(15 points) A group of researchers with biotechnology background are doing a waste management project. They collected data from 50 garbage dumps around Jakarta and found that the average amount of the waste is 8.500 ton per day in each garbage dump with standard deviation 154 ton per day (10 points) What is probability that in one garbage dump there will be garbage with amount between 7000 ton to 9000 ton per day? Hint calculate z-value first. (5 points) Calculate the confidence interval for garbage amount (with 5% significant level)? What is the interpretation or meaning of the values?

The angles 75° and ∠2 are alternate interior angles.

Option D is the correct answer.

We have,

From the figure,

55°, ∠3, and 75° forms a straight angle.

Alternate angles are pairs of angles formed when a transversal line intersects two parallel lines.

Alternate angles are equal in measure, which means they have the same angle degree value.

So,

75° and ∠2 are alternate angles.

Thus,

75° and ∠2 are alternate angles.

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Based on the information given, we know that the probability of finding 3 people in a household is the same as the probability of finding 4 people. Therefore, the probability that a randomly chosen American household contains 2 or 5 people is 1/6.

To determine the probability that should replace "?" in the table, we first need to recognize that the sum of probabilities for all possible outcomes must equal 1. Given that the probability of finding 3 people in a household is the same as the probability of finding 4 people, let's denote that probability as x.

Since the "?" represents the remaining probability, we can set up an equation:
x + x + ? = 1

The sum of the probabilities for all possible outcomes must equal 1. We know that there are 4 possible outcomes (households with 2, 3, 4, or 5 people).

Simplifying the equation:
3x + ? = 1

Since we know that the probability of finding 3 people in a household is the same as the probability of finding 4 people, we can set up another equation:

Now, let's plug in the answer choices and see which one gives us a valid probability distribution:

a) 0.04:
2x + 0.04 = 1
2x = 0.96
x = 0.48 (Invalid, since x should be the probability for finding 3 or 4 people and it's greater than the maximum probability value of 1)

b) 0.09:
2x + 0.09 = 1
2x = 0.91
x = 0.455 (Invalid for the same reason as options a)

c) 0.32:
2x + 0.32 = 1
2x = 0.68
x = 0.34 (Valid, as it falls within the probability range of 0 to 1)

d) 0.16:
2x + 0.16 = 1
2x = 0.84
x = 0.42 (Invalid for the same reason as options a)

Based on the calculations, option c (0.32) should replace "?" in the table, as it creates a valid probability distribution with the given conditions.

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The smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.

To find the smallest number of terms needed to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6, we need to use the formula for the partial sum of a series. The partial sum of the given series up to n terms is:

S(n) = IM8 + 12e + 0.49(2^2) + 0.49(3^2) + ... + 0.49(n^2)

We want to find the smallest value of n such that the error between S(n) and the true value of the series is less than 10^-6. The error between S(n) and the true value of the series can be approximated by the absolute value of the next term in the series:

|an+1| = 0.49((n+1)^2)

So we need to find the smallest value of n such that:

|an+1| < 10^-6

0.49((n+1)^2) < 10^-6

(n+1)^2 < (10^-6)/0.49

n+1 < sqrt((10^-6)/0.49)

n < sqrt((10^-6)/0.49) - 1

n < 11.75

Since n must be a whole number, the smallest value of n that satisfies this inequality is n = 11. Therefore, we need at least 11 terms to obtain an approximation of the series IM8 12ke 0.49k2 accurate to 10-6.

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The probability of drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time is approximately 0.00012, or 0.012%.

To determine the probability of drawing three sevens in a row from a standard deck of cards without replacement, we can use the following method:

Step 1: Identify the total number of cards in a standard deck. A standard deck has 52 cards (13 ranks and 4 suits).

Step 2: Determine the number of sevens in the deck. There are 4 sevens (one from each suit).

The probability of drawing a seven from a standard deck of 52 cards is 4/52 or 1/13, since there are four sevens in the deck. After the first seven is drawn, there are 51 cards left in the deck, of which three are sevens. So the probability of drawing a second seven is 3/51. Similarly, after the second seven is drawn, there are 50 cards left in the deck, of which two are sevens. So the probability of drawing a third seven is 2/50.


Step 3: Calculate the probability of drawing the first seven. This would be the number of sevens divided by the total number of cards:
P(1st Seven) = 4/52

Step 4: After drawing the first seven, there are now 51 cards left in the deck and only 3 sevens remaining. Calculate the probability of drawing the second seven:
P(2nd Seven) = 3/51

Step 5: After drawing the second seven, there are now 50 cards left in the deck and only 2 sevens remaining. Calculate the probability of drawing the third seven:
P(3rd Seven) = 2/50

Step 6: To find the probability of all three events happening in a row, multiply the individual probabilities:
P(Three Sevens) = P(1st Seven) * P(2nd Seven) * P(3rd Seven) = (4/52) * (3/51) * (2/50)

Step 7: Calculate the result:
P(Three Sevens) = (4/52) * (3/51) * (2/50) = 0.0012 (approximately)

The probability of drawing three sevens in a row from a standard deck of cards without replacement is approximately 0.0012, or 0.12%.

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A. 2x + 3 = 5 + 2x has infinitely many solutions because the variable terms cancel out, leaving the statement 3 = 3, which is always true, regardless of the value of x.

The cost of one small order of fries at the Burger Palace is $1.09. The correct answer is not given in any option.

The price is another name for the cost of a thing from the perspective of a consumer. This is the price the seller sets for a product, which takes into account both the cost of manufacture and the markup the seller adds to increase profits.

Let's say a hamburger costs x dollars and a small order of French fries costs y dollars.

x--------> the cost of one hamburger

y--------> the cost one small order fries

we know that

2x+y=6.50

5x+5y=17.75

using a graph tool

see the attached figure

the solution is

x=2.5

y=1.09

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The complete question is

At The Burger Palace, 2 hamburgers and 1 small order of fries costs $6.50. The Clarke family ordered 5 hamburgers and 5 small orders of fries and paid $17.75.

Select the TWO equations that fit the scenario described above.

A) 2x+y=6.50

B) 6.50x+17.75y=5

C) 2x+5y=24.25

D) 5x+5y=6.50

E) 5x+5y=17.75

a)  A is not diagonal because it is not possible to find a matrix P such that A = PDP^-1, where D is a diagonal matrix.

b) A is not diagonalizable.

(a) A is diagonalizable but not diagonal: One possible example of such a matrix A would be:

A = [[1, 1], [0, 5]]

The characteristic polynomial of A is det(A –λ I) = (1 - λ)2(5 –λ), as given. The eigenvalues of A are λ1 = 1 and λ2 = 5, both of which have algebraic multiplicity 2. The eigenvectors corresponding to λ1 = 1 are [1, 0] and [1, 1], while the eigenvector corresponding to λ2 = 5 is [0, 1]. It can be verified that the eigenvectors are linearly independent and thus form a basis for R2. Therefore, A is diagonalizable.

However, A is not diagonal because it is not possible to find a matrix P such that A = PDP^-1, where D is a diagonal matrix.

(b) A is not diagonalizable: One possible example of such a matrix A would be:

A = [[1, 1], [0, 1]]

The characteristic polynomial of A is det(A –λ I) = (1 - λ)^2, which has a repeated eigenvalue of λ = 1. The eigenvectors corresponding to λ = 1 are [1, 0] and [0, 1], but they do not form a basis for R2 because they are linearly dependent. Therefore, A is not diagonalizable.

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Any value of b within this range would satisfy the original expression "23 > b ≥ -276".

The given expression is "23 > b ≥ -276". This means that b can take any value between -276 and 23, inclusive of -276 but not inclusive of 23.

To understand why this is the case, we can break down the expression into two parts: "23 > b" and "b ≥ -276".

The first part, "23 > b", means that b is less than 23. In other words, b can take any value that is less than 23. For example, b could be 22, 10, or even -100, as long as it is less than 23.

The second part, "b ≥ -276", means that b is greater than or equal to -276. This means that b can take any value that is greater than or equal to -276. For example, b could be -276, -200, or even 0, as long as it is greater than or equal to -276.

Putting these two parts together, we can see that b can take any value that is both less than 23 and greater than or equal to -276. This range of values for b is inclusive of -276 but not inclusive of 23, meaning that b cannot equal 23.

In numerical form, we can write the range of values for b as:

-276 ≤ b < 23

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Answer:

The correct answer is c.) 3/36.There are three favorable outcomes (2, 11, and 12) out of a total of 36 possible outcomes (assuming a fair six-sided number cube). Therefore, the probability of X being a 2, 11, or 12 is 3/36, which can be simplified to 1/12.

Step-by-step explanation:

Answer:

b = 12 Km

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

b² + 16² = 20²

b² + 256 = 400 ( subtract 256 from both sides )

b² = 144 ( take square root of both sides )

b = [tex]\sqrt{144}[/tex] = 12

476 and 1/12, In summary, the answer to 43 and 5/12's times 11 is 5713/12 or 476 and 1/12.

To solve this problem, we need to convert the mixed number 43 and 5/12 into an improper fraction. We can do this by multiplying the whole number (43) by the denominator of the fraction (12), and adding the numerator (5) to get the total number of twelfths:

43 x 12 + 5 = 521/12

Now, we can multiply this fraction by 11:

521/12 x 11 = 5713/12

To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1:

5713/12

This is the final answer. However, if we want to express it as a mixed number, we can divide 5713 by 12 to get the whole number part (476) and the remainder

(1). Therefore, the final answer can also be written as:

476 and 1/12

In summary, the answer to 43 and 5/12's times 11 is 5713/12 or 476 and 1/12.

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The statement "A single, extremely large value can affect the median more than the mean" is True.

The median is the middle value when the data is arranged in ascending or descending order, and it is less affected by extreme values because it only considers the position of the value, not its actual magnitude.

On the other hand, the mean (average) takes into account the values themselves and can be heavily influenced by outliers. An extremely high or extremely low data value is called an outlier.

Outliers can skew the mean, pulling it towards their extreme value, while the median remains relatively unaffected. So the statement is True.

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The length of MS is 10 cm and diameter of the circle is RS

Given that the midpoint of PQ is M

RM is 10 cm and PQ is 24 cm

We have to find the length of MS

As M is midpoint then RM=MS

MS = 10 cm

Now the diameter of the circle is RS because it passes through middle of the circle which is center O

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When the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic.

When the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic.

The formula for the confidence interval for the population mean when the population standard deviation is known is given by:

CI = X ± z(α/2) * σ/√n

Where:

X is the sample mean

σ is the population standard deviation

n is the sample size

z(α/2) is the z-score corresponding to the desired level of confidence (e.g. for a 95% confidence interval, α = 0.05 and z(α/2) = 1.96)

The z-statistic is used in this formula to determine the width of the confidence interval. It is based on the standard normal distribution and represents the number of standard deviations the sample mean is from the population mean. The z-score is calculated using the formula:

z = (X - μ) / (σ/√n)

Where μ is the population mean.

The z-score is used to find the critical values for the confidence interval, which are obtained by multiplying it by the standard error of the mean (σ/√n). These critical values define the endpoints of the confidence interval.

In summary, when the population standard deviation is known, the confidence interval for the population mean is based on the z-statistic, which is used to calculate the critical values for the confidence interval.

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The z-score for 0.7129 is approximately 0.55. The value of c is 0.55, rounded to two decimal places.

1. We're given P(2 > c) = 0.2643, which means the area under the standard normal distribution curve between 2 and c is 0.2643.

2. We'll use the z-table or a calculator with a standard normal distribution function to find the corresponding z-score for c.

3. To find the area to the left of c, we need to first find the area to the left of 2. The z-score for 2 is 0.9772 (from the z-table or using a calculator).

4. Now, subtract the given area (0.2643) from the area to the left of 2: 0.9772 - 0.2643 = 0.7129.

5. Look up the z-score corresponding to the area 0.7129 in the z-table, or use a calculator with the inverse standard normal distribution function. The z-score for 0.7129 is approximately 0.55.

6. Therefore, the value of c is 0.55, rounded to two decimal places.

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Mike works 39 hours per week at Job A and 20 hours per week at Job B.

We need to formulate some expressions here.

Let:

Hours Mike works at Job A = x

Hours Mike works at Job B = y

We know that:

x + y = 59 ---------- equation 1

We also know that he makes $6 per hour at Job A, and $7 per hour at Job B, and his total pay is $374. So we can set up another equation based on his total pay:

6x + 7y = 374 --------- equation 2

Now we have two equations with two unknowns, which we can solve simultaneously.

Using substitution method:

solve for x in terms of y:

x = 59 - y

We can substitute this expression for x into equation 2:

6(59 - y) + 7y = 374

Simplifying and solving for y:

354 - 6y + 7y = 374

y = 20

So Mike works 20 hours per week at Job B. We can substitute this value for y into equation 1 to find x:

x + 20 = 59

x = 39

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Answer:

C. When they're done, José always fills the gas tank.

The expression that will help in finding the surface area of the net are

The external surface area of three-dimensional objects is referred to as the surface area, and is generally calculated in square units.

Calculating the surface area of certain 3D shapes requires one to use different formulas. depending on the shapes

The shapes encountered here are

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The difference is: Marginal cost is the money paid for producing one more unit of a good. Marginal revenue is the money earned from selling one more unit of a good.

Marginal cost (MC) is the additional outlay expended by a producer when they fabricate and supply one supplementary unit of an item or service. It symbolizes the replace in total costs caused by producing one extra piece.

Marginal revenue (MR), on the other hand, is the supplementary turnover generated when an establishment deals one more piece of a good or service. It signifies the transformation in complete revenue attained from selling an supplemental product.

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They discount you $250 from the television cost.

Discount is defined as a deduction from the usual cost of something.

Since the television cost $1250 and when you bought it they gave you a 20% discount. We can say:

discount = 20% of $1250

discount = 20/100 * $1250

discount = $250

Therefore, they discount you $250

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Question in English

A television cost $1250 and when we bought it they gave us a 20% discount. How much did they discount us?

Since a straightedge lacks measurement gradients, it can only be used to create or draw straight lines—not to measure length.

An instrument for drawing straight lines or ensuring their straightness is a straightedge or straight edge. It is typically referred to as a ruler if its length is marked with uniformly spaced markings. If no markings are present, it is just a straight edge.

Straight lines can be measured and marked with a ruler. A straight edge won't help you measure, but since they are typically more robustly constructed than rulers, they are a better tool for drawing straight lines. Most of the time, rulers can be used as a straight edge.

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Answer:

2700

Step-by-step explanation:

im pretty sure that volume is length times width times height so

if u times these 3 numbers together its 2700

The 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it can be calculated using a statistical formula. The formula for a confidence interval is: CI = p ± zsqrt((p(1-p))/n)

Where CI is the confidence interval, p is the proportion of interest (in this case, 0.48 or 48%), and z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.645 for 90% confidence), sqrt is the square root function, and n is the sample size (in this case, 331).

Plugging in the values, we get:

CI = 0.48 ± 1.645sqrt((0.48(1-0.48))/331)

CI = 0.48 ± 0.062

Thus, the 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it is (0.418, 0.542). This means that we can be 90% confident that the true proportion of Americans who decide not to go to college because they cannot afford it falls between 41.8% and 54.2%.

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Answer:

Step-by-step explanation:

Maximum :)

A) The same z-score and find the area to the left of it, which is 0.1562.

b) The 75th percentile of the defect length distribution is 33.32 mm.

C) The 15th percentile of the defect length distribution is 19.21 mm.

d)The values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10% are 17.95 mm and 38.05 mm, respectively.

(a) To find the probability that the defect length is at most 20 mm, we need to calculate the z-score first:

z = (20 - 28) / 7.9 = -1.0127

Using a standard normal table or a calculator, we can find that the probability of a z-score less than or equal to -1.0127 is 0.1562. Therefore, the probability that the defect length is at most 20 mm is 0.1562.

To find the probability that the defect length is less than 20 mm, we can use the same z-score and find the area to the left of it, which is 0.1562.

(b) To find the 75th percentile of the defect length distribution, we need to find the z-score that corresponds to the area of 0.75 in the standard normal distribution. Using a standard normal table or a calculator, we can find that this z-score is approximately 0.6745.

Then, we can solve for the defect length:

z = (x - 28) / 7.9

0.6745 = (x - 28) / 7.9

x - 28 = 0.6745 * 7.9

x = 33.32

Therefore, the 75th percentile of the defect length distribution is 33.32 mm.

(c) To find the 15th percentile of the defect length distribution, we need to find the z-score that corresponds to the area of 0.15 in the standard normal distribution. Using a standard normal table or a calculator, we can find that this z-score is approximately -1.0364.

Then, we can solve for the defect length:

z = (x - 28) / 7.9

-1.0364 = (x - 28) / 7.9

x - 28 = -1.0364 * 7.9

x = 19.21

Therefore, the 15th percentile of the defect length distribution is 19.21 mm.

(d) To find the values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%, we need to find the z-scores that correspond to the areas of 0.1 and 0.9 in the standard normal distribution. Using a standard normal table or a calculator, we can find that these z-scores are approximately -1.2816 and 1.2816, respectively.

Then, we can solve for the defect lengths:

z = (x - 28) / 7.9

-1.2816 = (x - 28) / 7.9

x - 28 = -1.2816 * 7.9

x = 17.95

z = (x - 28) / 7.9

1.2816 = (x - 28) / 7.9

x - 28 = 1.2816 * 7.9

x = 38.05

Therefore, the values that separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10% are 17.95 mm and 38.05 mm, respectively.

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Answer:

Solving the inequality for y in 37<7 would be

y<2

The price elasticity of demand when the price is $32 per orange is 2

To calculate the price elasticity of demand, we need to use the formula:

E = (%Δq / %Δp) x (p/q)

where E is the price elasticity of demand, %Δq is the percentage change in quantity demanded, %Δp is the percentage change in price, and p/q is the average price-quantity ratio.

Given that the weekly sales of Honolulu Red Oranges is given by q = 1040 - 20p, we can find the derivative of q with respect to p as follows:

dq/dp = -20

This tells us that for every $1 increase in price, the quantity demanded will decrease by 20 units.

At a price of $32 per orange, the quantity demanded is:

q = 1040 - 20(32) = 424

If the price were to increase to $33 per orange, the new quantity demanded would be:

q' = 1040 - 20(33) = 404

Using these values, we can calculate the percentage changes in price and quantity demanded as:

%Δp = [(33 - 32) / 32] x 100% = 3.125%

%Δq = [(404 - 424) / 424] x 100% = -4.72%

The average price-quantity ratio is:

(p+ p')/2q = [(32 + 33)/2]/424 = 0.015

Now we can calculate the price elasticity of demand as:

E = (%Δq / %Δp) x (p/q) = (-4.72 / 3.125) x 0.015 = -0.023

Since the price elasticity of demand is negative, we know that Honolulu Red Oranges have an inelastic demand at a price of $32 per orange. This means that a 1% increase in price will lead to a less than 1% decrease in quantity demanded.

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The length of the major arc DFE is 10.11 π ft.

Given that, a circle C, with central angle 100°, and radius 7 yards,

We need to find the length of the major arc DFE,

The length of an arc = central angle / 360° × circumference

The central angle for the arc DFE = 360° - 100° = 260°

So, the length = 260° / 360° × π × 14

= 10.11 π ft

Hence, the length of the major arc DFE is 10.11 π ft.

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Answer:

B: 4.5

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

0.32 + /100 = 0.54 + 32/100

0.32 + x/100 = 0.54 + 0.32

x / 100 = 0.54

x = 54

So, the answer is 54