Factorise fully - 4x² - 16x

(x, y) = (0,0) is the solution of the system of equations.

Simultaneous 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.

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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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.

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) Total Number of Subsets of A:
In set theory, any set is a subset of itself. Additionally, the empty set is a subset of every set. As a result, there are 2^12 subsets of A.

Number of Subsets of A = 2^12 = 4096

(b) Number of Subsets of A having One or More Elements:
To find the number of subsets of A having one or more elements, we must subtract the empty set from the total number of subsets of A.
∴ Number of Subsets of A having One or More Elements = (2^12) − 1 = 4095

(c) Number of Subsets of A having Exactly One Element:
We can use the formula given below to compute the number of subsets of A having exactly one element. Here, n represents the number of elements in the set.

Formula: nC1 = n
∴ Number of Subsets of A having Exactly One Element = 12C1 = 12

(d) Number of Subsets of A having Two or More Elements:
Using parts (b) and (c), we can obtain the number of subsets of A having two or more elements by subtracting the number of subsets of A having exactly one element from the number of subsets of A having one or more elements.
∴ Number of Subsets of A having Two or More Elements = (2^12) − 1 − 12 = 4083.

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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

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.

Answer: 2540

Step-by-step explanation: 1350-80=1270. 1270/0.5=2540

Answer: 67

Step-by-step explanation:67 x1

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)

The normal probability plot for the following sample deduce by z = (X - mean) / standard deviation as following steps.

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.

The steps to calculate the z-percentiles for the given sample:

Find the mean of the sample:

mean = (0.82 + 0.88 + 0.88 + 1.06 + 1.09 + 1.14 + 1.30 + 1.33 + 1.48 + 1.50 + 1.57 + 1.64 + 1.64 + 1.70 + 1.76 + 1.83) / 16 = 1.235

Find the standard deviation of the sample:

First, find the sum of the squared differences between each observation and the mean:

(0.82 - 1.235)^2 + (0.88 - 1.235)^2 + (0.88 - 1.235)^2 + (1.06 - 1.235)^2 + (1.09 - 1.235)^2 + (1.14 - 1.235)^2 + (1.30 - 1.235)^2 + (1.33 - 1.235)^2 + (1.48 - 1.235)^2 + (1.50 - 1.235)^2 + (1.57 - 1.235)^2 + (1.64 - 1.235)^2 + (1.64 - 1.235)^2 + (1.70 - 1.235)^2 + (1.76 - 1.235)^2 + (1.83 - 1.235)^2 = 2.9878

Next, divide the sum by the sample size minus 1 and take the square root: standard deviation = sqrt(2.9878 / 15) = 0.4323

Use the formula z = (X - mean) / standard deviation to calculate the z-percentile for each observation in the sample.

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To calculate the z-percentile for each observation in the sample.: Find the mean of the sample, Find the standard deviation of the sample and then use the formula z = (X - mean) / standard deviation.

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.

The steps to calculate the z-percentiles for the given sample:

Find the mean of the sample:

mean = (0.82 + 0.88 + 0.88 + 1.06 + 1.09 + 1.14 + 1.30 + 1.33 + 1.48 + 1.50 + 1.57 + 1.64 + 1.64 + 1.70 + 1.76 + 1.83) / 16

mean = 1.235

Find the standard deviation of the sample:

First, find the sum of the squared differences between each observation and the mean:

(0.82 - 1.235)² + (0.88 - 1.235)² + (0.88 - 1.235)² + (1.06 - 1.235)² + (1.09 - 1.235)² + (1.14 - 1.235)² + (1.30 - 1.235)² + (1.33 - 1.235)² + (1.48 - 1.235)² + (1.50 - 1.235)² + (1.57 - 1.235)² + (1.64 - 1.235)² + (1.64 - 1.235)² + (1.70 - 1.235)² + (1.76 - 1.235)² + (1.83 - 1.235)² = 2.9878

Next, divide the sum by the sample size minus 1 and take the square root:

standard deviation = √(2.9878/15)

standard deviation = 0.4323

Use the formula z = (X - mean) / standard deviation to calculate the z-percentile for each observation in the sample.

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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]

Answer:  What is this equation

Step-by-step explanation:

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

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. 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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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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She purchased 4 Paper Lanterns, 12 Bags of Balloons, 11 Garlands, and 4 Banners if she paid $145. 50.

The cost of lanterns is $6.50

Mrs Murphy bought 4 lanterns

Multiply the cost of one lantern ($6.50) by the number of lanterns bought (4) 6.50 multiplied by 4 equals 26

The cost of banners is $5.25

Mrs Murphy bought 4 banners

Multiply the cost of one banner ($5.25) by the number of banners bought (4) 5.25 multiplied by 4 equals 21

Mrs Murphy bought 3 times as many balloons as she did lanterns

So, you multiply the number of lanterns bought (4) by 3

This gives 12

We then multiply the cost of each balloon ($5.00) by the number of balloons bought (12)

5.00 multiplied by 12 equals 60

Mrs Murphy bought 7 more garlands as she did lanterns

So, we add 7 to the number of lanterns bought (4)

7 plus 4 equals 11

To find the cost of the total garlands bought

We multiply the cost of each garland ($3.50) by the number of garlands bought (11)

3.50 multiplied by 11 equals 38.5

Now we can add up the costs of all the items

26+21+60+38.5=145.50

145.50 was the total amount she spent so we know it is the correct answer.

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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.

Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

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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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.

The National Football League (NFL) is an American football league that is based in the United States. The NFL records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 NFL teams for one full season.The data collected by the NFL shows that passing has a significant impact on the percentage of games won by a team. Teams that have a higher average number of passing yards per attempt tend to win more games than those with a lower average. Additionally, teams that have a lower number of interceptions thrown per attempt also tend to win more games than those with a higher number of interceptions thrown per attempt.The data also shows that the conference a team plays in does not have a significant impact on the percentage of games won by a team. This means that a team's conference is not a good indicator of its performance.The NFL should continue to record data on passing to help teams improve their performance. Coaches can use this data to identify areas for improvement and develop strategies to help their teams win more games.

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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.

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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Answer:11

Step-by-step explanation:

0.05723 is 0.05223 greater than 0.005.

"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 "&gt;".

"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 "&lt;".

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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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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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:

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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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