In the diagram below, DE is parallel to
AB. If the length of AB is the same as
the length of DC, AC = 9, and
DE = 4, find the length of DC.

The equivalent expression is -1. 8h + 0.7

Algebraic expressions are defined as expression that are composed of variables, terms, coefficients, factors and constants.

They are also made up of arithmetic operations.

From the information given, we have that;

2.1 + (–3.7h) + 1.9h – 1.4

To simply this, we need to expand the bracket, we get;

2.1 - 3. 7h + 1.9h - 1.4

Now, collect the like terms, we get;

-3. 7h + 1. 9h + 2.1 - 1.4

Add or subtract the like terms

-1. 8h + 0.7

Hence, the expression is-1. 8h + 0.7

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Ratio of carnations to all flowers

= 4/13 or 4:13 or 4 carnations to 13 flowers.

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one.

Given,

There are 6 roses 8 carnations and 12 tulips

Total flowers = 6 + 8 + 12 = 26

Ratio of carnations to all flowers

= 8/26

= 4/13

or 4:13

or 4 carnations to 13 flowers.

Hence,

4/13 or 4:13 or 4 carnations to 13 flowers

is the ratio of carnations to all flowers.

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The lateral surface area of a cube the edge of 8 cm is 384cm^2.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object. Suppose that the cube in consideration has its side of 'a' units length.

Then, the surface area S of that cube is:

=6a^2

Given;

The edge of cube= 8cm

Now, the lateral surface area;

=6a^2

=6*8*8

=6*64

=384

Therefore, the lateral surface area will be 384cm^2.

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A 90% confidence interval based on a sample of size 200 would be more reliable than the original 90% interval.

This is because the larger sample size gives the interval a larger margin of error, meaning the interval is more likely to contain the true population means. This is due to the greater number of data points used to calculate the mean, which reduces the possibility of outliers skewing the results.

Additionally, the larger sample size increases the power of the test, meaning that the probability of getting a statistically significant result is increased. Therefore, the 90% confidence interval based on a sample of size 200 would be more reliable than the original 90% interval.

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4 chocolate and 6 butter cookies are included in a box of cookies. Miguel chooses a cookie at random and consumes it. He then chooses another cookie at random and eats it. He take 10 cookies.

Science, art, statistics, encryption, gaming, gambling, and other industries all make extensive use of randomness. To test hypotheses, for instance, random assignment in randomized controlled trials and pseudorandom or random numbers in computer games like video poker. In order to produce non-deterministic data (such as a series of integers) to seed security algorithms, a TRNG is a function or apparatus based on an unpredictably occurring physical event termed an entropy source. Although chance and randomness are sometimes used interchangeably, they can have different meanings in various scientific contexts as well as in everyday life. Chance specifically has a wider range than randomness, which is frequently interpreted in accordance with more specialized mathematical connotations.

Based on the given condition,

4+6

Calculate the sum.

10

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Answer: 25/8 or 3.125 or [tex]3\frac{1}{8}\\ \\[/tex]

Step-by-step explanation: Length times width (L x w)

To prove that two triangles are similar, we must show that they have the same shape, but not necessarily the same size. This can be done by showing that the corresponding angles of the two triangles are equal and that the corresponding sides are in proportion.

To do this, we can use the Side-Side-Side (SSS) Similarity Theorem. This theorem states that if all three pairs of corresponding sides of two triangles are in proportion, then the two triangles are similar. To prove this, we must show that the ratio of each pair of corresponding sides is equal.

For example, let's say we have two triangles ABC and DEF. To prove that these two triangles are similar, we must show that the ratio of AB to DE is equal to the ratio of BC to EF. We can do this by solving the following equation:

AB/DE = BC/EF

If the equation is true, then the two triangles are similar.

We can also use the Angle-Angle-Angle (AAA) Similarity Theorem to prove that two triangles are similar. This theorem states that if all three pairs of corresponding angles of two triangles are equal, then the two triangles are similar. To prove this, we must show that the measure of each pair of corresponding angles is equal.

For example, let's say we have two triangles ABC and DEF. To prove that these two triangles are similar, we must show that the measure of angle A is equal to the measure of angle D, the measure of angle B is equal to the measure of angle E, and the measure of angle C is equal to the measure of angle F.

If the measures of the corresponding angles are equal, then the two triangles are similar.

Therefore, to prove that two triangles are similar, we must show that either the corresponding sides are in proportion (using the SSS Similarity Theorem) or the corresponding angles are equal (using the AAA Similarity Theorem).

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On a certain day, If 50 people enter the fair and $140 is collected, then there were 30 children and 20 adults attended the fair.

Let number of children be x

and let number of adult be y

Now, according to question

x+y = 50 …. ( equation 1)

and, according to cost of fair,

2x+4y= 140

x + 2y = 70 …. (equation 2)

solving equation 1 and equation 2 we get

y = 20

putting the value of y in equation 2 we get

x + 2y = 70

x + 2(20) = 70

x = 70-40

x = 30

Hence, there are 30 children and  20 adults in the fair.

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The total area of this rectangular deck is equal to: D. 564.5 ft².

Mathematically, the area of a rectangular deck can be calculated by using this mathematical expression:

Area of a rectangular deck, A = LW

Where:

Therefore, the area of the additional dimension can be calculated as follows;

Area of additional dimension, A = 20.25 × 18

Area of additional dimension, A = 364.5 ft².

Now, we can calculate the total area of this deck as follows;

Total area = original area + new area

Total area = 200 ft² + 364.5 ft²

Total area = 564.5 ft²

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Answer:

d

Step-by-step explanation:

The maximum number of edges in a simple undirected disconnected graph of n vertices can be any value that is less than or equal to n(n-1)/2.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

The maximum number of edges in a simple undirected disconnected graph of n vertices can be found using the formula for the maximum number of edges in an undirected graph,
E = n(n-1)/2.

However, for a disconnected graph, this formula only applies to each connected component of the graph separately. Therefore, the maximum number of edges in a simple undirected disconnected graph of n vertices is n(n-1)/2 for each connected component, so the total maximum number of edges is n₁(n₁-1)/2 + n₂(n₂-1)/2 + ... + nₐ(nₐ-1)/2, where n₁, n₂, nₐ are the number of vertices in each connected component.

So, in general, the maximum number of edges in a simple undirected disconnected graph of n vertices can be any value that is less than or equal to n(n-1)/2.

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The probability of students chosen have a cat and a dog is:P(cat and dog) = 9/25.

There are 25 students

Those that have cats 15

those that have a dog 16

while, 3 of them have neither

Take x = number of students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

Therefore, the number of students who own a cat and a dog is 9.

The probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

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In a class of 25 students, 15 of them have a cat , 16 of them have a dog and 3 of them have neither. Find the probability that a student chosen at random has a cat and a dog. Find the probability that a student chosen at random has a cat and a dog

Answer:

angle 1 = 45 degrees, angle 2 = 90 degrees

Step-by-step explanation:

For angle 1:

2 of the properties of a square are that it has 4 right angles (90 degrees) and the diagonals bisect the angles.

Angle BAD = 90 degrees

Ray AC bisects angle BAC. And by definition of bisection, angle 1 = 90/2 = 45 degrees

So angle 1 = 45 degrees

For angle 2:

Angle two is an angle of triangle BAE. Angles BAE and ABE are = 45 degrees because of what is stated above for angle 1.

Since the sum of the measure of the angles in a triangle is 180. We can solve for Angle 2 by doing 180 = 45 +45+ angle 2

180 = 90 + angle 2

angle 2 = 90 degrees

Answer:

88%, 88%, 85%

Step-by-step explanation:

You can check these by multiplying the first number given by the percentages below. (or finding how much the 2nd number is of the first number)

150 × .88 = 132

275 × .88 = 242

300 × .85 = 255

The normal distribution of nail lengths with mean 5.00 in and standard deviation of 0.03 in is used to find probability of lengths less than 4.94 in and between 4.97 and 5.03 in. 58th percentile length is also determined.

a) To find the number of nails less than 4.94 in long, we need to use the cumulative distribution function of the normal distribution. Let's assume X represents the length of the nails.

We have X ~ N(5.00, 0.03^2). To find the cumulative probability of X being less than 4.94, we can use the following formula:

P(X < 4.94) = P((X - 5.00)/0.03 < (4.94 - 5.00)/0.03) = P(Z < -2.33)

Where Z is a standard normal random variable. Using a standard normal table or calculator, we find that

P(Z < -2.33) = 0.01.

So, the probability of a nail being less than 4.94 in long is 0.01, and in a bag of 120 nails, we expect 120 * 0.01 = 1.2 nails to be less than 4.94 in long.

b) To find the probability that the length of nails are between 4.97 and 5.03 in long, we can use the cumulative distribution function again. We want to find the cumulative probability of X being less than 5.03 and subtract the cumulative probability of X being less than 4.97:

[tex]P(4.97 < X < 5.03) = P(X < 5.03) - P(X < 4.97) = P((X - 5.00)/0.03 < (5.03 - 5.00)/0.03) - P((X - 5.00)/0.03 < (4.97 - 5.00)/0.03) = P(Z < 0.99) - P(Z < -0.99)[/tex]

Using a standard normal table or calculator, we find that P(Z < 0.99) = 0.84 and P(Z < -0.99) = 0.16.

So, the probability of a nail being between 4.97 and 5.03 in long is

0.84 - 0.16 = 0.68.

c) The 58th percentile of all nails represents the value below which 58% of the nails fall. We can use the inverse cumulative distribution function to find this value. Let's assume X represents the length of the nails, and P(X < x) = 0.58. We have X ~ N(5.00, 0.03^2). To find x, we can use the following formula:

x = 5.00 + 0.03 * Z

Where Z is the standard normal random variable such that  P(Z < z) = 0.58

Using a standard normal table or calculator,

we find that Z = 0.84.

So, the length of nails at the 58th percentile is 5.00 + 0.03 * 0.84 = 5.0252 in long.

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Fuel used = 392 km * 7.9 liters/100 km = 31.068 liters, average speed = 74.4 km/h.

It is defined as the distance traveled by an object in a certain amount of time. The unit of speed is usually meters per second (m/s) or kilometers per hour (km/h). Speed is a fundamental concept in physics, as it is a measure of the motion of objects. It is also an important concept in engineering, transportation, and many other fields. The speed of an object can be determined by dividing the distance traveled by the time taken to travel that distance.  The magnitude of speed represents the rate of change of position, and the direction indicates the direction of the change.

To find the amount of fuel used to get to the gate, we need to multiply the distance traveled by the fuel consumption per kilometer.

1. Fuel used = 392 km * 7.9 liters/100 km = 31.068 liters. Rounding to the nearest whole number, the answer is 31 liters.

2. To find the average speed, we need to divide the distance traveled by the time taken.

Average speed = 392 km / (5 hours + 14 minutes/60) = 74.4 km/h.

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Answer:

W

Step-by-step explanation:

One input can only have one output! So, the x, y, and z diagrams are all wrong. So, the answer is W.

Answer:

12+16x-8

Step-by-step explanation:

No, as the confidence intervals for the two groups overlap.

From the given data,

The poll has an error of 34% of the people say they will vote for Bugs Bunny

⇒(34 ± 6)% ≈ 28% to 40%

⇒26% say they will vote for Baby Shark.

The confidence interval for the percentage of people supporting Baby Shark is

⇒(26 ± 6)% ≈ 20% to 32%

No, it is not possible to say with certainty that more people in the population support Bugs Bunny over Baby Shark based on this poll.

Since the confidence intervals for the two groups overlap , we cannot  say that in population, more people clearly support Bugs Bunny over Baby Shark.

Hence, the correct answer is: no, as the confidence intervals for the two groups overlap.

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Answer:

Step-by-step explanation:

boody boody

The value of the function is f ( 3 ) = 9

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the function be represented as f ( x )

Now , the equation will be

Substituting the values in the equation , we get

f ( x ) = 2x + 3   be equation (1)

On simplifying the equation , we get

y = 2x + 3

And , when x = 3

Substitute the value of x =3 in the equation , we get

f ( 3 ) = 2 ( 3 ) + 3

On further simplification , we get

f ( 3 ) = 6 + 3

f ( 3 ) = 9

Therefore , the value of f ( 3 ) is 9

Hence , the equation is f ( 3 ) = 9

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The proof of similar triangles are;

1)  Triangles ABC and EFG are not similar triangles.

2) Both triangles are similar triangles by AA Similarity Postulate

Similar triangles are defined as triangles that have the same shape, but then their sizes may vary. Now, all equilateral triangles, squares of any side lengths are examples of similar objects. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.

1) Triangles ABC and EFG are not similar because none of the corresponding angles nor corresponding sides are congruent to themselves.

2) Looking at both triangles formed, we can say that;

∠JLK ≅ ∠JMN by alternate angles postulate

∠JNM ≅ ∠JKL by alternate angles postulate

Similarly ∠J is congruent to itself by Reflexive property and as such both triangles are similar by AA Similarity postulate.

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The two x-values that the supplied vectors are orthogonal to are 0 and 10 respectively.

A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector.

The term can also refer to a quantity's mathematical or geometrical representation.

Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

A movement from one point to another is described by a vector. A vector quantity has a magnitude and a direction (size).

There is just magnitude for scalar quantities.

An arrow-labeled line segment can serve as a visual representation of a vector.

So, we have:

xi+2xj and xi - 5j

As is common knowledge, when two vectors are orthogonal, their dot product equals zero, which means:

(xi + 2xj)*(xi-5j) = 0

x*x+2x*-5 = 0

x²-10x = 0

x(x-10) = 0

x = 0 or x - 10 = 0

x = 0 or x = 10

Therefore, the two x-values that the supplied vectors are orthogonal to are 0 and 10 respectively.

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Answer:

the answer is in the picture

To construct and interpret 95% confidence intervals for the outcomes of each simulation, then option C. The confidence interval from the first simulation is (0.564, 0.616), and the confidence interval from the second simulation is (0.615, 0.665). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.564 and 0.616. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.615 and 0.665 is correct.

To calculate the confidence interval, we can use the formula for a normal approximation to the binomial distribution.

The standard error of the proportion is given by the formula SE = sqrt(p(1-p)/n), where p is the proportion of wins, and n is the number of games played. The 95% confidence interval is given by p +/- 1.96 * SE.

Plugging in the values from the first simulation, we have p = 590/1000 = 0.59, and n = 1000. So, SE = sqrt(0.59(1-0.59)/1000) = 0.0242. The 95% confidence interval is 0.59 +/- 1.96 * 0.0242 = (0.564, 0.616).

Similarly, for the second simulation, p = 640/1000 = 0.64, and n = 1000. So, SE = sqrt(0.64(1-0.64)/1000) = 0.0244. The 95% confidence interval is 0.64 +/- 1.96 * 0.0244 = (0.615, 0.665).

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A child's ticket cost is  $12.50 and an adult's ticket cost $25.00.

Two or more expressions with an Equal sign is called as Equation.

Given that Mr and Mrs Tan and their three children bought tickets for a 'Holiday- On-Ice' show.

Let x be the cost of a child's ticket, 2x be the cost of adult's ticket

The cost of all three children's tickets would be 3x and total cost of Mr. and Mrs. Tan's tickets would be 4x

So the total cost of all five tickets would be 3x + 4x = 7x.

We know that the total cost was $87.50

7x = 87.50

Divide both sides by 7

x = 87.50 / 7

x=12.50

Hence, a child's ticket cost is  $12.50 and an adult's ticket cost $25.00.

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Answer: 2x-3=10

(x=the number)

An equation of the line that passes through (1, 2) and is parallel to the given line is y=-5x+7.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, the coordinate point is (1, 2) and the line is y=-5x+4.

Here, slope of given equation is m₁= -5

We know that, the slope of parallel lines is equal. That is m₁=m₂.

Now, slope m₂=-5

Substitute, m=-5 and (x, y)=(1, 2) in y=mx+c, we get

2=-5(1)+c

c=7

Substitute, m=-5 and c=7 in y=mx+c, we get

y=-5x+7

Therefore, an equation of the line that passes through (1, 2) and is parallel to the given line is y=-5x+7.

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No, we cannot conclude that there is a difference in the mean number of surgeries performed by hospital or by day of the week.

The data provided would need to be further analyzed to determine if there is a statistically significant difference between the means. A t-test or ANOVA could be used to test for differences between the means.

1. The data provided shows the number of outpatient surgeries performed at three hospitals in the Tulsa, Oklahoma, area on each day of the week.

2. To determine if there is a difference in the mean number of surgeries performed by hospital or by day of the week, a statistical test needs to be conducted.

3. A t-test or ANOVA could be used to test for differences between the means.

4. The results of the test would need to be examined to determine if there is a statistically significant difference between the means.

5. At the 0.05 significance level, we cannot conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week.

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Answer:

3.36 dollars

Step-by-step explanation:

Original price is 2.80 dollars

we take 20% of 2.80 aka the original price.

(p.s 20% in just [tex]\frac{20}{100}[/tex] since % sign means divide by 100)

so,

= [tex]2.80 * \frac{20}{100}[/tex]

=0.56

This means that 20% increase results in 0.56 increase in dollars

So the price after this increase would become

2.80 + 0.56

=3.36 dollars

hope that helped