Find (x+4) (x²+x-2). Write your answer in standard form.
The product is

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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Answer: 16j^3+2

Step-by-step explanation:

Using the given transformations, namely translation and dilation, the correct statement is given as follows:

Segments YZ and Y''Z'' are proportional after the dilation and congruent after the translation.

The translation rule in this problem is given as follows:

(x, y) -> (x + 1, y - 1).

Meaning that the triangle was shifted:

The only change with the dilation was in the position of the triangle, hence the translated triangle is congruent to the original triangle.

The triangle was dilated by a scale factor of 4, meaning that the coordinates of each vertex of the triangle is multiplied by 4, changing the side lengths of the triangle, thus the dilated triangle is not congruent to the original triangle.

The angles keep the same measure for both cases, translation and dilation, hence the first two statements are incorrect.

The change in the side lengths is proportional, due to the scale factor of 4, hence the correct statement is:

Segments YZ and Y''Z'' are proportional after the dilation and congruent after the translation.

The correct options are missing and are given by the image at the end of the answer.

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Answer:

\((3 {}^{x} + 2)(3 {}^{x} + 2)\)

hope it is helpful to you

Inputting the values provided yields:

\((3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2\)

A + B = 5 - sqrt (34)after simplifying and solving for a + b. 

As a result, we have established that a + b=  0.27.

A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs or catheti. The legs can have different lengths and the Pythagorean theorem can be used to calculate the length of the missing side if the lengths of the other two sides are known. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. Right-angle triangles are used in many practical applications, such as in engineering, architecture, and trigonometry.

Since triangle ABC is a right triangle with CH perpendicular to AB, we can use the Pythagorean theorem to find the length of CH:

\(CH^2 = CB^2 - BH^2\)

Since triangle ABC is a right triangle, we have CB = AC, and since CH is on AB, we have BH = x. Substituting these values, we get:

\(CH^2 = AC^2 - x^2\)

We can also use the given values of x and h to find AC:

\(AC^2 = x^2 + h^2\)

Substituting this into the equation for \(CH^2\), we get:

\(CH^2 = AC^2 - x^2 = (x^2 + h^2) - x^2 = h^2\)

Taking the square root of both sides, we get:

CH = h = 4

Therefore, we have found that CH = 4.

Now we can use the fact that CH is an altitude of triangle ABC to find the area of the triangle in two different ways:

Area = (1/2) * CH * AB

Area = (1/2) * AC * BC

Setting these two expressions equal to each other and substituting the given values, we get:

(1/2) * 4 * (x + 4) = (1/2) * (3 + y) * 5

Simplifying and solving for y, we get:

2x + 8 = 15 - 5/2 * y

2x + 13/2 = 5/2 * y

y = 2x + 13/5

Using the given value of x, we can find y:

y = 2(3) + 13/5 = 6.6

Therefore, we have found that y + h = 6.6 + 4 = 10.6.

Finally, to find a + b, we can use the Pythagorean theorem on triangle ABC:

\(AC^2 + BC^2 = AB^2\)

Substituting the given values, we get:

\((3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2\)

Simplifying and solving for a + b, we get:

a + b = 5 - sqrt(34)

Therefore, we have found that a + b ≈ 0.27.

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The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.

When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.

Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.

We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.

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As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.

Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:

s + (r + 75) = (s + r) + 75

The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.

Let's take an example to illustrate this:

Suppose s = 10 and r = 20.

Using the original expression:

s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105

Using the expression with regrouped terms:

(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105

As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.

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The graph of the feasible region is attached

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

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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Answer:

10:

7/4π = 5.5(1decimql place)

11:

50π = 157.1(1 decimal place)

Step-by-step explanation:

the equation is (angle/360) X πr^2

After the raise, Tyler's brother will make $14 x 1.05 = $14.70 per hour.

Answer:

14 x 1.05 = 14.70

Step-by-step explanation:

You can not make the sum of two unalike terms.

To establish trust with Martina, the nurse should show respect, use non-verbal communication, incorporate play, involve the parent, and individualize the approach.

To establish a trusting relationship with Martina, the nurse can employ several approaches:

Respect and empathy: The nurse should approach Martina with genuine respect and empathy, recognizing her unique needs and individuality. This can be conveyed through a calm and patient demeanor.

Non-verbal communication: Since Martina may not be responsive to verbal cues, the nurse can utilize non-verbal communication to establish connection and trust. This can include maintaining eye contact, using gentle touch, and respecting Martina's personal space.

Play and familiar objects: Given Martina's engagement with the blue stuffed dog, the nurse can incorporate play into their interactions. Bringing familiar objects or toys that Martina finds comforting can help create a sense of familiarity and security.

Parental involvement: Involving Martina's mother in the care process can be beneficial. The nurse can communicate with the mother, seek her input, and involve her in the administration of medications. This helps build trust not only with Martina but also with her caregiver.

Individualized approach: Recognizing Martina's autistic disorder, the nurse should tailor their approach to her specific needs. Understanding her sensory sensitivities and preferences can help create a safe and comfortable environment.

By implementing these strategies, the nurse can foster trust and a positive therapeutic relationship with Martina, promoting her overall well-being and care.

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Complete Question:

What approach would help the nurse establish a trusting relationship with Martina, a 3-year-old with bronchitis and autistic disorder, who is intensely occupied with a blue stuffed dog and does not seem responsive to the nurse's presence in the room, while the mother is also present?

Answer:

A = 530.929158457

Answer:

Area = 706.8583471

Explanation:

The used law to measure the surface area of the sphere is

\(area \: = 4\pi \: {r}^{2} \)

Where (r) is the radius. The radius is half the diameter, so it will be half 13 which is equal to 7.5. By using this law:

\(4\pi \: {7.5}^{2} = 706.8583471\)

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 4)

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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Answer:

20

Step-by-step explanation:

5 times 4 = 20

Answer:

See below:

Step-by-step explanation:

To put the functions onto the graph, we can first get the slope of the equation, which is the handy factor in front of the "x" and we can also figure it out the y intercept with the +5 which will help us in that case.

If we use that, we can plot it and find out answer :)

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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The statistics that always corresponds to the 75th percentile in a distribution include the following: B. Third Quartile.

In Mathematics and Statistics, IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) of a data set is the difference between third quartile (Q₃) and the first quartile (Q₁):

IQR = Q₃ - Q₁ = 75th percentile - 25th percentile.

In this context, we can reasonably infer and logically deduce that the 75th percentile in a distribution is always equal to the third quartile.

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Answer: f(x)=(2x−1)(3x−2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(2x−1)(3x−2)

Answer:

One lamp is equal to 23 dollars

One table is equal to 42 dollars.

Step-by-step explanation:

We can solve this by first organizing what we have.

1 table (t) + 2 lamps (l) = 88.

2 tables (t) + 3 lamps (l) = 153.

_____________

===============

1t + 2l = 88

2t + 3l = 153

===============

-------------------------

If we multiply both sides by 2 on the first equation of

1t + 2l = 88

we could get

2t + 4l = 176.

If that is true, we can subtract the second equation of

2t + 3l = 153 from the new equation to get the price of a lamp.

    2t + 4l = 176

-    2t + 3l = 153

____________

= 0t + l = 23

One lamp is equal to 23.

We can check this by plugging it into an equation.

1 + 2(23) = 88

1t + 46 = 88

1t + 46 - 46 = 88 - 46

1t = 42

If one table equals 42, we can put this back into the second equation to check.

2 (42) + 3 (23) = 153

84 + 69 = 153

That is correct.

Another way to solve is to put this like a system of equations in a graph, by replacing "t" by "x" for example, and "l" by y.

Then you could put it into a graphing calculator and solve by looking for the place where the two lines converge or meet.

Since we put "x" for "t", that means that whatever the x-value is on the solution point, that is the cost of a table, and the y-value is the cost of the lamps.

Another way to solve, is to find the unit rate first by subtracting the first equation from the second equation.

    2t + 3l = 153

 -  1t + 2l = 88

____________

= t + l = 65

If t + l = 65, we can rearrange that equation to be something like t = 65 - l.

That means "t" is equal to 65 bucks minus a lamp.

We put this back into the first equation of

1t + 2l = 88

and replace "t" with the previous expression.

1(65 - l) + 2l = 88

Simplify/distributive property

65 - l + 2l = 88

65 - 65 - l + 2l = 88 - 65

-l + 2l = 23

l = 23

One lamp is equal to 23 bucks.

Confirmed :)

A lamp cost $23

Let the cost of a table be represented by x

Let the cost of a lamp be represented by y.

Since one table and two lamps cost $88, this can be represented as:

x + 2y = 88 ........ equation i

Since two tables and three lamps cost $153, this can be represented as:

2x + 3y = 153 ........ equation ii

Therefore, the equations are:

x + 2y = 88 ....... i

2x + 3y = 153 ....... ii

From equation i,

x + 2y = 88

x = 88 - 2y ...... iii

Put the value of x into equation ii

2x + 3y = 153

2(88 - 2y) + 3y = 153

176 - 4y + 3y = 153

Collect like terms

-4y + 3y = 153 - 176

-y = -23

y = 23

Therefore, a lamp cost $23

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Answer:

83050

Step-by-step explanation:

that's the answer to the question

Answer: 3/8

Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.

Answer:

C. (310 − 10) ÷ 15 = s

Step-by-step explanation:

The correct answer is C. (310 − 10) ÷ 15 = s. This is because we can use the following steps to find the equation:

First, we need to find how many pieces of candy were given out in total. Since there are 10 pieces left over in the bag, and the bag originally contained 310 pieces, we can subtract 10 from 310 to get 300 pieces given out.

Next, we need to find how many pieces of candy each student received. Since 15 pieces of candy were given to s students, we can divide 300 by 15 to get the number of students. This gives us 20 students.

Finally, we need to write an equation that relates the number of students (s) to the number of pieces of candy given out (300) and the number of pieces of candy per student (15). We can do this by using the inverse operations of subtraction and division. We can multiply both sides by 15 and then add 10 to both sides to get the equation:

(310 − 10) ÷ 15 = s

This equation can be used to find the number of students if we know the number of pieces of candy in the bag, the number of pieces left over, and the number of pieces per student.

But wait, there's more! If you act now, you can also get a bonus question for free! Here it is:

If s students each received 15 pieces of candy, and there are 10 pieces left over in the bag, how many cavities will they have after eating all the candy?

There are a few possible ways to approach this question, but here is one:

- First, we need to find how many pieces of candy each student ate. Since they received 15 pieces each, and there are no leftovers, we can assume they ate all of them. So each student ate 15 pieces.

- Next, we need to find how many cavities each piece of candy causes. This may vary depending on the type and quality of the candy, but let's assume that each piece causes 0.1 cavities on average. This means that for every 10 pieces of candy, one cavity is formed.

- Finally, we need to multiply the number of pieces each student ate by the number of cavities each piece causes, and then add up all the results for all the students. This will give us the total number of cavities for the whole group. We can use this formula:

c = (15 × 0.1) × s

where c is the number of cavities and s is the number of students.

Using this formula, we can plug in the value of s that we found

c = 1.5 × 20

c = 30

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

The expected value of the number of upgrades selected is 1.04.

The given probability mass function provides the probabilities for the number of upgrades purchased per customer. We are asked to find the expected value, which is a measure of central tendency in probability theory. To do this, we need to multiply each possible value of upgrades by its probability and then sum them up.

First, we need to figure out the value of f(3). We know that the sum of all probabilities in a probability mass function is 1. Therefore, we can use the given probabilities to calculate f(3) as follows:

1 = f(0) + f(1) + f(2) + f(3)

1 = 0.50 + 0.20 + 0.06 + f(3)

f(3) = 1 - (0.50 + 0.20 + 0.06)

f(3) = 0.24

Now that we know the value of f(3), we can calculate the expected value as follows:

E(X) = (0 x 0.50) + (1 x 0.20) + (2 x 0.06) + (3 x 0.24)

E(X) = 0 + 0.20 + 0.12 + 0.72

E(X) = 1.04

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