Factorise using identity 4y^2 - 12yz+9z^2​

a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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The Porter in Shakespeare's Macbeth imagines a variety of people knocking at the gate, including the "equivocator" (a person who speaks in double meanings), the "lieger" (an ambassador or messenger), the "fiend" (a devil), the "farmer's daughter" (a young woman), and the "porter" himself.

A porter is a person who is responsible for the maintenance of the entrance of a big house or building, including that of the main door. He opens the door, welcomes guests, and provides basic assistance as required. He is also in charge of ensuring the safety of the property and its occupants.

In Shakespeare's Macbeth, the porter is a comic character who provides some comic relief after Duncan's murder. When he hears knocking at the castle gate, he imagines that he is admitting various people from different professions, including the farmer, the equivocator, and the tailor.

The comic nature of his speech is intended to lighten the tension and set the tone for the upcoming scenes of murder, deceit, and betrayal.

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The values are

First plot two dots on 8

Then rest two on -8

Answer:

See below ~

Step-by-step explanation:

Solving :

The correct statement is "Since the data is variable and available, the given question is a statistical question." Therefore, option B is correct.

The question "How many times do Jack Nursing Home residents search the Internet each day?" is a statistical question because it is a variable that varies from person to person and from day to day. The purpose of the question was to collect data on Internet searches, indicating an interest in understanding the distribution and patterns of residents' search behavior.

Additionally, in the question he states that web search data is available. This means there is an opportunity to collect and analyze data to generate meaningful insights. This question is therefore a statistical question that takes into account the variability and availability of the data. 

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Answer:

Option C: x=3 and y= -6 is the correct answer.

Step-by-step explanation:

Given that:

x - 2y = 15     Eqn 1

2x+4y = -18    Eqn 2

Multiplying Eqn 1 by 2

2(x-2y=15)

2x-4y=30    Eqn 3

Adding Eqn 2 and Eqn 3,

(2x+4y)+(2x-4y)=-18+30

2x+4y+2x-4y=12

4x=12

Dividing both sides by 4

\(\frac{4x}{4}=\frac{12}{4}\\x=3\)

Putting x=3 in Eqn 2

2(3)+4y=-18

6+4y=-18

4y= -18-6

4y= -24

Dividing both sides by 4

\(\frac{4y}{4}=\frac{-24}{4}\\y=-6\)

Hence,

Option C: x=3 and y= -6 is the correct answer.

a. The recursive formula for the number of tulips Marko has is: \(Tn = Tn-1 + 5\), where Tn is the number of tulips in year n and Tn-1 is the number of tulips in year n-1.

b. The explicit formula for the number of tulips Marko has is: Tn = 20 + 5n, where Tn is the number of tulips in year n and n is the number of years since Marko started planting.

c. If this trend continues, there will be 90 tulips in 10 years.

d. If this trend continues, it will take Marko 40 years to have 200 tulips.

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The angle between the lines passing through (2, 5) and (4, -3), and (1, -2) and (3, 4) is approximately -32.7 degrees.

Example 1:

Find the angle between the lines with equations y = 2x + 3 and y = -3x + 1.

Solution:

To find the angle between the lines, we need to determine the slopes of the two lines.

The slope-intercept form of a line is y = mx + b, where m is the slope.

Comparing the given equations, we can see that the slopes of the lines are m1 = 2 and m2 = -3.

Using the angle between two lines formula, the angle θ between the lines is given by the equation:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values, we have:

tan(θ) = |(-3 - 2) / (1 + (2)(-3))|

= |-5 / (1 - 6)|

= |-5 / -5|

= 1

To find the angle θ, we take the inverse tangent (arctan) of 1:

θ = arctan(1)

θ ≈ 45°

Therefore, the angle between the lines y = 2x + 3 and y = -3x + 1 is approximately 45 degrees.

Example 2:

Determine the angle between the lines with equations 3x - 4y = 7 and 2x + 5y = 3.

Solution:

First, we need to rewrite the given equations in slope-intercept form (y = mx + b).

The first equation: 3x - 4y = 7

Rewriting it: 4y = 3x - 7

Dividing by 4: y = (3/4)x - 7/4

The second equation: 2x + 5y = 3

Rewriting it: 5y = -2x + 3

Dividing by 5: y = (-2/5)x + 3/5

Comparing the equations, we can determine the slopes:

m1 = 3/4 and m2 = -2/5

Using the angle between two lines formula:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values:

tan(θ) = |((-2/5) - (3/4)) / (1 + (3/4)(-2/5))|

= |((-8/20) - (15/20)) / (1 + (-6/20))|

= |(-23/20) / (14/20)|

= |-23/14|

To find the angle θ, we take the inverse tangent (arctan) of -23/14:

θ = arctan(-23/14)

θ ≈ -58.44°

Therefore, the angle between the lines 3x - 4y = 7 and 2x + 5y = 3 is approximately -58.44 degrees.

Example 3:

Find the angle between the lines passing through the points (2, 5) and (4, -3), and (1, -2) and (3, 4).

Solution:

To find the angle between the lines, we need to determine the slopes of the two lines using the given points.

For the first line passing through (2, 5) and (4, -3):

m1 = (y2 - y1) / (x2 - x1)

= (-3 - 5) / (4 - 2)

= -8 / 2

= -4

For the second line passing through (1, -2) and (3, 4):

m2 = (y2 - y1) / (x2 - x1)

= (4 - (-2)) / (3 - 1)

= 6 / 2

= 3

Using the angle between two lines formula:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values:

tan(θ) = |(3 - (-4)) / (1 + (-4)(3))|

= |(3 + 4) / (1 - 12)|

= |7 / (-11)|

= -7/11

To find the angle θ, we take the inverse tangent (arctan) of -7/11:

θ = arctan(-7/11)

θ ≈ -32.7°

Therefore, the angle between the lines passing through (2, 5) and (4, -3), and (1, -2) and (3, 4) is approximately -32.7 degrees.

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The approximate standard deviation of the sampling distribution of the proportion is 3.8%.

A standard deviation (or) is a measure of how widely distributed the data is in reference to the mean.

A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation implies that data is more spread out.

Now, as per the questions;

Whenever the population size is so very large, the PQ/N factor approaches zero, and the standard deviation equation becomes:

σp = √( PQ/n)

We don't know how so many listeners this same radio station has in this case, but we can assume it's a large number.

P = probability of listening at work, is 14% or 0.14

Q = probability of not listening at work, is (100- 14)% = 86% = 0.86

N = sample size, is 85

The sample standard deviation is then

σp = √(14×.86/85)

σp = 0.0376

σp = 3.8% (approximately)

Therefore, the approximate vale of the standard deviation is found to be 3.8 %.

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The correct question is-

If 14% of the listeners of a radio station listen to it while they are at work, what is the approximate standard deviation of the sampling distribution of the proportion for samples of size 85?

Answer:

1.x=(z/4)-y

2.b=(e-cd)/a

Step-by-step explanation:

1.

z=4(x+y)

Divide both sides by 4

z/4=x+y

Subtract y from both sides

(z/4)-y=x

Answer

x=(z/4)-y

2.

ab+cd=e

subtract cd from both sides

ab=e-cd

divide both sides by a

b=(e-cd)/a

Answer

b=(e-cd)/a

Answer:

\(1) x = \frac{z}{4} - y\)

\(2) b = \frac{e}{a} - \frac{cd}{a}\)

Explanation:

(1) Making x the subject: \(4(x + y) = z\)

To make x the subject of original expression, we send the x to the left side of expression and all of the other components to the right side of expression.

The detail procedure is described as following:

    \(4(x + y) = z\)

Apply associate property:

<=> \(4x + 4y = z\)

Send 4y to the right side (the sign of 4y must be changed from positive to negative):

<=> \(4x = z - 4y\)

Divide both sides by 4:

<=> \(x = \frac{z}{4} - y\)

(2) Make b the subject: \(ab + cd = e\),  applying the similar procedure in part (1):

      \(ab + cd = e\)

Send \(cd\) to the right side (the sign of

<=> \(ab = e - cd\)

Divide both sides by \(a\):

<=> \(b = \frac{e}{a} - \frac{cd}{a}\)

Hope this helps!

:)

The surface area of the larger sphere is 64π cm². therefore option A. 64π cm² is correct.

To find the surface area of the larger sphere, given the volumes of two spheres and the surface area of the smaller sphere, follow these steps:

1. Determine the ratio of the volumes of the spheres:

Volume ratio = Volume of larger sphere / Volume of smaller sphere

                     = (64π cm³) / (8π cm³)

                     = 8

2. Find the cube root of the volume ratio to get the ratio of their radii:

Radii ratio = cube root of volume ratio = cube root of 8 = 2

3. Since the surface area of a sphere is proportional to the square of its radius, find the ratio of the surface areas by

squaring the radii ratio:

Surface area ratio = (Radii ratio)² = (2)² = 4

4. Finally, multiply the surface area of the smaller sphere by the surface area ratio to get the surface area of the larger

sphere:

Surface area of larger sphere = Surface area of smaller sphere × Surface area ratio

                                                 = 16π cm² × 4

                                                = 64π cm²

So, the surface area of the larger sphere is 64π cm² (Option A).

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Answer:

6

Step-by-step explanation:

Because  y isn't it's  number

a. This is a voluntary response sampling strategy. Bias may occur because only those with strong opinions are likely to respond, which may not represent the views of all parents.

b. This is cluster sampling. Bias may occur if the selected school is not representative of the entire city's school system.

c. This is a census. Bias may occur if some parents do not return the survey, leading to nonresponse bias.

d. This is stratified random sampling. Bias may be minimized as each school is fairly represented, but nonresponse bias could still occur if some parents do not return the survey or respond to the phone call.

e. This is a voluntary response sampling strategy. Bias may occur as only those watching the news and with strong opinions are likely to participate, which may not represent the views of all parents.

f. This is convenience sampling. Bias may occur because only those attending the PTA meetings will have their opinions counted, which may not represent the views of all parents.

g. This is cluster sampling. Bias may occur if the selected classes are not representative of the entire city's school system.

h. This is systematic random sampling. Bias may be minimized as the sample is spread evenly throughout the enrollment records, but nonresponse bias could still occur if some parents are not available for the interview.

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Answer:

w= 40b

w=40× 5

w=200

......

Answer: w = 200

Step-by-step explanation:

40 x 5 is 200

Answer:

2nd graph from top

Step-by-step explanation:

a/ -5 ≥ 10

Multiply each side by -5, remembering to flip the inequality

a/-5 *-5 ≤ 10*-5

a ≤ -50

closed circle at -50 line going to the left

ANSWER :

The answers are :

a. 3.03

b. -9.09

c. 55.775 lbs

EXPLANATION :

The z-score formula is :

From the problem, we have :

a. z-score when x = 60 lbs.

That will be :

b. z-score when x = 30 lbs below the mean, the mean weight is 50 lbs, so it will be x = 50 - 30 = 20

The z-score will be :

c. weight when it is 1.75 standard deviations above the mean weight.

Above the mean weight denotes that the z-score is positive.

Substitute z = 1.75 and solve for x :

The expected value is 0.8, variance is 0.48, and standard deviation is 0.693 with the given probability.

a. The probability of getting one success in two trials with p=0.4 is given by the binomial probability formula:

f(1) = 2C1 * (0.4)^1 * (0.6)^1 = 0.48

b. The probability of getting zero successes is:

f(0) = 2C0 * (0.4)^0 * (0.6)^2 = 0.36

c. The probability of getting two successes is:

f(2) = 2C2 * (0.4)^2 * (0.6)^0 = 0.16

d. The probability of at least one success is:

P(at least one success) = 1 - P(no success)

= 1 - f(0)

= 1 - 0.36

= 0.64

e. The expected value of a binomial distribution with n trials and probability of success p is given by:

E(X) = np

In this case, n = 2 and p = 0.4, so:

E(X) = 2 * 0.4 = 0.8

The variance of a binomial distribution is given by:

Var(X) = np(1-p)

So:

Var(X) = 2 * 0.4 * 0.6 = 0.48

The standard deviation is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(0.48) = 0.693.

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Answer: 9-2 & -2-(-9)

Correct me if I'm wrong.

Step-by-step explanation:

A complete list of the numbers in the pattern: 3, 6, 10, 14, 18, etc.

The number pattern you described is as follows:

3,

(2*5)-4 = 6,

(2*7)-4 = 10,

(2*9)-4 = 14,

(2*11)-4 = 18,

The first number is 3, and then each subsequent number is found by multiplying the previous odd number by 2 and then subtracting 4.

For example, the second number is found by multiplying the first number by 2 and then subtracting 4, which gives us 6. The third number is found by multiplying the second number by 2 and then subtracting 4, which gives us 10.

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Answer: $206.70

Step-by-step explanation:

The coupon reduced the price of the television by 35% to:

= 300 * ( 1 - 35%)

= 300 * 65%

= $195

He then had to pay a 6% tax:

= Price * ( 1 + tax)

= 195 * ( 1 + 6%)

= 195 * 1.06

= $206.70

Hey there!

“Which expression is equivalent to 6(3x + 4)

6(3x + 4)

6(3x) + 6(4)

6(3x) = 18x

6(4) = 24

= 18x + 24

Possible answer: 18x + 24 ☑️

Good luck on your assignment and enjoy your day!

~Amphitrite1049:)

Answer:

usage patterns are a variable used in market segmentation.

Step-by-step explanation:

Usage patterns are a variable used in behavioral segmentation.

Behavioral segmentation is a marketing strategy that divides a market into different segments based on consumer behavior, specifically their patterns of product usage, buying habits, and decision-making processes. This segmentation approach recognizes that customers with similar behavioral characteristics are likely to exhibit similar preferences and respond in a similar manner to marketing initiatives.

Usage patterns, as a variable, help marketers understand and classify customers based on how they interact with a product or service. This can include factors such as the frequency of product usage, the amount of product used, the timing of purchases, brand loyalty, product benefits sought, and other behavioral indicators.

By analyzing usage patterns, marketers can identify distinct segments within their target market and tailor marketing strategies to meet the unique needs and preferences of each segment. This enables companies to develop more targeted marketing campaigns, optimize product offerings, improve customer satisfaction, and drive customer loyalty.

Overall, behavioral segmentation, including the consideration of usage patterns, allows companies to better understand and connect with their customers by aligning their marketing efforts with specific behaviors and motivations.

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The principal advantage of the Dodge-Romig tables is their simplicity. Therefore, the correct answer is D. simplicity.

The Dodge-Romig tables are statistical sampling tables used in quality control to determine the acceptance or rejection

of a production lot based on sample size and the number of defects found in the sample.

The principal advantage of the Dodge-Romig tables is their simplicity.

They provide a quick and easy method for determining the acceptability of a production lot, without the need for

extensive calculations or statistical knowledge.

This means that they can be used by personnel with limited training in quality control.

The principal advantage of the Dodge-Romig tables is their simplicity. While they can be used for receiving inspection,

their main benefit is in minimizing inspection time and effort by providing clear guidelines for lot sampling and

acceptance based on size and level of defects.

Additionally, their use can facilitate smaller lot sizes and more efficient quality control processes.

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If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

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y +9 >= -1

Sum of a number(y) and 9. Is greater than or equal to negative one. Sum means add, so add y, and 9. It has to be atleast negative one, so greater than (0,1,2,3...), or equal to(-1).

Hope this helps, if you have more questions, feel free to ask.

The sum of a number y and 9 is at least -1 as an inequality is y + 9 ≥ 1.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An expression,

The sum of a number y and 9 is at least -1.

To find the number in the numerator form,

The sum of y and 9,

y + 9

And the value is at least -1.

So,

y + 9 ≥ 1

Therefore, the inequality is y + 9 ≥ 1

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Step-by-step explanation:

Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …

The square root of a number, n, written

√n the number that gives n when multiplied by itself. For example,

√100=10 because 10 x 10 = 100

Examples

Here are the square roots of all the perfect squares from 1 to 100.

√ 1 = 1 since 1 ² = 1

√ 4 = 2 since 2 ² = 4

√ 9= 3 since 3 ² = 9

√ 16= 4 since 4 ² = 16

√ 25= 5 since 5 ² = 25

√ 36= 6 since 6 ² = 36

√ 49= 7 since 7 ² =29

√ 64= 8 since 8 ² = 64

√ 81= 9 since 9 ² = 81

√ 100= 10 since 10 ² = 100

Finding square roots of of numbers that aren't perfect squares without a calculator

1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.

2. Divide - divide your number by one of those square roots.

3. Average - take the average of the result of step 2 and the root.

4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.

Example: Calculate the square root of 10 () to 2 decimal places.

1. Find the two perfect square numbers it lies between.

Solution:

32 = 9 and 42 = 16, so lies between 3 and 4.

2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)

3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667

Repeat step 2: 10/3.1667 = 3.1579

Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623

Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001

If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.

Answer: answer for what?

Step-by-step explanation: oh I see it appeared iN wrong catogory I’m browsing History sorry