Question 9 Which of the following distributions has a mean that varies? I. The population distribution II. The distribution of sample data III. The sampling distribution of the sample mean
O ll only
O Il only
O Tonly
O all three distributions
O I and III

The expressions are expanded to give;

1. 2x² - 5x

2. 6x² + 8x

3. 6x² - 12xy

Algebraic expressions are defined as expressions consisting of  variables, coefficients, constants, terms and factors.

These expressions are also known to consist of mathematical operations, which includes;

From the information given, we have that;

a. x (2x - 5)

expand the bracket

2x² - 5x

b. 2x (3x+4)

expand the bracket

6x² + 8x

c. 6x(x-2y)

expand the bracket

6x² - 12xy

Hence, the expressions are 2x² - 5x, 6x² + 8x and 6x² - 12xy

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Answer:

1) 2x² - 5x

2) 6x² + 8x

3) 6x² - 12xy

Step-by-step explanation:

1) x ( 2x - 5 )

To expand the above, multiply both terms inside the brackets by x.

2x² - 5x

2) 2x ( 3x + 4 )

To expand the above, multiply both terms inside the brackets by 2x.

6x² + 8x

3) 6x ( x - 2y )

To expand the above, multiply both terms inside the brackets by 6x.

6x² - 12xy

Answer:

Answer: -⅔ and ⅔

Step-by-step explanation:

\( - \frac{2}{3} \times \frac{2}{3} = - \frac{4}{9} \\ \)

Answer:

Yes, the measurements 3cm, 4cm and 5cm are possible to create a triangle!

Step-by-step explanation:

The  maximum area of the rectangular pen using fencing next to river is 85130 feet².

This is a rectangle, and the length of the fencing is still 825 feet.

                                        river

Visualize it like this :~~~~~~~~~~~~~~~~~

                                |                       |

                             x |                       | x

                                |_____________|

                                           y

So the sum of the sides NOT along the river   x + x + y = 825,  and the area equals xy.

This makes the two equations:    2x + y = 825,   and A = xy.

To find the maximum area, we need to find A as a function of x or y.  I suggest solving the first equation for y and replacing that in the second equation.

                            y = 825 - 2x.    and A(x) = x(825-2x)

         We now need to maximize A(x) = 825x - 2x².

Remember, if x = -b/(2a), we find the x value of the vertex, the y value can be found by substitution.

So, since a = -2, and b = 825, x = -825/(-4) = 206.25 ft.  

If x = 206.25, y = 825 -  2(206.25) = 412.75.

So, the dimensions are 206.25 x 412.75

and the maximum area = 206.25 × 412.75 feet²

                                       = 85129.68 feet²

                                       = 85130 feet²

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In case of a 2.5% increase in your pay which is now $25,000, your new salary will be $25,625.

First, you need to determine the percent increase i.e.2.5% of 25,000 (old salary),

            2.5%      x     25,000     =     ?

           2.5/100   x    25,000     =  625

So, the $625 would be the increased amount in your salary which is equal to 2.5% of your old salary (i.e. 25,000).

In order to find out the amount of your new salary that you will be receiving, you have to add the increased amount to the amount of your old salary, as follows:

amount of the new salary =  amount of the old salary + percent increase

                                       =     $25,000 +   $625

                                       =       $ 25,625

When an increase of 2.5% is made in your salary which is now $25,000, then your new salary becomes $25,625.

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Answer:

1.03

Step-by-step explanation:

The increase is 3% above the original 100%, thus

multiplier = 100 + 3 = 103% = \(\frac{103}{100}\) = 1.03

Answer:

h=34

Step-by-step explanation:

If you know the measures of two sides and the angle between them, you can use the Law of Cosines to find missing parts of any triangle.

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is used to solve triangles when the measures of two sides and the included angle are known, or when the measures of all three sides are known.

The formula for the Law of Cosines is:

c² = a² + b² - 2ab cos(C)

where c is the length of the side opposite angle C, and

          a and b are the lengths of the other two sides.

The Law of Cosines is a powerful tool for solving triangles, particularly when the angles are not right angles. It allows us to determine the unknown sides or angles of a triangle based on the information provided

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Answer:

sin(x) = 12/13

Step-by-step explanation:

cos^(-1)(5/13) = 0.176

tan^(-1)(12/5) = 0.176

sin(0.176 radians) = 12/13

The solution to the simultaneous equation given is (3, 4)

Given the system of equation below

2x+y=10

3x-y=5

From equation 2, the value of y is expressed as:

y = 3x - 5

Substitute the result into equation to have:

2x + 3x - 5 = 10

5x - 5 = 10

5x = 15

x = 3

Since y = 3x - 5

y = 3(3) - 5

y = 4

Hence the solution to the system of equation is (3, 4)

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The amount of interest she will earn at the end of 3 years would be = $375

The principal amount of money saved by Chantal (p)= $5000

The interest rate that the amount generates (r)= 2.5%

The total time for the savings(t) = 3 years.

The simple interest generated S.I = P×T×R/100

= 5000×3×2.5/100

= 37500/100

= $375

Therefore the amount of money she will earn as interest after three years of savings would be = $375.

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Answer: the common number is 8 for 151 and 152

Step-by-step explanation: hope this helps

The statements that are true about the solution to the system of equations are

y coordinate, of the solution is = (-8) ,

x coordinate, of the solution is = (9) , and

The ordered pair that is solution to the system lies in Quadrant IV .

In the question ,

the system of equations are given as

4x+3y = 12   ...(1)

and 2x +3y = -6    ...(2)

to solve for x and y , we subtract equation (2) from equation(1) .

So , On subtracting , we get

(4x+3y)-(2x+3y)= 12-(-6)

4x+3y-2x-3y = 12+6

4x-2x +3y-3y = 18

2x = 18

x = 18/2

x = 9

Put x=9 in equation \((1)\), we get

4(9)+3y=12

36+3y=12

3y = 12-36

3y = -24

y= -24/3

y = -8

Since x coordinate is +9 and y coordinate is -8 ,

so the solution lies in Quadrant IV.

Therefore , The statements that are true about the solution to the system of equations are

y-coordinate, of the solution is =  (-8) ,

x-coordinate, of the solution is =  (9) , and

The ordered pair that is solution to the system lies in Quadrant IV .

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Answer:

Step-by-step explanation:

Based on the given conditions, formulate: 2500 x (1 - 8%)

Evaluate the equation/expression: 2300

get the result:2300

Answer: 2300

Answer:

-14x+6

Step-by-step explanation:

first, we distribute the -3.

-3(4x - 2) - 2x=-12x+6-2x

than, we conbide like terms

-12x+6-2x=-14x+6

Answer:

20.25inches

Step-by-step explanation:

Using the Pythagorean theorem,

h^2=7^2 +19^2

h^2=410

h=sqr 410=20.25inches

The representation of the angle with measure of 10π / 3 radians is presented in the image attached below.

In this problem we have the measure of an angle in standard position and measured in radians. Since representation of angles are between 0 and 2π radians, we need to find what angle between 0 and 2π radians is coterminal with the described angle:

θ = 10π / 3 - 2π

θ = 4π / 3

Then, the angle is coterminal with an angle of 4π / 3 radians.

Now we proceed to graph the angle by using the following formula:

(x, y) = (cos 4π / 3, sin 4π / 3)

The representation of the angle with measure of 10π / 3 radians is presented in the image attached below.

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M = C(1+r)^t

5675 = 350(1+0.0365/2)^t

5675=350×1.01825^t

t = 154.04

Answer:

Approximately 77 years

Step-by-step explanation:

V(t)=P(1+r/n)^nt

5675=350(1+.0365/2)^2t

16.214=1.01825^2t

log16.214=log1.01825^2t

log16.214=2t(log1.01825)

log16.214/2log1.01825=t

77=t

Answer:

No.

Step-by-step explanation:

It does not pass the vertical line test, so the relation is not a function. This is because there are x-values that have several y-values. To be a function, a relation must have x-values that only have one y-value each.

Hope this helps!

Answer:

No

Step-by-step explanation:

Because for any given point along the x-axis it has 2 values along y-axis.

For a relation to be a function it must have only one value at y-axis along any given point along the x-axis

Descriptive statistics are those that involve gathering, arranging, and summarizing data.

Brief informational coefficients known as descriptive statistics are used to sum up a given data set, which may be a sample of a population or a representation of the entire population. Measures of the central tendency or measures of variability make up descriptive statistics (spread).

A descriptive statistic's main function is to summarize data. Only the data set from which they were derived are statements made by descriptive statistics; they never extend further than the data you have.

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To solve a direct proportion problem with decimal numbers, you can follow the same steps as with whole numbers.

A direct proportion is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable.

To solve a direct proportion problem with decimal numbers:

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Answer:

-9

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1)

 (r - 11)/(4 - (-1)) = (r - 11)/5

So, (r - 11)/5 = -4

r - 11 = -20

r = -9

I dont know wht

way you are doing this but hope it helps

Answer:

No. The input 1.2 has 2 outputs.

Step-by-step explanation:

See attachment for complete question

The first circle represents the domain while the second represents the range of the function.

For a mapping to be a function, it must either be a one to one relationship or a many to one relationship.

One to one, in the sense that; there can be only one entry in the domain points to one entry in the range of the function.

Many to one, in the sense that: there can be multiple domain entries that point to one entry in the range of the function

However, from the attachment it can be seen that an entry in the domain (1.2) points to two entries in the range (6 and 8).

Hence, this does not represent a function.

Slope of the given graph function is -3/2 while the y-intercept: (0, 1)

What is slope intercept?

Finding the equation of a straight line in the coordinate plane is done using the slope intercept form. The connection that any point's coordinates on the line must satisfy is the equation of a straight line. Any point that is not on the line will not have coordinates that satisfy. The answer to this equation is simple to determine.

To Find :  equation of the line, in slope-intercept form

Solution:

Standard/ general form of equation of line in 2 variables is

Ax + By + C = 0

Slope intercept form is

y = mx + c

intercept form is

x/a  + y/b   = 1

Slope intercept form is

y = mx + c

m = Slope = -3/2

c = y intercept  =  1  

y  = (-3/2)x  + 1

equation of the line, in slope-intercept form is   y  = (-3/2)x  + 1.

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Algebra is a branch of mathematics that deals with mathematical statements and relationships in which symbols (such as x, y, and z) represent numbers or other unknown values. Harry has 62 quarters and 38 nickels.

How many of each coin does he have?

To find out how many of each coin Harry has, we need to use algebra. Let x be the number of quarters and y be the number of nickels. We know that:

x + y = 100 (because Harry collected 100 coins in total)

0.25x + 0.05y = 17.40 (because that's the total value of the quarters and nickels in dollars)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can subtract y from both sides to get:

x = 100 - y

Then we can substitute this value of x into the second equation and solve for y:

0.25(100 - y) + 0.05y = 17.40

25 - 0.25y + 0.05y = 17.40

25 = 17.40 + 0.20y

0.20y = 7.60

y = 38 (the number of nickels)

Now that we know the value of y, we can use the first equation to find the value of x:

x + 38 = 100

x = 62 (the number of quarters)

So Harry has 62 quarters and 38 nickels.

These symbols are used to represent quantities, and the operations and relationships between them are studied through the use of mathematical laws and rules.

Algebraic equations and formulas allow one to solve a wide variety of problems, including problems in physics, engineering, and other sciences, as well as in everyday life.

Algebraic concepts include variables, expressions, equations, and functions. It is the study of mathematical symbols and the rules for manipulating these symbols. Algebra is a powerful tool for solving problems by using mathematical models.

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