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Factoring completely involves three steps: identifying the GCF, applying the appropriate factoring method, and checking for additional factors. Factoring by grouping is used when there are four terms in an expression and common factors can be factored out separately. An example is given to illustrate the factoring by grouping process.

This technique is used when there are four terms in an expression and there is a common factor between the first two terms and the last two terms. The common factor is factored out separately from the two pairs, and then the resulting binomials are factored further.

Consider the expression 2x + 3y + 4x + 6y. In this case, we can group the terms as (2x + 3y) + (4x + 6y). Common factors can be factored out separately, resulting in (2x + 3y)(1 + 2).

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Using the data presented in the problem, you are asked to predict the probability that future customers will cancel their preorders. To find the probability, you have to divide the number of people who cancelled their preorders by the total number of people who preordered.

35 people / 140 people = .25 or 25% probability that the future customers will cancel their preorders.

Answer:

A

Step-by-step explanation:

Final answer:

In a normal distribution, the mean, median, and mode are all the same, since it is symmetric around the mean. The standard deviation affects the shape of the distribution, and the empirical rule states that most values lie within two standard deviations of the mean. Differences in symmetry may cause the mean, median, and mode to diverge, with the mean being most affected by skewness.

Explanation:

In a normal distribution, the mean is equal to the median and mode, by definition. This is because the normal distribution, which is also known as the Gaussian distribution, is symmetrically shaped like a bell curve around the mean (μ). The mean indicates the center of the distribution and the point of symmetry, while the median divides the data such that half of the values are above it and half are below. The mode is the most frequently occurring value in the data set, and in a perfect normal distribution, it coincides with the mean and median.

The standard deviation (σ) is a measure of the spread of the distribution. If the standard deviation is increased, the curve becomes wider and flatter, while a decrease in σ makes the distribution steeper and narrower. Additionally, the location of μ on the X-axis can shift the entire graph to the left or right, but the shape of the graph remains the same. The empirical rule helps us understand that approximately 95% of values lie within two standard deviations from the mean.

Drawing from the collaborative exercise provided, by recording the heights and creating histograms with smooth bell-shaped curves, one can calculate the mean and identify how characteristics such as skewness affect the mean, median, and mode, especially in non-symmetric distributions. In these cases, the mean can be influenced by the direction of the skew more than the median, pulling it towards the tail of the distribution.

Answer:

Step-by-step explanation:

The length measure of the second leg of the right-angle triangle is 12 units.

Given the parameter:

Hypotenuse = 15 units

Length of leg1 = 9 units

Length of leg2 = x

To determine the measure of the missing side length of the right triangle, we use the Pythagoras theorem.

It is expressed as:

( hypotenuse )² =  ( leg 1 )² + ( leg 2 )²

Plug in the given values:

( 15 )² =  ( 9 )² + ( leg 2 )²

Simplifying, we get:

225 = 81 + ( leg 2 )²

( leg 2 )² = 225 - 81

( leg 2 )² = 144

Take the square roots:

leg 2 = √144

leg 2 = 12 units

Therefore, the second leg measures 12 units.

The question is not complete, the complete question is:

A right triangle's leg is 9 and the hypotenuse is 15, What is the length of of the other leg of the triangle?

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Answer:

x=3.5 they did nothing wrong but I am pretty sure you meant not twenty but one hundred and twenty for that the answer is x=16

Step-by-step explanation:

To find the equation, we will form the general equation of a circle and then will find the equation that matches the equation we formed.

The general equation of a circle is given as

[tex](x-h)^2+(y-k)^2 = R^2[/tex]

where, the (h, k) are the coordinates of the center of the circle, and R is the radius of the circle.

The correct option is c.

the equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.

Given that the diameter of the circle is 8 units. therefore,

[tex]\rm{ Radius\ of\ the\ circle =\dfrac{Diameter}{2} = \dfrac{8}{2}[/tex]

The equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units can be found by substituting the values in the equation of a circle:

[tex](x-h)^2+(y-k)^2 = R^2[/tex]

Substituting the values,

[tex][x-(-2)]^2+[y-(-3)]^2 = 4^2\\\\ (x+2)^2+(y+3)^2 = 16[/tex]

[tex](x+2)^2+(y+3)^2 = 16\\\\ (x^2 + 4 + 4x)+(y^2+9+6y) = 16\\\\ x^2 + 4 + 4x+y^2+9+6y = 16\\\\ x^2 + 4x+y^2+6y = 16-4-9\\\\ x^2 + 4x+y^2+6y = 3\\\\ x^2 + 4x+y^2+6y -3 = 0[/tex]

Therefore, the equation which will be in the above form will be the equation we want. As we can see the above equation is similar to   option c.

To verify that we will plot the graph. The image given below represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.

Hence, the correct option is c.

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In this exercise we have to use the knowledge of triangles to calculate the value of the third side, so we have:

[tex]7

organizing the information given in the statement we find that:

Recognition of the Pythagorean theorem we have that will be:

[tex]c

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To find the height of the brick proportion of a wall, multiply the total wall height by the fraction representing the brick portion. For instance, if the wall is 220 cm high and 3/5 is brick, the brick portion's height would be 132 cm.

To determine the height of the brick proportion of the wall, you would need to know the total height of the wall first. Once you have the total height, you can calculate the height of the brick section by multiplying the total height by the fraction of the wall that is brick. For example, if 3/5 of the wall is made from brick, and the wall is 220 cm high, the calculation would be as follows:

Height of brick portion = Total height of the wall × Fraction of wall that is brick

Height of brick portion = 220 cm × (3/5) = 132 cm

Therefore, the height of the brick proportion of the wall would be 132 cm.

Answer:

x + 5x + 2x = 180  

8x = 180  

x = 22.5 degrees ( smallest angle),  Largest Angle = 112.5 degrees and the third angle = 45 degrees

Let's call the smallest angle x.  Then the largest angle is 5x and then the third angle is 2x since it is twice the smallest angle.  We know that the sum of all the angles in a triangle is 180 degrees.

Step-by-step explanation:

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Usain Bolt set world records for the 100-m and 200-m dashes with impressive maximum speeds and accelerations.

Usain Bolt of Jamaica set the world record for the men's 100-m dash in the 2008 Olympic Games in Beijing. He accelerated for 3.00 s to reach his maximum speed and maintained it for the race. Calculating his maximum speed and acceleration involves understanding his performance data.

For the 100-m dash, Bolt's maximum speed was approximately 12.19 m/s and his acceleration was 2.63 m/s². In the 200-m dash, his maximum speed using the same assumptions was 10.36 m/s. This insight into Bolt's remarkable athleticism showcases his exceptional speed and acceleration capabilities on the track.

Answer: {1, 2, 3, 4, 5, 6}

Step-by-step explanation:

Given : A student rolls a number cube whose six faces are numbered 1 through 6.

Then, the possible outcomes of rolling it = 1, 2, 3, 4, 5, 6

Then , the sample space for this experiment = set of all possible outcomes

= {1, 2, 3, 4, 5, 6}

When [tex]\( y = 10 \) and \( z = 5 \)[/tex], [tex]\( 0.3y + \frac{y}{z} \) equals \( 5 \)[/tex].

To evaluate the expression [tex]\(0.3y + \frac{y}{z}\) when \(y = 10\) and \(z = 5\)[/tex], follow these steps:

1. Substitute the given values of [tex]\(y\) and \(z\)[/tex] into the expression:

  [tex]\[0.3 \times 10 + \frac{10}{5}\][/tex]

2. Calculate each term separately:

  - [tex]\(0.3 \times 10 = 3\)[/tex]

  - [tex]\(\frac{10}{5} = 2\)[/tex]

3. Add the results:

  [tex]\[3 + 2 = 5\][/tex]

So, when [tex]\(y = 10\) and \(z = 5\)[/tex], the expression [tex]\(0.3y + \frac{y}{z}\) equals \(5\).[/tex]

1. Multiply 0.3 by 10:

  [tex]\[0.3 \times 10 = 3\][/tex]

2. Divide 10 by 5:

  [tex]\[\frac{10}{5} = 2\][/tex]

3. Add the results:

  [tex]\[3 + 2 = 5\][/tex]

Thus, when [tex]\(y = 10\) and \(z = 5\)[/tex], the expression [tex]\(0.3y + \frac{y}{z}\) equals \(5\).[/tex]

29 * 3 = 87

25 +29 = 54

x = 87 - 54 = 33

x = 33

Answer:

[tex](1+0.3)^{6}=(1)^6+6(1)^{5}(0.3)+15(1)^{4}(0.3)^{2}+20(1)^{3}(0.3)^{3}+15(1)^{2}(0.3)^{4}+6(1)^{1}(0.3)^{5}+(0.3)^{6}[/tex]

Step-by-step explanation:

This is an expansion of the expression [tex](a+b)^{6}[/tex]. In general you can expand expressions of this form by a formula known as the binomial theorem. This formula establishes that

[tex](a+b)^{n}=\sum_{k=0}^{n} {n\choose k} a^{n-k}b^{k}[/tex]

Where the coeficients [tex]n\choose k[/tex] are called binomial coeficients, and can be computed by the formula

[tex]{n\choose k} =\frac{n!}{(n-k)! k!}[/tex]

where [tex]n!=1\times 2\times 3\times \cdots\times n[/tex].