How do you factorise fully x³-x

Using proportions, the number of pounds that will be needed for a single serving is: one and three seventh pounds.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The number of pounds for 3 people is given by:

\(3 \frac{3}{7} = 3 + \frac{3}{7} = \frac{24}{7}\)

Hence, for one person, the number of pounds can be divided by three(multiplied by 1/3), hence:

\(\frac{24}{7} \times \frac{1}{3} = \frac{24}{21}\)

24 divided by 21 has a quotient of 1 and remainder of 3, hence as a mixed number, the amount is:

one and three seventh pounds.

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Answer:

Step-by-step explanation:

the awnser is cerrot.

The 15th term in the sequence a (n) = 9n - 12 as required to be determined in the task content is; 123.

It follows from the task content that the 15th term in the sequence whose nth term is defined by the equation; a (n) = 9n - 12 is to be determined.

Since tye formula for the nth term of the sequence is; a (n) = 9n - 12.

To determine the 15th term, we must substitute 15 for n in the equation as follows;

a (15) = 9 (15) - 12

a (15) = 135 - 12

a (15) = 123.

In conclusion, the 15th term of the sequence whose nth term is as defined is; 123.

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gAnswer

Range of the sample means = 3.34

Explanation

The range is defined as the difference between the highest and the lowest number. Mathematically,

Range = Highest number - Lowest number

So, the range of the sample means is the difference between the highest and the lowest sample means.

Range of the sample means =

(Sample mean with the highest value) - (Sample mean with the lowest value)

From the table, we can calculate the sample means. The sample mean is given as the sum of the variables divided by the number of variables.

Note that we are told that Charles used only the shaded columns to calculate three sample means. The shaded columns, grouped include

4, 3, 3. Mean = 3.33

8, 5, 7. Mean = 6.67

6, 4, 3. Mean = 4.33

5, 3, 6. Mean = 4.67

Sample mean with the highest value = 6.67

Sample mean with the lowest value = 3.33

Range of the sample means = 6.67 - 3.33 = 3.34

Hope this Helps!!!

Answer:

3:16 pm

Step-by-step explanation:

116 minutes =

60 minutes + 56 minutes =

1 hour and 56 minutes -->

1:20 + 1:56 = 3:16

Answer:g/ml

Step-by-step explanation:

Other is kg/l

Yes, linear regression can be used for time series forecasting and that lagged variables yield much more complex models than straight-line ones.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

With the help of one or more independent variables that can most accurately predict the value of the dependent variable, this type of analysis calculates the coefficients of the linear equation. The differences between expected and actual output values are minimized by linear regression by fitting a straight line or surface.

Therefore, Yes linear regression can be used for time series forecasting and that lagged variables yield much more complex models than straight-line ones.

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The simplification of \(\rm \sqrt{y^{3} } * \sqrt{y^{3} }\) is \(\rm y^{3}\).

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

Simplification is to make something easier to do or understand and to make something less complicated.

Given

\(\rm \sqrt{y^{3} } * \sqrt{y^{3} }\) is an expression.

\(\rm \sqrt{y^{3} } * \sqrt{y^{3} }\) is an expression is given

According to the exponent property.

\(\rm \sqrt{y^{3} } * \sqrt{y^{3} }\\\\y^{\frac{3}{2} } *y^{\frac{3}{2} } \\\\\)

when the base is the same powers get added, then

\(\rm y^{\frac{3}{2}+\frac{3}{2} } \\\\y^{\frac{6}{2}} \\\\y^{3}\)

So the simplification of \(\rm \sqrt{y^{3} } * \sqrt{y^{3} }\) is \(\rm y^{3}\).

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Answer:

y3

Step-by-step explanation:

Edge

Answer:

A. -6,-36

Step-by-step explanation:

Right on EDG 2021.

The vertex of the function f(x) = x² + 12x is (-6, -36).

Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given is a quadratic function,

f(x) = x² + 12x

Vertex of a quadratic function of the form f(x) = ax² + bx + c is the point (-b/2a, f(-b/2a))

Here, a = 1, b = 12 and c = 0

-b/2a = -12 / 2 = -6

f(-b/2a) = f(-6)

            = (-6)² + (12 × -6)

            = 36 - 72

            = -36

Hence the vertex of the given function is (-6, -36).

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Multiple regression analysis is applied when analyzing the relationship between one dependent variable and two or more independent variables. The goal is to determine the extent to which the independent variables predict the dependent variable.

Multiple regression analysis is a statistical technique used to explore and quantify the relationship between a dependent variable and multiple independent variables. It allows researchers to examine how changes in one or more independent variables impact the dependent variable, while controlling for the effects of other variables. By estimating the coefficients for each independent variable, the analysis provides insights into the strength, direction, and significance of their relationships with the dependent variable. This method is commonly employed in various fields, such as economics, social sciences, and business, to understand complex relationships and make predictions based on the interplay of multiple factors.

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In a triangle, The value of x is, 40°

And, The value of y is, 50°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The triangle is show in figure.

We know that;

In a triangle, the pair of two opposite sides are equal then there corresponding angles are also equal.

Now, By figure we can formulate;

⇒ x + x + 100 = 180

Solve for x;

⇒ 2x + 100 = 180

⇒ 2x = 180 - 100

⇒ 2x = 80

⇒ x = 40

Thus, The value of x = 40°

And, We get;

⇒ x° + y° + 90° = 180°

⇒ 40 + y + 90 = 180

⇒ y + 130 = 180

⇒ y = 180 - 130

⇒ y = 50°

Thus, The value of y = 50°

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Answer:

-2

Step-by-step explanation:

h(-5) represents the y value when x is -5.

Step-by-step explanation:

If you need help with how I got my answer, you can ask me.

\( \frac{2yx {}^{ - 4} }{(x {}^{ - 4}y {}^{4}) {}^{3} \times 2x {}^{ - 1}y {}^{ - 3} } \)

\( \frac{2yx {}^{ - 4} }{x {}^{ - 12}y {}^{12} \times 2x {}^{ - 1}y {}^{ - 3} } \)

\( \frac{2y x {}^{ - 4} }{2x {}^{ - 13} y {}^{ - 9} } \)

\( = x {}^{9} y {}^{ - 8} \)

\( = \frac{x {}^{9} }{y {}^{8} } \)

12.

\(( \frac{2u {}^{ 4} }{ - u {}^{2}v {}^{ - 1} \times 2uv {}^{ - 4} } ) {}^{ - 1} \)

\(( \frac{2u {}^{4} \times 1 }{ - 2 {u}^{3}v {}^{ - 5} } ) {}^{ - 1} \)

\(( - u v {}^{ 5} ) {}^{ - 1} \)

\( = - u {}^{ - 1} v {}^{ - 5} = - \frac{ 1}{uv {}^{5} } \)

13.

\( - \frac{2m {}^{4}n {}^{ - 1} }{( - m {}^{2}n {}^{ - 2}) {}^{ - 1} \times - nm {}^{ - 3} } \)

\( - \frac{2m {}^{4}n {}^{ - 1} }{ - m {}^{ - 2} n {}^{2} \times - nm {}^{ - 3} } \)

\( - \frac{2m {}^{4} n {}^{ - 1} }{m {}^{ - 5}n {}^{3} } = - 2m {}^{9} n {}^{ - 4} \)

\( = - \frac{2m {}^{9} }{n {}^{4} } \)

14.

\(( \frac{x {}^{3}y {}^{ - 4} }{ - {x}^{2} y {}^{ - 3} \times yx {}^{0} } ) {}^{3} \)

\(( \frac{x {}^{3}y {}^{ - 4} }{ - {x}^{ - 2}y {}^{ - 2} } ) {}^{3} \)

\(( - {x}^{5} y {}^{ - 2} ) {}^{3} = - x {}^{15} y {}^{ - 6} \)

\( - \frac{x {}^{15} }{ {y}^{6} } \)

15.

\( - \frac{yx {}^{4} \times - {y}^{3} z { }^{ - 4} }{(z {y}^{2} ) {}^{4} } \)

\( - \frac{ - y {}^{4} x {}^{4} z {}^{ - 4} }{ {z}^{4} y {}^{8} } = - y {}^{4} x {}^{4} z {}^{ - 8} = - \frac{(xy) {}^{4} }{ {z}^{8} } \)

16.

\( \frac{h {}^{7}j {k}^{4} }{4h {}^{4} } = \frac{1}{4} h {}^{3} = \frac{h {}^{3} jk {}^{4} }{4} \)

The difference in the rate of change between Function A and function B is -2.

The difference in the rate of change between function A and function B, we first need to identify the rate of change for each function. The rate of change, also known as the slope, represents how much the dependent variable (y) changes for every unit increase in the independent variable (x).

Let's assume function A is represented by the equation y = 2x + 3, and function B is represented by the equation y = 4x - 1.

For function A: y = 2x + 3, the coefficient of x is 2, indicating that for every unit increase in x, y increases by 2. Therefore, the rate of change for function A is 2.

For function B: y = 4x - 1, the coefficient of x is 4, indicating that for every unit increase in x, y increases by 4. Therefore, the rate of change for function B is 4.

Now, to find the difference in the rate of change between function A and function B, we subtract the rate of change of function B from the rate of change of function A:

Difference in rate of change = Rate of change of function A - Rate of change of function B

                          = 2 - 4

                          = -2

The difference in the rate of change between function A and function B is -2. This means that for every unit increase in x, function B increases at a rate that is 2 units greater than function A. It indicates that function B has a steeper slope and a faster rate of change compared to function A.

In summary, the difference in the rate of change between function A and function B is -2.

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Answer:

Complementary

x= 60

Step-by-step explanation:

Answer:

The angles are complementary.

X =  60

Step-by-step explanation:

Step-by-step explanation:

answer is 22 students in the team

how do u get it?

you know it is 80% of the students went for try out so you do 100% - 80% give you 20% students the number of students in the team already. so you do 20 / 100 x 110 students which already in the whole school over 1 which would give it 22

Answer:

(a)  (3, 0) and (-8, 0)

(b)  (-2.5, 0)

(c) x = -2.5

(d) f(-2.5) = -30.25

Step-by-step explanation:

Given quadratic function:

\(f(x)=(x-3)(x+8)\)

The x-intercepts are when \(f(x)=0\)

\(\implies f(x)=0\)

\(\implies (x-3)(x+8)=0\)

\(\implies (x-3)=0 \implies x=3\)

\(\implies (x+8)=0 \implies x=-8\)

Therefore, the x-intercepts are (3, 0) and (-8, 0)

Midpoint between two points:

\(\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad\)

\(\textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)\)

\(\implies \textsf{Midpoint of the x-intercepts}=\left(\dfrac{-8+3}{2},\dfrac{0+0}{2}\right)=\left(-2.5},0\right)\)

The extreme point of a quadratic function in the form \(f(x)=ax^2+bx+c\) is:

\(x=-\dfrac{b}{2a}\)

Therefore, expand the function so that it is in standard form:

\(\implies f(x)=x^2+5x-24\)

\(\implies a=1, b=5\)

Therefore, the extreme value is:

\(\implies x=-\dfrac{5}{2}=-2.5\)

Alternative method

A quadratic function has an extreme value at its vertex.

The x-value of the vertex is the midpoint of the x-intercepts.

Therefore, the extreme value is x = -2.5

\(\begin{aligned}\implies f(-2.5) & =(-2.5-3)(-2.5+8)\\& = (-5.5)(5.5)\\& = -30.25\end{aligned}\)

Answer:

Step-by-step explanation:

First we'll simplify this using the Sum Identity for sin(x + y) where \(x=\frac{3\pi}{2}\) and y = x. Notice we have 2 of those so we simplify first into

\(2sin(\frac{3\pi}{2}+x)=-2\) and divide away the 2 on the left to get

\(sin(\frac{3\pi}{2}+x)=-1\) and now we'll expand:

\(sin\frac{3\pi}{2}cosx+cos\frac{3\pi}{2}sinx=-1\) and go to your unit circle to find the sin and cos of \(\frac{3\pi}{2}\) and fill in where they go:

(-1cosx + 0sinx) = -1 which simplifies to

-1cosx = -1 so

cosx = 1 and

x = 0 or 2π, depending upon what your interval is.

The volume of an ice cube produced by this machine is of:

Volume ice cube = 1 inch³

  A volume is the physical space that an object occupies in space, although it is also defined as the capacity of space that a hollow object may have.

If this machine produces ice that has a cube shape with a side of 1 inch, then to know the value of the volume of these cubes we will use the following equation:

Volume cube = side x side x side

Volume cube = side³

side = 1 inch

Volume ice cube = 1 inch³

As the side is 1 the volume and area will be 1 but with corresponding unit

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(A) 55 hours was took for the temperature to decrease by 4. 4 degrees Celsius. Define h as the duration, in hours, that it took for the temperature to drop by 4.4 degrees Celsius.

The equation that describes the circumstance is as follows since the temperature decreased at a pace of 0.08 degrees Celsius per hour:

0.08h = 4.4

When we solve for h, we get:

h = 4.4 / 0.08 = 55

So, for the temperature to drop by 4.4 degrees Celsius, it took 55 hours.

(a) If the temperature after the 4. 4 degree drop was -2. 5 degrees Celsius, 1.9 degrees Celsius  was the temperature at noon.

Assume T0 is the ambient temperature at noon. Since the initial temperature was T0 and the reduction in temperature was 4.4 degrees Celsius, the following temperature is obtained:

T1 = T0 - 4.4

As a result, if t is the number of hours after midday, and we know that the temperature decreased by 0.08 degrees Celsius every hour, the temperature at time t is:

T(t) = T0 - 0.08t

The temperature following the drop was -2.5 degrees Celsius, thus we may set T1 to -2.5 and find T0 by solving for T0:

T1 = T0 - 4.4 = -2.5

T0 = -2.5 + 4.4 = 1.9

1.9 degrees Celsius was the temperature at midday as a result.

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There are 10 children.

The cost of the two shipping options will be the same when A. A package that weighs 4 pounds will cost $12 for both options.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The cost, y, can be represented by the equation y = 4 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $12 to send the box, represented by the equation y = 12.

This will be:

4 + 2x = 12

2x = 12 - 4.

2x = 8.

Divide.

x = 8 / 2

x = 4

The cost will be 12. The correct option is A.

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If we want to provide a 99% confidence interval for the mean of a population, the confidence coefficient will be 0.99. This means that there is a 99% probability that the true population mean falls within the calculated interval.

The confidence coefficient for a confidence interval represents the level of confidence we have in our estimate.

In the case of a 99% confidence interval, the confidence coefficient is 0.99. This means that we are 99% confident that the true population mean falls within the calculated interval. The confidence coefficient is derived from the desired level of confidence, which is typically expressed as a percentage.

A higher confidence level corresponds to a larger confidence coefficient. In practical terms, a 99% confidence interval indicates that if we were to repeat the sampling process multiple times and construct 99% confidence intervals, approximately 99% of those intervals would contain the true population mean.

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Answer:

y = -3x + 7

Step-by-step explanation:

I see points (0, 7) and (1, 4).

slope = m = (4 - 7)/(1 - 0) = -3

y-intercept = 7

y = mx + b

y = -3x + 7

The direct variation equation in the form x and y is y = 7.25x

As per the given data, the cost of renting a scooter y varies directly with the number of hours the scooter is rented x.

Suppose it costs $21.75 to rent the scooter for 3 hours.

Here we have to determine a direct variation equation in the form of y.

The renting cost (y) is directly proportional to the hours (x).

y ∝ x

y = kx.....(1)

Here k is known for the proportionality constant

From the given information we can find the value of k.

21.75 = k (3)

k = \($\frac{21.75}{3}\)

k = 7.25

Now we have to substitute the value of k in the equation (1)

We get:

y = 7.25x

Therefore a direct variation equation is y = 7.25x.

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Answer:

8

Step-by-step explanation:

Do |7 - 9| first, and you get -2, however since it is absolute value, you use the positive version, making it two. Now you have 5|2|-2. Multiply 5*2=10. Then subtract 2.

The coefficient used to assess the internal consistency of a measure typically refers to Cronbach's alpha coefficient.

The coefficient used to assess the internal consistency of a measure typically refers to Cronbach's alpha coefficient. This coefficient is a statistic that quantifies the internal consistency reliability of a scale or measure, specifically for measures with multiple items or indicators that are intended to measure the same underlying construct.

The coefficient ranges between 0 and 1, with higher values indicating greater internal consistency. Cronbach's alpha measures the extent to which the items in a scale or measure correlate with each other. It assesses how well the items are measuring the same underlying construct or concept.

In other words, the coefficient represents the proportion of variance in the observed scores that can be attributed to the true score, rather than measurement error or other extraneous factors. It indicates the degree to which the items in the measure are interrelated or consistent with each other, with higher values suggesting stronger internal consistency.

Researchers often use Cronbach's alpha to assess the reliability of scales in various fields, such as psychology, education, and social sciences, to ensure that the measure is measuring the construct consistently and accurately.

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We can make use of a slope field to sketch the two approximate solutions of the differential equation. The slope field for the differential equation is dy/dx.

a) We will now mark the point (0,4) on the slope field as shown in the image below.

Solution 1: We will begin at the point (0, 4) and move along the slope lines to obtain the first solution. This first solution is shown in blue in the image below,

Solution 2: For the second solution, we will begin at the point (0,4) and move along the slope lines in the opposite direction to obtain the second solution. This second solution is shown in red in the image below.

Substituting x = 0 and y = 4, we get: 4 = sin(0) + C4 = 0 + CC = 4

Therefore, the particular solution is: y = sin(x) + 4

Below is the graph of the solution: Graph of y = sin(x) + 4

We can compare this graph of the particular solution with the sketches in part (a).

The graph of the solution matches the first solution in blue.

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