Hey! I need help with these 2 questions! Thanks.

Yes, the product of (x - 3)^2 is a perfect square trinomial because it can be written as the square of the binomial (x - 3).

A perfect square trinomial is a trinomial of the form a^2 + 2ab + b^2, where a and b are terms that can be squared. When we expand the square of a binomial, we get a perfect square trinomial.

In this case, the binomial is (x - 3), and its square is (x - 3)^2. When we expand this expression, we get:

(x - 3)^2 = (x - 3)(x - 3) = x^2 - 6x + 9

This is a perfect square trinomial, because it can be written as the square of the binomial (x - 3). Specifically, we can write:

(x - 3)^2 = (x - 3)(x - 3) = (x - 3)^2

Therefore, the product of (x - 3)^2 is a perfect square trinomial.

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Answer:

x = 2.0909090

Step-by-step explanation:

Here is my solution.

By using a statistical method called regression to model the relationship between the number of earthquakes and various factors that may influence them, such as geological features or human activities.

To answer this question, we need to use a statistical concept called variance. In simple terms, variance measures how spread out a set of data is from its mean or average value.

In the case of earthquakes, we can use historical data to calculate the average number of large earthquakes that occur in the US per year, and then calculate the variance to see how much variation there is in the actual number of earthquakes from year to year.

By doing so, we can make predictions about the expected number of earthquakes in the future and estimate their variance.

In mathematical terms, the variance of a random variable X can be calculated as follows:

Var(X) = E[(X - μ)²]

Where E is the expected value operator, μ is the mean or average value of X, and ² means "squared." This formula tells us to subtract the mean from each value of X, square the result, take the average of these squared differences, and that gives us the variance of X.

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The total amount of money Mario, Giana, and Allan split was $2160. Giana received $640 less than Allan did.

Let x represent the sum of money Mario got.

Giana got three times

Allan got seven times

Total: 2x, 3x, 7x, or 12x.

Allan received $640 more than Giana, therefore

7x = 640 + 3x

4x = 640

x = 160

Total amount split is 12x, or 12 * 160, or $2160.

The total amount of money Mario, Giana, and Allan split was $2160. To determine the overall amount, we must first determine how much money each person received. We know that Giana received three times as much as Mario did, while Allan received seven times as much. So, using 2x, 3x, and 7x, respectively, where x is the amount of money Mario received, we can express how much each person earned.

We may draw up an equation to determine how much money Mario received by taking into account the fact that Allan received $640 more than Giana. It goes like this: 7x = 640 + 3x. x = 160 is the result of solving this equation. Mario thus received $160 whereas Giana received $480 after multiplying 3x by 3 * 160. Allan received $1120 since he was paid $640 more than Giana (7x = 7 * 160). Mario, Giana, and Allan divided the total amount of money as follows: 2x + 3x + 7x = 12x = 12 * 160 = $2160.

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Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is equal to the total change in the function's output divided by the total change in the input over the interval. In other words, it is the slope of the secant line that connects the two points on the function defined by the interval.

If the function is represented by y = f(x), the average rate of change of the function over the interval [-4, -3] can be calculated as:

Δy / Δx = (f(-3) - f(-4)) / (-3 - (-4))

So, to calculate the average rate of change, you would need to know the values of the function f(x) at x = -3 and x = -4. If you provide the equation for the function f(x), I can help you find the average rate of change.

Answer:

Area = 15a^3b^6

Perimeter: 10a^2b^4+6ab^2

Step-by-step explanation:

Formula For Area: L*W

Input The Numbers: 5a^2b^4 * 3ab^2

5a^2b^4 * 3ab^2 = 15a^3b^6

Area = 15a^3b^6

Formula for perimeter: P=2(l+w)

Input the Numbers: P = 2(5a^2b^4 + 3ab^2)

2(5a^2b^4 + 3ab^2) = 10a^2b^4+6ab^2

Perimeter: 10a^2b^4+6ab^2

Hope this helped!

The roots of the equation, f (x) = ( x - 6 )²( x + 2 )² are 6 and - 2.

The root of the function is calculated by setting the function equal to zero.

The given function is f (x) = ( x - 6 )²( x + 2 )²

we will separate the two equation and set them equal to zero.

( x - 6 )² = 0  ----  equation  ( 1 )

or

( x + 2 )² = 0 -------- equation ( 2 )

from the first equation, x = 6

from the second equation, x = - 2

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The complete question is below:

Find the roots of f(x) = (x - 6)² (x + 2)²

The expressions that show the number of students for each activity are;

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.

A set is a mathematical model for a collection of various things.

We are given;

Total number of students in the middle school = z

A) From the given table, we can deduce that;

B; Now, the expression to show the students that like either drama or dance is;

(1/7)z + 26 + (1/7)z + 22

>> (2/7)z + 48

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A middle school with z students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts A and B.

Table:

Activity:

Dance- 22 more than one-seventh of the students

Baseball- 24 fewer than four-sevenths of the students

Drama- 26 more than one-seventh of the students.

If on the following Tuesday, Terry fills out scale again and receives a score of 28 , then Terry's scores on the Self-Monitoring Scale do not appear to be Reliable .

The Terry's scores on the Self-Monitoring Scale do not appear to be reliable, because there is a significant difference between his score on Friday and his score on the following Tuesday.

The Reliability is defined as the consistency of measurement over time or across different conditions.

In this case, if Terry's scores on the Self-Monitoring Scale were reliable, we would expect them to be consistent or stable over time.

However, his score on Tuesday is significantly lower than his score on Friday suggests that there may be some inconsistency in his responses .

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Step-by-step explanation:

So working from the bottom

The last line for x > 20 shows 13 because of the top graph, the last line is 13 and there is nothing below it.

Now for x > 16, we go up a line and see 14

That's where you would add 14 + any number below it

14 + 13 = 27. So for x > 16, you'd write 27

Going up, we have X > 12. Same thing, we go up a line and see 19. So now we just add 29 and any number below that

19 + 14 + 13 = 46. So for x > 12, you'd write 46.

You'll do that for the rest of the table. hope that helps

A graph giving us a idea about relationship between the number of days and total amount of sunglasses is mentioned in the image attached below.

In this case, using Microsoft Excel, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot and the total number of sunglasses would be plotted on the y-axis (y-coordinate).

From the scatter plot (attached image) which shows the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 62

Hence, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and total amount of sunglasses.

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Answer:C

Step-by-step explanation:

The area of the right triangle with side lengths of 15cm and 12cm is 90 cm².

The area of triangle can be determined using the equation;

Area = 1/2 × base × height.

The angle described forms a right-triangle.

Area = 1/2 × base × height

Area = 1/2 × 12cm × 15cm

Area = 6cm × 15cm

Area = 90 cm²

Therefore, the area of the triangle is 90 cm².

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Answer: 20

Step-by-step explanation:

30-60-90 triangles are special: Their side lengths fall in a ratio of 1:2:[tex]\sqrt{3}[/tex], in order of Shortleg : hypotenuse : longleg

Since we know the short leg is 10, the hypotenuse must be double, or 20.

The correct answer to the given question about all of the diagonals drawn from a vertex of an n-gon is option b) n-1

If all of the diagonals are drawn from a vertex of an n-gon, the number of triangles formed is equal to the number of non-diagonal sides of the n-gon. To see why, imagine selecting a vertex of the n-gon and drawing all of the diagonals from that vertex. Each diagonal connects that vertex to a non-adjacent vertex of the n-gon, which splits the n-gon into a series of triangles. The total number of triangles formed is equal to the number of non-diagonal sides of the n-gon, because each non-diagonal side forms one triangle with the selected vertex and one of its adjacent vertices. An n-gon has n sides, so the number of non-diagonal sides is equal to n - 3. This is because each vertex is connected to two adjacent vertices, so there are n - 2 diagonal sides emanating from the selected vertex, and the remaining n - 2 sides are non-diagonal. In addition, there are three sides at the selected vertex that are not counted as non-diagonal sides, so we subtract 3 from n - 2 to get n - 3. Therefore, the answer is (B) n - 1.

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The corresponding p-value for this test statistic is 0.005, which is smaller than our significance level of α=0.05.

To begin, we define the population proportion of people who shop for groceries online in region A as p₁ and the population proportion of people who shop for groceries online in region B as p₂.

Our null hypothesis is that there is no difference in these proportions, which we can write as H0=> p₁ = p₂. Our alternative hypothesis is that there is a difference, which we can write as H1=> p₁ ≠ p₂.

Next, we need to calculate the sample proportions and standard errors for each region. We can do this using the formulas:

p₁ = x₁/n₁, p₂ = x₂/n₂

where x₁ and x₂ are the number of people in each sample who shop for groceries online, and n₁ and n₂ are the sample sizes. The standard errors are given by:

=> SE₁ = √(p₁(1-p₁)/n₁),

=> SE₂ = √(p₂(1-p₂)/n₂)

Using the given data, we find that p₁ = 0.16, p₂ = 0.24, SE₁ = 0.037 and SE₂ = 0.042.

We can now calculate the test statistic, which measures the difference between the sample proportions under the assumption that the null hypothesis is true. We use the formula:

z = (p₁ - p₂) / √(SE₁² + SE₂²)

Substituting the values we calculated, we get:

z = (0.16 - 0.24) / √(0.037² + 0.042²) = -2.83

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Complete Question:

A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.

On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

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Option C : The number of individual outcomes from flipping and rolling one time is 12.

A permutation is a selection of items from a set where the order of the items does matter. In this case, a permutation would be an ordered pair of a heads or tails outcome from flipping a coin followed by a 1, 2, 3, 4, 5, or 6 outcome from rolling a die.

The number of possible combinations is found by multiplying the number of possible outcomes for each event. In this case, there are two possible outcomes from flipping a coin (heads or tails) and six possible outcomes from rolling a die (1, 2, 3, 4, 5, or 6), so the number of combinations is:

2 (outcomes from coin flip) * 6 (outcomes from die roll) = 12

The number of permutations is equal to the number of combinations because the order of the items in each combination does not matter. So, there are 12 individual outcomes from flipping and rolling one time.

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Answer:

The value of the investment in 5 years.

Step-by-step explanation:

The description of the function states that it tells us the value of an investment at some point in the future (t), measured in years.  In other words, f(t).  When the time is 5 years, it would be written as f(5), and the t term in the function will be set to 5 for the calculation, which will yield the value of the investment at that time.

Answer:

n = (3/8)x+(45/8)

Step-by-step explanation:

3x+5 = 4(n-5)*(6/3)

Is this written correctly?

3x+5 = 4(n-5)*(6/3)

3x+5 = 8(n-5)      [Simplify: {4*(6/3) = 8)]

3x+5 = 8n-40      [Expand the parentheses]

8n-40 = 3x+5      [Rearrange]

8n = 3x+5 + 40    [Rearrange]

8n = 3x+45          [Simplify]

n = (3x+45)/8       [Divide both sides by 8]

n = (3/8)x+(45/8)    [Rearrange]

Answer:

a recipe uses y cups of flour and x cups of sugar the amount of flour is 4 times  the amount of sugar

my proof I took the quiz

By induction, it can be concluded that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders.

1. To prove by induction that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders, we can use the following steps:

2. Base case: For k = 1, we have a single node, and if we remove the root, there is no tree left.

3. Inductive hypothesis: Suppose that the result holds for some k = n, that is, if we remove the root of an n-th order binomial tree, it results in n binomial trees of the smaller orders.

4. Inductive step: We need to prove that the result also holds for k = n + 1. To do this, we consider a (n + 1)-th order binomial tree. According to the definition, this tree is formed by joining two n-th order binomial trees. Let's call them T1 and T2. If we remove the root of this tree, the two subtrees T1 and T2 will become the n binomial trees of the smaller orders. These n binomial trees are all distinct because they correspond to the different possible combinations of nodes in the two subtrees T1 and T2.

Therefore, by induction, it can be concluded that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders.

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The probability that the line pressure will surpass 13.0 bars during any measurement is P [Z > 13] = 0,1587, or 15.87%.

If the line pressure exceeds 13.0 bars, there is a chance that:

P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [Z 13] will be located in the z table when z (score) =

Z (score) equals (Z - 0) /

Z = (13 - 12)/1 (score).

the z-table, we then discover

P [ Z ≤ 13] = 0,8413

Finally . P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [ Z > 13 ] = 1 - 0,8413

P [Z > 13] = 0,1587, which is equal to 15,87%.One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprovable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it.

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Answer:

x=4

Step-by-step explanation:

since triangles LMJ and KLJ are = by hyp. and one side

<=> 4x+6=3x+10

<=> 4x-3x=10-6

<=> x=4

The commission amount the salesperson earn is $29.7.

The percentage formula is dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Selling price = $495

Commission = 6%

Now,

The amount of commission.

= 6% of 495

= 6/100 x 495

= 29.7

Thus,

The commission the salesperson earn is $29.7.

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The resulting expression of the algebraic expression  is 13r²(2rs + 4r³ - 3s⁴).

option C.

The resulting expression of the algebraic expression given as

26r³s + 52r^(5) - 39r²s⁴

can be determined by finding the highest common factor here and factorize out.

The highest common factor of the letters is r²

Factors of 26 = 1, 2, 13, 26

Factors of 39 = 1, 3, 13, 39

Factors of 52 = 1, 2, 4, 13, 26, 52

The highest common factor for the 3 numbers is 13.

Thus, in total, the highest common factor for the algebraic expression is 13r².

Finally, we have;

13r²(2rs + 4r³ - 3s⁴)

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The complete question is below:

Factor  26r³s + 52r^(5) - 39r²s⁴

The value of x in the triangle is 6√5

from the question, we have the following parameters that can be used in our computation:

The triangle

Using the above as a guide, we have the following:

x/20 = 9/x

Cross multiply the equation

so, we have the following representation

x^2 = 180

TAke the square root of hoth sides

This gives

x = 6√5

Hence, the solution of x is  6√5

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Answer:

$1350.68 to nearest cent.

Step-by-step explanation:

At the beginning $500 is deposited and this accumulates interest for 3 years At the end of first year it increases to 500( 1 + r) dollars

Then at the end of the 2 years its value is

500(1+ r)(1 + r)(

and at the end of 3 years value =

500(1 + r)(1 + r)(1 + r)

= 500(1 + r)^3 dollars

and as 1 + r = x we have:

500x^3 dollars

In the same way 200 for 2 years = 200x^2

and 600 for 1 year = 600x dollars.

Total = 500x^3 + 200x^2 + 600x.

b.

So, if the interest r = 2 % (= 0.02)

and x = 1.02

Total value after 3 years

= 500(1.02)^3 + 200(1.02)^2 + 600(1.02)

= 530.604 + 208.08 + 612

= $1350.684