Describe how to calculate each of the measures of central tendencies: mean, median, and mode. Be sure to include one description for each.

Answer:

-7

Step-by-step explanation:

-9+(-2)

-9+2=

-7

Answer:

B. The second choice.

Step-by-step explanation:

A function cannot have two points with the same x-coordinate.

If you graph two different points that have the same x-coordinate, they will both lie on the same vertical line. Therefore, if in a relation, more than one point lie on the same vertical line, then the relation is not a function.

Answer:

  √89

Step-by-step explanation:

The Pythagorean theorem relates the measures of sides in a right triangle. For legs 'a' and 'b' and hypotenuse 'c', it tells you ...

  c² = a² +b²

  c² = 5² +8² = 25 +64 = 89

  c = √89 . . . . the length of the third side

Answer:\(\sqrt{89}\)

Step-by-step explanation:

opposite=8

Adjacent=5

Hypotenuse= ?

Using pythagoras theorem,

\(Hyp^{2} = Opp^{2} + adj^{2}\)

\(Hyp^{2}\)= \(8^{2} +5^{2}\)

\(Hyp^{2}\)=64 +25

\(Hyp^{2} =89\)

Take the square root of both sides.Square and square root will cancel out leaving Hypotenuse

Hyp=\(\sqrt{89}\)

Check the picture below.

\(\cfrac{\sin(15^o)}{9}=\cfrac{\sin(B)}{12}\implies \cfrac{12\sin(15^o)}{9}=\sin(B)\implies \sin^{-1}\left( \cfrac{12\sin(15^o)}{9} \right)=B \\\\\\ 20.19^o\approx B\hspace{12em}\stackrel{180-20.19-15}{C\approx 144.81^o} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(15^o)}{9}=\cfrac{\sin(144.81^o)}{c}\implies c=\cfrac{9\sin(144.81^o)}{\sin(15^o)}\implies \boxed{c\approx 20.0}\)

Answer:

(x-3)^2 = 4

Step-by-step explanation:

2 (x-3)^2 + 6 = 14

Subtract 6 from each side

2 (x-3)^2  = 8

Divide each side by 2

2/2 (x-3)^2 + 6 = 8/2

(x-3)^2 = 4

A scatter plot would be more appropriate to help predict how many pages a 14-year-old reads.

A scatter plot is a graph that uses dots to represent values for two different variables. In this case, we have two variables: age and number of pages read per day.


By plotting the data points on a scatter plot, we can visualize any relationship between age and the number of pages read. Additionally, we can use the scatter plot to draw a line of best fit, which can be used to make predictions about how many pages a 14-year-old student may read.

On the other hand, a histogram would only show the distribution of the number of pages read and may not be as useful in predicting the number of pages a 14-year-old reads.


From the scatter plot, we can see that as age increases, the number of pages read per day tends to increase as well. Therefore, we can use the trend line to make a prediction about how many pages a 14-year-old read. The equation of the trend line is:

Pages read per day = 1.68 x Age - 1.49

Plugging in 14 for age, we get:

Pages read per day = 1.68 x 14 - 1.49 = 22.83

Therefore, we can predict that a 14-year-old would read about 23 pages per day on average.


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Answer:

answer 2

Step-by-step explanation:

3*4=12

Answer:

B.  5^6 x 3^12

Step-by-step explanation:

(5^2 x 3^4)^3 =

5 x 5 x 3 x 3 x 3 x 3 =

25 x 81 =

2025

2025^3 =

8,303,765,625

Option B is correct because,

5^6 x 3^12 =

5 x 5 x 5 x 5 x 5 x 5 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 =

15,625 x 531,441 =

8,303,765,625

Generally, Spanish is a Romance language that originated in the Iberian Peninsula. It is the second most spoken language in the world by number of native speakers and is widely used as a second language in many countries. Spanish is an official language in Spain and 21 other countries, including Mexico, Central America, South America, and the Caribbean. It is a major global language and has a rich cultural heritage, with a long literary tradition and a vibrant contemporary literary scene. Spanish is also an important language for international business and communication.

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Answer:

700

Step-by-step explanation:

Answer:

4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80

Answer:

48

Step-by-step explanation:

The average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75 when the function f(x)=20(1/4)ˣ.

Given that,

We have to find what is the function f(x)=20(1/4)ˣ average rate of change from x = 1 to x = 2.

We know that,

Average rate of change(A(x)) of f(x) over a interval [a,b] is given by:

A(x)=(f(b)-f(a))/b-a

We get the function:

f(x)=20(1/4)ˣ

Now, the average rate of change from x = 1 to x= 2

At x = 1

Then;

f(1)=20(1/4)¹=5

At x = 2

Then;

f(2)=20(1/4)²=1.25

Substitute these in above formula we have;

A(x)=f(2)-f(1)/2-1=-3.75

Therefore, The average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75 when the function f(x)=20(1/4)ˣ.

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The roots of the system of equations are x = 3.38586 and y = 2.61414, the error converges to 0 after the third iteration.

To solve this system of equations, we can use the Newton-Raphson method. This method starts with an initial guess and then uses a series of iterations to converge on the solution. In this case, we can use the initial guess x = y = 4.

The following table shows the results of the first few iterations:

Iteration | x | y | Error

------- | -------- | -------- | --------

1 | 4 | 4 | 0

2 | 3.38586 | 2.61414 | 0.06414

3 | 3.38586 | 2.61414 | 0

As you can see, the error converges to 0 after the third iteration. Therefore, the roots of the system of equations are x = 3.38586 and y = 2.61414.

The Newton-Raphson method is a relatively simple and efficient way to solve systems of equations.

However, it is important to note that it is only guaranteed to converge if the initial guess is close enough to the actual solution. If the initial guess is too far away from the actual solution, the method may not converge or may converge to a different solution.

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Answer:

1000 = 125 /65536

Step-by-step explanation:

Rewrite the expression using the negative exponent rule and then  Raise  

2  to the power of   21 . Cancel the common factor of  32. Combine  125  and  1 /65536

Answer:

Equation is incorrect

Answer (If you did the math):

1000 = 4000/2^21 or 1000 = 125/65536

Step-by-step explanation #1:

1. We know that 1000 is equal to 4000 * 1/4, meaning that the parenthesis is equal to 1/4. 1/4 is 2^-2 (Look below), and since 2^-21 does not equal 2^-2, so this equation is incorrect.

In a situation where:

\(y^{- x}\)  and -x is negative ------> \(y^{-x} = 1/y^{x}\) (And Vice Versa)

Step-by-step explanation #2 (If you did the math):

Open the parenthesis and make the 2^-21 into a fraction. This would be 1/2^21, which you would then multiply by 4000 to get 4000/2^21. You can now use a fraction calculator to calculate this value in fraction. 4000/2^21 simplifies to 125/65536.

Phase 5: The system of implementation is conversion.

Option B is the correct answer.

We have,

Phase 5 of the system development life cycle is commonly referred to as "Conversion" or "Systems Implementation."

During this phase,

The focus shifts from planning and designing the system to actually implementing it.

This phase involves the conversion of the old system to the new system, which includes activities such as data conversion, software installation, hardware setup, user training, and system testing.

The term "Conversion" is used because it signifies the transition from the old system to the new system.

It involves migrating data, processes, and operations from the existing system to the new system.

This phase ensures that the newly developed system is successfully integrated into the organization and becomes fully operational.

Thus,

Phase 5: The system of implementation is conversion.

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Answer: - 1

Step-by-step explanation:

(end after moveing back 4)      (start at 3)

                                 |<<<<<<<<<<<< |

--(-5)--(-4)--(-3)--(-2)--(-1)--(0)--(1)--(2)--(3)--(4)--(5)--

1. The factoring step is

sin²θ - cos²θ sin²θ = sin²θ (1 - cos²θ)

Then the Pythagorean identity is invoked:

cos²θ + sin²θ = 1   →   1 - cos²θ = sin²θ

so that

sin²θ - cos²θ sin²θ = sin²θ sin²θ = sin⁴θ

(third option)

2. Recall that a ² - b ² = (a - b) (a + b). The numerator here is such a difference of squares:

csc²x - 1 = (cscx - 1) (cscx + 1)

Then

(csc²x - 1) / (1 + sinx) = ((cscx - 1) (cscx + 1)) / (1 + sinx)

Recall that cscx = 1/sinx, so rewrite this as

… = ((1/sinx - 1) (1/sinx + 1)) / (1 + sinx)

In the numerator, pull out a factor of 1/sinx from both terms:

… = (1/sinx (1 - sinx) × 1/sinx (1 + sinx)) / (1 + sinx)

… = ((1 - sinx) (1 + sinx)) / (sin²x (1 + sinx))

Cancel the common factor of 1 + sinx :

… = (1 - sinx) / sin²x

Expand the fraction and rewrite sin in terms of csc :

… = 1/sin²x - sinx/sin²x

… = 1/sin²x - 1/sinx

… = csc²x - cscx

Factor out cscx to get the second option,

… = cscx (cscx - 1)

Saving money allows you to accumulate a large quantity over a period of time. Instead of spending money on small things, saving money helps you to buy things that are worth more. Saving money also helps me not spend money on unnecessary things that I don't need. The idea of saving money will help in the future when it comes time to take loans, pay off credit cards, buying a car, etc.

Answer:

I prefer to save money because you can buy better things in the future.  Say your have two items to buy.  One is lower in quality, but also cheaper and the other one is better quality, but is more If expensive.  If you bought the cheaper one, you might enjoy it for a little while, but may end up regretting your decision and want to buy the higher quality one.  If you chose to save for the higher quality one, you will enjoy it much longer.

Step-by-step explanation:

Answer:

Solution in photo

Step-by-step explanation:

Answer:

240.916

Step-by-step explanation:

1050/450

2.33333multiply by 35

81.66655 multiply by 2.95

In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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Answer:

4

Step-by-step explanation:

3*9=9(x-1)

x-1=3

x=4

Answer:

P and R

Step-by-step explanation:

P and R are similar because R is the same thing as P but 2 times bigger.

The nearest integer gives the following dates: Maximum value: January 24, Minimum value: July 10

Given the function:

y=3sin[ 2x/365] (x−79)]+12.

To find the days when the function has the maximum and minimum values, we need to use the amplitude and period of the function. Amplitude = |3| = 3Period, T = (2π)/B = (2π)/(2/365) = 365π/2 days. The function has an amplitude of 3 and a period of 365π/2 days.

So, the function oscillates between y = 3 + 12 = 15 and y = -3 + 12 = 9.The midline is y = 12.The maximum value of the function occurs when sin (2x/365-79) = 1. This occurs when:

2x/365 - 79 = nπ + π/2

where n is an integer.

Solving for x gives:

2x/365 = 79 + nπ + π/2x = 365(79 + nπ/2 + π/4) days.

The minimum value of the function occurs when sin (2x/365-79) = -1. This occurs when:

2x/365 - 79 = nπ - π/2

where n is an integer.

Solving for x gives:

2x/365 = 79 + nπ - π/2x = 365(79 + nπ/2 - π/4) days.

The answers are in days after January 1. To find the actual dates, we need to add the number of days to January 1. Rounding the values to the nearest integer gives the following dates:

Maximum value: January 24

Minimum value: July 10

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The box has dimensions of 11 inches, 12 inches, and 13 inches, and its volume is 1320 cubic inches. The surface area of the box is 826 square inches

The given problem is to determine the dimensions of a rectangular box with a known volume of 1320 cubic inches. We can start by using the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

Let's assume that the dimensions of the box are consecutive whole numbers. This means that we can express them as x, x+1, and x+2.

V = x(x+1)(x+2) = 1320

The Expression:-

x^3 + 3x^2 + 2x - 1320 = 0

This is a cubic equation that we can solve using various methods. One way is to guess and check values of x until we find one that satisfies the equation. By doing so, we find that x = 11 is a solution. Therefore, the dimensions of the box are 11 inches, 12 inches, and 13 inches.

To check our answer, we can use the formula for the surface area of a rectangular box, which is SA = 2lw + 2lh + 2wh. Substituting the values of l, w, and h, we get:

SA = 2(11)(12) + 2(11)(13) + 2(12)(13) = 826 square inches

Therefore, the box has dimensions of 11 inches, 12 inches, and 13 inches, and its volume is 1320 cubic inches. The surface area of the box is 826 square inches

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