Consider the function


h(x) = 1/2x– 3 with a restricted domain of {-2,0, 2, 10}.



What is the range of the function?

The length of the side /CD/ is 6√3 square units. Option A

The trigonometric function known as the sine of an angle describes the ratio between the lengths of the hypotenuse and the side opposite the angle in a right triangle. The sine function, sometimes known as "sin", is described as follows:

Sin = opp/adj

The sine function can be used to determine how a right triangle's angles and sides match up.

Let the altitude /CD/ be x

Using the sine of an angle;

Sin 60 = √3/2

√3/2 = x/12

x = √3/2 * 12

x = 6√3 square units

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The factors of x^2 - 64 are (x - 8)(x + 8) because it follows the difference of squares formula, giving the correct factorization that yields x^2 - 64 when multiplied.

To factorize x^2 - 64, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a - b)(a + b). In this case, a = x and b = 8. Applying the formula, we have (x - 8)(x + 8) as the factors of x^2 - 64. This is the correct factorization because when we multiply these factors, we get (x - 8)(x + 8) = x^2 - 64.

The other options provided (x - 4)(x + 16) and (x - 8)(x - 8) are not valid factorizations of x^2 - 64. The first option, (x - 4)(x + 16), does not yield x^2 - 64 when multiplied. The second option, (x - 8)(x - 8), is a repeated factor and does not represent the correct factorization. Therefore, the factors of x^2 - 64 are (x - 8)(x + 8).

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The explicit formula is [tex](n) = 1 * 1^{(n-1)} = 1[/tex] for all values of n and the number of cells after 10 generations will be 1.

The formula for finding the number of bacteria cells after each generation is given by

[tex]a(n) = a(1)r^{(n-1)}[/tex] where a(1) is the initial number of bacteria cells, r is the growth factor, and n is the number of generations.

The exponent n-1 indicates the number of generations.

To find the number of bacteria cells after 10 generations, we will substitute the given values in the formula.

We are given that a(n)= a(1)r"-1 where r is the growth factor and n is the number of generations.

We know that the initial number of bacteria cells is 1.

Thus, a(1) = 1.

Substituting these values in the formula, we get [tex]a(n) = 1 x r^{(n-1)}[/tex]. For 10 generations, n = 10.

Thus, the formula becomes [tex]a(10) = 1 x r^{(10-1)} = r^9[/tex].

Now, we need to find the value of r.

We are given that [tex]a(n) = a(1)r^{(-1)}[/tex], which means that a(n)/a(1) = 1/r.

Substituting [tex]a(n) = r^9[/tex] and a(1) = 1, we get: [tex]r^9/1 = 1/r[/tex]

Therefore, [tex]r^{10} = 1r = 1^{(1/10)} = 1[/tex]

Thus, the explicit formula becomes [tex]a(n) = 1 * r^{(n-1)}[/tex] = 1 for all values of n.

Therefore, the number of cells after 10 generations will be 1.

Summary: A formula that can be used to find the number of bacteria cells after each generation is [tex]a(n) = 1 * r^{(n-1)}[/tex] where a(1) is the initial number of bacteria cells, r is the growth factor, and n is the number of generations. To find the number of bacteria cells after 10 generations, we can substitute the given values in the formula. The explicit formula for the given problem is [tex]a(n) = 1 * r^{(n-1)}[/tex] where r = 1. Thus, the number of cells after 10 generations will be 1.

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The call center made approximately 676 calls per hour. In 7 hours, operators at a call center make 4,732 telemarketing calls.

To represent the number of phone calls made per hour at the call center, we can use the equation:

Number of phone calls made per hour = Total number of phone calls / Number of hours

Given that in 7 hours, operators at the call center made 4,732 telemarketing calls, we can substitute the values into the equation to find the number of calls made per hour:

Number of phone calls made per hour = 4,732 / 7

Performing the division:

Number of phone calls made per hour = 676

Therefore, the call center made approximately 676 calls per hour.

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The dimensions of a rectangular prism can be matched with the volume of the rectangular prism as follows:

To match the dimensions of the rectangular prism to the volume we need to know the formula or the volume of a rectangular prism. That is;

length * breadth * height.

So, for the dimensions given, we would simply multiply all the side lengths to arrive at the final volume of the rectangular prism. For the first one,

4 * 3 * 6 = 72 in³

6 * 3 * 2  = 36 in³

4 * 5 * 4  = 80 in³

2 * 9 * 3 = 54 in³

The results represent the final volumes of the rectangular prisms.

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The expression that represents the total amount Marissa spent is (x * 19.99 + y * 14.99) + (3 * 19.99 + 4 * 14.99).

In summary, the expression (x * 19.99 + y * 14.99) represents the cost of the initial purchase, where x is the number of shirts and y is the number of shorts. The expression (3 * 19.99 + 4 * 14.99) represents the cost of the additional purchase the next day, where 3 is the number of shirts and 4 is the number of shorts. By adding both expressions together, we get the total amount Marissa spent.

The first part of the expression, x * 19.99, calculates the cost of the x shirts at $19.99 each. Similarly, the second part, y * 14.99, calculates the cost of the y pairs of shorts at $14.99 each. These two terms represent the initial purchase.

The next part of the expression, 3 * 19.99, calculates the cost of the 3 additional shirts bought the next day. Similarly, 4 * 14.99 calculates the cost of the 4 additional pairs of shorts. These two terms represent the additional purchase.

By adding the cost of the initial purchase and the additional purchase, we obtain the total amount Marissa spent on shirts and shorts.

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the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.

To find th positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees, and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees,

we can use the following formulas:For a positive coterminal angle, add 360 degrees repeatedly until we reach the desired range.For a negative coterminal angle, subtract 360 degrees repeatedly until we reach the desired range.

Let's start with the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees.

To find this angle, we need to add 360 degrees repeatedly until we reach a value between 500 degrees and 1000 degrees.

So, we can write:47 + 360 = 407 (not in range)

407 + 360 = 767 (not in range)

767 + 360 = 1127 (not in range)

1127 + 360 = 1487 (not in range)

1487 + 360 = 1847 (not in range)

1847 + 360 = 2207 (not in range)

2207 + 360 = 2567 (not in range)

2567 + 360 = 2927 (not in range)

2927 + 360 = 3287 (not in range)

3287 + 360 = 3647 (not in range)

3647 + 360 = 4007 (not in range)

4007 + 360 = 4367 (not in range

4367 + 360 = 4727 (not in range)

4727 + 360 = 5087 (not in range

5087 + 360 = 5447 (not in range

)5447 + 360 = 5807 (not in range)

5807 + 360 = 6167 (not in range)

6167 + 360 = 6527 (not in range)

6527 + 360 = 6887not in range)

6887 + 360 = 7247 (not in range

)7247 + 360 = 7607 (not in range)

7607 + 360 = 7967 (not in range)

7967 + 360 = 8327 (not in range)

8327 + 360 = 8687 (not in range)

8687 + 360 = 9047 (not in range)

9047 + 360 = 9407 (not in range)

9407 + 360 = 9767 (not in range

)9767 + 360 = 10127 (not in range)

10127 + 360 = 10487 (not in range)

10487 + 360 = 10847 (not in range)

10847 + 360 = 11207 (in range)

Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 11207 - 10847 = 360 degrees.

To find the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees, we need to subtract 360 degrees repeatedly until we reach a value between -500 degrees and 0 degrees. So, we can write:

47 - 360 = -313 (not in range)

-313 - 360 = -673 (not in range)

-673 - 360 = -1033 (not in range)

-1033 - 360 = -1393 (not in range

-1393 - 360 = -1753 (not in range)

-1753 - 360 = -2113 (not in range)

-2113 - 360 = -2473 (not in range)

-2473 - 360 = -2833 (not in range

-2833 - 360 = -3193 (not in range

-3193 - 360 = -3553 (not in range)

-3553 - 360 = -3913 (not in range)

-3913 - 360 = -4273 (not in range)

-4273 - 360 = -4633 (not in range)

-4633 - 360 = -4993 (in range)

therefore, the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is -4993 - (-5183) = 190 degrees.

Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.

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By using a graphing calculator and a system of equations, we can determine the value of x and then calculate the lengths of the sides. Substituting the value of x into the dimensions, we can identify the longest side among the three.

Using a graphing calculator, enter the equation 2x^3 + 14x^2 + 12x - 400 = 0 and graph it. Find the x-values where the graph intersects the x-axis, which represent the solutions. Using the calculator's "zero" or "intersect" function, determine the numerical values of x. Substitute these values into the dimensions (x, 2x, and x/6) to find the lengths of the sides. Compare the lengths and identify the longest side. This process allows us to find the length of the longest side using a graphing calculator and a system of equations.

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To prove that AAGE and AOLD are congruent by SAS, the other information that is needed is: GE = LD.Explanation:To prove that two triangles are congruent using SAS (side-angle-side) postulate, we need to know.

Two sides and the angle between them in one triangle are congruent to the corresponding sides and angle in the other triangle.So, given AG = OL, AGE = OLD, and AEG = ODL, we can conclude that two angles and a side are equal in both triangles.However, to apply the SAS postulate, we need to have another pair of equal sides in both triangles. And that is given by GE = LD. Hence, option 1) is the correct answer.Other options don't provide the necessary information to prove the congruence of the two triangles using SAS.

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The volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]\(r\)[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .

To find the volume of material in the wall of the open cylinder, we need to calculate the difference between the volume of the outer cylinder and the volume of the inner cylinder. The outer cylinder has a radius of [tex]\(r + 2\)[/tex]cm, while the inner cylinder has a radius of [tex]r[/tex] cm. The length of both cylinders is [tex]9r[/tex] cm.

The volume of the outer cylinder can be calculated using the formula: [tex]\(V_{\text{outer}} = \pi \cdot (r + 2)^2 \cdot 9r\) cm^3[/tex].

The volume of the inner cylinder can be calculated using the formula: [tex]\(V_{\text{inner}} = \pi \cdot r^2 \cdot 9r\) cm^3[/tex].

To find the volume of material in the wall, we subtract the volume of the inner cylinder from the volume of the outer cylinder:

[tex]\[V_{\text{wall}} = V_{\text{outer}} - V_{\text{inner}} = \pi \cdot (r + 2)^2 \cdot 9r - \pi \cdot r^2 \cdot 9r= 9\pi r(r + 2)^2 - 9\pi r^3= 9\pi r[(r + 2)^2 - r^2]= 9\pi r[4r + 4].\][/tex]

Simplifying further:

[tex]\[V_{\text{wall}} = 36\pi r^2 + 36\pi r \text{ cm}³ = 36\pi(r^2 + r).\][/tex]

Therefore, the volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]r[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .

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Therefore, based on the given information, we can estimate that the total length of a western harvest mouse is approximately 5.7 inches.

The given information states that the average length of the head and body of a western harvest mouse is 2.9 inches, while the average length of the tail is 2.8 inches. To estimate the total length of the mouse, we can add these two measurements together:

Estimated total length = Average length of head and body + Average length of tail

Estimated total length = 2.9 inches + 2.8 inches

Estimated total length = 5.7 inches

Therefore, based on the given information, we can estimate that the total length of a western harvest mouse is approximately 5.7 inches.

It's important to note that this estimate represents the average length and may not accurately reflect the actual total length of each individual mouse. There may be variations in the lengths of different mice within the population. Factors such as genetics, age, and environment can influence the actual total length of a mouse. Therefore, the estimate serves as a general approximation and the actual total length of each mouse may differ slightly from the estimate of 5.7 inches.

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Yes, the probability of drawing a heart and then a diamond from a standard deck of 52 cards is indeed (13/52) x (13/52).

To calculate the probability of two independent events occurring, we multiply their individual probabilities. In this case, the probability of drawing a heart on the first card is 13 out of 52 because there are 13 hearts in a standard deck of 52 cards. The probability of drawing a diamond on the second card is also 13 out of 52 since there are 13 diamonds in the deck.

Therefore, the probability of drawing a heart and then a diamond is:

(13/52) x (13/52) = (169/2704) = 1/16 ≈ 0.0625 ≈ 6.25%

So, the probability of drawing a heart and then a diamond from a standard deck is 13/52 multiplied by 13/52.

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The correct total cost of the 5 tickets is $85.

The calculation that Maria is using to calculate the total cost of the tickets is incorrect. She is multiplying the number of tickets by $10 and $7 separately, instead of multiplying the number of tickets by the cost per ticket.

To correctly calculate the total cost of the tickets, Maria should multiply the number of tickets (5) by the cost per ticket ($17) as follows:

Total cost = 5 x $17 = $85

It seems that Maria made a mistake in her calculation by multiplying the number of tickets by two different values ($10 and $7) instead of using the actual cost per ticket. This mistake leads to an incorrect total cost of $50 + $35 = $85.

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Using algebraic equations, the value of the number assumed to be x is 13.

Let's assume that the number in question be "x". Thus, the expression can be written as:

2x + 9 = 5 (x - 6).

Let's solve this equation and find the value of x:

Distributing the 5 across the parentheses,

2x + 9 = 5x - 30  

Subtracting 2x from both sides,

we get, 3x = 39  

Dividing both sides by 3,

x = 13    

Thus, the number is 13.

Thus, we have found the number by forming and solving an equation.

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The value closest to the estimated average pet car population for European countries in 2010 is 15 million.

Given the table for pet car populations in 2002, we need to estimate the average pet car population for European countries in 2010 after each car population has doubled.

It can be observed that in 2002, Spain and Italy had the lowest pet car population while Germany and the United Kingdom had the highest.

In order to find the estimated average pet car population for European countries in 2010, we first need to find the pet car population for each country in 2010 after doubling their 2002 population.

The results are shown in the table below:

|Country|Pet car population in 2002

|Pet car population in 2010|

|-|-|-|

|France|22 million

|44 million|

|Germany|

30 million|

60 million|

|Italy|

8 million|

16 million| |Spain|6 million|12 million| |United Kingdom|28 million|56 million|

To find the estimated average pet car population for European countries in 2010, we need to sum up the pet car populations for all the countries in 2010 and then divide by the total number of countries (which is 5).

Adding all the pet car populations in 2010:

44 million + 60 million + 16 million + 12 million + 56 million = 188 million

The estimated average pet car population for European countries in 2010, closest to the calculated value, would be:

188 million/5 ≈ 38 million

Now, we need to find which of the given options is closest to this value. We can see that the option closest to 38 million is D.) 12 million.

However, this value is not the answer since it is too low compared to the estimated average.

Therefore, we can rule out option

D.) as the answer.

Now, we can look at the remaining options to determine which is closest to the average.

Option A.) 9 million is clearly too low, and

option C.) 18 million is too high.

Therefore, the answer is

option B.) 15 million,

which is the value closest to the estimated average pet car population for European countries in 2010.

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Dinosaur 2 is a more efficient walker in terms of having a pace angle closer to 180°.

To determine which dinosaur is a more efficient walker based on the pace angle, compare the pace angles of the two dinosaurs.

Analyze the given information:

Dinosaur 1:

Pace: 2.9 ft

Stride: 5.78 ft

Dinosaur 2:

Pace: 3.0 ft

Stride: 5.2 ft

To calculate the pace angle, use the following formula:

Pace angle = arccos(Pace/Stride)

For Dinosaur 1:

Pace angle = arccos(2.9/5.78) ≈ 59.43°

For Dinosaur 2:

Pace angle = arccos(3.0/5.2) ≈ 56.62°

Comparing the pace angles, Dinosaur 2 has a smaller pace angle (56.62°) compared to Dinosaur 1 (59.43°). Therefore, Dinosaur 2 is a more efficient walker in terms of having a pace angle closer to 180°.

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Given information:

Max invest $1000 in a savings account that earns simple 3% interest.

Let's suppose the duration he needs to keep his money in the savings account is t years.

The interest rate is given as 3% in decimal form = 0.03

Max invests $1000 on the savings account that earns 3% simple interest.

This implies that the interest he will earn after t years is given by:

Interest (I) = Principal × Rate × Time

I = 1000 × 0.03 × t

I = 30t

From the problem, he wants to earn $150 in interest.

So, 30t = 150

Solving for t:

$$\begin{aligned}30t &= 150 \\t &= \frac{150}{30} \\t &= 5 \;years \end{aligned}$$

Max needs to leave his money in the savings account for 5 years to make $150 in interest.

Therefore, the answer is 5 years.'

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The distance between Arcadia and Rockport is approximately 9.2 miles when rounded to the nearest tenth.

To determine the distance between Arcadia and Rockport, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

Let's consider Arcadia as point A, Rockport as point R, and the airport as point O. The distance from Arcadia to the airport is 7 miles (the length of side OA), and the distance from Rockport to the airport is 6 miles (the length of side OR). We want to find the distance between Arcadia and Rockport, which is the length of side AR.

Since Arcadia and Rockport are located in different directions (north and east) from the airport, we can form a right triangle with sides AO, OR, and AR.

Using the Pythagorean theorem, we have:

AR^2 = AO^2 + OR^2.

Substituting the given lengths, we get:

AR^2 = 7^2 + 6^2,

AR^2 = 49 + 36,

AR^2 = 85.

Taking the square root of both sides, we find:

AR = √85.

Approximating the square root of 85 to the nearest tenth, we have:

AR ≈ 9.2 miles.

Therefore, the distance between Arcadia and Rockport is approximately 9.2 miles when rounded to the nearest tenth.

It's important to note that this calculation assumes a direct path between Arcadia and Rockport. If there are obstacles or detours that would affect the actual path, the distance may differ. Additionally, rounding to the nearest tenth introduces some level of approximation, so the actual distance may be slightly different.

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According to the question the slope of the line parallel to the line containing side WV is -1.

To find the slope of the line parallel to the line containing side WV, we need to determine the slope of side WV.

Sure! Here are the coordinates of points [tex]T, U, V, and[/tex] [tex]W[/tex] properly aligned:

[tex]\[T &: (a, b) \\U &: (a + 2, b + 2) \\V &: (a + 5, b - 1) \\W &: (a + 3, b - 3) \\\][/tex]

To find the slope of the line parallel to the line containing side WV, we can calculate the slope between points W and V using the slope formula:

[tex]\[ \text{Slope} = \frac{{\text{change in } y}}{{\text{change in } x}} \][/tex]

Substituting the coordinates of points W and V into the formula:

[tex]\[ \text{Slope} = \frac{{(b - 1) - (b - 3)}}{{(a + 5) - (a + 3)}} \][/tex]

Simplifying the expression:

[tex]\[ \text{Slope} = \frac{{-2}}{{2}} \][/tex]

Therefore, the slope of the line parallel to the line containing side WV is -1.

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The final answer is that the original price of one jump rope before the sale was $8.29.

Let's start by using algebra to solve this problem.

If the original price of one jump rope is "x", then the sale price is "x - 1.90". We can set up an equation to relate the sale price and the original price:

2(x - 1.90) = 12.78

Simplifying and solving for "x", we get:

2x - 3.80 = 12.78

2x = 16.58

x = 8.29

Therefore, the original price of one jump rope was $8.29.

To check our answer, we can verify that the sale price of one jump rope is $6.39 ($8.29 - $1.90), and that two jump ropes at this price cost $12.78.

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A field project superintendent earns an annual salary of $72,800. This is a piece of information about the annual salary of a field project superintendent.

A field project superintendent is a person responsible for overseeing and managing construction projects. This position is responsible for ensuring that the construction project is completed on time, within budget, and in accordance with safety and quality standards. This person must have a thorough understanding of construction principles and techniques, as well as the ability to read and interpret blueprints and specifications.

A salary is a fixed amount of compensation paid to an employee for their work. The amount of salary is typically determined by the employee's position, job duties, and level of experience. Salaries are usually paid on a monthly or bi-weekly basis.

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To find the length of the missing base of the trapezoid, we can use the formula for the area of a trapezoid. Given that the longer base is 8 inches, the height is 3 inches, and the area is 21 square inches, we can substitute these values into the formula and solve for the missing base length.

The formula for the area of a trapezoid is A = (1/2)(b1 + b2)h, where A is the area, b1 and b2 are the lengths of the bases, and h is the height.

In this case, we know that b1 is 8 inches and h is 3 inches, and the area A is 21 square inches. We need to find the length of the missing base, which we'll denote as b2.

Substituting the known values into the formula, we have:

21 = (1/2)(8 + b2)(3)

Simplifying the equation, we get:

42 = 8 + b2

Subtracting 8 from both sides, we find:

b2 = 34

Therefore, the length of the missing base of the trapezoid is 34 inches.

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To write and evaluate an addition expression to determine Tressa's current score, we need to subtract the number of points she loses from her original score. The original score is 57.9 points and she loses 8.6 points.

So, Tressa's current score can be determined by adding the difference (which is -8.6) to her original score. Therefore, the addition expression to determine Tressa's current score can be written as:

57.9 + (-8.6)

To evaluate this expression, we simply need to add the numbers:

57.9 + (-8.6) = 49.3

Therefore, Tressa's current score is 49.3 points.

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With an 80% improvement in typing speed from an initial rate of 50 words per minute, you will be able to type 90 words per minute.

Increasing your typing speed by 80% means you will be able to type 80% more words in the same amount of time. Therefore, if your initial typing speed is 50 words per minute, an 80% improvement would result in a typing speed of 90 words per minute.

To calculate the new typing speed, we first find 80% of the initial typing speed.

80% of 50 is (80/100) * 50 = 0.8 * 50 = 40.

This means that your typing speed will increase by 40 words per minute.

To determine the new typing speed, we add the increase to the initial typing speed:

50 + 40 = 90.

Thus, after the 80% improvement, you will be able to type 90 words per minute.

In summary, with an 80% improvement in typing speed from an initial rate of 50 words per minute, you will be able to type 90 words per minute.


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There are 1 items are expected to be defective.

We have the information available from the question is:

On average that 0.026% of the items from a certain factory are defective.

Now, if 4000 items are checked, the number of defective items would be gotten by multiplying the percentage of defective items by the number of items checked.

We are required to find the number if defective items that we will find from 4000 items.

Therefore,

Number of defective items = 0.026% × 4000 = 1.04 approximately 1

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The radical form of[tex](-3x^3)^-^2/3 is 1 / (9x^2)[/tex].

To rewrite the expression[tex](-3x^3)^-^2/3[/tex] as a radical, we can use the fact that a negative exponent indicates that the base is in the denominator. Therefore, we can rewrite the expression as:

[tex]1 / (-3x^3)^(^2^/^3^)[/tex]

Using this concept, we can rewrite the exponent -2/3 as [tex]3\sqrt(1/-3^2)[/tex], where 3√ is the cube root. We also need to take the cube root of the absolute value of -3x^3 to ensure that the result is always positive.

To find the radical form, we can simplify the expression under the radical by raising it to the power of 3/2:

[tex](-3x^3)^(^2^/^3) = [(-3)^(^2^/^3^) * (x^3)^(^2^/^3^)]^3 = [(9 * x^2)^(^1^/^3^)]^3 = 9x^2[/tex]

Substituting this back into the original expression gives:

1 / (-3x^3)^(2/3) = 1 / (9x^2).

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This sample menu should feed around 6-8 people, depending on portion sizes. You can adjust the amounts of ingredients as needed to fit your specific needs. You may also be able to find some ingredients on sale or substitute them for cheaper options to save even more money. Happy planning!

If you're planning a dinner party with a budget of $50 and a menu that consists of 1 main dish, 2 side dishes, and 1 dessert, there are plenty of affordable options you can choose from. Here's a sample menu that should fit within your budget:Main Dish: Baked Chicken - $10Ingredients:4 chicken leg quarters - $6.004 tbsp olive oil - $0.501 tbsp salt - $0.101 tbsp pepper - $0.101 tbsp garlic powder - $0.101 tbsp paprika - $0.10Directions:Preheat oven to 400°F. Combine salt, pepper, garlic powder, and paprika in a small bowl.

Drizzle chicken with olive oil and rub spice mixture onto chicken. Place chicken in a baking dish and bake for 45-50 minutes until chicken is cooked through.

Side Dish 1: Garlic Roasted Potatoes - $4Ingredients:6 medium-sized potatoes - $1.501/4 cup olive oil - $0.751 tbsp salt - $0.101 tbsp pepper - $0.101 tb sp garlic powder - $0.10Directions:Preheat oven to 400°F. Wash potatoes and cut them into small cubes.

Combine potatoes with olive oil, salt, pepper, and garlic powder in a large mixing bowl. Spread the potatoes out in a single layer on a baking sheet and bake for 30-35 minutes until golden brown and crispy.

Side Dish 2: Sauteed Green Beans - $3Ingredients:

1 lb green beans - $2.001/4 cup butter - $0.501 tbsp garlic - $0.101/2 tbsp salt - $0.051/2 tbsp pepper - $0.05Directions:Bring a pot of water to a boil and blanch green beans for 2-3 minutes. Drain and rinse under cold water.  Combine flour, rolled oats, brown sugar, butter, cinnamon, and nutmeg in a mixing bowl. Use your hands to mix the ingredients together until crumbly. Spread the topping over the apples and bake for 35-40 minutes until golden brown and crispy.

Total cost: $25This sample menu should feed around 6-8 people, depending on portion sizes. You can adjust the amounts of ingredients as needed to fit your specific needs. You may also be able to find some ingredients on sale or substitute them for cheaper options to save even more money. Happy planning!

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We cannot calculate the efficiency without knowing the weight of the man and the time taken to lift him about motor.

Given that:

The input power of the motor is 6200 watts.The formula for efficiency is;Efficiency = (Output power / Input power) × 100%The motor is used to operate a lift. Therefore, the power output of the motor is used to lift the man and overcome frictional forces, etc.

A motor is a device that transforms electrical energy into mechanical energy, allowing motion to be created or machines to be operated. In myriad applications spanning numerous industries, it is fundamental. Electric motors, which are frequently used in household goods, transportation, and industrial machinery, use the electromagnetic theory to generate rotational motion.

They are made up of a rotor, which rotates in reaction to being subjected to force, and a stator, which produces a revolving magnetic field. Motors come in a variety of sizes and configurations to meet various needs, and they can be categorised according to their power source, such as AC motors or DC motors. Motors are essential to modern technology and automation, powering anything from home appliances to vehicle propulsion.

We know that the man has a weight (W) and is being lifted at a certain height (H), so the power output can be calculated using the following formula;Power Output = W × H / t, where t is the time taken to lift the man.

Substituting the given values;Power Output = W × H / tEfficiency = (Power Output / Input Power) × 100%Therefore;Efficiency = (W × H / t) / 6200 × 100%

We cannot calculate the efficiency without knowing the weight of the man and the time taken to lift him.

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Therefore, Clausen has 32 cards.The correct answer is Clausen has 32 cards.

Juan and Clausen are playing a card game called "Magic." The number of cards they have is in a ratio of Juan: Clausen = 7:4. Juan has 56 cards. To find the number of cards Clausen has, we can use the concept of ratios and proportions.Since the ratio of Juan's cards to Clausen's cards is 7:4, we can say that Juan has 7x cards, where x is a constant.

Similarly, Clausen has 4x cards.Now, we know that Juan has 56 cards. We can use this information to find the value of x.7x = 56

Dividing both sides by 7, we get:

x = 8

Now that we know the value of x, we can find the number of cards Clausen has.4x = 4(8) = 32

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The property that justifies Emily's first step include the following: C. division property of equality.

In Mathematics and Geometry, the Commutative Property of Addition states that when two (2) or three (3) numerical values (numbers) are added together, the output (end result) would always remain the same, irrespective of the way in which the numerical values are arranged.

Generally speaking, the Commutative Property of Addition allows the addends to be re-ordered without causing a change in the result, output, or outcome.

By applying the division property of equality to Emily's equation, we have the following;

2(-3x² + 2) + 4 = 18x² - 20

2(-3x² + 2) + 2(2) = 2(9x² - 10)

(-3x² + 2) + 2 = (9x² - 10) ⇒ (division property of equality)

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