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The SAS standard for similarity of triangles states that triangles are similar if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent.

Statement : The statement can be expressed as follows:

If two triangles ABC and DEF are such that

∠A=∠D and AC /DF =AB/DE

then △ABC∼△DEF

Proof :

Given: △ABC and △DEF are such that

AC /DF =AB/DE and ∠A=∠D

To Prove : △ABC∼△DEF

Construction : Draw a line PQ such that DP= AB , DQ= AC

In △ABC and △DPQ

AB = DP ( by construction)

DQ= AC ( by construction)

∠A=∠D (given)

=> △ABC ≅△DPQ (by SSA congruence property)

AB/DE = AC/DF (given )

=> DP/DE = DQ/DF ( using AB = DP ; DQ= AC)

=> PQ||EF (by converse of B.P.T)

Now , ∠P =∠E and ∠Q =∠F ( by corresponding angles)

△DEF ≅ △DPQ (Using AAS congruence )

=> △ABC ∼△DEF ( because two congrunt triangles are always similar )

Hence proved .

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Answer:

1. 0.003

2. 0.5

3. 0.001343

4.0.05003

5. 0.670570

6. 1.01

Answer:

w1= -2, w2 = 5

Step-by-step explanation:

The optimal length of the order cycle associated with the minimum total cost of ordering and inventory holding is 2.50 days.

To determine the optimal length of the order cycle, we need to consider the trade-off between ordering costs and inventory holding costs. The order cycle refers to the time between placing orders for resin.

The total cost of ordering and inventory holding can be calculated using the Economic Order Quantity (EOQ) formula, which is given by:

EOQ = √((2 * D * S) / H),

where D is the annual demand, S is the ordering cost per order, and H is the holding cost per unit per year.

In this case, the annual demand (D) is 120 kg/day * 365 days = 43,800 kg/year. The ordering cost (S) is $150 per order, and the holding cost (H) is $0.4 per kg per day.

Plugging these values into the EOQ formula, we get:

EOQ = √((2 * 43,800 * 150) / (0.4 * 365)) = √(5256000 / 146) ≈ 464.19 kg.

The optimal order cycle is then calculated as EOQ divided by the daily demand, which gives us:

Optimal order cycle = 464.19 kg / 120 kg/day ≈ 3.87 days.

Rounding this value to two decimal places, the optimal length of the order cycle is 2.50 days, which minimizes the total cost of ordering and inventory holding for the billiard ball maker.

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The answer choice which represents a function among the given answer choices is; Choice B.

According to the given task content; the table which represents a function among the given answer choice is to be identified.

Recall that a function can be defined as a relation in which case; each input value is assigned not more than one value.

By observation, only the answer choice B has a combination of input and output values in which case; each input value is assigned only one output value.

Hence, since a function is a relation which is characterized by assigning only one output value to each input value; the correct answer choice is; Choice B.

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Answer:

z=2

Step-by-step explanation:

add 15 to both sides.

6z=-8z+28

add 8z to both sides.

14z=28

divide by 14 on both sides.

z=2

Answer:

z=2

Step-by-step explanation:

-15+6z=-8z+13

6z=-8z+28

14z=28

z=2

Answer: you take 4.50 multiply it by 4 for the chaperons and the teacher then multiply 4.50 by how many students there are then add those two together and there is your answer

Step-by-step explanation:

Given:

The perimeter of a rectangle is 84cm.

The length is 12 cm longer than the width.

Required:

We need to find the length and width of the rectangle.

Explanation:

Let l be the length of the rectangle and w be the width of the rectangle.

The length is 12 cm longer than the width.

Add 12 to the width to get the length.

Consider the perimeter of the rectangle formula.

Substitute l=12+w and P =84 in the formula.

Subtract 24 from both sides of the equation.

Divide both sides of the equation by 4.

Substitute w =15 in the equation l=12+w.

Final answer:

The length of the rectangle is 27 cm.

The width of the rectangle is 15 cm.

This statement is true. Statistical inference is the process of deriving conclusions about a population from a sample.

The process of statistical inference uses probability theory to draw conclusions from data. It is important to note that the conclusions drawn from a sample of data may not be accurate conclusions about the entire population.Statistical inference involves several steps. First, a random sample of data is selected from the population. Second, the data is analyzed to identify patterns and trends that may exist in the population. Third, a statistical model is used to make inferences about the population based on the sample data. In statistical inference, we use the following equation to calculate the probability of a certain event occurring: P(A|B)=P(B|A)P(A)/P(B), where A and B are two events. In this equation, P(A|B) is the probability that event A occurs given that event B has already occurred. P(B|A) is the probability that event B occurs given that event A has already occurred. P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.Statistical inference is a powerful tool for drawing conclusions from data.

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The area of a garden is the amount of space on the garden

The length is x - 4 and the width is 3x + 2

The area of the garden is given as:

\(Area = 3x^2 - 10x - 8\)

Expand the equation

\(Area = 3x^2 +2x- 12x - 8\)

Factorize the above equation

\(Area = x(3x +2) -4(3x +2)\)

Factor out 3x + 2

\(Area = (x-4) (3x +2)\)

The area of the garden is the product of its dimension.

Hence, the length is x - 4 and the width is 3x + 2

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Answer:

Simplify what though? i would answer u but plz put what im supposed to simplify

Step-by-step explanation:

Answer:

y = .9

Step-by-step explanation:

0.7(1.5+ y) = 3.5y - 1.47

Distribute

1.05 +.7y = 3.5y -1.47

Subtract .7y from each side

1.05 +.7y.-.7y = 3.5y-.7y -1.47

1.05 =2.8y -1.47

Add 1.47 to each side

1.05+1.47 = 2.8y

2.52 = 2.8y

Divide by 2.8

2.52/2.8 = y

.9 = y

Answer:

y = 0.9

C, the third one

Step-by-step explanation:

Examine this multistep equation with variables on both sides.

0.7(1.5 + y) = 3.5y - 1.47

Which of the following is the solution to this equation?

y = 0.09

y = 0.17

y = 0.9

y = 1.7

Answer:

x- intercept = 4 , y- intercept = - 2

Step-by-step explanation:

To find the x- intercept let f(x) = 0 , that is

\(\frac{x-4}{-x+2}\) = 0

The denominator cannot be zero as this would make f(x) undefined

Equating the numerator to zero

x - 4 = 0 ⇒ x = 4 ← is the x- intercept

To find the y- intercept let x = 0 , that is

f(0) = \(\frac{0-4}{-0+2}\) = \(\frac{-4}{2}\) = - 2 ← is the y- intercept

Answer:

The size of angle AEF is 15 degrees

Step-by-step explanation:

To calculate the size of angle AEF, we'll follow these steps:

Step 1: Identify the relevant triangles and angles:

From the given information, we have:

Square ABCD (with all angles 90 degrees)

Equilateral triangle DEF (all angles are 60 degrees)

Isosceles triangle ADE (AD = AE)

Step 2: Determine the relationships between angles:

In triangle ADE, since AD = AE (isosceles triangle), angle ADE = angle AED.

Step 3: Determine the angles in triangle DEF:

In an equilateral triangle, all angles are equal, so each angle in DEF is 60 degrees.

Step 4: Analyze the diagram:

Considering the information given, we can determine the following:

Angle DAE = 90 degrees - angle ADE = 90 degrees - angle AED

Angle DAE + angle ADE + angle AED = 180 degrees (sum of angles in triangle ADE)

Step 5: Calculate the size of angle AED:

From step 4, we have angle DAE + angle ADE + angle AED = 180 degrees. Since angle DAE = 90 degrees, we can substitute the values:

90 degrees + angle AED + angle AED = 180 degrees

Combining like terms:

90 degrees + 2 * angle AED = 180 degrees

Subtracting 90 degrees from both sides:

2 * angle AED = 90 degrees

Dividing both sides by 2:

angle AED = 45 degrees

Step 6: Calculate the size of angle AEF:

In triangle DEF, angle DEF = angle DFE = 60 degrees (as it's an equilateral triangle).

To find angle AEF, we can subtract angle AED from angle DEF:

angle AEF = angle DEF - angle AED = 60 degrees - 45 degrees

Calculating:

angle AEF = 15 degrees

Therefore, the size of angle AEF is 15 degrees.

The width of the last little parallelogram, 10/3, is determined by the provided statement.

Furthermore, despite the fact that this is never the case, every rhombus is considered to be a parallelogram. A quadrilateral is a form that is flat. They arrive in quartets. A parallelogram is formed by two opposing sides that are flat and proportional to one another. Parallelograms come in 4 distinct varieties, including 3 unique varieties. Rhombuses, triangular shapes, cubes, and squares are the four types.

The diagonal area products are equal.

Divide the two sides by 6 20/6 = x = 10/3 since 4*5 Equals 6 * x 20 Equals 6 * x

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The complete question is-

A large parallelogram is divided into four small parallelograms as shown. The areas of three of the four small parallelograms are labeled in the diagram. What is the area of the remaining small parallelogram?

To determine a rejection region for a test at level α using the fact that the sum of independent Poisson random variables follows a Poisson distribution, we calculate the critical values based on the desired significance level α and compare them with the observed sum of Poisson variables.

To determine a rejection region for a test at level α using the fact that the sum of independent Poisson random variables follows a Poisson distribution, we can follow these steps:

Specify the null and alternative hypotheses: Determine the null hypothesis (H0) and the alternative hypothesis (Ha) for the statistical test. These hypotheses should be stated in terms of the parameters being tested.

Choose the significance level (α): The significance level α represents the maximum probability of rejecting the null hypothesis when it is true. It determines the probability of making a Type I error (rejecting H0 when it is actually true). Common choices for α are 0.05 or 0.01.

Determine the test statistic: Select an appropriate test statistic that follows a Poisson distribution based on the data and hypotheses being tested. The test statistic should be able to capture the effect or difference being examined.

Calculate the critical region: The critical region is the set of values of the test statistic for which the null hypothesis will be rejected. To determine the critical region, we need to find the values of the test statistic that correspond to the rejection region based on the significance level α.

Use the Poisson distribution: Since the sum of independent Poisson random variables follows a Poisson distribution, we can utilize the Poisson distribution to determine the probabilities associated with different values of the test statistic. We can calculate the probabilities for the test statistic under the null hypothesis.

Compare the probabilities: Compare the probabilities calculated under the null hypothesis with the significance level α. If the calculated probability is less than or equal to α, it falls in the rejection region, and we reject the null hypothesis. Otherwise, if the probability is greater than α, it falls in the acceptance region, and we fail to reject the null hypothesis.

It is important to note that the specific details of determining the rejection region and performing hypothesis testing depend on the specific test being conducted, the data at hand, and the nature of the hypotheses being tested. Different tests and scenarios may require different approaches and considerations.

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Answer:

Paulina is reading a book with 677pages total. If she has already read 345 and plans to read 23 pages a day, how many days, x, will she nees to read at that pace until she finishes the entire book?

Step-by-step explanation:

\(345 + 23x = 677\)

23x=677-345

x=677-345/23

x=332/23

x= 14.43 days

Answer:

  A  { y | y ∈ ℝ, y ≠ -4, -3 }

Step-by-step explanation:

You want to know the range of the function shown in the graph.

The range is the vertical extent of the graph, the set of possible function output values.

Here, the function approaches the horizontal asymptote y = -3, but never has that output value. The "hole" at (5, -4) means the function never has the output value -4, either.

The range is all real numbers (ℝ) except -4 and -3.

There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.

Given that,

The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.

We have to find how many people and kids were allowed inside.

We know that,

We get equations as,

1.5x+4y=351 ----->equation(1)

The other equation is

x+y=1014 ----->equation(2)

Take the equation(2)

x+y=1014

y=1014-x

Substitute y=1014-x in equation(1)

1.5x+4y=351

1.5x+4(1014-x)=351

1.5x+2056-4x=351

1.5x-4x=351-2056

-2.5x=-1705

2.5x=1705

x=1705/2.5

x=682

Substitute x=682 in equation(2)

y=1014-x

y=1014-682

y=332

Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.

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Answer:

5√5

Step-by-step explanation:

125/25=5

√25=5

Answer:  5√5

Decimial form = 11.180339888

I reccomond not using decimal form

Step-by-step explanation:

One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.

A mole is a unit of measurement in chemistry that expresses the amount of a substance. It is defined as the number of entities (such as atoms, ions, or molecules) in a sample of the substance. The number of entities in one mole of a substance is known as Avogadro's number.

Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.

One mole of a substance is equal to Avogadro's number, which is approximately 6.022 x 10^23.

The mole of H2 (hydrogen gas) is the number of H2 molecules in a sample of hydrogen gas. One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.

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The margin of error with a sample size of 1600 will be smaller than the margin of error with a sample size of 100, assuming the same standard deviation and confidence level, meaning that we can be more confident in the accuracy of the estimate with a larger sample size.

Assuming that both samples have the same standard deviation, the margin of error for a 95% confidence interval for estimating a population mean can be calculated as

Margin of Error = z×(standard deviation/sqrt(sample size))

where z is the z-score corresponding to the desired confidence level (in this case, 1.96 for a 95% confidence level).

For a sample size of 100, the margin of error would be

Margin of Error (n=100) = 1.96×(standard deviation/sqrt(100))

For a sample size of 1600, the margin of error would be

Margin of Error (n=1600) = 1.96*(standard deviation/sqrt(1600))

Since the standard deviation is the same for both samples, the only difference between the two margins of error is the sample size. The margin of error is inversely proportional to the square root of the sample size, so as the sample size increases, the margin of error decreases.

In other words, the margin of error with a sample size of 1600 will be smaller than the margin of error with a sample size of 100, assuming the same standard deviation and confidence level. This means that we can be more confident in the accuracy of the estimate with a larger sample size.

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The slope for the situation is $2.96

Since the food delivery service charges $5.92 for every 2 meals delivered, plus a $2.50 service fee.

We need to find the slope for the food delivery service charge.

Since we have $5.92 for every 2 meals delivered, the slope is

$5.92/2 meals = $2.96

So, the slope for the situation is $2.96

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Answer:

The slope for the situation is $2.96

Step-by-step explanation:

The measure of angle BCA is 81 degrees.                                            

Answer:

hope you get it ........

here is a screenie of the answer !!

Answer:22

Step-by-step explanation: 1/2 = .5

.5x.5x.5

0.125 x 176= 22

The probability will:

a) Increase.

b) decrease.

c) increase.

We know that as larger is the size (or the diameter at least) of the hole, the easier will be to lading the skee ball on that hole.

So "If the size of the 40-point hole is enlarged, the probability... "

If you increase the size, then it will be easier to land the ball, thus we can conclude that the probability will increase.

" If the 40-point hole is made smaller, the probability..."

Opposite as the case above, this time will be harder to land the ball, thus the probability will decrease.

"If the 40-point hole stays the same size, but the scoring zone is made smaller, the probability..."

If the ball is thrown in a random way, such that the probability of landing in any region of the scoring zone is the same, then the probability of landing on the 40-point hole is equal to the quotient between the area of the hole and the total area of the scoring zone.

Thus, is you decrease the area of the scoring zone, then the probability increases.

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Answer: The probability will:

a) Increase.

b) decrease.

c) increase.

Answer:

8.89 feet

Step-by-step explanation:

\(\sqrt{79}\) = 8.888, rounded to nearest hundredth would be 8.89

a) The percentage of students who failed the exam, given that they completed the exam review, is of: 15.38%.

b) The percentage of students who failed the exam, given that they did not complete the exam review, is of: 42.86%.

c) There is a negative association between failing the exam and completing the exam review.

A percentage is obtained by the division of the desired amounts by the total amounts, which is then multiplied by 100%.

For item a, these amounts are given as follows:

Hence the percentage is of:

p = 10/65 x 100% = 15.38%.

Then, for item b, the desired and total amounts are given, respectively, by:

Hence the percentage is obtained as follows:

p = 15/35 = 0.4286 = 42.86%.

Thus it can be concluded that there is a negative association between failing the exam and completing the exam review, as not completing the exam review makes you significantly likelier to not pass.

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