in exercises 1 and 2 find the scale factor. then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality
​

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

False. The center of a semisimple Lie algebra is usually not trivial.

Step-by-step explanation:

The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.

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Answer:

IM not too sure but i think 30

Step-by-step explanation:

Answer:

There would be 30 fruits in total.

Step-by-step explanation:

9 to 15 = 12 to 18

12+18=30

True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

Given,

In the question:

To see the graph :

Mark all the statement that are true.

Now, According to the question:

From the graph,

Equations are expressions of two mathematical expressions t such as two numbers, functions. An equality between quantities and operations, usually with an equal sign "=".

Functions is a correspondences between two sets that are not empty each element in the set of input values can corresponds to a element in a set of output values that is unique.

Hence, True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

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The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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Answer:

AUB={1,2,3,4,5,7,8,9}

ALL THE NUMBERS WITHOUT REPEATING

AnB={5}

THE NUMBER THE HAVE IN COMMON

(AnB)n(BnC)={5}not too sure

CUD={1,3,6,7,8,10}

The solution to the inequality expression is x ≥ -3

Given the inequality expression

–3(x + 1) ≤ 6

Expand

-3x - 3 ≤ 6

Add 3 to both sides of the equation

-3x-3+3≤ 6+3

-3x≤ 9

Divide through by -3

x ≥ -3

The graph of the solution is attached to below

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Given that:

- The glider pilot sights the landing area at an altitude of 1050 feet above the ground.

- The landing area is 6000 feet from a point directly below the plane.

Since have to find the glide angle (angle of depression), you need to draw the following Right Triangle using the data provided in the exercise:

Where the glide angle (angle of depression) is θ.

In order to find its measure, you need to use the following Inverse Trigonometric Function:

In this case:

Substituting values into the formula and evaluating, you get:

Hence, the answer is: Option 2.

Answer:

-110601

Step-by-step explanation:

All you have to do is replace the variables with their value. So the equation would look like this,

6(-8)³ - 9

Always solve the parenthesis first ending up with

-48³ - 9

Now the exponents,

-110592 -9

Here we just subtracting getting the answer of...

-110601

Hope that helps and have a great day!

Answer:

19,683

Step-by-step explanation:

\(27^4-9^5+3^9\) is divisible by 25

The expression is given as:

\(27^4-9^5+3^9\)

Express all terms of the expression as a base of 3

\(27^4-9^5+3^9 = (3^3)^4-(3^2)^5+(3^9)\)

Remove the brackets

\(27^4-9^5+3^9 = 3^{12}-3^{10}+3^9\)

Factor out 3^9 from the expression

\(27^4-9^5+3^9 = 3^9(3^{3}-3^{1}+1)\)

Evaluate all exponents

\(27^4-9^5+3^9 = 3^9(27-3+1)\)

Simplify

\(27^4-9^5+3^9 = 3^9(25)\)

The above equation means that:

Hence, \(27^4-9^5+3^9\) is divisible by 25

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Answer:

According to the proposed interrogate, as well as the graph provided, the correct answers to such are identified as B. Y = -2x + 5 and C. 2x + y = 4.

Step-by-step explanation:

To evaluate such, a comprehension of linear Cartesian data is required:

Slope = rise/run. If there is a negative rise, the direction of the line is proportional to the left-hand side as it exponentially grows or augments in units.

Y-intercept: The peculiar point in which the linear data observed intersects the y-axis.

X-intercept: The peculiar point in which the linear data observed intersects the x-axis.

Since this is a negative linear, all negative slopes apply.

The interrogate states, “Check all that apply.” Thus, there may be more than one correct answer, shall such be disseminated.

A. Cannot be the answer as the line should have been a horizontal line contained within quadrants I and II on the Cartesian Plane.

B. Contains a negative slope, thus is disclosed as a correct answer.

C. This configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

2x + y = 4

Y = -2x + 4 <== Slope-Intercept Form (Contains a negative slope, thus considered a correct answer.

D. Likewise, this configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

X - y = 9

-y = -x + 9

Y = x - 9 <== Slope-Intercept Form (Cannot be considered as the correct answer, given the positive slope configuration, thus is marked out).

Thus far, as evaluated, the correct answers to the proposed interrogate, as according to the linear data provided in the Cartesian Plane is acknowledged, and henceforth disseminated, as B. Y = -2x + 5 and C. 2x + y = 4.

*I hope this helps.

Answer:

The slope is -1

Step-by-step explanation:

You can find this by using the \(\frac{y_2-y_1}{x_2-x_1}\) formula.

Plugging in the numbers, you'd get \(\frac{-2-3}{2-(-3)} = \frac{-2-3}{2+3} = \frac{-5}{5} = -1\)

Answer:

(a) The average number of passengers that will be on each flight is 28.8.

(b) Everyone will have a seat on about 84.4% of the flights.

Step-by-step explanation:

The correct question is:

Suppose that past experience shows  that about 10% of passengers who are schedule to take a particular flight fail to show up. For this  reason, airlines sometimes overbook flights, selling more tickets than they have seats, with the  expectation that they will have some no shows. Suppose an airline used a small jet with seating  for 30 passengers on a regional route and assume that passengers are independent of each other in  whether they show up for the flight. Suppose that the airline consistently sells 32 tickets for every  one of these flights.

(a) On average, how many passengers will be on each flight?

(b) How often will they have enough seats for all of the passengers who show up for the flight?

Solution:

Let the random variable X measure the number of passengers (out of 32) who show up for a flight.

For each passenger  there is a 90% chance of showing up, so X is a binomial random variable with n = 32 and p = 0.90.

(a)

The average of a binomial random variable is:

\(\text{Average}=np\)

Compute the average number of passengers that will be on each flight as follows:

\(\text{Average}=np\)

             \(=32\times 0.90\\=28.8\)

Thus, the average number of passengers that will be on each flight is 28.8.

(b)

To have enough seats for all of the passengers who show up for the flight, the value of X must be less than or equal to 30.

Compute the value of P (X ≤ 30) as follows:

P (X ≤ 30) = 1 - P (X > 30)

                = 1 - P (X = 31) - P (X = 32)

                \(=1-[{32\choose 31}\ (0.90)^{31}\ (1-0.90)^{32-31}]-[{32\choose 32}\ (0.90)^{32}\ (1-0.90)^{32-32}]\\\\=1-0.122087-0.034337\\\\=0.843576\\\\\approx 0.844\)

Thus, everyone will have a seat on about 84.4% of the flights.

The value of n for the given equation is n = -1/4.

Finding the values of x that fulfil the quadratic equation can be done using the quadratic formula, which can be used to address a variety of issues in mathematics, physics, engineering, and other disciplines. The equation can be used to identify the roots of a quadratic equation even if it has complex roots or roots that are irrational because the formula works for any values of a, b, and c. The quadratic formula, a key tool in the study of quadratic functions and equations, is derived by completing the square of the quadratic equation.

The given equation is ny² + 2y - 4 = 0.

Given that it has exactly one root, thus the discriminant of the equation is:

b² - 4ac.

(2)² - 4(n)(-4) = 4 + 16n

4 + 16n = 0

16n = -4

n = -4/16

n = -1/4

Hence, the value of n for the given equation is n = -1/4.

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Answer:

30\%30%30

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

9514 1404 393

Answer:

  100

Step-by-step explanation:

The % symbol can be thought of as a shorthand way to write /100. That is, the symbol can be replaced by /100 wherever you see it, and vice versa:

  23% = 23/100

23 is the numerator of the fraction with denominator 100.

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

From the question, we have the following parameters that can be used in our computation:

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2

From the question, we have the following parameters that can be used in our computation:

-3/4 + 2/5x = 7/20x -1/2

The first step is to collect the like terms

So, we have

2/5x - 7/20x = 3/4 - 1/2

This represents an equation of the possible way to begin solving for x

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Answer:

that is true

Step-by-step explanation:

hope this helps

If a new data point at 12 is added to the graph, The mean will increase more than the median, but both will increase.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order.

Given a graph with the data points as,

1, 2, 2, 2, 3, 4, 4, 4, 5

Mean = (1 + 2 + 2 + 2 + 3 + 4 + 4 + 4 + 5) / 9 = 27 / 9 = 3

Median = 5th term = 3

When 12 is added, new data set has 10 data points.

1, 2, 2, 2, 3, 4, 4, 4, 5, 12

Mean = (1 + 2 + 2 + 2 + 3 + 4 + 4 + 4 + 5 + 12) / 10 = 3.9

Median = average of 5th and 6th term = (3 + 4) / 2 = 3.5

Hence the correct option is The mean will increase more than the median, but both will increase.

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The complete question is given below.

Answer: 2 (x+5)

Step-by-step explanation:

Answer:

x+5

Step-by-step explanation:

try to add the all up then divide by 3

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Answer:

714

Step-by-step explanation:

587,714 they arrange in orderly form

A number greater than 714,587 is 714,588

The complete question is added as an attachment

From the attached figure, we have:

Passengers = 714,587

Numbers greater than 714,587 would have a value greater than 714,587

This is represented as:

x > 714,587

The above inequality represents numbers greater than 714,587

An example of such number is 714,588

Hence, a number greater than 714,587 is 714,588

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Answer:

12.5pages

Step-by-step explanation:

50pages ×6hours=300 and then we divide by 8 to get 37.5(the number of pages printed by david in 6 hours)

subtract 37.5 from 50 to find the number of pages printed by andy

By applying the unitary method, counting 67 colonies on a plate with 1ml of the 1:1,000,000 dilution indicates that 67,000,000 bacteria were present in 1ml of the original sample.

The unitary method is a mathematical technique that involves finding a unit value and using it to solve problems. In this case, we need to determine the number of bacteria present in 1ml of the original sample.

The dilution factor represents the ratio of the volume of the original sample to the volume of the diluted sample. In this case, the dilution factor is 1:1,000,000, which means that 1ml of the original sample was diluted with 1,000,000ml of a diluent solution to obtain 1ml of the diluted sample. Therefore, the number of bacteria in the original sample is 1,000,000 times the number of bacteria in the diluted sample.

Now, let's use the colony count to determine the number of bacteria in the diluted sample. We are told that 67 colonies were counted on the plate with 1ml of the 1:1,000,000 dilution. This means that each colony represents the growth of a single bacterium in the diluted sample. Therefore, the number of bacteria in the diluted sample is 67.

Using the unitary method, we can now determine the number of bacteria in 1ml of the original sample. We know that the number of bacteria in the original sample is 1,000,000 times the number of bacteria in the diluted sample. Therefore:

Number of bacteria in original sample = Dilution factor x Number of bacteria in diluted sample

Number of bacteria in original sample = 1,000,000 x 67

Number of bacteria in original sample = 67,000,000

So, the answer is that 67,000,000 bacteria were present in 1ml of the original sample.

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The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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Answer:

Step-by-step explanation:

a