Given: P(A1)= 0.17 P(A2)= 0.07 P(A3)= 0.13 P(A1 OR A2)=0.18 P(A2 OR A3)=0.18 P(A1 OR A3)=0.19 P(A1 AND A2 AND A3)=0.01 Let x be the number of defects that are present.

P(X = 0) = 1 - 0.19 = 0.81

P(A1 OR A2 OR A3) = (0.37) - (0.19) + 0.01 = 0.19 (is this correct ?)

if yes, then is it okay to calculate P(X=2) by summing the intersections P(A1 AND A2) + P(A2 AND A3) + P(A1 AND A3) and subtracting P(A1 AND A2 AND A3) ?

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

x = 15, y = 120

Step-by-step explanation:

the triangle has all 3 sides the same since there are the 3 lines going through a side. this means all corners are same.

add all corners of triangle to get 180

180/3= 60

4x= 60

x=15

the other corner next to y is 60 as well.

if I add the corner to y, I will get 180 and form a straight line

60 + y = 180

y= 120

Answer:

9.7 x 2.84 and 6.25 x 4.76

Step-by-step explanation:

i just got them right lol

Answer:

the first and third one

Step-by-step explanation:

i did edg.

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed. Therefore, the correct answer is 200%.

Speed is a measure of how quickly an object or person moves from one point to another. It is usually expressed in terms of distance traveled over time, for example, miles per hour or kilometers per hour.

To calculate this, we need to find the time taken for her to reach her home if her speed is doubled.

If her initial speed is 40 km/hr, then by doubling her speed, she will be travelling at a speed of 80 km/hr.

By travelling at this speed, she can reach her home in half an hour i.e. 30 minutes.

Therefore, the time taken to reach her destination by doubling her speed is 30 minutes.

The time taken to reach her destination while travelling at her initial speed is 2 hours.

To calculate the percentage increase in speed, we have to find the ratio of the time taken to reach her destination when the speed is doubled to the time taken to reach her destination when the speed is not doubled.

Therefore, the percentage increase in speed

= (30/120) x 100

= 25%.

Since she needs to double her speed to reach her home in half an hour, the percentage increase in speed required is 100%.

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed.

Therefore, the correct answer is 200%.

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Answer:

the slope is;

The amount of water in the reservoir is increasing at a rate of 50 cubic feet each hour.

Explanation:

The formula for slope is;

Given the points;

Substituting the values;

Therefore, the slope is;

The amount of water in the reservoir is increasing at a rate of 50 cubic feet each hour.

Using the slope form equation

Using the second point (12, 6)

The answer is D and E.

Answer:

6 and 10

Step-by-step explanation:

edge 2021 pls give brainliest

We could draw the following Venn's diagram:

Therefore,

13 students listened only rock music

6 students listened classical and Jazz music,but not rock.

28 students listened classical or jazz music, but not rock.

41 students listened to music in exactly one of the musical styles.

23 students listened to music in exactly two of the musical styles.

17 students did not listen to any of the musical styles.

Answer:

3 laps per minute

Step-by-step explanation:

Take the number of laps and divide by the minutes

18/6 = 3 laps per minute

Answer:

3 laps per min

Step-by-step explanation: divide 18 and 6

Answer:

\(x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²\)

Step-by-step explanation:

Given

\(x(2x+y+5) - 2(x\²+xy+5) + y(x + y)\)

Required

Simplify

We have:

\(x(2x+y+5) - 2(x\²+xy+5) + y(x + y)\)

Open brackets

\(x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²\)

Collect like terms

\(x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²\)

\(x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²\)

Answer:

Step-by-step explanation:

in this specific case the two legs are congruent:

b = 18

For the Pythagorean theorem

a = √ 2 * 18^2 = 18√2

The surface area of the rectangular prism is 46m²

Surface area of a rectangular prism = 2(width×length + height×length + height×width)

SA = 2(wl + hl + hw)

= 2(2.5×4 + 2×4 + 2×2.5)

= 2(10 + 8 + 5)

= 2(23)

= 46m²

Therefore, the surface area of a rectangular prism is 46m²

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Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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Answer:

Step-by-step explanation:

\(i=2: \frac{3}{2} \times\frac{1}{3^2}=\frac{1}{6}\)

\(i=3: \frac{3}{2} \times\frac{1}{3^3}=\frac{1}{18}\)

\(i=4: \frac{3}{2} \times\frac{1}{3^4}=\frac{1}{54}\)

\(i=5: \frac{3}{2} \times\frac{1}{3^5}=\frac{1}{162}\)

\(i=6: \frac{3}{2} \times\frac{1}{3^6}=\frac{1}{486}\)

\(sum=\frac{121}{486}\)

Answer:

3: 6, 9, 12, 15, 18

5: 10, 15, 20, 25, 30

7: 14, 21, 28, 35, 42

Step-by-step explanation:

Well, this is simple. Each multiple is that number plus the same number.

3: 3+3, 3+3+3, 3+3+3+3, 3+3+3+3+3, 3+3+3+3+3+3

3: 6 + 9 + 12 + 15 + 18

5: 5+5, 5+5+5, 5+5+5+5, 5+5+5+5+5, 5+5+5+5+5+5

5: 10, 15, 20, 25, 30

7: 7+7, 7+7+7, 7+7+7+7, 7+7+7+7+7, 7+7+7+7+7+7

7: 14, 21, 28, 35, 42

-Chetan K

Answer:

r= 7k/3

Step-by-step explanation:

Answer:

r=7k/3

Step-by-step explanation:

4r-12k=r-5k

4r=r-5k+12k

4r=r+7k

4r-r=7k

3r=7k

r=7k/3

The mean of sample a is equal to the mean of the population, it is likely that the sample is representative of the population, but it is not a guarantee of it.

If the mean of sample a is equal to the mean of the population, then it can be concluded that sample a is representative of the population. The mean of a sample is an estimate of the population mean, and if the sample mean is equal to the population mean, it indicates that the sample was randomly selected and is representative of the population.

However, it is important to note that the equality of the sample mean and the population mean does not guarantee that all other statistics, such as the standard deviation or the distribution shape, are equal. Sampling variability and the size of the sample can also impact the similarity between the sample and population statistics.

In conclusion, if the mean of sample a is equal to the mean of the population, it is likely that the sample is representative of the population, but it is not a guarantee of it. Further statistical analysis is needed to determine the representativeness of the sample and its similarity to the population.

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Answer:

\(a_{n}\) = 8 + (n-1)6

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

520-355 = 165

165/355 = 0.46

0.46 x 100 = 46

Answer:

2364 in

Step-by-step explanation:

1,224+1,140=2364

Answer:

$17 dollars a month and the relationship is 3 apart

Step-by-step explanation:

Answer:

C=4M+13

Step-by-step explanation:

Remember that as the number of movies M increases, the cost C increases too. For each additional movie, the cost increases by $4. This is added to the monthly fixed membership fee of $13.

Answer:

1a. 3y = 18

1b. y + 7 = 18

1c. 2y + 4 = 18

Step-by-step explanation:

In each case, let's take the red boxes to be constant why the the green boxes represents the variable, y.

Thus,

1a. There are only 3 green boxes which gives us 18, therefore, the equation that expresses this would be:

3y = 18

1b. We have 7 red boxes which represents the constant, 7.

We also have 1 green box which represents the variable, y. Therefore, the equation that expresses this would be:

y + 7 = 18

1c. We have 4 red boxes = 4

We have 2 green boxes = 2y

Therefore, we would have:

2y + 4 = 18

Answer:

3x^2 +3x +16

Step-by-step explanation:

do you need an explanation? if so I can put it in the comments

Answer:

the coefficient of x is an implied 1

any variable that's by itself without a coefficient has an implied 1

Step-by-step explanation:

I hope this helps :)

Answer:

The value is   \(P( X < 0.09) = 0.070781\)

Step-by-step explanation:

From the question we are told that

   The population proportion is  p =  0.11

   The sample size is n =  529

Generally given that the sample size is large enough (i.e n > 30), then the mean of this sampling distribution is mathematically represented as

      \(\mu_{x} = p = 0.11\)

Generally the standard deviation of this sampling distribution is

        \(\sigma = \sqrt{ \frac{ p (1 - p )}{n} }\)

=>     \(\sigma = \sqrt{ \frac{ 0.11 (1 - 0.11 )}{529} }\)

=>     \(\sigma = 0.01360\)

Generally the probability that the proportion of defective bottles in a sample of 529 bottles would be less than 9% (0.09) is mathematically represented as

     \(P( X < 0.09) = P(\frac{X - \mu_{x}}{\sigma} < \frac{0.09 -0.11}{ 0.01360} )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

     \(P( X < 0.09) = P(Z< -1.47 )\)

Generally from the z table  the  area under the normal curve to the left corresponding to -1.47 is  

       \(P(Z< -1.47 ) = 0.070781\)

So

       \(P( X < 0.09) = 0.070781\)

Complete question :

A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0 : μ = 12 against H1 : μ < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is xbar = 11.5. Suppose that the distribution of the sample mean is approximately normal.

Answer:

0.02275

Step-by-step explanation:

Given :

Population mean μ = 12

Standard deviation, σ = 0.5

Sample size, n = 4

Observed statistic, xbar = 11.5

H0 : μ = 12

H1 : μ < 12

The test statistic = (xbar - μ) ÷ σ/sqrt(n)

Test statistic =. (11.5 - 12) ÷ 0.5/sqrt(4)

Test statistic = - 0.5 ÷ 0.5/2

Teat statistic = - 0.5 / 0.25 = - 2

Since, it is stated that, distribution is approximately normal ; then we can use the Z distribution and obtain our Pvalue.

We could obtain P value using the Pvalue Z distribution calculator at α = 0.05, 1 - tail

Pvalue = 0.02275

Or

P(x < - 2) = 0.02275 (Z distribution table)

The statement All rectangles are squares because they have 90 degree angles, the opposite sides are parallel and all the sides are congruent is not true.

What is parallelogram?

A geometric shape that is defined as a quadrilateral with two pairs of parallel sides is called parallelogram. it is a flat shape with four straight sides where opposite sides are parallel and equal in length. The opposite angles of a parallelogram are also congruent (equal in measure).

The third statement is all rectangles are squares because they have 90 degree angles the opposite sides are parallel and all the sides are congruent.

It is false because while all squares are rectangles and have 90 degree angles and congruent sides, not all rectangles have congruent sides

Therefore, not all rectangles are squares. A rectangle is defined as a quadrilateral with four right angle but the sides can be of different lengths.A square is a special type of rectangle where all four sides are congruent.

So, above statement is wrong.

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Answer:

C

Step-by-step explanation:

The required value of h, representing the height of the three-dimensional rectangle, is 12.

The diagonal of a three-dimensional rectangle is defined by the equation d² = x² + y² + h². To solve for h, we can rearrange the equation as follows:

h² = d² - x² - y²

Given the values d = 13, x = 3, and y = 4, we can substitute them into the equation:

h² = 13² - 3² - 4²

h² = 169 - 9 - 16

h² = 144

Taking the square root of both sides, we find:

h = 12

Therefore, the value of h, representing the height of the three-dimensional rectangle, is 12.

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