In Exercise 5.12 , we were given the following joint probability density function for the random variables Y1 and Y2, which were the proportions of two components in a sample from a mixture of insecticide: f(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhere
Are Y1 and Y2 independent?
The conclude that the Y1 and Y2 are not independent.
The joint probability density function for the random variables Y1 and Y2 for a mixture of insecticide isf(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhereTo verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Therefore, we need to find the marginal density functions of Y1 and Y2.Probability Density Function:We know that for a given joint probability density function, the probability density function of Y1 is given by integrating over all possible values of Y2, and vice versa.Mathematically,P(Y1)=∫0∫1f(y1,y2)dy2... (1)P(Y2)=∫0∫1f(y1,y2)dy1... (2)Using equation (1) to calculate P(Y1), we get, P(Y1)=∫0∫1f(y1,y2)dy2=∫0∫1(2)dy2=2... (3)Similarly, we can use equation (2) to calculate P(Y2) as follows:P(Y2)=∫0∫1f(y1,y2)dy1=∫0∫1(2)dy1=2... (4)Product of marginal density functions:Now we can find the product of marginal density functions as follows:P(Y1)P(Y2)=2×2=4... (5)Thus, to verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Since 2 ≠ 4, Y1 and Y2 are not independent. Hence, we can conclude that the Y1 and Y2 are not independent.
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The volume of this prism is 4950cm3.
The area of the cross-section is 110cm2.
Work out x
Answer:
45cm
Step-by-step explanation:
length × cross section = volume
in this case we call the unknown [tex]x[/tex]
so
[tex]x[/tex] x 110 = 4950
to get [tex]x[/tex] you divide the volume by the cross section
[tex]\frac{4950}{110}[/tex]= [tex]x[/tex]
so [tex]x[/tex] = 45cm
Find M BC using picture below
Based on the picture, we can use the Pythagorean theorem to find MBC. Therefore, MBC is equal to [tex]7[/tex]√2.
What three categories of theorems are there?Theorem of Linear Pairs Two angles are supplementary if they create a linear pair. Additional theorem, Two angles are congruent if they are supplements of the same angle.
Theorem of congruent complements an of thes., but it will be the first of a series of events that will result in a new set of rules and the.
First, we can find AB:
AB = √(AD² + BD²)
= √ [tex](3^2 + 4^2)[/tex]
= √[tex](9 + 16)[/tex]
= √ [tex]25[/tex]
[tex]= 5[/tex]
Next, we can find AC:
AC = √(AD² + CD²)
= √[tex](3^2 + 8^2)[/tex]
= √ [tex](9 + 64)[/tex]
= √[tex]73[/tex]
Finally, we can find BC:
[tex]BC = √(AB^2 + AC^2)[/tex]
= √(5² + (√73)²)
= √(25 + 73)
= √98
= 7√2
Therefore, m Bc is = 7√2
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How much greater is 0.05723 then 0.005?
0.05723 is 0.05223 greater than 0.005.
What is greater than?"Greater than" is a comparison term used to indicate that one quantity or value is larger or more than another quantity or value. It is represented mathematically by the symbol ">".
What is lesser than?"Lesser than" is a comparison term used to indicate that one quantity or value is smaller or less than another quantity or value. It is represented mathematically by the symbol "<".
In the given question,
To find out how much greater 0.05723 is than 0.005, we can subtract 0.005 from 0.05723:0.05723 - 0.005 = 0.05223
Therefore, 0.05723 is 0.05223 greater than 0.005.
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Calculate the area and perimeter of this rectangle.
Answer:
Area: 391.92 ft²
Perimeter: 84.4 ft
Step-by-step explanation:
Area of rectangle = L × W
We Take
13.8 × 28.4 = 391.92 ft²
Find the Perimeter of the Rectangle
We Take
28.4 + 13.8 + 28.4 + 13.8 = 84.4 ft
So, Area: 391.92 ft²
Perimeter: 84.4 ft
Answer:
Area = 391.92 square feet
Perimeter = 84.4 feet
Step-by-step explanation:
The area of a rectangle is the product of its width and length.
The perimeter of a rectangle is twice the sum of its width and length.
Given the width of the rectangle is 28.4 feet and its length is 13.8 feet:
[tex]\begin{aligned}\textsf{Area of the rectangle}&=\sf width \times length\\&=28.4 \times 13.8\\&=391.92 \sf \;\;square\;feet\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=\sf 2(width +length)\\&=2(28.4 +13.8)\\&=2(42.2)\\&=84.4 \sf \;\;feet\end{aligned}[/tex]
Suppose Elena has $5 and sells pens for $1.50 each. Her goal is to save $20 to buy a t-shirt. She does not spend any money while she is saving money.
Let p represent the number of pens Elena sells. Write an expression for how much money she saves in total after selling p pens.
Write an equation using your answer from question 1, showing that she saves exactly $20.
Solve the equation you wrote from question 2. What do you notice about your value for p?
What if Elena wants to have some money left over? Write an inequality using your expression from question 1 to show this.
Write down other values for p where Elena would have money left over.
Write an inequality using p, to describe the values of p where she would be able to buy the tshirt and still have money left over.
In conclusion the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc. The equation showing that Elena saves exactly $20 is:
5 + (1.5)p = 20
Why it is?
The expression for how much money Elena saves after selling p pens is:
Total money saved = 5 + (1.5)p
The equation showing that Elena saves exactly $20 is:
5 + (1.5)p = 20
Solving the equation:
5 + (1.5)p = 20
(1.5)p = 15
p = 10
We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.
If Elena wants to have some money left over, we can write the inequality:
5 + (1.5)p > 20
Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.
To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:
5 + (1.5)p > 20
(1.5)p > 15
p > 10
Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.
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Suppose we select one 2015 Spotify user at random
and record his or her age and whether his or her favorite music genre is pop.
(a) Draw a tree diagram to model this chance process.
(b) Find the probability that the person identifies his or her favorite music genre as pop.
(c) Suppose the chosen person identifies his or her favorite music genre as pop. What’s the probability
that he or she is aged 13–24?
Answer:11
Step-by-step explanation:
National Collegiate Athletic Association (NCAA) statistics show
that for every 75,000 high school seniors playing basketball, about 2250 play
college basketball as first-year students. Write the ratio of the number of first-
year students playing college basketball to the number of high school seniors
playing basketball.
Answer: 100:3
Step-by-step explanation:
Answer:
the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.
Step-by-step explanation:
The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.
The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.
To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.
So the ratio can be expressed as:
2,250/75,000
To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:
2,250/75,000 = 3/100
an urn contains p black balls, q white balls, and r red balls; and n balls are chosen without replacement. a. find the joint distribution of the numbers of black, white, and red balls in the sample. b. find the joint distribution of the numbers of black and white balls in the sample. c. find the marginal distribution of the number of white balls in the sample.
a. The joint distribution of the numbers of black, white, and red balls in the sample is given by P(x, y, z) = nCx * nCy * nCz / (p + q + r)Cn, where x is the number of black balls, y is the number of white balls, z is the number of red balls, and n is the total number of balls chosen.
b. The joint distribution of the numbers of black and white balls in the sample is given by P(x, y) = nCx * nCy / (p + q)Cn, where x is the number of black balls, y is the number of white balls, and n is the total number of balls chosen.
c. The marginal distribution of the number of white balls in the sample is given by P(y) = nCy / qCn, where y is the number of white balls, and n is the total number of balls chosen.
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find the volume of a pyramid with a square base, where the area of the base is 4.6 cm 2 4.6 cm 2 and the height of the pyramid is 2.3 cm 2.3 cm. round your answer to the nearest tenth of a cubic centimeter.
The volume of pyramid is 3.5 cm³.
To find the volume of a pyramid with a square base, where the area of the base is 4.6 cm² and the height of the pyramid is 2.3 cm, we can use the following formula:
V = (1/3)B*h
Where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid. Substitute the given values into the formula and solve:
V = (1/3)(4.6)(2.3)V = 3.53 cm³
Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is 3.5 cm³. Therefore, the volume of pyramid is 3.5 cm³.
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Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
The access code for a car's security system consist of six digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?
If an access code for a car's security system consist of six digits and the first digit cannot be zero and the last digit must be even, then the number of different codes available are 4,500,000
Since the first digit cannot be zero, we have 9 choices for the first digit. For each of these 9 choices, there are 10 possibilities for the second digit (0-9).
Similarly, there are 10 possibilities for the third digit, 10 for the fourth digit, 10 for the fifth digit, and 5 (0, 2, 4, 6, 8) for the last digit.
Therefore, the total number of possible access codes is:
9 x 10 x 10 x 10 x 10 x 5 = 4,500,000
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A manufacturer of paper used for packaging requires a minimum strength of 1400 g/cm2. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour’s production and a strength measurement is recorded for each. The standard deviation of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 140 g/cm2, and the strength measurements are normally
distributed.
a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?
b) If the mean of the population of strength measurements is 1450 g/cm2, what is the
approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400?
The sample mean is 1450g/cm², the standard deviation is 44.3 g/cm² and the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2 is 0.8708
What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?a) The sampling distribution of the sample mean of n = 10 test pieces of paper is approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:
mean of sample mean = mean of population = 1450 g/cm²
standard deviation of sample mean = standard deviation of population / square root of sample size
= 140 g/cm2 / √(10)
= 44.3 g/cm²
Therefore, the sampling distribution of the sample mean is approximately normal with mean 1450 g/cm2 and standard deviation 44.3 g/cm2.
b) To find the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2, we need to standardize the sample mean using the sampling distribution calculated in part (a):
z = (x - mean of sample mean) / standard deviation of sample mean
= (1400 - 1450) / 44.3
= -1.13
Using a standard normal distribution table or calculator, we can find the probability that z is less than -1.13 and subtract that probability from 1 to find the probability that z is greater than -1.13:
P(z > -1.13) = 1 - P(z < -1.13)
= 1 - 0.1292
= 0.8708
Therefore, the approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm² is 0.8708.
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a random sample of 15 recent college graduates found that starting salaries for attorneys in new york city had a mean of $102,342 and a standard deviation of $21,756. there are no outliers in the sample data set. construct a 95% confidence interval for the average starting salary of all attorneys in the city.
The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a p-value of 1-∝.
So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]
Now, find M as such
[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ
In which is the standard deviation of the population and n is the size of the sample.
[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.
The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.
So the correct answer is:
(91331.94, 113352.06)
Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.
Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.
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Complete Question:
A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices
A). (89869.82, 114814.18)
B). (90292.73, 114391.27)
C). (91331.94, 113352.06)
D). (90371.37, 114312.63)
Someone please help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
Answer:
D
Step-by-step explanation:
First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.
Hope this helps.
pls help Are the following lines parallel, perpendicular, or neither?
y = 2/3x − 4
y = −3/2x − 7
Responses
Parallel
Perpendicular
Neither
Answer:
Perpendicular.
Step-by-step explanation:
To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form
y = 2/3x - 4 ==> slope = 2/3
y = -3/2x - 7 ==> slope = -3/2
Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.
Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1
(2/3) * (-3/2) = -1
Since the product of the slopes is -1, the two lines are perpendicular.
Therefore, the answer is: perpendicular.
At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?
Answer:
Step-by-step explanation:
Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:
999n = 727272
To solve for "n", we divide both sides by 999:
n = 727272/999
Using a calculator or long division, we get:
n ≈ 728.56
Therefore, each pizza has approximately 728 slices.
what is 1 half of 68 ?
Answer:
34
Step-by-step explanation:
1/2 multiplied by 68=34
34 is 1 half of 68 .
Here, we have,
given that,
what is 1 half of 68
we know that,
Half of a number can be found by dividing the number by 2.
i.e. we have to find half of 68,
for that, we need to divide 68 by 2
so, we get,
To find half of 68:
68 / 2 = 34
Therefore, half of 68 is 34.
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solve simultaneously 4x-y=3x+1y 4x+3y=x+6y
(x, y) = (0,0) is the solution of the system of equations.
simultaneous equationSimultaneous equations are a set of two or more equations that contain multiple variables, which must be solved at the same time. The solution to the system of equations is the set of values of the variables that satisfy all of the equations in the system simultaneously.
The given system of equations is:4x - y = 3x + y
4x + 3y = x + 6y
Simplifying the first equation by moving all the y-terms to the left-hand side and all the x-terms to the right-hand side, we get:
4x - 3x = y + y
x = 2y
Substituting this value of x into the second equation, we get:
4(2y) + 3y = (2y) + 6y
8y + 3y = 8y
11y = 0
y = 0
Substituting y = 0 into the equation x = 2y, we get:
x = 2(0)
x = 0
Therefore, the solution to the system of equations is:
x = 0 and y = 0
Hence, (x, y) = (0,0) is the solution of the system of equations.
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Evaluate the expression
z + 3x4
A. 27
B. 32
C. 56
D. 1,304
The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.
The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.
z + 3x4 = 15 + 3x4
= 15 + 12
= 27
Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).
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____The given question is incomplete , the complete question is given below:
Evaluate the expression, where z = 15
z + 3x4
A. 27
B. 32
C. 56
D. 1,304
Write down the smallest possible answer.
The answer of the given factor and multiplication term for the positive integers are 3.
What about integers?Positive, negative, and zero digit whole numbers are all included in the category of integers. They can be stated without any fractional or decimal components and are a subset of the real numbers. On a number line, integers can be visualized as positive numbers to the right of zero and negative numbers to the left.
Define Multiplication term:In mathematics, a multiplication term is a mathematical expression that involves the multiplication of two or more factors. The factors can be numbers, variables, or a combination of both. Multiplication terms are commonly represented using the multiplication symbol "×" or the dot "." symbol.
For example, in the expression 2x × 3y, the multiplication term is 2x × 3y, which involves the multiplication of the factors 2x and 3y.
According to the given information:If you want to find the smallest possible value of the given term we have that,The smallest factor of 15 is 1.
The smallest multiple of 3 is 3so, the smallest answer is 1x3 = 3.
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Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?
Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).
In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:
final amount = 5.00 - 5.00 - (5.00 * 0.045)
final amount = 5.00 - 5.00 - 0.225
final amount = 4.775
Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.
A sports club had 130 members last summer. This summer, due to some renovations, it has 182 members. What is the percent of increase in the number of members?HELP PLSSSSS
Answer:
Step-by-step explanation:
312
Answer:
36.92%
Step-by-step explanation:
180-132=48. Now we have to find 48 of 130 to find the percentage increase. 48 out of 130 = which equals 36.92.
Classify each as Polynomial or Not a Polynomial.
1.) 9x-^3 - 2y
2.) 2x^2 - 4√x
3.) 2x 2/3 - 4y
4.) 20x^2
5.) w/2 + 7
6.) 4y/2x
7.) -20x^2 + y
Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Exactly how many erasers did stefanie buy?
Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Stefanie bought total 10 erasers.
Equation:
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal.
According to the Question:
The number of erasers bought by Stefanie:
Let we denote the number of erasers bought by her by x (an unknown variable)
Then we will have:
Total amount before tax = cost of one package of pencil + cost of erasers
$4.25 = $1.75 + X × $0.25
⇒ 4.25 = 1.75 + 0.25x
Now,
we will perform subtraction by 1.75 and division by 0.25 on both sides.
4.25 = 1.75 + 0.25x
Subtracting 1.75 both side:
4.25 -1.75 = 0.25x
⇒ 2.5 = 0.25x
Dividing by 0.25 on both sides:
2.5/0.25 = 0.25x/0.25
⇒ x = 10
Thus, Stefanie bought total 10 erasers.
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Write and solve an equation to answer the following question. The Smith family rented a recreational vehicle for a seven-day vacation. The cost to rent the recreational vehicle was $80 plus $0.50 per mile. How many miles were driven if the total cost was $1350?
Answer: 2540
Step-by-step explanation: 1350-80=1270. 1270/0.5=2540
Find the total amount and total interest after six months if the interest is compounded every quarter. Principal =₹10 000 Rate of interest =20% per annum.
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000
Step-by-step explanation:
A researcher randomly chooses 1000 Kentucky families to estimate the proportion of all American families who routinely eat dinner together. What is the population? a) The 1000 Kentucky families b) All Kentucky families c) All American families d) All families around the world
The population in the given scenario of a researcher randomly choosing 1000 Kentucky families to estimate the proportion of all American families who routinely eat dinner together is all American families (option c).
In the given scenario, the population is all American families. The researcher has randomly chosen 1000 families from Kentucky to estimate the proportion of all American families who routinely eat dinner together. The researcher is using the sample of 1000 Kentucky families to make inferences about the population of all American families. By assuming that the sample is representative of the population, the researcher can use statistical methods to estimate the proportion of all American families who routinely eat dinner together. So, option C is the correct answer.
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Y=3x+3 what is the slope and y intercept
Answer:
y-intercept is (0,3) and the slope is 3
Step-by-step explanation:
Answer: the slope is 3x while 3 is the y-intercept.
Step-by-step explanation:
5my × 5ym = ?
Can you multiply two terms with the same 2 coefficients in different positions like the example above?
Answer:
In the example given, 5my × 5ym, you can simplify it using the commutative property of multiplication as follows:
5my × 5ym = 5 × 5 × m × m × y × y
= 25m²y²
So, the answer is 25m²y².