, a), (d, b), (d, d)}
Therefore, R3 = {(a, a), (a, b), (a, c), (a, d), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, a), (d, b), (d, d)}.
b. $3: This represents the composition of relation S with itself three times.
To find S3, we need to perform the composition operation on S three times:
S3 = S ∘ S ∘ S
Calculating S ∘ S:
S ∘ S = {(a, a), (a, d), (b, a), (d, c)}
Now, let's calculate S ∘ S ∘ S:
S ∘ S ∘ S = S ∘ (S ∘ S)
= S ∘ {(a, a), (a, d), (b, a), (d, c)}
= {(a, a), (a, c), (a, d), (b, a), (b, c), (b, d), (d, a), (d, c)}
Therefore, S3 = {(a, a), (a, c), (a, d), (b, a), (b, c), (b, d), (d, a), (d, c)}.
c. R ∪ S: This represents the union of relations R and S.
R ∪ S = {(a, b), (a, d), (a, c), (b, c), (c, c), (d, a), (b, d)}
d. R ∩ S: This represents the intersection of relations R and S.
R ∩ S = {(d, a)}
e. S - R: This represents the set difference of relation S and relation R.
S - R = {(a, c), (b, d)}
Therefore:
a. R3 = {(a, a), (a, b), (a, c), (a, d), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, a), (d, b), (d, d)}.
b. S3 = {(a, a), (a, c), (a, d), (b, a), (b, c), (b, d), (d, a), (d, c)}.
c. R ∪ S = {(a, b), (a, d), (a, c), (b, c), (c, c), (d, a), (b, d)}
d. S - R = {(a, c), (b, d)}
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Find the value of x. Then find the angle measures of the polygon.
The value of x is 125.
what angle sum property of hexagon?The formula for the angle sum property is, S = ( n − 2) × 180°, where 'n' represents the number of sides in the polygon.
The sum of all interior angles is equal to 720 degrees, where each interior angle measures 120 degrees. The sum of all exterior angles is equal to 360 degrees, where each exterior angle measures 60 degrees.
Using angle sum property
120+120+120+100+x+x+10=720
2x+470= 720
2x= 720-470
2x= 250
x=125
hence, the value of x is 125.
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A red kite is 140 feet off the ground and is rising at 7 feet per second. A blue kite is 315 feet off the ground and is rising at 4 feet per second. Determine how long will it take for the red and blue kites to be the same height. Round your answer to the nearest tenth of a second
Answer:
58 seconds
Step-by-step explanation:
Given the following :
Elevation of red Kite = 140 ft off the ground
Rising rate = 7 feets per second
Elevation of blue Kite = 315 feets
Rising rate of blue Kite = 4 feets per second
Determine how long will it take for the red and blue kites to be the same height.
Let number of seconds = t
Red Kite = 140 + 7t
Blue Kite = 315 + 4t
Red Kite = Blue Kite
140 + 7t = 315 + 4t
7t - 4t = 315 - 140
3t = 175
t = 175/3
t = 58.333
t = 58s (nearest tenth(
Graph y≤1−3x. brianly
Answer:
B
Step-by-step explanation:
[tex]\leq[/tex] means everything to the left of, and also everything on the line since it's equal to as well, so B is the correct answer
QUESTION 12 12.1 Let V and W be vector spaces and V→ W be a linear transformation. For v EV, prove that T(-v) = -T(v). (3) 12.2 Let T: M22 → M22 be defined by T(A) = A+AT. Show that T is a linear transformation.
12.1 To prove that for a linear transformation T from vector space V to vector space W, T(-v) = -T(v) for any vector v in V.
12.2 To show that the function T: M22 → M22 defined by T(A) = A + AT is a linear transformation.
12.1 Let T be a linear transformation from vector space V to vector space W. We need to prove that T(-v) = -T(v) for any vector v in V.
To do this, we consider the properties of a linear transformation.
First, we know that T(0) = 0, where 0 is the zero vector in V and W.
Now, let's consider T(v) + T(-v). Using the linearity property of T, we have T(v) + T(-v) = T(v + (-v)) = T(0) = 0.
Since T(v) + T(-v) = 0, it follows that T(-v) = -T(v), which proves the desired result.
12.2 We are given the function T: M22 → M22 defined by T(A) = A + AT, where A is a 2x2 matrix.
To show that T is a linear transformation, we need to verify two properties:
Additivity: T(A + B) = T(A) + T(B) for any matrices A and B in M22.
Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in M22.
For the additivity property, we have T(A + B) = (A + B) + (A + B)T. By expanding this expression, we get T(A + B) = A + B + AT + BT.
Similarly, T(A) + T(B) = A + AT + B + BT. It is evident that T(A + B) = T(A) + T(B), satisfying the additivity property.
For the homogeneity property, we have T(kA) = kA + (kA)T = kA + kAT.
Similarly, kT(A) = k(A + AT) = kA + kAT. It is clear that T(kA) = kT(A), fulfilling the homogeneity property.
Since the function T satisfies both the additivity and homogeneity properties, we conclude that T is a linear transformation.
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Emily earns $15 for each car she washes. Create an equation to represent the relationship between the number of cars washed,c, and the amount, in dollars, Emily earns, m.
Answer:
15c = m
Step-by-step explanation:
for every car she washes she learns 15 dollars. So you would multiply the number of cars she washes by 15 to get the amount she earns
I need help with these four problems please
Solve for x: 1:5x = 30
Solve for x: 2/3x = - 12
Solve for x: 2/3x - 1 = 5
Solve for x: 4(x - 2) - 3 = 9
Answer:
x = 20
x = -18
x = 7/15
x = 5
Connor bought a baseball card eight years ago that has depreciated (goes down in value) by $120 since he purchased it. Find the average yearly change in value of the card.
Answer:
The average yearly change in the value of the card is $15 every year.
Step-by-step explanation:
Average Change
The change in the value of the baseball card bought by Connor was $120 in 8 years.
The average yearly change in value is calculated as:
Avg Change=$120 / 8 years = 15 $/yr
The average yearly change in the value of the card is $15 every year.
answer question number 5
Answer:
36 is answer
Step-by-step explanation:
A cube has 6 sides.
216÷6=36
so therefore one side is 36 cubic inches
[tex]\tt Step-by-step~explanation:[/tex]
[tex]\tt Step~1:[/tex]
Let's solve for one side first. The equation to solve for one side with only the volume provided is V ^ 1/3.
[tex]\tt 216^{\frac{1}{3}} \\216^{\frac{1}{3}} =6[/tex]
One side of the cube is 6, so that means all sides of the cube is equal to 6.
[tex]\tt Step~2:[/tex]
To find the area of one side of the cube, we take one side and multiply it by itself, since the formula for solving for the area is length • width.
[tex]\tt 6*6=36[/tex]
[tex]\large\boxed{\tt Our~final~answer:Area~of~one~side=36~in.^2}[/tex]
To check our answer, we can multiply 36 by 6 and see if it equals to 216.
[tex]\tt 36*6=216=correct[/tex]
What is the aim of hypothesis testing? What does hypothesis
testing achieve that could not be otherwise achieved?
2) give an example showing all the steps of the hypothesis
testing:
State a claim that
The aim of hypothesis testing is to make inferences or conclusions about a population based on sample data. It allows us to objectively analyze the evidence provided by the data and make decisions based on that evidence. By comparing the observed data to what would be expected under a specific hypothesis, hypothesis testing helps us evaluate whether the data supports or contradicts the claim being tested.
Hypothesis testing provides a structured and systematic approach to assess the validity of a claim or hypothesis. Hypothesis testing achieves several objectives that cannot be otherwise achieved:
Objectivity: Hypothesis testing provides a framework that helps remove personal biases and subjectivity from the decision-making process. It requires formulating clear hypotheses, defining appropriate statistical tests, and following predetermined rules to reach conclusions. This objectivity ensures that decisions are based on evidence rather than personal opinions or preferences.
Quantification of uncertainty: Hypothesis testing allows us to quantify the level of uncertainty associated with the conclusions drawn from the sample data. It provides measures such as p-values and confidence intervals that indicate the likelihood of obtaining the observed results under the null hypothesis. These measures help in assessing the strength of evidence and determining the level of confidence in the conclusions made.
Generalization to the population: Hypothesis testing enables us to make inferences about the population based on the sample data. By testing a hypothesis on a representative sample, we can draw conclusions that extend beyond the observed data. This generalization provides insights and knowledge about the larger population, allowing us to make informed decisions and predictions.
Example of hypothesis testing:
Claim: A new fertilizer leads to an increase in crop yield by at least 10%.
Step 1: Formulate the null and alternative hypotheses:
Null hypothesis (H0): The new fertilizer has no effect on crop yield or increases it by less than 10%.
Alternative hypothesis (Ha): The new fertilizer increases crop yield by at least 10%.
Step 2: Set the significance level (alpha):
Determine the desired level of significance to make a decision. Let's assume alpha = 0.05.
Step 3: Collect and analyze the data:
Implement the new fertilizer on a sample of crops.
Measure the crop yield for each sample plot and calculate the sample mean.
Step 4: Conduct the hypothesis test:
Use an appropriate statistical test, such as a one-sample t-test, to compare the sample mean to the hypothesized value of 10% increase.
Calculate the test statistic and the corresponding p-value.
Step 5: Make a decision and interpret the results:
If the p-value is less than the significance level (alpha), reject the null hypothesis.
Conclude that there is evidence to support the claim that the new fertilizer increases crop yield by at least 10%.
If the p-value is greater than the significance level (alpha), fail to reject the null hypothesis. Conclude that there is insufficient evidence to support the claim.
Step 6: Draw conclusions and report the findings:
Summarize the results, including the test statistic, p-value, and the decision made.
Provide interpretations and recommendations based on the findings, considering the limitations and context of the study.
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Suppose a class of 100 students took their statistics final and their grades are shown in the table below. A B C D F 25 28 34 10 3 What is the probability that if from this class, two students are randomly selected that both students will receive an "A"? [answer] (round answer to fourth decimal place and leave as decimal, do not put as %).
The probability that if from this class, two students are randomly selected that both students will receive an "A" is **0.025**.
There are 25 students in the class who received an "A" on the final exam. The probability that the first student selected will receive an "A" is 25/100 = 0.25.
Once the first student has been selected, there are 24 students remaining. There is still a probability of 24/99 that the second student selected will also receive an "A".
Therefore, the probability that both students selected will receive an "A" is:
```
0.25 * 0.24 = 0.06
```
This can be rounded to **0.025** to the fourth decimal place.
To calculate the probability that two students selected will receive an "A", we can use the following formula:
```
Probability = (Number of desired outcomes)/(Total number of possible outcomes)
```
In this case, the number of desired outcomes is 2, because there are 2 ways to select two students who both received an "A". The total number of possible outcomes is 100C2, which is the number of ways to select 2 students from a group of 100.
We can use the `nCr` function on most graphing calculators to calculate 100C2. The answer is 4950.
Therefore, the probability that two students selected will receive an "A" is:
```
Probability = (2)/(4950) = 0.00040
```
This can be rounded to **0.0004** to the fourth decimal place.
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Which of the following functions is graphed below?
A. y = [X]+7
B. y = [X] +5
C. y = [x] -7
D. y = [x]-5
Answer: A
Step-by-step explanation:
the value of y varies directly with x. when y = 25 x = 3/4. what is the value of y when x is 4 7/8
Answer:
y = 161 [tex]\frac{1}{2\\}[/tex]
Step-by-step explanation:
You can make this more visually understandable first:
y = 25 = ?
x = 3/4 = 4 [tex]\frac{7}{8}[/tex]
The change from 3/4 to 4 7/8 is 13/2, so the change between 25 and ? must be 13/2 as well.
25 * 13/2 = 325/2
= 162 1/2
