The triangles are congruent by the SSS congruence theorem.

Triangles A B C and D E C are connected at point C. Triangle A B C is reflected across B C and then is rotated about point C to form triangle D E C.

Which rigid transformation(s) can map TriangleABC onto TriangleDEC?

reflection, then rotation
reflection, then translation
rotation, then translation
rotation, then dilation

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

for more such questions on sampling method

https://brainly.com/question/13219833

#SPJ8

Answer:

If Andrea plays eight games at the arcade and wins 20 tickets per game then 8 x 20= 160.

If Andrea plays nine games at the arcade and wins 20 tickets per game then 9×20 = 180.

A= 9 games

Step-by-step explanation:

Hope this helped you!

/21 and /84

/28 and /42

/28 and /84

/42 and /84

/84 and /84

Answer:

Any with denominators of which their lowest common multiple is 84; for pairs of fractions these are:

whole numbers and /84

/2 and /84

/3 and /28

/3 and /42

/3 and /84

/4 and /21

/4 and /42

/4 and /84

/6 and /28

/6 and /84

/7 and /12

/7 and /84

/12 and /14

/12 and /21

/12 and /28

/12 and /42

/12 and /84

/14 and /84

/21 and /28

There are further possible fractions when there are three at a time, and so on upwards. With 12 fractions at a time they can all have different denominators, namely:

whole numbers, /2, /3, /4, /6, /7, /12, /14, /21, /28, /42 and /84

Though there are other possibilities with one or more repeated denominators.

With 13 or more fractions, some of them of necessity will have the same denominator since there are only 12 factors of 84, namely: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 & 84.

The fractions having the lowest common denominator of 84 will be 3/4, 1/7, and 1/6. The correct option is A.

The fraction is defined as the division of the whole part into an equal number of parts. In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.

The lowest common factor of 84 will be calculated as below:-

3/4, 1/7, 1/6

Take the numbers in the denominator and find the common factor between them.

4, 7, 6

Divide by 2, to get 2, 7, 3

Divide by 2 to get 1, 7, 3

Divide by 7 to get 1, 1 , 3

Divide by 3 to get 1 , 1, 1

Multiply all the numbers by which it is divided.

LCD = ( 2 x 2 x 7 3 ) = 84

Therefore, the fractions having the lowest common denominator of 84 will be 3/4, 1/7, and 1/6. The correct option is A.

To know more about fractions follow

https://brainly.com/question/78672

#SPJ2

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

-3/4

Step-by-step explanation:

We conclude that the interval in which the function decreases is (1.5, 3]

The ball is decreasing when the graph, reading from left to right, is going downwards.

Particularly, in this parabola that opens downwards, the graph will decrease after the vertex.

And we can see that the vertex is at x = 1.5

And we also see that the graph of the function ends at x = 3.

Then we conclude that the interval in which the function decreases is (1.5, 3]

If you want to learn more about parabolas:

https://brainly.com/question/4061870

#SPJ1

Answer:

−3/2

Step-by-step explanation:

Hope this helps

:D

1.00065528... Is the correct answer.

Answer:

The expression "5.25x + 1246x" is equivalent to "1771x"

The inequality that represents the values of x is expressed as:

7/4 < x < 11/2.

According to the triangle inequality theorem, any two sides of a triangle, when added, must be greater than the length of the third side.

Therefore, applying the triangle inequality theorem, we have:

2x + 4 + 6x > 18

8x + 4 > 18

8x > 18 - 4

8x > 14

x > 14/8

x > 7/4 or 7/4 < x

Therefore, the possible value of x would be: 7/4 < x < 11/2

Learn more about triangle inequality theorem on:

https://brainly.com/question/29916338

#SPJ1

The rows and columns of the positive integers greater than three are as shown. And the number 5018 is found in the third column.

When performing a permutation test, you repeatedly rearrange one of the variables without affecting the other variable (s). From the given table, we can start with column 4. Here, each row has about 6 numbers. That is singular row has numbers from columns 1 to 6 and an even row from columns 7 to 2.

Then subtract 5018 by 3. We get 5018-3=5015.

Divide this by 6,

5015/6 = 836.

So 5018 is located in an even row from 7 to 2.

Therefore, 5018 is located in the 836th row and 3rd column.

So the required answer is E) 3.

To know more about permutation:

https://brainly.com/question/1216161

#SPJ4

Answer:

Let the number of courses that are worth 3 credits each be x and those worth 4 credits be y. With the given information, you can write the following equations:  

x + y = 48

3x + 4y = 155

You can solve the above equations by method of elimination/substitution

x + y = 48 ⇒ x = 48 - y (Now, substitution this equation into 3x + 4y = 155)

3(48 - y) + 4y = 155

144 -3y + 4y = 155

y + 144 = 155

y = 11

Now plug this solution back into x = 48 - y  

x = 48 - 11 = 37  

Check work (by plugging the solutions back into the 3x + 4y and see if it's equal to 155):

3(37) + 4(11) = 155

Answer: There are 37 of the 3-credit course and 11 of the 4-credit course

Answer:

x=2at/(1+t²)

dx/dt =[(1+t²)(2at)'-(2at)(1+t²)']/(1+t²)²

dx/dt=[(1+t²)(2a)-(2at)(2t)]/(1+t²)²

dx/dt=[2a+2at²-4at²]/(1+t²)²

dx/dt=[2a-2at²]/(1+t²)²

y=[b(1-t²)]/(1+t²)

dy/dt=[(1+t²)(b(1-t²))'-b(1-t²)(1+t²)']/(1+t²)²

dy/dt=[((1+t²)(-2bt)-b(1-t²)(2t)]/(1+t²)²

dy/dt=(-2bt-2bt³-2bt+2bt³)/(1+t²)²

dy/dt=(-4bt)/(1+t²)²

dy/dx=(dy/dt)/(dx/dt)

dy/dx=[(-4bt)/(1+t²)²]/[(2a-2at²)/(1+t²)²]

Cancelling common denominator

dy/dx=(-4bt)/(2a-2at²)

dy/dx=(-2bt)/(a-at²)

dy/dx=(2bt)/(at²-a)

Differentiating the above equation

y''=d²y/dx²=D[(2bt)/(at²-a)]

y''=[(at²-a)D(2bt)-(2bt)D(at²-a)]/(at²-a)²

y''=[(at²-a)(2b)(dt/dx)-(2bt)(2at)(dt/dx)]/(at²-a)²

dt/dx=(1+t²)²/(2a-2at²)

y''=[(at²-a)(2b)[(1+t²)²/(2a(1-t²))]-

(4abt²)[(1+t²)²/(2a-2at²)]/(at²-a)²

y''=[(-b)(1+t²)²-(2bt²)[(1+t²)²/(1-t²)]/(at²-a)²

y''=[(-b)(1+t²)²(1-t²)-(2bt²)(1+t²)²]/[(1-t²)(at²-a)²]

y''=[b(1+t²)²(t²-1)-2bt²(1+t²)²]/[(1-t²)(at²-a)²]

Step-by-step explanation:

Answer:

"Ratio " seems to be the appropriate choice.

Step-by-step explanation:

Height: Should be represented in inches, centimeters, feet, respectively., and therefore can't be smaller than 0 (zero).

The triangles are similar by SSS congruence of triangles.

What is SSS congruence of triangles?

The two triangles are congruent if the three sides of one triangle are the same as the corresponding three sides (SSS) of the other triangle.

We are given two triangle ABC and PQR.

In order to see whether these are similar or not, we will use the SSS congruence of triangles.

The ratio of sides are:

⇒AB : PQ = 8 : 6

⇒AB : PQ = 4 : 3

Similarly,

⇒BC : QR = 12 : 9

⇒BC : QR = 4 : 3

Similarly,

⇒AC : PR = 12 : 9

⇒AC : PR = 4 : 3

Since, the ratio of all the sides is same so, the triangles are similar.

Hence, the triangles are similar by SSS congruence of triangles.

Learn more about SSS congruence from the given link

https://brainly.com/question/30105734

#SPJ1

Since, there are multiple questions so, the question answered above is attached below

Answer:

see explanation

Step-by-step explanation:

Using the identities

tan x = \(\frac{sinx}{cosx}\) , sin²x = 1 - cos²x

sin2x = 2sinxcosx

Consider left side

cosθ × sin2θ

= \(\frac{sin0}{cos0}\) × 2sinθcosθ ( cancel cosθ )

= 2sin²θ

= 2(1 - cos²θ)

= 2 - 2cos²θ

= right side , then established

The area of the sector in terms of π is 35.6π inches squared.

The area of the sector is approximately  111.6 inches square

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅ = 200 degrees

r = 8 inches

area of the sector = 200 / 360 × 8²π

area of the sector = 200 / 360 × 64π

area of the sector =12800π/  360

area of a sector = 35.6π inches squared

Let's find the area of the sector with π = 3.14

area of a sector = 35.6 × 3.14 = 111.6 inches square

learn more on sector here: https://brainly.com/question/22972014

#SPJ1

The required percentage decrease in the population is given as 9%. Option C is correct.

The population of the town is 20,000. \(P = 20,000 (1-0.09)^t\)represents the change in population each year.

The percentage is the ratio of the arrangement of matter to the overall arrangement of matter multiplied by 100.

Here,
Given expression  \(P = 20,000 (1-0.09)^t\)

In the above expression 0.09 represents the rate of change,

When multiplied it by 100 gives the percentage decrease of the population each year,
= 0.09 × 100%
= 9%

Thus, the required percentage decreased 9%.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ1

Answer:

96-49=47

Step-by-step explanation:

he goes down then up so 47

Answer:

-47

Step-by-step explanation:

-96 + 49

-47

The required expression is (x / 5) + 9

Given that we have to build an equation for the statement "9 more than the quotient of x and 5,

So,

This expression represents the quotient of x divided by 5, and then adding 9 to the result.

Therefore,

"9 more than the quotient of x and 5" can be written mathematically as:

(x / 5) + 9

Hence the required expression is (x / 5) + 9

Learn more about expression click;

https://brainly.com/question/15994491

#SPJ1

Answer:

.52

Step-by-step explanation:

sorry

Answer:

\(k = 2.6\)

Step-by-step explanation:

Given

\(5k + 3.8 = 3k + 9\)

Required

Solve

\(5k + 3.8 = 3k + 9\)

Collect like terms

\(5k -3k+ 3.8 = 3k -3k + 9\)

\(2k+ 3.8 = 9\)

Subtract 3.8 from both sides

\(2k+ 3.8 - 3.8= 9 - 3.8\)

\(2k= 9 - 3.8\)

\(2k = 5.2\)

Divide through by 2

\(k = 5.2/2\)

\(k = 2.6\)

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

for such more question on composite functions

https://brainly.com/question/10687170

#SPJ8

12 dolars / 20 dolars

the percentage is

(20-12) / 20

= 8/20

= 40 %

Answer:

3/4

Step-by-step explanation:

Hope this helps! :)

The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

For more such questions on number, click on:

https://brainly.com/question/24644930

#SPJ8

Function f(4) = -10 and if g(x) = 2 , x = 0.

To find f(4), we will observe the graph of f(x).

According to the graph of f(x),

when x = 4, y is -10 which means when x is 4 value of f(4) is -10.

To find the value of x when g(x) is 2, we will observe the graph of g(x).

According to the graph of g(x),

when y = 2, x is 0 which means that when x is 0, the value of g(x) is 2.

Hence, f(4) is -10 and x = 0 when g(x) = 2.

To learn more about Function here:

https://brainly.com/question/14418346

#SPJ1

The expression in the mathematical form will be (1/4)( 2 - 3x ) / ( 2x ).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The word form of the expression is given as adding one-fourth of two subtracted from thrice a number to twice the same number.​

The expression can be written as,

E = (1/4)( 2 - 3x ) / ( 2x ).

Hence, the expression will be (1/4)( 2 - 3x ) / ( 2x ).

To know more about an expression follow

https://brainly.com/question/14268778

#SPJ1

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).

Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.

Here,

\(\bar x\) =1.267, s=1.23, n=30

The standard error is Se= 1.23/√30

= 0.2246

Item a:

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

Item b:

Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.

\(\bar x\pm tS_c\)

\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479

\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861

Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.

To learn more about the confidence interval visit:

https://brainly.com/question/14041846.

#SPJ1