Triangle A'B'C' is a rotation of triangle ABC by 60 degrees using Q as the center.
Select ALL statements that MUST be true.
-Angle ABC is 60 degrees.
-Angle AQA' is 60 degrees.
-Points C and C' coincide.
-Triangles ABC and A'B'C' are congruent.
-Angle ABC is congruent to angle A'B'C'
-Segment BC is congruent to segment B'C'
-Segment BQ is congruent to segment C'Q.
-Segment AQ is congruent to segment A'Q.

Answer: 1/6.

Step-by-step explanation:

3/18 is just 1/6 because you have to divide the numerator and denominator by 3.

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

Answer:

20

Step-by-step explanation:

The given curve is the rectangular hyperbola

xy = constant

Constant = xy = 4*5 =20

or

constant = xy = 5*4 = 20

or

Constant = xy = 10*2 = 20

Simple random sampling is least likely to guarantee that the sample will be representative and unbiased.

Simple random sampling is a technique that is used in research in which each member of the population is given an equal chance of being selected. It's the most straightforward and most basic technique for selecting a random sample. Sampling is a statistical method used to gather and analyze data from a subset of a population to provide estimates, hypotheses, or projections of the whole population. A sample is a subset of a population chosen to represent it since it would be difficult to collect data on the entire population. A sample is thus chosen using sampling techniques, which are statistical approaches for choosing representative samples that guarantee unbiased and precise results.

Biased sampling is a type of sampling method that can lead to misleading or erroneous conclusions. It happens when the sample that has been chosen is not representative of the population it is meant to represent. Biased sampling occurs when the selection method used to obtain the sample is flawed.

Learn more about Simple random sampling visit:

brainly.com/question/30403914

#SPJ11

Answer using slope formula:

\(\frac{y2-y1}{x2-x1}\)

We can find the slope.

Substitute:

\(\frac{5-2}{2-1}\)

Subtract:

\(\frac{3}{1}\)

\(\frac{3}{1}= 3\)

Our slope is 3.

Now we will use Point Slope formula:

\(y-y1=m(x-x1)\)

To find our equation.

I will use the first ordered pair, (1,2).

Substitute:

\(y-2=3(x-1)\)

Your answer is C. (y − 2) = 3(x − 1).

Hope this helped! :)

The dimensions 36 x 27 inches are too small to allow a 48-inch piece of glass to fit through it.

To learn more about dimensions, refer to:

https://brainly.com/question/1605852

#SPJ9

The answer to the question is option A: 2 vertices have an odd degree.

To answer this question, we need to first understand what vertices and odd degrees mean in graph theory. A vertex is a point in the graph, and degree refers to the number of edges that are connected to that vertex. An odd degree means that a vertex is connected to an odd number of edges.

Looking at the map of bridges, we can see that there are several vertices where the bridges intersect. To determine the odd degree of each vertex, we need to count the number of bridges that intersect at that point.

Starting at the top left corner of the map, we can count the number of bridges that intersect at each vertex. The first vertex has three bridges connected to it, so its degree is odd. The same is true for the second vertex, which also has three bridges connected to it. Moving down the map, the third and fourth vertices both have two bridges connected to them, making their degrees even. Finally, the fifth vertex has three bridges connected to it, giving it an odd degree.

So, the answer to the question is option A: 2 vertices have an odd degree. It's important to note that in a graph, the sum of the degrees of all vertices must be even, so the fact that there are only two vertices with odd degrees tells us that there must be an even number of vertices with even degrees.

Visit here to learn more about odd degree:

brainly.com/question/29005721

#SPJ11

Answer:

They lost a total of $5.074.53

Step-by-step explanation:

I believe the question is asking how much money the company lost in these four months, so you would just add 1051.51 and 4023.02

Hope this helps! I apologize if I'm incorrect

Answer:

c

Step-by-step explanation:

in order for it to be a triangle the smaller sides have to add up to be greater than the longest side

for a 5+14=19 so that is not a triangle because the  side dont add up to be greater than 19

for b 14+8=22 so that is also not a triangle because the sides dont add up to be greater than 24

for c 5+15=20 so that is a triangle because to 2 shorter sides added are greater than the longest side

for d 14+9=23 so that is not a triangle because the two smaller sides dont add up to be greater than 24

Answer:

90 obtuse

Step-by-step explanation:

According to the question the value of ST is 3 + 4x.

Value is the worth or importance that is placed on something. It can refer to tangible items such as money, goods, or services, or intangible concepts such as a person's beliefs, attitude, or sense of self-worth. Values are essential for guiding decisions and behaviour. They provide a framework for understanding what is important to an individual or a society, and can inform how people interact with their environment.

Given equation : 4x + 3 = ST
To find the value of ST, we need to subtract 4x from both sides of the equation.
4x + 3 - 4x = ST - 4x
3 = ST - 4x
Now, add 4x to both sides of the equation.
3 + 4x = ST
Therefore, the value of ST is 3 + 4x.

To learn more about value
https://brainly.com/question/843074
#SPJ1

The expression that best describes the length of the rectangle, given that the area is 2\(c^2\) - 5c - 3 and the width is c - 3, is (2\(c^2\) - 5c - 3) / (c - 3).

To find the length of a rectangle, we need to divide the area by the width. In this case, the area of the rectangle is given as 2\(c^2\) - 5c - 3, and the width is c - 3. Dividing the area by the width gives us the length.

By using polynomial long division, we divide 2\(c^2\) - 5c - 3 by c - 3. The result of this division gives us the expression for the length of the rectangle: (2\(c^2\) - 5c - 3) / (c - 3).

It's important to note that this expression is valid as long as the width, c - 3, is not equal to zero. If c - 3 equals zero, then the width would be undefined, and the length of the rectangle would not be defined either.

Learn more about rectangle here:

https://brainly.com/question/29123947

#SPJ11

Answer:

a) ¿Cuál es el sabor favorito de los niños?

Chocolate con 50%

b) ¿Cuál es el sabor que menos les gusta a los niños?

Fresa con 20%

c) ¿Qué número de niños representan el 15%, 35% y 50%?

Tenemos 10 hijos,

Por lo tanto

1) 15% = 1.5

2) 35% = 3.5

3) 50% = = 5

Step-by-step explanation:

Se encuestó a 10 niños sobre su preferencia por el sabor del pastel. Fresa 20%

Chocolate 50%

Vainilla 30%.

a) ¿Cuál es el sabor favorito de los niños?

El sabor favorito de los niños es el sabor con mayor porcentaje = Chocolate con 50%

b) ¿Cuál es el sabor que menos les gusta a los niños?

El sabor que menos les gusta a los niños es el sabor con el menor porcentaje = Fresa con 20%

c) ¿Qué número de niños representan el 15%, 35% y 50%?

Tenemos 10 hijos,

Por lo tanto

1) 15% = 15% × 10 = 1,5

2) 35% = 35% × 10 = 3,5

3) 50% = 50% × 10 = 5

Answer:

the answer is 9 and 8

Step-by-step explanation:

because 9 times 8 equal 72 which means 9 and 8 can be found as a square root of 72.

hope this help can you give me brainliest

\(g = \frac{x}{5} - \frac{6}{5x} - \frac{3}{5} \)

Step-by-step explanation:

\(3 + 5g = \frac{ {x}^{2} - 6 }{x} \\ 5g = x - \frac{6}{x} - 3 \\ g = x - \frac{ \frac{6}{x} - 3}{5} \\ g = \frac{x}{5} - \frac{ \frac{6}{x} }{5} - \frac{3}{5} \)

The integral is divergent because the Comparison Theorem can be used to compare it to a known divergent integral. By comparing the given integral to the integral of 1/x^2, which is known to diverge, we can conclude that the given integral also diverges.


To determine whether the given integral is convergent or divergent, we can use the Comparison Theorem. This theorem states that if f(x) ≤ g(x) for all x ≥ a, where f(x) and g(x) are nonnegative functions, then if the integral of g(x) from a to infinity is convergent, then the integral of f(x) from a to infinity is also convergent.

Conversely, if the integral of g(x) from a to infinity is divergent, then the integral of f(x) from a to infinity is also divergent. In this case, we want to compare the given integral ∫ [infinity]. 0 x (x^3 + 1) dx to a known divergent integral. Let's compare it to the integral of 1/x^2, which is known to diverge.

To compare the two integrals, we need to show that 1/x^2 ≤ x(x^3 + 1) for all x ≥ a. We can simplify this inequality to x^4 + x - 1 ≥ 0. By considering the graph of this function, we can see that it is true for all x ≥ 0. Therefore, we have established that 1/x^2 ≤ x(x^3 + 1) for all x ≥ 0.

Since the integral of 1/x^2 from 0 to infinity is divergent, according to the Comparison Theorem, the given integral ∫ [infinity]. 0 x (x^3 + 1) dx is also divergent.

To know more about Integral visit.

https://brainly.com/question/31433890

#SPJ11

Answer:

5,809 m^2

Step-by-step explanation:

50/2=25 m

25^2 times 3.14=1,962.5 m^2

70/2=35 m

35^2 times 3.14=3,846.5 m^2

1,962.5+3,846.5=5,809 m^2

Answer:

2/1/5/6/7/9

Step-by-step explanation:

1.2

2.1

3.5

4.6

5.7

6.9

The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

To know more about Equation visit:

brainly.com/question/28243079

#SPJ1

Answer:

8 hours

Step-by-step explanation:

Given that:

Money spent by Jacqueline to rent a bicycle = $33.50

Per hour charges for the bicycle for renting the bicycle = $4

Processing fee charged for renting the bicycle = $1.50

To find:

The number of hours, \(x\) for which Jacqueline rented the bicycle.

Solution:

Charges for 1 hour = $4

Charges for \(x\) hours = $\(4x\)

Processing fee = $1.50

Total fee charged for renting the bicycle is nothing but the sum of processing fee and the charges for \(x\) hours charged by the bike rental facility.

Total money spent = Processing Fee + Charges for \(x\) hours

Total money spent = 1.50 + 4\(x\) = 33.50

\(\Rightarrow 4x = 32\\\Rightarrow x = \bold{8\ hours}\)

So, Jacqueline rented the bicycle for 8 hours.

Answer:

Step-by-step explanation:

The two angles would equal 180°.

(7x - 5) + (5x + 19) = 180

Combine like terms.

12x + 14 = 180

Simplify by isolating the variable

12x + 14 = 180

------ -14 ----------

12x = 166

Divide both sides by 12

x = 13.833

To nearest tenth, 13.8

The correct answer is the Beta-binomial model. Bayesian analysis is a statistical approach that incorporates prior knowledge or beliefs about a parameter of interest and updates it based on observed data using Bayes' theorem.

In the case of a binary choice, where the outcome can be either yes or no, Bayesian analysis seeks to estimate the probability of success (yes) based on available information.

The Beta-binomial model is a commonly used model in Bayesian analysis for binary data. It combines the Beta distribution, which represents the prior beliefs about the probability of success, with the binomial distribution, which describes the likelihood of observing a specific number of successes in a fixed number of trials.

The Beta distribution is a flexible distribution that is often used as a prior for modeling probabilities because of its ability to capture a wide range of shapes. The Beta distribution is characterized by two parameters, typically denoted as alpha and beta, which can be interpreted as the number of successes and failures, respectively, in the prior data.

The binomial distribution, on the other hand, describes the probability of observing a specific number of successes in a fixed number of independent trials. In the context of Bayesian analysis, the binomial distribution is used to model the likelihood of observing the data given the parameter of interest (probability of success).

By combining the prior information represented by the Beta distribution and the likelihood information represented by the binomial distribution, the Beta-binomial model allows for inference about the probability of success in a binary choice.

The other options mentioned, such as the Normal-normal model and the Gaussian model, are not typically used for binary data analysis. The Normal-normal model is more suitable for continuous data, where both the prior and likelihood distributions are assumed to follow Normal distributions. The Gaussian model is also suitable for continuous data, as it assumes that the data are normally distributed.

In summary, the Beta-binomial model is the appropriate model for Bayesian analysis of a binary choice because it effectively combines the Beta distribution as a prior with the binomial distribution as the likelihood, allowing for inference about the probability of success in the binary outcome.

Learn more about Bayes' theorem at: brainly.com/question/33143420

#SPJ11

Answer:

(1,2) or equation form: x=1 y=2

Step-by-step explanation:

Used system of equations and doubled checked!

The sum of first 100 terms of the series is  0.686 with error less than 0.00005

The given series is

Tₙ = \(\frac{1}{n_3 +1 }\)

Since, \(\frac{1}{n_3 +1 } < \frac{1}{n_3}\)

The given series is convergent by the comparison Test.

The remainder Tₙ for the comparison series ∑ 1/n³ was estimated in this example using the remainder estimate for the Integral Test.

There we found that

\(T_n \leq \int\limits^\infty_n {\frac{1}{x^3} \, dx\)

Solving the integration,

=> \(\int\limits^\infty_n \frac{-1}{2x^2}\, dx\)

=> \(\frac{1}{2n^2}\)

So, \(T_n \leq \frac{1}{2n^2}\)

Therefore , the reminder Rₙ for the given series satisfies

Rₙ ≤ Tₙ ≤ 1/2n²

with n = 100 we have

=> R₁₀₀ ≤ 0.00005

Using a programmable calculator , we find that

\(\sum^\infty_{n=1} \frac{1}{n^3 + 1} = \sum^\infty_{100=1} \frac{1}{n^3 + 1}\)

=>  0.686 (approximately)

with the error less than 0.00005

To know more about Sum of series here

https://brainly.com/question/4617980

#SPJ4

The estimated cost of expanding the planned new clinic by 15.6 thousand ft2 would be $1,101,196.

The estimated cost of expanding a planned new clinic by 15.6 thousand ft2 when the appropriate capacity exponent is 0.62, and the budget estimate for 185,000 ft2 was $15.6 million is $1,101,196.

Let's find out how.

The cost C of constructing a building can be estimated using the formula

C=kA^x

where k and x are constants depending on the type of building and the location and A is the floor area of the building.

To find out the cost of expanding a planned new clinic by 15.6 thousand ft2, we need to estimate k and x. Given, the budget estimate for 185,000 ft2 was $15.6 million.

Thus, we can find k as follows:

k = C/A^x = 15,600,000/185,000^0.62

k = 135.28

We can now use this value of k to find the cost of expanding the planned clinic.

The floor area of the expanded clinic is

(185000 + 15.6) = 185015.6 ft2.

Hence the cost will be:

C = kA^x = 135.28*(185015.6)^0.62

C = $16,701,192.78

However, we need to find the cost of expanding by 15.6 thousand ft2 only, which is 15.6/100 = 0.156 times the total floor area.

Thus, the estimated cost of expanding the planned new clinic by 15.6 thousand ft2 would be $16,701,192.78 x 0.156 = $1,101,196.

Answer: $1,101,196 (keep 3 decimals in your answer).

To know more about estimated cost visit:

https://brainly.com/question/29995509

#SPJ11

Answer:

its A

Step-by-step explanation:

If rectangle has sides measuring (2x +7) units and (5x +9) units then expression that represents the area of the rectangle is \(10x^2+53x+63\) and degree of this expression is 2 and we proved that it satisfy closure property .

A quadrilateral with four right angles is called rectangle .

Given that sides are (2x+7) and (5x+9)

Hence area of rectangle can be calculated as

\((2x+7)(5x+9)\\\\2x(5x+9)+7(5x+9)\\\\10x^2+18x+35x+63\\\\10x^2+53x+63\\\)

Now we can see that this is a second degree polynomial

We got polynomial   \(10x^2+53x+63\) by multiplying two polynomial (2x+7) and (5x+9) hence it's closure property .

If rectangle has sides measuring (2x +7) units and (5x +9) units then expression that represents the area of the rectangle is \(10x^2+53x+63\) and degree of this expression is 2 and we proved that it satisfy closure property .

To learn more about rectangle visit :https://brainly.com/question/19819849

The probability that the alleged father was not the father is: 0.024, or 2.4% and The probability that the alleged father could be the father is: 0.953, or 95.3%.

To calculate the probability that the alleged father was not the father, we first need to calculate the z-score for a pregnancy length of 240 days and for a pregnancy length of 306 days. The z-score formula is:

where x is the pregnancy length, mu is the mean pregnancy length, and sigma is the standard deviation of pregnancy length.

For a pregnancy length of 240 days, the z-score is:

For a pregnancy length of 306 days, the z-score is:

To calculate the probability that the alleged father was not the father, we need to find the area under the normal distribution curve to the left of the z-score for a pregnancy length of 240 days and to the right of the z-score for a pregnancy length of 306 days, and then add these probabilities together. Using a standard normal distribution table or calculator, we find that the probability to the left of z = -3.08 is approximately 0.001, and the probability to the right of z = 2.00 is approximately 0.023. Therefore, the probability that the alleged father was not the father is:

To calculate the probability that the alleged father could be the father, we need to find the area under the normal distribution curve between the z-scores for a pregnancy length of 240 days and a pregnancy length of 306 days. Using a standard normal distribution table or calculator, we find that the probability between z = -3.08 and z = 2.00 is approximately 0.953. Therefore, the probability that the alleged father could be the father is:

Learn more about probability

https://brainly.com/question/24756209

#SPJ4