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The similarity statements are;

SV/RS = TV/TU

AC/AB = CE/ED

Formally, two triangles ABC and DEF are similar if and only if:

Their corresponding angles are congruent, meaning that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F.

The corresponding sides are in proportion to each other, meaning that the ratio of the length of side AB to side DE is equal to the ratio of the length of side BC to side EF, which is also equal to the ratio of the length of side AC to side DF.

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Answer:

hope this helps:)

Step-by-step explanation:

Answer:

sin θ = (√119)/12

tan θ = (√119)/5

csc θ = 12/(√119)

cot θ = 5/(√119)

Five trigonometric functions of θ are

sinθ = \(\frac{\sqrt{119} }{12}\)cosθ = \(\frac{5}{12}\)tanθ = \(\frac{\sqrt{119} }{5}\)cosecθ = \(\frac{12}{\sqrt{119} }\)secθ = \(\frac{12}{5}\)cotθ = \(\frac{5}{\sqrt{119} }\)

"The trigonometric functions of θ are functions of an angle. sine, cosine, and tangent are familiar trigonometric functions. The trigonometric functions relates the angles of a triangle to the length of its side."

Let θ be an acute angle of a right angle triangle

"An acute angle ("acute" meaning "small") is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees."

"A right angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).

"The side opposite the right angle is called the 'hypotenuse'. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°."

"An 'opposite' side is the one across from a given angle."

"An 'adjacent' side is next to a given angle. We use special words to describe the sides of right triangles."

we have,

cosθ = \(\frac{5}{12}\)

secθ = \(\frac{12}{5}\)

Hypotenuse side = 12

Adjacent side = 5

∴ Opposite side = \(\sqrt{hyp^{2}-adj^{2} }\)= \(\sqrt{12^{2}-5^{2} }\) = \(\sqrt{119}\)

sinθ = \(\frac{opp}{hyp}\) = \(\frac{\sqrt{119} }{12}\)

tanθ = \(\frac{opp}{adj}\) = \(\frac{\sqrt{119} }{5}\)

cosecθ = \(\frac{hyp}{opp}\) = \(\frac{12}{\sqrt{119} }\)

cotθ  = \(\frac{adj}{opp}\) = \(\frac{5}{\sqrt{119} }\)

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\(x^4-13x^2+12=0\\\)

Let \(x^2=x\)

\(x^2-13x+12=0\\(x-12)(x-1)=0\\x=1,12\\x^2=1,12\\x=1,-1,\sqrt{12},-\sqrt{12}\)

Answer:

x = ± 1, x = ± 2\(\sqrt{3}\)

Step-by-step explanation:

Given

\(x^{4}\) - 13x² + 12 = 0

Use the substitution u = x² , then

u² - 13u + 12 = 0 ← in standard form

(u - 1)(u - 12) = 0 ← in factored form

Equate each factor to zero and solve for u

u - 1 = 0 ⇒ u = 1

u - 12 = 0 ⇒ u = 12

Now substitute x² = u back, that is

x² = 1 ( take the square root of both sides )

x = ± \(\sqrt{1}\) = ± 1

x² = 12 , then

x = ± \(\sqrt{12}\) = ± \(\sqrt{4(3)}\) = ± 2\(\sqrt{3}\)

Answer:

3) 1,134

Step-by-step explanation: (9x6=54) and (54x21=1134)

Just mutlipication!

Answer:

B=54

C=54

Step-by-step explanation:

180-72=108

108/2=54

54*2=108

108+72=180

The main answer is 7x²-12/14x-72. To arrive at this answer, you need to use FOIL method (First, Outer, Inner, Last) to multiply the two expressions together.

This means multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms. After simplifying the resulting expression, you get the main answer of 7x²-12/14x-72.
The main answer to the product of (x^(1/7)-3/8)(x^(1/7)-3/8) is 7x^(2/7) - 3/4x^(1/7) + 9/64.


To find the product, you should apply the distributive property (also known as FOIL) by multiplying each term in the first parentheses by each term in the second parentheses:

1. First terms: (x^(1/7)) * (x^(1/7)) = x^(2/7) (using the rule of exponents, a^(m) * a^(n) = a^(m+n))
2. Outer terms: (x^(1/7)) * (-3/8) = -3/8x^(1/7)
3. Inner terms: (-3/8) * (x^(1/7)) = -3/8x^(1/7)
4. Last terms: (-3/8) * (-3/8) = 9/64

Now, combine the like terms (outer and inner terms):

7x^(2/7) - 3/4x^(1/7) + 9/64

So, the product of (x^(1/7)-3/8)(x^(1/7)-3/8) is 7x^(2/7) - 3/4x^(1/7) + 9/64.

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Average There are 120 ways to choose the three positions so that at least one freshman and one sophomore is chosen.

There are a total of 4 possible combinations of freshman and sophomore for the three positions, with at least one of each:

1. Freshman President, Sophomore Vice-President, Sophomore Treasurer

2. Sophomore President, Freshman Vice-President, Sophomore Treasurer

3. Freshman President, Sophomore Vice-President, Freshman Treasurer

4. Sophomore President, Freshman Vice-President, Freshman Treasurer

For each of the four combinations, there are 10 possible ways to choose the specific freshmen and sophomores for the positions (5 freshmen and 5 sophomores). That means there are 40 possible ways to choose the three positions with at least one freshman and one sophomore. Multiplying this by the 3 possible orders of the positions (President-Vice-President-Treasurer, President-Treasurer-Vice-President, Vice-President-President-Treasurer) gives us a total of 120 possible ways to choose the three positions so that at least one freshman and one sophomore is chosen.

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Answer:

288 good ways

Step-by-step explanation:

:)

Answer:

(i) 88°

(ii) 23°

Step-by-step explanation:

See the picture below.

The numbers added in red are the angle measures. The numbers added in black are the order in which each angle measure was written.

ABCD is a rhombus, so all sides are congruent.

Triangle BCD is isosceles with sides DC and BC congruent, so <DBC is congruent to <BDC. From the sum of the measures of the angles of a triangle, we get m<DCB. Opposite angles of a rhombus are congruent, so m<A = m<DCB. From the sum of the measures of the angles of a triangle and from isosceles triangle ADB we get m<ADB and m<ABD. From m<DBC and supplementary angles, we get m<CBE. From isosceles triangle BCE, we get m<BCE.

To find the area of a triangle using trigonometry, you can use the formula A = (1/2)bh, where A represents the area, b is the base of the triangle, and h is the corresponding height.

If you have an acute triangle, you can use trigonometric ratios to find the height. For example, let's say you know the length of one side (a) and the measure of the angle opposite to that side (A). To find the height, you can use the formula h = a * sin(A), where sin(A) represents the sine of angle A.

If you have a right triangle, you can use the lengths of the two legs (a and b) to find the area. The height of the triangle will be one of the legs, and the base will be the other leg. You can then use the formula A = (1/2)ab to calculate the area.

Here's an example to illustrate the process:
Suppose we have a right triangle with a base of 6 units and a height of 8 units. We can use the formula A = (1/2)bh, plugging in the values to get A = (1/2)(6)(8) = 24 square units.

In summary, to find the area of a triangle using trigonometry:
1. If you have an acute triangle, use trigonometric ratios to find the height.
2. If you have a right triangle, use the lengths of the two legs to find the area.

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This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).

Given that,

The statement is a confidence interval is the rejection region of a two-sided test.

We have to say if the statement is true or false.

We know that,

In statistics, a confidence interval describes the probability that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of predicted observations are frequently used by analysts.

Therefore, This statement is False as the confidence interval is also known as acceptance region, is a set of values for the test statistic for which the null hypothesis is accepted(two tailed).

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Answer:

9-16y

Step-by-step explanation:

9-x^2y when x=4

plus in 4: 9- (4)^2y

=9-16y

Answer:

(x - 3) ( 2x+1)

Step-by-step explanation:

(x - 3) ( 2x+1)

2x^2 + x - 6x -3

2x^2 - 5x -3

So, my answer is right!

Answer:

38

Step-by-step explanation:

Three consecutive even integers can be represented by x, x+2, x+4.  The sum is 3x+6, which is equal to 108.  Thus, 3x+6=108.  Solving for x yields x=34.  However, the question asks for the largest number, which is x+4 or 38.  Please make sure to answer what the question asks for!

You could have also plugged in the answer choices.  If you plugged in 38 as the largest number, then the previous even integer would be 36 and the next previous even integer 34.  The sum of 34, 36, and 38 yields 108.

Answer:

y=-7

Step-by-step explanation:

y-3=-2(x+5)

distribute the -2 into the ( )

y -3= -2x -10

cancel to -2x

y- 3 = -2(0) -10

y-3 = -10

  +3   +3

y= -7

Hope this helps!!

The y-intercept is -7 if the equation of the straight line is y - 3 = -2(x+5).

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

We have a straight line equation:

y - 3 = -2(x+5)

y - 3 = -2x - 10

Plug x = 0 to get the y-intercept

y - 3 = -2(0) - 10

y = -10 + 3

y = -7

Thus, the y-intercept is -7 if the equation of the straight line is  y - 3 = -2(x+5).

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Answer:

n = 4.5

Step-by-step explanation:

5.8n + 3.7 = 29.8 ( subtract 3.7 from both sides )

5.8n = 26.1 ( divide both sides by 5.8 )

n = 4.5

Answer:

so the answer to this is n= 4.5

Step-by-step explanation:

so first because you can't subtract the one with the variable you subtract 3.7 from 3.7 and 29.8 - 3.7 that cancels the 3.7 so it looks like this

5.8n + 3.7=29.8

         -3.7   -3.7

5.8n = 26.1

____   ____  n= 4.5    the lines means divide

5.8        5.8

Answer:

f(-2) = 3

Step-by-step explanation:

Have a nice day!

and please tell me if I am wrong.

Answer: 3

Step-by-step explanation:

If you carefully look at the table, when f(x) is -2, x is 3

The probability that the proportion of tickets sold in a sample of 865 tickets would differ from the population proportion by greater than 3% would be 0.0456, rounded to four decimal places.

By using the following formula, we can find the standard error in the population:

SE = √(p(1-p)/n),

where p is population proportion and n is sample size.

Since p = 0.2 and n = 865 in this instance, Therefore,

SE = √(0.2 × 0.8 / 865) = 0.015.

The z-score is then determined by dividing (0.03 - 0) by 0.015, which is 2.

We can determine that the likelihood of receiving a z-score larger than 2 or less than -2 is around 0.0456 using a conventional normal distribution table.

So, the likelihood that the proportion of tickets sold in a sample of 865 tickets would deviate from the general proportion by more than 3% is roughly 0.0456, rounded to four decimal places.

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Answer:

1. 1 1/3

2. 1 1/2

3. 4 1/2

Step-by-step explanation:

hope this helps:)

Answer: Number 1 is B  Number 2 is D Number 3 is C  Number 4 is D Number 5 is A

Step-by-step explanation:

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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Answer:

30 degrees - its been a minute since I done that type of math

To collect the necessary data, you would need to gather information such as:

Demand data: Collect historical sales data to analyze patterns, seasonality, and trends in customer demand. This data helps in estimating future demand and forecasting sales.

Lead time data: Determine the time it takes for the inventory to be replenished once an order is placed. This includes gathering data on supplier lead times, shipping durations, and any potential delays.

Holding cost data: Calculate the cost of holding inventory over a specific period, considering expenses like warehousing, storage, insurance, and depreciation. This data helps in evaluating the financial impact of inventory holding.

Ordering cost data: Identify the costs associated with placing orders, such as administrative expenses, transportation costs, and any applicable fees. This information is necessary for assessing the expenses incurred when restocking inventory.

Stockout cost data: Quantify the potential costs of stockouts, including lost sales, customer dissatisfaction, and penalties for failing to meet service level agreements. Understanding the impact of stockouts assists in determining the trade-off between holding excess inventory and the risk of stockouts.

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To collect the necessary data, you would need to gather information such as:

Demand data:

Collect historical sales data to analyze patterns, seasonality, and trends in customer demand. This data helps in estimating future demand and forecasting sales.

Lead time data:

Determine the time it takes for the inventory to be replenished once an order is placed. This includes gathering data on supplier lead times, shipping durations, and any potential delays.

Holding cost data:

Calculate the cost of holding inventory over a specific period, considering expenses like warehousing, storage, insurance, and depreciation. This data helps in evaluating the financial impact of inventory holding.

Ordering cost data:

Identify the costs associated with placing orders, such as administrative expenses, transportation costs, and any applicable fees. This information is necessary for assessing the expenses incurred when restocking inventory.

Stockout cost data:

Quantify the potential costs of stockouts, including lost sales, customer dissatisfaction, and penalties for failing to meet service level agreements.

Understanding the impact of stockouts assists in determining the trade-off between holding excess inventory and the risk of stockouts.

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To obtain the lateral surface area of a triangular pyramid, you need to calculate the combined area of all the triangular faces excluding the base.

Here's the step-by-step process:

1. Identify the base and the height of the triangular pyramid.

The base is a triangle, and the height is the perpendicular distance from the base to the apex of the pyramid.

2. Calculate the area of each triangular face.

For each triangular face, you need to determine the length of the base of the triangle (b) and the corresponding height (h) perpendicular to that base.

Calculate the area of each face using the formula: Area = (1/2) * base * height.

3. Sum up the areas of all the triangular faces.

Add up the areas of all the triangular faces to obtain the lateral surface area.

The formula for the lateral surface area (LSA) of a triangular pyramid can be expressed as:

LSA = Area_face1 + Area_face2 + Area_face3 + ...

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L = 1.3245 is  the legnths of the pen's sides .

What is area and perimeter?

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)

So W = 30 - 2L.

Area = L x W = L (30 - 2L) = 30L - 2L^2.

This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .

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We draw the conclusion that the results are significantly different since the null hypothesis was rejected, which means that a different proportion of people than 0.3 had clinical illness.

With the aid of a statistical test, researchers weigh the evidence in favor of and against the null and alternative hypotheses, which are two opposing claims: The null hypothesis (H0) states that there is no population impact. Alternative hypothesis (Ha or H1): The population is affected.

Given,

Among susceptible individuals exposed to a particular infectious agent 30% generally develop clinical disease. out of a random sample of 100 people suspected of exposure to the agent only 20 developed clinical disease.

Let X be the random variable to determine the proportion of people who have clinical illness.

n: The overall number of people who were exposed to a specific infectious pathogen.

p: The percentage of sample members who have a clinical illness.

Selected subjects who experience clinical disease are the experiment's success.

As a result, the variables are n = 100 and p = 0.30.

It is necessary to determine whether exposure to the agent outcome may be entirely accounted for by coincidence.

A P-value is a probabilistic indicator of the likelihood that an observed outcome effect is accidental.

Using the default level of significance = 0.05, the level of significance is not defined.

One percentage z-test is the best suitable test for the aforementioned assertion.

The alternate and null hypothesis is

H0: p = 0.3

H1:: p ≠ 0.3

Where p is the percentage of the population that develops a clinical illness.

R may be used to calculate the p-value and test statistic.

The instruction is as follows:

x = 20; n = 100; p = 0.3; prop.test

The result looks like this: - The p-value obtained from the output above is 0.03817.

Decision principle:

When significance is 5%,

If the p-value is below 0.05, reject the null hypothesis.

Accept the contrary.

Because the p-value was 0.03817 0.05

The null hypothesis is disproven.

In conclusion:

We draw the conclusion that the results are significantly different since the null hypothesis was rejected, which means that a different proportion of people than 0.3 had clinical illness.

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Answer:

10x + 30=140. Kegan has to mow his neighbors lawn 11 times.

Answer:

11 more times.

Step-by-step explanation:

Ok, so what do we know?

We know that he wants to buy a skateboard that will cost $140.

He already saved $30.

To raise the remaining money needed, he mows his neighbor’s lawn and charges $10 each time he completes the job.

What do we want to find?

How many times Kegan needs to mow his neighbor's lawn to have enough money to buy the skateboard.

Ok we also need to write an equation.

$140-$30=$110

My equation will be 110 ÷ 10 = x.

Using this equation, I can solve for x.

110 ÷ 10 = 11.

So Kegan will need to mow 11 more times to have enough money for the skateboard.

Answer:

4 /9

Step-by-step explanation:

Given that :

Number of faces on a number cube = 6

Sample space for two number faces = 6² = 36

Probability that sum of a roll is 7 or 11:

Probability = number required outcome / Total possible outcomes

Number of Required outcome = number of 7's + number of 11's

Number of 7's = 6

Number of 11's = 2

Total = 8

Total possible outcomes = 6² =36

P(sum of 7 or 11 ) = 8 /36 = 4 /9